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Dilatation wave/soliton dynamics in variable density flows

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1 Author(s)
Hokenson, Gustave ; Dynamics Technology, Inc., Torrance, California 90505

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The dynamics of dilatation has been investigated for variable density flows which exhibit a temporal evolutionary character. In lieu of decomposing the conservation of mass equation (appropriate for strictly nondiffusive/incompressible flows) and utilizing div u = 0 to generate a Poisson pressure equation, the closure relation ’’small div u’’ was used. This suggests an approximate decomposition of the div u governing equation into a steady elliptic pressure equation and a time‐dependent equation for nonacoustic waves which governs div u (herein denoted by Ω~): (∂Ω~/∂τ)-[1+∫Ω~dx~-(1/4 Re)(∂ lnρ~/∂x~)](∂Ω~/∂x)=Ω~2+(1/Re)(∂2Ω~/∂Ω~2), utilizing the exact equations of continuity and momentum. The solution of this (’’vorticity‐like’’) equation provides information on how an initially small div u field evolves, frequently into a solitary wave. Should the dilatation remain ’’small,’’ rather than be (nonphysically) forced equal to zero, the full conservation relations may be utilized. However, if div u grows large, the elliptic pressure equation is inconsistent with the untampered governing equations. The motivation for this approach is to provide a structure within which: (1) small diffusive/compressibility effects may be studied, (2) the significance of div u physics, in flows which are traditionally treated as approximately dilatation free, may be analyzed, and (3) evolutionary pressure transport formalisms may be developed and evaluated for computational efficiency/accuracy and the inclusion of nonlinear acoustic waves.

Published in:

Journal of Applied Physics  (Volume:53 ,  Issue: 5 )