Three-Dimensional Flow around Blunt Bodies

Moretti, Gino; Bleich, Gary

doi:10.2514/3.55340

Cited by 46 publications

(2 citation statements)

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“…The magnetohydrodynamic (MHD) interaction of an ionized flow with a magnetized body moving in the atmosphere at a hypersonic speed was modelled as early as the 1950s, initiated with theoretical approaches (Bush 1958;Lévy 1963;Levy & Petschek 1963;Jarvinen 1965) and afterwards complemented by numerical simulations stimulated by space flight and atmospheric entry problems (signal blackout, wall heating, drag monitoring…). Numerical resolution of the Euler equations for the aerodynamic blunt-body problem at supersonic speeds was developed in the 1960s (Moretti & Abbett 1966;Moretti & Bleich 1967;Rusanov 1976), soon followed by numerical resolution of the MHD equations (Coackley & Porter 1971), and has reached a high level of accuracy.…”

Section: Introductionmentioning

confidence: 99%

Analytic model of a resistive magnetohydrodynamic shock without Hall effect

Berton

2018

J. Fluid Mech.

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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$\unicode[STIX]{x1D712}_{1}<50^{\circ }$.

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Section: Introductionmentioning

confidence: 99%

Analytic model of a resistive magnetohydrodynamic shock without Hall effect

Berton

2018

J. Fluid Mech.

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“…Shock fitting schemes have been used for simulations of compressible flow with welldefined shocks since 1960s. Moretti and collaborators developed efficient and reliable codes using shock fitting for steady and time-dependent flows [39][40][41][42] . In order to compute shock velocities, the Rankine-Hugoniot conditions were used with a compatibility equation along a generator of the characteristic conoid reaching the shock.…”

Section: Shock-fitting Methodsmentioning

confidence: 99%

Direct Numerical Simulations of Turbulent Flow Interactions with Strong Shocks Using Shock-Fitting Method

Rawat

Zhong

2011

49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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Canonical problem of interaction of a normal shock and isotropic turbulence is fundamental to many important scientific and engineering applications. Most widely used shock capturing methods for the numerical simulation of compressible flows are inherently dissipative, only first order accurate and may incur numerical oscillations near the shock waves. Since high order methods are critical for direct numerical simulation of turbulent flows, we use a shock-fitting method that has been shown to be fifth-order accurate near as well as away from the shock. Moreover, unlike shock-capturing schemes, there are no spurious oscillations even with very strong shock waves. We carry out Direct Numerical Simulation (DNS) of canonical shock-turbulence interaction problem for flows with mean Mach numbers ranging from 2 to 20 and turbulent Mach number varying from 0.12 to 0.38. A Reynolds number based on Taylor microscale, Re , of up to 40 is used, requiring more than 30 million grid points per simulation. Such high mean Mach number values have never been considered in past for study of shock turbulence interactions. Some new trends are observed in turbulent statistics as mean Mach number is increased. Maximum value of streamwise velocity fluctuations downstream of the shock is found to be initially decreasing as Mach number is increased but for stronger than Mach 8 shocks this trend reverses. Similarly maximum streamwise vorticity fluctuations in post-shock flow first increase and then decrease as mean Mach number is increased. We observe that vorticity fluctuations return to isotropy behind the shock for some cases. Increasing mean Mach number and Reynolds number leads to delay in the return to isotropy in the vorticity fluctuations. Overall, the results generally confirm the findings by earlier numerical simulations and provide new trends for stronger shocks than those considered by numerical studies in the past.

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Spatial marching techniques for approximate solutions to the hypersonic blunt body problem

Blottner

1988

Numerical Methods in Fluids

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Two reduced forms of the Euler equations which allow spatial marching in subsonic flow regions are investigated for solving the inviscid blunt body problem. An analysis of the eignevalues to determine the properties of the steady and unsteady forms of the governing equations is performed. The steady forms of both the thin shock layer equations and the pressure gradient splitting method are appropriate for a marching solution technique. Numerical results from the thin layer equations are less accurate, and the suitability of this approach in a global iteration procedure is questioned as the analysis shows information is not transmitted upstream. The pressure gradient splitting method gives more accurate results with a single downstream march and appears better suited for use in a global iteration procedure to obtain the complete solution of the Euler equations. Further evaluation of the pressure gradient splitting method shows that it can be readily applied over a range of Mach numbers, and the accuracy of the results is only slightly dependent on the free-stream Mach number.

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Three-Dimensional Flow around Blunt Bodies

Cited by 46 publications

References 4 publications

Analytic model of a resistive magnetohydrodynamic shock without Hall effect

Analytic model of a resistive magnetohydrodynamic shock without Hall effect

Direct Numerical Simulations of Turbulent Flow Interactions with Strong Shocks Using Shock-Fitting Method

Spatial marching techniques for approximate solutions to the hypersonic blunt body problem

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