Unsteady Viscous Flow between Two Parallel Disks with a Time-Varying Gap Width and Central Fluid Source : The Case in which the Rate of Flow from the Source is Forcibly Varied with Time

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A theoretical analysis is presented for the unsteady laminar flow of an incompressible fluid between parallel disks with a time-varying gap width and a central fluid source. The gap width h and the flow rate q of the source are independently varied arbitrarily with time. New series solutions to the Navier-Stokes equations are obtained on the basis of an original asymptotic expansion in the radial direction and a new theory of "multifold series expansion" in the time variable. The solutions can precisely describe the complicated nonlinear interaction between the two coexisting flows. Experiments were carried out for the case where h and q were changed sinusoidally with a variety of mean values, amplitudes and phase differences. It has been confirmed that the present solutions agree very well with the experiments over a wide range of the flow conditions and the variations of h(t) and q(t).
一般社団法人日本機械学会の論文
1990-08-15