J

AN EXPERIMENTAL INVESTIGATION

OF THE SEPARATING/REATTACHING

FLOW OVER A BACKSTEP

F.

Progress Research Report

Cooperative Agreement No.: NCC2-465

for the period

January 1, 1991 - August 31, 1991

Submitted to

National Aeronautics and Space AdministrationAmes Research Center

Moffett Field, California 94035

Experimental Fluid Dynamics BranchJoseph G. Marvin, Chief

David M. Driver, Technical Monitor

Fluid Dynamics DivisionPaul Kutler, Chief

Prepared by

ELORET INSTITUTE1178 Maraschino Drive

Sunnyvale, CA 94087Phone: 408-730-8422 and 415-493-4710

Telefax: 408-730-1441

K. Heinemann, President and Grant Administrator

Srboljub Jovic, Principal Investigator

10 December, 1991

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INTRODUCTION

This progress report covers the grant period from January until the end of August1991.

Reynolds number effencts on the evolution of the turbulence structure in the re-

covery region of a turbulent separated flow generated by a backward-facing step were

studied experimentally. Five different flow conditions and four Reynolds numbers were

investigated. All single-point measurements were conducted on the plane of symmetry of

the wind tunnel starting at approximately x/h = 10 for each flow condition. The upper

limit of the measuring domain depends upon the physical size of the tunnel and ranged

from 50 to 114 step heights. It is apparent that the most of the boundary layer recovery

was captured by the experiment. Normal stresses, shear stress, mixing length scales and

eddy viscosity are shown in this progress report while the higher order velocity products

related to the diffusion of the turbulence energy are planned for latter stages of the data

analysis.

EXPERIMENTAL CONDITIONS AND TECHNIQUES

The experiments were conducted in the same tunnel as described in the previous

progress reports. This is a 200 x 400 mm low-speed suction-type wind tunnel with a

4.0m long test section. The recovery of the boundary layer was investigated for five dif-

ferent flow conditions or four Reynolds numbers with one Reynolds ( Rh = 25500) num-

ber being obtained by the two different combination of Ure/ and h.

Initial condition

Reynolds number based on the step height, h, and the reference velocity, Uref, up-

stream of the step ranged from 6800 to 37000. Experiments were conducted for five

different combinations of the reference velocity, Ur¢/, and the step height, h, which are

given in the table bellow.

Table 1. Flow conditions

Rh Ur i(m/s)

6800 6.0

10500 6.0

255OO 14.7

25500i 10.0

370001 14.7

h(mm)

17

26

26

38

38

The boundary layer upstream of the step was turbulent and fltlly developed such that

the incoming boundary layer thickness was approximately constant in all five cases.

Experimental Tech.nique

Direct measurements of the skin friction coefficient were obtained using the Laser-oil in-

terferometry technique.. A normal hot-wire probe was used to measure the of a stream-

wise velocity flictuations, u t, very close to the wall.. In some streamwise locations the

first measuring point was as low as one wall unit. A cross hot wire probe was used to

measure u 2, v 2 and B-_. The first point for these measurements was about g+ = 20 wallunits.

RESULTS AND DISCUSSION

Skin friction coefficient distributions for different Reynolds numbers are shown

in Figure 1. Negative values of skin friction in the recirculating zone reduce as the

Reynolds number, Rh increases. In the recovery region, skin friction asymptotically ap-

proache distribution for highest value of Reynolds number. Mean velocity profiles nor-

malized by the measured friction velocity, u,-, for Rh = 25500 are shown in Figure 2. It

is apparent that the law of the wall is violated sufficiently close to the mean reattach-

ment point reflecting nonequilibrium nature of the flow in this region. Further down-

stream, for :r/h >_ 30, mean velocity profiles correlate well with the standard law-of-

the-wall distribution in the near wall region. This suggests that the near-wall turbu-

lence structure may resemble that found in a regular equilibrium boundary layer. This

notion is further confirmed by the fact that the distributions of Urms/U,, Vrm_/U,- and

--uu/u 2 ( see Figure 3. for Rh = 25500) agree well with Klabanoff's measurements in

the near wall region. It appears that the near-wall structure recovered by the distance

of 30h downstream from the step. Note should be made that the Reynolds numbers of

the two experiments were comparable. The Reynolds numbers based on the momentum

thickness of the Klebanoff and the present experiment were 7500 and about 7000 respec-tively.

The turbulence structure of the outer flow region reflected by Urm,/U,-, V,-m,/U,-9

and -uv/u; approaches the structure of an equilibrium boundary layer at a much

slower rate than near the wall. The Reynolds shear stress is shown in Figure 4 for the

tested Reynolds number range. Higher energy content, present in the wake region for

all Reynolds numbers, is due to the presence of the large coherent structures convected

downstream from their origin in the free shear layer region. The rate of the brake-down

of these structures and their approach to that found in a regular equilibrium turbulent

boundary layer depends on the intensity of the perturbation imposed by the step. The

intensity of a perturbation is generally a function of Ra, 6/h, E_ ( expansion ratio) and

the state of the upstream boundary layer ( turbulent or laminar). In this experiment the

expansion ratio, E,-, varied from 1.1 for Rh = 6800 to 1.2 for Rh = 37000, therefore it

is safe to say that the adverse pressure gradient due to the different expansion ratios did

not play an important role in flow dynamics. Pressure coefficient measurements for the

different Reynolds numbers are planned for the next ph_e of the project. In all cases

the incoming boundary layer was a fully developed turbulent boundary layer with ap-

proximately constant boundary layer thickness, 5 = 30 to 34ram. Hence, the parameter

6/h changed only due to the variation of the step height and it varied between 0.8 and 2.

According to Bradshaw & Wong (1972) the strength of perturbation for 6/h in the given

range can be regarded as a strong to weak perturbation.

Turbulence mixing length scale, l/5, distributions ( Figure 5.) obtained fl'om tile

mean velocity and the shear stress distributions indicate a presence of structures in

the outer region with much larger length scales than those found in a regular bound-

ary layer. The slope of the 1/5 distribution near the wall and close to the reattaclnnent

zone is nmch greater from the value of h'. = 0.41, where _; is yon I(firm_n's constant.

The slope nlonotonically approaches the above value of 0.41 for greater downstream dis-

tances. It appears that a more intense perturbation is created for a greater -Rh when

the parameter 5/h is kept constant ( see Figure 5(b) and 5(c), for Rh = 10500 and

Rh = 25500). Consistently, eddy viscosity distributions, v/U,5* vs. g/_5 ( see Figure 6,

(5* is the displacement thickness), which were obtained from the measured shear stress

and mean velocity distributions for different Rh, indicate nmre intense mixing of tile

flow than in a regular turbulent boundry layer. Neither the outer layer mixing length

scale nor the eddy viscosity distribution does not approach those found in an equilib-

rium boundary layer even at x/h = 114 (see Figure 5(a) and 6(a) for Rh = 6800). This

behavor shows that the transport of momentum due to turbulence, which is contained

in triple velocity products or diffusion terms, still has a memory of perturbation experi-

enced by the flow in the separated region. Additional analysis of triple products of ve-

locity fluctuations will be presented in the next progress report.

FUTURE PLANS

The experiment in a recovery region of the separated flow indicated that the flow

has not reached the equilibrium boundary layer structure even after .c/h > 100 down-

stream of the step. While the turbulence structure approaches the regular boundary

layer structure near tile wall downstream of the step, the outer region structure rernain

dominated by large structures advected downstream from the free shear layer region.

It is expected from the two-point ineasurements made at, x/h, = 38 that the multi-

point measurements of a velocity field can give very fruitful results. Hence. an objective

of the future study is to analyze simultaneous velocity field using a rake of seven X-wires

to investigate the evolving turbulence structure of the separated flow. These meas_tre-

meats will be performed for Rh = 25500 and possibly for one smaller Reynolds number.

ACKNOWLEDGMENT

The author is indebted to J. Marvin and D. Driver for their continuous

encouragement throughout the experiment.

References

Head: M.R.. and Bandyol)adhyay, P. 1981 New Aspects of Turbulent Boun(lary- layer

structure..1. Fluid Mech.. 107, 297.

4

Bradshaw, P. and 'VVong, F.Y.F., 1971, The Reattachment and Relaxation of a Turbulent

Shear Layer. Y. Fl.aid Mech. 52, 113.

Jovic, S. and Browne, L.W.B. 1990 Turbulent Heat Transfer Mechanism in a Recovery

Region of a Separated Flow. Engineering T_rb'ulence Modelling and Ezperirnent_ Pro-

ceeding_ of the International Symposi_tm on Engineering T_rbuIence Modeling and Mea-

surements, September 24-28, ed. W. Rodi and E.N. Ganic.

Moin, P. and Moser, R.D. 1989 Characteristic-eddy decomposition of turbulence in a

ehannel.d. Fluid Mech. 200, 471.

Theodorsen, T. 1952 Mechanism of Turbulence. In Proc. 2nd Midwe_tern Conf. on

Fluid Mech., Ohio State University. Columbus, Ohio.

Townsend, A.A. 1976 The Structure of the T_Lrb_lent Shear Flow. Cambridge UniversityPress.

5

Figure Captions

Figure 1. Skin friction distribution for different Reynolds numbers.

Figure 2. Mean velocity profiles in wall coordinates for Rh = 25500.

Figure 3. Reynolds stress profiles for Rh = 25500. (a) U,.m_/U_-; (b)v,-m_/u,-; (c)

Figure 4. Shear stress profiles for different Reynolds numbers Rh: (a) 6800;

(b) 10500; (c) 25500; (d) 25500; (e) 37000.

Figure 5. Mixing length scale distribution for different Reynolds numbers Rh:

(a) 6800; (b) 10500; (c) 25500; (d) 25500; (e) 37000.

Figure 6. Eddy viscosity distributions for different Reynolds numbers Rh: (a)

6800; (b) 10500; (c) 25500; (d) 25500; (e) 37000.

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