Numerical solutions of ideal MHD equations for a symmetric blunt body at hypersonic speeds

Augustinus, Justin; Hoffmann, Klaus A.; Harada, Shigeki

doi:10.2514/6.1998-850

Cited by 15 publications

(3 citation statements)

References 13 publications

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“…There have been several recent works on developing upwind schemes for MHD equations with shock capturing capability [19,20] . Most of these methods are second order accurate TVD schemes.…”

Section: Methodsmentioning

confidence: 99%

Numerical Simulation of Secondary Flow in a Weakly Ionized Supersonic Flow with Applied Electromagnetic Field

Rawat

Zhong

Singh

et al. 2005

36th AIAA Plasmadynamics and Lasers Conference

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This paper investigates, by numerical simulation of Navier Stokes equations, Magnetohydrodynamic (MHD) effects of an imposed electromagnetic field on secondary flow in a plasma wind tunnel with a weakly ionized supersonic flow in the range of Mach number 2.6 to 3.0. The imposed magnetic field is generated by a magnet flushmounted in the tunnel side wall. Flow is pre-ionized by an R-F discharge and DC electric field is generated in the flow by electrodes flush-mounted in the top and bottom walls, perpendicular both to the flow velocity and the magnetic field. The electrical conductivity of the flow varies between 0.1 and 0.5 mho/m. The magnetic Reynolds number of the flow is small so induced magnetic field is neglected. The governing equations of the MHD flow, which are the Navier-Stokes equations with the applied electromagnetic force terms, are computed by a third-order upwind numerical scheme. A series of cases with different imposed magnetic fields, electric fields and electrical conductivities, for two different stagnation pressures at the nozzle entrance, were investigated. A strong secondary flow was observed in the cold flow, i.e. flow with magnetic field and electric field switched off. However when a strong electric field is applied at constant electrical conductivity, the Mach number in the inviscid core is seen to drop. Also, the boundary layer thickness increases. More importantly, the strong cross flow is reduced downstream of the zone of electric field imposition. The negative magnetic field, acting in conjunction with the strong electric field further retards the flow and generates stronger secondary flow. To account for the scenario when time lag is large between application of electromagnetic field and Joule heating of flow, calculations were carried out by neglecting Joule heating terms in energy equation. Actual solutions are expected to be in between those obtained with and without considering Joule heating effects. In absence of Joule heating, constant acceleration (retardation) of flow was observed with accelerating (retarding) electromagnetic field although the changes in flow properties were minor as compared to the Joule heated flow with same electromagnetic fields. Under the assumption of no Joule heating, accelerating magnetic fields reduce the secondary flow while retarding flow makes the secondary flow stronger. Flow with a lower Reynolds number is expected to be more stable because of viscous effects. On the contrary, secondary flow near side wall is observed to be stronger for cold flows of lower Reynolds number. Also, Lower Reynolds number flow is observed to be affected more strongly by applied electromagnetic forces. In general, an accelerating magnetic field applied with electric field was observed to produce much lower secondary flow than the retarding magnetic field in same situation for almost all of the cases considered in the study.

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“…There have been several recent works on developing upwind schemes for MHD equations with shock capturing capability [19,20] . Most of these methods are second order accurate TVD schemes.…”

Section: Methodsmentioning

confidence: 99%

Numerical Simulation of Secondary Flow in a Weakly Ionized Supersonic Flow with Applied Electromagnetic Field

Rawat

Zhong

Singh

et al. 2005

36th AIAA Plasmadynamics and Lasers Conference

View full text Add to dashboard Cite

show abstract

“…There have been several recent works on developing upwind schemes for MHD equations with shock capturing capability [33,34] . Most of these methods are second order accurate TVD schemes, which may not be accurate enough for the numerical simulation of instability waves in supersonic boundary layer.…”

Section: Methodsmentioning

confidence: 99%

Numerical Simulation of Supersonic Boundary Layer Stability with Applied Electromagnetic Field in a Weakly Ionized Flow

Singh

Zhong

Gogineni

2004

35th AIAA Plasmadynamics and Lasers Conference

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This paper investigates, by direct numerical simulation, the effect of an imposed electromagnetic field on a weakly ionized supersonic boundary layer in the range of 2.7 to 3.0 in a supersonic plasma wind tunnel, located at the non-equilibrium thermodynamics laboratory, under J. W. Rich and I. Adamovich, at the Ohio State University [1]. The main emphasis of the study is on MHD effects on the supersonic boundary layer. The imposed magnetic field is generated by a magnet flush-mounted in the tunnel side wall and the electric field is generated in this supersonic flow, pre-ionized by the RF discharge, by applying a DC field using electrodes flush-mounted in the top and bottom walls, perpendicular both to the flow velocity and the magnetic field. The electrical conductivity of the flow varies between 0.1 and 0.5 mho/m. The magnetic Reynolds number of the flow is small so that the induced magnetic field is neglected. The governing equations of the MHD flow, which are the Navier-Stokes equations with the applied electromagnetic force terms, are computed by a third-order upwinded numerical scheme. A series of cases with different imposed magnetic fields, electric fields and electrical conductivity, for two different stagnation pressures at the nozzle entrance, have been investigated for the mean flow. Calculations on the second mode instability are planned. It is found that in the presence of electric fields and the absence of magnetic fields, i.e. joule heating, the flow at the centerline heats up strongly leading to retardation in the flow velocity. The boundary layer thickness also increases and the mean Mach number is brought down. In the presence of magnetic field only, it is observed that the boundary layer profile changes depending on the direction of the field and, also the effect on the boundary layer is less in magnitude compared to the effect of joule heating on the same. The magnetic field is limited in its ability to mitigate the effects of an imposed electric field on the flow field. Unsteady calculations are currently underway and comprehensive conclusions on effects of external electromagnetic fields are expected in future. We have also undertaken three dimensional calculations to understand the effects of the sidewall on the flow profile.

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“…As numerical simulations come to play a vital role in studying the motion of ionized gases in hypersonic flows [4,33], space propulsion [42], and space physics [15], great emphasis has been placed on the development of numerical schemes for the system of magnetohydrodynamic equations. Out of the various possibilities, Godunov-type schemes-encouraged by successful applications to the Euler equations-are considered to be highly effective in resolving discontinuities such as shock waves for high speed flow problems.…”

Section: Introductionmentioning

confidence: 99%

On Godunov-Type Schemes for Magnetohydrodynamics

Myong

Roe

1998

Journal of Computational Physics

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Numerical solutions of ideal MHD equations for a symmetric blunt body at hypersonic speeds

Cited by 15 publications

References 13 publications

Numerical Simulation of Secondary Flow in a Weakly Ionized Supersonic Flow with Applied Electromagnetic Field

Numerical Simulation of Secondary Flow in a Weakly Ionized Supersonic Flow with Applied Electromagnetic Field

Numerical Simulation of Supersonic Boundary Layer Stability with Applied Electromagnetic Field in a Weakly Ionized Flow

On Godunov-Type Schemes for Magnetohydrodynamics

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