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Experiments in Fluids

, Volume 19, Issue 3, pp 173–187 | Cite as

The evolution of initially uniform shear flow through a nearly two-dimensional 90° curved duct

  • H. J. Lim
  • M. K. Chung
  • H. J. Sung
Originals

Abstract

An experimental study has been made in a nearly two-dimensional 90° curved duct to investigate the effects of interaction between streamline curvature and mean strain on the evolution of turbulence. The initial uniform shear at the entrance to the curved duct was varied by an upstream shear generator to produce five different shear conditions; a uniform flow (UF), a positive weak shear (PW), a positive strong shear (PS), a negative weak shear (NW) and a negative strong shear (NS). The variations of surface pressure and the mean velocity profiles along the downstream direction under different initial shears are carefully measured. The responses of turbulent Reynolds stresses and triple velocity products to the curvature and the mean strain are also investigated. The evolution of turbulence under the curvature with the different shear conditions is described in terms of the turbulent kinetic energy and the various length scales vs the angular distance θ or a curvature parameters S c which is defined by S c = (U/R)/(dU/dy- U/R). The results show that the turbulent kinetic energy and the integral length scale are augmented when S c < 0.054 whereas they are suppressed when S c > 0.054. It is also observed that the micro-length scales of Taylor and Kolmogoroff are relatively insensitive to the curvature.

Keywords

Turbulent Kinetic Energy Reynolds Stress Angular Distance Shear Condition Downstream Direction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

Cpw

wall static pressure coefficient, \(C_{pw} = 2(P - P_{{\text{ref}}} )/{}_\rho U_c^2\)

D

duct width = 190 mm

d

turbulent diffusion

H

duct height = 600 mm

k

turbulent kinetic energy, k = \(\overline {q^2 }\)/2

L

streamwise integral length scale or duct length

l

characteristic length scale

n

normal distance from curved surface

P

wall static pressure

Pref

wall static pressure at x = 8D

p

pressure fluctuation

{ovq}2

{ovu}2 + {ovv} + {ovw}2

q

({ovq}2)1/2

R

radius of curvature

ReD

Reynolds number based on U c and D, \({\text{Re}}_D = U_c D/v\)

S

ratio of curvature strain to straight mean strain, \(S = (U/R)/(dU/dy)\)

Sc

ratio of curvature strain to total mean strain, \(S_c = (U/R)/(dU/dy - U/R)\)

t

time

U, V, W

mean velocity components in x,y,z coordinates, respectively

Uc

centerline mean velocity at x = 8D

u, v, w

velocity fluctuations in x,y, z coordinates, respectively

u

characteristic velocity scale

{ovu}2, {ovv}2, {ovw}2

Reynolds normal stresses in the x,y,z coordinates, respectively

{ovuv}

Reynolds shear stress

{ovu}3, {ovv}3, {ovu}2{ovv}, {ovuv}2

triple velocity products

x,y, z

streamwise, transverse and spanwise coordinates

Greek symbols

δ

boundary layer thickness

ɛ

dissipation

η

Kolmogoroff micro-length scale

λ

Taylor micro-length scale

gn

kinematic viscosity

φ

pressure-velocity correlation term

θ

flow angle in curved duct

ϱ

density of air

τ

non-dimensional development time, \(\tau = (x/U)|dU/dy|\)

τ0

modified non-dimensional development time, \(\tau _c = (x/U)|dU/dy - U/R|\)

Subscripts

o

initial value at θ=10°, y/D =-0.1

w

surface wall

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References

  1. Ahmad QA; Luxton RE; Antonia RA (1976) Characteristics of a turbulent boundary layer with an external turbulent uniform shear flow. J Fluid Mech 37: 369–396Google Scholar
  2. Barlow RS; Johnston JP (1988) Structure of a turbulent boundary layer on a concave surface. J Fluid Mech 191: 137–176Google Scholar
  3. Bruun HH; Tropea C (1985) The calibration of inclined hot-wire probes. J Phys E Sci Instrum 18: 405–413Google Scholar
  4. Chung MK; Kyong NH (1989) Measurement of turbulent dispersion behind a fine cylindrical heat source in a weakly sheared flow. J Fluid Mech 205: 171–193Google Scholar
  5. Crane RI; Sabzvari J (1984) Laser-Doppler measurements of Gortler vortices in laminar and low-Reynolds-number turbulent boundary layers. In Laser Anemometry in Fluid Mechanics (Ed. R.J. Adrian). Lisbon: LadoanGoogle Scholar
  6. Ellis LB; Joubert PN (1974) Turbulent shear flow in a curved duct. J Fluid Mech 62: 65–84Google Scholar
  7. Eskinazi S; Yeh H (1956) An investigation on fully developed turbulent flows in a curved channel. J Aeronaut Sci 23: 23–35Google Scholar
  8. Fujita H; Kovasznay LSG (1968) Measurement of Reynolds stress by a single rotated hot wire anemometer. Rev Sci Instrum 39: 1351–1355Google Scholar
  9. Gillis JC; Johnston JP; Moffat RJ; Kays WM (1980) Turbulent boundary layer on a convex curved surface. Stanford University Dept. Mech. Engng Rep. HMT-31Google Scholar
  10. Gibson MM; Verriopoulis CA; Vlachos NS (1984) Turbulent boundary layer on a mildly curved convex surface: Part 1: Mean flow and turbulence measurements. Exp Fluids 2: 73–80Google Scholar
  11. Hoffmann PH; Muck KC; Bradshaw P (1985) The effect of concave on turbulent boundary layers. J Fluid Mech 161: 371–403Google Scholar
  12. Holloway AGL; Tavoularis S (1992) The effects of curvature on sheared turbulence. J Fluid Mech 237: 569–603Google Scholar
  13. Hunt IA; Joubert PN (1979) Effects of small streamline curvature on turbulent duct flow. J Fluid Mech 91: 633–659Google Scholar
  14. Jeans AH; Johnston JP (1982) The effects of concave curvature on turbulent boundary layer structure. Stanford University Dept. Mech. Engng Rep. MD-40Google Scholar
  15. Meroney RN; Bradshaw P (1975) Turbulent boundary layer growth over a longitudinally curved surfaces. AIAA J 13: 1448–1453Google Scholar
  16. Moffat RJ (1988) Describing the uncertainties in experimental results. Exp Thermal and Fluid Science 1: 3–17Google Scholar
  17. Muck KC; Hoffmann PH; Bradshaw P (1985) The effect of convex surface curvature on turbulent boundary layers. J Fluid Mech 161: 347–369Google Scholar
  18. Nagano Y; Tagawa M (1990) A structural turbulence model for triple products of velocity and scalar. J Fluid Mech 215: 639–657Google Scholar
  19. Ramaprian BR; Shivaprasad BG (1977) Mean flow measurements in turbulent boundary layers along mildly curved surfaces. AIAA J 15: 189–196Google Scholar
  20. Ramaprian BR; Shivaprasad BG (1978) The structure of turbulent boundary layers along mildly curved surfaces. J Fluid Mech 85: 273–303Google Scholar
  21. Rohr JJ; Itsweire EC; Heiland KN; van Atta CW (1988) An investigation of the growth of turbulence in a uniform mean shear flow. J Fluid Mech 187: 1–33Google Scholar
  22. Rose WG (1966) Results of an attempt to generate a homogeneous turbulent shear flow. J Fluid Mech 25: 97–120Google Scholar
  23. So RMC (1975) A turbulence velocity scale for curved shear flows. J Fluid Mech 70: 37–57Google Scholar
  24. So RMC; Mellor GL (1973) Experiment on convex curvature effects in turbulent boundary layers. J Fluid Mech 60: 43–62Google Scholar
  25. So RMC; Mellor GL (1975) Experiment on turbulent boundary layers on a concave wall. Aero Q 26: 25–40Google Scholar
  26. Tavoularis S; Karnik U (1989) Further experiments on the evolution of turbulent stresses and scales in uniformly sheared turbulence. J Fluid Mech 204: 457–478Google Scholar
  27. Townsend AA (1976) The Structure of Turbulent Shear Flow. Cambridge: Cambridge University pressGoogle Scholar
  28. Yavuzkurt S (1984) A guide to uncertainty analysis of hot-wire data. J Fluids Eng 106: 181–186Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • H. J. Lim
    • 1
  • M. K. Chung
    • 1
  • H. J. Sung
    • 1
  1. 1.Department of Mechanical EngineeringKorea Advanced Institute of Science and TechnologyTaejonKorea

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