Abstract
A solution of the highly complex unsteady compressible flow field inside a cylindrical resonance tube has been obtained numerically, assuming one dimensional, viscous, and heat conducting flow, by solving the appropriate fluid dynamic and energy equations. The resonance tube is approximated by a right circular cylinder closed at one end with a piston oscillating at resonant frequency at the other end. An iterative implicit finite difference scheme is employed to obtain the solution. The scheme permits arbitrary boundary conditions at the piston and the end wall and allows assumptions for transport properties. For the example considered herein, the solution predicts a rise of 95°F in the mean end wall temperature, from 60°F to 155°F, in 14.313 milliseconds which is in good agreement with the experimentally observed values. The solution would also be valid for tapered tubes if the variations in the cross-sectional area are small. In successfully predicting the resonance tube results, an innovative simple but stable solution of unsteady fluid dynamic and energy equations is provided here for wide ranging research, development, and industrial applications in solving a variety of complex fluid flow heat transfer problems. The method is directly applicable to pulsed or pulsating flow and wave motion thermal energy transport, fluid-structure interaction heat transfer enhancement, and fluidic pyrotechnic initiation devices.
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