Uniform Flow and a Region near The Stagnation Point: The Vorticity Equation and its Balance

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Year:
2018
Type of Publication:
Article
Keywords:
Suction, Boundary Layer, BL, Airfoil, Flow, Turbulence, Viscous, Vorticity, Velocity, Distribution, Balance, Equation, Fluid Dynamics, Applied Math, No-Slip, Drag, Friction
Authors:
Steve Anglin
Journal:
IJISM
Volume:
6
Number:
3
Pages:
97-98
Month:
May
ISSN:
2347-9051
Abstract:
A local description for the uniform flow past the leading surface of a bluff body such as a cylinder is to consider the region near the stagnation point. The body surface is assumed to be flat, locally and corresponds to the boundary at y = 0 with the stagnation point at x = 0, y = 0. If the flow is inviscid, the flow is locally given by the u = alpha times x and v = - alpha times y, for alpha > 0. The corresponding stream function is psi = alpha * x*y. We show that this satisfies the inviscid flow boundary conditions at the surface but not the viscous conditions. We formulate the vorticity equation using the stream function and show that a solution can be found with psi = alpha * x *f(y/delta) for some function f of eta that satisfies the viscous conditions and matches the inviscid flow far above the surface. We determine the length scale delta and derive the nonlinear differential equation for f of eta and find the vorticity balance in this flow
Full text: IJISM_745_FINAL.pdf

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