NASA CONTRACTOR REPORT 177379

'The Effects of Anisotropic Free-Stream

Turbulence on Turbulent Boundary Layer

Behavior

Fang Liang-Wei

Jon A. Hoffman

THE EFFECTS OF ANISOTfiOPIC FBEE-STBEAH N86-16192

TURBULENCE ON TUB BOLE NT BOUNDAR Y LA YEB •

BEHAVIOB Beport,. 1 Jul, 1984: - 1 Jul.;/1985

(California Polytechnic State Univ.), 43 p Dnclas

Hc;&03/aF ADI ; ._!..-. . CSCL OH G3/o_2 _j)36&9 __

CONTRACT NSG-2391

November 1985

NASA
NASA CONTRACTOR REPORT 177379

Fang Liang-Wei

Nanjing Aeronautical Institute

Peoples Republic of China

Jon A. Hoffman

Aeronautical Engineering Department

California Polytechnic State University

San Luis Obispo, CA 93407

Prepared for

Ames Research Center

Under Grant NSC 2381

NASA

National Aeronautics and

Space Administration

Ames Research Center

Moffett Field, California 94035
ABSTRACT

The effects of near-isotropic and highly anisotropic free-stream turbulence

on mean flow properties and properties of the turbulent structure of turbulent

boundary layers in a near zero pressure gradient flow has been experimentally

evaluated. Turbulence levels varied from 0.5% to 8.0% and the momentum

thickness Reynolds number varied from 800 to 1100.

The results indicate that the effects of free-stream turbulence on the

classical boundary layer properties for near-isotropic turbulence which have

been published by other investigators are similar to the case of highly

anisotropic turbulence fields, while the effects of free-stream turbulence on

the properties of the turbulent structure within the boundary layer for the

case of near-isotropic turbulence are quite different compared to the highly

anisotropic case.
INTRODUCTION

Turbulent boundary layers or other shear layers generated in engineering

generally lie beneath a significantly turbulent stream. A good example is the

flow in a multistage axial turbomachine, in which the disturbances felt by the

boundary layers on the blades of one of the later rows include: (1) periodic

unsteadiness due to the rotating wakes of upstream stages; (2) periodic strong

bursts of turbulence due to the wakes of the blades in the preceeding few rows;

and (3) circumferentially homogeneous and anisotropic turbulence generated by

the blade rows far upstream.

The free-stream turbulence levels encountered in practical fluid flow

problems can vary over a wide range. The turbulence levels in free flight are

very much less than 1% whereas the flow in turbomachines may have turbulence

levels as high as B% to 10%. When the free-stream turbulence scale is much

larger than that of a turbulence shear layer (or boundary layer thickness), the

boundary layer may be considered to experience an unsteady external flow; for

this case, Parikh (1) has shown that the time averaged velocity profile is the

same as the velocity profile with a steady external flow. Turbulence with a

scale much snaller than that of a shear layer decays rapidly and has no

practical relevance. Only turbulence with scales of the same order as the

thickness of the shear layer have been found to exert a significant effect on

the mean properties of the shear layer.

The effect of turbulence level on boundary layer behavior has not gone

unnoticed; recent published papers relate to the idealized nearly-homogeneous
nearly-isotropic turbulence case and have mainly been restricted to boundary

layers without pressure gradients. Investigations by KLine (2), Huffman (3)f

Meier (4), and recent papers by Hancock (5), Raghunathan (6), and Castro (7)

have shown that the boundary layer skin-friction and the integral properties of

the boundary layer are very sensitive to the free-stream turbulence level for

/q /U > 1%» and may be unaffected at lower intensities of turbulence. Investigations by other authors were performed with nearly homogeneous, nearly

isotropic turbulence and the influence of isotropy on the above interaction is

not yet understood. This is particularly important for a multistage axial

turbomachine,- as mentioned previously. Sullery (8) investigated the freestream turbulence effects on compressor cascade wakes. His results indicated

that the wake decay is faster for the case of high free-stream turbulence

levels and the drag coefficient decreased slightly as the turbulence level was

increased. Sullerey's results, however, were limited to/q /U < 2.781 which

is much lower than the turbulence levels generated by a compressor in a

turbomachine.

The present paper will document some of the effects of free-stream

turbulence on the integral properties of turbulent boundary layers and properties of the turbulent structure in a near zero pressure gradient flow. The

turbulence level range investigated varies from 0.5J to 8%. Attention is

concentrated on cases when the free-stream turbulence fields are near-isotropic

(generated by grid sets) and anisotropic (generated by rod sets with a

significant downstream flow contraction).

-iii-
NOMENCLATURE

b = channel height

b = rod length

B = strip width of the grids sets

C = channel length

c.. = skin friction coefficient = T

D = rod diameter

H = shape factor of boundary layer = $*/ 9

Ip tO to

k = turbulent kinetic energy = (u+v+ w )/2

M = mesh size of the grid sets and rod sets

n = number of grid set strip or rods

f ^"^^" r ,L ^^^T O

/ q = total RMS turbulence quantity =y (u + v + w

1

 )/3

r = radius of rod set geometry

Rey. = Reynolds number based on channel width = UfflW^/ v

Reg = momentum thickness Reynolds number = U_6/v

R = free-stream autocorrelation coefficient in flow direction at

diffuser inlet

R = free-stream cross-correlation coefficient in y direction at

y

 diffuser inlet

s = gap between grid sets and inlet section

Um = average free-stream velocity in flow direction

U = mean velocity in flow direction

UT = shear velocity = /7~~T .

w / P

U* = non-dimensional velocity = u / U

t i t

u ,v ,w = turbulence component velocities

-i-
Symbols

W1

x,y,z

. *

6

0

XX

Xy

T

w

P

v

ACf

AH

= channel width

= cartesian coordinates

= non-dimensional distance = Uty/v

= boundary layer thickness

= boundary layer displacement thickness

= boundary layer momentum thickness

= free-stream integral scale of turbulence in x direction

= free-stream integral scale of turbulence in y direction

= wall shear stress

= fluid density

= kinematic viscosity

= fractional change in skin friction

= fractional change in shape factor

Subscript

o = value in absence of turbulence generating grid or rod

-2-
EXPERDCHT.AL PROGRAM

aratus

The experimental system used for the investigation, shown in Fig. 1 ,

consists of a base-plate and top-plate 'for upstream rods and grids, a throat, a

straight channel, a plenum chamber, a fan and a noise attenuator. The fluid,

air, is drawn through the system with a five horsepower centrifugal fan. The

flow rate is controlled by adjusting a throttle which is located between the

exit section of the fan and the inlet section of the noise attenuator. Screens

and filters located in the plenum are used to improve flow conditions at the

fan inlet.

Throat and Straight Channel

The straight channel was constructed out of clear lucite; the channel width

dimension (W^ is 26 mm. The channel height/inlet width ratio (b/VL) is 5.86

and the channel length/ inlet width ratio (C/W.) is 4.88. In the channel,

boundary layers develop. The channel has four pressure taps located upstream

of the channel exit section. The throat of the straight channel has an ASME

standard nozzle shape. Masking tape applied to the throat caused transition

fron a laminar to a turbulent boundary layer to begin at the location of the

tape rather than randomly along the channel walls. The measuring station was

located at 1 mm upstream of the channel exit section. The Reynolds number,

based on the width of the channel, is 7.8 x 10 .

TAlfb.Miftn.ee Generation

Rods and grids used for turbulence generation were placed between the baseplate and top-plate upstream of the throat as illustrated in Figs. 1 and 2.

- 3 -
The rod length/ channel height ratio was fixed at 1.71 for all rod sets. All

grids were rectangular-mesh rectangular-bar biplane grids except for one which

was a commercial screen. A gap between the grid sets and the face of the inlet

channel (S) is shown in Fig. 1. Geometrical information about all upstream rod

sets and grid sets are presented in Table 1 .

and Data Processin

The primary data record in the experiments were velocity profiles in the

*

boundary layers, turbulence levels, auto and cross correlation coefficients

(used to obtain turbulence length scales), and Reynolds stress measurements.

Wall skin friction was measured with a Preston tube using the calibration table

of Head et al., (9). The Preston tube was also used as a pi tot tube for

boundary layer velocity profiles measurements. Turbulence measurements were

obtained by using two model 1010A T.S.I, constant temperature hot wire

anemometers, two model 1005B linearizers, a model 1015A correlator, two model

H.P. 3400A true rras meters and a T.S.I. 1076 true rms meter. In order to

obtain turbulence quantities averaged for 10 second periods, the d.c. output

fron the rear panel of the rms meter was fed into a H.P. 221 2A voltage to

frequency converter and then into a H.P. 5223L electronic counter. A Tektronix

dual beam oscilloscope was used to monitor the turbulence signal.

The turbulence levels in the streamwise direction were obtained using

single hot wires mounted in a micrometer traversing device. Free-stream

turbulence levels in the y and z directions were obtained by using probes

with single wires inclined 45° to the mean stream direction. Free-stream

longitudinal correlation coefficients were obtained using a single hot wire

placed normal to the flow. Values of the longitudinal integral scales of

- 4 -
turbulence (x ) were obtained by integration of the area under curves of the

longitudinal correlation coefficient (Rx) versus a distance corresponding to

the time delay of the hot wire signal (Taylor's hypothesis). Cross correlation

coefficients (R ) were obtained using probes with two parallel wires (the wires

being displaced by different distances) along with a 1015A correlator. Lateral

integral scales (x ) were then obtained by integrating the area under curves of

R versus the distance between the wires. Reynolds stress profiles in boundary

layers were measured by using an x hot wire probe along with the correlator

taking the (A-B) rms value and mean value from linearizers.

A flattened pitot tube (or Preston tube) with tip outside and inside

dimensions, measured in the y direction, of 0.3 mm and 0.15 mm respectively,

was mounted on a Unislide traversing mechanian whose position accuracy was

better than 0.025 ram. Inclined manometers were used for all pressure

measurements. A pressure loss coefficient across the rods and grids was

experimentally obtained for each rod set and grid set. This pressure loss,

along with a pressure differential between the pressure from taps located in

the top-plate and base-plate upstream of the rods,' and the pressure from static

taps located upstream of the channel exit, was used to determine the freestream channel velocity.

- 5 -
RESULTS AND DISCUSSION

The Effects of Free-stream Turbolence on the Classic Boundary Laver Properties

Hot wire spectra of free-stream turbulence at the measuring station are

shown in Fig. 3. Discrete peak values were not detected from the signal

indicating that the periodical vortices shed by the rods have decayed to random

turbulence. Therefore, the hot wire measures a real free-stream random

turbulence. Isotropy occurs primarily due to the flow contraction downstream

of the turbulence generator. ...... .

Nondimensional velocity profiles for various levels of turbulence are shown

in Fig. 4. An increase in the free-stream turbulence results in flatter

velocity profiles implying an increase in the momentum transport across the

boundary layer. Fig. 5 shows nondimensional velocity profiles for both

isotropic and anisotropic free-stream turbulence at approximately the same

turbulence level. It shows that the velocity profile for anisotropic freestream turbulence is slightly more full compared with isotropic turbulence.

The influence of free-stream turbulence on boundary layer thickness (6)

is shown in Fig. 6. The variation of 6 is nonlinear. The influence of

anisotropic turbulence on 6, however, is a little bit larger than for an

isotropic turbulence field. The results from Fig. 5 and Fig. 6 imply that the

momentum transport across the boundary layer for anisotropic turbulence is a

little bit stronger than for the case of an isotropic turbulence field at the

same free-stream turbulence level.

- 6 -
The combined effect of the flattening of the velocity profile and the

increase in 6 results in significant changes in the nondimensional integral

properties of the boundary layer shape factor (H) as shown in Fig. 7. The

trends of the present results are the same as those of other published papers

(4) (6).

The influence of free-stream turbulence on the nondimensional shape factor

/ tp /"To

AH/H with three values of ^ v /vu are shown in Fig. 8, along with the

results of Raghunathan (6) and Kline (2). The present results are in close

agreement with the other investigators. The results also show that there is no

noticeable difference between the highly anise-tropic and near-isotropic

turbulence cases.

The law of the wall and the law of the wake in the boundary .layer are shown

in Fig. 9. The skin friction coefficients (0 for these plots are based on

Preston tube measurements. The plots show that the law of the wall of the form

U/UT = A + B log (UTy/v) holds good for all values of free-stream turbulence,

confirming that the law of the wall is unaffected by the change in free-stream

turbulence. The law of the wake (outer layer), however, is very sensitive to

free-stream turbulence level. The strength of the wake component is seen to

decrease when the free-stream turbulence level increases, but it is not very

sensitive to the isotropy ratio of the turbulence field (Fig. 10).

The influence of free-stream turbulence level on cf andAcVcp can be

observed from Fig. 11. The increase in turbulence level results in an increase

in cf and Ac£/cfo. The curve shows nonlinear effects at turbulence levels

lower than 4% which is in agreement with the experimental data represented by a

curve fit (Acf/cf = 12.60/q'2/Um)

1

*

4

 of data from Raghunathan (6).

- 7 -
Hancock (5) found a linear correlation between the increase in skin

friction and decrease in shape factor. The one-to-one correspondence between

changes in cf and changes in the profile shape factor H obtained in this study

is consistent with Hancock's result as shown in Fig. 12.

Hancock (5) also reviewed the extensive literature and undertook some

particularly careful experiments designed to extend the previously rattier

limited range of turbulence length scale ratios. His results showed that the

effect of free-stream turbulence (nearly isotropic) depends significantly on

both the free-stream level and the length scale ratio. His data clearly

demonstrates that not only does the effect of free-stream turbulence increase

with increasing turbulent intensity but also that the effect decreases with

increasing length scale ratio. A simple empirical correlation was found by

Hancock that relates the increase in skin friction A cVc- at constant Re

i f O 9

(momentum thickness Reynolds number) to a free-stream turbulence and length

Hi

scale combined parameter (/u /Uffl)/(Ax/ 6*2). Hancock limited his study to

values of ReQ in excess of 2000 in order to avoid serious Reynolds number

effects.

Recently, Castro (7) extending Hancock's work to low monentun thickness

Reynolds numbers, Re Q = 1000. Castro's results showed that "direct Reynolds

number effects are significant and such effects reduce as the level of freestream turbulence rises."

The range of Re0 of the present experiment varies from 800 to 1100.

Obviously, a Reynolds number effect should exist. In order to check the

present results to look at both the effects of length scale and Reynolds

number, extensive free-stream turbulence length scale measurements were

- 8 -
obtained by using a single hot wire along with a correlator. The

 A

versus (/u /U )/(A / 6 + 2) interdependence is shown in Fig. 13. Castro's

results are also shown in the plots. It can be seen that both the present data

and Castro's data are very close and are both lower than Hancock's results. It

therefore appears that Hancock's argument can be extended to the case of

anisotropic free-stream turbulence fields.

°f Free— atrftajfl Tlirb.UlPnce Qfl the T\jrt?yilence Structure of a

Boundary

Huffman et al. (3) have clearly demonstrated that for nearly iso tropic

free-stream turbulence the turbulence properties in the boundary layer are more

strongly affected by changes in the free-stream turbulence level than are any

of the classical boundary layer properties. In the present experiment, the

effect of anisotropic free-stream turbulence on the turbulent structure of a

boundary layer is investigated. A large number of turbulence parameters within

a boundary layer were measured using different kinds of hot wire probes.

Fig. 14 shows the region in the turbulence intensity-length scale plane

covered by the present work. Both A and A for the anisotropic case are

* y

slightly larger compared to the isotropic case at the same turbulence level and

the order of magnitude of A and A are on the same order of the boundary layer

** *

thickness.

The distribution of turbulence within the boundary layer for various levels

of free-stream turbulence are shown in Fig. 15. Fig. 16 shows the turbulent

kinetic energy (2k/U^) distribution within the boundary layer. Note that the

free-stream velocity, Um, does not change with changes in turbulence level. It

is seen fron the figures that the turbulence level and turbulent kinetic energy

- 9 -
in the outer layer are sensitive to the free-stream turbulence, whereas the

turbulence level and turbulent kinetic energy near the wall do not change

appreciably with change in the free-stream turbulence. Fig. 17 shows the

Reynolds stress distribution with different free-stream turbulence levels

within boundary layers. Huffman indicated that the Reynolds stress and

turbulent kinetic energy are largely unaffected by the free-stream turbulence

level for y/6 < O.U; the present results agree with these findings. Consequently, it can be concluded that the inner layer shear stress producing

mechanism is universal and is largely unaffected by external conditions of

either isotropic or anisotropic turbulence fields.

Fig. 18 and 19 plot the distribution of three nns components of the

velocity fluctuation /u'2/Um, ^v

 2/Um, ^w

'

2/u

m within the boundary layer.

The comparison of these components with different free-stream turbulence levels

for near-isotropic and highly anisotropic turbulence are shown in Fig. I8a and

I8b respectively. It shows that all the components of velocity fluctuations

with high free-stream turbulence levels are higher than for the case of low

turbulence levels in the outer part of the boundary layer. Fig. 19 shows a

comparison between the highly anisotropic and near-isotropic case at the same

free-stream turbulence level. It is seen that for y/6 > 0.4. the/u'2/U — m

component for anisotropic turbulence is lowest and the other components

/to / 10

Uv /Um and/w /Um) are higher compared to the near-isotropic case. Therefore the eddy axis generated by rod sets and the contraction of the channel

make a contribution to isotropy.

- 10 -
CONCLUSIONS

The effect of anisotropic free-stream turbulence level on the classic boundary

layer properties: i.e., 6 , 6 */6, H, AH/HQ| c^., AC^/C^, can be summarized as

follows:

1. The present results of the effect of anisotropic free-stream turbulence

level on the classic boundary layer properties are similar to those of

other recent works for isotropic turbulence, i.e., (a) boundary layer

•

thickness and skin friction increase with increasing turbulence level; '

(b) the mean velocity nondimensionalized with IL remains largely

unchanged in inner region of the boundary layer; however, there is a

marked reduction in the wake component as the free-stream turbulence

level increase; and (c) the shape factor H decreases with increased

turbulence level due to the reduced wake-component.

2. The present experimental results confirms both the results of recent

published papers by Hancock (5) and Castro (7), i.e., the effect of

free-stream turbulence decreases with increasing free-stream length

scale, and momentum thickness Reynolds number has a significant effect

when the ReQ < 2000.

The effects of free-stream turbulence on the structure of a turbulent boundary

layer reveal a different influence for near-isotropic and highly anisotropic

\

free-stream turbulence fields.

- 11 -
1. The turbulence level and Reynolds stress distributions within the

boundary layer are sensitive to free-stream turbulence in the outer

part of the boundary layer, and are largely unaffected in the inner

layer.

2. The velocity fluctuation components in the outer part of the boundary

layer for anisotropic free-stream turbulence have quite different nns

values compared to the near-isotr'opic case. The longitudinal fluctuation component, generally, is lower for highly anisotropic free-stream

turbulence compared to the isotropic turbulence case, while the lateral

and normal fluctuation components are much higher compared to the nearisotropic case. Thus, the advection of the free-stream turbulent

energy has directivity in the outer part of boundary layer.

- 12 -
ACKNGUL

The authors gratefully acknowledge the support of this investigation by NASAARC through Grant NSG-2391.

- 13 -
BIBLIOGRAPHY

1. Parikh, P. G. , Reynolds, W. C. and Jayaranan, R. , "Behavior of an Unsteady

Turbulent Boundary Layer." AIAA Journal, Vol. 20, No. 6, June 1982, pp.

2. KLine, S. J. , Lisin, A. V. and Waitman, B. A., "Preliminary Experimental

Investigation of Effects of Free-Stream Turbulence on Turbulent Boundary

Layer Growth." NASA TN D-368, 1960.

3. Huffman, G. D. , Zimmerman, D. R. and Bennett, W. A., "The Effect of FreeStream Turbulence Level on Turbulent Boundary Layer Behavior." AGARD,

No. 164 on Boundary Layer Effects in Turbomachines, edited by J. Surugus,

April, 1972.

4. Meier, H. U. and Kreplin, H. P., "Influence of Free-Stream Turbulence on

Boundary Layer Development." AIAA Journal, Vol. 18, 1981, p. 11.

5. Hancock, P. E. and Bradshaw, P., "The Effect of Free-Stream Turbulence on

Turbulent Boundary Layers." ASME Journal of Fluids Engineering, Vol. 105,

September 1983, p. 284.

6. Raghunathan, S. and McAdam, R. J. W. , "Free-Stream Turbulence Effects on

Attached Subsonic Turbulent Boundary Layer." AIAA Journal, Vol. 21, No.

4, 1983.

7 . Castro, I. P. , "Effects of Free-Stream Turbulence on Low Reynolds Number

Boundary Layers." ASME Journal of Fluids Engineering, Vol. 106, September

1984.

8. Sullerey, R. K. and Sayeed Khan, M. A., "Free-Stream Turbulence Effects on

Compressor Cascade Wake." Journal of Aircraft, Vol. 20, No. 8, 1983.

9. Head, M. R. and Rechenberg, I., "The Preston Tube as a Means of Measuring

Skin Friction." Journal of Fluid Mechanics, Vol. 14, 1962.

10. Green, J. E. , "On the Influence of Free-Stream Turbulence on a Turbulent

Boundary Layer as it Relates to Wind Tunnel Testing at Subsonic Speeds."

AGARD Report 602, 1973.

- 14 -
TABLE 1

Geometrical Upstream Rod Sets and Grid Sets

Grid Set

1

2

3

4

5

6

7

Rod Set

1

2

3

4

5

B/VI

0.034

0.122

0.122

0.176

0.244

0.305

0.351

D/W.,

0.092

1.28

3.03

3.9

5.9

B/M

0.108

0.25

0.31

0.36

0.40

0.353

0.332

D/N

0.27

0.57

0.74

0.61

0.71

n

screen

3 x 11

3 x 13

3 x 11

5 x 14

4 x 10

1 x 7

n

32

7

5

5

4

S/W,

0.12

0.12

0.12

0.12

0.06

0.12

0.12

s/v1

r/W,

r/W.,

4.62

5.51

7.32

9.76

11.2

- 15 -
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- 18 -
BASEPLATE

Fig. 2

Rod Set Geometry Nomenclature

- 19 -
f(UI)(1/Hr)

10

Spectra] Density Curves of Inlet Free-Stream Turbulence

with Three Different Rod Sets

- 20 -
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&

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1. Report No. 2. Government Accession No.

OR - 177379

4. Title md Subtitla

"The Effects of Anisotropic Free-Stream Turbulence

on Turbulent Boundary Layer Behavior

•7. Author(s)

Fang Liang-Wei and

Jon A. Hoffman

9. Performing Organization Name and Address

California Polytechnic State

University San Luis Obispo, CA 93407

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546

3. Recipient'! Catalog No.

5. Report Date

November 1985

6. Performing Organization Code

8. Performing Organization Report No.

10. Work Unit No.

T-7526

11. Contract or Grant No.

NSG-2391

t3

- tOS&Ssesrfe&T?11**

7-1-84 to 7-1-85

14. Sponsoring Agency Code

505-61-71

IS. Supplementary Notes

Technical Monitor: David G. Koenig & Michael Dudley, Mail Stop 247-1

NASA Ames Research Center, Moffett Field, CA 94035, Phone: 415) 694-5046

16. Abstract

The effects of near-isotropic and highly anisotropic free-stream turbulence on mean flow properties and properties of the turbulent structure of

turbulent boundary layers in a near zero pressure gradient flow has been experimentally evaluated. Turbulence levels varied from 0.5% to 8.0% and the

momentum thickness Reynolds number varied from 800 to 1100.

The results indicate that the effects of free-stream turbulence on the

classical boundary layer properties for near -isotropic turbulence which

have been published by other investigators are similar to the case of highly

anisotropic turbulence fields, while the effects of free-stream turbulence

on the properties of the turbulent structure within the boundary layer for

the case of near-isotropic turbulence are quite different compared to the

highly anisotropic case.

17. Key Words (Suggested by Author(s))

boundary layer, turbulence,

performance

19. Security Qassif. (of this report)

Unclassified

18. Distribution Statement

Subject category - 02

Unclassified -

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21. No. of Page*

38

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