On the structure of a class of aerothermodynamic shocks

Blythe, P. A.; Petty, D. G.; Schofield, Damian; Wilson, J. L.

doi:10.1017/s0022112069000590

Cited by 1 publication

(4 citation statements)

References 11 publications

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“…The precursor to this motion will still be described by the non-linear theory of $4.4.1 in general. All of these results are originally due to Blythe (1969) and illustrate something of the complexities introduced into otherwise elementary flow situations by the presence of relaxation. However, one is not finished yet as the results in this and in the previous subsection imply a limitation on the size of (a2-1).…”

Section: 42mentioning

confidence: 91%

“…The situation covered by these approximate deductions can be recognised as wholly consistent with the exact results of Q3.2 and 4.1, and it actually extends these results in numerous helpful ways; it also constitutes the analytical counterpart to the numerical computations outlined briefly in $4.2. There are some limitations, which it is not vital to make explicit here, especially since there are some more, strongly-related, matters to follow, but the interested reader can consult the original work by Blythe (1969) or any of the reviews and developments by Lick (1970), Becker (1972) and Clarke and McChesney (1976).…”

Section: Non-linear Efects In Small Disturbance Jieldsmentioning

confidence: 99%

“…Far-field behaviour, in the sense that (u2-1)x/2a1 o o ~c o is large, has been discussed for the acoustic case in $2.5.2. Blythe (1969) showed that changing to coordinates where the gauge function A ( € ) is still to be found, gives the following equation for V ( 1 ) :…”

Section: 42mentioning

confidence: 99%

“…It transpires that the correct coordinates in the new circumstances, when (a2-~) = O ( E ) , are: (4.17) with u2: €u(y(', Y'). Blythe (1969) and simultaneously, using a somewhat different set of arguments, by Ockendon and Spence (1969). It is a hyperbolic equation, with characteristics x' = constant and , B = constant, where , B is defined so that (cf (4.13) and the remarks which follow about the exact characteristic parameter /3).…”

Section: The Case Of Small Relaxing-mode Energymentioning

confidence: 99%

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Gas dynamics with relaxation effects

Clarke

1978

Rep. Prog. Phys.

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T h e way in which gas-phase chemical reactions and the excitation of internal modes of molecular energy storage can be collectively described as relaxation processes is explained. A set of equations which is suitable for a general account of gas flows with relaxation processes is exhibited, and the main part of the discussion of developments over the past decade or so is occupied with situations for which the transport effects of viscosity, heat conduction and mass diffusion are negligible, or sufficiently highly localised as to be so.T h e dissipative-dispersive character of acoustic waves is described with some emphasis on the large effect of absorption on high-frequency waves which travel at the frozen sound speed and on the relatively smaller, bulk-viscosity-like, influence on low-frequency disturbances which travel at the slower equilibrium sound speed. Signalling problems in equilibrium atmospheres show exponential decay at the precursor wave head and diffusive behaviour in those regions which travel at the equilibrium sound speed, as well as the effects of geometric attenuation for other than planar waves. The exploitation of the acoustic approximation in studies of flow problems is described.The effects of a dis-equilibrium atmosphere on acoustic wave propagation, and the consequent possibility of exponential amplification of disturbances, is described with reference to explosion and combustion phenomena, as well as a possible link with upper-atmosphere gravity waves.The analysis and explanation of shock-wave structure is briefly discussed with the aid of Hugoniot curves and Rayleigh lines, and the two main classes, of fully dispersed and partly dispersed waves, are defined. Weak Taylor shocks and fully dispersed waves are compared, with emphasis on the strong limitations on the use of equivalent bulk viscosities to describe relaxation effects. T h e way in which a population inversion can occur in internal molecular modes is illustrated by the case of a partly dispersed shock in a gas with two relaxing modes which have significantly different relaxation times.The way in which disturbances of finite amplitude behave is discussed, with special reference to characteristics theory, for both equilibrium and dis-equilibrium relaxing atmospheres. Modern theories of the non-linear wave propagation of small-amplitude disturbances are described with special reference to their role in the sonic boom problem and to the evolution of fully and partly dispersed shocks.

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Section: 42mentioning

confidence: 91%

Section: Non-linear Efects In Small Disturbance Jieldsmentioning

confidence: 99%

Section: 42mentioning

confidence: 99%

Section: The Case Of Small Relaxing-mode Energymentioning

confidence: 99%

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