Jet diffusion in proximity of a wall

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NATIONAL ADVISORY CO~MITT FOR AERONAUTICS


TECHNICAL MEMORANDUM NO. 1214


JET DIFFSIO IN nP OOXIMITY OF A WAiL'

By D. KIchemann


SUMMARY


When auxiliary jet engines are installed on eai'frames, as
well as in some new doslgns, the jot engines are mounted in such
a way that the jet stream exhausts in close proximity to the
fuselage. This report deals with the behavior of the jot in
close proximity to a two-dimensional surface. The experiments
were made to find out whether the axially symmotr'.ic stream tcnds
to approach the flat surface. This report is the last of a series
of fot'r partial test reports of the GCttingen program for
the installation of jet engines, dated October 12, 19143. This report
is the complement of the report on intake in close proximiLy to
a well.


I. INTRODUCTION


Considerable confusion still attends the installation of turbojet
engines as regards the discharging jet, especially when it comes
near other parts of the airplane and interference phenomena are
possible. If the engine is mounted near to the fuselage, there is
apprehension that the jet will adhere to it with consequent
undesirable heating and possibly also dr&g incre?.se. The purpose
of the present report is to treat these problems in somewhat greater
detail.

The feared jet processes are caused by the nearness of the wall.
In order to secure more general and fundamental data, all special
wall forms were disregarded and the jet was measured in the
proximity of a flat well. This precluded the processes which
S depend on the particular pressure distribution at the wall and
in the surrounding space. Furthermore, the work was done on a cold
jet, principally on account of experimental facility. The extent
to which fundamental phenomena were suppressed by it must be left

*"Strahlausbreitung in WandnEhe." Zentrale fUr Wissenschaftliches
Berichtswessen der Luftfahrtforschung des Generalluftzeugmeisters (ZWB)
BerlftkAdlershof, Untersuchungn und Mittellungen Nr. 3057, December 31,
1943.








NACA TM No. 1214


to future experiments., As variable parameters there remain
the velocity of the jet, for which as criterion the mean velocity vA
in the exit of the engine model is chosen, and the outer
flow velocity -o; and indeed it suggests itself to once consider
the difference vA vo and then the quotient vA/Vo as significant,
Another parameter is the distance a of the exit cone from the
wall (that is, the distance of the point of exit closest to the
wall from the wall), and lastly the design of the fairing between
engine and wall will also play a part. In every case, the three-
dimensional variation of the jet downstream from the exit must be
measured.


II. CONVERSION TO OTHER OPERATING CODITIONIS


In view of the multiplicity of potential variations, it is
desirable to establish simplifying connections. For practical
purposes it would be more advantageous to be able to use easily
made static tests (without stream flow) and. to compute all phases
with stream flow from it. Such a process is described in the
following:

It is assumed that the general state of flow (v) results,
in first approximation, from the superposition of the stream
flow (vo) with the jet flow (vI):


v = v' + vo (1)


This implies that the jot diffusion is to depend only on the
difference of the velocity in the jet (vA) and outside of the
jet (vo), so that the velocity v in the form (v Vo)/(vA vo)
for fixed particles is independent of the operating condition.
A certain difficulty is involved in the finding of the location
of these particles, that is, to pass from the velocity transforma-
tion (1) to the related transformation of the coordinates. A
rectangular system of body axes (x, y, z) is used with x in
the flow direction and the time coordinate t, with x = 0 (plane
of exit) for t = 0. Th- space coordinates of the particles
are functions of the time. Thus for equal time intervals t we
get a relation between the coordinates x,y,z of the particle
in the general flow (vo / 0) and the coordinates x,y',zt of
the flow without stream flow (v, = 0).
1The problems of model similarity and reproduction of the hot-jet
in wind-tunnel tests are discussed in reference 1.







NACA TM No. 1214


It further is assumed that transverse flows
hence that the velocity has the direction of the
y = y' and z = z'. This leaves the connection
and x' and t to be determined.
dx dx'
V = -; Vt = -
at d.t


can be disregarded,
x -axis, so that
between x and t


the velocity relation (1) then reads


dx dx1
-- =-- + Vo
dt dt


which, integrated, gives


x(t) = x'(t) + v t


In this equation t is yet to be eliminated
with the aid of (2) by means of the velocity
which is accessible to measurement:


/
t = /
V o


and to be replaced
v1 = v'(x',y,z),


d' '
vt(x',y,z)


In this manner the desired transformation of the coordinates


i nx'/d
x -- I o
vo
Vo


v'(xl,y,z)
7,i


follows from (4), made dimensionless with the diameter
exit nozzle and'the average velocity VA' = vA vo in


d of the
the exit


nozzle. This transformation states that planes normal to the x-axis
are not maintained, but that according to the velocit:. distri-
bution v'(x',y,z) the x displacement for the faster particles is
less than for the slower ones. In practice v'/vAI would be
measured, the integration carried out, and the x corresponding
to x' caluclated by (6). There the area cf small velocity would
cause difficulties, especially for the points x a 0, j + z2> d/2,
since v' with x )O must approach zero in a certain way in order
that the integral may exist. Moreover, the niumerical evaluation
in this area requires extreme accuracy of measurement.









NACA TM No. 1214


A detailed check of the practicability of these assumptions
was outside the scope of the present report. A thorough discussion -
with consideration of the transverse motions must be the object
of a special investigation. For the present, these assumptions
were, after several other simplifications, simply used as basis
for the test program. Since the potential core with its high
dynamic pressures and presumably high temperatures is of particular
interest in the application, v' = constant was taken
equal to vA' = vA vo. Therefore,

x = X vA/Vo (7)
d d VA/o 1

This assumption is, of course, justified only for the region around
the jet axis up to the dissolution of the potential core; however,
in this region alone is the assumption of velocity parallel to
the x-axis satisfied. In view of the mixing motion, it would
physically be more logical if a mean velocity within the actual
mixing zone were regarded as characteristic. The transformation (7)N ....
has the advantage of always permitting measurement in planes where
x = constant.


III. EXrRIMniTAL PROGRAM


In all tests, the difference vA vo was kept constant (= 33 m/s).
The first operating condition with zero stream velocity was:

State I: vo = 0; vA = 33 m/s; VA/Vo =c"; x = x',

the second, with comparatively low stream velocity:

State II: v = 11 m/s; vA = 44 m/s; VA/o = 4; x = 1.33 x'

and the third, with greater stream velocity:

State III: vo = 33 m/s; vA = 66 m/s; VA/Yo 2 x = 2x'.

It was found during the measurements that the states I and III
were in most cases sufficient for explaining the principal processes.

The wall distances themselves were limited to a few values, to
a = d (large distance) and a = d/2(small distance); for comparative
purposes, data with the jet motor were also mcasu ed without a
wall (a =c).







NACA TM No. 1214


The lining between engine and wall was kept especially slender
in several cases, since Kunze s tests had shown the importance of
adequate ventilation between jet and wall. As contrast to this
"good" fairing, a particularly "poor" fairing we.s used (figi 1).
These cowlings all te-minated with the exit plane of the power unit.
In one instance, the good version was shifted backward by -d and
cylindrically cut out toward the jet, creating a type of "tunnel."

A model engine with installed blower was used. The measurements,
made in tunnel No. 2, included total pressure and etatic pressure
in y and z direction through the jet axic at various distances
x from the exit nozzle.


IV. FIESULTS


It is found that our knowledge of turbulent diffusion processes
is in no way sufficient to explain definitely the individual
phenomena.


1. Without Wall

Figures 2 to 4 represent the velocity dlistributlons in the
jet at various distances from the exit nozzle for the three
operating conditions. It portrays the cunvcntional -attern of
jet diffusion and. it must be conceded that the foregoing simplifying
assumptions hold only very roughly. For the gr'rdutl decrease in
the potential core with increasing distance the given transformation
is practical, but greater differences occur in the transformation
of the mixing zone, which is in general smaller Lhan the assumption
stipulates. If the coordinate relation (6) were more accurately
taken into account and thus the .'-eator values of x ascribed to
the areas of lower velocity, the agreement would be better. Such
agreement would then be obtained in che boundar;; zone if the mean
velocity in the mixing zone were used as basis, .-hile the de/iacions
in the potential core would become grELacr. It is rcad-ly apparent
that exact agreement is attained in no instun'ye, hence thac ochor
physical processes must also play a part. These are due in part
to the boundary layer on the outer' engine ourfaco hi;:h is particularly
plain in state III and by which the jet is initial,.- enveloped by
a cushion of retarded air; but with it the entire part history of
the outside flow is involved, so that more general predictions are
rendered extremely difficult. Morecver, even for reasons of pure
potential theory, a different jot seems to form with stream flow
than without it. 1While in state I e~ectangular velocity distribution
exists in the exit cone and a jet contracLion is scarcely noticeable,








6 MACA TM No. 1214


the latter is plainly evident in state III as a velocity increase in
the potential core. This geometrical jet deformation could be
induced by the shape of the outer contour which (in adhering flow)
gives the velocity at the edge of the nozzle an inwardly directed
radial component. The jet deformed by the approach flow gives, of
course, a different basis for the mitra of the jct.

2. Large Wall Distance

In this instance, the failing with its boundary layer and the
boundary layer at the wall itself are involved. For comparison,
the velocity distribution in the boundary layer at the wall in
the unaffected state was plotted in the same manner as in the
diagrams of figure 5.

In analyzing the results with the good fairing in figures 6
and 7 the section parallel to the wall (y direction) discloses
practically no deviations from the corresponding state without
wall. Only the planes normal to the wall (z direction) manifest
at greater distance from the nozzle minor differences which reveal
a slight travel of the jet toward the wall when no outside flow is
present. But in state III just the opposite occurs: The maximum
of the velocity distribution travels perceptibly awLy .from the
wall. The wake flow of the fairing is scarcely noticeable and
the boundary layer at the wall also appears to experience no
substantial variation by the flow.

On the poor- fairing (figB. 8 and 9) the conditions are
different. While in state I the jet Ptill seems to move a little
nearer to the wall than with the good fairing, with stream flow
it ceases to move away fram the wall and moves into the dead-air
region introduced by the fai-ing.

To get same idea of the form of the jet in the various fairings,
figure 10 represents the linus of equal velocity in a section normal
to the flow, as well as was possible according to the measurements.
The good as well as the bad fairing show- a form no longer axially
symmetrical, which, however, is flattened out at the well side
in the first case and ovally pulled toward the wall in the other.
The movement of the velocity maximum in different directions is
plainly visible. According to this, it might be suspected that
the good ventilation of the space between enginL and wall with the
good fairing forms a definite air cushion which pushes the jet
away from the wall. This concept is supported by the conditions
in a horizontal section throuUh the jet in figure 11.









NACA TM No. 1214


However, in spite of these dissimilarities, the effects are
comparatively small. In the proximity of a flat wall, the
possibility of a ventilation from the sides is so great as to
preclude the existence of jet adherence even with an extremely
poor fairing.


3. Short-Wall Distance

One noteworthy fact is that the aforementioned processes
are repeated with the short wall distance, hence are not limited
to the comparatively large distance from the wall. As with the
good fairing, there is a slight movement toward the wall in
the absence of stream flow and a movement away from ic with
increasing stream flow (figs.. 12 and 13).

The fairing with tunnel extending backward beyond the afterbody
of the-engine unit is of practical interest for the reason that
in many cases it.is the only way to obtain a sufficiently elongated
form. This fairing likewise exhibits no markedly unfavorable
behavior. The jet naturally adheres in this case at the tunnel
(figs. 14 and 15). This tunnel surface was therefore to have
no projected area in the flight direction for reasons of resistance.
Since, however, the tunnel must be adapted to the form of the jet,
and this is not known at once for the different cngine units,
difficulties may arise, so that, if at all possible, sech a tunnel
fairing should be avoided.

It is perhaps not immediately comprehensible why in these
measurements only these few generalized types of fairings were
investigated and the form of the fairirn not further varied,
to establish, for example, which form could be still designated
as good. According to the cited results, however, the solution
of such a problem does not appear possible at once, since it was
seen that geometrical conditions such as the form of the afterbody
of the engine unit or the past history of the outer flow have some
effect on the phenomena, so that a separation of these problems
from the others for the installation of given conditions seems
hardly correct, and the Reynolds number and the temperature
conditions would then also have to be taken into account: Hence
the limitation to basic experiments. That the conditions in an
installed jet-propulsion unit are similar in the fundamental
phenomena is shown by the wind-tunnel tests on an auxiliary
turbojet ryit model mounted below the fuselage on the Heinkel 119
(reference 2). So, in order to be absolutely certain about the
jet diffusion for a specific design, a test on the total model









NACA TM No. 1214


is probably unavoidable, and judged by past experiences, a water-channel
test is best suited for this purpose.


Translation by J. Vanier
National Advisory Committee
for Aeronautics


REFERENCES


1. Brennecke, H.: Messungen an dem Modell einer Strahlantriebsgondel.
Forschungsbericht Nr. 1723, 1943.

2. BEuerle, H. and Hildenbrand, H.: Widerstands und Schubinderung
bei nachtraglichen Anbau eines TL-Triebwerkes unter den Rumpf
der He 219. Untersuchungen und Mittellungen Nr. 3041, 1943.

3. Kiuchemann, D. and Weber, J.: Uber die Strbmung an ringfdrmigen
Verkleidungen. XI. Mitteilung: Wandnahe Einl'aufe. gttersuchungen
und Mitteilungen Nr. 3051, 1943.





NACA TM No. 1214 9



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NACA TM No. 1214 17









Lines of equal velocity in Jet
(y,z plane normal to approved flow)


With wall, a = d;
good fairing
State III
x/d = 8





V/ 1/.6


With wall, a = d;
bad fairing
State III
x/d = 8








/vo -e.,

0.9


Figure 10.


Exit


/vo =oW0.9



Wall


Exit


Wall


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