Ovais U. Khan

Validity of Low Magnetic Reynolds Number Formulation of Magnetofluiddynamics

*† ‡ Validity of low magnetic Reynolds number approximation has been evaluated by conducting numerical experimentation with both the full magnetofluiddynamic (MFD) formulation and the low magnetic Reynolds number formulation. MFD equations in their classical form and under low magnetic Reynolds number approximation are presented and numerically solved using four-stage modified Runge-Kutta scheme augmented with the Total Variation Diminishing model in post-processing stage. An attempt has been made to compare the results obtained by the two available approaches. The results obtained from low magnetic number approximation compare well with the results obtained by solving the full MFD equations for low ranges of magnetic Reynolds number.

Computational aspects of high-speed flows with applied magnetic field

High-speed flows over the surface of hypersonic airfoil subjected to several types of applied magnetic field distributions are numerically simulated. The governing equations are composed of the Euler equation modified to include the effect of magnetic field. In the current applications, the low magnetic Reynolds number approximation is utilized and the Hall effect and ion slip have been neglected. A fourth-order modified Runge-Kutta scheme augmented with the Davis-Yee symmetric Total Variation Diminishing model in post-processing stage is used to solve the magnetogasdynamics equations. The flow simulations are compared to the existing solutions. A good agreement between the present analysis and the available normal shock data is demonstrated. It has been found that the location and distribution of the imposed magnetic field have dominant effects on the flow parameters and the shock standoff distance.

Flow Control Over a Backward-Facing Step with Application of a Magnetic Field

High-speed flows over a backward-facing step that is subject to an applied magnetic field are numerically simulated. The global domain of computation has been decomposed into upstream and downstream domains from the step location. The low magnetic Reynolds number approximation under a multiblock grid approach is used for modeling the backstep flow. Flux-vector splitting for the convective terms and central differencing for the diffusion terms are used. A time-explicit multistage Runge–Kutta scheme for time integration is implemented. Pressure distribution for the Navier–Stokes analysis is found to be in good agreement with the experimental data. Different typesofmagnetic fielddistributionsareinvestigated.Bothuniformandvariableelectricalconductivitydistributions havebeenconsidered.Ithasbeenobservedthatanincreaseintheseparationzoneanddisplacementofobliqueshock wave toward the exit section occurs subsequent to application of the magnetic field. Comparison of results obtained with uniform and variable electrical conductivities has shown a reduction in magnetic interaction for variable electrical conductivity.

Numerical Investigation of Magnetogasdynamic High Speed Flows

High speed flows over leading edge of hypersonic airfoil subject to an applied magnetic field is numerically simulated. The governing equations are composed of the Euler equation modified to include the effect of magnetic field. In the current applications, the low magnetic Reynolds number approximation is utilized. A four-stage modified Runge-Kutta scheme augmented with the Davis-Yee symmetric Total Variation Diminishing model in post-processing stage is used to solve the magnetogasdynamic equations. The flow simulations are compared to the existing solutions.

Unsteady Supersonic Flows over a Backward-Facing Step with Applied Magnetic Field

DOI: 10.2514/1.42190Time-dependentbehaviorofshock/boundary-layerinteractionhasbeeninvestigatednumericallyforflowsoverabackward-facingstep.Usingamultiblock-gridstrategy,theglobaldomainofcomputationhasbeendecomposedintotwo subdomains representing upstream and downstream regions from the step location. First, Navier–Stokesanalysishasbeenperformedtoinvestigatetheunsteadyshock/boundary-layerinteraction.Subsequently,magneto-fluid-dynamicscomputationshavebeenperformedtoexploretheeffectsofappliedmagneticfieldovertheunsteadynature of the problem and its use for local flow control. A time-explicit modified Runge–Kutta scheme with total-variation-diminishing limiters under a multiblock-grid approach has been implemented. The governing equationsare composed of the Navier–Stokes equation modified to include the effect of magnetic field under low-magnetic-Reynolds-number approximation. The effects of an applied magnetic field and a time-dependent magnetic field onthe flowfield have been investigated.It has been shown thatthe application of magnetic fieldincreases the unsteadynature of the problem.

Numerical Investigation of Decomposed Magnetofluid Dynamics Equations

In addition to the two commonly used formulations for magnetofluid dynamics, a third formulation based on the decomposition of the magnetic field for solving full magnetofluid dynamics equations is explored. The governing equations are transformed to a generalized computational domain and discretized using a finite difference technique. A time-explicit multistage Runge―Kutta scheme augmented with total variation diminishing limiters for time integration is implemented. The developed codes have been validated with the existing closed-form solution of the magnetic Rayleigh problem. Results obtained from the decomposed magnetofluid dynamics equations compare well with results obtained by solving the classical full magnetofluid dynamics equations for a wide range of magnetic Reynolds numbers. It is shown that the decomposed magnetofluid dynamics technique requires substantially less computation time compared with classical full magnetofluid dynamics equations for the solution involving flowfields with high imposed magnetic fields.

Computational Aspects of Magneto-Fluid-Dynamics Formulations

*† There are two formulations available for modeling magnetofluiddynamics (MFD) flow fields. (1) The classical full MFD (FMFD) equations and (2) low magnetic Reynolds number approximation. In addition, a third formulation–decomposed MFD (DMFD) equations, based on decomposition of total magnetic field for solving full MFD equations has also been proposed and validated in the available literature. In this work, computational performance of the existing MFD formulations has been investigated. The governing equations are transformed to a generalized computational domain and discretized using a finite difference technique. Time-explicit multistage Runge-Kutta scheme augmented with total variation diminishing (TVD) limiters for time integration is implemented. Time-dependent flow field over a flat plate with imposed magnetic field has been considered for investigating the performance of each MFD formulation. It has been found that the performance of DMFD equations is increased compared to FMFD equations when strong magnetic field is applied. Furthermore, it is shown that the low magnetic Reynolds number approach requires minimum amount of time to provide the solution and remains valid only for small values of magnetic Reynolds numbers.

Numerical Investigation of Decomposed Full Magneto-Fluid-Dynamics Equations

In addition to the two commonly used formulations for magnetofluid dynamics, a third formulation based on the decomposition of the magnetic field for solving full magnetofluid dynamics equations is explored. The governing equations are transformed to a generalized computational domain and discretized using a finite difference technique. A time-explicit multistage Runge―Kutta scheme augmented with total variation diminishing limiters for time integration is implemented. The developed codes have been validated with the existing closed-form solution of the magnetic Rayleigh problem. Results obtained from the decomposed magnetofluid dynamics equations compare well with results obtained by solving the classical full magnetofluid dynamics equations for a wide range of magnetic Reynolds numbers. It is shown that the decomposed magnetofluid dynamics technique requires substantially less computation time compared with classical full magnetofluid dynamics equations for the solution involving flowfields with high imposed magnetic fields.

Time Accurate Analysis of Supersonic Flows over a Backward-Facing Step with Applied Magnetic Fields

*† Time dependent behavior of shock/boundary layer interaction has been investigated numerically for flows over backward facing step. Magnetohydrodynamics computations have been performed to explore the effects of applied magnetic field over unsteady nature of the problem. Time-explicit modified Runge-Kutta scheme with TVD limiters under multiblock grid approach has been implemented. The governing equations are composed of the Navier-Stokes equation modified to include the effect of magnetic field. In the current applications, the low magnetic Reynolds number approximation is used. Results for NavierStokes analysis agree well with the available data. It has been found that application of magnetic field can enhance the unsteady nature of the problem.