Higher-order boundary-layer solution for unsteady motion of a circular cylinder
The higher-order boundary-layer solution for an impulsively moving circular cylinder with uniform velocity and an exponentially accelerating cylinder in incompressible, relatively high-Reynolds-number flow of short duration is considered. A perturbation method is employed to linearize the two-dimensional vorticity equation by a double-series expansion with respect to the Reynolds number and the time. A matched asymptotic expansion is carried out to define the proper boundary conditions between the viscous and inviscid layers for the linearized first-, second-, and third-order boundary-layer equations. Singularities appear in the viscous displacement velocities and skin frictions in the higher-order approximate solutions that coincide with the singularity of the first-order approximate solution. These singularities have alternating signs and increasing magnitudes so an attempt was made to remove the effects of the singularity of the lower-order solution. However this attempt at removing a singularity by superposing even stronger singularities makes the solution worse around the singularity, and the boundary-layer assumptions break down at that point.
- Research Organization:
- Stanford Univ., CA (USA)
- OSTI ID:
- 6418172
- Country of Publication:
- United States
- Language:
- English
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