Numerical Analysis for MHD Flow Control

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AIAA 2008-4221
Numerical Analysis for MHD Flow Control Using
Air-Core Circular Magnet Tomoyuki Yoshino,
Satoshi Kondo, Takayasu Fujino and Motoo
Ishikawa University of Tsukuba, Japan
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MHD Flow Control
Applying magnetic field
Reentry
Reduction of flow velocity in shock layer
Increase of shock standoffdistance Reduction of
AerodynamicHeating
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Objective
A lot of previous numerical studies
dipole magnet or unrealistic magnetic field
To examine influences of magnetic distributions
utilizing real air-core circular magnet on wall
heat flux in reentry flights by means of
numerical simulation
Air-core circular magnet

• Various size and position of magnet under
  constant magnetic energy
• Various flight conditions

Magnetic field
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Basic Equations for Gasdynamics
Mass conservation equations
Convection terms ? AUSM-DV scheam
(N,O,N,O,N2,O2,NO,N2,O2,NO,e-)
Parks Two-Temperature Model
Momentum conservation equations
11 Chemical Species and Dunn and Kangs model
Total energy conservation equation
Vibrational-electronic-electron energy
conservation equation
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Basic Equations for Electrodynamics
Steady Maxwell Equations
The generalized Ohms law
Galerkin finite element method
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Magnet Conditions
Rmag
L Self inductance I Coil current
Basic Equation for Externally Applied Magnetic
field
Biot-Savart law
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Magnet Conditions
Rmag
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Examples of Magnetic Field Distribution
0
Bmax0.33
Bmax0.56
Bmax1.31
Rmag0.2
Rmag0.8
Rmag0.4
Rmag Magnet outer radius
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Distribution of Wall Heat Flux
(Altitude 59 km)
Freestream condition Pressure 23.6
Pa Temperature 248.1 K Velocity 5.5 km/s
(Altitude 59 km)
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Distributions of Electrical Conductivity
MHD off
Rmag0.2
Freestream condition Pressure 23.6
Pa Temperature 248.1 K Velocity 5.5 km/s
(Altitude 59 km)
0
100
S/m
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Distributions of Lorentz Force
Rmag0.2
Rmag0.6
Rmag0.4
Rmag0.6
Rmag0.4
Rmag0.2
Freestream condition Pressure 23.6
Pa Temperature 248.1 K Velocity 5.5 km/s
(Altitude 59 km)
0
10000
N/m3
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Relations Between Maximum Wall Heat Flux and
Magnet Outer Radius (Altitude 59 km)
Freestream condition Pressure 23.6
Pa Temperature 248.1 K Velocity 5.5 km/s
(Altitude 59 km)
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Distribution of Wall Heat Flux
(Altitude 71 km)
Freestream condition Pressure 4.0
Pa Temperature 214.9 K Velocity 7.0 km/s
(Altitude 71 km)
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Distributions of Electrical Conductivity
59 km
63 km
71 km
Rmag0.6
Rmag0.6
Rmag0.6
800
10
S/m
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Relations Between Maximum Wall Heat Flux and
Magnet Outer Radius (Altitude 71 km)
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Influence of Shape of Blunt Body
Matsuda et al. experimentally and numerically
demonstrated influence of body and magnetic
configuration effect on shock layer enhancement
by the applied magnetic field.
Model and magnetic configuration effect on shock
layer enhancement by an applied magnetic field
Physics of Fluids, Vol. 20, 027102(2008)
Spherical blunt model
Flat-faced model
The magnetic flux density at the stagnation point
had the same strength for the two cases.
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Magnetic Field Distribution
In the case of relatively large magnet (Rmag0.8)
Blunt body with small radius of curvature
Blunt body with large radius of curvature
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Magnetic Field Distribution
In the case of relatively small magnet (Rmag0.4)
Blunt body with large radius of curvature
Blunt body with small radius of curvature
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Relations Between Maximum Wall Heat Flux and
Magnet Outer Radius (Altitude 63 km)
Freestream condition Pressure 14.0
Pa Temperature 237.1 K Velocity 6.2 km/s
(Altitude 63 km)
Rratio1.00
Rratio1.67
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Relations Between Maximum Wall Heat Flux and
Magnet Outer Radius (Altitude 71 km)
Rratio1.00
Rratio1.67
Freestream condition Pressure 4.0
Pa Temperature 214.9 K Velocity 7.0 km/s
(Altitude 71 km)
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Conclusions
The present study has numerically examined
influences of magnetic distributions utilizing
air-core circular magnet on wall heat flux under
the constant magnetic energy condition in reentry
flights.

• At high altitude where the high electrical
  conductivity can be obtained all over the shock
  layer, large magnet is better than small magnet
  in order to decrease the wall heat flux, though
  the magnetic flux density of large magnet is
  weaker than that of small magnet.

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Conclusions

• At low altitude where the area with high
  electrical conductivity and strong MHD
  interaction is localized, small magnet is better
  than large magnet under the constant magnet
  energy condition.
• The effect of the body radius of curvature is
  rather small at high altitudes, compared to the
  effect at low altitudes.

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The case to increase wall heat flux(altitude 71
km, coil outer radius 0.2 m)
Flight condition Altitude 71 km Velocity 7.0
km/s
reattachment point
cyclic domain
Wall heat flux
Stream line for plasma flow
Excessively and locally strong magnetic field
generates cyclic domain.
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Previous numerical studies Relations
between drag and altitude
Future Work
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Relations between flight velocity and flight
altitude
Future Work
Externally applied magnetic field dipole magnet
We will examine influences of MHD flow control
utilizing real air-core circular magnet on the
flight trajectory and aerodynamic heating.
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Magnetic field distribution
In the case of relatively large magnet (Rmag0.8)
Blunt body with large radius of curvature
Blunt body with small radius of curvature
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Distribution of Externally Applied Magnetic Field
The present study varies the value of the
parameter B0 over a range of 0.0 to 0.5 T.
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Relations between Maximum wall heat flux
and magnet outer radius
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Distribution of Lorentz force
71km
59km
12000
N/m3
Rmag0.6
Rmag0.6
0
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Distribution of Wall Heat Flux
(Altitude 63 km)
Freestream condition Pressure 14.0
Pa Temerature 237.1 K Velocity 6.2 km/s
(Altitude 63 km)