Computational Fluid Dynamics for the 21st Century pp 385-400 | Cite as

# Numerical Investigation of Magnetohydrodynamic Effects in Real Gas Flows

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## Summary

A compressible viscous magnetohydrodynamic (MHD) solver has been developed to investigate the use of MHD control techniques in the weakly ionized gas flows found in several hypersonic regimes. Numerical solutions are obtained by solving Powell’s 8-wave formulation of the governing equations in generalized coordinates using a modified Runge-Kutta time integration scheme and second-order accurate spatial discretization. The symmetric Davis-Yee Total Variation Diminishing (TVD) flux limiters are employed. The capability to simulate the behavior of real gases by including equilibrium air curve-fits has been added to the code that also includes models for variable electrical conductivity. A study of the effect of magnetic fields on scramjet inlet flows with air assumed to be frozen and in thermo-chemical equilibrium is presented.

## Keywords

AIAA Paper Total Variation Diminishing Flux Limiter Variable Electrical Conductivity Shock Standoff Distance## Nomenclature

- γ
Specific heat ratio

- λ
Eigenvalue

- Ф
_{ξ'}Ф_{η} Flux limiter functions

- μ
_{f} Magnetic permeability of the fluid

- τ
Viscous stress tensor

- α
Degree of ionization

- σ
Variable electrical conductivity

- ρ
Gas density

- δ,δ
Entropy correction variables

*v*_{fξ},*v*_{fη}Fast wave velocities in ξ,η directions

- ξ,η
Generalized coordinate parameters

*V*_{sξ},*V*_{sη}Slow wave velocities in ξ,η directions

- B
Magnetic field vector

- B
_{x} Magnetic field component,

*x*-direction- B
_{y} Magnetic field component,

*y*-direction- B
_{z} Magnetic field component,

*z*-direction*Cs*Speed of sound

- E
Electric field vector

- E
Flux vector component in

*x*-direction- e
_{t} Total energy per unit mass

- F
Flux vector component,

*y*-direction- g
Limiter function

- I
Identity tensor

- J
Electrical current density vector

- J
Jacobian of transformation

- k
Boltzmann constant,1.38×10

^{−23}J/K*M*_{∝}Freestream Mach number

- P
Pressure

- P
*r* Prandtl number

- Q*
MHD Interaction parameter

- Q
Field vector

- q
Heat flux vector

- Re
_{∞} Reynolds number

*Rem*_{∝}Magnetic Reynolds number

*T,T*_{tran}Translational temperature

*T*_{e}Electron Temperature

*T*_{υ}Vibrational Temperature

- u
Velocity component in the

*x*-direction- v
Velocity component in the

*y*-direction- V
Velocity vector

- V
_{∝} Free-stream velocity

- V
_{ax} Alfven wave velocity,

*x*-direction- V
_{ay} Alfven wave celocity,

*y*-direction- W
Velocity component in the

*z*-direction

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## References

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