DFVLR Deutsche Forschungs- und 

Versuchsanstalt 

fOr Luft- und Raumfahrt 

Forschungsbericht 

NASA-CR-176604 

19860011251 

Shear Layer Excitation, 

Experiment versus Theory 

Dietrich W. Bechert and Bernhard Stahl 

DFVLR 

Institut fOr Experimentelle Stromungsmechanik 

Gottingen 

Abteilung Turbulenzforschung, Berlin 

DFVLR-FB 84-26 

LIBRARY COpy 

.iufl 1 ./ 1986 

LANGLEY RESEARCH CENTER 

LIBR~RY. NASA 

LANGLEY STATION 

HAMPTO~. VIRGINIA 

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der Deutschen Forschungs- und Versuchsanstalt Hir Luft- und Raumfahrt e.V. (DFVLR), 

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Postfach 906058, 5000 Koln 90. 

ISSN 0171-1342 
DFVLR Deutsche Forschungs- und 

Versuchsanstalt 

fUr Luft- und Raumfahrt 

Forschungsbericht 

Shear Layer Excitation, 

Experiment versus Theory 

Dietrich W. Bechert and Bernhard Stahl 

DFVLR 

Institut fUr Experimentelle Stromungsmechanik 

Gottingen 

Abteilung Turbulenzforschung, Berlin 

84 pages 

40 figures 

2 tables 

23 references 

DFVLR-FB 84-26 
Hanuskript eingereicht am 30. Juli 1984 

2 
Stability, Aeroacoustics, Shear Layers, Jets 

Dietrich W. BECHERT and Bernhard STAHL 

Institut fOr Experimentelle Stromungsmechanik der DFVLR, Gottingen 

Abteilung Turbulenzforschung, Berlin 

Shear Layer Excitation, Experiment versus Theory 

DFVLR-Forschungsbericht 84-26, 1984, 84 pages, 40 figs., 2 tabs., 23 refs., 

21,50 DM 

The acoustical excitation of shear layers is investigated. Acoustical excitation 

causes, e. g., the so-called "orderly structures" in shear layers and jets. 

Also, the deviations in the spreading rate between different shear layer 

experiments are due to the same excitation mechanism. The present investigations focus on measurements in the linear interaction region close to the 

edge from which the shear layer is shed. Report is given on two sets of 

experiments (Houston 1981 and Berlin 1983/84). The measurements have 

been carried out with shear layers in air using hot-wire anemometers and 

microphones. The agreement between these measurements and the theory is 

good. Even details of the fluctuating flow field correspond to theoretical 

predictions, such as the local occurrence of negative phase speeds. 

Stabilitat, Aeroakustik, Scherschichten, Strahlen 

(In englischer Sprache) 

Dietrich W. BECHERT und Bernhard STAHL 

Institut fur Experimentelle Stromungsmechanik der DFVLR, Gottingen 

Abteilung Turbulenzforschung, Berlin 

Scherschlcht-Anregung. Vergleich von Experiment und Theorie 

DFVLR-Forschungsbericht 84-26, 1984, 84 Seiten, 40 Bi/der, 2 rabel/en, 

23 Uteraturstel/en, 21,50 DM zzgl. MWSt 

Eine Scherschicht wird akustisch angeregt. Akustische BeeinflLissungen dieser 

Art treten bei Scherschichten und Triebwerksstrahlen meistens auf und 

erklaren die Existenz .. geordneter Strukture_n". Die Unterschiede in der Ausbreitungsrate von Scherschichten bei verschiedenen Experimenten kommen. 

ebenfalls durch akustische Anregung zustande. Die jetzigen Experimente 

konzentrieren sich auf den Bereich Iinearer Scherschichtbeeinflussung im 

Bereich der Abstromkante. Ober zwei Reihen von Experimenten wird berichtet 

(Houston 1981 und Berlin 1983/84). Die Messungen wurden an Scherschichten 

in Luft mit Hitzdrahtanemometern und Mikrofonen ausgefOhrt. Die Obereinstimmting mit der Theorie ist gut und geht bis in Details des Wechselstromungsfeldes, wie etwa das lokale Auftreten von negativen Phasengeschwindigkeiten. 

Shear Layer Excitation, Experiment versus Theory *) 

Deutsche Forschungs- und Versuchsanstalt fUr Luft- und Raumfahrt 

Forschungsbereich Stromungsmechanik 

lnstitut fUr Experimentelle Stromungsmechanik 

Abteilung Turbulenzforschung 

MUller-Breslau-StraBe 8, 0-1000 Berlin (West) 12 

Berlin, 1m Marz 1984 

Komm. Forschungsbereichsleiter: 

Prof. Dr.rer.nat. H.L. Jordan 

lnstitutsleiter: 

Prof. H. Hornung, Ph.D. 

Abteilungsleiter: 

Dr.-lng. E. Pfizenmaier 

Verfasser: 

Dr.-lng. D.W. Bechert 

Dipl.-lng. B. Stahl 

*) Supported by NASA Lewis Research Center Grant NAG 3-198 (1981) 

and by the Deutsche Forschungsgemeinschaft Grant Be 889/1-1 

(1982-84) • 

3 
StabiLity, Aeroacoustics, Shear Layers, Jets 

Shear Layer Excitation, Experiment versus Theory 

Summary 

The acoustical excitation of shear layers is investigated. 

Acoustical excitation causes,e.g.,the so-called "orderly structures" in shear layers and jets. Also, the deviations in the 

spreading rate between different shear layer experiments are due 

to the same excitation mechanism. The present investigations focus on measurements in the linear interaction region close to the 

edge from which the shear layer is shed. We report on two sets of 

experiments (Houston 1981 and Berlin 1983/84). The measurements 

have been carried out with shear layers in air using hot wire 

anemometers and microphones. The agreement between these measurements and the theory is good. Even details of the fluctuating 

flow field correspond to theoretical predictions, such as the 

local occurence of negative phase speeds. 

StabiLitat, Aeroakustik, Scherschichten, StrahLen 

Scherschicht-Anregung. Vergleich von Experiment und Theorie 

Ubersicht 

Eine Scherschicht wird akustisch angeregt. Akustische Beeinflussungen dieser Art treten bei Scherschichten und Triebwerksstrahlen meistens auf und erklaren die Existenz "geordneter Strukturen". Die Unterschiede in der Ausbreitungsrate von Scherschichten 

bei verschiedenen Experimenten kommen ebenfalls durch akustische 

Anregung zustande. Die jetzigen Experimente konzentrieren sich 

auf den Bereich linearer Scherschichtbeelnflussung im Bereich der 

Abstromkante. Uber zwei Reihen von Experimenten wird berichtet 

(Houston 1981 und Berlin 1983/84). Die Messungen wurden an Scherschichten in Luft mit Hitzdrahtanemometern und Mikrofonen ausgeflihrt. Die Ubereinstimmung mit der Theorie ist gut und geht bis 

in Details des Wechselstromungsfeldes, wie etwa das lokale Auftreten von negativen Phasengeschwindigkeiten. 

4 
Contents page 

1. Introduction............................................. 7 

2. Relevant facts from theory............................... 9 

2.1. Basic assumptions................................... 9 

2.2. Excitation field.................................... 11 

2.3. Velocity distributions, one stream case ............. 15 

2.4. Velocity distributions, two stream case ............. 20 

3. Short information on the facility........................ 21 

4. Mean flow field.......................................... 23 

5. Excitation sound field .•...•...........................•. 27 

6. Interaction measurements................................. 32 

6.1. Extrapolated field data............................. 32 

6.2. Direct comparison of the field data ................. 35 

6.3. Phase measurements .................................. 42 

6.4. Measurements at higher Strouhal numbers .•......•.... 45 

7. Conclusions.............................................. 49 

8. References............................................... 52 

; 

9. Appendices............................................... 55 

9.1. Appendix A: Glossary of symbols ..................... 55 

9.2. Appendix B: Experimental apparatus .................. 59 

9.2.1. Facility Houston .................•.............•.. 59 

9.2.2. Facility Berlin ................................... 62 

9.2.3. Boundary layer suction............................ 69 

9.2.4. Vibration system ..................•......•........ 72 

9.2.5. Background noise ......................•........... 78 

9.3. Appendix C: Typing errors of DFVLR-FB 82-23 ......... 83 

5 

1. Introduction 

The fact that sound waves cause wavelike perturbations and 

orderly vortex formations in shear layers and jets has been known 

for at least one hundred years [1,2]. Even excellent photographs 

of shear layers demonstrating the evolution of vortices are 

available for more than fifty years, s~e Fig. 1. 

Fig. 1 Roll-up process in a shear layer. Photograph taken by 

F. Michel, 1932 [3]. 

Observations on excited jets led to the development of the stability theory of flows by Lord Kelvin, von Helmholtz and Lord 

Rayleigh. The interest of theoreticians in the following century 

was concentrated on determining the limits of the stability of 

flows and on the evolution of the instability waves including 

their nonlinear development. 

On the other hand, little attention had been paid to the understanding of the initial observations, i.e., that instability 

waves in shear layers are tied to acoustical waves. During the 

last decade, it was demonstrated that also turbulent flows can 

7 
be dominated by instability waves and the subsequent evolution 

of turbulent vortices [4]. Also, the significance of acoustic 

excitation became evident in turbulent shear flows, as it was in 

the analogous case of laminar shear layers [5,6]. Moreover, the 

observation that the broad band noise emission of turbulent jets 

can be enhanced by acoustical tone excitation [7,8,9] has increased interest in the forcing mechanism of instability waves. 

Thus, a small number of theoretical papers on acoustical shear 

layer excitation has emerged in the past ten years [10t13]. 

Unfortunately, these papers did not produce results which were 

easily verifyable by experimentalists. In addition, there was 

no guideline on what the relevant quantities to be measured were, 

and how to proceed in such an experiment. One of the authors 

(D.W.B.) tried to produce the necessary theoretical data in a 

preceding report [14]. The present experimental investigation 

aims at verifying this theoretical material. 

We provide here two sets of data taken in different institutes. 

The first set was taken in 1981 by D.W. Bechert at the Univeristy 

of Houston, Tx., U.S.A .. However, it was suspected that these 

data might have been slightly contaminated by systematic errors 

caused, e.g., by: 

(i) overshoot of the mean velocity profile at the shear layer, 

(ii) too high vibration levels in the facility which caused 

problems with the vibration sensitivity of the microphones, 

(iii) partly unreliable electronic instruments, such as a beat 

frequency oscillator, which did not keep the excitation 

frequency sufficiently constant. 

Subsequently, the major possible error sources were scrutinized 

and it was concluded that the Houston data were at least of 

value in suggesting that the theory is correct. Thus, some data 

were published in 1983 [15]. 

8 
A second facility was then established in Berlin. The new data 

taken by B. Stahl and D.W. Bechert were much more reliable and 

reproducible. On the other hand, it turned out, that only very 

. few of the previous (Houston) data had to be rejected, and none 

of the published ones. In hindsight, it might appear that we 

were overscrupulous to carry out an experiment twice. However, 

the issue of shear layer excitation is so much confused by 

lacking thoroughness of previous authors, that it seemed worthwhile to have this double effort to solve the problem. 

2. Relevant facts from theory 

2.1. Basic assumptions 

We outline here the basic assumptions of the theory and the 

theoretical results from our previous report [14] relevant for 

. this experimental investigation. The following simplifying 

assumptions had been introduced in the theory: 

1. plane flow 

2. all fluctuating quantities harmonic in time,i.e.,«e-iwt 

3. linearized problem 

4. incompressible flow 

5. parallel mean flow 

6. invi scid flow 

7. infinitesimally thin shear layer. 

The assumptions (1) and (2) can be fulfilled easily in an 

experiment. The perturbation velocities should be small in 

comparison to the mean flow velocity so that linearity is still 

maintained (3). Linearity can be also checked directly in the 

experiment. This can be done by varying the excitation level and 

by observing the velocity fluctuations in the region of the 

highest fluctuations in the shear layer. If excitation level 

and velocity fluctuations are proportional, the system is linear. 

This linearity, however, applies only to a certain region downstream of the splitter plate edge. Beyond this linearity regime 

no data were taken in our experiments. The condition of incompressibility (4) can be maintained, at least for the interaction 

9 
region downstream of the splitter plate, if the Mach number is 

small, as shown in our theoretical report [14]. If we want to 

calculate the pressure distribution of the excitation field we 

can use incompressible flow theory (such as conformal mapping) 

if the acoustic wavelength is large compared to the typical 

dimension of the test section, i.e., the channel width of our 

facility. Conditions (5) to (7) are related to viscosity effects. 

Parallel mean flow (5) is reasonable to assume for a laminar 

shear layer if the Reynolds number is not too low. The condition 

of inviscid flow (6) has been shown to work remarkably well if, 

again, the Reynolds number is not too low [16,17]. The strongest 

restriction is the condition of an infi~tesimally thin shear 

layer (7). Consequently, we can expect a good agreement between 

the theory [14] and our measurements only at low Strouhal numbers, 

where the wavelength of the perturbations is large compared to 

the thickness of the shear layer. We can assume that deviations 

will occur where the conventional stability theory *) predicts 

deviations (in spatial amplification rate and wave number) between a simple step velocity profile, with thickness zero, and a 

real shear layer velocity profile. If we consider Michalke's 

theoretical results [16], see Fig. 2, we expect the onset of deviations at a Strouhal number, say, between se = 0.003 and 

se = 0.005. It should be mentioned that the Strouhal number 

se = f.e/U2 is calculated with the momentum thickness e of the 

shear layer velocity profile (therefore, the actual numbers of 

Sa are comparatively small). f is the excitation frequency and 

U2 is the mean flow velocity. 

Michalke's calculations in Fig. 2 have been carried out for a 

mean velocity profile with the shape of a hyperbolic tangent 

function. The magnitude growth of the instability waves is proportional to e ArX in the downstream direction x. A. is the wave ~ 

number of the instability waves. The relation to the more 

common symbols a i and a r is also given in Fig. 2. 

*) The term "conventional stability theory" means calculations 

on shear layers with properties invariable in the streamwise 

direction, i.e., parallel mean flow and the shear layer being 

extended from minus infinity to plus infinity. 

10 
0.08 

0.01. 

Ar8 =-Uj8 / 

t ~~hin"Shear f' layer 

5 e -

0.01 0.02 0.03 0.Ql. 

0.3 r----...,.......----r-----r----.,-....,......---, 

0.2 

0.1 t --- ---

"thin"shear 

layes- -- \.--

--- Sa .. 

O~_~~_~~ __ ~~~ __ ~~~~ 

o 0.01 0.015 0.020 0.025 

Fig. 2 Amplification rate (Ar8) and wave number (Ai 8) of a 

shear layer with finite thickness [16]. 

2.2. Excitation field 

One of the most relevant ideas in our previous theory [11,14,15] 

is the concept of field decomposition. The fluctuating field is 

split into one contribution produced by the exterior forcing 

(excitation field) and another produced by the shear layer per11 
turbation. Both together fulfill the conditions of equal pressure and equal displacement on both sides of the shear layer. 

The excitation pressure is transmitted through the shear layer 

and hence this pressure contribution is antisymmetrical with 

respect to the shear layer. The pressure contribution from the 

shear layer itself, on the other hand, is symmetrical with respect to the shear layer, see Fig. 3. 

'region "1"" \Xcitation source 

== 0, - !./excitation pressure 

\ /- -- ' __ .===7'===~...p===1 ~ -1- L // ./ ?'p~ ,,' -........ ",,/ splitter plate I-- x / \---- ~~~~ O2 \' i shear layer 

shear layer pressure 

I region "2"11 

Fig. 3 Field decomposition in antisymmetrical (excitation) and 

symmetrical (shear layer) parts of the pressure field. 

If we consider the most common case of an excitation, where the 

source is not too close to the trailing edge of the splitter 

plate, we find an excitation field which is parabolic (see 

Fig. 4). 

The distribution of this (instantaneous) excitation pressure 

field can be determined by conformal mapping [14]. Its magnitude 

can be found experimentally by measuring the pressure difference 

P1-P 2 = ~P12 on both sides of the splitter plate, not too far 

upstream of the trailing edge. The relevant quantity of the 

12 
Fig. 4 Instantaneous parabolic field of the exterior excitation. 

excitation field is the forcing velocity v f perpendicular to the 

shear layer. It is proportional to the pressure difference 6P12 

and obeys the following law [14]: 

(1) -i 

The coefficient i corresponds to a 90 0 phase shift in comparison 

to the phase of 6P12. t is the distance of the microphones (to 

measure 6P12lfrom the trailing edge of the splitter plate. We 

find that vf is proportional to 1/1X. This produces a singularity 

of vf at x = o. However, the complete flow field does not have 

any singularities at the trailing edge [14]. 

There is a deviation from the 1/lx law if the splitter plate is 

located in the center of a channel. This arrangement is typical 

for experiments, because one can produce only streams with finite 

width. For a calculation of this, more realistic case we assume 

that the sound sources are located in the channel far upstream 

of the trailing edge of the splitter plate. If the sound wave13 
length of the excitation is much larger than the channel width, 

the problem can be solved analytically by conformal mapping [14). 

The result differs slightly from equation (1), i.e., 

(2) v f =-i 

In this equation 2d is the width of the channel. We find that 

the field is still parabolic in the vicinity of the plate edge, 

but it decays more rapidly in the downstream direction. 

To plot the data of v f ' measured in a channel, we may use a 

dimensionless form. Since these data are taken in air at rest 

with the mean velocity U2 = 0 we cannot use any reference velocity which contains this quantity. If we assume, hypothetically, 

a sound excitation far upstream in the channel, we can use the 

fluctuating velocity there, u oo • It has the value [14): 

(3) 

With that reference velocity, we may write eq. (2) for 

convenience *) 

(4) 

In an experiment, it is also possible to determine directly the 

value of v f and its relation to the excitation pressure difference 6P12. For this purpose we take measurements with only the 

*) Throughout this paper, a quantity between vertical bars like, 

e.g., Ivfl means the modulus or peak value of this quantity 

during one cycle of a sinusoidal vibration. 

14 
excitation sound field switched on. In the vicinity of the plate 

edge we produce under almost all conceivable excitation conditions a standing pressure field. The local fluctuating pressure 

can be measured with a pressure probe with a typical resolution 

of 1f1,5 mm. We can measure, e.g., the pressure Ipl as a function 

of y in sections of x=const. The gradient alpl/ay, which can be 

evaluated graphically at y=o, allows to determine v f by using 

the Euler equations. We find 

(5) Ivfl= pw 

l.W. 

ay (y=o)· 

The evaluation.of the real distribution of v f in the test section 

as compared to equations (1) and (2) will be shown in section 5 

of this paper. 

2.3. Velocity distributions, one stream case 

With mean flow switched on, we have an interaction between excitation field and shear layer. The theory for this interaction 

is explained extensively in our previous publications [11,14,15). 

First, we provide here the solutions for the one stream case 

where the mean flow velocity above the shear layer is zero 

(U1 = 0). For the resulting v velocity perpendicular to the mean 

flow and just above the shear layer in the fluid at rest we find 

a general solution [14): 

(6) 

with 

(7) w (i+1 ) w (i-1) 

If we insert v f from eq. (1) we obtain 

(8) i erfG - _e_ erfYA 2

A2 ..,xX x r---J 

1 1~-1 

15 
The expression erf ~ becomes unity for wx/u2 » 1, and the 

second expression in the brackets of eq. (8) vanishes for 

wX/U2 »1 because it is exponentially decaying. So we have for the 

mean value of v 1 : 

(9) e wx/U2 f for WX I-U2»1 

In fact, this equation is already valid above wx/U2~1.5. The 

quantity 16P121/p/U2wi has the dimension of a velocity and may 

be used as a new reference velocity of the excitation 

(10) 

On the other hand, it is also convenient to divide all fluctuating quantities by this reference velocity to obtain dimensionless quantities, like 

( 11) 

In addition, it is useful to introduce dimensionless length 

scales in the form of Strouhal numbers, namely 

( 12) y 

Hence, equation (9) becomes quite simple 

(13 ) 

However, equations like (8), (9) or (13) cannot be verified 

easily, because it is very difficult to measure small v-velocity 

components in a mean flow 5 (in x-direction)'. It is much more 

convenient to measure accurately fluctuating u-velocities with, 

16 
e. g., a hot wire probe. In addition, it is also preferable, to 

take hot wire measurements in a region with mean flow (region 

"2" in Fig. 3 below the shear layer with y~o)rather than in a 

fluid at rest. For the fluctuating u-velocity at y= -0, just 

below the shear layer, the theory [14,151 provides a very simple 

analytic solution *), i.e., 

(14 ) -i 

with the modulus 

(15 ) 

Unfortunately, again this velocity cannot be measured directly. 

The real fluctuating velocities inside the shear layer cannot be 

predicted by a theory for an infinitesimally thin shear layer. 

There is, however, a way to extrapolate the experimental data 

taken outside of the ,shear layer to obtain the value of 1~21 at 

y=-o. We plot the data measured in the potential field outside 

the shear layer on logarithmic paper and extrapolate linearly 

towards the center of the shear layer (see Fig. 5). 

This procedure should work at least for locations farther downstream, where we expect an exponential decay in y-direction of 

the instability waves. 

The data in our previous publication [151 and in section 6.1. of 

this report are evaluated with this procedure. The technique is 

useful to plot our numerous data, but it has also its limitations. 

This will become evident,if we consider numerically calculated 

distributions of 1~21. Such data had been provided in our theory 

*) Eq. (14) is mistyped in our theory report [141, the negative 

sign had been omitted. A list of typing errors of this report 

[14) is given in the appendix. 

17 
x = const. 

to 1 

x=const. 

Fig. 5 Mean flow velocity profile and logarithmic plot of the 

fluctuating velocity lu21 with extrapolation. 

report [14]. Fig. 6 shows these theoretical data for various 

- distances x upstream and downstream of the splitter plate edge. 

From Fig. 6 we see, that an extrapolation for y = -0 at small x 

produces too low values of lu21 = -0. At sufficient distance, - y 

say, at x > 0.5 the extrapolation is valid, though. 

A direct comparison between measurements and computed values, 

like in Fig. 6, is more conclusive and it will be also carried 

out for one series of data. 

As we have seen in section 2.2., the acoustical excitation does 

not produce under all circumstances a 1/{X law for the forcing 

velocity v f (see eq. (1». It may deviate by the existence of 

channel walls and may decay, therefore, more rapidly in the 

downstream direction, see eq. (2). An estimation of this in18 
10 r----,----,----.----~----~--~--~ 

6 

6 

5 

4 r-~~-

3 

2 

1.5 

t 1 

lu21 .8 

.6 

.5 

.4 

.3 L..----~~----------------~ 

.2 

)(=-2 

.15 

y--

0.1 

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 o 

Fig. 6 Computed values of lu21 in the mean flow region y~o, 

from [14]. 

19 
fluence can be also found in our theory report [14]. The magnitude of the shear layer fluctuations decreases by a coefficient 

(16 ) 'IT 

C = (1 - 16 

However, as an influence of the finite channel width 2d this 

plays only a role for the Houston data. For the lowest Strouhal 

number, we obtain there a fluctuation magnitude decreased by 

11.2 %. For the higher Strouhal numbers, this has no perceivable 

effect anymore. 

2.4. Velocity distribution, two stream case 

There is still another basic difference between the theoretical 

results displayed so far and an experimental situation. In an 

experiment with a shear layer located in a channel" the mean 

flow velocity in the region y>o above the shear layer (see 

Fig. 3) cannot be kept zero. If it were zero, the entrainment of 

the shear layer would produce a significant recirculation in the 

region y>o,and also the shear layer itself would be deflected. 

Thus, in the present experiments, the mean flow velocity ~1 

above the shear layer was 10 % of the mean flow velocity U2 below the shear layer. So we have the velocity ratio a: 

(17 ) 0.1 

The presence of the second stream changes the distribution of 

the fluctuating field slightly. In our theory report [14] we 

have also considered this case. We find for u 2 

(18 ) 

with 

( 19) 

ii = -i·;; • ~~+ia.e~lX+l-ia.e~2X~ 2y =_0 4(1+a 2 ) Ir- Ir1 2 

1 ,1,1,2 = 1+a2 [i(l+a)±(l-a)] 

and with x wx/u2 , as before. Also the reference velocity, 

given by eq. (10), remains the same. For the modulus lu21 we 

20 
can derive from eq. (18) 

(20) 

>< 2(1-0)X+e-2(1-o)X+2COS(~ + (1+0» 2 2arctgo-arctg 1-0 

This boils down to 

(21) for 0 0.1 . 

Eq. (21) produces values of \u2 \ lower than eq. (15). The comparison with the experiments will also show a better agreement. 

We do not possess, however, any computed field data like for the 

case 0 = U1/U2 = o. Nevertheless, from our understanding of the 

interaction process we can assume, that for x < 0 the excitation 

field will dominate, so the values of u2 for t~e two cases should 

not differ significantly there. For distances x > 1 the instability wave should dominate. Here, the decay in y-direction should 

be enhanced by the coefficient (1+0)/(1+0') due to the fact that 

the wave number in x-direction is increased by this coefficient. 

This follows from a consideration of the induced velocity field 

of an infinitely extended instability wave. Or, roughly speaking, 

a wave field propagating in x-direction with wave number a 

decays exponentially with e-\ay\ in the y-direction. This latter 

consideration allows at least to estimate the distribution of 

\u2 \ for 0 = 0.1 if it is known for 0 = 0, the one stream case. 

3. Short information on the facility 

Fig. 7 shows the test section of the experimental setup. The 

splitter plate in the center of a rectangular channel separates 

the mean flow region (U=U2 at y<o) from a region of very slow 

entrainment flow (°1:0.1°2 at y>o). The initial shear layer 

21 
thickness can be controlled by boundary layer suction through a 

slit in the splitter plate near the plate edge. 

plate 

shear layer 

y 

~hot wire probe 

vibrating plate rectangular channel 

Fig. 7 Experimental arrangement. 

The excitation is provided by two vibrating plates driven 

electromagnetically and adjusted in antiphase so that a surging 

motion around the edge of the splitter plate is produced. The 

magnitude of the excitation field ist measured by two microphones on both sides of the splitter plate. The pressure difference P1-P2 = 6P12 is a direct measure for the acoustic excitation. 

In order to prevent effects of the suction slit on the sound 

field, the oscillating flow through the slit can be compensated 

acoustically by a piston speaker in the suction duct. This 

piston speaker can be adjusted in magnitude and phase so that 

zero oscillating flow condition through the slit is achieved. 

This is checked by a second hot wire probe (not shown in Fig.7) 

inserted into the slit. In this way, the suction slit can be 

sealed acoustically. 

22 
We think, that this short information is sufficient to understand 

the measured data in the following sections. On the other hand, 

it cannot be understood how comparatively involved these measurements really are without reading the more detailed description 

of the experimental apparatus in the appendix; The flavour of 

the project can be appreciated much better if one knows explicitly where we used, e.g., the following items: 

(i) lady's stockings 

(ii) coffee sifters 

(iii) an empty barrel 

(iv) a garden hose 

(v) a vacuum cleaner. 

4. Mean flow field 

The data in this investigation had been taken under 4 different 

mean flow conditions, i.e., mean flow velocity 6 m/s or 12 m/s 

with boundary layer suction *} off or on. For each data set, 

Houston 1981, and Berlin 1983/84, the mean velocity distributions have been measured (see Figs. 8 and 9). 

The Houston data show a little overshoot in the potential flow 

region, which is due to an interaction between screen and nozzle 

(see also appendix, section 9.2.1.). If we consider the differences between measurements without and with boundary layer 

suction, we see that 

(i) indeed, the boundary layer suction decreases the initial 

shear layer thickness effectively, and 

(ii) on the other hand, farther downstream, the shear layer 

spreading rate is increased. 

*} Suction rate: 28·3 l/min (Houston) and 34.0 l/min (Berlin). 

The rate was the same for 6 m/s and 12 m/s mean velocity. The 

splitter plate breadth was 100 rom in both facilities. 

23 
I\) 

"'" 

15r. ----r---~--~----,_--_.--_, 

Imlsl 

t 

o 

no suction 

O2 = 6mls 

e =0.479mm 

A X=50mm 

x =40mm 

/ ~X=30mm /// =20mm 

0

1 .111111 

-6 ,~)p o n\ 

y_ ImmJ +6 

Im~~1 :;: 7 

I 

o 

no suction 

U2=12m/s 

e =0.395mm 

01 x=1~m~1 -6 0 1"",,1 +6 

y -----'-

15.r-----r-----r-----r-----r-----T-----, 

ImlsJ 

o 

with suction 

02=6m/s 

e =0.244mm 

01 A_ ".""'~¥ _0', ON 

-6 0 ImmJ +6 

y15r.-----r-----r-----r-----r----~----_, 

Im/SJ, 

~---=~$C.~~.~~~----77 

t 

o 

with suction 

O2 = 12m/S 

e =O.200mll1 

0 1 x=l,mm~?04 

-6 0 ImmJ +6 

y--

Fig.8 Mean flow distribution (Houston 1981). 
Im~~1 ::: i 8 I m/sl 

1 ~ no suction . \;9}:18~ x =30 mm 

~ I t I with suctiorr 

02=6m/s i;x=20mm O2 = 6m/s 

a =0.420mm / o a = 0.230mm I::::> 

0' r I 0 

-10 0 1 .... 1 10 -10 0 1....,1 10 

y--- y---

IV 

U1 

14 14 

Imlsll Imlsl \W ....... ~ no suction =30mm with suction 

O2 = 12m/s r=20mm O2 =12m1s 

a =0.363mm e =0.22Smm 

I::::> I I::::> 

01 C='"J 01 1-

-10 0 Imml 10 -10 0 Imm) 10 

y--- yFig. 9 Mean flow distribution (Berlin 1983/84). 
Thus, the boundary layer suction produces a smaller shear layer 

thickness only over a certain downstream distance. In addition, 

we see that it is hard to define a meaningful shear layer thickness 8. The situation becomes even more complex, if we consider 

the splitter plate wake which is in particular visible for the 

Berlin measurements (where we have no turbulent separation at 

the splitter plate like in the Houston data). A definition (see 

also Fig. 10) like 

dy 

would lead, with the present data, to a momentum thickness which 

always varies with x. On the other hand, we would prefer to have 

a simple reference quantity for the shear layer thickness. A 

quantity, however, which does not vary very much within the first 

15 mm downstream of the plate edge is the slope of the mean 

velocity profile. Therefor~, we use a definition which, admittedly, is not very sophisticated,but appeared to be suitable (see 

Fig. 10). 

y .. 

t profile 

u 

~ ____ -...L. U, 

Fig. 10 On the definition of 8. 

26 
(i) we determine the slope of the initial profile at, say, 

x=1mm, where the slope is still identical with that of the 

plate boundary layer 

(ii) we replace the real velocity profile with a hyperbolic 

tangent profile of the same slope 

(iii) we determine the points A and B where the slope line intersects with the lines U=o and U=U 2 , and we determine the 

horizontal distance of the two points A and B. For a hyperbolic tangent profile this distance would be 4 times the 

momentum thickness a. 

We take this artificial momentum thickness a as our reference 

quantity. This reference quantity is not too dissimilar to 

Freymuth's am [17]. Readers who are not satisfied with this crude 

definition of the momentum thickness a might redefine it with 

the data of Figs. 8 and 9. 

5. Excitation sound field 

The shear layer is excited by two vibrating plates which are 

driven by electromagnetic loudspeaker systems. In both sets of 

data (Houston 1981 and Berlin 1983/84) the same vibrating plates 

had been used. The vibrating plates are operating in antiphase, 

i.e., both are moving up and down simultaneously and produce a 

surging flow around the splitter plate edge. The boundary layer 

suction slit in the splitter plate is not drawn in Fig. 11. 

During the excitation field measurements, it is sealed anyway. 

The geometry of our test sections is shown in Fig. 11. To the 

left hand side of the test sections a nozzle is connected from 

which the mean flow comes. The region below the symmetry line 

contains the stream of high velocity U2 . During the excitation 

field pressure measurements, however, the mean flow is switched 

off. 

Before the data are taken, the pressure probe is moved to the 

symmetry line y=o at a distance not too close (about x=10 mm) 

to the edge of the splitter plate. The vibrating plates are 

27 
vibrating plate 

1----160 --- o 

~ 13 

~+f4:Jx 

motion 

-1 

I 0 

U1 

~ 

i 

pressure probe 1~ 

160 210 

- -- '/ '/ '/ 

r, ~ 

Fig. 11 Configuration of the test sections. Above: Houston 1981, 

below: Berlin 1983/84. 

28 
operated at the frequency of the, later following, shear layer 

experiment. Then, the phase and magnitude of the vibrating plates 

is adjusted so that we obtain zero pressure at the probe location. 

With this anti-symetrical adjustment we take the excitation 

field data. A typical data plot can be seen in Fig. 12. The 

modulus of the pressure ipi is plotted linearly on the horizontal 

axis and the vertical distance y from the symmetry line in the 

test section corresponds to the vertical axis. The phase of p 

shifts by 180°, if we move the probe from negative y to positive 

y, so we have indeed an anti symmetric pressure field. Theoretically, the pressures for the various x should all be zero at 

y=o. For the facility is not completely symmetrical, this occurs 

exactly only at the location where the zero adjustment has been 

made. 

A graphical evaluation of the forcing velocity v f following the 

procedure of section 2.2. is shown in Fig. 13. The data of the 

Houston facility (see Fig. 11) follow exactly the prediction of 

eq. (4). The vibrating plates of the Berlin facility are located 

more downstream. This produces a vf-distribution which follows 

more the desired 1/IX distribution of an "infinite" facility. 

In the regime, where the shear layer interaction data are taken, 

up to x = 30 mm (x/d = 0.2), the Berlin facility shows ~ 

deviations from the 1/1X law. 

For the case with flow, the excitation level 6P12 is sometimes 

not maintained. In particular in the Berlin facility, the excitation field is sometimes slightly changed due to impedance changes 

of the nozzle with flow. The evaluation of the data is based, 

however, on a direct measurement of 6P12 (with flow) by microphones inserted flush to the side-wall. This requires, that the 

sound field is strictly two-dimensional, which has been checked 

carefully. By the way, the proper adjustment of the sound field 

is not crucial for the shear layer excitation experiments. 

Nevertheless, it is dependent on an accurate determination of ->- -+-

6P12=P1-P2' which is in fact a difference of two vectors. This 

difference can be taken electronically with two microphones. For 

29 
[mm\ 

5 

t mm 

mm 

y 

o 

-5 

0.4 [N/m2 ) 0.8 

Fig. 12 Fluctuating pressure distribution in the test section 

without flow. Data taken at f=200 Hz in the Berlin· facility. 

x is the distance downstream of the trailing edge of the 

splitter plate, given in mm. 

30 
10 

t 

I vII 

uoo 1.0 

0.1 

0.D1 

uoo I: --- t VI 

uc: -x 

~ ~~. 

, .... ~ v,'" 1ft>: 

0, 

~ .. -

~ 

~ -" ." 

'\\ eq.(4) ., 

° 

0.1 

xld - ° ~ f = 100 Hz. Houston 1981 

x ~ f = 100HZ} Berlin 1983/84 

+ ~ f = 200Hz 

5 

Fig. 13 Fluctuating velocity distribution of the forcing field 

. v f . Comparison between experimental data under different configurations (see Fig. 11) and theory with channel of width 2d. 

better accuracy, however, one microphone is used which is moved 

from location "1" to location "2". In both locations, magnitude 

P1' P2 and phase <P l' cP 2 relative to an arbitrary reference 

phase are measured. I~P121 is then determined by vector sub31 
traction, namely 

For those who are not aquainted with the logarithmic dB-scale of 

pressures, we provide here also the conversion from pressure 

read in dB from sound level meters, to pressures in N/m', as we 

use them here 

(24) p [N/m'] 

6. Interaction measurements 

6.1. Extrapolated field data 

The shear layer is excited at one single frequency. In order to 

suppress the background noise the velocity signal taken with a 

hot wire probe is filtered at the same frequency. We will show 

here data of !U2 !y=o' extrapolated from measurements outside 

the shear layer in the potential flow. We follow the procedure 

suggested in Fig. 5, section 2.3 •• As we have mentioned already, 

the extrapolation scheme is well suited for a data survey, but 

it tends t~ underpredict the velocity values !~2Iy=o for small 

distances x from the splitter plate edge. In Figs. 14 and 15 we 

see the data taken in Houston*) and in Berlin. The Houston data 

show a trend of lower values for small Strouhal numbers which 

can be explained with a lower excitation due to a narrower test 

section. The trend is well predicted by our equation (16) in 

section 2.3 .• For higher Strouhal numbers we see a general trend 

of increasing fluctuation levels well above the theoretical prediction. Significant deviations begin at Sa = 0.005, as expected 

*) We should mention, that the data shown in Fig. 14 are the 

same as those published in [15]. The Strouhal numbers, however, 

are slightly different. This has two reasons. First, the mean 

velocity data to determine the momentum thickness a of the shear 

layer have been revisited in order to avoid such data where 

probe interference had changed the measurement of the shear 

layer profile. Secondly, the momentum thickness a is now chosen 

according to the procedure suggested in section 4. 

32 
10r--------r------~r_----~----~--------~----~ 

3 

theory. eq.I211 

101=0.102 1 

Symbol 

0 

• 0 

• 0 

t:. 

* 

Sa 02(mlsl 

0.005 13.5 

DOO2B 6.49 

0.0027 13.05 

0.0024 13.76 

0.0023 6.53 

0.0019 6.79 

0.0007 13.28 

1 theory. asympt.1 

f(Hzl It.p~ (Hlm2 1 Suction 

177 1.079 NO 

75 0.341 ~ 

179 1.079 YES 

83 1.079 NO 

31.6 0.341 NO 

51.4 0.341 YES 

49.6 1.079 YES 

0.3~----~------~------~------~------~----~ o 2 3 

xFig. 14 Shear layer excitation (Data Houston 1981). Experiments 

with finite shear layer thickness S versus theory for an infinitesimally thin shear layer. The diagram shows the dependence of 

the fluctuation velocity 1~2Iy=0 on the downstream distance x for 

various Strouhal numbers Ss=fS/U2• 

33 
10r-----.------.-----r----~----_,----_,.,----~ 

3 

theory, eq.(21) 

101=0.102 ) 

Symbol 

• 0 

Y 

V 

• 0 

. / 

O'i7 / 

. // ./ .. /,/ / / . . ,/ / 

Q, ~ /' -01=0 

• /y / 01 =0.1 O2 / 

~ / /b / 

1 theory, asympt. ) 

S9 1021m/ii f IHzl It.P1ziIN/m21 Suction 

0.0059 12 195 0.236 NO 

0.0059 6 154 0.0939 YES 

0.0041 12 135 0.789 NO 

0.0041 6 106 0.0642 YES 

0.0023 12 75 0337·0.634 NO 

0.0023 6 59 0.774 YES 

x---

Fig. 15 Shear layer excitation (Data Berlin 1983/84). Experiments with finite shear layer thickness 9 versus theory for an 

infinitesimally thin shear layer. As in Fig. 14, also this diagram shows the dependence of the fluctuation velocity 1;2 Iy=o 

on the downstream distance x for various Strouhal numbers S9' 

34 
in section 2.1. For comparison, we show eq. (21), the theoretical 

prediction for 61 = 0.1 62 , as well as its asymptote for large x. 

We have drawn also the asymptote for °

1 = 0, the one stream case, 

Le., eq. (13) which is the asymptotic form of eq. (15). This 

comparison shows clearly the influence of the second stream. The 

real situation, however, is more complex. In the mean flow profiles we see a wake caused by the splitter plate which is filled 

gradually for increasing downstream distance x (see section 4 on 

the mean flow field). Therefore, it makes sense to plot both 

theoretical curves. 

6.2. Direct comparison of the field data 

For one comparatively low Strouhal number, 58 = 0.0023, we show 

here measured and computed IU21-field data, see Figs. 16 and 17. 

In the diagrams in each Figure we see a plot of the mean velocity 

distribution 6 and, with another velocity scale, a (jagged) plot 

of lu21. Both are original data from the X-Y-plotter. The quantity y on the horizontal axis is the distance perpendicular from 

the center of the shear layer. The different diagrams represent 

different locations upstream and downstream of the edge of the 

splitter plate. The dotted line represents calculated data of lu21 

from [14] with 61 = o. The symbol "TS" (Two Stream Case) at y=o 

stands for the analytic solution (eq. (21» of IU2Iy=0. For the 

case where the second stream with 61 = 0.1 62 is taken into 

account. For one single downstream location (x = +1)we have 

estimated the whole field using the considerations in section 

2.4. We see, that the data are well predicted by the theory. In 

particular, a discrepancy at small and negative X, as suggested 

by the extrapolated data (Figs. 14 and 15), does not exist. 

The choice of the or1g1n of y is puzzling at first glance, because y = 0, the center of the shear layer, is not identical with 

the location of the splitter plate wall, as required by the theory. The theory is developed only for an infinitesimally thin 

shear layer and thus both locations are identical there. However, 

since there are no infinitesimally thin shear layers in reality, 

we have to live with this conflict. We observe also, that in 

cases where the distribution of lu21 shows a stronger decay in 

35 
IN 

'" 

101- I 15 15 

I to I /0 I ! 5 I 5 

10 10 I Nl I ,. 0:;, 

Iu~. theory wall I:J IUzl. theory I O~ t -

l t \: 05 ~ I ~ iii ~ ~ ---l ~ e ---1 - E ... - N - I 2,0 :J I;:) 

luzL experiment IUzl. experiment I Ol Ol 0 0 0 0 -20 -10 Y'mm'- 0 -20 -10 Y'mml- 0 I I I I 1 I I I 

-0.8 -0.4 y- O -0.8 -0.4 y- O 

1.0~ 1

15 15 10 I /0 /0 I 5 5 I 10 10 '1 N I:J luzl. thea~\ ." 1-T S '.2.. 

O~ t t 0.5 ~--- I 

I ~ I ,. E 

2, I;:) I 

IUzl • experiment Iuzl. experiment I 

OL OL 0 0 0 0 -20 -10 Ylmml- 0 -20 -10 Ylmml- 0 I I I I I I 

-0.8 -0.4 y- O -0.8 -0.4 y- O 

Fig. 16 Velocity fluctuation lu21 for varying distance y from the s~ear layer. The plots show 

measurements upstream of and at ehe trailing edge. --- = theory for U =0. The experiment is 

carried out for 01=0.1 U2 • For this latter case, the analytic solutiod at y=o is given (TS), 

eq. (21).Also the mean flow U is shown. 5 6=0.0023, 16P121=0.634 N/m2 , l=13 mm. 
w 

..... 

toI- lS 

10 , 1 15 

0 /0 

5 5 

10 TS -;;; I 10 

.~ l I~ 

~t -

t lit 0.5 

1 ~ E r f I::> 1111_1 iOvnor;I"ftont ~ ! 

IU21. experoment 

o OL 0 o 1 1 , ----

-20 -10 Ylmml- 0 ! I 

o 0' I i 

-20 -10 Ylmml- 0 I I! 

-OB -0.4 y_ 0 -<l.B -0.4 y_ 0 

151 to' 1 15 

/u to 

5~ 

1 r'>c 

10 

O~ L t ,_- . ~ 

~tJrz::m.m 0 

05 

!2. 

o 0' I ,115 

-20 -10 Ylmml- 0 I , !! 

o o o -20 -10 0 o ! Ylmm!, 

-O.B -0.4 y_ 0 -OB -0.4 y- 0 

Fig. 17 Velocity fluctuation \u2 \for varying distance y from the shear layer. The_diagrams 

different locations downstream of the trailing edge. --- = theory for U = o. For x = 1 the 

theory is also extrapolated to include the second stream U1=0.1·U2 , "TS~ shows the analytic 

at y = 0, eq. (21). The mean flow is also shown. Other parameters as before. 

show 

value 
the -y direction, in particular at high Strouhal numbers, an 

extrapolation to the "center" of the shear layer can become 

arbitrary and meaningless. In our data evaluation, this means 

that the extrapolation scheme breaks down above, say, S8=0.007. 

The trend, that with increasing Strouhal number the decay of 

lu21 in y-direction is enhanced is worth a little further discussion. In a dimensionless representation, however, with 

lu21 plotted versus y, this change in the decay rate should be 

much less dramatic. Nevertheless, if we consider Fig. 2 we see 

that the real wave number assumes higher values than the theory 

of an infinitesimally thin shear layer would predict. This produces higher decay rates in the y direction. Our measurements 

basically confirm this, see Fig. 18. 

In Figs. 16, 17 and 18, only the IU21-distribution outside the 

shear layer in the potential flow region was shown. The development of the lui fluctuations inside the shear layer is shown in 

Fig. 19. We see the evolution of a steep maximum corresponding 

to the velocity distribution of the stability calculation of a 

shear layer with spatial amplification [16]. Upstream of and at 

the edge of the splitter plate, the fluctuation levels are comparatively low. There is no indication of a singularity at the 

plate edge which is in agreement with our previous investigations on this issue [18]. As we have mentioned earlier, nonlinearities occur first in locations downstream of the plate 

edge and inside the shear layer. A direct linearity test for 

lu21 can be seen in Fig. 20 in the lower diagram. There, measurements at two different excitation levels are shown. If a doubling of the excitation level produces twice the magnitude of 

the fluctuation velocities, we can consider the system as linear. 

Fig. 20 shows also another important feature of such measurements: there is always contamination by background noise. The 

typical background noise comes from the flow-producing apparatus, 

i.e., blower, bends, separation and turbulence in the flow-carrying ducts etc. In particular, low frequency noise below about 

100 Hz is very difficult to attenuate by mufflers. In our facilities, we find broad band low frequency noise without pronounced 

38 
2.0 .....----.--r----,---,----r----r-----, 

0.5 

I x = 1.0 II 

... ,,-----... - ~----. 

--~----. 

if-'¥"- • 

• • 

o 

--.----

0.2 L-----L_--l-_-L-_...1--_'-----'-_...-.J 

-0.7 -0.5 -0.3 -0.1 ... 

yexperiment: 

o ~ Sa = 0.0053 

"l ~ Sa = 0.0041 

• ~ Sa = 0.0023 

theory: 

- ~ 0,/02 = 0 

--- ~ O,! O2 = 0.1 

Fig. 18 Decay rate of the velocity fluctuationlu21 perpendicular 

to the shear layer at a downstream distance x = 1.0. The Strouhal 

number S8 is varied. 

39 
15~,----~-----,-----, 

05 

10 

ir~ ~rO 

I-.-_L -_._, I 

, I 

' x =-1 \. 

x=-25.5mm I 

I 

I 

wall 

-) 

/1U1 

Ol 01 ! joN' i ~ 

-10 yl ..... l_ 0 

-04 y-- 0 

olol 

-10 Ylmml-

--- 0 i ~ 

! I I 

-0.4 y- 0 

15r'----~------~----~ 15r'----~r-----~----_, 

0.5 ---~~ 

t ~ t ~ I "2 .. 5 

051- r.--L O I 10~ ---, I 

}~ ~~ I ::~?~ I 'l 

_10 ~\ ) UI 

Ol 01- .,- -10 ' : lIZ Ylmml- 0 

Ol oJ.- ~I~. L ,. 

'~ 

-10 yl ..... l_ 0 

-C.4 . ' 

y- o -0.4 y- o 

OL 01 I 

-10 Ylmml- 0 , , I 

Ol Or I 

-10 Ylmml- 0 I I I 

-0.4 y_ 0 -04 y_ 0 

Fig. 19 Velocity fluctuation in the shear layer for varying x. Sa 0.0023. Excitation levels 

as in Figs. 16 and 17. 
15.------.------.------.----",-----. 

5 

10 

t 

~ t E 

.!.! 

N 

il. 

~ I~ 

0 

-0.8 

15 

5 

~ t E 

~ 

N 

2. 

2' I~ 

0 0 

-20 

-0.8 

~ 

~ 

-10 

-0.4 

-10 

-0.4 

Y(mm(- I 

yY(mm(lyo 

o 

.~"'-.-

0 

( 

O 

Fig. 20 Background noise in the fluctuation velocity field as compared to the measured signal with tone excitation*). The 

measurements are taken upstream (x=-1) and downstream (x=+1) of 

the trailing edge of the splitter plate. The plot at x=1 shows 

also the linearity of the system by comparing with a fluctuation 

velocity distribution taken at half the magnitude of the tone ~xcitation. For comparison also the mean velocity distribution 

U is shown. Sa = 0.0023. Excitation level as in Figs. 16 and 17. 

*) The background noise in Fig. 20 is taken with an RMS meter, 

b£t the scale is the same as for the sinusoidal signals, i.e., 

12 times the RMS signal. 

41 
peaks in the spectrum. However, also this noise excites the shear 

layer in the same way as our pure tone excitation does. What we 

see in Fig. 20, labeled as "background" noise is the narrow band 

filtered *) signal at the frequency of the excitation, but the 

excitation is switched off in this case. Uncorrelated background 

noise begins to become critical for the measurements, if it is 

more than about 1/2 (= -6 dB) the magnitude of the signal. For 

- 6 dB background noise contamination, the systematic error becomes 12 %. By the way, this has to be kept in mind also for the 

measurement of the excitation level, 6P12. These background noise 

problems cannot be avoided, because increasing the excitation 

level decreases the possible downstream range of the measurements, because nonlinearities occur earlier. We see from this 

example, that a low-noise facility, narrow-band filtering and a 

proper adjustment of the excitation level is very essential for 

the quality of the measurements. 

Finally, it should be mentioned, that the background noise level 

in Fig. 20 is comparatively high. In fact, it must not be higher 

than shown there, in order to avoid significant errors. In the 

other measurements, in general, the background noise contamination is much lower. 

6.3. Phase measurements 

Phase measurements are most crucial to verify the theory. In 

these measurements, the phase of u 2 , the fluctuating velocity 

at y < 0, in the mean stream, is measured. The reference phase 

is that of the vector of the excitation pressure difference 

P1-P2 = ~P12. Figs. 21 and 22 show data sets taken at constant 

distance y from the shear layer. The phase is plotted versus 

the downstream location x. The data referred to as "theory" had 

been interpolated from the computed tables given in our previous 

theory report [14). The phase angle is counted positive,if there ~ 

is a phase lag compared to 6P12 (which is the same nomenclature 

*) All filtered data are taken with a Brliel & Kjaer 2020 narrow 

band filter with 3.16 Hz bandwidth. Only the spectra shown in 

the appendix, section 9.2.5., are taken with a different bandwidth. 

42 
00 

C\ 

E 

<II -900 

\/I .................... ~ ............. . 

C 

.<: 

0.. IExperiment (Houstonl! 

-1800 

-20 -10 o 10 20 Imml 30 

F 

.. 

\/I 

C 

.<: 

0.. 

x_ 

00 

-90 0 F-;;.;-;;;--.--.. -.. -=t-=:;-""-:;;;-;;:;-:;:--;:;-:::t ... ~._ .. ;: .... :::: ..... ;, ... 

-1800 

-20 -10 0 10 20 ImmJ 30 

-0.75 

x0 

xr'i 

~~Phones 

~=.;~""'"~I---r--------- {P2) I ~ u05 

'T' . 1 2 

~·-·-t~-=1----r\~~ 

- O2 hot wire probe 

to 

Fig. 21 Phase measurements of the u 2 velocity fluctuations. The 

reference phase is the phase of the pressure difference ~P12 

P1-P 2' 

Parameters, dimensional: 

52 = 13.5 mis, f = 82.5 HZ; I~P121 = 0.75 N/m2; i 

8 = 0.395 rom. without boundary layer suction. , Parameters, nondimensional: 

S8 = 0.0024 

-y [rom) I 3 I 5 I 10 I 20 

0.768 

43 

13 mm. 
0° 

E '" 

<II -90° - .. III " 0 

..r: 

Q. IExperiment (Berlin)1 

-180° 

-20 -10 o 10 20 Irnml 30 x0° 

E '" -90° 

<II 

. '0== 1~\/';?",,:=-=~~2 III 

0 

..r: 

Q. -180° 

ITheoryl 

-20 -10 o 10 20 1",,,,1 30 

-0.75 

x_ 

o 

x-

.l'i 

~~oPhones 

~I----J--------- 'p I 'I'-

0.5 

\.,2..' I, u2-

_ 0-

2 

·-·--t·:=J~~~· """"""'" 

hot wire probe 

to 

Fig. 22 Phase measurements of the u 2 velocity fluctuations. The 

reference phase is the phase of the pressure difference ~P12 

P1-P2· 

Parameters ,dimensional: 

U2 = 12 m/s; f = 65 HZ; I~P121 = 0.75 N/m2; £= 13 mm. 

8 = 0.225 mm; with boundary layer suction. 

Parameters, nondimensional: 

S8 = 0.00122 

-~ 15 20 [mm] I 5 

0.51 0.68 

44 
as in the tables [14]). The data have been taken in two different facilities (Houston and Berlin) and at two different Strouhal numbers Se. The Berlin data show more jitter due to background noise. The agreement, however, is remarkable. We see only 

minor discrepancies farther downstream, caused by a slightly 

lower phase speed than anticipated by the "thin shear layer" 

theory. This comes not unexpected for a shear layer of finite 

thickness (see Fig. 2). Near the trailing edge, there is a local 

region of negative phase speed *), as predicted by the theory. 

This does not indicate negative group speed or any feedback from 

downstream locations, it is a side effect in the potential field 

around an excited shear layer. 

The general trend of the measurements is quite simple: for negative x, upstream of the edge, we find the phase of the excitation 

field, which is dominating there. For regions of positive x, 

farther downstream of the edge, the instability wave dominates, 

with a phase speed close to the mean flow speed °

2. The planes 

of equal phase are inclined for spatial stability waves. Therefore, we have different phases for different y at constant downstream location x. 

6.4. Measurements at higher Strouhal numbers 

For higher Strouhal numbers we cannot compare the experimental 

data with a detailed theory, but some simple considerations provide an understanding of the measurements. The data which we show 

are taken at Se = 0.0136, close to the frequency where maximum 

amplification occurs (see Fig. 2). First, we show some fluctuation magnitude measurements, Fig. 23. We see, that the decay of 

lui in the y direction is so rapid, that the decay takes place 

essentially within the shear layer. The velocities outside the 

*) We have found such local regions of negative phase speed already in previous experiments [18, 19] also inside the shear 

layer. There, the location where the phase measurements were taken, was the local lui maximum location which shifts in its y 

position for small distances x from the trailing edge. So the con- clusion of having found negative phase speeds had then still some ambiguity in it. For regions farther downstream, however, where 

the shear layer has developed, the procedure cannot be criticized. 

45 
8 

3 /0 

t t 

~ ~ • 

2: I::> lui 

0 ~20 -10 1 1 Ylmm),-

-4 -2 y8 

3 /0 

t t 

~ ~ 

• 

2 I::> 

0 Q20 -10 1 1 Y1mml-

-4 -2 y8 

3 /0 

1 ~ 

S" .::> 

-0 0 

-20 -10 Ylmm\- 1 1 

-4 -2 yFig. 23 Distribution of the lui velocity fluctuations at higher 

Strouhal number Sa = 0.0136, close to the condition of maximum 

spatial amplification. Excitation pressure difference ~P12 = 

0.103 N/m2 , t = 13 mm, no boundary layer suction. 

46 
shear layer are produced essentially by the excitation field, 

which has very low induced lui-levels close to the shear layer. 

So we find, in particular at small x, a very low lui-level close 

to the shear layer, which looks almost like a local node. 

In Fig. 24 we see phase measurements at the same Strouhal number. 

The general trend is the same as at lower Strouhal numbers: We 

have the excitation field and its phase dominating at negative x, 

upstream of the trailing edge. Far downstream, say, at x > 25 rom 

in our diagram, the instability wave with its tilted wave fronts 

dominates. The intermediate region looks more puzzling, but is 

easy to explain. We know that the instability wave influence 

decays exponentially for increasing y. So the x location where 

the instability wave takes over is different for different y. At 

Y = -5 mm, e.g., the instability wave takes over just at the 

trailing edge. For greater distances y, this transition point 

shifts more towards the downstream direction. The superposition 

of these two fields produces locally regions of negative phase 

speed. If we want to extrapolate this trend to even higher Strouhal numbers, we will find a very detailed local structure like 

the one Pfizenmaier [20) found in a jet at very high Strouhal 

numbers. But we have to stress this again: the local occurence of 

negative phase speeds in our experiments is a consequence of the 

interaction of propagating shear layer waves and (essentially) 

standing sound waves. It does not allow the conclusion that these 

regions are produced by sources located downstream. This is only 

a warning; we do not deny effects from downstream in general. A 

discussion on downstream effects, and the conclusion that they are 

probably weak, is given in [14). 

47 
1800 

90 

01 

E 

.. 00 

III 

C 

.J::: 

Q. 

-90 

-180 

-20 -10 

I 

-20 -10 o _ 10 20 30 xFig. 24 Phase measurements of the u2 velocity fluctuations. The 

reference phase is the phase of the pressure difference 

6P12=P1-P2· 

Parameters, dimensional: 

U2 = 6 m/s; f = 195 HZ;i6P12i = 0.103 N/m'; 2 

a = 0.42 rom, without boundary layer suction. 

Parameters, nondimensional: 

Sa = 0.0136 

-y [rom] I 5 I 10 1 15 I 20 

-y 4.08 8.16 12.24 16.32 

48 

13 rom· , 
7. Conclusions 

We have carried out hot wire and microphone measurements to check 

our previous theory of the acoustical excitation of shear layers 

[14]. This theory suggested that the fluctuation field can be 

split into two constituents: 

(a) the excitation pressure field which is transmitted through 

the shear layer, and 

(b) the pressure field which, as a reaction, is produced by the 

shear layer itself. 

The excitation (a) generates an anti symmetrical field close to 

the splitter plate edge. Therefore, it produces a pressure difference (16P121) on both sides of the splitter plate. On the other 

hand, the field induced by the shear layer (b) is symmetrical 

with respect to the shear layer; hence it does not contribute to 

the pressure difference 16P121 on both sides of the splitter 

plate. Consequently, the pressure difference 6P12 is the relevant 

quantity for the acoustical excitation.*) In addition, our previous theory provides numerical data for velocity fluctuation 

levels and phase angles in the flow field near the plate edge. 

Moreover, this theory does not contain any empirical constants. 

The experiments have been carried out in two similar facilities 

(Houston 1981 and Berlin 1983/84). The measurements were conducted with a shear layer in the center of a channel having a 

rectangular cross section and with air as a fluid. The acoustical 

excitation was provided by two vibrating plates, which produced a 

surging motion around the splitter plate edge, from which the 

shear layer was shed. The shear layer was initially laminar and 

its thickness could be controlled by boundary layer suction. The 

data were taken in the vicinity of the trailing edge of the 

*) Note that 16P1 1 = Itp 21 = Ip -p 1 is a difference of two 

vectors, i.e., of two pres~ures with ~ifferent modulus and phase. 

This means that either 16p 1 is measured directly with two 

microphones or calculated ltter an independent measurement of 

the two pressures and their phases, using eq. (23) in section 5. 

49 
splitter plate. There, all fluctuating quantities were small and 

a comparison with the above mentioned linear theory appeared to 

be meaningful. In addition, the measurements were concentrated 

on comparatively low Strouhal numbers where a comparison with the 

theory for a "thin" shear layer [14] makes sense. Also the socalled large scale structures in a shear layer correspond to low 

Strouhal numbers. Therefore, the present investigation may provide some solid background information on how these structures 

can be generated or enhanced. However, we do not show any own 

flow visualization pictures here, because the interaction region 

near the trailing edge exhibits comparatively low fluctuation 

levels and hence flow visualization would show an apparently undisturbed laminar flow there. 

The present measurements are based on: 

(i) a determination of the magnitude of excitation by microphone 

measurements of the pressure difference 6P12 on both sides 

of the splitter plate, and 

(ii) hot wire measurements of the u-fluctuation levels and their 

phase in the region of the mean flow below the shear layer. 

The latter hot wire measurements are compared with computed 

theoretical values [14]. The agreement between theory and experiment is very encouraging, in particular in the validity range 

of "thin" shear layer theory , i.e., for Strouhal numbers 

S ~ 0.005 *). The measurements show even minor details that were 

predicted by the theory, such as local regions of negative' phase 

speeds of the u-fluctuations. However, these regions of negative 

phase speeds have nothing to do with upstream effects of sound 

sources located downstream in the turbulent she~r layer. They 

are nothing else but an accurately predicted side effect of the 

*) The Strouhal number appears to be comparatively low. This is 

due to the definition of Sa which is calculated with a small 

quantity, i.e., the momentum thickness, which is much smaller 

than other typical dimensions of the shear layer. In that context, 

it is worth mentioning, that the whole range of amplified instability waves of a shear layer is in the range 0 < Sa < 0.04. 

50 
shear layer excitation. 

Finally, it should be mentioned, that we have now experimental 

proof of the existence of a Kutta condition for the fluctuating 

flow of an excited shear layer shed from a trailing edge. The 

statement is valid for low Strouhal numbers at least up to 

Sa = 0.005. This can be concluded from the fact that the measured velocity and phase distributions fit very well the theoretical values calculated for this condition. It supports also the 

theoretical proof of the same issue, given in our previous investigations [14]. 

The theory which is now shown to be valid predicts the fluctuating potential flow field outside the shear layer. A prediction 

of the fluctuations inside the shear layer is also possible, at 

least downstream of the interaction region at the edge. This can 

be done by adjusting the potential field of our "thin" shear 

layer theory to the calculated potential field for a shear layer 

with finite thickness, but infinitely extended in the streamwise 

direction [16]. Thus, the complete perturbation input of a shear 

layer exposed to a sound field can be predicted. Of course, this 

statement is only valid for low Strouhal numbers, Sa ~ 0.005, but 

it may be also useful for estimations at higher Strouhal numbers. 

Acknowledgemen t 

The present work has been sponsored partly by NASA Lewis (Contract NAG 3-198) and by the Deutsche Forschungsgemeinschaft (Contract Be 889/1-1). Most of the equipment used in Berlin comes 

from earlier DFG contracts, e.g., the vibration systems (Wi 8/35) 

and the blower as well as the probe traverse hardware (Wi 8/37). 

The improved electronic instrumentation of the probe traverse 

was prepared by B. Simon. 

The authors were encouraged by Professor A.K.M.F. Hussain (University of Houston) to carry out this research. He helped also 

to arrange for one of the author's (D.W.B.) visit as an associate 

professor to Houston in this joint U.H.-DFVLR project. 

51 
8. References 

(1) Leconte, J. 

(2) Tyndall, J. 

(3) Michel, F. 

(4) Crow, S.C. 

Champagne, F.H. 

(5) Dziomba, B. 

(6) Gutmark, E. 

Ho, C.-M. 

(7) Bechert, D.W. 

Pfizenmaier, E. 

[ 8 ) Moore, C. J. 

[9] Deneuville, P. 

Jaques, J. 

On the influence of musical sounds on the flame of a jet of coal-gas. 

The London, Edinburgh, and Dublin 

Philosophical Magazine and Journal 

of Science 12 (1858), pp. 235-239. 

Sound. 

London: Longmans, 1867. 

Larm und Resonanzschwingungen im 

Kraftwerksbetrieb. 

(Noise and resonant vibrations in 

power plants.) 

Berlin: VDl-Verlag, 1932. 

The authors owe this reference to 

Dr. A. Dinkelacker, who found this 

book in L. Prandtl's private library. 

Orderly structure in jet turbulence. 

J. Fluid Mech. 48 (1971), pp. 547-

591. 

Experimentelle Untersuchung zum EinfluB von Anfangs- und Randbedingungen auf die Ausbreitung einer frei- en zweidimensionalen Scherschicht. 

Dissertation, Techn. Univ. Berlin, 

Fachbereich 9, 1981. 

Preferred modes and the spreading 

rates of jets. 

Phys. Fluids 26 (10), October 1983, 

pp. 2932-2938:-

On the amplification of broad band 

jet noise by a pure tone excitation. 

J. Sound and Vibr. 43 (1975), 

pp. 581-587. -

The role of shear-layer instability waves in jet exhaust noise. 

J. Fluid Mech. 80 (1977), pp. 321-

367. 

Jet noise amplification: a practically important problem. 

AlAA 4th Aeroacoustics Conference, 

Oct. 3 -5 , 1977, Atlanta/Ga., 

AlAA paper 77-1368. 

52 
[10] Crighton, D.G. 

Leppington, F.G. 

[11] Bechert, D.W. 

Michel, U. 

[12] Mohring, W. 

[13] Rienstra, S.W. 

[14] Bechert, D.W. 

[15] Bechert, D.W. 

[16] Michalke, A. 

[17] Freymuth, P. 

[18] Bechert, D.W. 

Pfizenmaier, E. 

[19] Bechert, D.W. 

Pfizenmaier, E. 

Radiation properties of the semiinfinite vortex sheet: the initial 

value problem. 

J. Fluid Mech. 64 (1974), pp. 393-

414. 

The control of a thin free shear 

layer with and without a semi-infinite plate by a pulsating flow 

field. 

ACUSTICA II (1975), pp. 287-307. 

On flows with vortex sheets and 

solid plates. 

J. Sound & Vibr. 38 (1975), pp. 403-

412. 

Edge influence on the response of 

shear layers to acoustic forcing. 

Ph. D. Thesis, Univ. Eindhoven, 

Netherlands, June 1979. 

Excited waves in shear layers. 

DFVLR-FB 82-23 (1982). 

A model of the excitation of large 

scale fluctuations in a shear layer. 

AlAA 8th Aeroacoustics conference, 

April 11 -13 , 1983, Atlanta/Ga., 

AlAA paper 83-0724. 

On spatially growing disturbances 

in an inviscid shear layer. 

J. Fluid Mech. 23 (1965), pp. 521-

544. --

On transition in a separated lami- nar boundary layer. 

J. Fluid Mech. 25 (1966), pp. 683-

703. --

Optical compensation measurements on the unsteady exit condition at a nozzle discharge edge. 

J. Fluid Mech. 71 (1975), pp. 123-

144. --

On wavelike perturbations in a free 

jet travelling faster than the mean flow in the jet. 

J. Fluid Mech. 72 (1975), pp. 341-

352. 

53 
[20] Pfizenmaier, E. 

[21] Bechert, D.W. 

[22] Bechert, D.W. 

[23] Beranek, L.L. 

Zur Instabilitat des schallbeeinfluBten Freistrahls. 

DLR-FB 73-69 (1973). 

Available in English: 

On the instability of a sound-influenced free jet. 

ESRO TT 122 (1973). 

Die Steuerung eines ebenen turbulenten Freistrahls durch eine seitliche Wechselstromung, erzeugt in 

einem Schallfeld. 

(The control of a plane turbulent 

jet by a perpendicular fluctuating 

flow generated in a sound field.) 

Z. Flugwiss. 24 (1976) 1, pp. 25-

33. --

Versuchseinrichtungen zur Untersuchung der Steuerung eines ebenen 

Freistrahls durch Schall. 

(Facility to investigate the control of a plane jet by sound.) 

Bericht: Hermann-Fottinger-Institut 

fur Stromungstechnik, TU Berlin, 

Juni 1966. 

Acoustic Measurements. 

New York: J. Wiley & Sons, 1965. 

54 
9. Appendices 

9.1. Appendix A 

Glossary of Symbols 

d 

dB 

dBA 

erf (z) 

f 

i 

R. 

p 

u 

half width of the two-dimensional channel of the test 

section 

logarithmic unit for the fluctuating pressure, the 

relation to linear units is given by eq. (24) 

"A-weighted" fluctuating pressure. This unit was 

established to simulate the frequency dependence of ~he 

sensitivity of the human ear. Thus, very low frequencies, 

say, below 200 Hz do not enter in the dBA level significantly. For details see textbooks in acoustics, e.g., 

[23], p. 892 

2 z -S2 

error !unction, defined as erf(z)=-- f e ds 

Ino 

!requency of the excitation f w/2rr 

!maginary unit i = r-T 

distance between the edge of the splitter plate 

pressure pickup devices, i.e. , the microphones, 

sides of the plate 

and the 

at both 

£ressure. The fluctuating pressure, i.e., the deviation 

from the ambient atmospheric pres$ure. All perturbation 

quantities are proportional to e-~wt 

reference ~ressure of the pressure fluctuations: 

Po = 2·10- N/m2 

fluctuating pressure above the splitter plate (see 

Fig. 3) 

fluctuating pressure below the splitter plate (see 

Fig. 3) 

pressure difference 6Pl = P1-P2. Note that this is a 

vector difference, so t~e phases of Pl and P2 have to 

be taken into account. (see eq. (23) ~n sect~on 5.) 

fluctuating pressure in the ~ettling chamber 

time 

fluctuating velocity component in the x-direction. All 

fluctuating quantities are proportional to e-iwt 

fluctuating u velocity component above the shear layer 

at y > 0 

55 
u'" 

ii 

v 

x 

-

x 

y 

-

y 

C 

fluctuating u velocity component below the shear layer 

at y < 0 

reference velocity, defined by eq. (10) as 

It.P 12 1 

p 1U2w R. 

fluctuating velocity at large negative x in a channel 

with a splitter plate where the sound sources are assumed to be located at x = -'" • This quantity is re- lated to the pressures at the-Splitter plate by eq. (3) 

It.P12 1 _ u = ./n/d 

'" pw/t 

dimensionless fluctuating velocity in x direction, 

ii = u/uref 

Peak value modulus of the dimensionless velocity u2 ' 

the index "2" labels the region below the splitter plate, 

y < o. 

fluctuating velocity component in the y direction. All 

fluctuating quantities are proportional to e-~wt 

fluctuating v velocity of the acoustic !orcing field 

fluctuating v velocity above the shear layer for y > o. In equations (6), (8), (9), (11) and (13) we mean the 

velocity just above the shear layer v 1 y=+o 

dimensionless v velocity above the shear layer, defined 

as "'1 = v 1/uref 

horizontal coordinate in direction of the mean flow 

dimensionless horizontal coordinate, defined as x = xw/U2 

vertical coordinate 

dimensionless vertical coordinate, defined as y = yw/52 

Coefficient, decreasing the value of the shear layer 

fluctuations due to the influence of the channel walls 

of the test section. C is defined by eq. (16) 

filtered background noise pressure in dB/Hz, taken in 

different locations, see Figs. 38-40 

Strouhal number calculated with the momentum thickness ! of the shear layer and defined as Sa = f.a/52 

56 
"TS" 

p 

o 

w 

e 

TS refers to the two stream case and indicates in the dia~r~ms, where it is-used, the value of the velocity 

lu21 Just below the shear lay~r at y = -0. In this calculated value, the low speed U1 of the second stream 

above the shear layer is taken into account. 

mean flow velocity in x direction 

mean flow velocity above the shear layer for y > 0 

mean flow velocity be!ow the shear layer for y < o. U2 is much greater than u1• 

!maginary part of the complex wave number a of an instability wave (ia = A) 

Eeal part of the same complex wave number 

imaginary part of the complex wave number of the instability wave in a shear layer 

real part of the complex wave number of the instability wave in a shear layer 

complex wave number of the instability wave in a shear 

layer 

w (i+1 ) w (i-1) 

U2 

dimensionlesss wave number of the instability wave, see eq. (19) 

density of the fluid, in our experiments air at room temperature 

v~locity ratio of the two streams above (U1 ) and below. 

(U2 ) the shear layer. 0 = U1/U2 

phase angles of the pressure P1 and P2' respectively. 

The reference phase may be arb1trary, e.g., the phase 

of the beat frequency oscillator which drives the ex- citation sound field 

radian frequency of the excitation sound field w = 2rrf 

momentum thickness of the shear layer, for definition see Fig. 10 in section 4. 

Indices: The index "1" denotes quantities above the shear layer 

(y > 0) • 

The index "2" denotes quantities below the shear layer 

(y < 0). 

The tilde "_,, denotes dimensionless quantities. 

57 
The quantities between vertical bars, e.g., lu21 refer 

to the peak value of these quantities in a sinusoidal 

vibration. 

The dB or dBA readings of broad band signals in the 

appendix, section 9.2.5. refer to the RMS value of 

these signals. 

The background noise in Fig. 20 was taken with an RMS 

meter, but the scale is the same as for the sinusoidal 

signals, i.e., 12 times the RMS signal is given there. 

58 
9.2. Appendix B: Experimental apparatus 

9.2.1. Facility Houston 

Fig. 25 shows a sketch of the facility which had been established 

in 1981 at the University of Houston. The air supply consists of 

a centrifugal fan having backward curved blades in a cast aluminum impeller and with a casing of high aerodynamic quality ("American Standard"), driven by a D.C. motor with variable shaft 

speed. In addition, the fan has a comparatively low noise output. 

The fan-motor unit has a separate suspension to prevent vibrations from being transmitted to the facility. The fan is connected by an elastic hose and with a little diffuser to two commercial broad band mufflers. To the other side of the mufflers a 

long diffuser is connected. This diffuser contains 3 regular 

screens to keep the flow attached. A little settling chamber is 

connected to the diffuser, which produces also a merging from 

circular to quadratic cross section. A nozzle follows with two 

ultra-fine screens (200 x 200 mesh x 0.0021" diameter, stainless 

steel wire cloth; equivalent to 8 wires per mm, each wire 

0.053 rom in diameter) at its entrance section. This nozzle is 

connected to the high-speed side of the test section. The exact 

dimensions of the test section are given in Fig. 11 in section 5. 

The height of the test section channel is 100 mm and the maximum 

mean flow velocity is 17 m/s. The second stream is merely driven 

by the entrainment of the shear layer. Its velocity is about one 

tenth of the mean stream velocity. There is some turbulence generated by local separations in the duct of the second stream. However, this does not seem to have a perceivable influence on the 

measurements. 

The whole structure is mounted on saw-horses on a wooden 

frame in an anechoic chamber (see Fig. 26). In principle, it is 

not necessary to use an anechoic chamber for such an experiment, 

but usually it is the room with the lowest background noise in a 

laboratory. Also, the noise from fan, suction blower and cooling 

fans from the electronic instrumentation propagates and decays 

with distance like in open air and thus, if the spatial distance 

is a few meters from the test section, this does not affect the 

59 
0-

o 

D. C. motor 

2 super-fine screens 

stream 

entrainment air 

vibra"ting plate shear layer 

Fig. 25 Schematic view of the facility at the University of Houston. 
'" 

Fig. 26 Side view of the facility at the University of Houston, installed in the anechoic 

chamber of the Department of Engineering. 
measurements. 

This facility as well as the one we used in Berlin are very quiet 

indeed. At operational air speed (U2 = 12 m/s) the facility is 

almost inaudible, the dominant noise sources (for the ear) are 

the flow separations from the probe supports immersed into the 

main stream. The authors claim that they have never seen (or 

better: heard) such silent shear layer or jet facilities except 

the facility which had been used by Wehrmann, Michalke and Freymuth [17]. 

To move the pressure and velocity probes in the test section a 

mini-computer controlled traverse with stepper motors is used. 

The traversing speed can be changed by the computer software. 

The traverse is used in continuous motion during the continuous 

plots on an X-Y-plotter. This admitted abuse of the traverse is 

difficult to carry out, because the stepper motors cause significant vibration of the probes. To suppress these vibrations an 

inertia mass with an elastic link is used between stepper motor 

and the driving screw of the traverse, which moves the probes. 

The benefit of this continuous data recording is a very rapid 

data acquisition. It produces curves which show even minor subtleties of the measurements at once. In addition, the complete 

data acquisition could be disconnected from the (overloaded, 

time sharing) central process computer of the U.H. turbulence 

laboratory which again accelerated the experiments by one order 

of magnitude. The instrumentation is partly visible in Fig. 26. 

Because it is very similar to the instrumentation of our Berlin 

facility, it is not discussed here in detail. 

9.2.2. Facility Berlin 

In Fig. 27 a sketch of the Berlin facility can be seen. Some 

parts are omitted, e.g., the air supply unit. We use again a 

centrifugal fan with backward curved blades which is driven by 

a D.C. motor with variable speed. The shaft speed is controlled 

by a digital control unit, built by our electronics shop (DFVLR 

DMR II). To suppress noise we use a muffler. The settling chamber (see Fig. 27) is also used as a muffler by a glass fiber 

filling. A double nozzle is attached to the settling chamber. Be62 
tween settling chamber and nozzle we use again an ultra-fine 

screen on the side of the main stream (left in Fig. 27). The low 

speed on the right hand side is produced by a high flow resistance with foam, a ultra-fine screen and perforated metal sheet. 

Here, we use a very fine metal sheet with holes which are hardly 

visible to the naked eye (9 circular holes per rom2 , hole diameter 

0.3 rom). The same material is used to cover the "windows" to 

which the vibration systems are attached at the sides of the test 

section (see Fig. 28). 

The boundary layer control bleeding holes (see Fig. 27) are the 

solution of a serious problem in this type of facility. Without 

these holes, the boundary layer distribution is not even in the 

vertical direction on the splitter plate. In particular, in the 

center of the splitter plate, the boundary layer exhibits a bulge 

in the distribution, very different from the expected Blasius 

velocity profile. After a long series of tests, this deficiency 

could not be attributed anymore, as argued initially, to perturbations caused upstream of the nozzle. In fact, this deficiency 

is due to a secondary flow, from the corners to the center line, 

inside the nozzle. The bleeding holes provide a pressure distribution inside the nozzle, which eliminates this secondary flow 

and with it the bulge' in the mean velocity profile. In the 

sketch in Fig. 27 it is not indicated that the bleeding holes 

are covered with the fine perforated metal sheet mentioned above. 

This produces a smooth flow in and around the bleeding holes. 

The photograph in Fig. 29 shows the test section from the side, 

as well as the traverse to move the probes. This traverse is 

driven by D.C. motors whose speed can be varied continuously. 

The local position of the traverse corresponds to the digital 

output of a position encoder. This digital signal is fed to a 

digital/analog converter which controls the X-Y-plotter to record 

the data. A direct analog voltage output of the traverse would 

have been simpler and cheaper, but the above described system 

was available. Nevertheless, also this comparatively accurate 

system was checked by dial gages on the traverse. 

The measuring instruments are shown in Fig. 30. The little plexi63 
'" ~ 

from air supply super-fine screen 

glass fiber . 

filling I J 

perforated metal plates 

Fig. 27 Schematic view of the facility in Berlin. 

foam layers + perforated 

metal plate + screen 

boundary layer control 

bleeding holes 

vibrating plate 

layer 
0'\ 

U"l 

Fig. 28 Test section of the facility in Berlin with hot wire probe and a 1/4"-condenser 

microphone (see arrow) in a position to measure P1 near the splitter plate edge. 
0\ 

0\ 

Fig. 29 Side view of the facility in Berlin with probe traverse. 
0"\ 

-.J 

Fig. 30 Measuring instruments of the facility in Berlin. 
glass box on the left hand side is the micromanometer (System Rechenberg) to measure the mean flow velocity with a pitot static 

tube. On the table we see also the X-Y-plotter which was used to 

record almost all data. The next pile of instruments to the right 

contains a little digital voltmeter on top for calibration and 

checking purposes. The two grey boxes below it are two phase 

meters *) (we would have needed only one, but both had litte deficiencies and could be checked against each other). Below that, 

still on the table, are two hot wire anemometers, type DFVLR 

HDA III. In the first following rack we have from top to bottom: 

(a) a beat frequency oscillator to drive the sound excitation 

and the slave filters, (b) two voltmeters to monitor the driving 

voltage of the vibration plates of the sound excitation, (c) two 

B & K 2607 measuring amplifiers for microphone and hot wire 

signals. On top of the two racks we have the digital motor control and a little counter to measure the frequency of the excitation. The rack on the right hand side (closest to the girl) contains from above (a) the digital traverse control and the digital/ 

analog converter for the spatial position signal of the traverse, 

(b) a four beam oscilloscope, (c) two power amplifiers with phase 

shift units for the vibrating plates of the acoustic excitation, 

(d) another amplifier and phase shift unit of the same type to 

control the piston speaker in the boundary layer suction duct,and 

(e) a two beam storage oscilloscope. For some of the measurements, 

i.e., the spectra, a Hewlett-Packard HP 5420 A Digital Signal 

Analyzer was used. Because its cooling fan is very noisy, it was 

kept outside the measuring room and is, therefore, not shown here. 

*) We would like to stress here that it is very difficult indeed 

to carry out phase measurements in a flow. A phase meter will 

show an output signal under all circumstances, even if the reading is nonsense. A typical situation is this: An analog phase me- ter is exposed to a slightly jittering signal close to 0° or 360~ 

the reading will be approximately 180°! SO the operation of the ' 

phase meters is to be checked carefully. One way to do this is to 

monitor the reference signal and the (rectangular) switching signal from the phase meter circuitry. Digital phase meters usually 

do not have this problem. on the other hand, they cannot be used 

in a simple way to produce a continuous data plot. 

68 
9.2.3. Boundary layer suction 

The design of the boundary layer suction system can be seen in 

Figs. 31 and ~. Fig. 31 shows on the left hand side the splitter 

plate with the suction slit. The suction air passes through a 

diffuser inside the plate. The flow resistance of a plastic foam 

element enforces an equal velocity distribution over the slit 

cross section. Subsequently, the air is removed through two tubes 

on both sides of the plate (the Houston facility had only one 

tube on each side which caused little, but audible broad band 

flow noise at the tube inlets). The plastic hoses connecting the 

splitter plate cavity with the manifold (see Fig. 31) have equal 

length. On the right hand side of Fig. 31 we see the piston 

speaker to compensate the A.C. flow through the suction slit 

(See also Fig. 29). Both sides of the loudspeaker piston membrane 

are connected by a little pressure exchange hose to prevent damage from static pressure loading. To suppress acoustic resonances 

in the suction duct system, we use a long (30 m) garden hose as 

an anechoic termination. For the suction blower which we use, a 

normal vacuum cleaner and thus a tremendous noise source, we had 

to devise an excellent muffler. Our muffler (see Fig. 32) consists of an ordinary 200 I sheet metal barrel filled with plastic 

foam flakes of the kind which are normally used to fill pillows. 

In order to prevent the flakes from clogging the duct connections, 

coffee sifters covered with elastic lady's stockings are glued 

onto the inner side of both lids of the barrel. This muffler is 

very efficient and thus the suction air flow is inaudible. 

The control valve and the flow meter (see Fig. 32) are downstream 

of the muffler because they also produce noise. The vacuum 

c~eaner is located in another room (in a box in the Houston facility) to avoid noise contamination. For the air flux might be 

too low to provide the necessary inner cooling of the vacuum 

cleaner,a bypass air stream is ingested through a bypass valve 

(See Fig. 32). The suction volume flux was 

Houston: 28.3 l/min 

Berlin: 34.0 l/min. 

69 
..... 

0 

perforated 

metal plate 

plastic 

foam 

splitter 

plate 

suction /' 

slit ~~ garden b) \ j ............ Piston 

hose speaker 

Fig. 31 Boundary layer suction: splitter plate, manifold and compensation piston speaker. 
~ 

test section 

anechoic 

termination 

=30m garden hose 

--

Fig. 32 Boundary layer suction: survey. 

building wall 

valve 

cleaner 
The slit width was 1.0 mm and the splitter plate breadth was 

100 mm, in both facilities. 

Finally, we should mention, that it turned out that the slit A.C. 

flow compensation with the compensation piston speaker had no 

perceivable effect on the shear layer excitation. This was most 

likely due to the high flow resistance of the foam ele~ent in 

the cavity of the splitter plate (see Fig. 31) and due to the 

suppression of resonance with the anechoic termination. Consequently, the slit A.C. flow compensation was after all not necessary and not used in our experiments. 

9.2.4. Vibration system 

The vibrating plates to produce the sound excitation were or~g~­

nally designed for another previous facility where the production 

of high sound levels was crucial [21, 221. This system was used 

in both, the Houston and Berlin experiments. Its vibrating plates 

consist of a balsa wood sandwich structure (see Fig. 33), which 

leads to a very low mass (7 g). The lowest eigenfrequency of the 

plate was calculated to be above 200 Hz. The complete vibrating 

elements with coils and cast silicone rubber bellows can be seen 

in Fig. 34. They are mounted inan aluminium structure shown in 

Fig. 35. The coils operate in the magnetic field of two commercial loudspeaker magnets designed for 37.5 Watts power input 

each. The total possible power input of the systems would be then 

150 Watts maximum. However, this high possible power is not used 

in our experiments, though it provides a considerable and safe 

linearity range. The magnitude limit is given in our low frequency range experiments by the maximum possible deflection of 

the plates which is ±3 mm, but even this is by far not reached 

in any of our experiments. The low frequency response of the system is impressive; there is no problem to run the vibrating 

plates at, say, 10 Hz. 

In the Berlin facility, the complete vibrating plate systems are 

suspended with steel ropes (see Fig. 28) and they are attached 

to the test section with a rubber foam frame. This suspension 

avoids vibrations from being fed into the test section. The vi72 
-...J 

W 

Fig. 33 Vibrating plates before being assembled. The sandwich structure is visible. Mass: 7 g each. 
" .., 

Fig. 34 Vibration units with coils and cast silicone rubber bellows suspensions. Mass: 60 g 

each. Maximal admitted acceleration: 3000 m/s2. 
" {J1 

Fig. 35 Vibration system partly assembled, without magnets. 
bration sensitivity of microphones is not appreciated widely and 

can lead to severe systematic errors. To give an example, 

Fi~ shows this sensitivity for a 1/4" Brliel & Kjaer microphone. The microphone is exposed to constant lateral acceleration 

of 0.1 g = 0.98 m/s' at various frequencies. The vertical axis 

of the diagram shows the apparent sound pressure level. This test 

with a microphone mounted on a shaker is impressive but not very 

helpful in an experimental situation, because the vibration sensitivity varies from microphone to microphone and depends also 

on how the microphone is mounted. Moreover, it looks as if not 

only the microphone cartridge but also the adjacent preamplifier 

is sensitive to vibrations. A useful test for the actual contamination of the microphon signal is the following: A jacket for 

the microphone is attached to the test section wall close to the 

measuring location, but not connected to the inner part of the 

test section. If the microphone is plugged into that jacket under 

measuring conditions, it is only exposed to the vibration and 

not to the sound. Thus, the measured signal is representative 

for the contamination alone. It should be mentioned, that, 

obviously, the vibration contamination and the sound signal 

80~----~-----r----~------~----~----~ 

t [dB) 

microphone 70 

reading 

60 

1/4"mic. 

"'" o;;~ 

50~----~----~------~----~------~--~ o 2 [kHz) 3 

frequency --

Fig. 36 Vibration sensitivity of 1/4" Brliel & Kjaer condenser 

microphone. The apparent sound pressure level is shown, if the 

microphone is exposed to a 0.1 g = 0.98 m/s' acceleration at 

various frequencies. 

76 
are completely coherent. Consequently, if the vibration signal 

is, say, 20 dB lower than the sound signal, the vibration contamination error is still 10 %. Vibration contamination was a major 

error source in the Houston measurements, but the validity of the 

measurements was checked in each case with the test procedure 

described above. In the Berlin measurements, this error is completely eliminated due to the better suspension of the vibration 

systems. 

Finally, we will comment on the electric adjustment of the vibrating plates. To produce an anti symmetric sound field *) the 

vibrating plates have to be adjusted in magnitude and phase. A 

magnitude adjustment is straight forward by the volume control of 

the amplifier. If one thinks of a phase adjustment, one thinks 

of an electronic circuit which changes the phase independent of 

the magnitude. This is comparatively difficult to achieve and, 

in fact, not necessary. If we insert a circuit as shown in 

Fig. 37 between oscillator and power amplifier we can change the 

from 

oscillator 

to power 

amplifier 

Fig. 37 Phase shift circuit for the adjustment of the vibration 

plates. 

*) A shear layer excitation experiment does not really require an 

anti symmetric sound field; the relevant quantity is ~P12 which 

has to be measured accurately. However, the u-velocity field far 

outside the shear layer does depend on the excitation field and 

thus the similarity between available theoretical data and field 

measurements becomes closer, if the sound field is adjusted 

properly in the anti symmetric shape. 

77 
phase over a range of almost 180°, together with a moderate 

change in magnitude. Another ±180° phase shift can be obtained 

by inverting the vibration system voltage by a simple switch. 

With such a control circuit for both vibrating plates any conceivable phase relation between the plates can be produced. The 

adjustment is still straight forward with (a) volume control of 

the power amplifier, and (b) coupled phase/volume control of a 

phase control circuit as shown in Fig. 37. The procedure requires 

a few consecutive control steps on each knob and can be carried 

out in a few minutes. 'I'he quantity to become zero (orbetter,say, 

-60 dB below the original signal) is the probe microphone output 

on the symmetry line of the facility under no flow condition (see 

Fig. 12 in section 5). 

9.2.5. Background noise 

The most relevant information on background noise is in how far 

it contaminates our (filtered) measurements taken at one single 

frequency, chosen between say, 30 Hz and 200 Hz. Such data have 

been given already in section 6, referred to as "background 

noise" *). The authors claim to have established facilities with 

exceptionally low noise. So we have to contribute at least some 

data on this issue. We measured in our Berlin facility the following quantities: 

(a) level and spectrum of the excitation pressure difference 

6P12 = P1 - P2 at a distance 2 = 13 mm upstream of the 

splitter plate edge 

(b) level and spectrum of the pressure P2 alone, at the same 

location 

*) The general term "turbulence level" does not make sense to 

the authors in the present context, because velocity fluctuations 

can be generated by both convected vorticity and by sound. In 

addition, the "turbulence level" depends crucially on the lower 

cut-off frequency of the measuring amplifiers and this cut-off 

frequency should be very low indeed. 

78 
(c) level and spectrum of the pressure Ps in the settling chamber. 

The spectra are shown in Figs. 38 to 40, the filter bandwidth 

was 6.25 Hz. The sound pressure levels (2 Hz - 20 kHz) are shown 

in the following Table *) 

U2 [m/s] t> P12[dB] P2[dB] P2 [dBA] ps[dB] 

0 53.7 57.5 36.8 57 

6 59.6 73.7 41.8 77.5 

8.5 - 81.6 67.9 86.4 

12 88.2 90.2 83 89.4 

17 - 95.5 89.6 99.8 

Table 1: Background noise, facility Berlin. 

In all cases, in particular in the settling chamber, the low frequency constituents of the spectrum are dominating. A careful inspection of the spectra reveals some more details: The contamination from the mains supply (50 Hz and its multiples) is very low 

and does not exist in the settling chamber. This suggests, that 

the peaks measured in the test section are from the acoustical 

humming of the instruments rather than from electronic contamination. The background noise spectrum at U2 = 0 is very smooth, 

which suggests electronic noise rather than real acoustic background noise, except at the very low frequencies. The noise in 

the settling chamber at 52 = 12 mls shows a regular pattern of 

broad humps. These are most likely not blower tones which would 

show up as sharp spikes. We think, it is the resonance pattern 

*) The dB or dBA readings of measured pressures with broad band 

srgnals in this section refer to the RMS levels of these quantities, whereas in the previous chapters where we deal with sinusoidal signals, the quantities between vertical bars, like lui, 

refer to the peak values of these quantities. The dBA reading 

differs from the dB reading, because in the dBA scale, the lower 

frequencies are more and more suppressed with decreasing frequencies. The dBA weighted scale was invented to simulate the 

sensitivity of the ear. For details see textbooks in acoustics, 

e.g., Beranek, Acoustic measurements [23]. 

79 
8o.------------.-------------r------------.-~ 

dB 

Hz 

f ----

~I----- \~0 

--- O2 

[Hz) 3000 

Fig. 38 Spectrum of the pressure difference bP12 at both sides 

of the splitter plate (Berlin data). The distance from the plate 

edge is ~.=13 mm. The filter bandwidth is 6.25 Hz. 

80.------------,------------.------------,--, 

dB 

Hz 

t 60 \ 

- \ 

~ 40 V ..___0 2 = 6 m/s 

a. \----

g \. 

N 

-' 

~ (fj) 

----

--- O2 

OLO--~~~----~10~00;=::::~~~20~0~0~~ba(-H-ZJ--~3~0~00~ f ____ 

Fig. 39 Spectrum of the pressure P2 near the edge of the splitter 

plate (Berlin data). t = 13 mm. The filter bandwidth is 6.25 Hz. 

80 
o 

.eCo '" 

80r------------,-------------r------------~~ 

: 40 

.5! 

o 

N 

" 

...J '" 

o~~--~~~~~~~--~ o 1000 2000 [Hz] 3000 

f ----

Fig. 40 Spectrum of the pressure Ps in the settling chamber 

(Berlin data). The filter bandwidth is 6.25 Hz. 

81 
of the air supply duct. We hesitate to speculate about the 

reasons for the very significant change in background excitation 

pressure level 6P12 (see Fig. 38) between 6 mls and 12 m/s. We 

would tend to attribute the very low frequencies, say, below 

100 Hz, to the flow producing apparatus, i.e., everything upstream of the settling chamber, because at such low frequencies 

the mufflers do not work anymore. If we consider the broad band 

noise spectrum at 12 mls (see Fig. 38), we see a maximum at about 

300-400 Hz. We have no conclusive explanation for this, but one 

candidate is the observed incipient turbulence in the corners of 

the test section, to which the microphones are exposed. All these 

ramifications, however, are of minor importance, except the low 

frequency noise, which indeed causes trouble with the measurements. 

For comparison, the Houston facility is much less documented; we 

have the following data (Table 2): 

U2 [m/s] P2[dB] P2[dBA] 

0 55 <43 

8.5 81 57 

17 91.5 77 

Table 2: Background noise, facility Houston. 

The dB measurements have been taken in the frequency range 

10 Hz to 200 kHz. The dB to dBA relation suggests again dominating low frequencies. However, some measurements in Houston, in 

particular the phase measurements (see section 6.3.),were much 

more stable. This suggests, that the low frequency background contamination may have been in the order of 10 dB lower than in the 

Berlin facility, for identical operation conditions. 

82 
9.3. Appendix C 

Typing errors of DFVLR-FB 82-23 

"Excited Waves in Shear Layers" by D.W. Bechert 

p. 22, line above eq. (34): ..• is equivalent to _ 1 r 

p. 30, eq. (60) is equal to zero. 

p. 35, eq. (69) should read: 

ii,1 

(69) for x > 0 

ii,2 =_i~ re~1X + e~2xl 

1l~1 If; J 

~ at e=1r ae 

p. 38, points P1 and P2 with capital letters in the text. 

p. 44, Fig. 10: 1ii,2 1 instead of lu21. 

p. 48, eq. (91) should read: 

(91 ) 

x+r o (x-x ) 2 +y2 o 0 

p. 50, eq. (96) should be multiplied by e A1x 

p. 54, eq. (110), valid for x > U /w o 

p. 73, footnote, •.• at a frequency of 100 Hz; 

p. 75, eq. (166) should read: 

llp12/lR:" = ••••• 

83 
p. 112, eq. (135) should read: 

r ",.'h 

1 

) 

Re 28 cosh' (y/28) 

(B5) 

SIro =_ pw' h tanh(y/28) 

28 cosh2 (y/28) 

p. 141, Table 3: There is no hint in the text that the "phase 0" 

is indeed a phase lag, and the reference phase is the 

phase of the (vector) differ.ence of the two pressures 

P1-P 2 = t.P 12· 

84 
End of Document