Viscous Effects in the Wedemeyer Model of Spin-up from Rest
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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The problem of impulsive spin-up from rest of a liquid filled a right- circular cylinder is treated. A numerical solution is obtained to the non-linear partial differential equation that governs the spin-up flow by the Wedemeyer model. An implicit, two-time level, second order, iterative finite difference technique is used. Approximations to an impulsive start are discussed. An analytical procedure is applied at the first time step of the calculation to avoid errors caused by a discontinuity in the boundary conditions. Conditions for the validity of the model are discussed and a detailed discussion is presented of tghe Ekman compatibility condition relating to azimuthal velocity. Representative results are shown demonstrating the effects of the problems parameters and different Ekman compatibility conditions on spin-up profiles, i.e., curves of azimuthal velocity vs radial coordinate. For several cases the spin-up results are validated by comparison with those of the Navier-Stokes equations.
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