A theoretical study of non-equilibrium blunt-body flows

An analytic model of a stationary hypersonic magnetohydrodynamic (MHD) shock with an externally applied magnetic field is proposed. Basically, original jump conditions at a plane oblique shock, analogous to the Rankine–Hugoniot formulae, with a moderately resistive air plasma downstream are derived. Viscous, thermal and Hall effects are neglected, but the plasma dissociation behind the shock causing a jump of isentropic exponent is also a major input of the model. Then, a shock-fitting procedure with ambient atmospheric conditions is worked out by the coupling of these MHD jumps with thermodynamic correlations and an electric conductivity model. For an application to atmospheric entry problems, the flow behind an axisymmetric blunt-body shock is modelled with a stream function satisfying these MHD jump conditions as boundary conditions. An important feature put into evidence is a similarity rule involving the hypersonic parameter$M_{1}\cos \unicode[STIX]{x1D712}_{1}$, which shows an aerodynamic correspondence between the upstream Mach number$M_{1}$and the velocity angle$\unicode[STIX]{x1D712}_{1}$. It also emerges that curvature effects become important past$30^{\circ }$and the assumption of a spherical shock also becomes untenable past$50^{\circ }$; therefore, we limit the model of shock thickness used in the MHD fitting to$\unicode[STIX]{x1D712}_{1}<50^{\circ }$.

Section: Prospectsmentioning

confidence: 99%

Analytic model of a resistive magnetohydrodynamic shock without Hall effect

Berton

2018

“…Next we compute 6(D,) for the experiments shown in figure 5. A similar calculation may be made for the theoretical results of Freeman (1958) and Conti (1966). For fixed values of 6, we can then plot the different non-equilibrium parameters with respect to each other.…”

Section: Resultsmentioning

confidence: 91%

“…The additional complications introduced by including real gas and non-equilibrium effects have, however, been tackled less frequently. Included in such theoretical studies relevant to our work we find the papers by Freeman (1958), Lick (1960), Hall, Eschenroeder & Marrone (1962), Lun'kin & Popov (1966) and Conti (1966).t Relatively few experimental results appear to be available on non-equilibrium stand-off distance of shock waves and those described in the literature were usually obtained in firing ranges. The first experiments of this type utilizing the vibra- tional excitation of chlorine gas as the non-equilibrium mode were presented by Schwartz & Eckerman (1956).…”

Section: Introductionmentioning

confidence: 99%

Experiments on shock stand-off distance in non-equilibrium flow

Wegener

Buzyna

1969

An experimental investigation of the non-equilibrium behaviour of the shock stand-off distance ahead of spheres at low supersonic Mach number is reported. An intermittent wind tunnel operating with a reacting gas mixture with one non-equilibrium mode is described. A non-equilibrium parameter after Damköhler is determined for the flow and the experiments cover a range of this variable from near-frozen to near-equilibrium states. The shock stand-off distance is measured and found to vary as expected between these two bounds with a low value at equilibrium. With all other variables governing shock standoff distance held constant, such measurements can also be used to determine the relaxation time of the non-equilibrium mode.

“…For convenience, we follow the numerical formulation of Conti (1966) for flow behind a circular-section shock wave of radius R,. In present terms, the flow along the stagnation streamline is computed by integrating equations ( 5 ) , with initial conditions given by the Rankine-Hugoniot (frozen) shock relations, and One can foresee that those solutions approaching the origin will be drawn to i t by the stable singularity, and this proves indeed to be the case in the numericaJ examples.…”

Section: Asymptotic Fit To Numerical Solutionsmentioning

confidence: 99%

Inviscid reacting flow near a stagnation point

Conti¹,

Dyke

1969

A reacting flow free of molecular transport exhibits noteworthy behaviour in the neighbourhood of a blunt, symmetrical stagnation point. A local analytical study using the Lighthill-Freeman gas model reveals the basic structure of such a flow. Chemical activity is found to affect some, but not all, of the local characteristics of the flow. Unaffected are the pressure and velocity fields near the stagnation point, where the pressure varies quadratically and the velocity varies linearly as in an inert flow. In addition, the stagnation point is found to be in chemical equilibrium for all non-zero reaction rates. On the other hand the density, temperature, and concentration fields are affected by the non-equilibrium reactions. The extent of this effect can be predicted on the basis of a reaction parameter that measures the rate of reaction in terms of the velocity gradient at the stagnation point. A rapidly reacting flow (with reaction parameter greater than unity) approaches the stagnation point with vanishing gradients of density and temperature, whereas a slowly reacting flow approaches with infinite gradients. The flow field is represented mathematically by functions that are regular along the body but non-analytic in the normal direction. Numerical computations support the validity of the local closed-form solution, and provide information on the local effects of the chemical history of the flow.