_tra_or Report 3551

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:_Jj_mjbulent Flow in a Pipe Bend

• M. Gibson,_ylor, and M. Yianneskis

__W-3258

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NASA Contractor Report 3551

Laser Doppler Measurements of Laminar

and Turbulent Flow in a Pipe Bend

M. M. Enayet, M. M. Gibson,

A. M. K. P. Taylor, and M. Yianneskis

Imperial College of Science and Technology

London, England

Prepared for

NASA Headquarters

under Contract NASW-3258

National Aeronautics

and Space Administration

Scientific and Technical

Information Office

1982

TABLE OF CONTENTS

SUMMARY

I. INTRODUCTION

2. EXPERIMENTAL ARRANGEMENT

2.1 THE TEST BEND

2.2 INSTRUMENTATION AND SIGNAL PROCESSING

2,3 SCOPE AND ACCURACY OF THE MEASUREMENTS

3. RESULTS AND DISCUSSION

3.1 FLOW VISUALIZATION

3.2 LAMINAR FLOW MEASUREMENTS

3.3 TURBULENT FLOW MEASUREMENTS

CLOSUREo

APPENDIX 1

APPENDIX 2

APPENDIX 3

APPENDIX 4

REFERENCES

FIGURES

TABULATED DATA FOR REYNOLDS NUMBER 500 MEASUREMENTS

TABULATED DATA FOR REYNOLDS NUMBER 1093 MEASUREMENTS

TABULATED DATA FOR REYNOLDS NUMBER 43000 MEASUREMENTS

DEFINITION OF SYMBOLS

Page

1

2

3

3

4

5

6

6

6

7

8

I0

16

22

39

4O

41

iii

SUMMARY

Laser-Doppler measurements are reported for laminar and turbulent flow

through a ninety-degree bend of circular cross section with mean radius of

curvature equal to 2.8 times the diameter. The measurements were made in cross-stream planes 0.58 diameters upstream of the bend inlet plane, in 30, 60, and

75 degree planes in the bend and in planes one and six diameters downstream of

the exit plane. Three sets of data were obtained: for laminar flow at Reynoldsnumbers of 500 and I093 and for turbulent flow at the maximum obtainable Reynolds

number of 43000. The results show the development of strong pressure driven

secondary flows in the form of a pair of counter rotating vortices in the

streamwise direction. The strength and character of the secondary flows werefound to depend on the thickness and nature of the inlet boundary layers: inlet

conditions which could not be varied independently of Reynolds number. The

quantitative anemometer measurements are supported by flow visualisation studies.

Refractive index matching at the fluid-wall interface was not used; themeasurements consist therefore of streamwise components of mean and fluctuating

velocities only supplemented by wall pressure measurements for the turbulent

flow. The displacement of the laser measurement volume due to refraction isallowed for in simple geometrical calculations. The results are intended for

use as benchmark data for calibrating flow calculation methods.

This research was supported by contracts from the CEGB Central Electricity ResearchLaboratories, London, England, and from the NASA Lewis Research Center, Cleveland,

Ohio, U.S.A.

I. INTRODUCTION

As a fluid flows through a straight pipe or duct and into a bend thepressure, which in the straight section is uniform across the flow, must adjustin the bend to counter centrifugal forces. The pressure is greatest at theouter wall farthest from the centre of curvature and least at the inner wallnearest the centre of curvature and the cross-stream pressure gradient in thebend has two well known effects on the flow. At the bend inlet the boundarylayer on the outer wall experiences the effects of a positive streamwisepressure gradient which may in a tight bend be strong enough to produce localseparation; conversely, the inner wall boundary layer is accelerated. Thereverse occurs at the pipe exit where local pressure gradients of the oppositesign appear as the flow adjusts to uniform pressure conditions downstream.Inside the bend the presence of side wall boundary layers ensures that theconditions for radial equilibrium cannot be satisfied exactly over the entirefield. The slow moving fluid in these layers is forced inwards towards thecentre of curvature and continuity ensures that the high speed fluid near theaxis is driven outwards. The result is a secondary flow superimposed on themain flow.

If the bend is of circular cross section, or its height is not toomuch greater than its width measured in the radial direction, the effect ofthe secondary flow is to displace the region of maximum velocity from thecentre towards the outer wall. If, however, the boundary layers are thin andthe secondary flow is weak the velocity distribution in the inviscid centralcore will approximate to that of a free vortex with velocity increasingtowards the centre of curvature. The effects of longitudinal curvature onthe boundary layers on the inner and outer walls also tend to counteract theeffects of pressure-driven secondary flow. In the inner boundary layer theshear stress is reduced by curvature and the boundary layer grows relativelyslowly. In the outer boundary layer the shear stress is increased and thelayer is retarded and thickened. Thus in the flow in a high narrow curvedchannel, where the secondary flows are weak and confined to the edge zones,the region of maximum velocity is found closer to the inner wall (I). Theeffects of curvature on laminar boundary layers are weak in ducts of moderateaspect ratio and are masked by the secondary flow; the fractional change inshear stress is of order 6/R (where _ z boundary layer thickness andR z radius of curvature). The effects of curvature on the turbulence inturbulent boundary layer flow are an order of magnitude greater (2) and maybe large enough to counteract the effects of secondary flow and to play asignificant role in determining the flow structure.

The presence and origin of secondary flow in bends have long beenknown and understood although obvious measurement difficulties associated withprobe explorations have hindered detailed investigation and have largelyrestricted experiments to flow visualization studies and overall pressure lossmeasurements. The former (3) show that a laminar boundary layer in a ninety-degree pipe bend is deflected through about 45 degrees while the deflexionof a turbulent layer does not exceed 30 degrees as might be inferred from thedifferent inlet profiles. Work done prior to 1970, which consists almostentirely of wall pressure measurements and pressure probe surveys of the outlet

plane, is summarized and reviewed by Ward-Smith (4). These data provide abasis for empirical pressure drop correlations but are necessarily too limited

to be used for the validation of flow calculation methods. The development

of these methods to the point where they can be used as standard design tools

has, fortunately, been paralleled by the development of the laser Doppler

anemometer which, by obviating the need for probe insertion, has made possible

more detailed measurement of complex flows including those in bends. Humphreyet al (5) report measurements of the longitudinal velocity component in

laminar flow through a strongly curved duct of square cross section. This work

is extended in (6) to the measurement in turbulent flow of two components ofmean velocity, two components of turbulent energy and one shear stress component;

similar measurements are also reported in (7) for laminar and turbulent flow

with thin inlet boundary layers.

The problem of flow in a round pipe, which is the subject of thepresent contribution, presents additional measurement difficulties and has

consequently received less attention. Rowe (8) reports total-pressuremeasurements in a mildly curved pipe bend while laser-Doppler measurements

appear to be limited to the laminar flow experiment described by Agrawal etal (9). The difficulties arise because in off-diameter planes the laser beamsare refracted at the fluid-wall interface unless care is taken to match the

refractive indices. If this is not done the measurements will be limited to

longitudinal components of mean and fluctuating velocity. The measurementvolume is displaced but to a position which can be located quite accurately

by simple calculation (lO).

In the present paper we report measurements of laminar and turbulentflow in and downstream of a tight 90-degree pipe bend. The results, which

complement and extend those of (5, 6, 7) are seen as a useful contribution

to the 'data bank' available for the further testing and development ofnumerical flow calculation methods.

Professor J.H. Whitelaw contributed valuable advice in numerous discus-

sions.

2. EXPERIMENTAL ARRANGEMENT

2.1 The test bend

The geometry and dimensions of the test bend are shown in Figure I. The

dimensions are similar to those of the square-sectioned bend of (6,7) with

radius of curvature equal to 2.8 times the internal diameter. The bend was

machined accurately from two halves of a rectangular plexiglass block split

in the plane of symmetry. It was thus possible to maintain a tolerance of

+ O.l mm on the internal diameter and to minimise refraction problems at the

external, air-plexiglass, interface by the retention of a rectangular external

section. The bendwas fixed in the horizontal plane downstreamof a straighttube of the samediameter (48 mm)and 240 mmlong; a second straight tube,480 mmlong, was fitted downstream. Photographs of the overall arrangementare shownin Figure 2.

Figure 3 showsdiagrammatically the closed circuit water flow rig inwhich the bendwas fitted immediately downstreamof a contraction fitted tothe plenumchamber. The flow rate was constantly monitored using Fischer andPorter precision flowmeters. The maximumobtainable Reynolds number, 4was 43000. For the turbulent flow measurementsthe water was seeded _ _ 'with minute quantities of milk in order to increase the scattering particleconcentration and, consequently, the particle arrival rate (ll).

2.2 Instrumentation and signal processing

The optical arrangement, which is similar to that described by Taylor

et al (7), is shown diagrammatically in Figure 4. The light beam generatedby a 5 mW helium-neon laser is focussed on to a radial diffraction grating,

collimated in order to reduce spherical aberration and then focussed to formthe scattering volume at the point of measurement in the bend. Measurements

in the vertical plane were made in the straight pipe sections at each end of

the bend. For these the light beam was turned through 90 deg using a mirrorwhich was optically flat to within one tenth of the wavelength of light.

Forward scattered light collected by the objective lens is focussed on and

passes through a pinhole to an EMI 9658 photomultiplier, the output from which

is processed in a Cambridge Consultants CCOI frequency tracking demodulatorand associated equipment shown in the block diagram of Figure 5. The principal

characteristics of the laser-Doppler anemometer are given in Table l below.

Table 1

Optical Characteristics of the Laser Doppler Anemometer

Focal length of imaging lens

Half-angle of beam intersection

Fringe separation (line-pair spacing)

Number of fringes in measuring volume

Intersection volume diameter calculated at

I/e2 intensity

Intersection volume length calculated at

I/e2 intensity

Photomultiplier pinhole diameter

Transfer constant

300 mm

9.110

1.9 um

84

0.167 mm

1.391 mm

0.50 mm

0.500 MHz/ms -l

2.3 Scope and accuracy of the measurements

Refraction of the laser beam at the water-plexiglass interface not onlydisplaces the measurement volume by an amount which can be readily calculated

but also, and more importantly, prevents the measurement of cross-sectionvelocity components. The method employed successfully for the latter in therectangular bend experiments (6, 7) fails for the round pipe because, unless

the refractive indices of the fluid and pipe wall are equal, the twin laserbeams entering the pipe in a plane at 45 degrees to the axis cannot converge.Consideration has been given to the use of fluids other than water which wouldallow the indices to be equalized. Unfortunately it turns out that such fluids

either possess highly unpleasant or toxic properties or are so viscous that itis difficult to realize Reynolds numbers high enough for turbulent flow. A

case in point is the experiment described by Agrawal et al (9) where the useof a glycerine-water mixture to match the indices limited the investigation tolaminar flow. Since the main objective of the present work is the study of

turbulent bend flow, the limitation on the scope of the measurements to stream-wise velocities only has had to be accepted at this stage.

There is no difficulty in measuring the streamwise velocities or incalculating the displaced position of the measurement volume. The measurementsare made at points along the optical axis which is refracted at the pipe wall

at an angle to the plane of symmetry to which it was originally parallel. Astraightforward calculation produces the beam trajectories shown in Figure 6.The actual location of the measurement points along the optical axis is

obtained by applying the correction described by Boadway and Karahan (lO) forthe effects of refraction due to the bend curvatures. These two corrections

have been applied independently to the results presented here. It was alsofound that signal quality was only slightly impaired by refraction and that

measurements were feasible for points in the flow distant more than one tenthof the radius from the wall in the vertical plane.

Estimated measurement errors are summarized in Table 2. Corrections

were not applied for the effects of finite transit time and instrument noisebroadening. Systematic errors of up to 2.5 per cent are mainly associated withvelocity gradient effects near the walls and have been included in the table.

Table 2

Measurement errors

Quantity systematic error Random errorx ±0.5 mm ±0.02 mm

y,z ±0.2 mm ±0.02 mm

0 ±0.30 ±0.170

±0.050 nil

UB (laminar) ±0.8% ±0.8%

UB (turbulent) ±I.5% ±0.5%

U/U B up to 2.5% ±1.5%

uYU B up to 3% up to ±3%

The measurementswere madein cross-stream planes 0.58 diametersupstream of the bendinlet plane,in 30, 60, and 75 degree planes in the bendand in planes at one and six diameters downstreamof the exit plane. Three setsof data were obtained: for laminar flow at Reynolds numbersof 500 and 1093and for turbulent flow at the maximumobtainable Reynolds numberof 43000.

3. RESULTS AND DISCUSSION

3.1 Flow visualization

Observation of hydrogen bubble paths in low speed flow revealed nounusual features such as the loc_separation reported in (5) for fullydeveloped flow through the square section bend. The visual observations wereentirely consistent with large scale secondary flow patterns detected bylaser Doppler anemometry. Hydrogen bubbles were generated in the flow by athin wire electrode inserted through static pressure tappings, the trajectorieswere photographed with typical results shown in Figure 7. Figures 7.1 and 7.2show bubble paths at the 15 and 30 degree stations where the inward movementof low velocity fluid in the upper part of the bend is clearly visible. Thesecondary flow appears to be directed inward at a greater angle at the 15degree station than further downstream at 30 degrees. The corresponding outward

movement of the core flow is shown by the distinct trace from the electrode

tip. Figure 7.3 shows the hydrogen bubble sheet generated near the outer wallat the 30 degree station; the flow here is upward and along the wall towardthe inside of the bend.

3.2 Laminar flow measurements

The results of velocity measurements at a Reynolds number of 500, meanvelocity I0.5 mm s-l, are presented graphically in Figures 8 and 9. The data

are tabulated in Appendix I. Figure 8 shows the inlet conditions: horizontal

and vertical velocity profiles 0.58 diameters upstream of the bend. The

boundary layer thickness is about 0.27 d so that there is a significantpotential core. The apparent slight asymmetry shown in the results is within

the estimated error band. Contours of the streamwise velocity in four cross-stream planes are presented in Figure 9 and show the effects of strong

secondary flow which displaces the region of maximum velocity to the outside

of the bend. The secondary flow develops gradually: in the 30 degree plane

the only visible effect is a thickening of the shear layer on the inside ofthe bend. By 60 degrees the secondary flow has become almost fully developed

as is shown by the distortion of the contours. The fourth set of contours,

in the plane one diameter downstream, shows that the secondary motion persists

without significant decay to this distance.

6

The effects of doubling the meanvelocity and Reynolds numberto23 mms-l and I093 respectively are shownin Figures lO and I I. The data aretabulated in Appendix 2. The inlet boundary layers are reduced in thicknessby about fifteen per cent to 0.23 d, the transverse pressure gradient isincreased and the secondary flow is intensified. The peak velocity in the 30degree plane is displaced from the plane of symmetrybut remains closer to thecentreline. This displacement, which persists downstream,has also beenobserved in the flow in a square bend (7). The shape of the contours near theoutside of the bend reflect scatter in the data attributable mainly todifficulties in locating accurately the measurementvolume near the wall andpartly, perhaps, to slight asymmetryin the flow.

In neither case do the measurementsshowany unexpected feature:the secondary flow superposedon the main motion is essentially as describedqualitatively in references (1) and (3); it develops gradually and persistsdownstreamafter the removal of the transverse pressure gradient responsiblefor its generation in the bend. The strength and location of the pressuredriven secondary flow dependon the inlet conditions and the Reynolds numberwhich could not be varied independently in the present experiments. Thestronger secondary flow observed at Re= I093 must be attributable mainly tothe increased centrifugal forces and transverse pressure gradient rather thanto the relatively small changesnoted in the initial conditions. The presentcontribution is of quantitative velocity data in the bend: these areconsidered to be accurate enough to be useful in checking the numerical accuracyof flow prediction methods.

3.3 Turbulent flow measurements

At the maximum flow velocity of 0.92 m s-l, Reynolds number 43000,

the inlet boundary layers are turbulent. The static pressure variation on the

bend wall is large enough to be measured accurately with the results shown inFigure 12. At the bend inlet the negative pressure gradient on the inner wall

is roughly twice the positive gradient on the outside. These initial gradientsresulting from the change from straight to curved flow disappear at about 25

degrees so that in the mid-section of the bend (25°<e <750 ) a quasi equlibriumcondition is reached with approximately uniform pressure on the inner and

outer walls. The transition to straight flow downstream is signalled by the

appearance of _trong gradients for 6 > 75 deg. The overall pressure drop

is about O.3pU_.

Laser Doppler measurements of the mean and r.m.s, fluctuation of the

streamwise velocity at inlet are shown in Figure 13 and contours of thesequantities at downstream stations in Figures 14 and 15. Numerical values are

tabulated in Appendix 3. The inlet boundary layers of Figure 13 are muchthinner, O.09d, than in the two laminar flows investigated and the presence of

a large central region of uniform velocity flow influences significantly the

development of secondary flow downstream. The mean velocity contours presented

in Figure 14 show that by the 30 degree plane the potential core has adjusted

to the cross-stream pressure gradient imposed by the bend and the region of

maximum velocity has been displaced toward the inside. The results alsodiffer from the corresponding laminar flow measurements in that the thicknessof the outer wall boundary layer is increased relative to that on the insideof the bend due mainly to the effects of the potential flow adjustment and thewall pressure gradients of opposite sign but also, quite possibly, to theeffects of longitudinal curvature on the turbulence structure. In the 60 degreeplane distortion of the contours suggests the presence of strong secondaryflow largely confined to the region of steep velocity gradients near the innerwall. This secondary flow grows with distance through the bend and by the 75degree plane extends over and beyond the inner half of the section. The removalof the transverse pressure gradient in the straight flow downstream results ina shift of the velocity maximum toward the outside. A large secondary flow,comparable with those observed in the laminar flow experiments, now extendsover the entire flow area and persists in the plane six diameters downstream ofthe bend where, however, the transverse velocity gradients have decayed to aboutone half of their values one diameter downstream.

The contours of turbulence intensity presented in Figure 15 areconsistent with those of the mean velocity. As is to be expected high valuesof the velocity fluctuation are associated with steep mean velocity gradientsand with the distortion of the symmetrical inlet flow.

These results may be compared with the measurements made by Humphrey,Whitelaw andYee(6) in a tight bend of square cross-section. The inletboundary layers of that flow were substantially thicker than in the presentflow and contained stress driven secondary flows towards the corners. As aresult the pressure driven secondary flow in the bend extended over the entireflow area as in the two laminar flows of the present study.

4. CLOSURE

The measurements show, as expected, the presence in bend flow ofstrong cross-stream flows produced by the inward motion of slow moving fluidin a radial pressure gradient. The strength of the secondary flow is influencedby the initial inlet flow conditions: when the inlet boundary layers are thin,as in the turbulent flow case reported here, the initial flow adjustment is aninward shift of the velocity peak in the potential core. The secondary flowthen develops initially in the inside of the bend. For all cases thesecondary flow takes some time to develop and its effects are still increasingby the exit and persist downstream.

The effects of refraction at the doubly curved fluid-wall interfaceprevent the measurement of cross-stream velocity components. The investigationof flows in the round bend to the same level of detail as has been achieved

previously in square bends will require refractive index matching. For the

streamwise velocity measurements reported here simple geometrical corrections

allow for the displacement of the measurement volume by refraction.

The laminar flow data may be used to check the numerical accuracy of

flow prediction methods; the turbulent flow measurements provide the additionalinformation needed to validate mathematical models of turbulence.

All

Appendix 1

Tabulated Data for Reynolds Number 500 Measurements

velocities normalised with the bulk velocity, UB = 0.0105 m/s.Symbols as defined in Figures 1 and 6.

x/d y/r

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Appendix 3

Tabulated Data for Reynolds Number 43000 Measurements

velocities normalised with the bulk velocity, UB = 0.92 m/s.Symbols as defined in Figures 1 and 6.

x/d

-.58

y/r z/r U/U B

00.90.80.70.60.50.40.30.20.I0.0

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0.9851.1051.1331.1371.1381.1371.1381.1381.1371.1391. 1381.1421.1421. 1421.1421. 1381.1371 .IIIO. 988

(u'/UB)Xl02 y/r

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APPENDIX 4

DEFINITION OF SYMBOLS

Roman Characters

Cp

d

6

P

Pref

R

r

Re

U

UB

U'

X

Y

Z

Pressure coefficient (figure 12)

Pipe diameter

Mass flow rate

Static pressure

Static pressure one diameter upstream of pipe bend

Radius of curvature of the bend

1Internal radius of pipe = _d

Reynolds number UBd/_

Streamwise mean velocity

Bulk velocity 4_/(Trpd 2)

R.m.s. streamwise velocity fluctuation

Distance measured along the pipe and bend centreline

Distance measured horizontally from centreline (figure l)

Distance measured vertically from centre]ine (figure l)

Greek Characters

B

6

e

I)

P

Half angle of beam intersection

Boundary layer thickness

Bend angle (figure I)

Angle substended at pipe centreline (figure 12)

Kinematic viscosity

Density

39

REFERENCES

I. Goldstein, S. (ed), (1938). Modern developments in fluid dynamics. Oxford.

2. Bradshaw, P. (1973) Effects of streamline curvature on turbulent flow.

AC_ARDograph 169.

3. Prandtl, L. (1952). Essentials of fluid dynamics. Blackie, London.4. Ward-Smith, A.J. (1971). Pressure losses in ducted flows. Butterworth,

London.

5. Humphrey, J.A.C., Taylor, A.M.K.P. and Whitelaw, J.H. (1977). Laminar

flow in a square duct of strong curvature. J. Fluid Mech. 83, 509.6. Humphrey, J.A.C., Whitelaw, J.H. and Yee, G. (1981). Turbulent flow in

a square duct with strong curvature. J. Fluid Mech. I03, 443.

7. Taylor, A.M.K.P., Whitelaw, J.H. and Yianneskis, M. (1981). Measurements

of laminar and turbulent flow in a curved duct with thin inlet boundary

layers. NASA Contractor Rep. 3367.

8. Rowe, M. (1970). Measurements and computations of flow in pipes. J. FluidMech. 43, 771.

9. Agrawal, Y., Talbot, L. and Gong, K. (1978) Laser anemometry study of flow

development in curved circular pipes. J. Fluid Mech. 85, 497.

lO. Boadway, J.D. and Karahan, E. (1981) Correction of laser Doppleranemometer readings for refraction at cylindrical interfaces. DISAInformation 26.

II. Durst, F., Melling, A. and Whitelaw, J.H. (1976). Principles and

practice of laser-Doppler anemometry. Academic Press, London.

40

0 °

l __

I-

1NSIO[

\

\

\

\

\ \

\

I

i Ii II It I

' i II

I

Figure ] Bend dimensions and co-ordinate system(Dimensions in mm) 41

42

Figure 2 Views of the test bend and instrumentation

21o>

IE00

43

44

I.IJ

Figure 5 Block diagram of Doppler signal processing system

45

INSIDE

Yi/r L .

SECTION A-A

I• ° I,D

sSi

OUTSIDE

OPTICALAXIS

Figure 6(i)

A , i__

Beam paths through test section. Bend section in e-yplane. Point P marks location of scattering volume

46Figure 6(ii) Cross-section through upstream and downstream tangents

Figure 7.1 Flow visualization: Re : 1093. Flow from top leftto top right; wire inserted at 0 = 150 , y/r = O, z/r = l.O

Figure 7.2 Flow visualization:

left to top right;

z/r = l .0

Re = I093. Flow direction from topwire inserted at 0 = 30°, y/r = O,

47

Figure 7.3 Flow visualization: Re=1093. Flowright to top left, wire inserted atz/r = 0

direction from tope = 30o , y/r = 1.0,

48

O.8

O.Z

Om d

Figure 8

A

O

AO

A

0

A

0

IW_)2o I

Q

6

6

m

6

I,, I I I.o -o.5 0 o.5

_/r ,slr

Horizontal, O_and vertica],A, profiles of mean velocityin the laminar approach flow 0.58 diameters upstreamof the inlet plane. Re = 500

49

I|

5O

I.I.I0m

_z

Figure I0

1.6

A0'4---

O'7.--

OC_--1'O

I i I

8

0000

A

0

0

0

z_

-o.5 o o.5 _.o_Ir, zlr

Horizontal,O, and vertical,_, profiles of mean velocityin the laminar approach flow 0,58 diametersupstream of the inlet plane, Re : 1093

51

_o -._

52

|I

¢D

d

¢D

LU

Z

e-

_J

"0O

c-

O

¢_ _.0

11 O

r--

o_,-Li.

0"4

0 o

45 °OUTSIDE

90 °

90 °135'

O o

INSIDE OUTSI DE

135 °

INSIDE

-2 -I

x/d

Figure ]2

0 15 30 45 60

0 e (degrees)

Wall static pressure variation.Re = 43 000

75 90

0 I 2

x/d

Turbulent flow,

53

AOAC_OAO o:o 6 o

o.8

o.6

o.4

o.f.

m

OL-t.0

0I •

qeAoAe• AOAO _eI

-o. 5' o o._

8

01.o

--- (x 102)

Figure 13 Profiles of mean velocity U/UR and turbulence intensityu'/UD in the turbulent approach flow 0.58 diameters upstreamof t_e bend. O horizontal,Avertical. Re = 43 000

54

e . _o °

¢

e- 75°

Figure 14(a)-(b) Contours of mean velocity U/UB in the bend.Turbulent flow, Re = 43 000

55

IN,_IOE=L

¢

Figure 14(d)-(e)

_= G=I.

Contours of mean velocity U/UR downstream ofbend. Turbulent flow, Re = 43"000

the

56

e= 30 °

G :_00 °

bm

Co

e = -/5 °

Figure 15(a)-(c) Contours of turbulence intensity (u'/UB)in the bend. Turbulent flow, Re = 43 OCO

57

Figure 15(d)-(e) Contoursof turbulence intensity (u'/U B) downstreamof the bend. Turbulent flow, Re= 43 000

58

1. Report No. 2. Government Accession No. 3.

NASA CR-3551

4. Title and Subtitle 5.

LASER DOPPLER MEASUREMENTS OF LAMINAR ANDTURBULENT FLOW IN A PIPE BEND 6.

7. Author(s) 8.

M.M. Enayet, M.M. Gibson, A.M.K.P. Taylor, and

M. Yianneskis 1-0.

9. Performing Organization Name and Address

Imperial College of Science and Technology

Mechanical Engineering DepartmentExhibition Road

London SW7 2BX_ England

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administrations

Washington, D.C. 20546 and

C. E.G.B. Central Electricity Research Laboratories

• London, England

15. Supplementary Notes

Final report. Project Manager, Louis A. Povinelli,

Division, NASA Lewis Research Center, Cleveland, Ohio

Recipient's Catalog No.

Report Date

May 1982

Performing Organization Code

Performing Organization Report No.

FS/81/19

Work Unit No.

'ii. Contract or Grant No.

NASW-3258

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

505 -32-12

Aerothermodynamics and Fuels44135.

16. Abstract

Measurements are reported of the streamwise components of velocity in the flow througha ninety-degree bend of circular cross section for which the ratio of radius of curvature

to diameter is 2.8. The results show the development of strong pressure driven second-ary flow in the form of a pair of counter rotating vortices in the steamwise direction.

Refractive index matching at the fluid-wall interface has not been employed; the displace-ment of the measurement volume due to refraction is allowed for in simple geometricalcalculations.

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

Secondary flowLaser Doppler anemometerDucts

18. Distribution Statement

Unclassified - unlimited

STAR Category 34

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price"

Unclassified Unclassified 61 A04

* For sale by the National Technical InformationService_Springfield, Virginia 22161NASA-Langley, 1982