# Control of turbulent separated flow over a backward-facing step by local forcing

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## Abstract

An experimental study was made of the flow over a backward-facing step. Excitations were given to separated flow by means of a sinusoidally oscillating jet issuing from a thin slit near the separation line. The Reynolds number based on the step height (*H*) varied 13000 ⩽ *Re*_{ H }⩽ 33000. Effect of local forcing on the flow structure was scrutinized by altering the forcing amplitude (0 ⩽ *A*_{0} ⩽ 0.07) and forcing frequency (0 ⩽ *St*_{ H }⩽ 5.0). Small localized forcing near the separation edge enhanced the shear-layer growth rate and produced a large roll-up vortex at the separation edge. A large vortex in the shear layer gave rise to a higher rate of entrainment, which lead to a reduction in reattachment length as compared to the unforced flow. The normalized minimum reattachment length (*x*_{ r })_{min}/*x*_{ x0 }was obtained at *St*_{ θ }≅ 0.01. The most effective forcing frequency was found to be comparable to the shedding frequency of the separated shear layer.

## Keywords

Vortex Reynolds Number Shear Layer Flow Structure Separate Flow## List of symbols

*a*_{0}forcing amplitude=(

*Q*_{forced}−*Q*_{unforced})/*U*_{0}*AR*aspect ratio=

*W/H**C*_{p}wall-pressure coefficient=(

*P*-*P*_{0})/(l/2)*ρU*_{0}^{2}*ER*expansion ratio=(2

*H*+*H*)/2*H**f*_{f}forcing frequency, Hz

*f*_{s}shedding frequency, Hz

*g*slit width = 1.0 ± 0.1 mm

*H*step height = 50 mm

*P*wall-static pressure, Pa

*P*_{0}wall-static pressure at

*x/H*= -2.0, Pa*Q*_{forced}total velocity measured at reference position for forced flow, m/s

*Q*_{unforced}total velocity measured at reference position for unforced flow, m/s

*Re*_{H}Reynolds number based on

*H*and*U*_{0},=*U*_{0}*H/v**St*_{H}Reduced forcing frequency, Strouhal number =

*f*_{ f }*H/U*_{0}*St*_{θ}Reduced forcing frequency based on the momentum thickness =

*f*_{ f }*θ*/*U*_{0}*U, V*streamwise and vertical time-mean velocity, m/s

*u*streamwise fluctuation velocity, m/s

*U*_{0}free-stream velocity, m/s

- \(\sqrt {\bar u^2 } \)
r.m.s. intensity of streamwise velocity fluctuation, m/s

*x*_{r}reattachment length, m

*X*_{r}_{0}reattachment length for

*A*_{0}= 0, m*x, y, z*distance of streamwise, vertical and spanwise respectively, m

*W*width of test section = 625 mm

## Greek symbols

- δ
boundary-layer thickness, cm

- δ
^{*} displacement thickness, cm

- γ
_{p} forward-flow time fraction

- ρ
density of air for measurement, kg/m

^{3}*v*kinematic viscosity of air for measurement, m

^{2}/s- θ
momentum thickness, cm

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## References

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