温度勾配のある細管内の圧力波の伝播(対流・拡散・渦・波動波動(2),一般講演)

概要

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This paper derives a one-dimensional wave equation for a pressure in a gas-filled, two-dimensional tube (channel) subjected to axial temperature gradient by averaging the linearized Navier-Stokes equations over the cross section. Thermoviscous effects appear in the form of memory integrals, whose relaxation functions are expressed analytically. The relaxation functions may be approximated according as a so-called Deborah number defined by the ratio of a typical relaxation time to a time concerned. It is revealed that the equation derived by the boundary-layer approximation is always valid as far as the Deborah number is greater than about 0.2. For a smaller value of the Deborah number, it is also revealed that the hereditary equation is reduced to a diffusion equation but the temperature gradient creates wave propagation.
日本流体力学会の論文
2009-09-02