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

The MFD keyword block allows the user to include body force source terms in the Navier-Stokes equations resulting from magneto-fluid dynamics effects. 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 (i.e., magnetic field, conductivity, current density, electric field, voltage, or Lorentz force) 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. When VOLTAGE BOUNDARIES is specified (see below), the current density, electric field, and voltage are automatically written into the .cfl file.

RELAX_MFD nriter

The MFD source terms in the Navier-Stokes equations will be relaxed over nriter iterations. The default for nriter is 1.

UPDATE nuiter

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

If VOLTAGE BOUNDARIES is used, nuiter must be 1 (the default). In this case, consider running a few iterations with VOLTAGE BOUNDARIES to compute the electric field, then restarting using EFIELD CFL instead of VOLTAGE BOUNDARIES.

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 forces 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 {CFL | FORCE FREQUENCY f [DUTY du] [SCALE sc] \ PHASES n PATTERNS p₁ p₂ ... p_n

	`CFL`		Read the Lorentz force field directly from the flow (.cfl) file
	`FORCE`		N_L Lorentz force distributions are stored in the flow (.cfl) file, defining a time-dependent cyclical force field. For each distribution the variable names for the Lorentz force components are `Lxi`, `Lyi`, and `Lzi`, where i varies from 1 to N_L. The appropriate distribution is read and used, based on the current integrated time and the specified phasing information, then scaled and applied.
	`FREQUENCY f`		Number of cycles/second for the Lorentz force field
	`DUTY du`		Fraction of each phase in which the Lorentz force will be applied. The default value is 1.0.
	`SCALE sc`		Scale factor. The Lorentz force will be multiplied 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 ... p_n`		The Lorentz force distribution to use in each phase. A total of n values must be specified, where n is the number of pattern phases specified with `PHASES`. For each phase, the value p_i is an integer, from 1 to N_L, defining the particular force distribution from the .cfl file to be applied for that phase.

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 {CFL | \ CONSTANT sigma | \ 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. [The keyword SIGMA may be used as an alias for CONDUCTIVITY.]

	`CFL`		Read the conductivity from the flow (.cfl) file
	`CONSTANT sigma`		Hold the conductivity constant at the value sigma
	`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 {CFL | CONSTANT bz | BLOCKS nbblocks}

This keyword specifies the magnetic field in tesla.

	`CFL`		Read the magnetic field from the flow (.cfl) file
	`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.

EFIELD {CFL | CONSTANT ey | BLOCKS neblocks}

This keyword specifies the electric field in Volts/meter.

	`CFL`		Read the electric 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.

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

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

	`CFL`		Read the electric potential 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.
	`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 (the default values are 1.0, but currently these must all be set to 0.0) and with an over-relaxation factor of vltfac (the default is 1.0, but a more typical value is 0.4).

Note that when VOLTAGE BOUNDARIES is specified, you must also use (separately) VOLTAGE PARAMETERS to specify the iteration controls for solution of the electric potential equation, even though they have default values. That's because the defaults for vltrx, vltry, and vltrz are all 1.0, but only 0.0 is currently allowed.

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       Bx    By    Bz

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

Last updated 17 Feb 2009