# Transient wall-jet flowing over a circular cylinder

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## Abstract

The transient flow of a two-dimensional wall-jet over a circular cylinder, following rapid initiation and termination, was investigated experimentally. Unsteady surface pressures and unsteady pressure-sensitive paint were used to gain a basic understanding of the flow physics. Jet initiation produced a starting vortex, upstream of which the Coandă flow developed, producing a large low-pressure peak. Immediately following jet termination, the pressure increased over the first quarter of the circumference, while the downstream separation region remained virtually unaffected. Simplifying analyses and dimensional arguments were used to show that the timescales characterizing the transient development of the integrated loads depend only on the square of the slot height and the kinematic viscosity and are thus independent of the jet velocity. Following jet initiation, the resulting loads varied according to a linear transient model, while small nonlinearities were observed following jet termination. Unsteady pressure-sensitive paint showed that the starting jet emerges from the slot in a two-dimensional manner and that streamwise streaks, identified as Görtler vortices, form well before the flow reaches steady state. During termination, the streamwise structures dissipate downstream initially, with the dissipation propagating upstream.

## Keywords

Shear Layer Streamwise Vortex Slot Width Separation Angle Momentum Coefficient## Abbreviations

*b*Span of the cylinder

*C*_{p}Pressure coefficient (

*p*_{∞}−*p*)*R*/(*p*_{0}−*p*_{∞})*h**C*_{R}Resultant force coefficient, \(F_{\text{R}} /\rho U_{j,\text{max} }^{2} R\)

- \(C_{\mu } (t)\)
Momentum coefficient, \(h/R(U_{j} (t)/U_{j,\text{max} } )^{2}\)

*D*Cylinder diameter

*F*_{N}Force per unit span, normal to the jet slot

*F*_{T}Force per unit span, tangential to the jet slot

*F*_{R}Resultant force on the cylinder

*h*Slot width

*p*Surface pressure

*p*_{0}Stagnation pressure

*p*_{∞}Ambient pressure

*Q*Jet volumetric flowrate

*R*Cylinder radius

*Re*Reynolds number \(\sqrt {\left( {p_{0} - p_{\infty } } \right)hR /\rho \nu^{2}}\)

*t*Time

*t*_{i},*t*_{t}Jet initiation, termination times

*U*_{j}Jet velocity

*θ*Azimuthal angle measured from the slot

*θ*_{s}Flow separation angle measured from the slot

*τ*Time constant

## Notes

### Acknowledgments

The authors acknowledge the support from the Grand Technion Energy Program (GTEP). JWG gratefully acknowledges the support of a Fulbright Global Scholar Award from the U.S. Department of State, administered by the United States-Israel Educational Foundation.

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