A STUDY OF THE DEVELOPMENT OF STEADY SEPARATED FLOWS. PART I. LINEARIZED ANALYSIS OF CIRCULAR EDDIES.
Technical rept. on Aerophysics,
LOCKHEED MISSILES AND SPACE CO SUNNYVALE CALIF
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The viscous structure of a separated eddy is investigated for the case of a simplified geometry. An analytical solution is obtained for an eddy bounded by a circular streamline, based on a linearized model. This solution shows in a simple manner the development from a completely viscous eddy at low Reynolds number to an inviscid rotational core at high Reynolds number. Quantitatively, the solution shows that a significant inviscid core exists for Reynolds number greater than 100. At low Reynolds number the vortex center shifts in the direction of the boundary velocity until the inviscid core develops at large Reynolds number, the inviscid vortex core is symmetric about the center of the circle, except for the effect of the boundarylayer displacement-thickness. Special results are obtained for velocity profiles, skin-friction distribution, and total power dissipation in the eddy. In addition, results of the method of inner and outer expansions are compared with the complete solution, indicating that expansions of this type give valid results for separated eddies at Reynolds numbers greater than about 25 to 50. The validity of the linear analysis as a description of separated eddies is confirmed to a surprising degree by numerical solutions of the full Navier-Stokes equations for an eddy in a square cavity. Author