Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P2.73 - Two-fluid model for 1D simulations of water hammer induced by condensation of hot vapor on the horizontally stratified flow
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 Material Information
Title: P2.73 - Two-fluid model for 1D simulations of water hammer induced by condensation of hot vapor on the horizontally stratified flow Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Tiselj, I.
Martin, C.S.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: condensation induced water hammer
1D two-fluid model
 Notes
Abstract: Condensation-induced water hammer has been studied on the experimental device described by Martin et. al. (2007). Transient flow was initiated by injection of hot ammonia vapor into a 6 m long horizontal pipe with 146.3 mm diameter partially filled with cold stagnant liquid. Ammonia was used as the working liquid with initial liquid temperatures between -22oC and -48oC and hot vapor temperatures around 15oC. After the valve opening, hot vapor enters the horizontal test section and (in most cases) a slug is being created near the open end of the test section. Condensation of the gas bubble captured behind the slug and the closed end of the test section accelerates the slug and a pressure surge of up to 5 MPa is being observed when the slug hits the closed end of the pipe. In the present paper, several experimental runs are simulated with 1D computer code WAHA (Tiselj et. al. 2004). WAHA was developed and tested for the column separation water hammer phenomena. Recent development of the code is being performed in the field of condensation-induced water hammer in horizontal pipes. WAHA code is based on one-dimensional six-equation two-fluid model with correlations for heat, mass, momentum transfer in stratified and dispersed flow. Hyperbolic partial differential equations are solved with a second-order accurate numerical scheme based on high-resolution shock capturing schemes well known in aerodynamics. Dispersed flow can be bubbly or droplet. Transition from stratified to dispersed (bubbly or droplet) flow is based on Taitel-Dukler correlation. For the purpose of the present study WAHA was upgraded with ammonia thermophysical tables and Chato-Dobson correlation for heat and mass transfer in stratified flow. This correlation includes condensation of the ammonia gas on the cold pipe wall, which is dominant in the first moments of the transient. Several modifications of the transition criteria from stratified to non-stratified flow are being tested as well as correlations for heat, mass and momentum transfer near the slug. Calculations are compared with pressure measurements. Results of the simulation represent a range of the 1D two-fluid model being used in the field of stratified-to-slug flow transition with heat and mass transfer.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Volume ID: VID00506
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: P273-Tiselj-ICMF2010.pdf

Full Text

7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Two-fluid model for 1D simulations of water hammer induced by condensation of hot
vapor on the horizontally stratified flow


I. Tiselj* and C. Samuel Martin**


Reactor Engineering Division, Jo2ef Stefan Institute,
Jamova 39, 1000 Ljubljana, Slovenia
iztok.tiselj@ijs.si
**School of Civil and Environmental Engineering, Georgia Institute of Technology,
Atlanta, Georgia 30332, USA
csammartin@ comcast.net




Keywords: condensation induced water hammer, 1D two-fluid model




Abstract

Condensation-induced water hammer has been studied on the experimental device described by Martin et. al. (2007). Transient
flow was initiated by injection of hot ammonia vapor into a 6 m long horizontal pipe with 146.3 mm diameter partially filled with
cold stagnant liquid. Ammonia was used as the working liquid with initial liquid temperatures between -220C and -480C and hot
vapor temperatures around 150C. After the valve opening, hot vapor enters the horizontal test section and (in most cases) a slug
is being created near the open end of the test section. Condensation of the gas bubble captured behind the slug and the closed end
of the test section accelerates the slug and a pressure surge of up to 5 MPa is being observed when the slug hits the closed end of
the pipe. In the present paper, several experimental runs are simulated with 1D computer code WAHA (Tiselj et. al. 2004).
WAHA was developed and tested for the column separation water hammer phenomena. Recent development of the code is being
performed in the field of condensation-induced water hammer in horizontal pipes. WAHA code is based on one-dimensional
six-equation two-fluid model with correlations for heat, mass, momentum transfer in stratified and dispersed flow. Hyperbolic
partial differential equations are solved with a second-order accurate numerical scheme based on high-resolution shock
capturing schemes well known in aerodynamics. Dispersed flow can be bubbly or droplet. Transition from stratified to dispersed
(bubbly or droplet) flow is based on Taitel-Dukler correlation. For the purpose of the present study WAHA was upgraded with
ammonia thermophysical tables and Chato-Dobson correlation for heat and mass transfer in stratified flow. This correlation
includes condensation of the ammonia gas on the cold pipe wall, which is dominant in the first moments of the transient. Several
modifications of the transition criteria from stratified to non-stratified flow are being tested as well as correlations for heat, mass
and momentum transfer near the slug. Calculations are compared with pressure measurements. Results of the simulation
represent a range of the 1D two-fluid model being used in the field of stratified-to-slug flow transition with heat and mass
transfer.


Introduction

Condensation-induced water hammer research at Jo2ef
Stefan Institute has been performed as a part of the EU
research project NURESIM (NUclear REactor SImulations)
and is being continued within the currently running EU
project NURISP (NUclear Reactor Simulation Platform).
Research is related to the simulations of stratified flows in
horizontal pipes. Main attention within NURESIM project
was paid to the CIWH scenario, where cold liquid was slowly
flooding a horizontal pipe filled with hot steam (Strubelj et.
al., 2010). Another type of CIWH scenario assumes injection
of hot steam into horizontal pipe partially filled with cold
liquid: this scenario is the main topic of JSI research within
NURISP project.
1) First type of CIWH can appear when the pipe filed with
hot steam is slowly flooded with cold water. This type of the


CIWH was shown to be a stochastic and thus very
unpredictable phenomena (Bjorge and Griffith, 1984,
Strubelj et. al., 2010). Models used to simulate Type 1 of the
CIWH were 1D two-fluid models and various 3D codes also
based on two-fluid models. Calculated results were
compared to experimental data from Hungarian
KFKI-PMK2 device. It was shown that neither 1D model nor
3D CFD model could accurately predict where and when the
slug will form, or if the slug will form at all.
2) Second type of CIWH can appear when hot steam
enters a pipe that is partially filled with cold liquid. The most
unstable part of the interface is always near the steam inlet
into the pipe, thus, it is more or less known where the slug
will be born. Experimental results for this type of the CIWH
were obtained by C.S. Martin (Georgia Tech, 2007). Since
the position of the slug formation is known, this type of
CIWH is less stochastic and more predictable than the type I


Paper No






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


of the CIWH. In the present paper computer code WAHA is
used as a platform for 1D simulations. The code is solving 6
equation 1D two-fluid model. WAHA code is using a special
type of numerical scheme that aims particularly at the fast
transients (like CIWH). Models that require verification and
validation are criteria that trigger transition from horizontally
stratified into slug regime of two-phase flow. These models
are required in 1D two-fluid models where horizontally
stratified flows are described with different set of
correlations than dispersed flows. The existing WAHA code
physical models were upgraded with correlations for steam
condensation on the cold walls of the horizontal pipes.
Inter-phase heat, mass and momentum exchange models in
horizontally stratified flows are already available in WAHA.
However these models require fine tuning for accurate
description of the CIWH with vapor injection.


Nomenclature


pipe c
pipe c
pipe c
interfa
matrix
matrix


ross-section [m2]
ross-section change due to elasticity [m2]
ross-section covered by phase k [m2]
cial area concentration
- temporal derivatives
- spatial derivatives


A
Ae
Ak
agf
A
B
C,
CD
Cvm
CVMI
D
d
do
E
e
Ffwall
Fk
fk
g
Htk
hk*
kk
Nuk
P
P.
Re
Qk

S


SR
Tk
t
Uk
v
Verit
Vr
X
Xsat
x
Greek l


a vapor volume fraction [m3/m3]


Cld~p
ahV


modified vapor volume fraction [m3/m3]
modified vapor volume fraction [m3/m3]
vector independent variables


p density [kg/m3]


Tg
0
0
Subsripts
f li


vapor source term [kg/(s m )]
inclination of the pipe
relaxation time

quid


g vapor
k liquid or vapor
m mixture
s saturation
i interface

Experimental Facility


An apparatus was designed by Martin et.al. (2007) to
simulate an industrial environment whereby ammonia liquid
is standing in a partially-filled horizontal pipe in thermal
equilibrium with ammonia gas above it. The essential
elements of the test setup consist of a horizontal pipe and a
high pressure tank containing hot ammonia gas as shown in
Fig. 1. The test pipe was a nominal 150 mm diameter, 6 m
long schedule 80 carbon steel pipe, having internal
diameter of 146.3 mm, and wall thickness 11 mm. The
pressure tank contained ammonia gas on top of liquid in
thermal equilibrium at ambient conditions inasmuch as the
entire test facility was outdoors. Between the pressure tank
and test pipe were three valves angle valve, solenoid valve,
and throttle valve -- and a metering orifice. The angle valve
remained fully open, while flow was initiated by a solenoid
valve for a given position of the throttle valve. The flow of
hot gas was controlled by manually positioning the throttle
valve for the existing ambient hot gas pressure. The ammonia
in the insulated test pipe was introduced from an ancillary
system containing a compressor, an auxiliary tank, and
another tank for purging non-condensible gases. For each test,
care was exercised to transfer ammonia liquid to or from the
test pipe to establish the desired depth and equilibrium
temperature. The principal measurements were (1) receiver
gas pressure (ambient temperature), (2) orifice-metered gas
flow (up to 0.45 kg/s), (3) static temperature and pressure of
saturated liquid and gas in test section (225-250 K, -0.45-1.6
bar), (4) dynamic gas pressures and shock pressures in test
section that reached up to 50 bar.
Fig. 2 shows schematic description of the
condensation-induced water hammer phenomena. Top of the
Fig. 2 shows initial conditions in the system cooled to
225-250 K. Initial depth of the liquid and initial temperature
and corresponding saturation pressure were modified in
different experimental runs. When the valve on the hot gas
inlet pipe is opened, hot gas enters the test section and can
induce slugging if the relative velocity between phases is
high enough. Gas velocity above the liquid interface depends
on inlet mass flow rate and on the condensation rate of the
gas on the cold walls of the pipe and cold surface of the liquid.
Once the slug is formed, very efficient heat transfer at the
head of the slug causes pressure difference between the tail
and the head of the slug and pushes the slug towards the
closed end. During the slug propagation the mass of the
liquid inside the slug grows and the water hammer pressure


Paper No


inter-phase drag coefficient [kg/m4]
dimensionless interfacial friction coefficient
virtual mass coefficient [kg/m3]
virtual mass term [N/m3]
pipe diameter [m]
pipe wall thickness [m]
average droplet diameter [m]
pipe elasticity modulus of the material [N/m2]
specific total energy [J/kg]
wall friction forces [N/m3]
drag force on phase k [N/m3]
dimensionless friction factor
gravity [m/s2]
volumetric heat transfer coefficient [W/(m3 K)]
specific internal enthalpy [J/kg]
thermal conductivity [W/(m K))
Nusselt number
pressure [Pa]
interfacial pressure [Pa]
Reynolds number
volumetric heat flux to phase k [W/m3]
stratification factor
source term vector
non-relaxation source term vector
relaxation source term vector
temperature [K]
time [s]
specific internal energy of phase k [J/kg]
velocity [m/s]
critical velocity [m/s]
relative velocity [m/s]
vapor quality
vapor quality at saturation
spatial coordinate [m]
letters






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


surge is registered when the slug hits the closed pipe end.


TRANSDUCERS
Static Pressure: PT(Gage); Pl; P2; PACE1; PACE2; PACE3; PACE4; PACE5
Dynamic Pressure: PCB1; PCB2; PCB3; PCB4
Static Temperature: RTD1; RTD2; RTD3; RTD4; RTD5
Dynamic Temperature: Thermocouples TC1; TC2; TC3; TC4; TC5


Fig. 1: Schematic of test pipe, orifice and pressure tank


I hot steam inlet


closed end


slug head




Fig. 2: Typical transient: red hot gas, blue cold liquid, top -
initial state, bottom slug.

Two-Phase Flow Model Of The WAHA Code

Mathematical model of the WAHA code is ID six-equation
two-fluid model similar to the models of RELAP5 (Carlson
et al, 1990) or CATHARE (Bestion, 1990) computer codes.
The basic equations are mass, momentum and energy
balances for vapor and liquid, with terms for pipe elasticity
and without terms for wall-to-fluid heat transfer. Continuity
equations for liquid and vapor (gas) phase are:


(1-a) + -p, ap +( I(1-a) p,v,
8a(t i-a) p + x
8t 8t 8x


OA(1-a) p v
St


8A(1-a)p pv/ ap
+A(1-a)--
8 x 8x


aa
A*CVM Ap, =AC, v, v,
8x
-AF v, +A(1-a)p, gcos0 -AF,


SAa pv, Aa pggv +Aap +
at 8x ax
aa
+A* CVM+Ap,- =-AC, Iv,v, +
ax
+AFgv, +Aap,gcosO-AFg,,


Internal energy balance equations for both phases are:

u 8 u f uf 9a p
ot ox 8t 8t
+(1 a) s--t I a) Pf Vx p-+p(l -)K +
a(l-a)vf ap
+P- +p(l-a)vfK K=
8x 8x
1 dA(x)
Qf -r,(u -u)+v,F,w-(1 -a)vpA d(x
A(x) dx

8ug 8ug 8a 8p aavg
a P a --+ap v--+p--+paK +p- a+
S8t 8x 8t 8t 8x

+pavgK d=

dA(x)
g g g g+vF,^ -avp dx
A(x) dx


+(1-a) pfvK f
ax


1 dA(x)
-Fg -(1-a) Pv Ax) dx
A(x) dx


(1) Specific total energy of liquid or gas is:


aapg a p +aapgvg ap
--ps +ap K +--p-v+ap, v,K 1P
at a 8t 8x x sx
g 1 dA(x)
S A(x) dx (2)

where the temporal changes of cross-section A(x,t) are
neglected in the denominators of the last term of equations
(1) and (2) (and also in Eqs. (5) and (6)). Momentum balance
equations for both phases are:


e=u+v2/2 (7)

Differential terms are collected on the left-hand side of the
equations and the non-differential terms are collected on the
right-hand side.
Terms that include constant K in Eqs. from (1) to (6) are
due to the elasticity of the pipe walls. According to Wylie and
Streeter (1978), speed c of a small pressure wave in 1D
elastic pipe filled with single-phase fluid should be reduced.
The following modification is thus introduced. Pipe


Paper No


Solenoid HEV


Angle Volve






Paper No


cross-section A(x,t) can vary along the coordinate
function of initial pipe geometry A(x) and due to the
change A,(p(x,t)).

A(x,t) = A(x) + A (p(x,t))

The pressure pulse changes the pipe cross-sec
accordance with linear relation:

dAe D dp
=K-dp
A(x,t) d E

where D is diameter, d is thickness and E is Young's n
of the elasticity of the pipe.

Closure relations
The WAHA code uses several different;
non-differential closure relations. Closure relati
two-phase flow are used to describe interfacial hea
and momentum transfer, wall friction, interfacial p
virtual mass term, equations of state etc. The equa
state for each phase k, where k is f for fluid and g fo
are:


dp,-(a P
d =- --


aP d,


Derivatives on the right-hand side of the Eq. (
determined by the ammonia property subroutines de
for the WAHA code using pressure and tempera
specific internal energy as input. Ammonia propel
pre-tabulated with subroutines developed on the I
IAPWS recommendations (Bukes, Dooley, 2001), an
at approximately 300 pressures (0 bar 2500 bar)
temperatures (195.5 K 1714 K).
The virtual mass term CVM in Eqs. (3) and (4) is
obtain hyperbolicity of the system:


av, t ax at gv


Value of the coefficient Cv, was tuned to ens
hyperbolicity of the two-fluid model equations.
virtual mass term does not ensure uncon
hyperbolicity of the equations. For very large
velocities (comparable to sonic velocity) c
eigenvalues may appear, however these velocities
relevant in realistic two-phase flows.
In dispersed flow it is assumed that the pressure
phases is the same. The water surface in hori
stratified flow can be wavy, therefore the interfacial
termp, is applied to describe pressure gradients:


x as a
pressure



(8)

tion in


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

interface heat transfer terms (Q,, Q,).
Terms due to the variable pipe cross-section.
Terms with wall friction (Ffwai, Fg,wai).
Term with volumetric forces (g cosO).
Sources from the points 1. and 2. are the so-called
relaxation source terms. They play crucial role in the case of
condensation-induced water hammer and therefore their
detailed description is given in the next section. Other,
non-relaxation source terms are terms with wall friction and
volumetric forces.


(9) Relaxation source terms
Relaxation source terms are inter-phase mass, momentum,
nodulus and energy exchange terms, which tend to establish thermal
and mechanical equilibrium between the phases.
Characteristic time scale of relaxation source terms can be
much shorter than the characteristic time scale of the acoustic
al and waves (terms are stiff and need special numerical treatment).
ons in Relaxation source terms are flow regime dependent.
it, mass Avery crude flow regime map (described below) has been
pressure, applied in the WAHA code, which is actually nothing more
tions of than search for the best fit of the macroscopic data, and is
ir steam open for improvement with the further comparison with the
experimental data. More detailed flow regime maps were
abandoned as they are developed for the steady-state flow
regimes. The accuracy of the existing more detailed flow
(10) regime maps in the area of fast transients comparing to our
crude flow regime map, is in our opinion not significantly
10) are higher, and does not justify their use in the WAHA code. The
veloped main goal of the WAHA correlations is to have correct
iture or correlations in the limit of high and low vapor volume
ties are fractions with their smooth transition into the single-phase
basis of flow, with possibility of their further tuning on the basis of
d saved the experiments. It is important to note that even the
and 350 "standard" single-phase wall friction correlations (RELAP,
CATHARE) turn out to be insufficient in the area of the fast
used to transients. The WAHA code offers an option of the "unsteady
wall friction model" that takes into account additional wall
friction due to the unsteadiness of the flow.
9 The WAHA code distinguishes two flow regimes (Fig. 3):
) 1 dispersed flow with stratification factor S= 0 and horizontally
11 stratified flow with S=1. There is also transition area
between both regimes with 0 ure the divided into bubbly flow (a< 0.5), droplet flow (a > 0.95) and
Applied transitional bubbly-to-droplet flow.


utiuInal
relative
complexx
are not

of both
zontally
pressure


p, = Sa(1 a)(pf p,)gD (12)
where S presents the stratification factor.
Terms that don't include derivatives are source terms and
they are flow regime dependent. Source terms in Eqs. (1)-(6)
are:
Terms with inter-phase drag (C,).
Terms with inter-phase exchange of mass and energy:
vapor generation rate (Fg),


Dispersed flow
Horizontally stratified Transitional area S=
Transitional area
flow
ow 1 > S > > 0 95 Droplet flow
S = 1 0 95 > a > 05 Transitional flow
a< 0 5 Bubbly flow
0.5 Vcnt Vent
0 Vr
Fig. 3: WAHA flow regime map.

Flow is dispersed with S= 0 if at relative velocity v, is larger
than the critical velocity:
l"vr "c rt

J ia (1-a)1
vcrit= gD(pf pg) +
S gP 9 ) (13)

This expression is an approximation based on the
Kelvin-Helmholtz instability. This critical velocity is at the





7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


same time maximum relative velocity, where two-fluid
model with applied interfacial pressure term and without
virtual mass term, is still hyperbolic. Flow is horizontally
stratified with stratification factor S = for vr < vcr,,rc/2 .
Flow is transitional between dispersed and horizontally
stratified, if v ..I ,/2< Ivv, Stratification factor S is
linearly interpolated between 0 and 1 in such case. This
approach is similar to the well-known Taitel-Dukler
correlation for transition from stratified to slug flow (Taitel,
Dukler 1976). From the standpoint of condensation-induced
water hammer modelling, this model represents a possible
area of the future work, however it was not changed in the
present study.
The most important set of correlations for the present
research are stratified flow correlations that are crucial for
accurate description of the initial phase of the transient
including the formation of the slug. Slug formation means
transition in different flow regime that requires different set
of correlations. Despite the fact that this work considers
modelling of 1D slug flow with two-fluid models, existing
slug flow correlations (see Lin, Hanratty 1986, or Issa,
Kempf, 2003 for example) are not directly applicable as they
give an averaged heat, mass and momentum transfer
correlations instead of instantaneous local values needed for
the present study. A single slug is being explicitly followed in
the present study with 1D two-fluid model. Such tasks are
expected to be performed with multidimensional CFD
analysis using some of the free surface tracking algorithms
and not in 1D two-fluid models. However, while the current
CFD codes might be able to describe the stratified flow with
condensation and also slug formation and development, one
can certainly expected problems with modelling of the thin
condensate film on the walls and water hammer shock waves
followed by the flashing of the liquid. And while we do
intend to test CFD models for condensation-induced water
hammer in the future, our present goal represents
development of the suitable 1D two-fluid model.

Inter-phase momentum transfer

The interfacial friction coefficient C, in momentum
equations is calculated from correlations, which are valid
for two-phase flow water-vapor and for two-component
flow water-ideal gas (similar to RELAP5 model). The
original WAHA correlations remain unchanged for the
present simulations and analyses have shown rather low
sensitivity of the results to the inter-phase friction
coefficients in stratified, dispersed and transitional flow.
Horizontally stratified flow interfacial friction coefficient
is calculated from the equation, which states that magnitude
of the drag force of the gas on the liquid is equal to the drag
force of the liquid on gas:

F,= F = C, (v -v ) (14)

interfacial friction coefficient is then calculated as:


1 (, v)2
( Pf, V)2


k =g,f


the vapor volume fraction a:
1. a < 0.5 (Bubbly flow):


C, pCaf
8


with drag coefficient of the slug:


C = 24(1 + 0.1Re 75)/Re


and interfacial area concentration:


ad = 3.6ab,, /do


where abb is modified vapor volume fraction, do is average
slug diameter and Re is Reynolds number.

2. a > 0.95 (Droplet flow):

C, =maxlp,gCag, 0. 1 (19)
(8


with the drag coefficient of the droplet:

C, =min(24(l+0.1Re 75)/Re, 0.5)

and the interfacial area concentration:


ag. = 3 .'I.,i. 10 4)/d0


where adp is modified liquid volume fraction and do is
average droplet diameter.

3. 0.5 inter-phase friction coefficient is calculated with
interpolation:

=(c- bubbly" (c droplet)( q) (22)


with exponent q:


( 0.95-a
q 0.95-0.5)


that was chosen to ensure smooth transition between
correlations in Eq. (16). and Eq. (19).

Dispersed-to-horizontally stratified interfacial friction
coefficient is calculated with interpolation:

C, =S(C,sied) + (1-S)(Cdpe) (24)

Inter-phase heat and mass transfer

Calculation of inter-phase heat and mass transfer were
significantly modified for the present condensation-induced
water hammer research. Original WAHA correlations do not
take into account wall heat transfer, which is an important
mechanism for the present work. are valid only for
water-vapor two-phase flow. The "standard" inter-phase
mass transfer (vapor generation rate F ) is calculated as:


where fk are friction factors, v, is interface velocity and
a g is interfacial area.
Dispersed flow coefficients are further divided according


F -f + ,g
g h -hf
9 f


where hk are specific enthalpies and Q,k are


Paper No





Paper No


liquid-to-interface and gas-to-interface heat fluxes. The
volumetric heat fluxes are calculated as:


Q,, = H,,(T -T, )


k fg


The heat transfer coefficients Hk depend on flow regime.
Beside the interphase heat and mass transfer,
condensation on the wall is taken into account as:


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

if slug head identified:
H,f = -Ca(1- a) Va f(T, Tg) v, c3
else
H, -0
enf =
endif


IfT Tf T I C4
f(Tf,ITg)= f T- "4
Tgr iS


Fg wal H,g-wao (Twall- T,)
F g wall : *
h* -h
9


T ;T > T


using Chato-Dobson correlation (Dobson, Chato, 1998) for
condensation rate in the horizontal pipe:

Nu = NU +( -(l f /rT)Nfod =

0.23Re'o2 Ga Pr 025
1+1.11x28 Ja

+(1- ,/;7T)0.0195Re8 Pr4qI4 fA(X,)

4k
H,g wall = Nulm D4 -
4k (28)
4k
H, =(1 -O /,r),Nfo~Cd D2

The first term in Chato-Dobson correlation represents part
of the coefficient, which represents contribution of the film
condensation on the wall and the second term represents
contribution of the forced-convective condensation on the
liquid-gas interface. The following variables are used in Eq.
(28): Rego Gas only Reynolds number, Ga Galilei number,
Ja Jacob number, <(/Xd) function of turbulent-turbulent
Lockhart-Martinelli parameter given in Dobson, Chato,
1998. Each term of Chato-Dobson correlation is used
separately: film condensation term in Eq. (27) and
forced-convection inter-phase exchange coefficient in Eq.
(26).
The vapor heat transfer coefficient H,g is calculated as
(similar in the RELAP5 code):
k
H,g = a, g 0.023Re8 (29)
D

Dispersed flow heat transfer is actually not present during
the transient the closest "approximation" of dispersed flow
can be seen at the head of the slug, where wave breaking
appears and causes much more efficient inter-facial heat
transfer than predicted by Chato-Dobson correlation. This
phenomena can be seen from the air-water experiments and
simulations of Bartosiewitz (2008) and experiment of
Vall6e et. al. (2010). Thus a very crude inter-phase heat and
mass transfer is used at the location of the slug head:


Values C1=1.5, C2=1, C3=0, C4=1, C5=1 were used in the
calculations collected in the Table 1 below. Head of the slug
is located with the gradient of the liquid superficial velocity:

if V((1- a)vv) < -0.05, slug head identified (31)

This is rather unusual approach for 1D two-fluid model and
actually represents some kind of inter-phase tracking within
the 1D two-fluid model. However, according to our
experience, this is the best way to perform
condensation-induced water hammer simulations with 1D
two-fluid model. If the slug, and especially the head of the
slug (where stratified heat and mass transfer correlations are
not applicable) is not successfully recognized and
condensation rate increased in that area, the simulations
exhibit rather poor results.
The vapor heat transfer coefficient H,g in dispersed
flow is calculated similar in the RELAP5 code, with a single
goal to almost instantaneously bring vapor to equilibrium:

H = (1+ 7.(100+ 25. 7)), (32)

where 77= max(-2,T, -7T) .
Unlike the standard WAHA code where transition
between horizontally stratified and dispersed flow
(stratification factor 0 < S <1) inter-phase heat transfer
coefficients are calculated with interpolation:

Hk =S(Hk-stried) +(1-S)(Hk-diped) (33)

the modified heat transfer coefficients are calculated as:


H, = max(H,k-satfied Hk-dspersed)


Inter-phase exchange correlations described with Eqs. (25)-
(34) are applied in WAHA code with minor correction
factors, that act at very low vapor or liquid volume fractions
and prevent negative values or extremely large values of
heat transfer coefficients.

Numerical Method


The system of six-equations model (Eqs. (1)
written in vectorial form:

- t &x


(6)) can be


where represents the non-conservative vector of the
independent variables:

vy = (p,a,f,vg,uf,u ) (36)






Paper No


further A and B are matrices of the system, and S is a
vector with non-differential terms in the equations.
Non-conservative schemes are known to converge to the
wrong solutions when shocks are present in the flow field,
however according to our experience (Tiselj, Petelin, 1997,
Tiselj et. al., 2004), non-conservative scheme does not seem
to be a big deficiency for short transients like water hammer
events.
The numerical scheme of the WAHA code is based on the
two step operator splitting and characteristic upwind method;
i.e. convection with non-relaxation source terms and
relaxation sources in Eq. (35) are treated separately:


A + B SN-R
t -x

A d -t


Each step of the operator splitting is performed with second
order accuracy. The applied operator splitting method is
formally first-order accurate. However, the numerical tests
showed, that despite the formally lower order of accuracy, the
results are practically the same as with the second-order
Strang operator splitting method.


Results and Discussion


Result of two simulations that were performed only with
stratified flow correlations for heat and mass transfer in Figs.
4. and 5. show a reasonable agreement between the pressure
measured in the experiments and simulation. First
experiment shown in Fig. 4 is case 03.01.01-13 with strong
pressure peak of 51 bar (see Table 1 for details of all
experimental runs and main results of the simulations). The
case 11.14.00-13 (Fig. 5) is experiment without recorded
pressure peak. Result in Fig. 4 shows that Chato-Dobson
correlation predicts reasonable condensation rate in the
horizontal test section, which results in a reasonable pressure
prediction. According to the calculations, slug is formed in
both cases due to the sufficiently large relative velocity


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

between the phases. However, since only stratified flow
correlations are used, the condensation rates ahead and
behind the slug are more or less the same and the slug is not
accelerated towards the closed end, but approaches the end
very slowly. Experiment 11.14.00-13 (Fig. 5) shows rather
smooth pressure growth, which means that liquid slug did not
develop in that experiment and that slug predicted by the 1D
two-fluid model does not exist. As is also shown later, the
existing 1D two-fluid model is not very accurate for the
experimental cases with small initial amount of the liquid.
It should be noted that static pressure measurement shown
in Fig. 4 does not include pressure peaks of the water hammer,
only some pressure fluctuations right behind and after the
pressure surge of the case 03.01.01-13 pressure are visible. It
is interesting to note that in the case 03.01.01-13 pressure
growth is stopped at time -1.4 s when the slug is formed and
stronger condensation at the head of the slug starts. However,
after the bubble behind the slug rapidly condenses and water
hammer peak is over (-1.9 s), the condensation rate remains
similar as in the Chato-Dobson based calculation.


2UUUUU


0 1 2 3 4 5 6
Fig. 4: Pressure (Pa) vs. time (s) at PACE3 static gas
pressure sensor: measurement (dashed) and calculation (solid
line) for test case 03.01.01.13.


Table 1: Overview of the selected experimental cases and corresponding simulations. Times of pressure peaks are given with
respect to the start of the gas injection. Times in Figures are given with respect to the starting time of the measurements.

experiment initial initial initial approximate hot gas measured time of calculated time of
pressure temperature vapor hot gas temperature pressure measured pressure calculated
in the in the test volume mass flow (K) peak pressure peak (bar) pressure
test section (K) fraction rate (kg/s) (bar) peak (s) peak (s)
section
(bar)
03.01.01-13 0.51 226.8 0.4736 0.31 293 51 0.58 56 0.58
03.01.01-14 0.55 228.6 0.4736 0.11 293 20 2.39 29 1.01
03.01.01-16 1.36 244.8 0.4736 0.32 295 27 0.63 17 0.92
05.21.01-12 0.45 224.8 0.4736 0.081 296 22 1.94 27 1.12
05.21.01-14 0.50 225.1 0.4736 0.15 296 44 0.81 43 0.83
11.13.00-31 0.52 227.8 0.4736 0.14 288 41 0.88 39 0.85
11.14.00-11 0.53 231.7 0.793 0.34 286 no shock / 47 0.76
11.14.00-12 0.57 232.1 0.793 0.42 287 25 0.98 48 0.66
11.14.00-13 0.65 233.9 0.883 0.43 287 no shock / 21 0.76






Paper No


350000

300000

250000

200000

150000


100000


50000 1-r---- ----
0 05 1 15 2 25 3 35 4 45 5
Fig. 5: Pressure (Pa) vs. time (s) at PACE3 static gas
pressure sensor: measurement (dashed) and calculation
(solid line) for test case 11.14.00-13.

Another effect is responsible for the differences in the
condensation rate at later times seen in Figs. 4. and 5.: pipe
wall, which is assumed to be at constant initial temperature
in the simulations, is in fact slowly warming up, reducing
the efficiency of the condensation. A conjugate heat transfer
model could be added in the two-fluid model to avoid that
effect, however, all the pressure peaks appear before the
times when these differences become relevant.
Similar agreement as seen in Fig. 4 and Fig. 5 exists for
other test cases collected in Table 1 and calculated with only
stratified flow heat and mass transfer correlations.

Water hammer modelling
An open issue remains upgrade of the two-fluid model
with a procedure that can recognize the head of the slug,
where inter-phase heat and mass transfer is much more
efficient than predicted by the Chato-Dobson correlation.
Slug head identification model from Eq. (31) was found to
predict the area of the slug head. Increase of the heat transfer
coefficients in the slug head region is performed with a
general model of Eq. (30). These two models with the
current values of the coefficients are being developed by
fitting of the calculations with the measurements and remain
open for further improvements.
Capabilities of the current form of both models gives
predictions of the condensation-induced water hammer
pressure peaks with accuracy shown in the Table 1, where
last 4 columns show measured and calculated magnitude
and time of the pressure peak. Good agreement of pressure
peak and timing is seen for cases 03.01.01-13, 05.21.01-14
and 11.13.00-31. Fig. 6 shows measured and calculated
pressure for the case 03.01.01-13, which can be considered
as a successful simulation. Secondary shock waves are seen
in computation and experiment. They are caused by a
classical "water column separation" mechanism, where
WAHA code is well tested and accurate. As shown in Fig. 7
that presents the same case, pressure peak causes only minor
changes in the integral condensation rate. Comparison of
Fig. 7 and Fig. 4. shows very similar calculated pressure
histories, despite the absence of the pressure peaks in Fig. 4.
Case 03.01.01-14 performed with slightly lower hot gas
mass flow rate and similar initial pressure and volume
fraction than cases 05.21.01-14 and 11.13.00-31 gives much


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

earlier time of water hammer than measured. Surprisingly,
comparing to the 03.01.01-14 slightly higher pressure peak
at earlier time was measured in the case 05.21.01-12, despite
even lower hot gas mass flow rate. This leads us to
conclusion, that tuning of the models cannot be performed
on one single experimental case due to the rather stochastic
nature of the whole phenomena. Thus, all the changes in the
models are continuously tested for all 9 test cases of the
Table 1.
Figs. 8 an 9 show an example of a simulation of modest
accuracy 05.21.01-12.


'11 14 00-testl 1strat out' u 1 5
/' FEB/EXPERIMENT/11 14 00/pace-pcb4-t11 exp u 1 4







/


Fig. 6: Measured (dashed) and calculated (solid) pressure
(Pa) vs. time (s) at the closed end for test 03.01.01-13.


500000


1 15 2 25 3 35 4 45 5
Fig. 7: Measured and calculated pressure(Pa) vs. time (s) in
the middle of the pipe (PACE3) for test 03.01.01-13.

The case 03.01.01-16 was performed at higher initial
temperature than other tests. Similar pressure peak is
measured and calculated, however, calculated pressure peak
occurs too late.
The worse results are obtained for high initial vapor
volume fractions. An example of poor simulation is given in
Figs. 10. and 11. for the case 11.14.00-11. Despite low
amount of liquid, 1D two-fluid model predicts formation of
the slug in all 3 cases 11.14.00-11, 12, 13. Slug formation is
followed by a strong water hammer, which is not seen in the
measurements at all, except a pressure peak of medium
magnitude in the case 11.14.00-12. As seen in Fig. 5 the
problem might not stem from the inter-phase heat and mass
transfer correlations but from the basic two-fluid equations


5e+06

4e+06

3e+06

2e+06

le+06


'03 01 01-test3 out' u 1 2
/ /FEB/ XPERIMENT/03 01 01/pace-pcb4-tl3dp exp' u 1 5 -----









1v






Paper No


and their capabilities to model stratified flows. Non-existing
slug in the case of Fig. 5 simulation is predicted even with
correlations for stratified flow. Pressure interface term that
makes the two-fluid model to behave like a shallow water
equations when stratification is assumed, is more accurate at
vapor volume fractions around 0.5, where circular pipe
behaves like a rectangular channel. At low (less than 0.2) or
high (higher than 0.8) vapor volume fractions the pressure
interface term might have a different form, which would
influence the dynamics of the large interfacial waves (slugs).


25e+06


2e+06


1 5e+06


le+06 F


500000


1 15 2 25 3 35 4 45
Fig. 8: Measured (dashed) and calculated (solid) pressure
(Pa) vs. time (s) at the closed end for test 05.21.01-12.


'05 21 01-test12NOV out u 1 5
140000 /FEB/EXPERIMENT/05 21 01/pace-pcb4-tl2dp exp'u 1 2---

120000

100000

80000

60000

40000

20000

0
1 15 2 25 3 35 4 45
Fig. 9: Measured and calculated pressure (Pa) vs. time (s) in
the middle of the pipe (PACE3) for test 05.21.01-12.
5e+06 ----------------------- ----
5e+ 6 11 14 00-test11 out u 1 2
/ /FEB/EXPERIMENT/11 14 00/pace-pcb4-t11 exp u 1 5 ----


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010



400000
S11 14 00-testll out u 15 ---
/ I FEB/EXPERIMENT/11 14 00/pace-pcb4-t11 exp' u 1.--'-
350000 -

300000 -

250000

200000

150000

100000 -

50000 --- l -----------
05 1 15 2 25 3 35 4 45
Fig. 11: Measured and calculated pressure (Pa) vs. time (s) in
the middle of the pipe (PACE3) for test 11.14.00-11.

All computations were performed with an input model
consisting of -170 volumes with the horizontal test section
discretized in 60 volumes. Grid refinement was performed
for all cases in the Table 1 with test section discretized into
120 volumes. Pressure peaks and times of the peaks obtained
on the refined grid were typically up to 5% different.

Conclusions

Condensation-induced water hammer has been studied on
the experimental device described by Martin et. al. (2007)
and simulated with 1D two-fluid model of the computer
code WAHA (Tiselj et. al. 2004). For the purpose of the
present study WAHA was upgraded with ammonia
thermo-physical tables and Chato-Dobson correlation for
heat and mass transfer in stratified flow. This correlation
includes condensation of the ammonia gas on the cold pipe
wall, which is dominant in the first moments of the transient.
Several modifications of the transition criteria from
stratified to non-stratified flow are still being tested as well
as correlations for heat, mass and momentum transfer near
the head of the slug. Current models for condensation in the
slug head are being developed as a best fit with various
experimental runs. Results of the simulation show that 1D
two-fluid model can capture the main phenomena of the
condensation-induced water hammer, however, reliable
prediction of the condensation-induced water hammer in the
current configuration is still not possible. Behaviour at
various initial temperatures, pressures and hot gas flow rates
are well described for initial filling of the pipe of around
50%, while non-existent condensation-induced water
hammers are predicted at low liquid fillings (10-20%).

Acknowledgements

This research was financially supported by the Ministry of
Higher Education, Science and Technology, Republic of
Slovenia, project no. J2-1134 and research project of the EU
7th FP NURISP


05 1 15 2 25 3 35 4 45
Fig. 10: Measured (dashed) and calculated (solid) pressure
(Pa) vs. time (s) at the closed end for test 11.14.00-11.


"05 21 01-testl2NOV out u'l 2
/ /FEB/EXPERIMENT/05 21 01/pace-pcb4-tl2dp exp u 1 5 ----















S --.- ._- ,-






Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

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