Domenic D'Ambrosio

Electromagnetic Fluid Dynamics for Aerospace Applications

Starting from the basic and general approach founded on the coupling between the Maxwell and the Navier- Stokes equations, the authors review some physical and mathematical models that are currently used in the aerospace engineering community for representing the behavior of electrically conducting flows subject to electromagnetic fields. Then, they present four different numerical methods for solving the magnetofluid dynamics equations in different formulations and for different magnetic Reynolds number regimes. For the sake of simplicity, the attention is focused on one-dimensional cases. Finally, numerical results obtained using the above mentioned numerical techniques on a magnetofluid dynamics shock-tube problem are compared and discussed

Numerical Prediction of Laminar Shock/Shock Interactions in Hypersonic Flow

Results are presented of a series of numerical simulations of experiments conducted at the ONERA ChalaisMeudon ResearchCenterandattheCalspan— University at Buffalo Research Centeron shock/shock interactions. The e owe eld characteristics are described with the aid of the numerical predictions, and the computed values of surface pressure and heat transfer are compared with the experimental measurements for purposes of verie cation andvalidation.Issuesrelatedtoboundaryconditions,gridconvergence,andtimeunsteadinessofthecomputational e uid dynamicssimulations are addressed, and thedife culties that characterize thevalidation of the computational results are put in evidence. Nomenclature F = e ux vector h = enthalpy, J/kg M = Mach number n = normal unit vector p = pressure, Pa R = radius, reference length, m Re = Reynolds number S = surface,m 2 T = temperature, K t = time, s U = primitive variables vector u; v = velocity components in the x and y directions, m/s V = velocity, m/s V = volume, m 3 W = conservative variables vector X = axis oriented in the direction between two cells x; y = Cartesian body axes, m 1n = distance from the wall of the e rst cell center, m µ = angular measurement, deg π = dynamic viscosity, kg/m ¢s Ω = density, kg/m 3 Subscripts c = cell cyl = cylinder I = inviscid t = time derivative V = viscous w = wall conditions X = space derivative 1 = freestream conditions Superscript 0 = stagnation conditions

Electromagnetic Fluid Dynamics for Aerospace Applications. Part I: Classification and Critical Review of Physical Models

The authors present a review of some physical and mathematical models that are currently used in the aerospace engineering community for representing the behavior of electrically conducting o ws subject to electromagnetic elds. Starting from the most general model, which couples the Navier-Stokes equations for non-equilibrium high-temperature gas dynamics with the Maxwell equations, they describe the simplications that are usually adopted to obtain the simplied models of magneto-uid dynamics (MFD). In this framework, they also survey the various reduced models that can be further extracted from the simplied MFD equations depending on the magnitude of the magnetic Reynolds number.

A NUMERICAL METHOD FOR SOLVING THE THREE-DIMENSIONAL PARABOLIZED NAVIER-STOKES EQUATIONS

A numerical technique that solves the parabolized form of the Navier-Stokes equations is presented. Such a method makes it possible to obtain very detailed descriptions of the flowfield in a relatively modest CPU time. The present approach is based on a space-marching technique, uses a finite volume discretization and an upwind flux-difference splitting scheme for the evaluation of the inviscid fluxes. Second order accuracy is achieved following the guidelines of the the ENO schemes. The methodology is used to investigate three-dimensional supersonic viscous flows over symmetric corners. Primary and secondary streamwise vortical structures embedded in the boundary layer and originated by the interaction with shock waves are detected and studied. For purpose of validation, results are compared with experimental data extracted from literature. The agreement is found to be satisfactory. In conclusion, the numerical method proposed seems to be promising, as it permits at a reasonable computational expense to investigate complex three-dimensional flowfields in great detail.

Plasmadynamic Simulations with Strong Shock Waves

This paper describes the computer simulation of an ionizing gas passing through a strong shock wave. A program module for solving the fluid dynamics equations for ions, electrons and neutrals, illustrating the effect of charge separation on the flow, is discussed. Previous solution modules in the present effort solved the Navier-Stokes equations, Maxwells equations and those for chemical and thermal nonequilibrium. This fourth module completes the set for describing the physics of hypersonic flow of an ionizing gas within an electromagnetic field. Argon gas is used in the present simulation.

Two-dimensional numerical methods in electromagnetic hypersonics including fully coupled Maxwell equations

We describe a numerical technique for solving the coupled Maxwell and Navier-Stokes equations. The method is based on altering the magnitude of the speed of light in the Maxwell equations in order to make the characteristic time scale of electromagnetism comparable with the one of fluid dynamics during the transient to a steady state solution. The method is not time accurate, but provides interesting results at steady state. It can also be used to numerically evaluate the applied magnetic field provided that the distribution of the latter is known on a surface that contains the magnetic field source (solenoid or permanent magnet). To test the technique, we show the results obtained on an axial symmetric configuration.

Numerical Prediction of Non-equilibrium Flows in Hypersonic Nozzles: State-to-State Kinetics Versus Macroscopic Models.

Numerical experiments are presented aimed at comparing the behavior of state-to-state chemical kinetics models with respect to the macroscopic thermochemical non-equilibrium models that are usually used in the numerical computation of high temperature hypersonic o ws. The comparison is focused both on the differences in the numerical results and on the computational effort related to the adoption of the each approach.

SHOCK-INDUCED SEPARATED STRUCTURES IN SYMMETRIC CORNER FLOWS

Three-dimensional supersonic viscous laminar flows over symmetric corners are considered in this paper. The characteristic features of such configurations are discussed and an historical survey on the past research work is presented. A new contribution based on a numerical technique that solves the parabolized form of the Navier-Stokes equations is presented. Such a method makes it possible to obtain very detailed descriptions of the flowfield with relatively modest CPU time and memory storage requirements. The numerical approach is based on a space-marching technique, uses a finite volume discretization and an upwind flux-difference splitting scheme (developed for the steady flow equations) for the evaluation of the inviscid fluxes. Second order accuracy is reached following the guidelines of the ENO schemes. Different free-stream conditions and geometrical configurations are considered. Primary and secondary streamwise vortical structures embedded in the boundary layer and originated by the interaction of the latter with shock waves are detected and studied. Computed results are compared with experimental data taken from literature.

Consistent Comparison of Macroscopic and State-to-State Kinetics in Hypersonic Flows

We present a comparison of numerical results in strongly expanding hypersonic flows that have been obtained using state-to-state and macroscopic thermochemical models. The macroscopic model, which includes direct cross coupling between chemical and vibrational relaxation, has been derived directly from the state-to-state kinetic rates. This makes the comparison the most consistent possible, as differences cannot be ascribed to original discrepancies in the used rates. The comparison is conducted in a N2-N system using the test conditions of the EAST facility nozzle experiment, for which experimental data are available.

A Numerical Method for Two-Dimensional Hypersonic Fully Coupled Electromagnetic Fluid Dynamics

We describe three mathematical models for predicting the interaction between electromagnetic fields and electrically conductive flows: one is based on the full coupling between the full Maxwell equations and the Navier-Stokes equations, a second one is based upon the application of the MHD approximation and the third one descends from the second under the assumption of low magnetic Reynolds number. Then, we discuss the insulating wall boundary condition, as it is applied to the three models, in case of a configuration where the magnetic field is perpendicular to a two-dimensional planar flow field. Finally, we propose a numerical method for solving the full magneto-fluid dynamics equations where the insulating wall boundary condition is implemented.