Wind-US User's Guide - Keyword Reference, MFD

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MFD - Magneto-Fluid Dynamics Model (block)

Structured Grids

MFD [OUTPUT {BFIELD | CONDUCTIVITY | CURRENT | EFIELD | VOLTAGE | LORENTZ}] [RELAX_MFD nriter] [UPDATE nuiter] [RADIATION emiss lref [tback]] {LORENTZ FILE FREQUENCY f [DUTY du] [SCALE sc] \ PHASES n PATTERNS p1 p2 p3 ... pn | {CONDUCTIVITY | SIGMA} {CONSTANT sigma | \ CFL | \ EQUILIBRIUM {ARGON | AIR | GAS} \ [POTASSIUM mk] | \ LINEAR t1 sig1 t2 sig2 | \ PREDICTED [USING] [LIN-RESSLER | BOEING]} BFIELD {CONSTANT bz | BLOCKS nbblocks | CFL} {EFIELD {CONSTANT ey | BLOCKS neblocks | CFL} | \ VOLTAGE {BOUNDARIES nvbnd | CFL | \ PARAMETERS mitvlt vlttol vltrx vltry vltrz vltfac} } | EXTERNAL [INPUT] [MODE] PEM } ENDMFD

The MFD keyword block allows the user to specify the magneto-fluid dynamics mode and input data for the desired forms of the magnetic and electric fields, the electrical conductivity, output variables, and approximate radiation energy losses. This capability is only available for structured grids.

Control Functions

MFD

Defines the beginning of the MFD block.

ENDMFD

Defines the end of the MFD block.

OUTPUT {BFIELD | CONDUCTIVITY | CURRENT | EFIELD | VOLTAGE | LORENTZ}

The specified data will be written into into the flow (.cfl) file. Multiple OUTPUT keywords may be specified, to write multiple types of data into the .cfl file.

RELAX_MFD nriter

The MFD source terms will be relaxed over nriter iterations. The default for nriter is 1.

UPDATE nuiter

The MFD source terms will be updated every nuiter Navier-Stokes iterations. The default for nuiter is 1.

RADIATION emiss lref [tback]

Estimate the energy loss due to thermal radiation of the fluid with emissivity emiss, optical depth lref, and background temperature tback (°R). The default for tback is the freestream static temperature.

Body Force Determination

The body force resulting from the MFD terms can be added in one of three ways: (1) by directly specifying the Lorentz force; (2) by specifying the conductivity, the magnetic field, and either the electric field or voltage; or (3) by reading the data from the .cfl file, stored there using an external solver.

Specifying the Lorentz Force

The following keyword is used to directly specify the Lorentz force. If this method is used, the CONDUCTIVITY, BFIELD, EFIELD, VOLTAGE, and EXTERNAL keywords are not allowed.

LORENTZ FILE FREQUENCY f [DUTY du] [SCALE sc] \ PHASES n PATTERNS p1 p2 p3 ... pn

nl Lorentz force distributions are stored in a .cem file named FOR015. This distribution is spread over space depending upon the phasing patterns. The pattern changes n times during a cycle.

FREQUENCY f Number of cycles/second
DUTY du Force is on the first du portion of a phase. The default value is 1.0.
SCALE sc Multiply the Lorentz force by sc before adding it to the equations. The default value is 1.0.
PHASES n Number of pattern phases in a cycle
PATTERNS p1 p2 p3 ... pn The Lorentz force distribution to use in each phase. Must correspond to the nl distributions stored in the .cem file.

Specifying the MFD Fields

If the MFD fields are being specified, you must use the CONDUCTIVITY and BFIELD keywords to specify the conductivity and the magnetic field, and either the EFIELD or VOLTAGE keywords to specify the electric field or voltage.

{CONDUCTIVITY | SIGMA} {CONSTANT sigma | \ CFL | \ EQUILIBRIUM {ARGON | AIR | GAS} [POTASSIUM mk] | \ LINEAR t1 sig1 t2 sig2 | \ PREDICTED [USING] [LIN-RESSLER | BOEING]}

This keyword specifies the electrical conductivity in mhos/meter.

    CONSTANT sigma    Hold the conductivity constant at the value sigma
CFL Read the conductivity from the flow (.cfl) file
EQUILIBRIUM {ARGON | AIR | GAS} [POTASSIUM mk]
    Estimate the electron density as a function of temperature for the indicated gas as input to the Lin & Ressler conductivity model. The default gas is air. If POTASSIUM mk is specified, the effect of the mass fraction mk of potassium will be included.
LINEAR t1 sig1 t2 sig2 Set the conductivity to sig1 at and below the temperature t1; to sig2 at and above the temperature t2; and use a linear distribution for temperatures between t1 and t2. The temperatures are in °R.
PREDICTED [USING] [LIN-RESSLER | BOEING]
    Use real-gas predicted electron densities for input to the indicated conductivity model. The default is the Lin & Ressler model.

BFIELD {CONSTANT bz | BLOCKS nbblocks | CFL}

This keyword specifies the magnetic field in tesla.

CONSTANT bz Hold the magnetic field constant at the value bz, in the z coordinate direction
BLOCKS nbblocks Specify the magnetic field by reading in nbblocks blocks of data containing the magnetic field vector at selected coordinate points. The data immediately follows the BFIELD BLOCKS keyword. See the Field Block Description for details and an example.
CFL Read the magnetic field from the flow (.cfl) file

EFIELD {CONSTANT ey | BLOCKS neblocks | CFL}

This keyword specifies the electric field in Volts/meter.

CONSTANT ey Hold the electric field constant at the value ey, in the y coordinate direction
BLOCKS neblocks Specify the electric field by reading in neblocks blocks of data containing the electric field vector at selected coordinate points. The data immediately follows the EFIELD BLOCKS keyword. See the Field Block Description for details and an example.
CFL Read the electric field from the flow (.cfl) file

VOLTAGE {BOUNDARIES nvbnd | CFL | \ PARAMETERS mitvlt vlttol vltrx vltry vltrz vltfac}

With this keyword the electric field is determined by specifying the electric potential.

BOUNDARIES nvbnd Specify the electric potential at nvbnd zonal boundary regions. The data immediately follows the VOLTAGE BOUNDARIES keyword. See the Voltage Boundary Description for details and an example.
CFL Read the electric potential field from the flow (.cfl) file
PARAMETERS mitvlt vlttol vltrx vltry vltrz vltfac
Iterate a maximum of mitvlt iterations (the default is 10,000) to a tolerance of vlttol (a positive value means to a level of vlttol, a negative value means |vlttol| orders of magnitude; the default is a level of 10⁻¹²) with implicit factors vltrx, vltry, and vltrz (currently these must all be set to 0.0) and with an over-relaxation factor of vltfac (a typical value is 0.4).

Using an External Solver

EXTERNAL [INPUT] [MODE] PEM

This keyword indicates that the MFD fields have been computed using external solver, and should be read from the .cfl file.

Field Block Description

By using the BFIELD BLOCKS and/or EFIELD BLOCKS keywords, the magnetic and/or electric field may be determined from blocks containing the field vector at selected coordinate points. Each block consists of eight points in space, with the corresponding field vector at each of those points. The region contained within the blocks is filled using tri-linear interpolation between the specified points. Up to eight blocks may be specified for each field type. The spatial locations of the blocks may overlap, with the later-specified blocks overwriting the earlier ones.

There are eight lines of input per block, one for each of the eight coordinate points. Each line contains six values - the x, y, and z coordinates, and the field vector components in the x, y, and z directions.

The following example specifies the magnetic field using two blocks. (The comments in a slanted font are not part of the input.)

   BFIELD BLOCKS 2
       60.0    0.0   0.0    0.0   0.0   0.0   Upstream plane of block 1
       60.0   20.0   0.0    0.0   0.0   0.0
       60.0    0.0   1.0    0.0   0.0   0.0
       60.0   20.0   1.0    0.0   0.0   0.0
      120.0    0.0   0.0    0.0   0.0  10.0   Downstream plane of block 1
      120.0   20.0   0.0    0.0   0.0   5.0
      120.0    0.0   1.0    0.0   0.0  10.0
      120.0   20.0   1.0    0.0   0.0   5.0
      120.0    0.0   0.0    0.0   0.0  10.0   Upstream plane of block 2
      120.0   20.0   0.0    0.0   0.0   5.0      (same as downstream of 1)
      120.0    0.0   1.0    0.0   0.0  10.0
      120.0   20.0   1.0    0.0   0.0   5.0
      180.0    0.0   0.0    0.0   0.0   0.0   Downstream plane of block 2
      180.0   20.0   0.0    0.0   0.0   0.0
      180.0    0.0   1.0    0.0   0.0   0.0
      180.0   20.0   1.0    0.0   0.0   0.0

        x      y     z       B_x    B_y    B_z

Voltage Boundary Description

Voltage boundaries are used to specify the boundary conditions at zone boundaries for the electric potential solver. The electric potential solver will take into account gradients and discontinuities in conductivity, as well as the electromotive force (EMF) induced by the fluid motion through the magnetic field. Currently, accurate voltage predictions require a grid with low skewness.

Up to 64 boundaries may be specified. The conditions at each boundary are specified on a single line, with eight values - zone, face, type, L1, L2, M1, M2, value - defined as follows:

    zone    Zone containing the boundary
face The boundary face, specified as a number from 1 to 6 corresponding to the i₁, i_max, j₁, j_max, k₁, and k_max face, respectively
type The boundary type, specified as 0 for a reflection boundary, and 1 for specified voltage
L1, L2, M1, M2 The indices on the face over which the boundary condition applies, as follows

    Face     Indices
    i₁ or i_max    j_low, j_high, k_low, k_high
j₁ or j_max    k_low, k_high, i_low, i_high
k₁ or k_max    i_low, i_high, j_low, j_high

value The voltage for specified-voltage boundaries; 0.0 for reflection boundaries

The following example specifies eight voltage boundaries. (The comments in a slanted font are not part of the input.)

   VOLTAGE BOUNDARIES 8
      1     1     0     1   30    1    1       0.0
      1     1     1    31   61    1    1       0.0
      1     2     1     1   31    1    1   10000.0
      1     2     0    32   61    1    1       0.0
      1     3     0     1    1    1   30       0.0
      1     3     1     1    1   31   61   10000.0
      1     4     1     1    1    1   31       0.0
      1     4     0     1    1   32   61       0.0

    Zone  Face  Type   L1   L2   M1   M2     Value

	`FREQUENCY f`		Number of cycles/second
	`DUTY du`		Force is on the first du portion of a phase. The default value is 1.0.
	`SCALE sc`		Multiply the Lorentz force by sc before adding it to the equations. The default value is 1.0.
	`PHASES n`		Number of pattern phases in a cycle
	`PATTERNS p1 p2 p3 ... pn`		The Lorentz force distribution to use in each phase. Must correspond to the nl distributions stored in the .cem file.

	`CONSTANT sigma`		Hold the conductivity constant at the value sigma
	`CFL`		Read the conductivity from the flow (.cfl) file
	`EQUILIBRIUM {ARGON \| AIR \| GAS} [POTASSIUM mk]`
			Estimate the electron density as a function of temperature for the indicated gas as input to the Lin & Ressler conductivity model. The default gas is air. If `POTASSIUM` mk is specified, the effect of the mass fraction mk of potassium will be included.
	`LINEAR t1 sig1 t2 sig2`		Set the conductivity to sig1 at and below the temperature t1; to sig2 at and above the temperature t2; and use a linear distribution for temperatures between t1 and t2. The temperatures are in °R.
	`PREDICTED [USING] [LIN-RESSLER \| BOEING]`
			Use real-gas predicted electron densities for input to the indicated conductivity model. The default is the Lin & Ressler model.

	`CONSTANT bz`		Hold the magnetic field constant at the value bz, in the z coordinate direction
	`BLOCKS nbblocks`		Specify the magnetic field by reading in nbblocks blocks of data containing the magnetic field vector at selected coordinate points. The data immediately follows the `BFIELD BLOCKS` keyword. See the Field Block Description for details and an example.
	`CFL`		Read the magnetic field from the flow (.cfl) file

	`CONSTANT ey`		Hold the electric field constant at the value ey, in the y coordinate direction
	`BLOCKS neblocks`		Specify the electric field by reading in neblocks blocks of data containing the electric field vector at selected coordinate points. The data immediately follows the `EFIELD BLOCKS` keyword. See the Field Block Description for details and an example.
	`CFL`		Read the electric field from the flow (.cfl) file

	`BOUNDARIES nvbnd`		Specify the electric potential at nvbnd zonal boundary regions. The data immediately follows the `VOLTAGE BOUNDARIES` keyword. See the Voltage Boundary Description for details and an example.
	`CFL`		Read the electric potential field from the flow (.cfl) file
	`PARAMETERS mitvlt vlttol vltrx vltry vltrz vltfac`
			Iterate a maximum of mitvlt iterations (the default is 10,000) to a tolerance of vlttol (a positive value means to a level of vlttol, a negative value means \|vlttol\| orders of magnitude; the default is a level of 10⁻¹²) with implicit factors vltrx, vltry, and vltrz (currently these must all be set to 0.0) and with an over-relaxation factor of vltfac (a typical value is 0.4).