Author： Müller B.
Publisher： Springer Publishing Company
ISSN： 0022-0833
Source： Journal of Engineering Mathematics, Vol.34, Iss.1-2, 1998-07, pp. : 97-109
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Abstract
A multiple-time scale, single-space scale asymptotic analysis of the compressible Navier-Stokes equations reveals how the heat-release rate and heat conduction affect the zeroth-order global thermodynamic pressure, the divergence of velocity and the material change of density at low-Mach-numbers. The asymptotic analysis identifies the acoustic time change of the heat-release rate as the dominant source of sound in low-Mach-number flow. The viscous and buoyancy forces enter the computation of the second-order `incompressible' pressure in low-Mach-number flow in a similar way as they enter the pressure computation in incompressible flow, except for a nonzero velocity-divergence constraint. If the flow equations are averaged over an acoustic wave period, the averaged velocity tensor describes the net acoustic effect on the averaged flow field. Removing acoustics from the equations altogether leads to the low-Mach-number equations, which allow for large temperature and density changes as opposed to the Boussinesq equations.
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