The wave system attached to a slender body in a supersonic relaxing gas stream. Basic results: the cone

Clarke, J. F.; Sinai, Yehuda

doi:10.1017/s0022112077000299

Cited by 8 publications

(12 citation statements)

References 10 publications

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“…which is the slender-cone frozen shock decay law given by Chou & Chu (1971) and Clarke & Sinai (1977). As r+co the local logarithmic decay rates given by (70) and (72) coincide.…”

Section: R(r O B ) = I ' O ( O B ) Exp { R R L ( O B ) / R O ( O B ) }mentioning

confidence: 81%

“…I n neither case was information given concerning the flow a t large distances from the body. Very recently Clarke & Sinai (1977) used matched asymptotic expansions allowing certain regions of the flow to be calculated even in the far field. Their method consists of an extension of that of Blythe (1969) to axisymmetric flow and is for slender cones.…”

Section: Introductionmentioning

confidence: 99%

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Supersonic flow of a vibrationally relaxing gas past a circular cone

Kao¹,

Hodgson²

1978

J. Fluid Mech.

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The steady supersonic flow of a vibrationally relaxing gas past a cone is studied using numerical methods. Near the tip of the cone the flow is obtained by means of a coordinate expansion and built on to this is a characteristic network used to obtain the remainder of the flow. Of particular interest is the development of the frozen shock at the tip into a relaxation-dominated wave at distances large compared with the width of the wave. The numerical results are presented in a concise similarity form which will permit accurate extrapolation to very weak waves in atmospheric air.

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“…which is the slender-cone frozen shock decay law given by Chou & Chu (1971) and Clarke & Sinai (1977). As r+co the local logarithmic decay rates given by (70) and (72) coincide.…”

Section: R(r O B ) = I ' O ( O B ) Exp { R R L ( O B ) / R O ( O B ) }mentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Supersonic flow of a vibrationally relaxing gas past a circular cone

Kao¹,

Hodgson²

1978

J. Fluid Mech.

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“…Taking λ = 0, the conclusions of the present paper can be compared with the analysis of Clarke and Sinai [19,20] for an unstratified medium. If the thickness to length ratio of the supersonic body is Cl 1, and r 0 L, where L is the length of the body, then the disturbance amplitude at r = r 0 is…”

Section: Discussionmentioning

confidence: 92%

“…The propagation of the sonic boom generated by an axisymmetric supersonic body in a medium characterised by a single relaxation mode was considered by Clarke and Sinai [19,20]. Their analysis takes full account of body shape, describing the development of the N-wave structure in the near-field, followed by the evolution of the shock structure over large ranges.…”

Section: Introductionmentioning

confidence: 99%

Effect of molecular relaxation on the propagation of sonic booms through a stratified atmosphere

Hammerton

2001

Wave Motion

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Nonlinear acoustic wave propagation through a stratified atmosphere is considered. The initial signal is taken to be an isolated N -wave, which is the disturbance that is generated some distance away from a supersonic body in horizontal flight. The effect of cylindrical spreading and exponential density stratification on the propagation of the disturbance is considered, with the shock structure controlled by molecular relaxation mechanisms and by thermoviscous diffusion. An augmented Burgers equation is obtained and asymptotic solutions are derived based on the limit of small dissipation and dispersion. For a single relaxation mode, the solution depends on whether relaxation alone can support the shock or whether a sub-shock arises controlled by other mechanisms. The resulting shock structures are known as fully dispersed and partly dispersed shocks, respectively. In this paper, the spatial location of the transition between fully dispersed and partly dispersed shocks is identified for shocks propagating above and below the horizontal. This phenomenon is important in understanding the character of sonic booms since the transition to a partly dispersed shock structure leads to the appearance of a shorter scale in the shock rise-time, associated with the embedded sub-shock.

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“…I n addition to the books by Vincenti and Kruger (1965) and Clarke and McChesney (1976) the following survey articles are recommended : Becker (1967Becker ( , 1970, Lick (1967Lick ( , 1970, Clarke (1969), Broer (1970 and Chu (1970). The following papers are also particularly illuminating: Blythe (1969), Ocltendon and Spence (1969), Chou (1972, Ishii (1976), Clarke and Sinai (1977) and Sinai and Clarke (1978). I n fact, major steps forward were taken already during the war by Bechert (1940Bechert ( ,1941a and Marx (1942) but their papers appear to have remained largely unnoticed.…”

Section: Wave Developmentmentioning

confidence: 99%

A TikhonovG-space not admitting a compact HausdorffG-extension orG-linearization

Megrelishvili¹

1988

Russ. Math. Surv.

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The properties of air at meteorological temperatures relevant to sound propagation and shock wave structure are reviewed. Of particular interest is the irreversible process of vibrational relaxation which describes the transfer of energy to or from the vibrational modes of the molecules and which dominates the absorption of audible sound in air. A detailed discussion of the structure and propagation of weak nonlinear waves in air shows that relaxation is again the dominant effect. As an alternative method to the usual approach of non-linear acoustics the exact gas-dynamic equations are solved numerically for a number of simple flow situations and exact results are obtained for the structure of steady waves. Estimates are obtained for the propagation distances required for the development of waveforms into steady profiles, and these distances are found under some circumstances to be greater than the dimensions of the Earth's atmosphere. The results are confirmed by laboratory experiments in CO2 and N2O and applied to waves in air with special reference to the sonic bangs of supersonic aircraft. Very recent results of applying the same alternative approach to periodic waves are reviewed briefly,

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The wave system attached to a slender body in a supersonic relaxing gas stream. Basic results: the cone

Cited by 8 publications

References 10 publications

Supersonic flow of a vibrationally relaxing gas past a circular cone

Supersonic flow of a vibrationally relaxing gas past a circular cone

Effect of molecular relaxation on the propagation of sonic booms through a stratified atmosphere

A TikhonovG-space not admitting a compact HausdorffG-extension orG-linearization

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