Characteristics of full and partial multiport diffusers discharging thermal wastes in open channel flow

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Characteristics of full and partial multiport diffusers discharging thermal wastes in open channel flow
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Florida Water Resources Research Center Publication Number 49
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Christensen, B. A.
Melville, J. G.
Parr, A. D.
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A. -


Publication No. 49


CHARACTERISTICS OF FULL AND PARTIAL
MULTIPORT DIFFUSERS DISCHARGING THERMAL
WASTES IN OPEN CHANNEL FLOW


By


B. A. Christensen
J. G. Melville
A. D. Parr


Civil Engineering Department
University of Florida
Gainesville


*

I -
.... V ~.
*.~*


.'.. ..-_ ".- : ... ; ''- "


iT


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.*~~










Characteristics of Full and Partial Multiport Diffusers
Discharging Thermal Wastes in Open Channel Flow



By



B. A. Christensen
J. G. Melville
A. D. Parr


PUBLICATION NO. 49



FLORIDA WATER RESOURCES RESEARCH CENTER



RESEARCH PROJECT TECHNICAL COMPLETION REPORT



OWRT Project Number A-035-FLA



Annual Allotment Agreement Numbers

14-34-0001-7019
14-34-0001-7020
14-34-0001-8010
14-34-0001-9010


Reported Submitted December, 1980




The work upon which this report is based was supported in part
by funds provided by the United States Department of the
Interior, Office of Water Research and Technology
as Authorized under the Water Resources
Research Act of 1964 as amended.















ACKNOWLEDGEMENTS


Appreciation is extended to the Office of Water Resources Research

and Technology, United States Department of the Interior, for financial

support on this project, and to Drs. W.H. Morgan and J.P. Heaney for their

administrative assistance and Ms. Mary Robinson for accounting assistance.

The participation of Messrs. R.J. Chernick and B.J. Swenty in most aspects

of the project was especially valuable.

The efforts of Mr. C.L. White and the staff of the Engineering

Machine Shop are gratefully acknowledged. The assistance of Ms. Alice

Moreau in typing the report deserve special thanks.















TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS . . . . . . ii

LIST OF TABLES . . . . . . v

LIST OF FIGURES . . . . . . vi

LIST OF SYMBOLS . . . . . . ix


CHAPTER

I INTRODUCTION . . . . . 1

II REVIEW OF LITERATURE . . . . 4

2.1 Single Jets . . . . . 4
2.1.1 The Simple or Momentum Jet . . 4
2.1.2 The Simple Plume . . . 7
2.1.3 The Buoyant Jet or Forced Plume . 8
2.1.4 The Effect of Crossflow . . 9
2.1.5 The Effect of Boundaries . . 11
2.2 Multiport Diffusers . . . . 13
2.2.1 Lateral Interference of Round Buoyant Jets 13
2.2.2 The Equivalent Slot Diffuser . . 15
2.2.3 Solutions for the Multiport and Slot
Diffusers . . . . 16

III ANALYSIS . . . . . . 18

3.1 Statement of the Problem . . . 18
3.2 Dimensional Inquiry . . . . 20
3.3 Experimental Objectives . . . 24
3.3.1 The CVx Parameter . . . 24
3.3.2 Isotherm Plots . . . 26
3.3.3 Velocity Distribution . . . 26

IV DESCRIPTION OF EQUIPMENT AND PROCEDURE . . 27

4.1 Introduction . . . . . 27
4.2 The Hydraulic Apparatus . . . 27
4.2.1 The Recirculating Flume . . 27
4.2.2 The Effluent Supply System . . 31
4.2.3 The Manifold and Manometers . . 32
4.2.4 The Diffuser Jets and Rack . . 36









CHAPTER Page

4.3 The Sampling Equipment . . . 38
4.3.1 The Thermistors . . . 38
4.3.2 The Velocity Meters . . . 39
4.3.3 The Data Acquisition System . . 44
4.4 The Process of Physical Modeling . . 46
4.4.1 Prototype Measurements . . 46
4.4.2 Planning of Experiments . . 47
4.4.3 The Experimental Procedure . . 49

V REDUCTION OF DATA . . . . 54

5.1 Temperatures . . . . 54
5.2 Velocities . . . . . 54

VI PRESENTATION AND DISCUSSION OF EXPERIMENTAL RESULTS 56

6.1 The CVx Parameter . . . . 56
6.2 Isotherm Plots . . . . 60
6.2.1 Cross Sections . . . 62
6.2.2 Plan Views . . . . 72
6.2.3 Jet Trajectories . . . 92
6.3 Velocities . . . . . 92

VII CONCLUSIONS . . . . . 99

7.1 Jet Angle . . . . . 99
7.2 Port Spacing . . . . . 99
7.3 Partial Diffuser . . . . 100


APPENDIX

A REGULATIONS . . . . . 102

B PROGRAMS . . . . . 107

C DATA . . . . . . 147


BIBLIOGRAPHY . . . . . . 154















LIST OF TABLES


Table Page

C-1 Flow Data . . . . . . 147

C-2 Temperature Drop from Manifold to Jets (oC) . 148

C-3 Thermistor Correction Factors . . . 151















LIST OF FIGURES

Figure Page

2-1 Jet Diffusion . . . . . 5

2-2 A Round Jet in a Uniform Cross Stream . . 10

2-3 Jet Interference for a Submerged Multiport Diffuser 14

2-4 Nozzle Orientation, B(z), Along the Diffuser Line . 17

3-1 Parameter Description . . . . 19

3-2 Diffuser Configurations . . . . 25

4-1 System Layout . . . . . 28

4-2 The Experimental Arrangement . . . 29

4-3 The Manifold . . . . . 33

4-4 Wall-mounted Manometers with Overflow Pipe and
Compressed Air Hose . . . . 35

4-5 The Diffuser Rack and Cover . . . 37

4-6a Thermistor Dimensions . . . . 40

4-6b Thermistor Array in Plexiglas Support . . 40

4-7 Novonic-Nixon Velocity Probe in a Flow Field . 42

4-8 Point Gauge Carriage Mounting for the Novonic-Nixon
Velocity Probes . . . . . 43

4-9 The Data Acquisition System: the Pink Input Box and
the HP 9825A Programmable Calculator . . 45

6-1 CVx(L/(H-h)) vs (x/L), e = 350 . . . 57

6-2 CV x(L/(H-h)) vs (x/L), 0 = 200 . . . 58

6-3 CVx(L/(H-h)) vs (x/L), eo = 100 . . . 59

6-4 CVx(L/(H-h)) vs (x/L), Jets 1-19, eo = 350, 200, 100 61
X 0










Figure

6-5

6-6

6-7

6-8

6-9

6-10

6-11

6-12

6-13

6-14

6-15

6-16

6-17

6-18

6-19

6-20

6-21

6-22

6-23

6-24

6-25

6-26

6-27

6-28

6-29

6-30


Level

Level

Level

Level

Level

Level

Level

Level

Level

Level


350

200

100

350

200

100

350

200

100

350


Section 1, 35

Section 1, 20

Section 1, 10

Section 2, 35

Section 2, 20

Section 2, 10

Section 3, 35

Section 3, 20

Section 3, 10

Section 4, 35

Section 4, 20

Section 4, 10

Section 5, 35

Section 5, 20

Section 5, 10


Level 4, 200


Page

0 . . . . . 6 3

1 . . . . . 64

0 . . . . . 65

0 . . . . . 66

0 . . . . . 6 7

0 . . . . . 68

0 . . . . . 6 9

0 . . . . . 70

0 . . . . . 71

0 . . . . . 73

0 . . . . . 74

0 . . . . . 75

0 . . . . . 76

0 . . . . . 77

0 . . . . . 78

. . . . . . 79

. . . . . . 80

. . . . . . 8 1

. . . . . . 8 3

. . . . . . 84

. . . . . . 85

. . . . . . 86

. . . . . . 8 7

. . . . . . 88

. . . . . . 8 9











Figure

6-31

6-32

6-33

6-34

6-35

6-36


viii


Level 4, 10 . . .

Profile, 35 . . ..

Profile, 20 . . .

Profile, 10 . . .

Transverse Discharge Distribution

Average Velocity Profiles .


Page

. . . . 91

. . . .. 93

. . . .. 94

. . . .. 95

. . . . 97

. . . . 98















LIST OF SYMBOLS


SYMBOL

A
0
A
p
b



B

CD

CV
x
D

Dm

E

E

FD

F
e
F
a
F.



g

h

H

m


DEFINITION

Jet area at the outlet

Prototype cross-sectional area

Nominal half-width of the jet or the distance
from the centerline to the point where the mean
velocity is I/e of that at the centerline

Equivalent slot width

Drag coefficient

Coefficient of temperature variation at a section

Jet diameter

Model jet diameter

Energy flux at a section

Energy flux at the jet outlet

Pressure drag force

Force due to the entrainment of ambient fluid

Ambient Froude number

Jet densimetric Froude number

Ambient/jet Froude number

Acceleration due to gravity

Height of port centerline above the bed

Depth of flow

Model average depth


DIMENSION

L2
L2

L



L





L
L


ML2/T3

ML2/T3

ML2/T

ML2/T






L2/T

L

L

L









SYMBOL

H
p
k

k

k
m
L

Ld


L
r
M


M
x
N

a
qj

Q

Qa

Qe

QO

Q



R
p






a
R.

s

S


DEFINITION

Prototype average depth

Jet to ambient velocity ratio

Prototype jet to ambient velocity ratio

Model jet to ambient velocity ratio

Port spacing

Diffuser length, or the distance between the
first and the last jet plus one port spacing

Length ratio of prototype to model

Number of nondimensional temperature readings at
a section

General mixing at some section

Number of in-use jets

Ambient discharge per unit width at each jet

Effluent discharge per unit length of diffuser

Volume flux at a section

Ambient discharge

Total effluent discharge of diffuser

Discharge of individual jet

Prototype discharge measurement

Ratio of the prototype discharge to that of the
model

Ratio of the dilution of a multiport diffuser to
that of an equivalent slot jet

Reynolds' number of the ambient flow

Jet Reynolds' number

Distance along the jet centerline

Arithmetic mean of all nondimensional temperatures
at a section


DIMENSION

L


2
L /T
L2/T

L /T
L3/T
L3/T

L /T

L3/T
L /T










SYMBOL

T

Ta
T
0
U

U
a
U
a,m
U
a,p
U
c
U.

U
0
U
r

s
U
S
U-

a
V
e
W

p
X


Greek Letters





Ah

AT
m
Ap


Entrainment coefficient

Inclination angle with respect to z-axis

Head drop across the orifice plate

Mixed temperature rise

Ambient flow density jet flow density

Vertical angle of discharge


DEFINITION

Temperature reading at a point

Temperature of ambient flow

Efflux jet temperature

Mean velocity at a point

Mean ambient velocity

Model ambient mean velocity

Prototype ambient mean velocity

Characteristic jet velocity

Jet centerline velocity

Velocity at the jet efflux section

Velocity ratio of prototype to model

Mean velocity at a point in the s-direction

Mean velocity downstream of diffuser

Depth averaged ambient velocity at each jet

Transverse entrainment velocity

Flume width

Prototype width

Longitudinal distance downstream from diffuser


DIMENSION

C
0
C

L/T

L/T

L/T

L/T

L/T

L/T

L/T

L/T



L/T

L/T

L/T

L/T

L

L/T

L


L
C

M/L3









N OITINIFED


SYMBOL l'iLi,

p Density of fluid M/L3

pa Ambient fluid density M/L3

p. Jet fluid density M/L3

v Kinematic viscosity of ambient L2 /T
a
v. Kinematic viscosity of effluent L2/T
iJ


NOISNEMID


J 1UI1















CHAPTER I

INTRODUCTION


Waste heat is beyond a doubt the largest pollution form associated

with electric power generation. Conventional fossil fuel plants have an

efficiency of about 40%, while modern nuclear power stations have efficiencies

of only 32%. For nuclear reactors, this means that for each kW of electrical

power produced, 2kW of waste power (as heat) must be rejected. In 1970, the

use of fuel for generating electric power in the United States amounted to 25%

of the total fuel consumed. Studies by Hubbert (1971), Swiss (1970), and

Morrison and Readling (1968) indicate that just after 2000 A.D., the amount

of fuel used for electrical generation in the U.S. may be one half of the

total fuel consumed. In addition, the growing scarcity of plant sites as

well as the economics of large units dictate even greater waste heat discharge

at individual locations. Obviously, there is increasing concern over the

impact of this waste heat on the environment.

There are two systems which transfer the condenser waste heat to the

atmosphere: once-through cooling and closed-cycle cooling. The former

involves taking water from a source, passing it over the condensers once,

and returning it to the receiving water. Disposal methods include surface

canals, single-port submerged pipes, and multiport diffuser-pipes. The

diffuser-pipe provides the most efficient mixing of the three by discharging

the heat effluent through high velocity jets near the bed of the receiving

body of water.









Closed-cycle cooling recirculates the cooling water and transfers heat

to the atmosphere through radiation, convection, conduction and evaporation.

The additional costs of closed-cycle cooling are significant enough to warrant

the use of the once-through system.

Regulations for the disposal of heated effluents in the state of Florida

are found in the Florida Administrative Code (Appendix A). Here it is stated

that on an individual basis the Department of Environmental Regulation may

establish a zone of mixing downstream of the diffuser for the dilution of

heated discharges. Beyond this mixing zone, no temperatures above 2.80C (50F)

shall be allowed. Also for all streamflow conditions no more than one-third

(1/3) of the width of the stream's surface and no greater than one-forth (1/4)

of the cross-sectional area shall be raised above ambient temperature. In

addition no heated water outside the mixing zone shall have a temperature above

32.20C (90F) in Northern Florida, and 33.3C (920F) in Peninsular Florida.

(Northern and Peninsular Florida are defined in the Florida Administrative Code).

With such stringent regulations it behooves the engineer to have some predictive

methods to use in presenting his case.

This work concerns itself with an undistorted physical model of a

multiport diffuser-pipe discharging heated water into a coflowing ambient.

Vertical jet angle and transverse discharge distributions are varied and the

resulting mixing characteristics are noted.

Chapter II presents an overview of the studies in this area. Investigations

of the simple jet and plume through those of the multiport diffuser are

described.

Chapter III contains an analysis of the problem and the experimental

objectives. Dimensional reasoning is used to identify the governing parameters.

The equipment and procedure are described in Chapter IV. The hydraulic

apparatus as well as the sampling instruments and the data acquisition system









are all detailed. The physical modeling process including prototype measure-

ments and calculations of model parameters are delineated, along with the

steps involved in a typical run.

Methods used for the reduction of data are explained in Chapter V,

while Chapter VI contains the experimental results and their discussion.

The parameters derived in Chapter III are analysed and compared. Temperature

and velocity plots aid in this process.

Finally, the results presented in Chapter VI are used to substantiate

the conclusions advanced in Chapter VII.















CHAPTER II

REVIEW OF LITERATURE


2.1 Single Jets

2.1.1 The Simple or Momentum Jet

The simple momentum jet is the basic component of the multiport diffuser.

It is formed when fluid of the same density as the surrounding is discharged

at a high velocity through a submerged outlet. Just out of the efflux

section the velocity distribution is uniform or "top hat". The very steep

velocity gradients generate high shear forces at the jet boundary. This

shearing accelerates and entrains the ambient fluid while decelerating the

periphery of the jet, leading to lateral jet mixing. Fully established flow

develops when the mixing eddies have penetrated to the centerline of the jet.

The zone of flow establishment is the longitudinal distance from the port to

the point of fully established flow (Figure 2-1).

Albertson, Dai, Jensen, and Rouse (1950) conducted the first comprehensive

study on simple jets, both slot and round, in a still receiving environment.

The analytical derivation was based on the assumptions that: 1) the pressure

is hydrostatic throughout the flow; 2) the diffusion process is dynamically

similar in all cases; 3) the mean velocity distribution varies according to

the normal probability function at each cross-section. Experiments were

conducted to verify the results and to provide the necessary coefficients. It

was found that the nominal jet width is proportional to the distance from the

efflux section. This study also confirmed the assumption that the velocity

profiles in the zone of established flow are similar and Gaussian. The


















7OnE~ Af


Zone of
established flow
.4*


w establishment

it








S"--' c'' l 0., c- c C 0
-- = 0# <


Nominal limits "- O,)
f diffusion region -
Q,~uJ U


Figure 2-1 Jet Diffusion (From Albertson, et al., 1950)


flo


0









centerline velocity was found to be inversely proportional to distance.

Albertson, et al. established the fact that the flux of momentum is constant.

Empirical evidence indicates that the pressure distribution is hydrostatic

in a jet issuing into an unconfined region. It follows, therefore, that since

the acceleration/deceleration are due to an internal tangential shear; the

momentum must be constant. The experimental results of this endeavor produced

the following relationships for a round jet in the zone of flow establishment:

Q/Q = 1 + 0.083 s/D + 0.0128 s2/D2 (2.1)

E/Eo = 1 0.090 s/D + 0.0058 s2/D2 (2.2)

Uj/U = 1 (2.3)

where:

s = distance along jet centerline

D = diameter of jet at efflux section
r
Q = rate of flow or volume flux at a section = U dA (2.4)
0
Q = efflux rate of flow = U A
E = energy flux at a section = f pU2U /2dA (2.5)
6
E = energy flux at the outlet = pU A /2 (2.6)

Us = mean velocity at a point in the s-direction

U = mean velocity at a point

U. = jet centerline velocity

U = velocity at the efflux section

A = jet area at the efflux section

p = density of fluid









The length of the zone of flow establishment was determined as 6.2 jet

diameters. For the zone of established flow for a round jet the formulae

follow:

Uj/U = 6.2 D/s (2.7)

Q/Qo = 0.32 s/D (2.8)
E/E = 4.1 D/s (2.9)

b/D = 0.2 s/D (2.10)


where b = nominal half-width of the jet, or the distance from the centerline

where the mean velocity is of that at the centerline.
e

2.1.2 The Simple Plume

A simple plume is defined as a source of density deficiency only.

Morton, Taylor, and Turner (1956) analyzed the simple plume in a linearly

density-stratified environment. This study introduced the integral method

of analysis which consists of integrating the equations for conservation of

volume flux, momentum, and density deficiency in the transverse direction.

The resulting expressions are dependent on the axial direction only. Morton

(1959) used this method to analyze the vertical forced plume. Full solutions

require an experimentally determined coefficient. Morton, et al. assumed the

following:

1) the rate of entrainment is proportional to some velocity

at that plume section, or

dQ/ds = 2TrU b (2.11)

where
a = entrainment coefficient, a function
of local buoyancy conditions.

U = characteristic velocity









2) the profiles of mean velocity and density deficit are

similar at all sections,

3) local density variations are small when compared to some

reference density.


Data by Albertson, et al. (1950) for a simple jet yields


a = 0.057


Data for a plume by Rouse, Yih, and Hemphreys (1952) gives


a = 0.082


Far away from the efflux section, the buoyant jet behaves like a plume with

a approaching 0.082.


2.1.3 The Buoyant Jet or Forced Plume

The buoyant jet is a combined simple jet and plume. The mass transport

associated with forced plumes are 1) convection by mean velocities; 2)

acceleration in the buoyant direction; and 3) turbulent diffusion due to

shear-generated eddies. In the zone of flow establishment the jet momentum

dominates over buoyancy. Density deficiency becomes increasingly important

as the jet velocities (momentum) become reduced.

Abraham (1963) conducted experiments on slot and round buoyant jets,

varying the vertical angle of discharge, 6 He too used the integral

technique; however, his coefficient is that of the jet spreading rate. This

coefficient is similar to the entrainment coefficient used by Morton, et al.

and goes to an asymptotic value for the simple jet and plume.

Fan (1967) extended the Morton type of analysis to cover the effect

of initial angle of discharge in stagnant linear density-stratified environ-

ments. Numerical solutions for different discharge angles and jet densimetric









Froude numbers were compared with laboratory experiments. The jet densimetric

Froude number, F., is defined as

Pj 1/2
F. = U /( a -p gD)1/2 (2.12)
0 p
a

where
a = ambient density

pj = effluent density

g = acceleration due to gravity


2.1.4 The Effect of Crossflow

The most obvious effect of a flowing receiving body on a buoyant jet

is to deflect the trajector in the direction of flow. The two forces which

act on a jet are the drag and the loss of momentum. Vortices develop down-

stream of the jet due to the shearing along the jet sides and the low pressure

wake region. These vortices, in turn, act on the jet itself. Consequently,

the jet section becomes horseshoe shaped with a wake region similar to that of

a solid body as seen in Figure 2-2 (Fan, 1967). The pressure drag force, FD,

is of the form:


FD = CD(Pa Ua2/2) 2b (2.13)

where
CD = drag coefficient

Ua = ambient velocity


Chan and Kennedy (1972) used the integral technique with a special entrainment

coefficient in their study on a jet in a crossflow. The experimental fluid

was air. Variation of the drag coefficient with the velocity ratio, k, was

determined. The velocity ratio is defined as:


k = U /Ua


(2.14)
























Uo

PC 1 0


Figure 2-2


S


A Round Jet in a Uniform Cross Stream (From Fan, 1967)









Fan (1967) has found variations in the CD from 0.1 to 1.7 through different

values of k and F. values.

The force due to the entrainment of the ambient fluid, Fe is expressed

as:

F = pa Ua (2TbV ) (2.15)


The entrainment concept was modified by Fan (1967) to yield for the transverse

entrainment velocity, V :


Ve = aU- Uj| (2.16)


where Ua U. is the magnitude of the vector difference between the ambient

and jet centerline velocities. When still assuming a Gaussian profile, values

of a are considerably higher (0.4 to 0.5) than in the case of stagnant ambient.

This indicates an increased dilution efficiency in the presence of a crossflow.

Wright (1977) conducted analytic and experimental studies on round

buoyant jets in a stratified and unstratified crossflow. This work differs

from those mentioned previously in that approximate solutions of jet behavior

was obtained through dimensional analysis and considering asymptotic relations.

The relations considered were those where the jet behavior is dominated either

by its initial momentum or density deficiency, and where the ambient velocity

is either relatively strong or approaches zero. Combinations of these four

asymptotic solutions can be used to describe the buoyant jet.


2.1.5 The Effect of Boundaries

The air-water interface has nearly the same effect on the buoyant jet

as a solid boundary. A slight rise in the water surface will occur depending

on the initial kinetic energy and discharge angle of the jet. Once surface

impingement occurs, the heated effluent will spread laterally in a layer of









certain thickness. Abraham (1963) reports experimental values of the surface

layer for a slot jet (or after lateral interaction for a multiport diffuser)

to be about 1/4 of the length of the trajectory.

Entrainment of the ambient flow decreases after the jet experiences

surface effects. Jirka and Harleman (1973) estimated the entrainment of the

surface layer for a two dimensional buoyant slot jet in a quiescent ambient

while Lee, Jirka, and Harleman (1974) did the same for an axisymmetric

buoyant jet.

The interaction of the buoyant jet with the bottom should reduce the

entrainment of the ambient fluid into the jet. Sharp and Wang (1975) found

experimentally, however, that for a horizontal buoyant jet experiencing bottom

effects, surface dilutions were 200 to 500% higher than for horizontal jets

not finding the bottom. The reasoning behind this phenomena is that the jet

attaches itself to the lower boundary, developing greater turbulence and

momentum exchange, while thus increasing its trajectory length and total

entrainment.

The analyses discussed previous to this section apply only to cases

with no boundary interference. The effect of the boundaries is to restrict

the flow field, producing a nonhydrostatic pressure distribution. The

entrained ambient fluid in constricted regions accelerates, resulting in a

local pressure drop. These low pressure areas cause the jet to attach itself

to boundaries as in the Sharp and Wang (1975) study. The hydrodynamic

conditions are thus very complex since the assumptions of similarity of

velocity profiles as well as that of a hydrostatic pressure distribution are

no longer valid. Consequently, the models of Albertson, et al., Morton,

et al., Abraham, Fan, Chan and Kennedy, and Wright are not readily applied

to buoyant jets in confined flows.









Paily and Sayre (1978) have developed a predictive method, based on

diffusion concepts, for determining the transverse temperature distribution

of shore-attached thermal plumes in rivers. Their model is two-dimensional,

assuming complete vertical mixing. Application is best suited to the far

field where mixing mechanisms characteristic of the ambient flow dominate.

Comparison of model results with field data shows good agreement.


2.2 Multiport Diffusers

The multiport diffuser is an efficient method for the injection of

thermal and chemical wastes into the hydrologic and coastal environments.

A high degree of dilution can be obtained in a relatively limited area, thus

minimizing the adverse effects of high pollution concentrations.


2.2.1 Lateral Interference of Round Buoyant Jets

Each jet issuing from the submerged multiport diffuser keeps it

identity until it begins to interact with adjacent jets. Figure 2-3 indicates

the process. Jet interference starts in the transition zone and continues

until complete interaction yields a two-dimensional jet profile. From this

point on, the diffuser behaves like a slot buoyant jet. Since the self-

similarity assumption is no longer valid in the transition zone, single jet

analysis cannot be extended into this region.

Transition is assumed to occur when

b = L/2 (2.17)

where L is the port spacing, or when the velocity profiles overlap to the

point where lateral entrainment is significantly reduced. Koh and Fan (1970)

compared this definition of transition with that of the point where the

entrainment of a round jet is the same as that for the equivalent slot jet.













PLAN


Figure 2-3


Jet Interference for a Submerged Multiport Diffuser
(From Jirka and Harleman, 1973)









Their investigation, confirmed by Jirka and Harleman (1973), showed that either

definition yields the same location of initial jet interaction.


2.2.2 The Equivalent Slot Diffuser

After lateral jet interference the multiport diffuser can be analyzed

as an equivalent slot diffuser. This concept is useful when applying mathe-

matical models to the field beyond the transition zone. The equivalent slot

diffuser is required to have the same volume and momentum flux per unit length

as its multiport counterpart. The equivalent slot, B, is defined as:


B = iD2/4L (2.18)

Cederwall (1971) compared the dilutions of the multiport diffuser and

the slot jet at the distance of lateral jet interference. Using the experi-

mentally determined relationships of Albertson, et al. for a simple jet he

found:

R = dilution of the multiport diffuser = 0.95
dilution of the equivalent slot jet

Following the same routine for a simple plume and employing results from

Morton, et al. and Rouse, et al., Cederwell determined:

R = 0.78

These values of R indicate approximately equal dilutions for the multiport

and equivalent slot diffusers.


2.2.3 Solutions for the Multiport and Slot Diffusers

Solution graphs for slot and round buoyant jets have been presented by

Abraham (1963), Fan and Brooks (1969), Brooks (1972), Jirka and Harleman (1973),

and others. These plots are for various vertical discharge angles. All

solutions must be adjusted for the initial zone of flow establishment. The

choice of model depends on the ambient conditions: stagnant or flowing,

stratified, shallow, etc.









Jirka and Harleman have also included angle of diffuser to crossflow,

as well as, two horizontal angle distributions normal, with jets perpendicular

to diffuser axis; and log, in which the jet angles vary logarithmically from

900 to 00 (Figure 2-4), or:


(z) = cot -1( log I + z (2.19)
T 1 z/D

where
g(z) = inclination angle with respect to the z-axis

The log distribution seems to be especially effective in partially confined

flows. A partially confined flow is one in which the diffuser only partially

experiences boundary effects e.g. a diffuser extending across half of the

river width.

No analytical models exist which take into account the effects of a

flowing, totally confined receiving body. The deflection mechanism is highly

complex with vortices and re-entrainment occurring. Also, jet attachment to

boundaries is a difficult phenomena to model.













normal


800


600


40


0 .2 .4 .6 .8 Z/ D
L-D


Example: log, 10 unidirectional nozzles



I t i J


Figure 2-4


Nozzle Orientation, B(z), Along the Diffuser Line
(From Jirka and Harleman, 1973)















CHAPTER III

ANALYSIS


The breakdown of normal buoyant jet assumptions precludes the develop-

ment of an analytical model for coflowing, totally confined receiving

environment. Instead, dimensional reasoning is used to isolate the governing

parameters. The investigation is similar to that advanced by Argue and

Sayre (1973).


3.1 Statement of the Problem

Consider the multiport diffuser in Figure 3-1 discharging hot water

into a coflowing, shallow, laterally confined receiving body. The parameters

that describe the ambient flow are:

H = free surface elevation

U a = mean velocity

W = width

p = density

v a = kinematic viscosity

The diffuser is characterized by:

D = jet diameter

h = height of port centerline above the bed

L = port spacing

Ld = diffuser length, or the distance between the first
and the last jet plus one port spacing

U = efflux jet velocity

e = vertical angle of discharge






19















L












//// ///////// / // / /PLAN

PLAN


H


- Ua ,ala a


PROFILE


Figure 3-1 Parameter Description









Ap = ambient flow density jet flow density, or pa p

v. = kinematic viscosity of effluent
J

The coordinate axes are oriented such that x is in the downstream direction;

y is directed upward from the bed, and z locates the transverse positions.

A general measure of mixing at some section is defined as Mx, while the ac-

celeration due to gravity is g.


3.2 Dimensional Inquiry

Some function of the proceeding variables should describe the mixing at

a section. The y and z dependence is eliminated by considering only a bulk

mixing criterion at the longitudinal distance, x. The functional steady-state

relationships starts as:


q(H, Ua, W, Pa' a', D, h, L, Ld, U 0e Ap, vj, Mx, g, x) = 0 (3.1)


Since there are sixteen variables in three dimensions, the Buckingham n theorem

states that thirteen dimensionless expressions exist which describe the problem.

Choosing H, U and Ap as the repeating variables, the following parameters

are deduced:

a a a 1 aN qa V
l- U Uo--- N 'Uoji( = F(3.2)
1 U0 U Iq N i= Uaq.)i k


where
Ua = depth averaged ambient velocity at each jet
a
qa = ambient discharge per unit width at each jet

= UYH (3.3)
a
q = effluent discharge per unit length of diffuser








U T/4 D2
=o U B (3.4)


N = number of in-use jets


The 71 term is transformed into Cedarwall's (1971) kinematic momentum flux

ratio by squaring and multiplying by H/B. The average of the V/k values at

each discharging jet is used in defining the parameter.


S-W (3.5)
2 H

may be neglected since the width to depth ratio is kept approximately constant
3
P U N uY
= a a 1 a ). = iF. (3.6)
3 Ap Ap +N -(i-I Ap i a J
Pa g qjp g q.
Pa aP

The ambient/jet Froude number, aFj is obtained by multiplying by the ambient

Froude number squared, the inverse velocity ratio, 1/k, and H/B. Ap/p is

determined from the mean of the first sand last ambient and effluent temperatures.

Again aF. is taken as the average of the values at each discharging jet.

U H U H
4 = IR (3.7)
a a

The Reynolds number of the ambient flow, JRa, found by dividing 74 by k; may be

neglected if the flow is fully turbulent, or

R > 600 (3.8)
a
75 = D/H (3.9)


The jet diameter to ambient depth ratio changed only slightly in this study

and is therefore omitted.


(3.10)


76 = h/H









Due to diffuser rack limitations, h/H varied somewhat and is therefore included.

T7 = L/H x/L (3.11)


A measure of the distance downstream in terms of the port spacing.

78 = Ld/H Ld/W (3.12)


is the ratio of the diffuser length to the total width.

g9 o= (3.13)


U H UD
S= R (3.14)
10 vj v j


The jet Reynolds number, R., is a combination of r5 and Tr 10. Jet Reynolds

dependence may be deleted provided:


R. > 2500 (3.15)


711 = Mx CVx (3.16)

where CVx follows from Argue and Sayre (1973) and is the coefficient of

(temperature) variation at a section, x:

M
( I s (S )2)12
CV = M-1 i=1 i (3.17)
x S-


where
M = number of nondimensional temperature readings, Si,
at some x

S = arithmetic mean of all S.'s at some x
1
T T
S. = a (3.18)
m









Qe(T Ta
ATm = Qe ( Qa (3.19)


= mixed temperature rise

T = temperature reading at a point

T = temperature of ambient flow
a
T = efflux jet temperature

Q = total effluent discharge
Qa = ambient discharge

U2 U
a = a = IF (3.20)
12 gH (gH)1/2 a


Taking the product of r and the square root of 1l2 yields the ambient Froude

number, F a. This parameter may be eliminated since it varied only slightly over

the experimental range.

x x L (3.21)
713 H H-h H-h


A measure of the distance downstream in terms of the height of water above the

ports is converted to a relative port spacing parameter through equation (3.9).

This factor follows from Argue and Sayre (1973) and is used subsequently in the

creation of the plane:

log [CVx (- )] vs. log (X) (3.22)

If we let CVx become the dependent variable the preceding analysis leads to

the following equation:


CVx j' H' x' W 0 ) (3.23)
xTk a H' L' P Y' O0' H-h)









3.3 Experimental Objectives

The main objective of this experiment is to describe thermal mixing

through the CVx parameter, isotherm, and velocity distributions.


3.3.1 The CV Parameter
x

The dimensional inquiry of the previous section has isolated seven para-

meters which govern the mixing at a section in this physical model. One

objective is to determine the variation of CVx with each of the terms sighted.

More specifically, with the total effluent discharge fixed (see subsection

3.4.2), seven diffuser configurations are chosen as Figure 3-2 depicts. Three

values of Ld/W are immediately recognized:


Ld/W = 0.5, 0.75, 0.95 (3.24)


corresponding to ten, fifteen, nineteen discharging jets, respectively. Each

of these arrangements, in turn is divided into unique combinations of five

port sections. Values of V/k and Fj. are also determined for the port groupings.

CVx is computed at


x = 0.5, 1.0, 2.0, 4.0, 6.0 m (3.25)


with the initial discharge angles set at


60 = 350, 200, 100 (3.26)


Nozzles directed upstream are not considered in this study at this leads to

decreased dilution due to stagnation and unsteady recirculation, Harleman,

et al. (1971). For e = 350 and 100


h = 0.0877 (3.27)
H














Discharging Jets

t Flow
5 6 7 8 9 10 11 12 13





A A A A A A A
1-19


1-10, 15-19



5-19


10-19


Ld/W


14 15

A A


18 19

A A


AA~/~AA


1-5, 15-19

AAAAAAAAAA
5-14

-5 A0 -4 A
1-5, 10-14


A-AA A


0.95


0.75


0.75


0.5


0.5


0.5


0.5


U j(cm/s)





48.0


60.8


60.8


91.2


91.2


91.2


91.2


V/ kt


11.03


5.62


7.88


3.43


2.43


3.99


2.54


t average values


Figure 3-2 Diffuser Configurations


2 3 4

A A A


jet no. I

A


125.8


76.6


109.0


67.7


46.2


79.0


48.7









on the average while for e = 200



h = 0.744 (3.28)


3.3.2 Isotherm Plots

Another objective of this study is to plot dimensionless cross sectional,

plan, and profile isotherms to graphically illustrate temperature distrubutions.

Cross sectional patterns are used to compare mixing and extent of stratification

at each section. Sectional surveys are conducted at the same x locations at

which CV is determined. Plan isotherms are used to determine jet interference,
x
while profiles delineate jet trajectories.


3.3.3 Velocity Distribution

Vertical velocity profiles and the transverse discharge distribution are

compiled from section 2 m downstream of the diffuser. In this way areas of

excessive longitudinal momentum flux can be noted for possible scouring problems

in prototype installations. Also temperature and velocity distributions are

compared.















CHAPTER IV

DESCRIPTION OF EQUIPMENT AND PROCEDURE


4.1. Introduction

The authors consider it important for the scientist not only to report

themethodology and results of his experimentation but also to describe and

evaluate his equipment. In this way it is hoped that future users will refine

and also report on such devices. Accordingly, a departure from the norm is

made in that comments on the performance of each piece accompanies its

description.


4.2 The Hydraulic Apparatus

The basic components of the experimental hydraulic apparatus include the

recirculating flume, the effluent supply system, the manifold, the manometers,

and the diffuser. A system layout is contained in Figure 4-1, while Figure

4-2 is a photo of the experimental arrangement.


4.2.1 The Recirculating Flume

All runs were conducted in the recirculating flume. This structure was

fabricated of concrete block, was concrete finished, and was sealed with

epoxy paint. The main channel is horizontal, 36.6 m (120 ft) long, 2.47 m

(8 ft) wide, and 61 cm (2.0 ft) deep. At midlength of the main flume is a

false-bottom section 6.10 m (20 ft) long and 34 m (13.5 ft) deep. Centered

in the false-bottom area is a sectioned glass wall 3.66 m (12.0 ft) long for

visual inspection and photography. The 52 kW (70 HP) flume pump has a

maximum discharge of 1.13 m3/s (40 cfs). Just downstream of this pump is











flow turners


sluice gate-

diffuser


manifold


manometer


heaters


cold water line


rack


hot water
line


Thomson weir


gate valve


main


flume sump

effluent pump
constant head tank


flow
straighteners


effluent
intake

effluent
return hose


Figure 4-1 System Layout

















. .
















Fig..e 4it










Figure 4-2 The Experimental Arrangement









the main delivery pipe with its gate valve and a return pipe with another

gate valve. Adjustment of these valves regulates the flow rate and depth.

The delivery pipe is 76 cm (2.5 ft) ID while the return is 50 cm (1.6 ft) ID.

Downstream of this are two sets of flow straighteners and a Thomson V-notch

weir. A Poncelet rectangular weir is also available for high discharges.

Beyond the weir are two more sets of flow straighteners, and a main channel.

The last structure in the main channel is the downstream sluice gate which

serves to regulate the water depth in the main flume and moderately regulate

discharge.

A trolley which spans the main channel provides the work-deck for

collecting data as well as calibrating velocity meters. A carriage, the range

of which is the channel width, provides the mount for the velocity meters.

For the most part, the flume is constructed and runs well. Its width

and maximum discharge make this structure particularly unique. The choice of

two weirs contributes significantly to the accuracy of discharge measurements.

Also, the flow rate varies little over many hours.

Difficulties inherent in the flume are the control and measurement of

the depth of flow. The downstream gate, which regulates the depth, presently

operates off a constant speed electric motor and a rack and pinion gear. To

fine set this gate, one must quickly turn the switch on and off, relying on

trial and error. This method is frustrating and time-consuming at best. A

variable speed motor with a rheostat control or a hand-operated crank may help

in this respect.

Problems in depth measurement arise out of: 1) the nonuniform flow

due to the zero bed slope; and 2) irregularities in the bed itself. The

bottom contains "hills" and "valleys" in both the longitudinal and transverse

directions. The writers have been involved in four experiments using this

flume, and in each, depth measurement has been a dilemna. One help might be









to make the bed truly horizontal. To accomplish this a low-viscosity, slow-

drying resin could be spread over the bottom hardening only after its found

its own level. An attempt was made to straighten the false-bottom section.

The old, badly warped 1.3 cm (1/2 in) exterior plywood was replaced with

marine plywood of the same thickness. Also the existing cedar support was

planed down in an effort to make it level. The results of this endeavor were

good, though not perfect.

In this study, for the reasons just outlined, depths were measured with

a dry rod at the centerline of the test section. This method was considered

the best available in lieu of the circumstances. A point gauge was used to

follow the overall depth fluctuations during a run.

The flow over the V-notch weir, though readily measureable for low

discharges, is totally deposited in the center of the main flume. This leads

to a rather distorted transverse velocity distribution. In an effort to

remedy this, concrete blocks placed directly downstream of the weir caused

the water to splash and roughly spread itself over the section. Fine tuning

was accomplished by squirting dye across the flume width and noting areas of

excess velocity. Wooden strips were then clamped to the flow straighteners

at these areas.


4.2.2 The Effluent Supply System

The effluent supply system consists of the pump, the piping, and the

heaters. The pump is a 1.5 kW (2 HP) "Sta-rite" model DMG. It is located

next to the flume pump and also supplies a constant head tank directly above.

The suction line draws from behind the weir in an effort to avoid the

turbulence-entrained air in the flume pump. The heated effluent discharge

was much smaller than the pump capacity. To prevent excessive strain on the

pump, a 3.8 cm (1.5 in) canvas fire hose returns a large percentage of the

flow to the area of intake.









A 5.1 cm (2 in) PVC pipe conveys the diffuser water to six 189 1 (50 gal),

12,600 kcal/h (50,000 Btuh), natural gas hot water heaters connected in parallel.

Gate valves, located in the 1.9 cm (0.75 in) incoming lines, allow individual

heaters to be bypassed. A 5.1 cm (2 in) galvanized steel pipe, insulated with

1.3 cm (0.5 in) wall neoprene ("rubbertex"), directs the flow to the manifold.

For visual inspection of flow patterns a 24.4 1 (6.4 gal) dye tank is

located just upstream of the manifold. The cylinder contains a spigot for

the release of coloring and a regulator with a check valve for pressurizing.

A 0.64 cm (0.25 in) tube extends from an adapter in the spigot to one in the

steel feeder pipe.

The pump, piping, and heaters are considered adequate for the job.

Strong surges from the pump, however, necessitates the use of a return line

as well as a surge tank. The constant head reservoir is used instead of the

latter.

The efficiency of the heaters, presently calculated as 65%, could be

increased through a preheat system. This may be accomplished by passing the

cold water supply through an axially back-and-forth copper line inside the

heater's chimney which is usually too hot to touch.


4.2.3 The Manifold and Manometers

The steel feeder pipe from the heaters expands to 7.6 cm (3 in),

adapts to PVC, then enters and extends the length of the manifold. Slots

are sawed in this line opposite to the exit ports, while supports keep it

centered.

The manifold is fabricated of 15.2 cm (6 in) PVC, capped on both ends,

and reinforced around the exit ports (Figure 4-3). The reinforcement consists

of PVC of equal size cut to form a "C" section by removing approximately 100.

This length was then snapped on the main section after the caps were in place.







































Figure 4-3


The Manifold









The exit holes were drilled and tapped through the double-walled pipe. An

air cock is located at the top center of this main piece.

The heated water exits the manifold through nineteen 1.9 cm (0.75 in)

galvanized pipes before entering the vinyl tubing to the jets. Each pipe

contains an orifice meter, an air cock, and a gate valve. Jets number 4, 8,

12, and 16, are equipped with a "tee" section between the gate valve and

tubing to accommodate the manifold thermistors. The orifice meter is constructed

of an aluminum annulus 0.43 mm (0.017 in) thick, 1.1 cm (0.44 in) ID, and

9 cm (3.5 in) OD secured between two 1.3 cm (0.75 in) galvanized flanges.

Pressure tappings consists of slots ground into the flange faces with holes,

drilled and tapped, to accommodate 0.64 cm (0.25 in) tube adapters.

Vinyl tubing with clamps to dampen oscillations, extends from the

adapters to the wall-mounted manometers. (Undampened the standpipes pulsate

with an average amplitude of 1 cm (0.4 in). Surges with a 9 cm (3.5 in)

amplitude have been observed.) Thirty-eight glass tubes, 0.6 cm (0.25 in)

OD, make up the battery of manometers. The glass tubes are connected at the

top to a common overflow pipe. A cock valve and an automotive tire valve

allow this pipe to be closed and pressurized with air to adjust the water

surface elevations to a convenient level (Figure 4-4).

The outstanding drawback of a manifold of this size is the adjustment

of port discharge. This task would take anywhere from 1 to 2 1/2 hours.

Obviously, the setting of one jet affects that of the others, and with

nineteen, the problem is significant. The extra initial investment and

increase head loss, characteristic of a good pin valve would have repaid

itself in saved time and accuracy during the experiment. Additionally, surges

from the pump makes discharge tuning difficult.































































Figure 4-4


146


Wall-mounted Manometers with Overflow Pipe and
Compressed Air Hose









The mainfold is structurally sound. The anticipated weak areas were

the junction of the 7.6 cm (3 in) PVC feeder pipe and the 15.2 cm (6 in) PVC

cap, as well as the taps in the PVC for the galvanized exit lines. No leaks

were observed in either joint thanks to the extra cement and the reinforcing,

respectively.

An additional asset of the system is its ability to hold a vacuum.

The main section of the manifold is located approximately 45 cm (18 in) above

the still water surface in the flume. While not in use this height of water

as a suction is applied. Considerable time is saved in this respect since

a leak would have necessitated purging the manometer tubes of air (a lengthy

process).


4.2.4 The Diffuser Jets and Rack

Vinyl tubing, 1.9 cm (0.75 in) ID, extends from the manifold; follows

the flume wall to beneath the false bottom, and is clamped to the jets. A

streamlined aluminum shield 70 cm (28 in) long attached to and extending

4 cm (1.6 in) from the wall serves to contain the tubes, in addition to

smoothly diverting the flow around the nineteen roughness elements.

The multiport diffuser consists of a rack support with friction held

1.3 cm (0.5 in) ID copper tubing as the jets (Figure 4-5). The rack is cedar,

5 cm x 5 cm (2 in x 2 in), treated with "Woodlife" wood preservative, and

extends the width of the flume. Bolts protruding from the ends of this plank

allow it to pivot in fixed angle iron brackets.

Jet angles are established by changing the rack angle. This is achieved

with precut plywood supports with aluminum bearing plates. Because of space

limitations, however, the 100 diffuser angle is secured by a sweat 450 copper

elbow and a 550 rack setting.







































Figure 4-5


The Diffuser Rack and Cover









Marine plywood 1.3 cm (0.5 in) thick with slotted holes to accommodate

individual jets covers the rack and braces.

The jets and rack functioned well throughout the experiment. No signs

of warping could be detected in the cedar support despite large short term

temperature fluctuations and repeated wetting and drying. A 450 elbow in the

copper tubing is most effective for ease in handling, especially for small jet

angles.

Hindsight is the best teacher. Equal lengths of vinyl tubing from the

manifold to the jets would have effected a more uniform manifold-jet temperature

drop distribution. A complete listing of temperature drops from the manifold

to the individual jets is contained in Appendix C-2.


4.3 The Sampling Equipment

Data was collected with thermistors and velocity meters, both of which

were read and compiled through the data acquisition system.


4.3.1 The Thermistors

YSI "banjo" thermistors, probe no. 408, were used to measure all tempera-

tures for calculations. (Total immersion Sama CT 15 thermometers were used as

a thermistor check.) The YSI probe has a maximum operating temperature of

1500C with a time constant of 0.6 seconds. The time constant is the time

required for the probe to measure 63% of the newly imposed temperature.

Approximately five "time constants" are required for a probe to read 99% of

the total change. The interchangability tolerance of the temperature sensors

is + 0.1oC (+ 0.18F) over the range used. Figure 4-6a illustrates the

thermistor dimensions. The sensing element, a temperature dependent resistor,

is housed in a disc with a wire support, both of which are stainless steel.

Three meter (10 ft) plasticized vinyl jacketed lead wires terminating with a









phone plug are standard. The manifold and ambient thermistor leads are 30.5 m

(100 ft) in length.

Fourteen thermistors were employed in this study one, positioned in a

tee section between the gate valve and the tubing of an in-use jet measured

efflux temperatures; another, placed approximately one meter upstream of the

diffuser in the center of the cross-section yielded ambient temperatures;

while the remaining twelve comprised a four vertically, by three, laterally,

array for downtream data (Figure 4-6b). The array spacing was 3.2 cm (1.3 in)

and 6 cm (2.4 in), respectively. The thermistor array was held in place with

three 3.2 mm (1/8 in) thick by 38 mm (1.5 in) wide plexiglas supports.

Automotive fuse holders provided quick release capabilities for individual

thermistors. The plexiglas supports were clamped to an aluminum brace, which

in turn hung from the carriage support on the trolley.

The YSI thermistors are considered excellent instruments. They are

adaptable to many uses and positions. An exceptional advantage is the small

time constant of probe no.408.

A constant temperature bath is needed to periodically check the thermistor

calibration, although the calibration seems very stable for both laboratory and

field measurement over several days of operating time. The accuracy of the

calibration needs to be checked, although these errors are probably negligible

due to the temperature correction technique used in the calculations (see

subsection 3.4.3).

A probe positioned very near the bed in the sampling array would have

yielded more complete isotherm plots.


4.3.2 The Velocity Meters

Two Novonic-Nixon type no. 403 velocity meters were employed for all

velocity measurements. The range of these instruments is 2.5 to 150 cm/s





40





17 gouge 1.0 cm



K- 3.8 cm 9.2 cm








Figure 4-6a Thermistor Dimensions


M i-l


Figure 4-6b Thermistor Array in Plexiglas Support









(0.082 to 4.92 fps) with an accuracy of + 2% of true velocity. Their operating

temperature is from 00 to 500C (32 to 122F) with an operating medium of water

or other fluids having similar conductive properties.

The probe consists of a measuring head supported by a thin shaft

46 cm (18 in) long with an electrical lead connection. The head consists of

a five blade impeller mounted on a stainless steel spindle, terminating in

conical pivots (Figure 4-7). These pivots run in jewels mounted in a sheathed

frame. The impeller is 10 mm (0.39 in) in diameter, machined from solid PVC

and balanced. An insulated gold wire within the shaft support terminates

0.1 mm (0.004 in) from each rotor tip. As the rotor is revolved through the

motion of a conductive fluid, the small clearance between the blades and the

shaft slightly varies the impedance between the shaft and the gold wire. This

impedance variation modulates a 15 kHz carrier signal, which in turn is used

to detect rotor revolutions.

The propeller meters were suspended from the carriage on the trolley

(Figure 4-8). The shafts of the instruments were clamped to stainless steel

rods at one location. For ease and accuracy of vertical positioning, the rods

were clamped at two points to the rack of a point gage. The conventional

point gage brackets were then bolted to the carriage. Lead weights of the

900 gm (2 lb) variety were secured to lowest clamp in an effort to reduce

vibrations brought about when moving the carriage.

The Novonic-Nixon meters are precision instruments with fine moving parts.

Since they are susceptible to suspended particles in the flow field, care

should be taken to insure clean water and flume. Two layers of window screen

were placed upstream of the first flow straightener in the main channel to

intercept the larger debris. Also, air bubbles trapped between the rotors

could yield erroneous readings.














































Fi ur 4- .. -Ve* P o ei. a F o F






rf
Figure 4-7 Novonic-Nixon Velocity Probe in a Flow Field












































S.
4- 1


Figure 4-8


Point Gauge Carriage Mounting for the Novonic-Nixon
Velocity Probes









The maintained accuracy of these velocity meters is rather poor. On

the average, in order to work within a +_ 2% deviation from true velocity

(Nixon Instrumentation Limited boasts a sustained capability + 1%), the

meters had to be recalibrated before every other use. This record is

improving slowly with time.

Despite their sensitivity and inability to hold the advertised accuracy,

the Novonic-Nixon meters are desirable instruments. The meter's small rotor

size, as well as its low velocity capabilities,are very strong assets.

The point gage mounting is considered an excellent method for suspending

the current meters. The instruments are easily removed from their brackets

with no deviation from the vertical setting. Also all the accuracy and

ease of a point gage and vernier is accrued.


4.3.3 The Data Acquisition System

The ability to collect, refine, and compile large quantities of data

was made possible through the data acquisition system. The system is composed

of two pieces of equipment: a pink input box and an HP 9825A desk-top

programmable calculator (Figure 4-9).

The input box contains the electronic circuitry which takes the raw

transmission from the measuring devices and converts it into usable signals

for the programmable calculator. The pink box, which was specifically

designed for coupling with an HP 9825A, has connectors for fifteen thermistors,

two Novonic-Nixon velocity meters, two Ott velocity meters, and ten Cushing

electromagnetic current meters. It also contains an electronic clock which

registers six counts per second. The input box was specially designed and

constructed for the University of Florida Hydraulic Research Laboratory by

Mook Enterprises of Meritt Island, Florida.


































.9 4*


t

I -.


Figure 4-9


The Data Acquisition System: the Pink Input Box and the
HP 9825A Programmable Calculator









The HP 9825A interfaces with the input box to provide program control

and data storage capabilities. The calculator has a 32-character LED display,

16-character thermal strip printer, and a typewriter-like keyboard with upper

and lower-case alphanumerics. There are twelve special function keys,

shiftable to twenty-four,as well as editing and system command keys. The

machine has a two track, built-in, tape cartridge drive, three input/output

(I/0) slots and four read only memories (ROM) slots. The string, advanced

programming, and extended I/O ROM's were utilized in this experiment. The

standard internal I/O storage is 6844 bytes with options available to increase

this to 31,400 bytes. The standard storage was used in this study. The

capacity of a tape cartridge is 250,000 bytes. The University of Florida

Hyraulic Research Laboratory also has a serial interface capability for the

HP 9825A. With this specialty the calculator can be used as a terminal to

the Northeast Regional Data Center's (NERDC) Amdahl 470 computer.

The data acquisition system seems to be the best investment the

Hydraulic Laboratory could have made. Data collection amounts to simply

changing the probe position and pressing a button, once the machine is programmed.

Days of calculation time are saved and the accuracy is greatly enhanced through

data storage and subsequent programming techniques. Also, the options to this

system (plotters, serial interface, increased memory, etc.) seem limitless.


4.4 The Process of Physical Modeling


4.4.1 Prototype Measurements

Prototype measurements of ambient velocity and depth were completed on

the Apalachicola River downstream of the Jim Woodruff Dam at Chattahoochee.

Cross-sectional bathymetries were determined with the University of Florida

Hydraulic Research Laboratory's 5.2 m (17 ft) motor launch and Benmar









echo-sounding recorder, model DR-68. River widths were found with a transit

and tape through conventional surveying triangulation. Discharge data was

supplied by the U.S. Army Corps of Engineers at the dam. The following

prototype specifications were observed:

discharge, Q = 495 m3/s (17,500 cfs)

cross-sectional area, A = 651.3 m2 (7011 ft )

width, W = 191 m (627 ft)

which gives:

average depth, H = 3.41 m (11.2 ft)

ambient mean velocity, Uap = 0.761 m/s (2.50 fps)

where the subscript p denotes prototype.

4.4.2 Planning of Experiments

Modeling considerations were based on ambient and jet densimetric

Froude number similarity. The ambient Froude number is defined as:

U
IF = a (4.1)
a (gH)1/2

Also, the velocity ratio (jet: ambient), k, was required to be identical in

the prototype and model. Due to the large width to depth ratio of the prototype

(W/H = 56) the complete river width was not modeled. (The mean depth and

velocity was, however.)

Since no multiport diffuser discharging thermal wastes exists on the

Apalachicola River, typical prototype diffuser characteristics were obtained

from literature. A prototype temperature rise above ambient of approximately

11C (20F) is indicated by Parr (1976) and Jirka and Harleman (1973) as

normal. Jirka and Harleman (pg. 272) also point out that jet velocities of








3.05 to 4.57 m/s (10 to 15 fps) are representative prototype values. Choosing

a prototype jet diameter of one-tenth the depth fixed that quantity at 34.1 cm

(1.12 ft). With a maximum efflux velocity of 4.57 m/s (15 fps) the maximum

jet discharge, qj, of the prototype becomes 417 1/s.

With these prototype parameters in mind, preliminary laboratory studies

of the six natural gas hot water heaters were conducted to determine the

total heat flux. Discharge and temperature measurements yielded a heat flux

value 49,420 kcal/h (196,100 Bth/h). Since a temperature rise of 11C (200F)

was desired, a total effluent discharge, Q ,e of 1.25 1/s (0.0441 cfs) became

fixed. For the extreme case of a ten jet diffuser the individual jet discharge

becomes 0.125 1/s. Froude modeling laws state that the ratio of the prototype

discharge to that of the model Qr' must be:


S= UL r2= L = 2 (4.2)

where U = velocity ratio Prototype
r model

Lr = length ratio (4.3)


It then follows:

= ( 417 2/5
r .125 = 25.7

The other model parameters now fall into place:

H
Hm = 341 cm = 13.3 cm (5.2 in) (4.4)
L 25.7

D
Dm = __ 34.1 cm = 1.33 cm (0.52 in) (4.5)
Lr 25.7

U
U = a,p_ 76.1 cm/s = 15.0 cm/s (0.492 fps) (4.6)
a,m Lr 25.7









where the subscript m indicates model values. A check of the velocity ratios

for the model and prototype yields k = km = 6.00. Since the experimental

width is fixed as that of the flume, or 2.57 m (8.1 ft), the portion of the

prototype width modeled becomes:


L W = 25.7 (2.47 m) = 63.5 m
rm

or 0.332 of the actual prototype width.


4.4.3 The Experimental Procedure

After the construction of the apparatus, the first step in the experi-

mental procedure was to calibrate meters. The jet orifice meters on the

manifold were calibrated in place with a stop-watch, bucket, and scale. A

linear least squares fit of jet discharge, Q versus A-hwas determined,

where A is the head drop across the orifice plate. The error of the curves

was found to be + 4% of the true discharge.

Before each run the calibration of the Novonic-Nixon velocity meters

was checked in the range of 8 to 20 m/s (0.26 to 0.66 fps). Mounted with

their normal supports on the carriage, the Nixon meters were pulled through

still water over a distance of 1.07 m (35 ft) with the trolley. The special

function keys on the calculator were used to execute immediate continue

program statements which read initial and final values of propeller

revolutions and time. The program, then computed the average frequency of

each current meter, the true velocity, and the percent error of the calibration

curves to be checked. If the absolute error was greater than 2% the

instruments were recalibrated. No less than ten points were used to determine

a linear least squares fit of prop frequency versus velocity. Appendix B

contains a complete program listing for the HP 9825A.

The Thomson weir was also calibrated over the limited range of 40.0

to 67.0 1/s (1.41 to 2.37 cfs) (the model flow rate was fixed at 49.2 1/s









(1.74 cfs)). Six points were used to define the curve with an accuracy of

+ 1.5%. Seventy velocities were taken at a section to specify the discharge.

Ambient conditions must be established in the recirculating flume.

Since it is a closed system, the adjustment of one valve affects that of the

others. The discharge valve outside the main pump, the valve in the return

pipe, and the downstream gate were all adjusted until the ambient model

parameters were those described in the preceding section. The flume discharge

is found by measuring the height of the water above the weir and using a

weir calibration formula. Once the hydrodynamic controls are set there is

no need to adjust them; unless, that is, someone tampers with them in the

meantime.

The experimental run begins when the main pump is started. After the

water behind the weir has risen sufficiently (about three minutes) the small

effluent supply pump is activated. The flume takes about an hour to stabilize

from this point.

Flume stabilization is not the critical time, however; rather manometer

purging and manifold adjustment are more lengthy processes. The manometer

tubes need to be purged if air becomes trapped in one or more. This is done

only after all the air traveling through the piping system has been released

through the manifold aircock. To rid the manometer tubes of air, the cock

valve in the manometer over-flow pipe is opened. The jet gate valves are

then closed, diverting the total jet discharge through the manometers. Once

a clean, airless flow is observed in the tubes the jet gate valves are

reopened and the overflow cock is closed. Compressed air is then applied

slowly to bring manometer water surfaces to a readable level. Depending on

how careful the experimentor was in pressurizing the manometer rack air

bubbles may exist in the tubes. These pockets may be worked out by vibrating

individual tubes or by repurging the tube battery. As stated earlier this









process was often circumvented by the ability of the manifold to retain a

vacuum.

For each run and vertical jet angle, the diffuser discharge distribution

was unique. Therefore, this distribution had to be set, or the manifold had

to be "tuned". Tuning consists of adjusting the jet gate valves until the

head drops for the desired discharges are noted on the manometer battery. To

dampen the amplitude of the surge-induced oscillations in the manometers,

tube clamps near the orifice meters are tightened.

By the time the manifold tuning was complete, any residual warm water

in the heaters had been flushed out, allowing for the determination of the

thermistors' correction factors. With water at ambient temperature flowing

through the system (temperature checks were made with thermometers), the

thermistor sampling array was placed in the flow field. A program was then

initiated which read all fourteen thermistors 500 times (377 sec) in rapid

succession, found the mean temperature for each probe, and computed the

average reading for all. The difference between the group average and that

of the individual thermistors was then determined and used as the probe

correction factor to be added to subsequent temperature readings. A listing

of these factors is to be found in Appendix C-3.

Once the correction factors were determined, the six hot water heaters

were ignited. When the temperature rise above ambient was 11C (20F) data

collection would commence.

Velocities were taken at one section 2 m (6.6 ft) downstream of the

diffuser. The sampling array consisted of five rows and fourteen columns.

The rows were spaced every 2.5 cm (1 in) from the bed in an effort to find

any excess jet-induced velocities. The columns started at 20.7 cm (8.1 in)

from the south flume wall and increased in increments of 17.4 cm (6.9 in).









Columns 12 and 13 were spaced 9.9 cm (3.9 in) apart due to the proximity of

the north flume wall. The two propeller meters were used to sample simultaneously

the same row of adjacent columns. A velocity program (Appendix B-3) read

initial values of prop revolutions and time, waited a prescribed time increment,

and took final values of the same quantities. The program would then determine

the velocities from the calibration formulae and print them for immediate

checking. After the sampling was complete, the matrix was stored on tape.

Velocity averaging times of 15, 30, 45, and 60 seconds were all tried. The

latter, which yielded the most consistent results in a reasonable time span,

was employed in all tests. Ambient velocities were taken in the same manner

but with a zero effluent discharge. Five points on a vertical at the

relative depths of:


y/H = 0.1504, 0.2352, 0.3679, 0.5754, 0.9000 (4.7)


were sampled to best describe the logarithmic velocity profile (Christensen

(1978)). A section 8 m (26 ft) downstream of the diffuser was chosen in an

effort to avoid flow disturbances effected by the protruding jets.

Temperature collection followed immediately that of velocities. Five

sections were sampled during this process, one at 6 m (19.7 ft), 4 m (13.1 ft),

2 m (616 ft), 1 m (3.3 ft), and 50 cm (1.6 ft). The data array at each

section was comprised of four rows and thirty-six columns. The rows had a

spacing of 3.2 cm (1.3 in) from the bottom while the columns started at 22 cm

(8.7 in) from the south flume wall and were incremented at 6 cm (2.4 in).

Temperatures were collected by progressively moving a 4 x 3 fixed thermistor

array laterally across the section. Each time this 4 x 3 matrix was read,

the ambient and manifold temperatures were also read. So, in essence, twelve

fourteen-point arrays were compiled at each section. Sampling started at









the downstream most section and proceeded upstream. Aprogramwas designed to

continuously sample all thermistors for eighty-one points each, the time of

which took 61 seconds. This program (Appendix B-3) then averaged the values

for each probe, applied a correction factor, and printed the temperatures

in a prescribed format. A polynomial of the sixth degree with resistance as

the independent variable best matched the manufacturer's data and was used as

the calibration curve for the thermistors. Accurate thermistor calibration

is necessary to verify this however. Again, after the section sampling was

complete the temperature matrices were stored on tape.

Jet trajectories and interference patterns for each jet discharge and

angle was found using a 11 x 4 x 18 temperature array. This matrix started

at the diffuser and proceeded longitudinally to one meter (3.28 ft) in in-

crements ofl0 cm (3.9 in). Four points on a vertical were sampled at a

spacing of 3.2 cm (1.3 in) from the bottom. The grid consisted of a detailed

view of jets number 9, 10, and 11; commencing at 4 cm (1.6 in) south of jet

number 9 and extending laterally in steps of 2 cm (0.8 in) to 6 cm (2.4 in)

north of jet number 11. This array was collected in the same manner as the

section grids.

Before the compilation of a run, the temperature drop from the manifold

to each jet was determined. This was accomplished by securing the ambient

thermistor to a wand and inserting it into each jet. Temperature drops to

the jets for each run are contained in Appendix C-2.















CHAPTER V

REDUCTION OF DATA


5.1 Temperatures

All temperature readings were normalized through equation 3.18. This

equation is the ratio of the temperature rise above ambient to the mixed

temperature rise assuming no losses.

Iostherms were generated through the Gould plotter of the Northeast

Regional Data Center (NERDC). The serial interface capability of the

HP 9825A was utilized to convert this machine into a terminal of NERDC's

main computer, the Amdhal 470. Three programs were implemented for this

task (see Appendix B): one yields cross-sectional isotherms; a second, plan

views; and the third, jet trajectories. Each program has the same serial

interface component as the first half. After signing onto the Amdhal 470

data was transferred from an HP cassette tape, through an acoustic coupler,

and into a saved file. Job Control Language (JCL) in another file was then

used to initiate a contouring program stored on disc. The JCL also supplies

the stored program with the data in the saved file. Finally, the contouring

program generates the isotherms on the Gould plotter.


5.2 Velocities

Current measurements were nondimensionalized with respect to the mean

velocity, which was taken as:

SQ + Q
U = WH (5.1)









The transverse discharge distribution was found by integrating the

velocity profile over the depth. A least squares linear curve of velocity

versus the natural log of depth was fitted through the data for this

purpose. The equation generated from this step was then integrated.

Values of the ambient velocity at each jet, needed to compute V/k

and IFj, were determined through the use of a canned Hewlett-Packard program

which fit a third-degree polynomial through the data and interpolated

between points. The ambient distribution used was the average of six.

Velocity profiles for each jet velocity were taken as the average over

the center half of the centermost diffuser (e.g. for Uu = 91.2 cm/s the

profiles were averaged over the center half of the diffuser arrangement

with active jets five through fourteen).















CHAPTER VI

PRESENTATION AND DISCUSSION OF
EXPERIMENTAL RESULTS


6.1 The CV Parameter
x

Equation 3.17 defines the coefficient of variation at a section, CV .

According to this expression, fully mixed flow occurs when CVx 0. After

Argue and Sayre (1973), the plane


log [CVx (H-h)] vs. log (T) 3.22


is plotted in Figures 6-1, 6-2, and 6-3 for e = 35, 200, and 10,

respectively. Groups of constant Ld/W are apparent with best mixing occurring

with jets one through nineteen active. This is to be expected, since for

the same effluent discharge, the entire width of the ambient flow is utilized

for dilution.

For less than full diffuser, the mixing is drastically reduced. Curves

seem to fit these points best due to the effect of transverse dispersion.

With Ld/W = 0.75, and for the cases of e = 350 and 100, mixing is only

slightly better for active jets five through nineteen. Higher aF. and V/k

values are thought to account for this. More simply, diffuser five through

nineteen has more jets located in the region of maximum ambient flow than

does one through ten, fifteen through nineteen (see Figure 3-2).

The group with the least mixing is represented by Ld/W = 0.5. Diffusers

one through five, ten through fourteen, and ten through nineteen have the














I I ~ I


f.0 1
!-0

4
.8-
.7k

.6-


Symbol jeTs

0 1-5,15-19
7 5-14
# 1-5,10-14
A 1-10,15-19
+ 5-19
0 1-19


N~C


i i 1 ( 1


4 .5 6 7 8 9 10 x/L


r t I


20 30 40 50 60 70 8090 100


Figure 6-1 CVx (L/(H-h)) vs (x/L), eo = 350


/ 'x
1L


I i ...* .. i.. .. --- A --- .. J ._ . f f f I. 1 -- --- 1 1 1






















/__
CV11 /
^ H-


1 I i I I I


"X -x


VX

O


jets

i-5, 15-19
5-14
1-5,10-14
1-10,15-19
5-19
1-19


3 4 5 6 7 8 9 10


Figure 6-2


x/L


20 30 40 50 60 7080 90I00
20 30 40 50 60 70 80 90100


CV (L/(H-h)) vs (x/L), e. = 200
x.0


I I i I i i I
























CV~ (H'ih ~


I I I


Symbol jaet
X 10-19
O i-5,15-19
V 5-14
@ I-5,;0-14
A i-10, 5-19
+ 5-19
0 1-19


, I' 1 i l I '


4 5 6 7 8 9 10 x/L


,,I I 7I i I I I I


20 30 40 50 60 70 8090 !00


Figure 6-3 CV (L/(H-h)) vs (x/L), 6 = 100
X0


,! -
.09
.08 -
.07-
3









same jet locations in the ambient flow and, assuming a symmetric ambient

discharge distribution, should give equal mixing. It is obvious for all

three angles that diffuser ten through nineteen yields the poorest mixing in

the limit, while active jets one through five, ten through fourteen gives

the best in the group. This is attributed to the fact that the latter arrange-

ment has essentially three ends for transverse mixing, while the former has

only one. Similarly, comparing diffusers five through fourteen and one through

five, ten through fourteen for each angle shows the latter to disperse more

fully even though it has lower values of V/k and aIF This indicates that

the lateral transfer of heat is as important a descriptor of the mixing

process as the momentum flux ratio or the ambient/jet Froude number.

Figure 6-4 compares the effect of the initial discharge angle, o ,

on the coefficient of variation distribution for the full diffuser. Over

an initial distance of less than ten port spaces downstream of the diffuser,

o = 350 yields the best mixing. The large jet angle deposits the effluent

in the more turbulent upper reaches of the flow field, leading to increased

dispersion. Similarly, the smaller angles are less likely to feel this

dispersive influence close to the diffuser.

As x/L 50, the discharge angle of 100 results in the best mixing.

In this case, the jet experiences a low pressure area on its downstream side

due to the drag effect. This causes it to become attached to the bottom,

resulting in a longer trajectory and, in the limit, increased dilution.

This is the same phenomena witnessed by Sharp and Wang (1973).


6.2 Isotherm Plots

Five section isotherm patterns were recorded for each run, with four

plans and one trajectory for each jet angle and velocity.











2.0







1.0
.9
.8
.7

.6

CVx (HLh .5


I I I I I I I


i I I I I I


aD








symbol Oo
0 350

O 200


I i I I I I I


I I I I I I


3 4 5 6 7 8 9 10


x /L


20 30 40 50 60 708090100


CV (L/(H-h)) vs (x/L), Jets 1-19, e0 = 350, 200, 10
X 0


Figure 6-4


I I I I I = f | I I









6.2.1 Cross Sections

The cross-sectional isotherm plots are helpful in relating to the

coefficient of variation. There are many things to note and compare for the

three values of e All isotherms are those for the full difusser.

Figures 6-5, 6-6, and 6-7 contain the plots at the first section

(x = 0.5 m) downstream of the diffuser for o = 350, 200, and 100, respectively.

For the jet angle of 350 the maximum temperatures are already nearing the

water surface; while for 0 = 200 the hot spots, which are of the same

magnitude, are at mid-depth. By extreme contrast, the maximim isotherms

for e = 100 are nearly at the bed with much hotter temperatures and sharper

gradients. Obviously, this section is not as well mixed as the others. For

all three angles, the majority of the heat is at the larger values of z/W.

This is probably due to the meandering of the maximum velocity in the flume,

diluting the left side more than the right.

The isotherm patterns at the second section (x = 1.0 m) are to be found

in Figures 6-8, 6-9, and 6-10 for the three jet angles. For eo = 350

turbulent mixing is the predominant heat transfer mechanism, although slight

surface heat loss exists due to the temperature gradient across this boundary.

Section two for 00 = 200 is nearly identical to that of 350 as the CVx diagram

in Figure 6-4 confirms. With e00 = 100 the jets are still clinging to the

bottom with higher temperatures, steeper gradients, and less mixing than the

other angles.

The nondimensional plots at section three (x = 2.0 m) are displayed in

Figures 6-11, 6-12, and 6-13 for each diffuser angle. The density deficit

of the fluid near the water surface for 0 = 350 and 200 hinders the mixing

process which wants to bring it toward the bed. The buoyant fluid near the

bottom for eo = 100 is working to bring the heated effluent into the more


























ISOTHERlMS, CfROSS SECTOfN, ,'H- 3. 767, H=- L4.2 I'M, 35 DEG, JET t-19


RELflTIVE WITH, 7,'R V 'i, [fiNN$FflERM~


IET L0ILH Iii1'-
A A A 2L


Figure 6-5 Section 1, 350



























i$,OTHEFBMS, CROSS SECTION, A.:-Hj -.61 H= 14~.3 UM, 20l DEG, JET" 1-19


D~~~7 TL t~L iT F AIDIDH, Z/NJ, LOOLKIN,, [III WISTB ERM~~


000






A A


JET LICRT~iii.NF


A A A A A A A A


I I I I I I -~


Figure 6-6 Section 1, 20





















ISO~THERMS, CROSS1~ SECTIOlN, X,-H= *3.68f, H=~ t5.0 01, 10: DlEG, JETS t-19

F;EL AlIVE WIDflH, ?/H, L13DKING ~r f~I
0~oDA .L -L5 a d U2 .9 D3 DJI 0-45 a-S a.J s 0 70J D-75 ~ 3 D.35 a-g B.9 a20












A AA A


Figure 6-7 Section 1, 10



























ISOTHERMS, -LFISS* S~ECT~ION, X/H= 7.0C40l, H= L4.7 CM, 35 DEG, JETS 1-19


IPF H1D1H, Z/H, Lfl[1LIN DOHNN3YRER



















JET LOCfRTI INS3


Lads MaT


LIS5 Ma.. n..5 0-9 DA f.S I-all


A A A A A A A


Figure 6-8 Section 2, 35'



























ISOlTHERMS, CROSS SECTION, X~/H- R. 972, H= 14.7 CM, 210 [DEG, JETS 1-19


,JI~aa II.0S G LaI 0. L5 U.2 0.2 I -10 U-15r


I- W HIDIN mi "lt I4-, EIIHN~SFRERM
fI u~ s ~ ,. QS n-fla D.05 U.7d 0-? a'5 OA~I S 9-2 LIS Jad


JET LOCRTIONS


Figure 6-9 Section 2, 20'



























ISOJTHERM3, CRI733 SECTION, X/H= 6.9h21, H= [5.2 CM, 10i DEG, JETS 1-i9


~~ ii -' ~~IDTIH, Z/N, LOOKINTC DOWNSTFfERAHj*1






. .. . .
J A / A' V








MET LOCVRTION'i
A A A A A AA A A A A A A



Figure 6-10 Section 2, 100





















ISiOTH~ERMS, CROSS SECIONMJ X/H- [[.13, H= L'4.4[ CM. 35 DEG, JETS 1-19


j.A Q.05 L. t


RELATIVE WIDTII, Z,'4 it, 000STh HEAH
0.15 0-2 DAS Men DAS D A5 r~ j..55 [LOU


OAS D-70 ~ a D-7 0as 0.25 0-0 09 lAo


--'.5.


.........

0's 0 o
I Vs
t AO. I.





ifNr


JET LI]IRTIF1NS


. A A I- A A A A .A


Figure 6-11 Section 3, 350


























T SOTHERMS, I BOS 'ECTCIJN. :'H:t-- 14.116, H= '14.'4 1,M, 20 DEfG JET, 1-193


a-a D LG D-s ELATI VE W4IflH, Z/ H, L'fDhTNG HINSTFEAM
LI I I.L]72 5 .~IDI D.-30 0715 DAG LI LU a-So [LD [LI60


OAS 077a rj'5s D 73A2 DAJ ma D9 I-da


JET LIJCRTIOW3
A A A A A A A A A


SAA A A A A A A


Figure 6-12


Section 3, 200


'.q


0 as


0,5





























ISOTHERMS, CROSS 'ECT['Jfl X/H- [3.86, H= L4.8 -:M, 10 [EC, JETS. 1-19


FELHTIVE HIEJTH-, ZH, LOPKTING, TAmrflHI1
2 la a.0 ni.Ld D. Ls r0.2i U.25 0-30I 07AS nd.I 07U 5 D;5 ld


0:05 D,7 075 07aa U-25 D.30 YS I-ad


JET LU' RTIONS
A A A -t A


A A A A A A A A A


Figure 6-13 Section 3, 100


1,OS


. . . . . .. .. .. ... .. ... . .






.. .. .. .. .. 1 ; .. .... .. .. ..I .. ... .. .. .. ... ....... .. .. ... .. .... ... .. ... .. .. .. .. .. ..









turbulent flow field and thus mix it better. This is evidenced at z/W = 0.35

where the hot water is rising to the upper area. At this point, the 100

diffuser results in a more uniform temperature distribution.

Figures 6-14, 6-15, and 6-16 are those thermal contours at section

four (x = 4.0 m). The S = 0.5 isotherm has almost disappeared for 0o = 350

and 200. Again if these sections were not labeled, they would be hard to

tell apart. Columns of ascending residual heat are to be seen at z/W = 0.2

and 0.48 for e = 10 in Figure 6-16. Since the contours are in increments

of 0.5, this plot shows 0.5 < S < 1.5.

The final section (x 6.0 m) can be seen in Figures 6-17, 6-18, and

6-19. The mixing process is slow for e = 350 and 200. The 100 diffuser

produces an almost constant-temperatured cross section.


6.2.2 Plan Views

Plan isotherm plots are useful in determining jet interaction, as well

as, the dilution of the core region for individual jets. All the plans

described in this subsection are for U. = 48.0 cm/s, which corresponds to

the jet velocity for the full diffuser.

The first plan views (i.e. those closest to the bed) are contained in

Figures 6-20, 6-21, and 6-22 for e0 = 350, 200, 100, respectively. The

black areas are the extremely hot cores with steep gradients. The dimension-

less temperatures are as indicated. Figure 6-22 shows the shift of many

contours in the downstream direction. This effect is due solely to the small

discharge angle of 100 and not to increased dilution. Due to equipment

limitations, it was not always possible to line up the thermistors with the

jets. Also, any slight lateral fluctuation in the jet would register hot

spots on two probes as seen in Figure 6-20. Obvious in Figure 6-21 is the

missing hot spot for jet eleven on the right. Again this is due to thermistor

alignment errors for close-to-jet measurements




























I SOTHERMS, CROflY 'ECT[ON, ':/H= 28.012, H= L4.4J CM, 15 [DEG, JETS 1-19~


RELRUIVE HTEBfH, 7/W, Li~lDKINi, DOirThN ERH
LUJl ti7lS a, LU a LS U.55 0:25 0.50 U-35 aS aill 6-I 550 D.55 0.8a


sos 570 sits sas SIS 555 515 155


JET LOC RTI ON:
A A A A A A A IA L A


AI &A A A A A A A A


I I 4


Figure 6-14 Section 4, 35


.. . ..1.. .... .. ..0. . .






............. .. ......0.



























5iOdTHERMS, C~ROSS SEr:THIN, X/H= 28.5~4, H= L'4.1 >I 20 D'EG, JETS 1-19


FRELRTIYE I yil. Z/N LOOKING DONS6fEHdN
-j DOf a-.s D La 07L D3 2 n-2 fl.3f UA D Ud -s a-a 05l D. D l nas L7.13 D-79 U.30 rj.35 fL391 OAS I Ad

















JET LIJIRTII1N'
A A A+



Figure 6-15 Section 4. 200






























ISflTHEPR13, C.ROS `,ErT[lN, _'H- 2756 H= [L4.7 CM, 10 DEG, JETS 1-19


RELRTNE ITDTK. Z/ LM' ING DiNNSFflERM
022s U7.2 L G L 0720 0.00S 0220 0.30 (2.23 s 0 05 005 a.900


-Q
Fflc~ I


0:25 3 D..s 073d] U.35 U09 071S 1220


JET LOCATION!
1A 1 A A 'A 21 -


A A it -- 2


Figure 6-16 Section 4, 100

























ISOTHERMS, CROSS; SECTION, X/H= 39.9, H= L5. 1 1M, 35 DEG, JETS I-P)


I 4105K NIK401MAMR
P-0 a D.5 LU D. UAS fL20 S~ U-2 .2U 1,35DU US i U U-S U-90


0.85 Ma3 1,-7S U-l 0-3 090 ~ U 5 I1-00


JET LOlL -TIONS


A_ -4 It' A+


Figure 6-17


Section 5, 350




























ISOTHERMS, CIO3 tJ';EC THM4. X/H= 098 H= 14.7 -`M, 20l DIEC, JETS 1-19


RELATIVE HIBI, Z/1 L0M~,*INC DIN4NS ;FEHH
~-a a5 UL 1I SUSJ ('S SU


L-0 Ma Ms-1 S D-S31 n-s 0-9 33 7 S3 LU


JET LICRPTIONS
A A A A A A A A A A


A A A A A A A A A


Figure 6-18 Section 5, 200


























ISOTHERMS, SPY5 EC:TION, ./H= 3929 H= 15.4 UM, 10l DEG, JETS 1-19


L H I DJH, L/W LUl KI NU 7.


JET LOCATI ONS
A A A A A A A A A A A A A A A A A A A


Figure 6-19 Section 5, 10'


rl ff5 D-70 Ms 0-1530 D.35 mal 0.9 I-ad





79
BflVHE~RHS, PLPN, f/H= 0. 220, H= 1q.5 CH, 35 DlEG, IiJ VRAfCN/S. JETS i,~
RELPTIVE HILIPH. P*A LL4IOMN DONCIRTE4H iVIB 14


SI ...... -. ... ... .. .
... .. . .






.. . . .


. . . . .. .. . . . ... . .
i f -, ':


~Io
/

I

s/i--.


JET LCirI:Nfl l'
ArA A
--------------- Figure 6-20 Level 1, 35- 4-- ---------------- -
Figure 6-20 Level 1 350








80



ISOTHERMS, PLRNH, T/H= 0.222, H= 14.4 CN, 20 DEG, U1.1= UL.0CN/S, JETS 9,1, &11


RELR T VE H DTH, Z/N LOOKlIG DOHN#ST;TREM fI',-1 :'
J.. im 1, 'IV I' im M.7 19.30 I,m 9.m 9.10 9r, .40 0.1 0, 5,.7,1 E5.,












-A


















Ir F
-A



F.



















:., 0












JET h

---- .....- ----g------ -- -6----- -- -e 1----1

Figure 6-21 Level 1, 200







81

ISfTHERMS, PLRN, Y/H= 0.193, H= 15.0 CN, ID DEG, UJ.J= U13.]CNS, JETS 9,1D, 41

RELATIVE WIDTH. Z/H l.iL [MIG DIMSTHRERH (XLU-t
m.a us ,at .. .70 ,,, D i s.m s.i s-,a s.- s.5 t- M 5.m s T s.an



/7 1\1




fI5


























Figure 6-22 Level 1, 10
S","









Si0 .0


















.JET LOUCTIORNS




Figure 6-22 Level 1, 10'









The second level plots are shown in Figures 6-23, 6-24, and 6-25 for

the three angles. At this depth and jet velocity, eo = 350 produces a

pronounced horseshoe shape contour of the type described by Fan (1967).

This phenomenon occurs as the sides of each jet is sheared and carried down-

stream by the ambient flow. Note the hot trails delineating this action.

Some dilution of the core region is to be seen while jet interference is

minimal. For a diffuser angle of 200 (Figure 6-24), the ambient seems to be

shearing the jets in a preferred direction obviously due to a transverse

velocity component. There are no horseshoe shapes here due to the small

jet angle. Little core dilution has occurred with minor jet interference.

With the jet angle set at 100, the isotherm plot of this level is similar to

that produced by a larger angle at the third level. The small oe is the

reason the hot water has progressed farther downstream than it has done at

the other settings.

Figure 6-26, 6-27, and 6-28 are the third level plan views. With

00 = 350 the core region becomes more dilute, but still exists. Jet inter-

ference has not occurred, while the horseshoe shape has nearly disappeared.

The jet centerline for 90 = 350 has reached a value of x/H = 1.75 while for

00 = 20 the core is at x/H = 2.5. Much lower centerline temperatures are

to be seen with 0o = 20! at this depth than at level two due to increased

length of travel. With 9o = 100 Figure 6-28 shows a slice of the top of the

jet.

Lastly, level four temperature patterns are contained in Figures 6-29,

6-30, and 6-31. No core region is visible at this depth for all jet angles.

Only a slight merging of jets is seen for o0 = 350in Figures 6-29. Almost

no sign of the jet is to be found with 00 = 100 and y/H = .832. Initially

for this angle, the jet passes under the majority of the ambient flow.













ISOFHERMS, PLRiN, T"/H= 0.1it1, Hl 114.5 CN, 35 DEC, UJ= V,.0CH/S. JEIS 9, 1D,411



RELH IE I RDTH, ?/H L0[( G DO1NSIFBElH (X[LI )
'-I- ^ t^ J ?_. _lL ^ '_ .i. y' ^3 i^ _" __ ja s^ .8 y


JET L6CfliONS
+- F - -- + A A


I 1- ------4 4 ----1 -1


1.0... .....


J'i[ T


1.0 (.-s


1J.
rn~
3)



~~.~1
3.)

3~),

I.
(.3
I.''
'-'.3
t-3


Figure 6-23 Level 2, 350












BOfTHERHS, PUPN, *f/'H= Ii. 44L, H 1U. 4 CH ,f [m'D DEG U J U. flCH/S' JET 9, 10B, ~.'It


PF;LR]V ]fT K L'h N 910TH Zl M G DflNM- I hEk~ !I:,IOL I


- AA
I- --- A -1-- 4


Figure 6-24 Level 2. 200







85


I' niHFlHF PFLRN, Y/H= A. 414l, H= 15.0 ID D IJ.J= L S.] CN/S, JETS 9,1D,. l1

RELTIVE M10TH, Z/" LiOlGt;[ DOKSTFEIH (X:l-L ]
-Y!a q.o 'iV a 90 40a to sn 4101 y 0m 1.;0 EB E, 5.70 o lB

1,15
"5 _5 1.5 5_____ _______ _____s








". \ 5
2.0 2 O:J.0













































JET LURTIOi,
aa


-.. r 6. 2 Iv I -




Figure 6-25 Level 2, 10'






o'6


ISOTHERMS, PLRN, G/H= l.G62, H= 11.5 CN, :, DEG, UJ= 4,8.r0CM/S, JETS 9,1 D,111

RELIJIVE NiDTH, Z, J LOI:,[G DONMSTFIRE (I:':[[)
. ... .. ... i~ n ..i i7 ~ D I E 'ii S.I -- ---a -- -- -- -a- F ...I E. I E----- ".;i '


. . .. . . . .
J N


JET L ih i HIiri;
.1 --- ---------l----+-- ---- ... --I--


Figure 6-26 Level 3, 350






87

BOfTHERMf3, PLAN, P/H= 6.CGG H= 1q.4 4T, 2D DEIG, UII- 4 I Er' 9,10,M

FELUiIVE WIDTH, -Z/ LOOK [NG DOfWCIRfERH :XIILD '








1







aA Iw












=V/1





JET bli'YIM6:


Figure 6-27 Level 3, 20'




Full Text

PAGE 1

WATER IiRESOURCES researc center Publication No. 49 CHARACTERISTICS OF FULL AND PARTIAL MULTIPORT DIFFUSERS DISCHARGING THERMAL WASTES IN OPEN CHANNEL FLOW By B. A. Christensen J. G. Melville A. D. Parr Civil Engineering Department University of Florida Gainesville UNIVERSITY OF FLORIDA

PAGE 2

Characteristics of Full and Partial Multiport Diffusers Discharging Thermal Wastes in Open Channel Flow By B. A. Christensen J. G. Mel vi 11 e A. D. Parr PUBLICATlON NO. 49 FLORIDA WATER RESOURCES RESEARCH CENTER RESEARCH PROJECT TECHNICAL COMPLETION REPORT OWRT Project Number Annual Allotment Agreement Numbers 14-34-0001-7019 14-34-0001-7020 14-34-0001-8010 14-34-0001-9010 Reported Submitted December, 1980 The work upon which this report is based was supported in part by funds provided by the United States Department of the Interior, Office of Water Research and Technology as Authorized under the Water Resources Research Act of 1964 as amended.

PAGE 4

ACKNOWLEDGEMENTS Appreciation is extended to the Office of Water Resources Research and Technology, United States Department of the Interior, for financial support on this project, and to Drs. W.H. Morgan and J.P. Heaney for their administrative assistance and Robinson for accounting assistance. The participation of R.J. Chernick and B.J. Swenty in most aspects of the project was especially valuable. The efforts of Mr. C.L. White and the staff of the Engineering Machine Shop are gratefully acknowledged. The assistance of Ms. Alice Moreau in typing the report deserve special thanks. i i

PAGE 6

TABLE OF CONTENTS AC KNOWLEDGEMENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS Page i i v vi ix CHAPTER I II III IV INTRODUCTION . REVIEW OF LITERATURE 1 4 2.1 Single Jets . . 4 2.1.1 The Simple or Momentum Jet 4 2.1.2 The Simple Plume . 7 2.1.3 The Buoyant Jet or Forced Plume. 8 2.1.4 The Effect of Crossf1ow . 9 2.1.5 The Effect of Boundaries 11 2.2 Mu1tiport Diffusers ... . 13 2.2.1 Lateral Interference of Round Buoyant Jets 13 2.2.2 The Equivalent Slot Diffuser . 15 2.2.3 Solutions for the Mu1tiport and Slot Diffusers 16 ANALYSIS 3.1 Statement of the Problem. 3.2 Dimensional Inquiry .. 3.3 Experimental Objectives 3.3.1 The CVx Parameter. 3.3.2 Isotherm Plots 3.3.3 Velocity Distribution DESCRIPTION OF EQUIPMENT AND PROCEDURE 4.1 Introduction .......... 4.2 The Hydraulic Apparatus .... 4.2.1 The Recirculating Flume .. 4.2.2 The Effluent Supply System 4.2.3 The Manifold and Manometers 4.2.4 The Diffuser Jets and Rack iii 18 18 20 24 24 26 26 27 27 27 27 31 32 36

PAGE 7

CHAPTER V VI VII APPENDIX A B C 4.3 The Sampling Equipment ..... 4.3.1 The Thermistors ..... 4.3.2 The Velocity ... 4.3.3 The Data Acquisition System 4.4 The Process of Physical Modeling. 4.4.1 Prototype Measurements 4.4.2 Planning of Experiments .. 4.4.3 The Experimental Procedure REDUCTION OF DATA 5.1 Temperatures. 5.2 Velocities PRESENTATION AND DISCUSSION OF EXPERIMENTAL RESULTS 6.1 The CVx Parameter 6.2 Isotherm Plots ..... 6.2.1 Cross Sections 6.2.2 Plan Views 6.2.3 Jet Trajectories 6.3 Velocities CONCLUSIONS 7.1 Jet Angle 7.2 Port Spaci ng 7.3 Partial Diffuser REGULATIONS DATA BIBLIOGRAPHY iv Page 38 38 39 44 46 46 47 49 54 54 54 56 56 60 62 72 92 92 99 99 99 100 102 107 147 154

PAGE 8

LIST OF TABLES Table Page C-l Flow Data . . . . 147 C-2 Temperature Drop from Manifold to Jets (OC) 148 C-3 Thermistor Correction Factors . 151 v

PAGE 9

Figure 2-1 2-2 2-3 2-4 3-1 3-2 4-1 4-2 4-3 4-4 4-5 4-6a 4-6b 4-7 4-8 4-9 6-1 6-2 6-3 6-4 LIST OF FIGURES Jet Diffusion. .. .... A Round Jet in a Uniform Cross Stream Jet Interference for a Submerged Multiport Diffuser Nozzle Orientation, 8(z), Along the Diffuser Line Parameter Description Diffuser Configurations System Layout . The Experimental Arrangement The Manifold ....... Wall-mounted Manometers with Overflow Pipe and Compressed Air Hose .... The Diffuser Rack and Cover Thermistor Dimensions .... Thermistor Array in Plexiglas Support Novonic-Nixon Velocity Probe in a Flow Field Point Gauge Carriage Mounting for the Novonic-Nixon Velocity Probes . .. .. .... The Data Acquisition System: the Pink Input Box and the HP 9825A Programmable Calculator CVx(L/(H-h)) vs CVx(L/(H-h)) vs (x/L), 6 = 35 o (x/L), 6 = 20 o CVx(L/(H-h)) vs (x/L), 60 = 10 CVx(L/(H-h)) vs (x/L), Jets 1-19, 6 0 = 35, 20, 10 vi Page 5 10 14 17 19 25 28 29 33 35 37 40 40 42 43 45 57 58. 59 61

PAGE 10

Figure Page 6-5 Section 1 35 63 6-6 Section 1 20 64 6-7 Section 1 10 65 6-8 Section 2, 35 66 6-9 Section 2, 20 67 6-10 Section 2, 10 . 68 6-11 Section 3, 35 69 6-12 Section 3, 20 . 70 6-13 Section 3, 10 71 6-14 Section 4, 35 73 6-15 Section 4, 20 . 74 6-16 Section 4, 10 . 75 6-17 Section 5, 35 76 6-18 Section 5, 20 77 6-19 Section 5, 10 78 6-20 Level 1 35 79 6-21 Level 1 20 80 6-22 Level 1 10 . 81 6-23 Level 2, 35 83 6-24 Level 2, 20 84 6-25 Level 2, 10 85 6-26 Level 3, 35 86 6-27 Level 3, 20 87 6-28 Level 3, 10 88 6-29 Level 4, 35 89 6-30 Level 4, 20 90 vii

PAGE 11

Figure Page 6-31 Level 4, 100 91 6-32 Profile, 350 93 6-33 Profi 1 e, 200 94 6-34 Profile, 100 95 6-35 Transverse Discharge Distribution . 97 6-36 Average Velocity Profiles . 98 viii

PAGE 12

SYMBOL B LIST OF SYMBOLS DEFINITION Jet area at the outl et Prototype cross-sectional area Nominal half-width of the jet or the distance from the centerline to the point where the mean velocity is lie of that at the centerline Equivalent slot width CD Drag coefficient CVx Coefficient of temperature variation at a section D Jet diameter Model jet diameter Energy flux at a section Energy flux at the jet outlet Pressure drag force Force due to the entrainment of ambient fluid Fa Ambient Froude number F. Jet densimetric Froude number J F. Ambient/jet Froude number a J g h H Acceleration due to gravity Height of port centerline above the bed Depth of flow Model average depth ix DIMENSION L2 L2 L L L L ML2/T3 ML2/T3 ML2/T ML2/T

PAGE 13

DEFINITION Prototype average depth k Jet to ambient velocity ratio kp Prototype jet to ambient velocity ratio k m Model jet to ambient velocity ratio Port spacing Diffuser length, or the distance between the first and the last jet plus one port spacing Lr Length ratio of prototype to model M Number of nondimensional temperature readings at a section M General mixing at some section x N Number of in-use jets R s Ambient discharge per unit width at each jet Effluent discharge per unit length of diffuser Volume flux at a section Ambient discharge Total effluent discharge of diffuser Discharge of individual jet Prototype discharge measurement Ratio of the prototype discharge to that of the model Ratio of the dilution of a multipbrt diffuser to that of an equivalent slot jet Reynolds' number of the ambient flow Jet Reynolds' number Distance along the jet centerline Arithmeti c mean of a 11 nondimensi ona 1 temperatures at a section x DIMENSION L L L L2/T L2/T L 3 /T L 3 /T L 3 /T L 3 /T L 3 /T L

PAGE 14

SYMBOL T DEFINITION Temperature reading at a point Temperature of ambient flow Efflux jet temperature Mean velocity at a point ambi ent velocity Model ambient mean velocity Prototype ambient mean velocity Characteristic jet velocity Jet centerline velocity Velocity at the jet efflux section U r Velocity ratio of prototype to model Greek Letters B L'lh Mean velocity at a point in the s-direction Mean velocity downstream of diffuser Depth averaged ambient velocity at each jet Transverse entrainment velocity Flume width Prototype width Longitudi na 1 di stance downstream from diffuser Entrainment coefficient Inclination angle with respect to z-axis Head drop across the orifice plate Mixed temperature rise Ambient flow density -jet flow density 8 0 Vertical angle of discharge xi DIMENSION o C LIT LIT LIT LIT LIT LIT LIT LIT LIT LIT LIT LIT L LIT L L

PAGE 15

SYMBOL DEFINITION DIMENSION P Dens; ty of fl u; d M/L3 Pa Ambient fluid density M/L3 p. J Jet fluid density M/L3 v Kinematic viscosity of ambient L2/T a v. Kinematic viscosity of effluent L2/T J xii

PAGE 16

CHAPTER I INTRODUCTION Waste heat is beyond a doubt the largest pollution form associated with electric power generation. Conventional fossil fuel plants have an efficiency of about 40%, while modern nuclear power stations have efficiencies of only 32%. For nuclear reactors, this means that for each kW of electrical power produced, 2kW of waste power (as heat) must be rejected. In 1970, the use of fuel for generating electric power in the United States amounted to 25% of the total fuel consumed. Studies by Hubbert (1971), Swiss (1970), and Morrison and Readling (1968) indicate that just after 2000 A.D., the amount of fuel used for electrical generation in the U.S. may be one half of the total fuel consumed. In addition, the growing scarcity of plant sites as well as the economics of large units dictate even greater waste heat discharge at individual locations. Obviously, there is increasing concern over the impact of this waste heat on the environment. There are two systems which transfer the condenser waste heat to the atmosphere: once-through cooling and closed-cycle cooling. The former involves taking water from a source, passing it over the condensers once, and returning it to the receiving water. Disposal methods include surface canals, single-port submerged pipes, and multiport diffuser-pipes. The diffuser-pipe provides the most efficient mixing of the three by discharging the heat effluent through high velocity jets near the bed of the receiving body of water. 1

PAGE 17

2 Closed-cycle cooling recirculates the cooling water and transfers heat to the atmosphere through radiation, convection, conduction and evaporation. The additional costs of closed-cycle cooling are significant enough to warrant the use of the once-through system. Regulations for the disposal of heated effluents in the state of Florida are found in the Florida Administrative Code (Appendix A). Here it is stated that on an individual basis the Department of Environmental Regulation may establish a zone of mixing downstream of the diffuser for the dilution of heated discharges. Beyond this mixing zone, no temperatures above 2.8C (5F) shall be allowed. Also for all streamflow conditions no more than one-third (1/3) of the width of the stream's surface and no greater than one-forth (1/4) of the cross-sectional area shall be raised above ambient temperature. In addition no heated water outside the mixing zone shall have a temperature above 32.2C (90F) in Northern Florida, and 33.3C (92F) in Peninsular Florida. (Northern and Peninsular Florida are defined in the Florida Administrative Code). With such stringent regulations it behooves the engineer to have some predictive methods to use in presenting his case. This work concerns itself with an undistorted physical model of a multiport diffuser-pipe discharging heated water into a coflowing ambient. Vertical jet angle and transverse discharge distributions are varied and the resulting mixing characteristics are noted. Chapter II presents an overview of the studies in this area. Investigations of the simple jet and plume through those of the multiport diffuser are described. Chapter III contains an analysis of the problem and the experimental objectives. Dimensional reasoning is used to identify the governing parameters. The equipment and procedure are described in Chapter IV. The hydraulic apparatus as well as the sampling instruments and the data acquisition system

PAGE 18

3 are all detailed. The physical modeling process including prototype measurements and calculations of model parameters are delineated, along with the steps involved in a typical run. Methods used for the reduction of data are explained in Chapter V, whil.e Chapter VI contains the experimental results and their discussion. The parameters derived in Chapter III are analysed and compared. Temperature and velocity plots aid in this process. Finally, the results presented in Chapter VI are used to substantiate the conclusions advanced in Chapter VII.

PAGE 20

2.1 Single Jets CHAPTER II REVIEW OF LITERATURE 2.1.1 The Simple or Momentum Jet The simple momentum jet is the basic component of the mu1tiport diffuser. It is formed when fluid of the same density as the surrounding is discharged at a high velocity through a submerged outlet. Just out of the efflux section the velocity distribution is uniform or "top hat". The very steep velocity gradients generate high shear forces at the jet boundary. This shearing accelerates and entrains the ambient fluid while decelerating the periphery of the jet, leading to lateral jet mixing. Fully established flow develops when the mixing eddies have penetrated to the centerline of the jet. The zone of flow establishment is the longitudinal distance from the port to the point of fully established flow (Figure 2-1). Albertson, Dai, Jensen, and Rouse (1950) conducted the first comprehensive study on simple jets, both slot and round, in a still receiving environment. The analytical derivation was based on the assumptions that: 1) the pressure is hydrostatic throughout the flow; 2) the diffusion process is dynamically similar in all cases; 3) the mean velocity distribution varies according to the normal probability function at each cross-section. Experiments were conducted to verify the results and to provide the necessary coefficients. It was found that the nominal jet width is proportional to the distance from the efflux section. This study also confirmed the assumption that the velocity profiles in the zone of established flow are similar and Gaussian. The 4

PAGE 21

Zone of flow establishment Zone of established flow II II /' top hat ,/""'" 7 --.".,.. /' ----------0 ----. --=:::.. __ L.__ Uo _------(-IU =u -'0-u
PAGE 22

6 centerline velocity was found to be inversely proportional to distance. Albertson, et al. established the fact that the flux of momentum is constant. Empirical evidence indicates that the pressure distribution is hydrostatic in a jet issuing into an unconfined region. It follows, therefore, that since the acceleration/deceleration are due to an internal tangential shear; the momentum must be constant. The experimental results of this endeavor produced the following relationships for a round jet in the zone of flow establishment: where: Q/Qo = + 0.083 siD + 0.0128 s2/D2 (2.1) E/Eo = 1 0.090 siD + 0.0058 s2/D2 (2.2) U/U o = (2.3) s = distance along jet centerline D = diameter of jet at efflux section Q = rate of flow or volume flux at a section = ["UsdA (2.4) Qo = efflux rate of flow = UoAofoo 2 E = energy flux at a section = pU U s/2dA 3 Eo = energy flux at the outlet = pUo Ao/2 Us = mean velocity at a pOint in the s-direction U = mean velocity at a point U. = jet centerline velocity J U o = velocity at the efflux section Ao = jet area at the efflux section p = density of fluid (2.5) (2.6)

PAGE 23

The length of the zone of flow establishment was determined as 6.2 jet diameters. For the zone of established flow for a round 'jet the formulae follow: U/U J 0 = 6.2 DIs Q/Qo = 0.32 sID E/Eo = 4.1 DIs bID = 0.2 sID 7 (2.7) (2.8) (2.9) (2.10) where b = nominal half-width of the jet, or the distance from the centerline where the mean velocity is of that at the centerline. 2.1.2 The Simple Plume A simple plume is defined as a source of density deficiency only. Morton, Taylor, and Turner (1956) analyzed the simple plume in a linearly density-stratified environment. This study introduced the integral method of analysis which consists of integrating the equations for conservation of volume flux, momentum, and density deficiency in the transverse direction. The resulting expressions are dependent on the axial direction only. Morton (1959) used this method to analyze the vertical forced plume. Full solutions require an experimentally determined coefficient. Morton, et ale assumed the followi ng: 1) the rate of entrainment is proportional to some velocity at that plume section, or where a = entrainment coefficient, a function of local buoyancy conditions. U = characteristic velocity c (2.11)

PAGE 24

2) the profiles of mean velocity and density deficit are similar at all sections, 3) local density variations are small when compared to some reference density. Data by Albertson, et al. (1950) for a simple jet yields a = 0.057 Data for a plume by Rouse, Yih, and Hemphreys (1952) gives a = 0.082 8 Far away from the efflux section, the buoyant jet behaves like a plume with a approaching 0.082. 2.1.3 The Buoyant Jet or Forced Plume The buoyant jet is a combined simple jet and plume. The mass transport associated with forced plumes are 1) convection by mean velocities; 2) acceleration in the buoyant direction; and 3) turbulent diffusion due to shear-generated eddies. In the zone of flow establishment the jet momentum dominates over buoyancy. Density deficiency becomes increasingly important as the jet velocities (momentum) become reduced. Abraham (1963) conducted experiments on slot and round buoyant jets, varying the vertical angle of discharge, 80 He too used the integral technique; however, his coefficient is that of the jet spreading rate. This coefficient is similar to the entrainment coefficient used by Morton, et al. and goes to an asymptotic value for the simple jet and plume. Fan (1967) extended the type of analysis to cover the effect of initial angle of discharge in stagnant linear density-stratified environ ments. Numerical solutions for different discharge angles and jet densimetric

PAGE 25

9 Froude numbers were compared with laboratory experiments. The jet densimetric Froude number, Fj' is defined as where P -p. F. = U / (a J gO) 1 /2 J 0 Pa P a = ambient density Pj = effluent density g = acceleration due to gravity 2.1.4 The Effect of Crossflow The most obvious effect of a flowing receiving body on a buoyant jet (2.12) is to deflect the trajector in the direction of flow. The two forces which act on a jet are the drag and the loss of momentum. Vortices develop downstream of the jet due to the shearing along the jet sides and the low pressure wake region. These vortices, in turn, act on the jet itself. Consequently, the jet secti on becomes horseshoe shaped with a wake regi on simi 1 ar to that of a solid body as seen in Figure 2-2 (Fan, 1967). The pressure drag force, F O is of the form: FO = Co(p U 2/2) 2b (2.13) a a where Co = drag coefficient Ua = ambient velocity Chan and Kennedy (1972) used the integral technique with a special entrainment coefficient in their study on a jet in a crossflow. The experimental fluid was air. Variation of the drag coefficient with the velocity ratio, k, was determined. The velocity ratio is defined as: (2.14)

PAGE 26

y ____ s -Ua fa, va t 9 Wake region ...,. / """'" 7 :>ox --Zone of flow establishment I I I I I I I I 7 7 7 I 7 7 7 7 7 7 7 Figure 2-2 A Round Jet in a Uniform Cross Stream (From Fan, 1967) --' a

PAGE 27

11 Fan (1967) has found variations in the Co from 0.1 to 1.7 through different values of k and Fj values. The force due to the entrainment of the ambient fluid, Fe' is expressed as: F = p U (2TIbV) e a a e (2.15) The entrainment concept was modified by Fan (1967) to yield for the transverse entrainment velocity, Ve: v = alIT U.! e a J (2.16) where !Ua Uj is the magnitude of the vector difference between the ambient and jet centerline velocities. When still assuming a Gaussian profile, values of a are considerably higher (0.4 to 0.5) than in the case of stagnant ambient. This indicates an increased dilution efficiency in the presence of a crossflow. Wright (1977) conducted analytic and experimental studies on round buoyant jets in a stratified and unstratified crossflow. This work differs from those mentioned previously in that approximate solutions of jet behavior was obtained through dimensional analysis and considering asymptotic relations. The relations considered were those where the jet behavior is dominated either by its initial momentum or density deficiency, and where the ambient velocity is either relatively strong or approaches zero. Combinations of these four asymptotic solutions can be used to describe the buoyant jet. 2.1.5 The Effect of Boundaries The air-water interface has nearly the same effect on the buoyant jet as a solid boundary. A slight rise in the water surface will occur depending on the initial kinetic energy and discharge angle of the jet. Once surface impingement occurs, the heated effluent will spread laterally in a layer of

PAGE 28

12 certain thickness. Abraham (1963) reports experimental values of the surface layer for a slot jet (or after lateral interaction for a multiport diffuser) to be about 1/4 of the length of the trajectory. Entrainment of the ambient flow decreases after the jet experiences surface effects. Jirka and Harleman (1973) estimated the entrainment of the surface layer for a two dimensional buoyant slot jet in a quiescent ambient while Lee, Jirka, and Harleman (1974) did the same for an axisymmetric buoyant jet. The interaction of the buoyant jet with the bottom should reduce the entrainment of the ambient fluid into the jet. Sharp and Wang (1975) found experimentally, however, that for a horizontal buoyant jet experiencing bottom effects, surface dilutions were 200 to 500% higher than for horizontal jets not finding the bottom. The reasoning behind this phenomena is that the jet attaches itself to the lower boundary, developing greater turbulence and momentum exchange, while thus increasing its trajectory length and total entrainment. The analyses discussed previous to this section apply only to cases with no boundary interference. The effect of the boundaries is to restrict the flow field, producing a nonhydrostatic pressure distribution. The entrained ambient fluid in constricted regions accelerates, resulting in a local pressure drop. These low pressure areas cause the jet to attach itself to boundaries as in the Sharp and Wang (1975) study. The hydrodynamic conditions are thus very complex since the assumptions of similarity of velocity profiles as well as that of a hydrostatic pressure distribution are no longer valid. Consequently, the models of Albertson, et al., Morton, et al., Abraham, Fan, Chan and Kennedy, and Wright are not readily applied to buoyant jets in confined flows.

PAGE 29

13 Paily and Sayre (1978) have developed a predictive method, based on diffusion concepts, for determining the transverse temperature distribution of shore-attached thermal plumes in rivers. Their model is two-dimensional, assuming complete vertical mixing. Application is best suited to the far field where mixing mechanisms characteristic of the ambient flow dominate. Comparison of model results with field data shows good agreement. 2.2 Multiport Diffusers The multiport diffuser is an efficient method for the injection of thermal and chemical wastes into the hydrologic and coastal environments. A high degree of dilution can be obtained in a relatively limited area, thus minimizing the adverse effects of high pollution concentrations. 2.2.1 Lateral Interference of Round Buoyant Jets Each jet issuing from the submerged multiport diffuser keeps it identity until it begins to interact with adjacent jets. Figure 2-3 indicates the process. Jet interference starts in the transition zone and continues until complete interaction yields a two-dimensional jet profile. From this point on, the diffuser behaves like a slot buoyant jet. Since the selfsimilarity assumption is no longer valid in the transition zone, single jet analysis cannot be extended into this region. Transition is assumed to occur when b = L/2 (2.17) where L is the port spacing, or when the velocity profiles overlap to the point where lateral entrainment is significantly reduced. Koh and Fan (1970) compared this definition of transition with that of the point where the entrainment of a round jet is the same as that for the equivalent slot jet.

PAGE 30

PLAN Round jets PROFI LE y o Transition zone 14 Fully developed two -dimensional jet x Figure 2-3 Jet Interference for a Submerged Multipart Diffuser (From Jirka and Harleman, 1973)

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15 Their investigation, confirmed by Jirka and Harleman (1973), showed that either definition yields the same location of initial jet interaction. 2.2.2 The Equivalent Slot Diffuser After lateral jet interference the multiport diffuser can be analyzed as an equivalent slot diffuser. This concept is useful when applying mathe matical models to the field beyond the transition zone. The equivalent slot diffuser is required to have the same volume and momentum flux per unit length as its multiport counterpart. The equivalent slot, B, is defined as: Cederwall (1971) compared the dilutions of the multiport diffuser and the slot jet at the distance of lateral jet interference. Using the experi mentally determined relationships of Albertson, et al. for a simple jet he found: R = dilution of the multiport diffuser dilution of the equivalent slot jet 0.95 Following the same routine for a simple plume and employing results from Morton, et al. and Rouse, et al., Cederwell determined: R = 0.78 These values of R indicate approximately equal dilutions for the multiport and equivalent slot diffusers. 2.2.3 Solutions for the Multiport and Slot Diffusers Solution graphs for slot and round buoyant jets have been presented by Abraham (1963), Fan and Brooks (1969), Brooks (1972), Jirka and Harleman (1973), and others. These plots are for various vertical discharge angles. All solutions must be adjusted for the initial zone of flow establishment. The choice of model depends on the ambient conditions: stagnant or flowing, stratified, shallow, etc.

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16 Jirka and Harleman have also included angle of diffuser to crossflow, as well as, two horizontal angle distributions normal, with jets perpendicular to diffuser axis; and log, in which the jet angles vary logarithmically from 90 to 0 (Figure 2-4), or: s(z) = cot log + Z/D) z/D (2.19) where s(z) = inclination angle with respect to the z-axis The log distribution seems to be especially effective in partially confined flows. A partially confined flow is one in which the diffuser only partially experiences boundary effects -e.g. a diffuser extending across half of the river width. No analytical models exist which take into account the effects of a flowing, totally confined receiving body. The deflection mechanism is highly complex with vortices and re-entrainment occurring. Also, jet attachment to boundaries is a difficult phenomena to model.

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normal f3 (z) r log ________ L-________ ________ -L ________ -L ________ o .2 .4 .6 .8 1.0 Example: log, 10 unidirectional nozzles End Figure 2-4 Nozzle Orientation, 8(z), Along the Diffuser Line (From Jirka and Harleman, 1973) 17

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CHAPTER III ANALYSIS The breakdown of normal buoyant jet assumptions precludes the development of an analytical model for coflowing, totally confined receiving environment. Instead, dimensional reasoning is used to isolate the governing parameters. The investigation is similar to that advanced by Argue and Sayre (1973). 3.1 Statement of the Problem Consider the multiport diffuser in Figure 3-1 discharging hot water into a coflowing, shallow, laterally confined receiving body. The parameters that describe the ambient flow are: The H = free surface elevation U a = mean velocity = wi dth Pa = density va = kinematic viscosity diffuser is characterized by: 0 = jet diameter h = height of port centerline above the bed L = port spacing Ld = diffuser length, or the distance between and the last jet plus one port spacing U o = efflux jet velocity 8 0 = vertical angle of discharge 18 the first

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19 ( n T C 0 L L C Ld W c c PLAN H H BED PROFILE Figure 3-1 Parameter Description

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= ambient flow density -jet flow density, or P a -Pj v = kinematic viscosity of effluent J 20 The coordi nate axes are ori ented such that xis in the downstream di recti on; y is directed upward from the bed, and z locates the transverse positions. A general measure of mixing at some section is defined as M x while the acceleration due to gravity is g. 3.2 Dimensional Inquiry Some function of the preceeding variables should describe the mixing at a section. The y and z dependence is eliminated by considering only a bulk mixing criterion at the longitudinal distance, x. The functional steady-state relationships starts as: (3.1) Since there are sixteen variables in three dimensions, the Buckingham IT theorem states that thirteen dimensionless expressions exist which describe the problem. Choosing H, U o and as the repeating variables, the following parameters are deduced: where = depth averaged ambient velocity at each jet qa = ambient discharge per unit width at each jet = iJYH a q. = effluent discharge per unit length of diffuser J (3.2) (3.3)

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21 (3.4) N = number of in-use jets The term is transformed into Cedarwall's (1971) kinematic momentum flux ratio by squaring and multiplying by H/B. The average of the V/k values at each discharging jet is used in defining the parameter. (3.5) may be neglected since the width to depth ratio 3 is kept approxi mate ly constant u:Y a ). = QE.. g q. Pa J n=. a J (3.6) The ambient/jet Froude number, an=j is obtained by multiplying by the ambient Froude number squared, the inverse velocity ratio, l/k, and H/B. is determined from the mean of the first sand last ambient and effluent temperatures. Again an=j is taken as the average of the values at each discharging jet. (3.7) The Reynolds number of the ambient flow, ffia found by dividing by k; may be neglected if the flow is fully turbulent, or (3.8) (3.9) The jet diameter to ambient depth ratio changed only slightly in this study and is therefore omitted. (3.10)

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22 Due to diffuser rack limitations, h/H varied somewhat and is therefore included. 'IT] = L/H + x/L (3.11) A measure of the distance downstream in terms of the port spacing. (3.12) is the ratio of the diffuser length to the total width. (3.13) (3.14) The jet Reynolds number, lRj' is a combination of 'IT5 and 'IT10. dependence may be deleted provided: Jet Reynolds lR. > 2500 J where CVx follows from Argue and Sayre (1973) and is the coefficient of (temperature) variation at a section, x: where M = number of nondimensional temperature readings, S., at some x 1 S = arithmetic mean of all Si's at some x T -T a S. = flT 1 m (3.15) (3.16) (3.17) (3.18)

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",T = m = T = T = a To = Qe = Qa = Q (T -T ) e 0 a Qe + Qa mixed temperature rise temperature readi ng at a point temperature of ambient flow efflux jet temperature total effluent discharge ambient discharge U 2 0 U a Tf12 = --+ gH (gH)1/2 = IF a 23 (3.19) (3.20) Taking the product of Tf and the square root of Tf12 yields the ambient Froude number, Fa. This parameter may be eliminated since it varied only slightly over the experimental range. (3.21 ) A measure of the distance downstream in terms of the height of water above the ports is converted to a relative port spacing parameter through equation (3.9). This factor follows from Argue and Sayre (1973) and is used subsequently in the creation of the plane: log [CVx (H:h)] vs. log L (3.22) If we let CV become the x dependent variable the preceding analysis leads to the fo 11 owi ng equation: CVx = l)J(t, lj' x Ld L (3.23) [' W' 80 H-h)

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24 3.3 Experimental Objectives The main objective of this experiment is to describe thermal mixing through the CVx parameter, isotherm, and velocity distributions. 3.3.1 The CVx Parameter The dimensional inquiry of the previous section has isolated seven para meters which govern the mixing at a section in this physical model. One objective is to determine the variation of CVx with each of the terms sighted. More specifically, with the total effluent discharge fixed (see subsection 3.4.2), seven diffuser configurations are chosen as Figure 3-2 depicts. Three values of Ld/W are immediately recognized: Ld/W = 0.5, 0.75, 0.95 (3.24) corresponding to ten, fifteen, nineteen discharging jets, respectively. Each of these arrangements, in turn is divided into unique combinations of five port sections. Values of V/k and aFj are also determined for the port groupings. CVx is computed at x '" 0.5, 1.0, 2.0, 4.0, 6.0 m (3.25) with the initial discharge angles set at (3.26) Nozzles directed upstream are not considered in this study at this leads to decreased dilution due to stagnation and unsteady recirculation, Harleman, et al. (1971). For e = 35 and 10 o h H 0.0877 (3.27)

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jet no. x Discharging Jets t Flow I 2 :3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 1-19 1-10,15-19 5 -19 10-19 (" 1-5, 15 19 5-14 15, 10 14 Ld/W 0.95 0.75 0.75 0.5 0.5 0.5 0.5 Figure 3-2 Diffuser Configurations U ( cm/ s) J 48.0 60.8 60.8 9l.2 9l.2 91.2 91 .2 V/kt 11 .03 5.62 7.88 3.43 2.43 3.99 2.54 t average values IF. t a J 125.8 76.6 109.0 67.7 46.2 79.0 48.7 i":: (J1

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26 on the average while for Go = 20 h H 0.744 (3.28) 3.3.2 Isotherm Plots Another objective of this study is to plot dimensionless cross sectional, plan, and profile isotherms to graphically illustrate temperature distrubutions. Cross sectional patterns are used to compare mixing and extent of stratification at each section. Sectional surveys are conducted at the same x locations at which CVx is determined. Plan isotherms are used to determine jet interference, while profiles delineate jet trajectories. 3.3.3 Velocity Distribution Vertical velocity profiles and the transverse discharge distribution are compil ed from secti on 2 m downstream of the diffuser. In thi s way areas of excessive longitudinal momentum flux can be noted for possible scouring problems in prototype installations. Also temperature and velocity distributions are compared.

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CHAPTER IV DESCRIPTION OF EQUIPMENT AND PROCEDURE 4.1. Introduction The authors consider it important for the scientist not only to report the methodology and results of his experimentation but also to describe and evaluate his equipment. In this way it is hoped that future users will refine and also report on such devices. Accordingly, a departure from the norm is made in that comments on the performance of each piece accompanies its description. 4.2 The Hydraulic Apparatus The basic components of the experimental hydraulic apparatus include the recirculating flume, the effluent supply system, the manifold, the manometers, and the diffuser. A system layout is contained in Figure 4-1, while Figure 4-2 is a photo of the experimental arrangement. 4.2.1 The Recirculating Flume All runs were conducted in the recirculating flume. This structure was fabricated of concrete block, was concrete finished, and was sealed with epoxy paint. The main channel is horizontal, 36.6 m (120 ft) long, 2.47 m (8 ft) wide, and 61 cm (2.0 ft) deep. At midlength of the main flume is a false-bottom section 6.10 m (20 ft) long and 34 m (13.5 ft) deep. Centered in the false-bottom area is a sectioned glass wall 3.66 m (12.0 ft) long for visual inspection and photography. The 52 kW (70 HP) flume pump has a maximum discharge of 1.13 m 3/s (40 cfs). Just downstream of this pump is 27

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hot water heaters flow turners sluice gate --------diffuser ----man i fold -----________ manometer rack hot water line Thomson weir cold water linegate valve main return flume sump effluent pump constant head tank "111, I.,., flow Figure 4-1 System Layout flow J} 28 main flume return flume flow straighteners effluent intake effluent return hose

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.r-s QJ 0.. X LLJ QJ I-.r-LL. 29

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30 the main delivery pipe with its gate valve and a return pipe with another gate valve. Adjustment of these valves regulates the flow rate and depth. The delivery pipe is 76 cm (2.5 ft) 10 while the return is 50 cm (1.6 ft) 10. Downstream of this are two sets of flow straighteners and a Thomson V-notch weir. A Poncelet rectangular weir is also available for high discharges. Beyond the weir are two more sets of flow straighteners, and a main channel. The last structure in the main channel is the downstream sluice gate which serves to regulate the water depth in the main flume and moderately regulate discharge. A trolley which spans the main channel provides the work-deck for collecting data as well as calibrating velocity meters. A carriage, the range of which is the channel width, provides the mount for the velocity meters. For the most part, the flume is constructed and runs well. Its width and maximum discharge make this structure particularly unique. The choice of two weirs contributes significantly to the accuracy of discharge measurements. Also, the flow rate varies little over many hours. Difficulties inherent in the flume are the control and measurement of the depth of flow. The downstream gate, which regulates the depth, presently operates off a constant speed electric motor and a rack and pinion gear. To fine set this gate, one must quickly turn the switch on and off, relying on trial and error. This method is frustrating and time-consuming at best. A variable speed motor with a rheostat control or a hand-operated crank may help in this respect. Problems in depth measurement arise out of: 1) the nonuniform flow due to the zero bed slope; and 2) irregularities in the bed itself. The bottom contai ns "hi 11 s" and "va 11 eys" in both the 1 ongitudi na 1 and transverse directions. The writers have been involved in four experiments using this flume, and in each, depth measurement has been a dilemna. One help might be

PAGE 48

31 to make the bed truly horizontal. To accomplish this a 1 m'll-vi scosity slow drying resin could be spread over the bottom hardening only after its found its own level. An attempt was made to straighten the false-bottom section. The old, badly warped 1.3 cm (1/2 in) exterior plywood was replaced with marine plywood of the same thickness. Also the existing cedar support was planed down in an effort to make it level. The results of this endeavor were good, though not perfect. In this study, for the reasons just outlined, depths were measured with a dry rod at the centerline of the test section. This method was considered the best available in lieu of the circumstances. A point gauge was used to follow the overall depth fluctuations during a run. The flow over the V-notch weir, though readily measureable for low discharges, is totally deposited in the center of the main flume. This leads to a rather di storted transverse vel oci ty di stri buti on. In an effort to remedy this, concrete blocks placed directly downstream of the weir caused the water to splash and roughly spread itself over the section. Fine tuning was accomplished by squirting dye across the flume width and noting areas of excess velocity. Wooden strips were then clamped to the flow straighteners at these areas. 4.2.2 The Effluent Supply System The effluent supply system consists of the pump, the piping, and the heaters. The pump is a 1.5 kW (2 HP) "Sta-rite" model It is located next to the flume pump and also supplies a constant head tank directly above. The suction line draws from behind the weir in an effort to avoid the turbulence-entrained air in the flume pump. The heated effluent discharge was much smaller than the pump capacity. To prevent excessive strain on the pump, a 3.8 cm (1.5 in) canvas fire hose returns a large percentage of the flow to the area of intake.

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32 A 5.1 cm (2 in) PVC pipe conveys the diffuser water to six 189 1 (50 gal), 12,600 kcal/h (50,000 Btuh), natural gas hot water heaters connected in parallel. Gate valves, located in the 1.9 cm (0.75 in) incoming lines, allow individual heaters to be bypassed. A 5.1 cm (2 in) galvanized steel pipe, insulated with 1.3 cm (0.5 in) wall neoprene C'rubbertex") directs the flow to the manifold. For visual inspection of flow patterns a 24.4 1 (6.4 gal) dye tank is located just upstream of the manifold. The cylinder contains a spigot for the release of coloring and a regulator with a check valve for pressurizing. A 0.64 cm (0.25 in) tube extends from an adapter in the spigot to one in the steel feeder pipe. The pump, piping, and heaters are considered adequate for the job. Strong surges from the pump, however, necessitates the use of a return line as well as a surge tank. The constant head reservoir is used instead of the 1 atter. The efficiency of the heaters, presently calculated as 65%, could be increased through a preheat system. This may be accomplished by passing the cold water supply through an axially back-and-forth copper line inside the heater's chimney which is usually too hot to touch. 4.2.3 The Manifold and Manometers The steel feeder pipe from the heaters expands to 7.6 cm (3 in), adapts to PVC, then enters and extends the length of the manifold. Slots are sawed in this line opposite to the exit ports, while supports keep it centered. The manifold is fabricated of 15.2 cm (6 in) PVC, capped on both ends, and reinforced around the exit ports (Figure 4-3). The reinforcement consists of PVC of equal size cut to form a "C" section by removing approximately 100. This length was then snapped on the main section after the caps were in place.

PAGE 50

'. (--"'-. :. -'.' A 33

PAGE 51

34 The exit holes were drilled and tapped through the double-walled pipe. An air cock is located at the top center of this main piece. The heated water exits the manifold through nineteen 1.9 cm (0.75 in) galvanized pipes before entering the vinyl tubing to the jets. Each pipe contains an orifice meter, an air cock, and a gate valve. Jets number 4, 8, 12, and 16, are equipped with a IIteell section between the gate valve and tubing to accomodate the manifold thermistors. The orifice meter is constructed of an aluminum annulus 0.43 mm (0.017 in) thick, 1.1 cm (0.44 in) 10, and 9 cm (3.5 in) 00 secured between two 1.3 cm (0.75 in) galvanized flanges. Pressure tappings consists of slots ground into the flange faces with holes, drilled and tapped, to accomodate 0.64 cm (0.25 in) tube adapters. Vinyl tubing with clamps to dampen oscillations, extends from the adapters to the wall-mounted manometers. (Undampened the standpipes pulsate with an average amplitude of 1 cm (0.4 in). Surges with a 9 cm (3.5 in) amplitude have been observed.) Thirty-eight glass tubes, 0.6 cm (0.25 in) 00, make up the battery of manometers. The glass tubes are connected at the top to a common overflow pipe. A cock valve and an automotive tire valve allow this pipe to be closed and pressurized with air to adjust the water surface elevations to a convenient level (Figure 4-4). The outstanding drawback of a manifold of this size is the adjustment of port discharge. This task would take anywhere from 1 to 2 1/2 hours. Obviously, the setting of one jet affects that of the others, and with nineteen, the problem is significant. The extra initial investment and increase head loss, characteristic of a good pin valve would have repaid itself in saved time and accuracyduri ng the experiment. Additi ona lly, surges from the pump makes discharge tuning difficult.

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( Figure 4-4 Wall-mounted Manometers with Overflow Pipe and Compressed Air Hose 35

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36 The mainfold is structurally sound. The anticipated weak areas were the junction of the 7.6 cm (3 in) PVC feeder pipe and the 15.2 cm (6 in) PVC cap, as well as the taps in the PVC for the galvanized exit lines. No leaks were observed in either joint thanks to the extra cement and the reinforcing, respectively. An additional asset of the system is its ability to hold a vacuum. The main section of the manifold is located approximately 45 cm (18 in) above the still water surface in the flume. While not in use this height of water as a suction is applied. Considerable time is saved in this respect since a leak would have necessitated purging the manometer tubes of air (a lengthy process). 4.2.4 The Diffuser Jets and Rack Vinyl tubing, 1.9 cm (0.75 in) ID, extends from the manifold; follows the flume wall to beneath the false bottom, and is clamped to the jets. A streamlined aluminum shield 70 cm (28 in) long attached to and extending 4 cm (1.6 in) from the wall serves to contain the tubes, in addition to smoothly diverting the flow around the nineteen roughness elements. The multiport diffuser consists of a rack support with friction held 1.3 cm (0.5 in) ID copper tubing as the jets (Figure 4-5). The rack is cedar, 5 crnx 5 cm (2 in x 2 in), treated with IIWoodlifell wood preservative, and extends the width of the flume. Bolts protruding from the ends of this plank allow it to pivot in fixed angle iron brackets. Jet angles are established by changing the rack angle. This;s achieved with precut plywood supports with aluminum bearing plates. Because of space limitations, however, the 10 diffuser angle is secured by a sweat 45 copper elbow and a 55 rack setting.

PAGE 54

37 L i IV .1' .' I' QJ > 0 u \j C ItS U ItS ex: QJ C" III 4-4.,... 0 QJ l-Ll") I '<;t QJ 0) .,...

PAGE 55

38 Marine plywood 1.3 cm (0.5 in) thick with slotted holes to accomodate i ndi vi dua 1 jets covers the rack and braces. The jets and rack functioned well throughout the experiment. No signs of warping could be detected in the cedar support despite large short term temperature fluctuations and repeated wetting and drying. A 45 elbow in the copper tubing is most effective for ease in handling, especially for small jet angles. Hindsight is the best teacher. Equal lengths of vinyl tubing from the manifold to the jets would have effected a more uniform manifold-jet temperature drop distribution. A complete listing of temperature drops from the manifold to the individual jets is contained in Appendix C-2. 4.3 The Sampling Equipment Data was collected with thermistors and velocity meters, both of which were read and compiled through the data acquisition system. 4.3.1 The Thermistors YSI "banjo" thermistors, probe no. 408, were used to measure all tempera tures for calculations. (Total immersion Sarna CT 15 thermometers were used as a thermistor check.) The YSI probe has a maximum operating temperature of 150C with a time constant of 0.6 seconds. The time constant is the time required for the probe to measure 63% of the newly imposed temperature. Approximately five "time constants II are required for a probe to read 99% of the total change. The interchangability tolerance of the temperature sensors is O.loC over the range used. Figure 4-6a illustrates the thermistor dimensions. The sensing element, a temperature dependent resistor, is housed in a disc with a wire support, both of which are stainless steel. Three meter (10 ft) plasticized vinyl jacketed lead wires terminating with a

PAGE 56

39 phone plug are standard. The manifold and ambient thermistor leads are 30.5 m (100 ft) in length. Fourteen thermistors were employed in this study one, positioned in a tee section between the gate valve and the tubingofan in-use jet measured efflux temperatures; another, placed approximately one meter upstream of the diffuser in the center of the cross-section yielded ambient temperatures; while the remaining twelve comprised a four vertically, by three, laterally, array for downtream data (Figure 4-6b). The array spacing was 3.2 cm (1.3 in) and 6 cm (2.4 in), respectively. The thermistor array was held in place with three 3.2 mm (1/8 in) thick by 38 mm (1.5 in) wide plexiglas supports. Automotive fuse holders provided quick release capabilities for individual thermistors. The plexiglas supports were clamped to an aluminum brace, which in turn hung from the carriage support on the trolley. The YSI thermistors are considered excellent instruments. They are adaptable to many uses and positions. An exceptional advantage is the small time constant of probe no. 408. A constant temperature bath is needed to periodically check the thermistor calibration, although the calibration seems very stable for both laboratory and field measurement over several days of operating time. The accuracy of the calibration needs to be checked, although these errors are probably negligible due to the temperature correction technique used in the calculations (see subsection 3.4.3). A probe positioned very near the bed in the sampling array would have yielded more complete isotherm plots. 4.3.2 The Velocity Meters Two Novonic-Nixon type no. 403 velocity meters were employed for all velocity measurements. The range of these instruments is 2.5 to 150 cm/s

PAGE 57

40 17 gauge \ 1.0 em -1 r-I{ P a 9.2 em /////A I P --.-J Figure 4-6a Thermistor Dimensions Figure 4-6b Thermistor Array in Plexiglas Support

PAGE 58

41 (0.082 to 4.92 fps) with an accuracy of 2% of true velocity. Their operating temperature is from 0 to 50C (32 to 122F) with an operating medium of water or other fluids having similar conductive properties. The probe consists of a measuring head supported by a thin shaft 46 cm (18 in) long with an electrical lead connection. The head consists of a five blade impeller mounted on a stainless steel spindle, terminating in conical pivots (Figure 4-7). These pivots run in jewels mounted in a sheathed frame. The impeller is 10 mm (0.39 in) in diameter, machined from solid PVC and balanced. An insulated gold wire within the shaft support terminates 0.1 mm (0.004 in) from each rotor tip. As the rotor is revolved through the motion of a conductive fluid, the small clearance between the blades and the shaft slightly varies the impedance between the shaft and the gold wire. This impedance variation modulates a 15 kHz carrier signal, which in turn is used to detect rotor revolutions. The propeller meters were suspended from the carriage on the trolley (Figure 4-8). The shafts of the instruments were clamped to stainless steel rods at one location. For ease and accuracy of vertical positioning, the rods were clamped at two points to the rack of a point gage. The conventional point gage brackets were then bolted to the carriage. Lead weights of the 900 gm (2 lb) variety were secured to lowest clamp in an effort to reduce vibrations brought about when moving the carriage. The Novonic-Nixon meters are precision instruments with fine moving parts. Since they are susceptible to suspended particles in the flow field, care should be taken to insure clean water and flume. Two layers of window screen were placed upstream of the first flow straightener in the main channel to intercept the larger debris. Also, air bubbles trapped between the rotors could yield erroneous readings.

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42 or-l..L.. 3 o r-l..L.. to t:: or-QJ ..0 o c.... oru o r-QJ ::> t:: o X or-:z: I u t:: o > o z

PAGE 60

43 Figure 4-8 Point Gauge Carriage Mounting for the Novonic-Nixon Velocity Probes

PAGE 61

44 The maintained accuracy of these velocity meters is rather poor. On the average, in order to work within a + 2% deviation from true velocity (Nixon Instrumentation Limited boasts a sustained capability + 1%), the meters had to be reca1ibrated before every other use. This record is improving slowly with time. Despite their sensitivity and inability to hold the advertised accuracy, the Novonic-Nixon meters are desirable instruments. The meter's small rotor size, as well as its low velocity capabi1ities,are very strong assets. The point gage mounting is considered an excellent method for suspending the current meters. The instruments are easily removed from their brackets with no deviation from the vertical setting. Also all the accuracy and ease of a point gage and vernier is accrued. 4.3.3 The Data Acquisi.tion System The ability to collect, refine, and compile large quantities of data was made poss i b 1 e through the da ta acqui s i ti on sys tem. The sys tem is composed of two pieces of equipment: a pink input box and an HP 9825A desk-top programmable calculator (Figure 4-9). The input box contains the electronic circuitry which takes the raw transmission from the measuring devices and converts it into usable signals for the programmable calculator. The pink box, which was specifically designed for coupling with an HP 9825A, has connectors for fifteen thermistors, I two Novonic-Nixon velocity meters, two Ott velocity meters, and ten Cushing electromagnetic current meters. It also contains an electronic clock which registers six counts per second. The input box was specially designed and constructed for the University of Florida Hydraulic Research Laboratory by Mook Enterprises of Meritt Island, Florida.

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Figure 4-9 The Data Acquisltion System: the Pink Input Box and the HP 9825A Programmable Calculator +::0 U1

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46 The HP 9825A interfaces with the input box to provide program control and data storage capabilities. The calculator has a 32-character LED display, 16-character thermal strip printer, and a typewriter-like keyboard with upper and lower-case alphanumerics. There are twelve special function keys, shiftable to twenty-four,as well as editing and system command keys. The machine has a two track, built-in, tape cartridge drive, three input/output (I/O) slots and four read only memories (ROM) slots. The string, advanced programming, and extended I/O ROM's were utilized in this experiment. The standard internal I/O storage is 6844 bytes with options available to increase this to 31,400 bytes. The standard storage was used in this study. The capacity of a tape cartridge is 250,000 bytes. The University of Florida Hyraulic Research Laboratory also has a serial interface capability for the HP 9825A. With this specialty the calculator can be used as a terminal to the Northeast Regional Data Center's (NERDC) Amdahl 470 computer. The data acquisition system seems to be the best investment the Hydraulic Laboratory could have made. Data collection amounts to simply changing the probe position and pressing a button, once the machine is programmed. Days of calculation time are saved and the accuracy is greatly 'enhanced through data storage and subsequent programming techniques. Also, the options to this system (plotters, serial interface, increased memory, etc.) seem limitless. 4.4 The Process of Physical Modeling 4.4.1 Prototype Measurements Prototype measurements of ambient velocity and depth were completed on the Apalachicola River downstream of the Jim Woodruff Dam at Chattahoochee. Cross-sectional bathymetries were determined with the University of Florida Hydraulic Resea'rch Laboratory's 5.2 m (17 ft) motor launch and Benmar

PAGE 64

47 echo-sounding recorder, model DR-68. River widths were found with a transit and tape through conventional surveying triangulation. Discharge data was supplied by the U.S. Army Corps of Engineers at the dam. The following prototype specifications were observed: discharge, Qp = 495 m 3/s (17,500 cfs) cross-sectional area, Ap = 651.3 m 2 (7011 ft2) width, Wp = 191 m (627 ft) which gives: average depth, Hp = 3.41 m (11.2 ft) ambient mean velocity, Ua,p = 0.761 m/s (2.50 fps) where the subscri'pt p denotes prototype. 4.4.2 Planning of Experiments Modeling considerations were based on ambient and jet densimetric Froude number similarity. The ambient Froude number is defined as: Ua 1F = (4.1) a (gH)1/2 Also, the velocity ratio (jet: ambient), k, was required to be identic'a1 in the prototype and model. Due to the large width to depth ratio of the prototype (W/H = 56) the complete river width was not modeled. (The mean depth and velocity was, however.) Since no multiport diffuser discharging thermal wastes exists on the Apalachicola River, typical prototype diffuser characteristics were obtained from literature. A prototype temperature rise above ambient of approximately 11C (20F) is indicated by Parr (1976) and Jirka and Harleman (1973) as normal. Jirka and Harleman (pg. 272) also point out that jet velocities of

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48 3.05 to 4.57 m/s (10 to 15 fps) are representative prototype values. Choosing a prototype jet di.ameter of one-tenth the depth fixed that quantity at 34.1 cm (1.12 ft). With a maximum efflux velocity of 4.57m/s (15 fps) the maximum jet discharge, qj' of the prototype becomes 417 lIs. With these prototype parameters in mind, preliminary laboratory studies of the six natural gas hot water heaters were conducted to determine the total heat flux. Discharge and temperature measurements yielded a heat flux value 49,420 kcal/h (196,100 8th/h). Since a temperature rise of 11C (20F) was desired, a total effluent discharge, Qe' of 1.25 lis (0.0441 cfs) became fixed. For the extreme case of a ten jet diffuser the individual jet discharge becomes 0.125 lis. Froude modeling laws state that the ratio of the prototype discharge to that of the model Qr' must be: Q = U L 2 = L 1/2 L 2 = L 5/2 r r r r r r where U = velocity ratio Prototype r model Lr = length ratio It then follows: 417 2/5 Lr = (.125) = 25.7 The other model parameters now fall into place: H = = 341 cm = 13.3 cm (5.2 in) m Lr 25.7 D D = ---P= 34.1 cm = 1.33 cm (0.52 in) m Lr 25.7 U U = = 76.1 cm/s = 15.0 cm/s (0.492 fps) a,m Lr 25.7 (4.2) (4.3) (4.4) (4.5) (4.6)

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49 where the subscript m indicates model values. A check of the velocity ratios for the model and prototype yields kp = k m = 6.00. Since the experimental width is fixed as that of the flume, or 2.57 m (8.1 ft), the portion of the prototype width modeled becomes: = 25.7 (2.47 m) = 63.5 m or 0.332 of the actual prototype width. 4.4.3 The Experimental Procedure After the construction of the apparatus, the first step in the experi mental procedure was to calibrate meters. The jet orifice meters on the manifold were calibrated in place with a stop-watch, bucket, and scale. A linear least squares fit of jet discharge, Qo' versus v'Xhwas determined, A is the head drop across the orifice plate. The error of the curves was found to be + 4% of the true discharge. Before each run the calibration of the Novonic-Nixon velocity meters was checked in the range of 8 to 20 m/s (0.26 to 0.66 fps). Mounted with their normal supports on the carriage, the Nixon meters were pulled through still water over a distance of 1.07 m (35 ft) with the trolley. The special function keys on the calculator were used to execute immediate continue program statements which read initial and final values of propeller revolutions and time. The program, then computed the average frequency of each current meter, the true velocity, and the percent error of the calibration curves to be checked. If the absolute error was greater than 2% the instruments were recalibrated. No less than ten points were used to determine a linear least squares fit of prop frequency versus velocity. Appendix B contains a complete program listing for the HP 9825A. The Thomson weir was also calibrated over the limited range of 40.0 to 67.0 lis (1.41 to 2.37 cfs) (the model flow rate was fixed at 49.2 lis

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50 (1.74 cfs)). Six points were used to define the curve with an accuracy of + 1.5%. Seventy velocities were taken at a section to specify the discharge. Ambient conditions must be established in the recirculating flume. Since it is a closed system, the adjustment of one valve affects that of the others. The discharge valve outside the main pump, the valve in the return pipe, and the downstream gate were all adjusted until the ambient model parameters were those described in the preceding section. The flume discharge is found by measuring the height of the water above the weir and using a weir calibration formula. Once the hydrodynamic controls are set there is no need to adjust them; unless, that is, someone tampers with them in the meantime. The experimental run begins when the main pump is started. After the water behind the weir has risen sufficiently (about three minutes) the small effluent supply pump is activated. The flume takes about an hour to stabilize from this point. Flume stabilization is not the critical time, however; rather manometer purging and manifold adjustment are more lengthy processes. The manometer tubes need to be purged if air becomes trapped in one or more. This is done only after all the air traveling through the piping system has been released through the manifold aircock. To rid the manometer tubes of air, the cock valve in the manometer over-flow pipe is opened. The jet gate valves are then closed, diverting the total jet discharge through the manometers. Once a clean, airless flow is observed in the tubes the jet gate valves are reopened and the overflow cock is closed. Compressed air is then applied slowly to bring manometer water surfaces to a readable level. Depending on how careful the experimentor was in pressurizing the manometer rack air bubbles may exist in the tubes. These pockets may be worked out by vibrating individual tubes or by repurging the tube battery. As stated earlier this

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51 process was often circumvented by the ability of the manifold to retain a vacuum. For each run and vertical jet angle, the diffuser discharge distribution was unique. Therefore, this distribution had to be set, or the manifold had to be "tuned". Tuning consists of adjusting the jet gate valves until the head drops for the desired discharges are noted on the manometer battery. To dampen the amplitude of the surge-induced oscillations in the manometers, tube clamps near the orifice meters are tightened. By the time the manifold tuning was complete, any residual warm water in the heaters had been flushed out, allowing for the determination of the thermistors' correction factors. With water at ambient temperature flowing through the system (temperature checks were made with thermometers), the thermistor sampling array was placed in the flow field. A program was then initiated which read all fourteen thermistors 500 times (377 sec) in rapid succession, found the mean temperature for each probe, and computed the average readi ng for all. The difference between the group average and that of the individual thermistors was then determined and used as the probe correction factor to be added to subsequent temperature readings. A listing of these factors is to be found in Appendix C-3. Once the correction factors were determined, the six hot water heaters were ignited. When the temperature rise above ambient was 11C (20F) data collection would commence. Velocities were taken at one section 2 m (6.6 ft) downstream of the diffuser. The sampling array consisted of five rows and fourteen columns. The rows were spaced every 2.5 cm (1 in) from the bed in an effort to find any excess jet-induced velocities. The columns started at 20.7 cm (8.1 in) from the south flume wall and increased in increments of 17.4 cm (6.9 in).

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52 Columns 12 and 13 were spaced 9.9 cm (3.9 in) apart due to the proximity of the north flume wall. The two propeller meters were used to sample simultaneously the same row of adjacent columns. A velocity program (Appendix B-3) read initial values of prop revolutions and time, waited a prescribed time increment, and took final values of the same quantities. The program would then determine the velocities from the calibration formulae and print them for immediate checking. After the sampling was complete, the matrix was stored on tape. Velocity averaging times of 15, 30, 45, and 60 seconds were all tried. The latter, which yielded the most consistent results in a reasonable time span, was employed in all tests. Ambient velocities were taken in the same manner but with a zero effluent discharge. Five points on a vertical at the relative depths of: y/H = 0.1504, 0.2352, 0.3679, 0.5754, 0.9000 (4.7) were sampl ed to best descri be the 1 ogarithmi c velocity profil e (Chri stensen (1978)). A section 8 m (26 ft) downstream of the diffuser was chosen in an effort to avoid flow disturbances effected by the protruding jets. Temperature collection followed immediately that of velocities. Five sections were sampled during this process, one at 6 m (19.7 ft), 4 m (13.1 ft), 2 m (616 ft), 1 m (3.3 ft), and 50 cm (1.6 ft). The data array at each section was comprised of four rows and thirty-six columns. The rows had a spacing of 3.2 cm (1.3 in) from the bottom while the columns started at 22 cm (8.7 in) from the south flume wall and were incremented at 6 cm (2.4 in). Temperatures were collected by progressively moving a 4 x 3 fixed thermistor array laterally across the section. Each time this 4 x 3 matrix was read, the ambient and manifold temperatures were also read. So, in essence, twelve fourteen-point arrays were compiled at each section. Sampling started at

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53 the downstream most section and proceeded--upstream. A program was designed to continuously sample all thermistors for eighty-one points each, the time of which took 61 seconds. This program (Appendix B-3) then averaged the for each probe, applied a correction factor, and printed the temperatures in a prescribed format. A polynomial of the sixth degree with resistance as the independent variable best matched the manufacturer's data and was used as the calibration curve for the thermistors. Accurate thermistor calibration is necessary to verify this however. Again, after the section sampling was complete the temperature matrices were stored on tape. Jet trajectories and interference patterns for each jet discharge and angle was found using a 11 x 4 x 18 temperature array. This matrix started at the diffuser and proceeded longitudinally to one meter (3.28 ft) in increments oflO cm (3.9 in). Four points on a vertical were sampled at a spacing of 3.2 cm (1.3 in) from the bottom. The grid consisted of a detailed view of jets number 9,10, and 11; commencing at 4 cm (1.6 in) south of jet number 9 and extending laterally in steps of 2 cm (0.8 in) to 6 cm (2.4 in) north of jet number 11. This array was collected in the same manner as the section grids. Before the compilation of a run, the temperature drop from the manifold to each jet was determined. This was accomplished by securing the ambient thermistor to a wand and inserting it into each jet. Temperature drops to the jets for each run are contained in Appendix C-2. (

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5.1 Temperatures CHAPTER V REDUCTION OF DATA All temperature readings \'Iere normalized through equation 3.18. This equation is the ratio of the temperature rise above ambient to the mixed temperature rise assuming no losses. Iostherms were generated through the Gould plotter of the Northeast Regional Data Center (NERDC). The serial interface capability of the HP 9825A was utilized to convert this machine into a terminal of NERDC's main computer, the Amdhal 470. Three programs were implemented for this task (see Appendix B): one yields cross-sectional isotherms; a second, plan views; and the third, jet trajectories. Each program has the same serial interface component as the first half. After signing onto the Amdhal 470 data was transferred from an HP cassette tape, through an acoustic coupler, and into a saved file. Job Control Language (JCL) in another file was then used to initiate a contouring program stored on disc. The JCL also supplies the stored program with the data in the saved file. Finally, the contouring program generates the isotherms on the Gould plotter. 5.2 Velocities Current measurements were nondimensionalized with respect to the mean velocity, which was taken as: (5.1) 54

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55 The transverse discharge distribution was found by integrating the velocity profile over the depth. A least squares linear curve of velocity versus the natural log of depth was fitted through the data for this purpose. The equation generated from this step was then integrated. Values of the ambient velocity at each jet, needed to compute V/k and aWj' were determined through the use of a canned Hewlett-Packard program which fit a third-degree polynomial through the data and interpolated between points. The ambient distribution used was the average of six. Velocity profiles for each jet velocity were taken as the average over the center half of the centermost diffuser (e.g. for U u = 91.2 cm/s the profiles were averaged over the center half of the diffuser arrangement with active jets five through fourteen).

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6.1 The CV Parameter x CHAPTER VI PRESENTATION AND DISCUSSION OF EXPERIMENTAL RESULTS Equation 3.17 defines the coefficient of variation at a section, CV x According to this expression, fully mixed flow occurs when CVx + O. After Argue and Sayre (1973), the plane log [CVx vs. log ([-) 3.22 is plotted in Figures 6-1, 6-2, and 6-3 for 8 0 = 35, 20, and 10, respectively. Groups of constant Ld/W are apparent with best mixing occurring with jets one through nineteen active. This is to be expected, since for the same effluent discharge, the entire width of the ambient flow is utilized for dilution. For less than full diffuser, the mixing is drastically reduced. Curves seem to fit these points best due to the effect of transverse dispersion. With Ld/W = 0.75, and for the cases of 80 = 35 and 10, mixing is only slightly better for active jets five through nineteen. Hi gher 1F. and V /k a J values are thought to account for this. More simply, diffuser five through nineteen has more jets located in the region of maximum ambient flow than does one through ten, fifteen through nineteen (see Figure 3-2). The group with the 1 east mi xi ng is represented by LivJ = 0.5. Diffusers one through five, ten through fourteen, and ten through nineteen have the 56

PAGE 75

J x_ i -1 0 I I -i .8r .7r-i I i \ V i f ) i .sr I I J ,;:1-'-1 4L I ... 5 '1 I i I Jeti I I .3r v IO-lS; ...... l 0 1-5,/5-19 I \l 5-14 I 1-5,10-14 D.. 1-10,15-19 .2/+ 5-19 I 0 1-19 x/L 20 30 50 60 70 80 90 100

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1.0 .9 cv (H r. ) ,6 ,5 .4 .2 Sym;:.ol X 0 "V ta A + 0 jets 10-19 1-5,15-19 5-!4 1-5,10-14 1-10,15-19 5-19 1-19 6 7 8 910 20 30 40 50 60 7080 90100 x/L Figure 6-2 CVx(L/(H-h)) vs (x/L), eo = 20 01 (X)

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( L \ CV x ,H -h ) i.0 .er .8,-'7r' .6 .5 '" -+ +.2. Symbol Jeh X 10-19 0 1-5,15-19 \J 5-14 1-5,10-14 D. HO,15-!9 + 5-19 l 0 1-19 I I I I I I I 1 i .073 4 5 6 7 8 9 10 x/L 20 30 40 50 60 70 8090 100 Figure 6-3 CV (L/(H-h)) vs (x/L), e = 100 x 0 (J1 \.Q

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60 same jet locations in the ambient flow and, assuming a symmetric ambient discharge distribution, should give equal mixing. It is obvious for all three angles that diffuser ten through nineteen yields the poorest mixing in the limit, while active jets one through five, ten through fourteen gives the best in the group. This is attributed to the fact that the latter arrangement has three ends for transverse mixing, while the former has only one. Similarly, comparing diffusers five through fourteen and one through five, ten through fourteen for each angle shows the latter to disperse more fully even though it has lower values of V/k and JFj This indicates that the lateral transfer of heat is as important a descriptor of the mixing process as the momentum flux ratio or the ambient/jet Froude number. Figure 6-4 compares the effect of the initial discharge angle, 6 0 on the coefficient of variation distribution for the full diffuser. Over an initial distance of less than ten port spaces downstream of the diffuser, 8 = 35 yields the best mixing. The large jet angle deposits the effluent o in the more turbulent upper reaches of the flow field, leading to increased dispersion. Similarly, the smaller angles are less likely to feel this dispersive influence close to the diffuser. As x/L + 50, the discharge angle of 10 results in the best mixing. In this case, the jet experiences a low pressure area on its downstream side due to the drag effect. This causes it to become attached to the bottom, resulting in a longer trajectory and, in the limit, increased dilution. Thi sis the same phenomena witnessed by Sharp and (1973). 6.2 Isotherm Plots Five section isotherm patterns were recorded for each run, with four plans and one trajectory for each jet angle and velocity.

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1.0 .9 .8 .7 .6 ( L ) .5 CVx H-h .4 .3 Figure 6-4 CVx(L/(H-h)) vs (x/L), Jets 1-19, 80 = 35, 20, 10 (J)

PAGE 80

62 6.2.1 Cross Sections The cross-sectional isotherm plots are helpful in relating to the coefficient of variation. There things to note and compare for the three values of 80 All isotherms are those for the full difusser. Figures 6-5, 6-6, and 6-7 contain the plots at the first section (x 0.5 m) downstream of the diffuser for 8 0 = 35, 20, and 10, respectively. For the jet angle of 35 the maximum temperatures are already nearing the water surface; while for 8 0 = 20 the hot spots, which are of the same magnitude, are at mid-depth. By extreme contrast, the maximim isotherms for 8 0 = 10 are nearly at the bed with much hotter temperatures and sharper gradients. Obviously, this section is not as well mixed as the others. For all three angles, the majority of the heat is at the larger values of z/W. This is probably due to the meandering of the maximum velocity in the flume, diluting the left side more than the right. The isotherm patterns at the second section (x 1.0 m) are to be found in Figures 6-8, 6-9, and 6-10 for the three jet angles. For 8 = 35 o turbulent mixing is the predominant heat transfer mechanism, although slight surface heat loss exists due to the temperature gradient across this boundary. Section two for 8 0 = 20 is nearly identical to that of 35 as the CVx diagram in Figure 6-4 confirms. With 8 0 = 10 the jets are still clinging to the bottom with higher temperatures, steeper gradients, and less mixing than the other angles. The nondimensiona1 plots at section three (x 2.0 m) are displayed in Figures 6-11, 6-12, and 6-13 for each diffuser angle. The density deficit of the fluid near the water surface for 8 = 35 and 20 hinders the mixing o process which wants to bring it toward the bed. The buoyant fluid near the bottom for 8 0 = 10 is working to bring the heated effluent into the more

PAGE 81

ISIHHERMS. CREISS UH= 3.767, H= [4.2 01. 35 DEG, JETS 1-19 AELRTI'(E Zlfl. DI]flHSfAEAH _D.aa D.as D.La O.LS 0.25 D.ga D,gS D,YO C.YS D sa 0,55 c,sa D.SS D.1a 0.15 o.sa 0.a5 D,. l.aa -.,-...;...-.... '.0: . .. .... .... ; .... ..... ......... ,,' .... .... ; .. .. JET UJCATIml:3 :=: Figure 6-5 Section 1, 35

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ISOTHERMS. CROSS SECTION. X/H= 3.671, H= lij.3 eM. 20 DEG, JETS 1-19 RELRlI'iE DI1W{STAEAM JI.oa [LOS !L Lil IL LS ru!s 0"311 IL:l5 r.UJQ o.lJS O.5i1 [1-55 [Ulll fLas 0_70 IL75 [LSI! D.3"5 ru1[1 O.!lS Lila i l" """::' t ::J:", '" JET l!]CRTI iJriS .!.. t.. .!.. .!.. .!.. A .A .A .!.. .!.. .!.. .!.. t.. .A .A .A p, ----r 8 Figure 6-6 Section 1, 20 O'l

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rsnTHERMS. X/H= 3.680, H= 15.0 eM. 10 DEG, JETS 1-19 .Jl.oa g' =t'F m= .-0 :D ..... -"" m,::-aa. ." -I :::I: -<:0 --.... :.. :::1:0 Q .. Q D.05 A D.lO D.l5 D;2a ,!. ,!. ,!. :? I I 8 D.25 D.sa RELATHE OllfJN::'fAEflH 0.S5 O.YO D.Y5 0.50 0.55 D.ea D.Ss 0.70 0.75 0.30 0.35 D.ga LOO I I I I I I I I I I I JET Cltl:3 ,!. A A .& A a A A A A. & A A Figure 6-7 Section 1,10 O"l (]"I

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.." -! :x: = "" = ISClTHERr1S, CROSS SECTrClN, UH= 7.Ql!O, H= ll!.7 01, 3S DEG, JETS 1-19 O.LO O.LS fJ .. ;!11 /.$ ffi: :-':': . . .. . .... r"r: r'" .JET liJCRTI DNS D.BS 0.70 D.15 D.30 D.S5 Lao : I. '5 A A A A A ____ ____ -+ ______ ____ ____ -+ ______ ____ ____ -+ ____ ______ +____ ____ ______ +____ -r ____ -+ ______ ____ ____ -+ ______ __ 8 Figure 6-8 Section 2, 35

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ISOTHERMS, CROSS SECTION, K/H= 6.972, H= lij.7 eM, 20 DEG, JETS 1-19 D.OS D.Is D.:!I'J D.:!5 D.g. D.SS D.75 0.30 D.gS /.1) .. ................ -...... ................................ -.......... .. .. .JET LOCRTIOW=; ____ -+ ______ +-____ -+ ______ +-____ -+ ______ +-____ -+ ______ +-____ ______ ____ ______ ____ ____ ____ ____ ____ ____ ____ ____ Figure 6-9 Section 2. 20

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ISOTHERMS, CROSS 3ECTrON, X/H= 6.921, H= [5.2 01, 10 DEG, JETS 1-19 AELRTI'iE VH, LIJDKING DO fJNSfA EAM ...Il:ao D.as D.la D.l' tI .2S D;ga o.gS D.UO 0.U5 D.50 D.55 D.SO D.SS 0.'0 D.75 n.ao 0.3, [I.!ll) l.OO I I I I I 8 :xrfl r-= :D .... -...: ""0 0;" me ..., -f ;>= :-::? .. ::1:= '" ,., Q 01 JET UJCATI IJN:3 6. 6. 6. 6. 6. eo. eo. eo. A A A 6. 6. 6. 6. 6. eo. eo. eo. 8 I I I I I Figure 6-10 Section 2, 100

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CRO:3S SECTam. UH= lli.13, H= lli.1i 01. 35 DEG, 1-19 RELRTI'/E IHD1H. Zill. LIlDKING DIJIlNSTAEAH ____ ____ ___ _____ 8 .JET lIXRTI ems Fi.gure 6-11 Section 3, 35

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ISlJTHERMS, CR(lSS UH= lIL06, H= lL!.L! CM, 20 DEG, .JETS 1-19 D.as D.LO D.LS 0 .. 211 tl.25 0.S5 D.70 D.sa D.35 i.ao .. . .... : ..... : ..... ............................... .. .. .JET U'JCATI (INS __ :3 Figure 6-12 Section 3, 20 ""-J o

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ISBTHERMS. CROSS SECTION. X/H= 13.86, H= eM. 10 DEG, JETS 1-19 RELRm'E IoIIDTH. UlflWlG OOfltlSTAEAH Jr:a_a ____ ____ D+:j_S ____ 4D._ua _____ DrU5 _____ 8 :fS+1":':: ; . .:.' 1.0: : . . .. . . . ..... : ..... : ..... ; ..... : ..... : .... ... : ..... : .... . : : : ;. : : : : . ..... :: V .. .' .... : : : /,0' : : : : : .. ., ... ... : ":'" .... : .... : ..... ; ....... ... :-... : ........ : .... : ... .. .. ..' .. .. . ; ..... ; ..... ; ..... ; .... ..... :. .. ... . ; .... ; ..... ; ..... : ...... ; ..... ; ..... ; ...... ; ..... : ..... ; .... ..... ; ..... : .... ..... ; ... . .. .... .. ... ',' JET UJGRTI Figure 6-13 Section 10

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72 turbulent flow field and thus mix it better. This is evidenced at z/W = 0.35 where the hot water is rising to the upper area. At this point, the 100 diffuser results in a more uniform temperature distribution. Figures 6-14, 6-15, and 6-16 are those thermal contours at section four (x 4.0 m). The S = 0.5 isotherm has almost disappeared for 8 = 350 o and 200 Again if these sections were not labeled, they would be hard to tell apart. Columns of ascending residual heat are to be seen at z/W = 0.2 and 0.48 for 80 = 100 in Figure 6-16. Since the contours are in increments of 0.5, this plot shows 0.5 < S < 1.5. The final section (x 6.0 m) can be seen in Figures 6-17, 6-18, and 6-19. The mixing process is slow for 8 0 = 350 and 20. The 100 diffuser produces an almost constant-temperatured cross section. 6.2.2 Plan Views Plan isotherm plots are useful in determining jet interaction, as well as, the dilution of the core region for individual jets. All the plans described in this subsection are for U j = 48.0 cm/s, which corresponds to the jet velocity for the full diffuser. The first plan views (i.e. those closest to the bed) are contained in Figures 6-20,6-21, and 6-22 for 8 0 = 35,20,100 respectively. The black areas are the extremely hot cores with steep gradients. The dimensionless temperatures are as indicated. Figure 6-22 shows the shift of many contours in the downstream direction. This effect is due solely to the small discharge angle of 10 and not to increased dilution. Due to equipment limitations, it was not always possible to line up the thermistors with the jets. Also, any slight lateral fluctuation in the jet would register hot spots on two probes as seen in Figure 6-20. Obvious in Figure 6-21 is the missing hot spot for jet eleven on the right. Again this is due to thermistor alignment errors for close-to-jet measurements

PAGE 91

rSElTHERMS. CREISS SECT!eN. UH= 28.02. H= llj,.lj, 01, 35 [lEG, JETS 1-19 .JI_OO ;:.,f'2 m ... r"" :0 ;j ...,: n1.::) 0;' mo ..., ...j :::J: -.:? "" ... ::I:"" "" ., '" e D_as A D_LO D_LS D_20 D_25 A .!o. A A D_ga RELRlI'/E Z/W, LllOKItlG D;UO 0;U5 0;50 D;S5 0;60 ..................... .JET LJJCATHmS .!!o. .!!o. .!!o. a a a .!o. Figure 6-14 Section 4, 350 D_SS 0_7Q D.?S o_ao .!o. A A A o_as O_gO :M .!!o. .!!o. .!!o. LOO -.....t W

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rSCITHERMS. CRClSS SECT[ClN, XlH= 28.51l:, H= ll!.1 20 [lEG, ,JETS 1-19 "'p.aa 8+D.as RELAlI'IE Zlfl. UJDKING oafmSfREAI'! O;YO 0;50 0;55 O.SO O;LO 0;l5 0.25 m", r-"'" ::l .... """ "'0 -i ::0: ::0:"," "J '" : ..... : ..... .... ':' .... .. .... : ..... .... : ......... .. .................... A A A a & & L .JET liJCRTI OtIS ? I 8 Figure 6-15 Section 4. 20 D.BS 0.10 a.,s D.as .. .... .. .. .... : ..... .... : (J,'5, A A 0.'5 A Laa -....J ..j::::.

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SECTION, X/H= 27.56, H= 14.7 CM. 10 DEG, JETS 1-19 "p.oa 8' D.as ".la O.lS D.25 RELRlI'/E LOElt\ING DI]flNSrAERH ";:15 D;UO ".us D.sa 0.55 D.dO D.SS D.'5 D.3a o..:!s LaO I. .. .... : ..... : ..... ;. .... ;. .. JET LOCATI ONS Figure 6-16 Section 4, 100

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CROSS SECT[oN, X/H= 38.96, H= lS.l 01. 35 OEG, JETS 1-19 RELRTH'E Ufl. [)afUlSTREAH J+:a_Q _____ _____ _____ :3 /.0 .... .. ................ ................ .... _. ........ -................ .. .. .. .. . . . .. . .JET U1CATI ;::HlS A A A 8 Figui'e 6-17 5, 35

PAGE 95

rSeJTHERMS. CReJSS SECTreJN. XlH= 11,0.98. H= l4.7 eM. 20 DEG. JETS D.as D.La D.LS 0.2a [U!S ... ;. .... .. .; ..... .............. :.. A A A A = a a a a D.S5 0.70 D.3a 0.35 0.15 I Lao I I ...JET liJCRTI eJt
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ISBTHERMS. CROSS SECT[BN. X/H= 39.29, H= l5.ij eM. 10 DEG, JETS 1-19 RELATI'lE IoII01H. UtJ, UHltlING oaNNSTAEAIi Jl.aa Q.as D.La D.25 D.gO D.gS D.ija D.ijS 0.55 D.sa D.JI5 0.1a 0.15 D.as Lao 8 In .. . ..... ........... u, .. 'Ff .. .. .. /,0 ... : ..... : ...... : ..... ; ..... : ...... : ..... : .... . u' .. .. .................. ... . . . .. .. .. ................................. . JET UJCATI otlS /.0 ':=. Figure 6-19 Section 5, 10

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79 ISOTHERt1S. PLRH, Y/H= 0.220, H= eN, 3S DEG, UJ= lIB.oeMlS, .JETS 9,10,&11 ... '" ., '" .. o 'J .. '" 'J '" ... c '" :.1..-_-+ ." ....... ......... ..... ........................ .. . .. ... .... !....... .......:..,.... . : ... ... .. .. .. .. .. .. .. .. .. .. .. ,. . .. ............ .. ........ ........... ........ ............. ...... .......... ....... ............... ............................................... -.. ,. ... ................... ........ ....... ............ .. ................. ................... -. ..... .... ....... .................... . ....... ............... ",'" .. ,',. .................... .............. ; ....... ;. .............. ;. ....... : ........ : ... .. .. .. ., .. .. .. .. .. .. .. .. .. .. .. .. . j ... ; ; j ; ....... : JET A Figure 6-20 Levell, 35

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ISOTHERtS, PLRN, r IH= 0.222, H= 1 Ul eH. 20 OEG.IJ.J= LIS. neHlS. JETS 9,1 0, FiELRTlI'E MlDTH. ZifJ Df..1MMSTRERJ1 (XlO-l) __ -lqr_q_0 __ __ \+iro __ --4Yi,-7o ___ 5rlJl 5rlO 5jlll a ;' '" '" .. a .. '" .. .. Q '" a ... .. a c .. a . . . . .. ....... ...................................... .......... ............................ : ....... .... .. ....... ....... ; ........ : ........ : .. ... .. .. .. .. .. .. .. .. .. . . . . .. ....... ...... ; .. .... ; ....... :. .... i ....... ; ........ .. . .. ... ....... ..... ,; ...... ,; ....... ; ....... ; ....... ..... .. .. .. .. .. .. .. . JET S.ro I /,. a Figure 6-21 Levell. 20 80

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ISOTHERtS, PLRN, Y/H= 0.193, H= 15.0 to DEC;, UJ= JETS 9,10.&11 RELRTlVE NJOTH, Ufl OONMS1RERri fXlD-l) ____ 4gr_gU ____ ____ \+lro ____ ____ ____ __ __ ____ __ -45i_ro __ __ ____ __ -413u .::1 .... o .. .::1 '" '" o '" ;. o JET LI'CRTWNS t.. o Figure 6-22 Levell, 100 81

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82 The second level plots are shown in Figures 6-23, 6-24, and 6-25 for the three angles. At this depth and jet velocity, 8 0 = 35 produces a pronounced horseshoe shape contour of the type described by Fan (1967). This phenomenon occurs as the sides of each jet is sheared and carried down-stream by the ambient flow. Note the hot trails delineating this action. Some dilution of the core region is to be seen while jet interference is minimal. For a diffuser angle of 20 (Figure 6-24), the ambient seems to be shearing the jets in a preferred direction obviously due to a transverse velocity component. There are no horseshoe shapes here due to the small jet angle. Little core dilution has occurred with minor jet interference. With the jet angle set at 10, the isotherm plot of this level is similar to that produced by a larger angle at the third level. The small 8 is the o reason the hot water has progressed farther downstream than it has done at the other settings. Figure 6-26, 6-27, and 6-28 are the third level plan views. With 8 = 35 the core region becomes more dilute, but still exists. Jet intero ference has not occurred, while the horseshoe shape has nearly disappeared. The jet centerline for 8 0 = 35 has reached a value of x/H 1.75 while for 8 = 20 the core is at x/H 2.5. Much lower centerline temperatures are 0 to be seen with 8 0 = 20! at this depth than at level two due to increased length of travel. With 80 = 10 Figure 6-28 shows a slice of the top of the jet. Lastly, level four temperature patterns are contained in Figures 6-29, 6-30, and 6-31. No core region is visible at this depth for all jet angles. Only a slight merging of jets is seen for 8 = 35 in Figures 6-29. Almost o no sign of the jet is to be found with 80 = 10 and y/H = .832. Initially for this angle, the jet passes under the majority of the ambient flow.

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j .. _., ,-r"j;-: '-1 o.!'l o ... ,"1 '-',1 ., .. q ISOfHERMS. PLRH, 1'IH= 11= CH, 35 DEC. U.h lJ3.0CHIS .JETS 9,ID.411 U .. ; ..... : .. : .. 4 .. .. /.0 . .. .. : : : .) .. ; : \: : .. .... : ....... : ....... : ...... .... : .. .. . ... ... .. .. i: \ J .. .. .. .. .. .. . .................... .. JET LGCIHIONS ., A b ... ---j-----+----1-----!----+---+----+----. -----1 ------j---t----+----i---t---t ., Figure 6-23 Level 2, 35 83

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'" a 84 .. --+.---+----+__--_+_ ---/----+._----f---.--+---t-----t---------i Figure 6-24 Level 2. 20

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PLRlI. l/H= O.LWl. H= 15.0 eM. 10 DEG. U.J= YB.OCN/S .JETS g, lO.W RELATm MlDTH. 1.:/11 OOMMS1RERH WD-I) ____ ___ ____ __ __ __ __ _+5._ID __ ___ '" '" ;" '" rn '" a '" '" ." '" '" '" '" '" ." .... '" a :L IS loS .. : ....... .. ... : .................... 1 ..... ; ...... j." .. ; .. I I .. ,1.P f:\:/'o: ......... ." : 0., : \2/:\::/: -: 0 0 0 0 JET L IJ C h h -_+---t-I Figure 6-25 Level 2. 10 135

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ISOTHERtjS, PLRtI, (lH= O. E:62. H= 1 q. 5 ::s [lEG. UJ= l!:3.0CH/S, JETS 9,1 D .s;11 /.0 .. -. .. .. I,,, ... ...... ,.. .' .. ..... ... .. m h : 2.0 \ : JET LIJCHfHlN::: II /.0 .... .-....... 1.0 : : r .. :r1:1: 2.S: ,.: ...... ; ............ . . --+-------+--------------+1 ----t----t-1 -+---+.-------\---+_ Figure 6-26 Level 3, 35 86

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m a '" '" ISOfHERMS, PLRN, T/H= 0.666, H= eM, 20 DEG, UJ= ij8.0CH/S, JETS 9,10,&11 FiELRll'l'E W]DTH, WD-l ) Y.lJO till till Y.10 loaD \.[1] S.rIl 5,lD S,1I] S,Cl] 5.YO s,ro f.,Ell I -+----}---4---.---+------f-.: : +----------i--------+------+---{_ I n ;1\:"s: ......... ,. ... ,. (\ ................. : '2.,0 : :, / .:. -2.7\ Figure 6-27 Level 3, 20 (\:1.,0 .. .', ... ,. '.' .: ........ . . . .... ; ..... r1\ .. : '2.,S: : . . . .. .. .. .... . . .. 87

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a '::l ISOTHERMS, PLRN. T/H= 0.612, 0,., S,W 1 5.7D 1 m ., : .... ... .... ...... : : .:. .... .. .:..".. .. . . ....... : ..... .... : ..... HR; .. .. ... .. ... .... ..: ... (11\ ............................ "'" I',' i:, .... ....... .:, .:_, '@'O'O:l .... :. .. ... .... .. : ... ... . .'1 ......................... : """: : : : : : : """ '" ............ ......... : ... : ..... --t-----, 1 lET '-iJ. 1 1-iJ. I --+--------1 6-28 Level 3, 10 88

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89 ISOTHERMS. PLRN. T/H= 0.882. H= 11.5 eN. 35 DEC. UJ= UB.oeN/S, JETS 9,10,&11 '" '" '" -:I ........... rtl:j rI' -1 /\ z G) -1 2'::l I' r 0 (f)1lJ -1;' :D(J z (-) 1"'1 -." .( --" ........ '" '" (J '" '" '" -:I : \: : ..... \. .: .... ..... ,,',." W ::: : 0,0: : , , c l '" -:I & & ---+--+----11----f------t----j-----+----c--+--_+_ --+---+ Figure 6-29 Level 4, 35

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I' ,o '" a "' '" 90 ISOTHEmlS, PLRtl, Y/H= 0.13813, H= n.ll 200E[;, UJ= llB.oeM/S, JET'; 9,10,l.ll /'S .\J. W : 0.5. ...... ..... ."., ... 0.0 ::, , , 2;0 .. Q .,,', . . : /.0 : : . . . . ; ...... ; ....... : ........ : ..... : k 'T' o . . .. ........ .... .... '" ....... .. . . . . . : : (J.o: : : : 'I : : .. ,. . JET +-------+---1-----+-----+--.--1----+ Figure 6-30 Level 4, 20 .. \? ..... / '\' . . . , ........ ............ ..... .. ,. . : 0,0 : ,

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.. a .. '" a '" '" ," '" a ," ... '" ," '" ., ," ISDfHERt,IS. PlRtI. Y/H= 0.832. H= 15.0 eM. 10 DEG. IJJ= 1!8.0CMlS, .JETS 9,10,&11 .?,o A I : :' ,. .. ...... :....... ...... :....... .... ..: ..... ,.! ....... ....... :. .. .. ': .. .. .. . o /'["''[' \ (),o (): Q.O : ... ... ; ............. ; ...... ... : ........ ; ....... :, ....... : ....................... . .......................................................... .. . ....... ...... i ...... ...... ': .............. : ... .. ... . .. ..... ':.' .... . : 0,0 : : n: ............. .............. : ....... .. .. f .. ) .. : . .. : ...... ....... : ... \J : . . . .. ............... ............. ........... . JET A f5 ....... ---4 Figure 6-31 Level 4, 100 91

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92 6.2.3 Jet Trajectories Each trajectory is one slice out of the three dimensional data array from which the plan views were formed. All profile jet isotherms were computed at the vertical plan downstream of jet number ten. This subsection confines itself to the jet velocity of 48.0 cm/s, or that of full diffuser. Figure 6-32 maps the jet trajectory for 8 0 = 35. The blackened portion in the lower left corner indicates the jet source with high temperature gradients. The jet rises to the surface relatively soon at x/H 4.5. What appears to be a hot spot at x/H 1.6 is an idiosyncracy of the plotting program and the data input. The data value in the third rowt third column registers higher than its neighbors because it is in the direct path of the jet. The program reads this as an isolated temperature rise and closes contours around it. Either a better program, or a data point halfway between row two, column two and row three, column three would resolve this problem. The jet path with 8 = 20 is found in Figure 6-33. This trajectory is o more flattened with the jet finding the water surface at x/H 6.0. The program/data problem is most evident in this plot. With 8 0 = 10 (Figure 6-34) the jet ascends to a depth of y/H 0.4 and levels out. The high temperatures are retained at the lower levels. 6.3 Velocities Current measurements were made at one section two meters downstream of the diffuser for all runs. The data is presented in two manners: the transverse distribution of the vertically averaged values, and profiles averaged over some portion of the width The most prominent distortions of the transverse velocity distribution occurs with the partial diffuser, especially Ld/W = 0.5. It seem logical that the maximum jet velocity, coupled with a partial diffuser, should effect

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O,'j: o 31.0 RELRTIVE LONGITUDINAL DISTANCE. X/H cP 00 0.50 1.00 1.50 2.00 2.50 :3.00 :3.50 q.OO q.50 5.00 5.50 5.00 6.50 7.00 1.50 o o Figure 6-32 Profile, 35 w W

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ISOTHERMS. JET TRRJECTORT. UJ= 4B.OCM!5, H= lY.Y eM. 20 OEG '" o ::oF' me> ,'" :D -l --< ,O'e 0;" me -" -l ::I: ::1:0 '" '" <> 1'3,0 RELATIVE LONGITUDINAL DISTANCE. X/H cPfOO 0.50 1.00 1.50 2.00 2.50 :).00 3.50 5.00 5.50 6.00 6.50 7.00 7.50 I I I I I I I I I I I I I l--l c o Figure 6-33 Profile, 20 \.0 .p.

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130THERI'13, :T TRRJECTORT 48. OCM/S, 1::1 C',._ ;::::: I 1 C1 [IE C; me OJ -; ::c t ::i Co c I 11.$ c c 0.50 RELATIVE LONGITUDINRL DISTRNCE. X/H 1.00 1.50 2.00 2.50 3.00 j.50 5.00 5.50 6.00 I I I I I I I I I I Figure 6-34 Profile, 100 6.50 7.00 7.50 I I I (J1

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96 the ambient discharge per unit width the most. Figure 6-35 is a plot of the nondimensional vertically average velocity, ijY, over the relative width for the three jet angles plus ambient. Jets five through fourteen are active in this figure. The diffuser adds longitudinal momentum to the ambient flow along its length. This action entrains and diminishes the ambient flow to each side of the effluent source while boosting the velocities of the central flow field. For the same jet velocity this distortion should be proportional to the cosine of the angle of discharge. In this way 80 = 10 should effect the ambient distribution slightly more, which is what Figure 6-35 shows. Partial diffusers not tuned to the ambient flow will scour and modify the bathymetries downstream of the point of discharge. Figure 6-36 delineates the velocity profiles for each jet velocity and angle as well as the ambient. For each jet velocity the profile is averaged over the center half of the centermost partial diffuser. The plots indicate excess velocities near the bed for 8 = 10, especially when U. = 91.2 cm/s. o J The warped profile for 80 = 35 is probably due to the surface impingement which was noticed during the experimental run. The same is true for 80 = 20 at U j = 91.2 cm/s. Obviously, a high discharge angle will not completely eliminate scouring at some points downstream of the diffuser.

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1.4 1.3 1.2 1.1 1.0 -y U 9 U .8 .7 .6 .5 .4 .3 .1 z/w .5 -----0o = 350 0 ---0--= 200 ......... ;6: ....... = 100 -tt--ambient Jet Loca tions .6 .7 '. .... '. .... '" ...... ...... \ '. 'a. \ Figure 6-35 Transverse Discharge Distribution 1.0

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10 I I I. I 1\ 9 t-\,Z f if! at"'" i ,.; ..... /, \ .. ,: I, 7 ti I ,i J ,: I I / I j/ I : I L :/ I H j/j u.=91.2 cm/s I I ;1... U.= 48 cm/s 5 IV.. J I: TJ I I ,'.y J I,...... : ... \1 I \ 4 \ ..... I ... J I .... I... I 4 r "\. i if, I: I' : I, 3 /', ... \ } 1 \ : .. 2 t"'" !rv' / .... .. / .i9 .' I I / / / / .,'" ./'" ./ I o I 1.2 U/O 1.0 Symbols: 1.1 1.2 1.0 1.1 1.2 I. 0 1.1 ---0--9 = 200 .... ,6, .... 9 = 100 --0-ambient -0-90=350 0' 0' Figure 6-36 Average Velocity Profiles lD 00

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7.1 Jet Angle CHAPTER VII CONCLUSIONS The best mixing for large distances downstream of the diffuser happens with a jet angle of 10. This is true since, at 8 0 = 10, buoyancy of the effluent works with the mixing process to transport the heat from the bottom to the water surface. However, there are three major drawbacks to this setting, all arising out of the jet attachment to the bed: 1) excessive bed scour, 2) prolonged exposure of the benthic organisms to the heated effluent, and 3) poor initial mixing. These are rather high prices to pay for good dilution over a long reach. With 8 0 = 35 the initial mixing is good since this angle puts the effluent into the more turbulent zone of the flow field. The surface impingement noticed with this setting will probably upset channel navigation. The most promising angle is that of 20. The initial mixing is nearly of as much value as that for 8 0 = 35. Also, after a moderate distance the dispersion properties for this setting are better than that of 35. 7.2 Port Spacing No jet interference was observed in the plan isotherms for any of the runs. A decreased port spacing would give some lateral jet merging and

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100 perhaps a better initial dilution. Inspection of the plan views indicates that a reduction in L to three-quarters the present value might yield the proper amount of round jet interference. 7.3 Partial Diffuser For the same quantity of heat to be injected into the ambient it has been shown in Figures 6-1, 6-2, and 6-3 that partial diffusers perform much less efficiently than the full. It has been shown that for Ld/W = 0.5 more than one diffuser end greatly enhances mixing. It was concluded that for this diffuser length transverse dispersion is as important a parameter as V/k and aFj. Figure 6-35 indicates a dangerously distorted velocity distribution, typical of one generated by a partial diffuser. ,This diffuser pump effect would tend to channelize the ambient flow resulting in erosion/deposition problems. To reduce the distorted ambient velocity distribution it would be necessary to decrease the momentum input and thus U j This, however, is contrary to the idea of good mixing. The optimal design is to match the diffuser discharge distribution to that of the ambient.

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APPENDIX A REGULATIONS

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102 Exerpt from the Florida Administrative Code, Chapter 17-3 relating to the discharge of heated effluents into the waters of Florida. 17-3.05 Water quality standards; specifics. (3) All discharges or proposed discharges of heated water into receiving bodies of water (RBW) which are controlled by the state shall be subjected to a thorough study to assess the consequences of the discharge upon the environment. The state shall be divided into two general climatological zones: Peninsular Florida, which varies from tropical in nature to temperature but is modified by the peninsular configuration and is the area south of latitude 300N (excluding Gulf and Franklin Counties); and Northern Florida which is temperate and continental and is the area above latitude 300N plus the portions of Gulf and Franklin Counties which lie below 30oN. (a) Heated water discharges existing on July 1, 1972: 1. Shall not increase the temperature of the RBW so as to cause substantial damage or harm to the aquatic life or vegetation therein or interfere with beneficial uses assigned to the RBW. 2. Shall be monitored by the discharged to ensure compliance with this rule, and 3. If the Department, pursuant to notice and opportunity for hearing, finds by preponderant evidence that a discharge has caused substantial damage, it may require conversion of such discharge to offstream cooling or approved alternate methods. In making determinations regarding such conversions, the Department may consider: a. The nature and extent of the existing damage; b. The projected lifetime of the existing discharge; c. Any adverse economic and environmental (including nonwater quality) impacts which would result from such conversion; and d. Suchotl1er factors as may be appropriate. (b) Heated water sources proposed for future discharges into RBW controlled by the state shall not increase the water temperature by more than the monthly temperature limits prescribed for the particular type and location of the RBW. New sources shall include all expansions, modifications, alternations, replacements, or repairs which result in an increased output of ten percent (10%) or more of the level of energy production which existed on the date this rule became effective. Water temperatures shall be measured by procedures approved by the Florida Department of Pollution Control (DPC). In all cases where a temperature rise above ambient is prescribed, the lower of the two limitations shall be the control temperature. (c) Definitions. (i) Ambient (natural) temperature of a RBW is the existing temperature of the receiving water at a location which is unaffected by man-made thermal discharges and a location which is also of a depth and exposure to wind and currents which typify the most environmentally stable portions of the RBW. (ii) Coastal waters shall be all waters in the state which are not classified as fresh waters or as open waters. (iii) A cooling pond is a body of water enclosed by natural or constructed restraints which has been approved by the Florida DPC for purposes of controlling heat dissipation from thermal discharges.

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10J (iv) An existing heat source is any thermal discharge (a) which is presently taking place, or (b) which is under construction or for which a construction or operating permit has been issued prior to the effective data of this rule. (v) Fresh waters shall be all waters of the state which are contained in lakes and ponds, or are in flowing streams above the zone in which tidal actions influence the salinity of the water and where the concentration of chloride ions is normally less than 1500 mg/l (vi) Open waters shall be all waters in the state extending seaward from the most seaward 18-foot depth contour line (threefathom bottom depth contour) which is offshore from any island; exposed or submerged bar or reef; or mouth of any embayment or estuary whi ch is narrowed by headl ands. Contour 1 i nes sha 11 be determined from Coast and Geodetic Survey Charts. (vii) The point of discharge (POD) for a heated water discharge shall be primarily that point at which the effluent physically leaves its carrying conduit (open or closed), and discharges into the waters of the state, or, in the event it is not practicable to measure temperature at the end of the discharge conduit, a specific point designated by the Florida Department of Pollution Control for that particular thermal discharge (viii) Heated water discharges are the effluents from commercial or industrial activities or processes in which water is used for the purpose of transporting waste heat, and which constitute heat sources of one million British Thermal Units per hour (1,000,000 BTU/HR.), or greater. (ix) Blowdown shall mean the minimum discharge of recirculating cooling water for the purpose of discharging materials contained in the water, the further buildup of which could cause concentrations in amounts exceedi ng 1 imits established by best engi neeri ng practi ce. (x) Recirculating cooling water shall mean (d) Mohthly and Maximum Temperature Limits (i) Fresh Waters -Heated water. with a temperature at the POD more than 5F higher than the ambient (natural) temperature of any:. stream shall not be discharged into such stream. At all times under all conditions of stream flow the discharge temperature shall be controlled so that at least two-thirds (2/3) of the width of the stream's remains at ambient (natural) temperature. Further, no more than one-fourth (1/4) of the cross-section of the stream at a transverse perpendicular to the flow shall be heated by the discharge. Heated water with a temperature at the POD more than 3F higher than the ambient (natural) temperature of any lake or reservoir shall not be discharged into any fresh waters in Northern Florida regardless of the ambient temperature of the RBW. In Peninsular Florida, heated waters above 92F shall not be discharged into fresh waters. (ii) Coastal Waters -Heated water with a temperature at the POD more than 2F higher than the ambient (natural) temperature of the RBW shall not be discharged into coastal waters in any zone during the months of June, July, August, and September. During the remainder of year, heated water with a temperature at the POD more than 4F higher than the ambient (natural) temperature of the RBW shall not be discharged into coastal waters in any zone. In addition, during June,

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104 July,August, and September, no heated water with a temperature above 92F shall be discharged into coastal waters. Further, no heated water with a temperature above 90F shall be discharged into coastal waters during the period of October thru May. (iii) Open Waters Heated water with a temperature at the POD up to 17F above ambient (natural) temperature of the RBW may be discharged from an open or closed conduit into open waters under the following restraints: The surface temperature of the RBW shall not be raised to more than 97F and the POD must be sufficient distance offshore to ensure that the adjacent coastal waters are not heated beyond the temperatures permitted in such waters. (iv) Cooling Ponds The temperature for heated water discharged from a cooling pond shall be measured at the POD from the pond, and the temperature limitation shall be that specified for the RBW. (e) General. (i) Daily seasonal temperature variations that were normal to the RBW before the addition of heat from other than natural causes shall be maintained. (ii) Recapitulation of temperature limitations prescribed above: ZONE LAKES COASTAL OPEN REMAINDER NORTH 90F Max. 90F 92F Max. 90F Max. 97F Max. AM. +5F 3F. AM. +2F AM. + 4F AM. +17F PENIN. 92F Max. 92F Max. 92F Max. 90F Max. 9]oF Max. AM. +5F AM. +3F AM. +2F +4 of AM. +17F (f) Upon application on a case by case basis, the Department may establish a zone of mixing beyond the POD to afford a reasonable opportunity for dilution and mixture of heated water discharges with the RBW, in the following manner: (i) Zones of mixing for thermal discharges from non-Tecjrculated cool i ng water systems and process water systems of new sources shall be allowed if supported by a demonstration, as provided in section 316(a), Public Law 92-500 and regulations promulgated thereunder, including 40 C.F.R. Part 122, by an applicant that the proposed mixing zone will assure the protection and propagation of a balanced, indigenous population of shell fish, fish, and wildlife in and on the body of water into which the discharge is to be made and such demonstration has not been rebutted. It is the intent of the board that to the extent practicable, proceedings under this provision should be conducted jointly with proceedings before the federal government under section 316(a), Public Law 92-500. (ii) Zones of mixing for blowdown discharges from recirculated cooling water systems, and for discharges from non-recirculated cooling water systems of existing sources, shall be established on the basi's of the physical and biological characteristics of the RBW.

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105 (iii) When a zone of mixing is established pursuant to this subsection 17-3.05(3)(f), Florida Administrative Code, any otherwise applicable temperature limitations contained in section 17-3.05(3), Florida Administrative Code shall be met at its boundary; however, the Department may also establish maximum numerical temperature limits to be measured at the POD and to be used in lieu of the general temperature limits in section 17-3.05(3), Florida Administrative Code, to determine compliance by the discharge with the established mixing zone and the temperature limits in section Florida Administrative Code.

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APPENDIX B

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Novonic-Nixon Velocity Meter Calibration 0: 1 dk 2 1: fmt 1 ,c16 2: fmt 0,c2,f6.2,c4 3: ent X 4: dim A$[16], T[2] N[2], "M[2] 5: wtb 2,21,1,2,17,18 6: 'I/tc 2,0 7: IIfirstll: red 2.1, A$; prt A$ 8: val(A$[I,4}rN[lJ; val(A$[10J)+T[lJ 9: gto 27 10: IIsecondll: red 2.1, A$; prt A$ 11: val (A$[ I,4 J )+N[ 2J; val (A$[ 6, 9J 2J; val (A$[ 1 OJ )+T[ 2J 12: (T[ 2J-T[ 1] )/6+T 13: (N[ 2J-N[ 1] )/T+N; (M[ 2J 1]) 14: X*30. 48/T +V 15: wrt 16,IIT=II,T,lIsecll; wrt 16,IIN=II,N, IIHzlI; wrt 16: wrt 16,IIV=II,V,lIcm/sll 17: wtb 2,1,2,17,18 18: spc 19: if M<16.2;.537473M + 2.035552+B 20: if N<13;.650525N + 2.269538+A 21: If M>16.2;.538173M + 2.137244+B 22: If N>13;.640911N + 2.532485+A 23: (A-V )*1 OO/V+E; (B-V )*1 OOV+F 24: wrt 16,IIE=II,E,II%I1; wrt 16,IIF=II.F,II%1I 25: spc 26: stp 27: end *19633 Comments: The keys are stored as: fO: cont 7 fl: cont 10 The following variables are defined as: x = distance in feet over which the calibration occurs A$ = string variable from pink box containing the raw data Ti = first and last raw times (1/6 sec) N. = first and last counts for probe 401 107

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M. = first and last counts for probe 403 T = time in seconds to travel distance x N = frequency of probe 401 (Hz) M = frequency of probe 403 (Hz) V = true velocity in cm/s A = calculated velocity from previous calibration curve for probe 401 B = calculated velocity from previous calibration curve for probe 403 E = percent error for probe 401 F = percent error for probe 403 108

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109 Least Squares With Percent Error For Velocity Meter Calibration 0: IIPart I: Least Squares Program; Y vs x, Y vs Z; M = No. of Points": 1: fxd 6 2: ent 3: dim X[M], Z[M], Y[M], V[M], E[M], F[M] 4: 5: N + 6: ent X[N], Z[N], yeN] 7: rO + Y[ rl + X[ N] Y[ r2 + r3 + X[ r4 + 8: r5 + ZeN] r6 + r7 + 9: if N
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Definitation of variables: v .. = measured velocity in cm/s 1 ,J N. = first and last counts for probe 401 1 M. = first and last counts for probe 403 1 T. = first and last raw times (1/6 sec) 1 A$ = string variable from pink box containing raw data T = averaging time P = column loop counter S = raw loop counter I,R = dummy counters N = frequency of probe 401 (Hz) = frequency of probe 403 (Hz) F = file on which velocities are recorded 112

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Temperatures at a Section ,0: ent R,I 1: dim C[ R 14 J, A$[ 16 J, Q[ 1 4 J, O[ 14], S[ l!4 J 2: 2.24590155e-19+r6 3: -3.2385192478e-15+r5 4: 1.9163714546e-ll+r4 5: -6.0364045705e-8+r3 6: 1. 10839151 02e-4+r2 7: 8: 1.0594497153-e2+rO 9: fmt 0,c5,f2.0,cl,f2.0,c2 10: fmt 1.f6.0c7 11 : fmt 2, c 16 12: fmt 3,c5,f7.3,cl 13: fmt 4,c2,f2.0,c4,f8.4 14: fmt 5,c2,f2.0,c4,f8.4 113 15: 0194+S[ 1 J; -. 0009+S[ 2J;. 0082+S[ 3J ; -. 0595+S[ 4J; -. 0345+S[ 5J ; -. 0814+S[ 6J 16: 0443+S[ 7J ; -. 0217+S[ 8J ; -. 0188+S[ 9]-. 0222+S[ 1 OJ; 0297+S[ 11 ] ; 04lG5+S[ 12J 17: -. 0325+S[ 13J ; .21 03+S[ 14 J 18: O+N 19: N+ l+N 20: ent P 21: 1+f'.1 22: 23: if (M+l-tM)<15; jmp-l 24: wrt 16.1, I, IIpoi nts II; spc 25: wtb 2,37;wtb 2,6;wtc 2,0; wtb 2,248 26: O+L 27: red 2.2,A$; va1(A$[10J)/6+r7 28: L+l+L; O-+M 29: 247-16M+J 30: O+K 31: wtb 2,J 32: red 2.2, A$ 33: l+K+K 34: ifK=1;gto32 35: M+ 36 val (A$[1,4J)+0[M] 37: if M<14; gto 29 38: O .. 39 : 40 :fO'tctO MOM 41 0 M 42: 5-0 MOM 43: (e.8""Q.M,}*294.120M 44: rO+rl *O[ MJ+r2*0[ MJ+4+r5*0[ r"lJ+5+6*0[ rJf6 +C[ N,MJ

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45: C[N,M]+Q[M]+Q[M] 46: if M<14; gto 39 47: if L 7; 9 to 47 68: if 1>6; gto 42 69: gto 33 *1489

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Jet Trajectory 31: ent U,r1,H,F,D; 1df F,T[*]; 1-+1; l-+N;3-+A; 10+B 32: l-+G; 0+0; .5-+P; 5-+Q; 15-+S; fmt 1,2f5.0,7f10.3; fmt 2,7f10.3,2f5.0 33: if 1=1; II JET TRAJECTORY, Uj="-+A$[ 1 ,32]; str(U )-+A$[ 33,37] 34: if 1=1; "cm/s ,H="-+A$[ 38,45]; str(H)-+A$[ 46",50J; "cm"-+A$[ 51 ,54J 120 35: if 1=1; str(D )-+A$[ 55 ,57]; II DEG"-+A$[ 58,61]; IIII-+A$[ 62,76] 36: if 1=2; "RELATIVE DEPTH, Y/H"-+A$[1,19J; III1-+A$[20,77]; str(-19)-+A$[78,80J 37: if 1=3; "RELATIVE LONGITUDINAL DISTANCE, X/W-+A$[l ,35J; 111I-+A$[36,77] 38: if 1=3; str(3B+Q)-+A$[78,80J 39: if 1=6; str(3.2/H)-+A$[1,10]; str(6.4/H)-+A$[11 ,20]; str(9.6/H)-+A$[21 ,30] 40: if 1=6; str(12.8/H)-+A$[31,40] 41: gto 54 42: l-+R 43: (r1+10(J-1))/9.5H*S)-+Y 44: str(Y)-+A$[(R-1)*10+1,R*10] 45: if (J+1-+J)<12; if (R+1-+R)<9; gto 43 46: gto 54 47: 2-+J; O-+R 48: str(T[N,J])-+A$[l+10*R,(R+1 )*10] 49: if (R+1-+R)<8; if (J+1-+J)<13; gto 48 50: gto 54 51: if (J+1-+J)<13; O-+R; gto 48 52: if (N+1-+N)<5; gto 47 53: gto 10 54: if f1g 4; gto 56 55: gto 54 56: cfg 4; dsp I 57: if 1=4; wrt 10.1,A,B,OG,OG,.544G,.57G,0,P,2S; wrt 10,13;5-+1; gto 54 58: if 1=5; wrt 10.2,Q,S,G,0,-.2G,P,5G,0,0; wrt 10,13; 6-+1; gto 39 59: wrt 10,A$; wrt 10,13; III1-+A$; if (I+1-+I; gto 51 60: if 1=9; gto 47 61: if 1=7; 1-+J 62: if 1>6; gto 42 63: if 1<7; gto 33 *11304

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121 Definition of Variables Common to All Three Isotherm Programs: H = depth of flow (cm) F = file number on which nondimensional data is stored (HP cassette) D = discharge angle in degrees T = data array n,r I = line counter N = row of data array and loop counter A = number of rows-1 B = number of columns -1 G = 1: All parameters are sent as some function of an alphanumeric character. G is the unity multiple of many parameters. The IIwrt 10.211 statement requires alphanumerics. o = 0 (see G) P = increment between contours Q = length of vertical (X) axis before reduction S = length of horizontal (Y) axis before reduction V = location of data columns along the Y-axis before reduction J = column of data array and loop counter R = loop counter so as not to exceed eight data points per line Definition of Variables Cross Section: X = distance from diffuser to section (cm) B$ = discharging jets, e.g. 111-10, 15-1911 r3 = diffuser configuration parameter for positioning the jet locations symbols on plot = 1 for B$ = 1-19 = 2 for B$ = 1-10, 15-19

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r3 = 3 for B$ = 5-19 = 4 for B$ = 1-5, 10-14 = 5 for B$ = 1-5, 15-19 = 6 for B$ = 5-14 = 7 for B$ = 10-19 W = i niti a 1 column value E = adjustment for jet location symbols starting value M = increment between jet location symbols Definition of Variables Plan: rl = longitudinal distance from diffuser to first data row (cm) Y = distance from bed to plain of plan view (cm) U = jet velocity (cm/s) Q = S in this case Definition of Variables -Jet Trajectory rl = longitudinal distance to first data column U = jet velocity (cm/s) 122

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23 AUGUST 1978 LISTING OF CONTOUR C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C THIS IS A SPECIAL PROGRAM TO READ AND PLOT VELOCITY CONTOURS. OF THE IOWA CONTOUR SUBROUTINE. R. MCCURDY MARCH 23, 1976 A JET LOCATION STARTING VALUE AM DATA MATRIX TO BE CONTOURED AY LOCATION FOR FIRST STAR IN FIRST GROUP B JET LOCATION INCREMENT BY LOCATION FOR FIRST STAR IN SECOND GROUP BNDRY VECTOR OF DIRECTIONS ON BOUNDARY CLO STARTING CONTOUR LEVEL CLl HIGHEST CONTOUR LEVEL DEL CONTOUR INCREMENT FACT FACTOR TO SCALE SIZE OF PLOT IQ LOCATES Y AXIS, NAME, AND JET LOCATIONS IQ=O TRAJECTORY IQ=l PLAN AND SECTION IT PLOT LINE TYPE: IT=l CONTINUOUS LINE IT=2 DASHED LINE LINE LENGTHS) IT=-1,-2 SUPERPOSITION ON PREVIOUS PLOT IXS STARTING X-LOCATION OF BOUNDARY IYS STARTING Y-LOCATION OF BOUNDARY IZ TYPE OF STAR LINE NL NUMBER OF LINKS ON BOUNDARY, = NUMBER OF CELLS AROUND EDGES OF DATA MATRIX NS NUMBER OF SIDES NSA NUMBER OF STARS IN FIRST GROUP FOR TYPE (IZ) NSB NUMBER OF STARS IN SECOND GROUP FOR TYPE (IZ) QIQ X-LOCATION OF FIGURE NAME SCX X-AXIS SCALE FACTOR, L IN PLOT j L IN PROTOTYPE SCY Y-AXIS SCALE FACTOR, L IN PLOT j L IN PROTOTYPE TH NUMBER OF DEGREES BETWEEN AXES, 10
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c DIMENSION DIMENSION AY(7),BY(7),NSA(7),NSB(7)

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23 AUGUST 1978 LISTING OF CONTuuR DATA AY(1),AY(2),AY(4),AY(S)/4*0.OSO/,AY(3),AY(6)/2*O.2S0/ 1 AY(7)/O.SOO/ DATA BY(1),BY(3),BY(6),BY(7)/4*0.0/,BY(2),BY(S)/2*0.7S0/, 1 BY(4)/0.SOO/ DATA NSA(l )/T9/ ,NSA(2) ,NSA(6) ,NSA(7)/3*10/ ,NSA(3)/lS/ ,NSA(4), 1 NSA(S)/2*S/ DATA NSB(l),NSB(3),NSB(6),NSB(7)/4*0/,NSB(2),NSB(4),NSB(S)/3*S/ INTEGER BBC,BBI,BBF,BNDRY(300) SOl FORMAT (19A4) S02 FORMAT (2IS,2Fl0.4,SF10.0) S03 FORMAT (8Fl0.3) 505 FORMAT (7Fl0.3,2I5) 551 FORMAT (18A4, 18) 600 FORMAT (lHl,19X,19A4//) 601 (lHO,'PARAMETERS:"/1H, 'M=',I3,', N=',I3,', NS=',I3,', NL=' 1,I3/1H ,'IT=',I3,', TH=',F5.1,', SCX=',F5.3,', SCY=',F5.3/1H 2 I CLO=',F5.1,', DEL=',F5.1,', CLl=',F5.1,', A=',F6.4,', B=',F6.4) 602 FORMAT (lHO,'X GRIDLINES:"/(lH ,8F8.3) 603 (1 HO, 1 BOUNDARY LINKS FROM ORIGIN COUNTERCLOCKWISE: 1 ) 605 FORMAT (lHO,'BBI= 1,13,1, BBF= 1,13,1, NN= ',I2/(lH ,815)) 606 FORMAT (lH ,8Fl0.3) 607 FORMAT (lHO,'Y GRID LINES:' /(lH, 8F8.2) 608 FORMAT (lHO,'DATA MATRIX: I) 609 FORMAT (lH 'XLN=' ,F5.1, I, YLN=' ,F5.1, I, SVX=I ,F5.1, I, SVY=I, 1 F5.1/1H ,'XIN=',F5.1,', YIN=',F5.2,5X,' CLN=',F5.2,' IZ=',I2, 2 1 IQ= 1 ,12) 1 READ (5,501,END=9999) NAME WRITE (6,600) NAME READ (5,551) XLABL,LX,YLABL,LY READ (5,502) M,N,A,B,SCX,SCY,CLO,DEL,CLl NL=M+M+N+N IT=l TH=90. NS=4 WRITE (6,601) M,N,NS,NL,IT,TH,SCX,SCY,CLO,DEL,CL1,A,B READ (5,505) XLN,YLN,SVX,SVY,XIN,YIN,CLN,IZ,IQ WRITE (6,609)vXLN,YLN,SVX,SVY,XIN,YIN,CLN,IZ,IQ MP=M+l NP=N+l READ (5,503) (XGL(I),I=l,MP) READ (5,503( (YGL(I),I=l,NP) WRITE (6,602) (XGL(I),I=l,MP) WRITE (6,607) (YGL(*),I=l,NP) WRITE (6,603) BBC=-2 N (J"I

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BBF=O DO 8 J=l,NS BBC=BBC+2 ...... N 0'\

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23 AUGUST 1978 LISTING OF CONTOUR BBI=BBF+1 IF (J,EQ.l) BBF=M IF (J.EQ.2) BBF=M+N IF (J.EQ.3) BBF=M+M+N IF (J. EQ. 4) -BB 1+1 DO 7 I=BBI,BBF 7 BNDRY (I)=BBC 8 WRITE (6,605) BBI,BBF,NN,(BNDRY)I),I=BBI,BBF) 9 DO 1 1=1, MP 10 READ (5,503) (Afl1(I ,J) ,J=l ,NP) (6,608) DO 15 1=1 15 WRITE (6,606)(AM(I,J),J=1,NP) 999 IXS=l IYS=l XZA=XLN XJL=-0.6 XAR=-0.3 IYLN=YLN XJTB=0.05 XJTE=-0.05 XJ=XLN QIQ=O.O IF (IQ.EQ.l) XZA=O IF (IQ.EQ.l) XJL=XLN-0.4 IF (IQ.EQ.l) XAR=XLN-0.2 IF (IQ.EQ.l) XJTB=XLN+0.05 IF (IQ.EQ.l) XJTE=XLN-0.05 IF (IQ. EQ.l) QIQ=-l. CALL PLOTS (CLN, 21 0,2,2. ,1 ) CALL FACTOR (SCX,SCY) CALL SYMBOL (QIQ,0.,0.15,NAME,90.,76) CALL AXIS (O.,O.,XLABL,LX,XLN,O.,SVX,XIN) CALL AXIS (XZA,0.,YLABL,LY,YLN,90.,SVY,YIN) DO 700 1=1 700 XGL(I)=(l.-XGL(I))*XLN DO 701 1=1 ,NP 701 YGL(I)=YGL(I)*YLN 1=1 J=l CALL PLOT (XGL(I),YGL(J),3) DO 801 K=l ,NL L=BNDRY(K) IF (L.EQ.0.OR.L.EQ.l.0R.L.EQ.7) 1=1+1 N -.....J

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IF (L.EQ.3.0R.L.EQ.5.0R.L.EQ.5) 1=1-1 IF (L.EQ.1.0R.L.EQ.2.0R.L.EQ.3) J=J+1 IF (L.EQ.5.0R.L.EQ.6.0R.L.EQ.7) J=J-l

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23 AUGUST 1978 801 CALL PLOT (XGL(*),YGL(J),2) CALL LINEWT (3) DO 101 J=2,NP CALL PLOT (XGL(1),YGL(J),3) 101 CALL PLOT (XGL(MP),YGL(J),2) DO 102 I=2,MP CALL PLOT (XGL(I),YGL(1),3) 102 CALL PLOT (XGL(I),YGL(NP),2) IF (IZ.EQ.O) GO TO 200 e DRAW TICK MARKS CALL LINEWT (0) CALL PLOT (XJ,0.,3) CALL PLOT (XJ,YLN,2) Y1=YLN DO 11 0 1=1, IYLN CALL PLOT (XJTB,Y1,3) CALL PLOT (XJTE,Y1,2) 110 Y1=Y1-1.0 C LOCATE JETS YP=(AY(IZ)+A) *YLN LISTING OF CONTOUR CALL SYMBOL (XAR,YP,.15,2,90.,-1) NN-NSA (IZ)-l DO 120 I=l,NN YP=YP+B*YLN 120 CALL SYMBOL (XAR,YP,.15,2,90.,-1) IF (NSB(IZ).EQ.O) GO TO 140 YP=(BY(IZ)+A)*YLN CALL SYMBOL (XAR,YP,.15.2,90.,-1) NN=NSB(IZ)-l DO 130 I=l,NN YP=YP+B*YLN 130 CALL SYMBOL (XAR,YP,.15,2,90.,-1) 140 Y3=YLN/2.-1. CALL SYMBOL (XJL,Y3,.15,'JET LOCATIONS' ,90.,13) 200 CALL LINEWT (-1) CALL CONTUR (AM,M,N,CLO,DEL,CL1,IT,TH,XGL,YGL,BNDRY,IXS,IYS,NL) CALL FACTOR (1.,1.) CALL PLOT (0 .. 0.,999) GO TO 1 9999 STOP END N 1.0

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23 AUGUST 1978 LISTING OF CONOUR SUBROUTINE CONTUR(AM ,CLO ,DEL ,CL 1, IT, TH ,XGL, YGL ,BNDRY ,IXS, lIYS,NL) INTEGERBNDRY (300) DH1ENSION AIV1(50,50) ,XGL(50), YGL(50) C 00025 C THIS IS TO PREVENT CLO FROM BEING CHANGED IN t,1AIN PROGRAM CLO=CLO IZX=O 00026 C GENERATE REGION MAP REG 00027 CALL GRM(BNDRY IXS, IYS ,NL 1 ,N+ 1) 00028 10 IF (IT) 60,90,15 00029 C NORMAL CONTOUR IF IT>O 00030 C CHECK FOR BOUNDS ON THETA 00031 15 THE=TH*3.141593/180. 00032 IF(TH-l0.)89,22,22 00033 22 IF(TH-170.)24,24,89 00034 24 IF(TH-90.)28,28,26 00035 C MOVE ORIGIN OF PLOT IF TH>90 00036 26 YMOVE=-COS(THE)*YGL(N+1) 00037 CALL PLOT(YMOVE,0.0,-3) 00038 GO to 60 00039 28 CONTINUE 00040 60 D=IABS(IT)-l 00041 C 00042 62 CAL SCAN (AM ,rH 1 N+ 1 ,CLO, D ,XGL THE, YGL IZX ,BNDRY IXS, I YS ,NL) 00043 C 00044 64 CLO=CLO+DEL 00045 C CONTINUE IF NEXT COUTOUR LEVEL LESS THAN CLl 00046 IF (CLO-CL1) 62,62,90 00047 89 WRITE (6,91)TH 00048 C STOP PROGRAM IF TH OUT OF BOUNDS 00049 90 RETURN 00050 91 FORMAT(' THETA BAD' ,F8.3) 00051 END 00052 w o

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23 AUGUST 1978 LISTING OF CONTOUR C SUBROUTINE SCAN (AM,M,N,CL,D,XGL,TH,YGL,IZX,BNDRY,IXSA, 1 IYSA,NLS) INTEGER BNDRY (300) LOGICAL*l REG(83,83) DIMENSION AM(50,50,IRC(1200),X(1600,Y(1600) DIMENSION DIMENSION IPT(3,3),INX(8),lNY(8) COMMON ,NT ,IX,IY ,IDX,IDY ,ISS,IT ,NP,NQ,JT, lPY,IRC,CV,X,Y,IPT,INX,INY,DL,THE,IXS,IYS,NL,REG C INITIALIZE THE COMMON BLOCK VARIABLES C C NP=O DL=D THE=TH NT=N CV=CL IXS=IXSA IYS=IYSA NL=NLS C SKIP IF IZX NOT 0 (IE FIRST TIME THROUGH) C I F (I ZX ) 3 1 ,3 C SET UP THE INCREMENTAL ELEMENT USED BY CONTOURING ROUTINES C (THIS IS NOT THE SAME AS USED FOR BNDRY 1 I PT (1 1) =8 IPT(l,2)=1 IPT(1,3)=2 IPT(2,1)=7 IPT(2,3)=3 IPT(3,1)=6 IPT(3,2)=5 IPT(3,3)=4 IZX=2 103 INX(l)=-l INX(2)=::.1 INX(3)=0 INX(4)=1 INX(5)=1 INX (6 )=1 INX(7)=O 00053 00054 00056 00059 00060 00061 00062 00063 00064 00065 00066 00067 00068 00069 00070 00071 00072 00073 00074 00075 00076 00077 00078 00079 00080 00081 00082 00083 00084 00085 00086 00087 00088 00089 --' 00090 w --' 00091 00092 00093 00094 00095 J

PAGE 151

INX(8)=-1 INY(l)=O INY(2)=1 INY(3)=1 INY(4)=1 00096 00097 00098 00099 00100 --I W N

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23 AUGUST 1978 LISTING OF CONTOUR INY(5)=0 00101 INY(6)=-1 00102 INY(7)=-l 00T03 INY(8)=-1 00104 3 CONTINUE 00105 C INITIALIZE CONTOUR MEMORY 00106 DO 58 J=1,800 00107 58 IRC(J)=O 00108 ISS=O 00109 C INITIALIZE X Y WITH FIRST POINT OF BOUNDARY 00110 2 IL=l 00111 IXL=IXS 00112 IYL=IYS 00113 C 00114 C SEARCH BOUNDARY FOR CONTOUR CROSSINGS 00115 C USE NEXT LINK OF BOUNDARY 00116 C 00117 51 00118 IYL1=IYL+INY(1+BNDRY(IL) 00119 C CHECK FOR CONTOUR CROSSING LINK UNDER STUDY 00120 IF (AM(IXL,IYL)-CV) 55,30,30 00121 55 IF (AM(IXL1,IYL1)-CV) 30,56,56 00122 C CONTOUR FOUND TO CROSS LINK 00123 56 IX=IXLl 00124 IY=IYLl 00125 IDX=INX(l+BNDRY(IL)) 00126 IDY=-INY(l+BNDRY(IL)) 00127 C THE CONTOUR THAT HAS BEEN FOUND 00128 CALL TRACE(AM,X6L,Y6L,BNDRY) 00129 30 IL=IL+l 00130 C CONTINUE SEARCH ON BOUNDARY UNTIL ALL LINKS HAVE BEEN TESTED 00131 IF (IL.GT.NL) GQ TO 40 00132 IXL=IXLl 00133 IYL=IYLl 00134 GO TO 51 00135 C 00136 C INTERIOR SEARCH BEGINS 00137 ...... C 00138 w w 40 CONTINUE 00139 ISS=l 00140 DO 20 I =3 00141 DO 10 J=3,NT 00142

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C USE REGION MAP TO SEARCH ONLY INTERIOR POINTS IF (REG(I+1,J).AND .. NOT.REG(I+2,J).OR .. NOT.REG(I,J)) GO TO 10 IF (.NOT.REG(I+1,J).AND .. NOT.REG(I+2,J)) GO TO 10 IF (AM(I-1,J-l)-CV) 5,10,10 5 IF (AM(I,J=l)-CV) 10,7,7 7 CONTINUE 00143 00144 00145 00146 00147 00148 w ..j:::>

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23 AUGUST 1978 LISTING OF CONTOUR C CONTOUR CROSSING HAS BEEN FOUND ICM=l 00*(1 )+J-l IF(NP) 12,11,12 C CHECK TO AVOID REPEATING CONTOUR 12 DO 9 10=1, NP IF (IRC(ID).EQ.ICM) GOT TO 10 9 CONTINUE C C NEW CONTOUR CROSSING HAS BEEN FOUND C 11 IX=I IY=J-l IDX=-l IDY=O CALL TRACE (AM,XGL,YGL,BNDRY) 10 CONTINUE 20 CONTINUE 60 RETURN END 00149 00150 00151 00152 00153 00154 00155 00156 00157 00158 00159 00160 00161 00162 00163 00164 00165 00166 00167 ....... W 01

PAGE 155

23 AUGUST 1978 LISTING OF CONTOUR C SUBROUTINE TRACE (AM,XGL,YGL,BNDRY) INTEGER BNDRY (300) LOGICAL*l REG(83,83) DIMENSION AM(50,50),IRC(1200),X(1600),Y(1600) DIMENSION XGL(50),YGL(50) DIMENSION IPT(3,3),INX(8),INY(8) COMMON /PLT/MT,NT,IX,IY,IDX,IDY,ISS,IT,NP,N,JT, 1 PY,IRC,CV,X,Y,IPT,INX,INY,DL,THE,IXS,IYS,NL,REG C THIS SUBROUTINE FOLLOWS A CONTOUR FROM IT INITIAL DISCOVERY POINT C PY=O.o RS=SIN(THE) RC=COS (THE) 501 JT=O N=O XM=MT -1 XT=NT-l IXO=IX IYO=IY ISX=IDX+2 ISY=IDY+2 IS=IPT( ISX, 1SY) JTB=O ISC=1S IF (ISO-8) 18,18,17 17 ISO=ISO-8 18 IT=O 5 CALL CALC (AM) IF (IT+JT-l)49,49,47 47 XS=X(N-l) YS=Y(N-l) X(N-l)=X(N) Y(N-l)=Y(N) X(N)=XS Y(N)=YS 49 1S=IS+l JT=IT 9 IF (IS-9)8,7,7 7 IS=1S-8 8 IDX=INX (IS) 00168 00170 00172 00]74 00175 00176 00177 00178 00179 00180 00181 00182 00183 00184 00185 00186 00187 00188 00189 00190 00191 00192 00193 00194 00195 00196 00197 00198 00199 00200 00201 00202 00203 00204 --' w 00205 0"'1 00206 00207 00208

PAGE 156

ISY=INY(IS) IX2=IX+IOX IY2=IY+IDY JTB=JTB+1 IF (JTB-1600)51,51,308 308 WRITE (6,103) CV,X(N),Y(N) 1 03 (1 HO, I CONTOUR LINE AT LEVEL ", F4. 1 I 00209 00210 00211 00212 00213 00214 WAS TERMINATED AT X=I ,00215 W '-l

PAGE 157

23 AUGUST 1978 LISTING OF CONTOUR lF3.1,' Y=I ,F3.1,'BECAUSE IT CONTAINED MORE THAN 1600 POINTS' ) RETURN 51 IF (ISS) 10,10,20 20 IF (IX-IXO) 12,21,12 21 IF (IY-IVO) 12,22,12 22 IF (IS-ISO) 12,23,12 23 CALL CALC(AM GO TO 73 10 IF (.NOT.REG(IX2+1,IY2+1)) GO TO 50 12 IF (CV -Ar4(IX2, I,Y2) )206,206,5 206 IF (IDX**2+IDY**2-1)213,6,213 213 DCP=(AM(IX,IY)+AM(IX2,IY)+AM(IX,IY2)+AM(IX2,IY2))/4.0 IF (DCP-CV)5,217,217 217 IF (INX(IS-l)) 214,215,214 214 IX=IX+IDX IDX=-IDX PY=2.0 CALL CALC(AM) IX=IX+IDX GO TO 6 215 IY=IY+ IDY I DY=:"IDY PY=2.0 CALLCALC(AM) IY=IY+ IDY 6 IF (AM(IX-1,IY)-CV)306,16,16 306 NP=NP+1 IRC(NP)=100*IX+IY 16 IS=IS+5 IX=IX2 IY=IY2 GO TO 9 50 CONTINUE 65 IF (AM(IX-l,IY)-CV)307,73,73 307 NP=NP+1 IRC(NP)=100*IX+IY 73 CONTINUE DO 74 I=l,N NX=X( 1) NY=Y (I) 00216 00217 00218 00219 00220 00221 00222 00223 00224 00225 00226 00227 00228 00229 00230 00231 00232 00233 00234 00235 00236 00237 00238 00239 00240 00241 00242 00243 00244 00245 00246 00247 00248 00249 00250 00251 00252 00253 00254 00255 w co

PAGE 158

c C X AND Y ARE CORRECTED FOR GIVEN GRID VALUES XGL AND YGL C IF NY.EG.NT) GOT TO 75 Y(I)=YGL(NY)+(Y(I)-NY)*(YGL(NY+1)-YGL(NY)) GO TO 76 75 Y(I)=YGL(NY) 76 IF (NX.EQ.MT) GO TO 77 00256 00257 00258 00259 00260 00261 00262 00263 W \.0

PAGE 159

23 AUGUST 1978 LISTING OF CONTOUR C C C C X IS ADJUSTED FOR A NON ZERO THETA X(I)=(XGL(NX)+(X(I)-NX)*(XGL(NX+1)-XGL(NX)+Y(I)*RC GO TO 74 77 X(I)=XGL(NX)+Y(I)*RC 74 CONTINUE IDL=DL THE CONTOUR JUST TRACED IS PLOTTED X(N+ 1)=0. X{N+2)=1. Y{N+ 1)=0. Y{N+2}=1. CALL LINE {X,Y,N,l,O,O} 85 RETURN END 00264 00265 00266 00267 00268 00269 00273 00274 00275 00276 00277 00278 00279 o 00281 00282 ...... ..j:::. o

PAGE 160

23 AUGUST 1978 LISTING OF CONTOUR C SUBROUTINE CALC(AM) LOGICAL*l REG(83,83) DIMENSION AM(50,50),IRC(1200),X(1600),Y(1600) DIMENSION IPT(3,3),INX(8),INY(8) COMMON /PLT/MT,NT,IX,IY,IDX,IDY,ISS,IT,NP,N,JT, 1 PY,IRC,CV,X,Y,IPT,INX,INY,DL,THE,IXS,IYS,NL,REG C THIS SUBROUTINE INTERPOLATES LINEARLY TO DETERMINE THE X Y LOCATION C OF A CONTOUR CROSSING C IT=O N=N+1 IF (IDX**2+IDY**2-1)20,1,20 1 IF (lOX) 10,2,10 2 X(N)=IX Z=IY IY2=IY+IDY DY=IDY 41 Y(N)=((AM(IX,IY)-CV/(AM(IX,IY)-AM(IX,IY2)))*DY+Z RETURN 10 Y(N)=IY W=IX DX=IDX IX2=IX+IDX 44 X (N)= ((AM( IX, IY)-CV)/ (AM( IX, IX2, IY)) )*DX+W RETURN 20 IX2=IX+IDX T=IY+IDY W=IX Z=IY DX=IDX DY=IDY DCP= (N.1( IX, IY IY)+AM( IX, IY2 )+AM( IX2, IY2)) / 4.0 IF (PY-2.0)24,21,24 24 IF (DCP-CV)21,21,25 21 AL=AM(IX,IY)-DCP 23 V=.5*(AL+DCP-CV)/AL 27 X(N)=V*DX+W Y(N)=V*DY+Z PY=O.O RETURN 00283 00284 00286 00287 00288 00289 00290 00291 00292 00923 00294 00295 00296 00297 00298 00299 00300 00301 00302 00303 00304 00305 00306 00307 00308 00309 00310 00311 00312 00313 00314 00315 00316 00317 00318 00319 --' ..J::::> 00320 --' 00321 00322 00323

PAGE 161

25 IT=' AL=AM(IX2,IY2)-DCP 33 V=.5*(AL+DCP-CV)/AL 28 X(N)=-V*DX+W+DX Y(N)=-V*DY+Z+DY RETURN END 00324 00325 00326 00327 00328 00329 00330 --' +=N

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23 AUGUST 1978 LISTING OF CONTOUR C SUBROUTINE GRM(BNDRY,IXSA,IYSA,NLS,M,N) INTEGER BNDRY (200) LOGICAL*l REG(83,83) DIMENSION IRC(1200),X(1600),Y(1600) DIMENSION IPT(3,3),INX(8),INY(8) COMMON/PLT/MT,NT,IX,IY,IDX,IDY,ISS,IT,NP,NQ,JT, PY,IRC,CV,X,Y,IPT,INX,INY,DL,THE,IXS,IYS,NL,REG C GRM GENERATES A LOGICAL ARRAY REG THAT REPRESENTS THE REGION OF C INTEREST WITH 1 IS AND OIS C C INITIALIZE COMMON VARIABLES C C IXS=IXSA IYS=IYSA NL=NLS MT=M NT=N C SET UP THE INCREMENT VECTOR ARRAY FOR BNDRY C C INX(l)=-l INX(2)=,..1 INX(3)=0 INX(4)=1 INX(5)=1 INX(6)=1 INX(7)=O INX(8)=-1 INY(l)=O INY(2)=1 INY(3)=1 INY(4)=1 INY(5)=0 INY(6)=-1 INY(7)=-l INY(8)=-1 C INITIALIZE REG AT ALL ZERO C +2 NP2=NT+2 00331 00333 00334 00335 00336 00337 00338 00339 00340 00341 00342 00343 00344 00345 00346 00347 00348 00349 00350 00351 00352 00353 00354 00355 00356 00357 00358 00359 00360 00361 00362 00363 00364 00365 00366 00367 -' 00368 .j::::. w 00369 00370 00371 00372

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c DO 10 I=1,MP2 DO 10 J=1,NP2 10 REG(I,J)=.FALSE. INITIALIZE FIRST LINK IXL=IXS+1 IYL=IYS+1 00373 00374 00375 00376 00377 00378

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23 AUGUST 1978 LISTING OF CONTOUR C C C C C C C C PUT BOUNDARY INTO REG DO 20 I=l,NL IXL=IXL-INX(l+BNDRY(I)) IYL=IYL+INY(l+BNDRY(I)) REG(IXL,IYL=.TRUE. 20 CONTINUE FILL IN INTERIOR OF REGION WITH 1 IS IXB=IXS+l IYB=IYS+l DO 50 1=1 ,NL IXL=IXB IYL=IYB IDIR=2+BNDRY(I) IF(IDIR.LE.7) GO TO 30 IDIR=IDIR-8 30 CONTINUE IDX=INX(l+IDIR IDY=INY(l+IDIR) 35 IXL=IXL-IOX IYL=IYL+IDY IF(REG(IXL,IYL)) GO TO 36 REG(IXL,IYL)=.TRUE. GO TO 35 36 CONTINUE IXB=IXB-INX(l+BNDRY(I)) IYB=IYB+INY(l+BNDRY(I)) 50 CONTINUE I'JRITE IF DESIRED ... (6,1001) 1 001 (10 I, I REG I ,/ / / I REGION IN X DIRECTION 1, COLUMNS IN Y DIRECTION' ,///,1 REPRESENTS INTERSECTIONS OF DATA C 2ELL BOUNDARIES 1,/ ,I SHOULD HAVE SAME NmBER OF T AND COLUMNS 3AS DATA MATRIX I ,///) DO 40 I=1,MP2 40 WRITE (6,1000) (REG(I,J),J=1,NP2) 1000 (II ,B1Ll) RETURN END 00379 00380 00381 00382 00383 00384 00385 00386 00387 00388 00389 00390 00391 00392 00393 00394 00395 00396 00397 00398 00399 00400 00401 00402 00403 00404 00405 00406 00407 00408 00408 00409 00410 00412 00413 00414 00415 00416 00417 --' +'> 01

PAGE 165

APPENDIX C DATA

PAGE 166

TABLE C1 -Flow Data* Run 8 Jets Date Ld/H IT H 6p/pa U V/k a ]F. 0 a 0 J (0) (em/s) (em) (xl0 3 ) (em/s) 35 1-19 780612 .95 12.4 14.6 3.66 48.0 9.68 116.3 2 35 10-19 780613 .50 12.5 14.4 4.21 91.2 2.69 54.6 3 35 1-5, 15-19 780615 .50 12.4 14.7 4.08 91. 2 2.53 49.8 4 35 5-14 780616 .50 12. 1 14.8 4.09 91. 2 3.99 79.3 5 35 1-5, 10-14 780617 .50 12.2 14.7 4.04 91. 2 2.60 52.2 6 35 5-19 780618 .75 12.2 14.6 3.79 60.8 8.06 118.1 7 35 1-10,15-19 780619 .75 12.2 14.4 3.94 60.8 5.69 79.7 8 20 1-19 780621 .95 12. 1 14.4 3.82 48.0 11 .42 128.9 9 20 1-10,15-19 Z80622 .75 12.0 14.5 3.98 60.8 5.54 75.0 10 20 5-19 780623 .75 12.3 14.4 4.05 60.8 7.80 107.2 11 20 10-19 780624 .50 12. 1 14.6 4.11 91. 2 3.75 73.4 12 20 1-5, 15-19 780626 .50 11 .9 15.1 3.96 91. 2 2.40 45.4 13 20 5-14 780627 .50 11 .8 15.2 4.13 91.2 3.88 72.6 14 20 1-5, 10-14 780628 .50 11.7 15.3 4-.23 91. 2 2.49 44.4 15 TO 1-19 780715 .95 12.0 15.0 3.77 91. 2 12. 00 132.3 16 10 10-19 780716 .50 11.7 15.3 3.88 91.2 3.85 75.0 17 10 1-5, 10-14 780718 .50 11 .9 15. 1 3.92 91. 2 2.52 49.6 18 10 5-14 780722 .50 11 .9 15.0 3.86 91. 2 4.09 85.0 +=:> 19 10 5-19 780723 .75 11.8 15. 1 3.96 60.8 7.79 101 .5 '-l 20 10 1-5, 15-19 780724 .50 11.8 15.0 4.05 91.2 2.35 43.4 21 10 1-10,15-19 780725 .75 12.0 14.8 3.95 60.8. 5.64 75.1 *D = 1.32 em, L = 12.3 em for all runs h = 1.3 em, except for 80 = 20 then h = 1.1 em H = average of five sections

PAGE 167

148 TABLE C2 Temperature Drop from Manifold to Jets (QC) Run 1 2 3 4 5 6 7 ifo 1 d jet probe 16 16 16 8 4 8 8 jets 1 .147 -.187 -.235 .018 2 .056 -.207 -.235 .002 3 .039 -.179 -.271 .004 4 .069 .137 -.204 .037 5 .067 -.166 .096 -.247 .619 .009 6 120 .034 .577 .059 7 .136 .058 .691 .090 8 .185 .092 .793 .151 9 .140 .039 .678 .120 10 121 .073 .061 .114 .630 .112 11 125 .006 .061 -.126 .683 12 1.026 .032 .088 -.103 .860 13 1 136 -.006 .189 -.075 .893 14 .777 .028 .244 .047 .954 15 1.137 .009 .024 .733 .196 16 1 138 .032 .038 .847 .243 17 .399 .041 .006 .795 .218 18 1.073 .031 -.034 .746 .242 19 1. 192 .102 .025 .940 .272 Average .478 .035 -.082 .096 -.156 .658 .118

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149 (cont'd) TABLE C2 Temperature Drop from Manifold to Jets (OC) Run 8 9 10 11 12 13 14 Manifold jet probe 8 8 8 16 16 12 12 jets 1 .345 .041 .145 -.098 2 .301 .015 .189 -.095 3 .209 -.056 -.176 -.098 4 .364 .021 -.161 -.054 5 .314 .0lD .180 .143 .019 -.085 6 .223 -.008 .083 -.090 7 .343 .046 .120 -.038 8 .365 .081 .184 -.021 9 .322 .127 .167 -.032 10 .326 .127 .221 .284 -.004 .078 11 .355 .207 .105 -.003 .. 027 12 .373 .239 .085 .019 .033 13 .406 .271 .094 .054 .042 14 .407 .239 .090 .165 .127 15 .459 .216 .215 .086 -.027 16 .415 .254 .293 .098 .004 17 .442 .228 .252 .120 .020 18 .470 .260 .221 .139 -.052 19 .562 .356 .351 .211 .031 Average .368 .113 .216 .131 -.084 .007 -.018

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150 (cont'd) TABLE C2 Temperature Drop from Manifold to Jets (OC) Run 15 16 17 18 19 20 21 Manifold jet probe 12 12 12 12 12 4 4 jets 1 .224 .147 .358 .548 2 151 .250 .337 .459 3 .139 .177 .269 .550 4 .561 .160 .254 .548 5 .627 .049 .369 .607 .240 .459 6 .338 .336 .501 .465 7 .254 .404 .435 .474 8 .603 .376 .674 .433 9 .375 .432 .616 .526 10 .255 .382 .188 .412 .446 .336 11 .450 .338 .223 .431 .634 12 .443 .326 .237 .246 .310 13 .329 .363 .380 .468 .430 14 .517 .362 .449 .550 .579 15 .437 .433 .700 .315 .632 16 .410 .278 .362 .237 .565 17 .543 .440 .495 .467 .533 18 .607 .380 .502 .426 .626 19 .534 .348 .469 391 .576 Average .410 .365 .226 .402 .517 .330 .412

PAGE 170

151 TABLE C3 Thermistor Correction Factors Run Probe 1 2 3 4 5 6 7 1 .0248 .0072 .0315 .0240 .0140 .0053 .0124 2 .0034 .0006 .0064 .0084 .0087 -.0177 -.0034 3 .0613 .0394 .0462 .0512 .0240 .0492 .0539 4 -.0609 -.0727 -.0739 -.0575 -.0813 -.0714 -.0657 5 -.0707 -.0408 -.0440 -.0512 -.0582 -.0441 -.0335 6 -.0625 -.0898 -.0834 -.0791 -.0788 -.0784 -.0800 7 .0580 .0334 .0382 .0517 .0270 .0514 .0583 8 .0188 -.0074 -.0212 -.0039 -.0429 -.0193 .0117 9 -.0651 -.0359 -.0421 -.0376 -.0460 -.0223 -.0319 10 -.0516 -.0239 -.0275 -.0246 -.0317 -.0132 -.0303 11 .0262 .0101 .0289 .0289 .0082 .0076 .0031 12 -.0606 -.0428 -.0489 -.0375 -.0608 -.0320 -.0317 13 -.0673 -.0380 -.0324 -.0275 -.0392 -.0263 -.0285 14 .2462 .2607 .2223 .1547 .3571 .2110 .1890

PAGE 171

152 (cont'd) TABLE C3 Thermistor Correction Factors Run Probe 8 9 10 11 12 13 14 1 .0201 .0158 .0215 .0343 -.0027 .0020 .0117 2 .0095 -.0058 .0072 .0090 -.0062 -.0065 .0019 3 .0528 .0437 .0436 .0427 .0392 .0399 .0396 4 -.0639 -.0774 -.0762 -.0739 -.0783 -.0582 -.0707 5 -.0344 -.0361 -.0515 -.0331 -.0503 -.0512 -.0460 6 -.0624 -.0983 -.0914 -.0801 -.0897 -.0764 -.0763 7 .0576 .0444 .0462 .0512 .0632 .0531 .0446 8 -.0007 -.0078 .0034 -.0264 -.0074 .0018 -.0266 9 -.0303 -.0231 -.0342 -.0193 -.0304 -.0340 -.0347 10 -.0277 -.0181 -.0229 -.0106 -.0219 -.0182 -.0258 11 .0306 .0131 .2800 .0272 .0076 .0139 .0165 12 -.0297 -.0389 -.0429 -.0431 -.0352 -.0286 -.0435 13 -.0285 -.0135 -.0258 -.0225 -.0245 -.0235 -.0283 14 .1070 .2020 .1949 .1446 .2365 .1895 .2377

PAGE 172

l53 (cont'd) TABLE C3 Thermistor Correction Factors Run Probe 15 16 17 18 19 20 21 1 .0105 .0253 : .0043 .0080 .0083 .0082 .0194 2 -.0004 .0038 -.0074 -.0019 -.0047 -.0058 -.0009 3 .0551 .0518 .0392 .0338 .0350 .0449 .0082 4 -.0713 -.0695 -.Q588 -.0622 -.0499 -.0517 -.0595 5 -.0550 -.0300 -.0512 -.0461 -.0383 -.0325 -.0345 6 -.0745 -.0924 -.0908 -.0752 -.0896 -.0896 -.0814 7 .0823 .0616 .0656 .0650 .0523 .0472 .0443 8 .0126 -.0037 .0011 .0133 -.0142 -.0208 -.0217 9 .0301 -.0203 -.0374 -.0249 -.0196 -.0247 -.0188 10 -.0355 -.0148 -.0361 -.0259 -.0234 -.0194 -.0222 11 .0114 .0105 .0040 .0142 .0116 .0121 .0297 12 -.0355 -.0265 -.0298 -.0218 -.0306 .0373 -.0405 13 -.0330 .0181 -.0359 -.0403 -.0299 .0350 -.0325 14 .1634 .1222 .2330 .1638 .1932 .2046 .2103

PAGE 173

BIBLIOGRAPHY Abraham, G. 1963. "Jet Di ffusi on in Stagnant Ambi ent Fl ui d, II Delft Hydraulic Laboratory, Publication No. 29. Adams, LL June, 1972. "Submerged Multiport Diffusers in Shallow ttJater \"ith Current," M.LT., S.M. Thesis (Civil Engineering). Albertson, M.L., Dai, Y.B., Jensen, R.A., and Rouse, H. 1950. II Diffusi on of Submerged Jets, II Trans. ASCE, 115. Argue, J.R. and Sayre, W.W. July, 1973. liThe Mixing Characteristics of Submerged Multiple-Port Diffusers for Heated Effluents in Open Channel Flow," Iowa Institute of Hydraulic Research, Report No. 147, Iowa City. Brooks, N.H. December, 1972. "Dispersion in Hydrologic and Coastal Environments," W.M. Keck Laboratory of Hydraulics and Water Resources, Report No. KH-R-29, California Institute of Technology. Camp, T.R. and Graber, S.D. February, 1968. "Dispersion Conduits," Proceedings ASCE, J. Sanitary Engineering Division, 94, 31-39. Cederwall, K. April, 1971. "Buoyant Slot Jets into Stagnant or Flowing Environments," W.M. Keck Laboratory of Hydraulics and Water Resources, Report No. KH-R-25, California Institute of Technology. Chan, T. L. and Kennedy, J. F. August, 1972. "Turbul ent Nonbuoyant or Buoyant Jets Discharged into Flowing or Quiescent Fluids," Iowa Institute of Hydraulic Researc.h Report No. 140, Iowa City. Christensen, B.A. 1978. Hydraulic Measurements, Class Notes. Fan, L. -H. October, 1967. "Turbul ent Buoyant Jets into Strati fi ed or Flowing Ambient F1uids," W.M. Keck Laboratory of Hydraulics and Water Resources, Report No. KH-R-15, California Institute of Technology. Fan, L. -H. and Brooks, N. H. March, 1966. Di scussi on of "Hori zonta 1 Jets in Stagnant Fluid of Other Density," by Abraham, G., Proceedings ASCE, J. of Hyd. Div., HY2. Fan, L.-H. and Brooks, N.H. January, 1969. "Numerical Solution of Turbu1 ent Buoyant Jet Problems, II Keck Laboratory, Report No. KH-R-18, California Institute of Technology. 154

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Harleman, D.R.F., Hall, L.C., and Curtis, T.G. September, 1968. "Thermal Diffusion of Condenser Water in a River During Steady and Unsteady Flows," Ralph M. Parsons Laboratory for Hater Resources and Hydrodynamics, M.LL, Report No. 111, Cambridge, Massachusetts. 155 Harleman, D.R.F. and Jirka, G, and Stolzenbach, K.D. June, 1971. "A Study of Submerged Multiport Diffusers for Condenser Water Discharge with Application to the Shoreham Nuclear Power Station," M.LT. Parsons Laboratory for Water Resources and Hydrodynamics, Technical Report No. 141. Hubbert, K. 1971 liThe Energy Resources of the Earth, II Sci. Amer., 224 (3):60-70. Jain, S.C., Sayre, W.W., Akyeampong, Y.A., McDougall ,D., and Kennedy, J.F. September, 1971. "Model Studies and Design of Thermal Outfall Structures Quad-Cities Nuclear Plan," Iowa Institute of Hydraulic Research, Report No. 135, Iowa City. Jirka, G. and Harleman, D.R.F. 1973. liThe Mechanics of Submerged Multiport Diffusers from Buoyant Discharges in Shallow Water," Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, M.I.T., Report No. 169, Cambridge, Massachusetts. Koh, R.C.Y. and Fan, L.-N, October, 1970. "Mathematical Models for the Prediction of Temperature Distributions Resulting from the Discharge of Heated Water in Large Bodies of Water," EPA Water Pollution Control Research Series 16130 DWO. Larsen, .J. and Hecker, A.M. January, 1972. "Design of Submerged Diffusers and Jet Interaction," ASCE Nat. Resources Engineering Meeting, Atlanta, Georgia, Reprint 1614. Lee, J.H.W., Jirka, G.H., and Harleman, D.R.F., 1974. "Stabilityand Mixing of a Vertical Round Buoyant Jet in Shallow Water," R.M. Parsons Laboratory for Water Resources and Hydrodynamics. Department of Civil Engineering, M.I.T., Technical Report No. 195. Lieseth, P. Manifold in Engineering Berkeley. November, 1970. "Mi xi ng of Mergi ng Buoyant Jets from a Stagnant Receiving Water of Uniform Density," Hydraulic Laboratory, Report No. HEL 23-1, University of California, List, E.J. and Imberger, J. 1973. "Turbulent Entrainment in Buoyant Jets and Plumes," ASCE, J. of Hyd. Div., Vol. 99, HY9. Morri son, W. E. and Readl i ng, C. L. L968. II An Energy Model for the United States ... to the Years 1980 and 2000," U.S. Bureau of Mines, Information Circular 8384, U.S.G.P.O., Washington, D.C. Morton, B.R., Taylor, G.L, and Turner, J.S. 1956. "Turbulent Gravitational Correction from and Instantaneous Sources," Procedings Royal Society, London.

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Morton, B.R. 1959. "Forced Plumes," J. Fluid Mech., Vol. 9. Paily, P.P. November, 1975. "Thermal Regime of the Upper Mississippi and Missouri Rivers," Iowa Institute of Hydraulic Research, Report No. 185, Iowa City. 156 Paily, P.P. and Sayre, W.W. May, 1978. "Model for Shore-'Attached Thermal Plumes in Rivers," ASCE, J. of Hyd. Div., HY5. Parker,F.L. and Krenkel, P.A. December, 1969. "Thermal Pollution: Status of the Art," Vanderbilt University, Department of Environmental Resources Engineering, Report No.3, Nashville, Tennessee. Parr, A.D. May, 1976. "Prototype and Model Studies of the Diffuser-Pipe System for Discharging Condenser Cooling Water at the Quad Cities Nuclear Power Station," Ph.D. thesis, The University of Iowa. Rawn, A Bowerman, F. R., and Brooks, N. H. 1961. "Di ffusers for Disposal of Sewage in Sea Water," Trans. ASCE, 126, Part III. Rouse, H., Yih, C.S., and Humprheys, H.W. 1952. "Gravitational Convection from a Boundary Source," Tellus, 4. Sharp, J.J. and Wang, C.-su. 1973. "Boundary Effects on Dilution of Buoyant Jets, II in Water Poll uti on Research in Canada (edited by G.J. Farquhar). Toronto, Canada, University of Toronto Press. Streeter, V.L. and Wylie, E.B. 1975. Fluid Mechanics. (6th ed.) New York: McGraw-Hill. Swiss, M. 1970. "Comecon's Energy Reserves," Energy Int. 7(2): 15-18. Vigander; S., Elder, R.A., and Brooks, N.H. February, 1970. II Internal Hydraulics of Thermal Discharge Diffusers," Proc. ASCE, J. Hydraulics DiVision, 96, 509-527 Wright, S.J. May, 1977. "Effects of Ambient CrossfloltJ and Density Stratification on the Characteristic Behavior of Round Turbulent Buoyant Jets," W.M. Keck Laboratory of Hydraul;:cs and Resources, Report No. KH-R-36, California Institute of Technology.