科研之友
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摘要
Pursued herein are the closed-form solutions of the Navier-Stokes equations for both planar channel and circular duct flows, influenced by either periodic or aperiodic pressure gradients, of which the amplitudes are sufficiently low to yield laminar incompressible flows. The analyses conducted for the unsteady flows parallel to the walls lead to the analytical solutions that encompass not only the long-time oscillations by periodic pressure gradients, but also the transient start-up flows commencing from zero velocity due to arbitrary aperiodic pressure gradients. With the standard methods employed, the present solutions generalizing the classic ones are written in the forms rendering the explicit dependence on the pressure gradient, and are numerically validated by the existing solutions of simple sinusoidal oscillations and a flow involving an aperiodic impulsive pressure gradient. By virtue of their functional forms, the present solutions can be applied with any pressure gradients, even if the gradients are not in closed forms.
- 出版日期2017-3
