ACTA MECHANICA S I N I C A , V o l . 6 , N o . 2 , M a y 1 9 9 0

Science Press, Beijing , China

Allerton Press , I N C . , New Y o r k , U . S . A .

I SSN 0567- 7718

T H E E F F E C T O F C O M P L I A N T C O A T I N G S O N C O H E R E N T

S T R U C T U R E I N T U R B U L E N T B O U N D A R Y L A Y E R S *

Shu Wei Liu Weiming

( Tianjin University )

ABATRACT : The velocity profile, turbulence intensity profile, streaky structure and bursting frequency in turbulent boundary layers over a fiat plate with compliant coatings were investigated by Laser Doppler Anemometry and condi- tional sampling techniques. This experiment led to the conclusions that in boundary layer flows on a compliant wal l , as compared with that on a rigid wal l , the log law region was extended further away from the wall , and that the maximum value of each turbulence intensity profile in the near wall region was reduced and the bursting frequency obviously decreased with the compliant coatings. One point worthy of notice was that the above results were very much like those of polymer drag reduction experiments.

KEY WORDS : compliant coat ing, coherent structure

I . I N T R O D U C T I O N Whether the wall friction for well-developed turbulent flows could be reduced with compliant

wall or not has been a controversial problem. The experiments made in air by Blick et a l . (1969)Ell proved that friction could be reduced 25%, but Bushnell et a l . (1977)I 21 showed tha t , according to the research done at N A S A , drag in turbulent air flow could not be reduced by compliant walls. McMichael et a l . (1980) t 31 further pointed out that the experiments of Blick et a l . had some drawbacks and some improper interpretation of the d a t a . Recently Riley et a l . (1988)I 41 made a good review on the research of compliant coatings. The studies on compliant coatings mainly concen- trated on whether drag could be recduced and on the interaction of compliant coating with fluid flows, but the effect of compliant coating on the turbulence coherent structure had not been investigated that much according to the papers published. The present authors thought that drag reduction was closely related to whether turbulent large scale coherent structures were affected or no t . The phenomena revealed in this paper were interesting, especially due to the fact that up to now there is no good method which can be used to measure the wall shear stress.

In this paper the effect of compliant coatings on coherent structure in developed turbulence was investigated by L D A , conditional sampling techniques and hydrogen bubble visualization. Some inter- esting results were obtained.

I I . EXPERIMENTAL E Q U I P M E N T AND PROCEDURE This experiment was carried out in a 6 m long, 450 m m deep and 250 mm wide plexiglass water

channel. The velocity of the flow could be continually adjusted in the range of 3 - - 30 c m / s . And the water level was controlled by a multi-hole end valve and being monitored by an automatic wat- er-level-tracking-meter to ensure a constant water depth during the experiment. A plastic flat plate of 4.5 m long was mounted horizontally in the channel 30 mm from the bo t tom. The turbulence inten- sity of the channel free flow was in the range of 2.8% - - 5 .3%, so the transition Reynolds number for the boundary layer flows Re~. tr = (3.3 - - 9 ) x 104 according to Van Driest-Blumer formula I s I . In this experiment measurements were made at a place 3.6 m from the leading edge of the plate ,and the Reynolds numbers Rex were larger than 3 x 105 so as to assure the boundary layer flows to be well-developed turbulent flows. The compliant coatings used were made of commercially available gel- a t in , and 3 kinds of compliant coatings were used in this experiment, the weight ratio of gelatin to water were 2%, 3 % , and 4% respectively .The gelatin solutions were poured in a channel of 800mm long, 230 mm wide on the p la te , and condensed into the compliant coatings after 16 hours . It was

Received 21 April 1989. * The project is supported by the National Natural Science Foundation of China.

98 ACTA MECHANICA SINICA 1990

pointed out by Gad-el-Hak (1986)[ s I that the compliant coatings made this way could be used within 8 hours during which the change of the dynamic characteristics could be ignored at room temperature, and in this experiment all measurements were made within this time l imitat ion.

Instantaneous velocity was measured by LDA in this experiment and the analog output of the LDA was sampled, stored and processed by a personal computer . Turbulence bursting frequencies were detected by the VITA method , which was illustrated in detail in [ 7 ] and [ 8 ] . Luchick et a l . (1987)f 91 recently proposed that modified U-level method was the best method to detect bursting frequency, and in this experiment the same method with the same parameters as that of Luchick et a l . was employed . The two methods , VITA and modified U-level, brought nearly same results.

H I . RESULTS AND DISCUSSIONS 1. Time average velocity profile The time average velocity profiles of turbulent boundary layer flows over rigid or compliant walls

were shown in F ig . 1 and F ig . 2. The data were taken at the same Reynolds number with the same ve- locity measuring system.

20!

16

12

+ ~ o rigid wall [

/

o 3% ~ c o m p l i a n t w a l l + o 4

+ 4% J /

R ~ : = 3 . 3 x l o s / + o ~ o /

_ ~ r " ~ l i i 4 8 12

U(cm/s) Fig. 1 Time average velocity profile

24

16

o rigid wall 4

4 2 % ~ " 4 z~ 4- p< § .

+4%~ 3% I compliant wall 4~ ~ o~/~~176

o o +1.o.--

U + = 2 .441n Y + + 4 . 9

I 1 I I I I I I 1 2 3 5 10 20 30 50 100 2 0 0 300

y§

Fig. 2 Time average velocity profile

It was shown in F ig . 1 and F ig . 2 that the log law region of the compliant wall boundary layer flows was further away from the wall than tha t of rigid wall flows. This phenomenon was considered a feature related to the reduction of the wall friction and appeared in many experiments on drag reduc- tion by polymer solution, by compliant coatings and by dilute suspension of clay. But Gad-el-Hak et a l . (1984)ll0] maintained that the log law region of the turbulentboundary layer flows on compliant coatings was the same as that on rigid wails , according to their experiments. We think that using the same A and B in the log law formula as that for rigid wall flows to calculate friction velocity u . in [ 10] was more unjustified than using the same A and different B, so the differences between flows

Vol .6, No .2 Shu & Liu : Effect of Compliant Coatings on Coherent Structure 99

over rigid walls and compliant walls could not be found in the way of [ 10]. In the present pape r , the data as shown in F ig . 1 were raw data without any processing and u , in F ig . 2 was determined by data in the sublayer. Due to limitations of measureing techniques, only 2 - - 3 points in the sublayer for compliant wall flows Could be obtained, and so u �9 for rigid wall flows was calculated using the da- ta in the log law region, which was relatively more reasonable.

2 . Turbulence Intensity Profiles The profiles of root mean square of streamwise fluctuating velocity scaled by free flow velocity

(%) were shown in F ig . 3 , in which the data were taken at the same Reynolds number and by the same measureing method .

60 Rex=3.3xlo s o rigid wall

a 2% 40 /o"-~ o 3% ~ compliant wall

u~

r , , ,

3 5 10 20 30 50 100 200 300 y+

Fig.3 Profiles of t urbulenc~ intcnsRy

F ig . 3 showed that the turbulence intensity profile of rigid wall flow had a peak of 0.46 at .3,+ = 8, which was in good agreement with the classical result of peak value 0.4 given by Klebanoff. But the peak values in the profiles for compliant wall flows were less than 0.38 , and the profiles tended to be flatter. It should be noted that the same tendency was found by Luchick et al .(1988 )Iul in research on drag reduction by polymer solution, and this was the first time that the phenomenon was found in compliant wall flows.

Since in F ig . 3 the e was the root mean square of fluctuating velocity scaled by free flow veloci- t y , the decreasing of e meant reduction of fluctuating intensity. It seems that the compliant wall made turbulence intensity smaller and played a very important role in surpressing turbulent intensity and preventing large scale eddies' from taking energy from mean flow.

3 . Streaky Structure Hydrogen bubble flow visualization techniques was used to visualize the streaky structures in tur-

bulent flows over compliant walls and over rigid walls at the same flow condit ions, and one group of the pictures taken are shown in F ig . 4 ,

(a) compliant wall flow (b)rigid wall flow Fig �9 4 Streaky structure (Uoo= 13.7 cm/s, y=2 ram)

It was shown in Fig .4 that there was streaky structure in the near wall region of compliant wall turbulent flow. By analysing a large number of images recorded by video recorder at y+ = 10, it was found that the average streak spacing 2 + for rigid wall flow was about 108, and that 2 + for compli- ant wall flow was about 8 2 . 2 + was a statistic average value scaled by viscous length. It was quite

t00 A C T A M E C H A N I C A S I N I C A 1990

difficult to get very accurate data about the spacings because in spanwise direction, the low-speed streaks moved, merged and were produced, but one definite thing was that ~r for compliant wall flow was statisticly less than 2 + for rigid wall flow.

4 . Bursting Frequency Two kinds of conditional sampling techniques, VITA method and U-level method, were used to

detect bursting frequency in this experiment. Measurements indicated that results obtained by the'two methods were nearly the same if sampling time was long enough (about 20 minuts ). Measurements were carried out at y+= 15 at different Reynolds numbers for Fig. 5 and Fig .6, where Reo is the Reynolds number characterized by momentum thickness 0, f + was the average bursting frequency scaled by boundary layer flow inner parameters u . and v, U~ was the free flow velocity, and h the water depth. Reo ranges from 650 to 1850.

0,010

+

0.005 -+ 4- A

I 5 0 0 1 0 0 0

v c ~

o rigid wall

o 3% compliant wall + 4%

a 0 A +

+ O +

0 o

1500

0

r +

Re9 900

Fig. 5 The relationship of bursting frequency scaled by boundary layer flow. inner parameters with Reynolds number

~- 0.3

o rigid wall 0.5

~2% 1 o / ~ v 3% compliant + 4%" wall /

o

0.1

500 l 0 O0 -- Reo

o

l~oo

z~

D

20OO

Fig. 6 The relationship of bursting frequency scaled by boundary layer flow outer variables with Reynolds number.

The bursting frequency in rigid wall flows was independent of Reynolds number when scaled with the wall region parameters, on the other hand, it increased as Reynolds number increased when scaled by outer variables of boundary layer flows, which was the same as in Shu et al. (1988)[71 Bursting frequency of compliant wall flows was much smaller than that of rigid wall flows, and whether scaled by inner or by outer parameters it increased as Reynolds number increased. Decrease of bursting fre- quency due to compliant coating indicated that bursts were restrained by compliant coatings.

Number of bursts appearing in unit time for compliant wall flows was much smaller than that for rigid wall flows detected with the same threshold level and sampling time, It indicated that in compli- ant wall flows large scale fluctuations decreased and the whole fluctuating intensity became smaller. It

Vol . 6 , No .2 Shu & Liu " Effect of Compl iant Coat ings on Coherent St ructure 101

was a very interesting poin t that perhaps the phenomenon stated above meant that the ability of tur- bulent large scale eddies to take energy from the mean flow was weakened, leading to drag reduction.

IV. CONCLUSIONS It was for the first time that LDA, conditional sampling and visualization techniques were used to

study the effect of compliant coatings on coherent structure in turbulent boundary layers and the following results were obtained :

1. In boundary layer flows over compliant walls the log law region was further shifted away from the wall than that in rigid wall boundary layer flows at the same Reynolds number .

2 . The turbulence intensity in the near wall region was smaller in compliant wall flows than that in rigid wall flows at the same Reynolds number , and its profile was flatter in compliant wall flows than that in rigid wall flows.

3 . The dimensionless average streak spacing was smaller in compliant wall flow than that in rigid wall flow at the same distance from the wall and at the same Reynolds number .

4 . Bursting frequency of flows over compliant wall were much smaller than that of flows over rig- id wall .

I t is very difficult at present to determine whether the friction can be reduced with compliant coatings, since there is no reliable method which can be used to accurately measure the surface stressses. But it is interesting to note that the results in this paper are very much like the results of polymer solution drag reduction studies.

Although several types of compliant coatings wer:~ made in this experiment, differences among them and so effects of different coatings on turbulence coherent structure could not be found in this ex- periment.

REFERENCES 1] Bl ick ,E.F. , Walters,R.R., Smith,R. , C h u , H . , AIAA Pap. No.69-165.(1969). 2] Bushnel l ,D.M., Hefner ,J .N. , Ash ,R .L . , Phys. Fluids,20, 10,(1977), 31 3] McMichael,J.M., Klebanoff, P . S . , Mease,N.E. , ProoressinAstronutics,72,(1980), 410--438. 4 ] Riley, J. J . , Gad-eI-Hak ,M. , Metcalfe, R . W . , Ann. Rev. Fluid Mech. 30, (1988), 393 - - ,420. 5 ] White, F .M. , Viscous Fluid Flow ,McGraw-Hill Book Company, (1974). 6] Gad-e l -Hak,M. ,J .Appl . Mech., 39,4,(1986), 206. 7] ShuWei,TangNing,ActaMech.Sinica,4,4(1988), 291. 8] ShuWo,TangNing,AdvancesinHydrodynamic,3,3,(1988), 28 (in Chinese) . 9] Luchick,T.S. , Tiederman,W.G., d. Fluid Mech., 174,(1987), 529.

[10] Gad-el-Hak,M.,Blackwelder,R.F. , Riley,J.J . , J. Fluid Mech., 140, (1984), 257-- 280. [11] Luchick,T.S., Tiederman,W.G., J. Fluid Mech., 190,(1988), 241.