Nonequilibrium blunt-body flow using the method of integral relations

Baron, Judson R.; Shih, Wei-Chuan

doi:10.2514/3.2493

Cited by 7 publications

(2 citation statements)

References 9 publications

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“…Unfortunately, the presence of the unknown p,,requires this to be done iteratively. Of the results presented in these two papers, the most significant is figure 5 of Shih & Baron (1964), which shows a spread in stagnation pressures, with the non-equilibrium values lying between the equilibrium and frozen values. (There is no noticeable spread between the equilibrium and non-equilibrium values of temperature and species concentrations.)…”

Section: Review Of Previous Analysesmentioning

confidence: 99%

On stagnation-point conditions in non-equilibrium inviscid blunt-body flows

Vinokur

1970

J. Fluid Mech.

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In non-equilibrium inviscid blunt-body flows, the state of the gas at the stagnation point is known to be in thermodynamic equilibrium for all finite relaxation times. The dependence of this state on the non-equilibrium processes and body geometry is investigated for the most general conditions. The stagnation-point state is always found to be in a narrow range bounded on one side by the state obtained in an equilibrium flow. The other bound, called the frozen limit, is far removed from the state obtained in an identically frozen flow (infinite relaxation times). For certain state variables, the frozen-limit value lies outside the range determined by frozen and equilibrium flow. Significant errors are found in several published predictions of the stagnation-point state, resulting from the non-analytic approach to equilibrium in nearly frozen flow.The two bounds on the pressure are expressible in terms of the normal shock density ratios for equilibrium and frozen flow. The actual pressure for an arbitrary flow situation is found to depend only on the shock nose radius and the relation between density and time in the relaxation zone behind a normal shock wave. If the density law is given by a single relaxation model, a closed form expression for the pressure is obtained. The analysis is carried out for both plane and axisymmetric flows, and is also valid for non-equilibrium free-stream conditions.

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Section: Review Of Previous Analysesmentioning

confidence: 99%

On stagnation-point conditions in non-equilibrium inviscid blunt-body flows

Vinokur

1970

J. Fluid Mech.

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“…Dorodnitsyn's numerical method of integral relations (Hayes & Probstein 1959) has been used by several authors in the forms of scheme I (where the shock layer is divided into longitudinal strips) and scheme I1 (transversal strips) to study non-equilibrium flows. Shih & Baron (1964), and Springfield (1964) used a onestrip, scheme I formulation to deal with full-chemistry air models. Belotserkovskii & Dushin (1964) treated reacting oxygen flows by means of scheme 11, on the grounds that it is better suited to follow the abrupt changes exhibited by nonequilibrium flow variables across the shock layer.…”

Section: Introductionmentioning

confidence: 99%

A theoretical study of non-equilibrium blunt-body flows

Conti

1966

J. Fluid Mech.

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Non-equilibrium inviscid flows behind a spherical-segment shock wave are investigated with the method of series truncation. This semi-analytical technique developed at Stanford is based on a systematic co-ordinate-perturbation scheme. The flow variables are expanded in series in powers of the longitudinal curvilinear co-ordinate leading away from the stagnation point. The problem is thus reduced to one of numerical integration of ordinary differential equations for functions of the normal co-ordinate. Unlike the similar situation of the Blasius series in boundary-layer theory, the present scheme–having to deal with elliptic equations–must resort to series truncation. As a consequence, a truncation error is introduced. The present paper shows a simple way of reducing this error.The simplified air chemistry adopted is based on non-equilibrium dissociation and recombination of oxygen diluted in inert nitrogen. A wide spectrum of non-equilibrium régimes is investigated for a fixed set of flight conditions. In particular, near-frozen flows are followed to the vicinity of the stagnation point through a region of large temperature and concentration gradients located near the body. This equilibrium-drive region, arising from the singular nature of the frozen limit, is studied in some detail.

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Inviscid hypersonic flow around blunt bodies

Kaattari

Katzen

1965

AIAA Journal

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Nonequilibrium blunt-body flow using the method of integral relations

Cited by 7 publications

References 9 publications

On stagnation-point conditions in non-equilibrium inviscid blunt-body flows

On stagnation-point conditions in non-equilibrium inviscid blunt-body flows

A theoretical study of non-equilibrium blunt-body flows

Inviscid hypersonic flow around blunt bodies

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