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

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## 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## List of Symbols

*C*_{pw}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

*P*_{ref}wall static pressure at

*x*= 8*D**p*pressure fluctuation

*{ovq}*^{2}*{ovu}*^{2}+*{ovv}*+*{ovw}*^{2}*q*(

*{ovq}*^{2})^{1/2}*R*radius of curvature

*Re*_{D}Reynolds number based on

*U*_{ c }and*D*, \({\text{Re}}_D = U_c D/v\)*S*ratio of curvature strain to straight mean strain, \(S = (U/R)/(dU/dy)\)

*S*_{c}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*U*_{c}centerline mean velocity at

*x*= 8*D**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, \(\tau = (x/U)|dU/dy|\)

*τ*_{0}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

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