Computation of low-speed flow with heat addition

A perturbation expansion is used to obtain a system of conservation laws for compressible flows that is valid at arbitrarily low Mach numbers. These equations are rendered hyperbolic by adding an artificial time derivative to the energy equation, thus introducing pseudoacoustic waves with a speed th...

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Bibliographic Details
Published in:AIAA journal 1987-06, Vol.25 (6), p.831-838
Main Authors: Merkle, Charles L, Choi, Yun-Ho
Format: Article
Language:English
Subjects:
aerodynamics
compressible flow
Compressible flows
shock and detonation phenomena
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
iterative method
numerical analysis
Physics
stability
thermodynamics
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Summary:A perturbation expansion is used to obtain a system of conservation laws for compressible flows that is valid at arbitrarily low Mach numbers. These equations are rendered hyperbolic by adding an artificial time derivative to the energy equation, thus introducing pseudoacoustic waves with a speed the same order as the particle velocity. Traditional time-iterative schemes are shown to be effective in solving this system numerically. Stability calculations of the complete vector system indicate unconditional stability at all Mach numbers in the absence of gravity. This instability is amplified by approximate factorization thus precluding solutions with gravity below this Mach number level. Computations of strong heat addition in low-Mach-number flow both with and without gravity confirm the stability predictions.
ISSN:0001-1452
1533-385X
DOI:10.2514/3.9708