Model options

In this section it is described how the input file can be configured in order to specify the settings of the problem at hand. The input file must be passed as first argument to the MFIX-Exa executable.

The following inputs must be preceded by “mfix.”

	Description	Type	Default
gravity	Gravity vector (e.g., mfix.gravity = -9.81 0.0 0.0) [required]	Reals	0 0 0
advect_density	Switch for turning ON (1) or OFF (0) fluid density evolution	Int	0
advect_enthalpy	Switch for turning ON (1) or OFF (0) fluid temperature evolution	Int	0
solve_species	Switch for turning ON (1) or OFF (0) fluid species mass fraction evolution	Int	0
constraint_type	Select which constraint to apply to the problem. Available options include: ‘incompressiblefluid’ for incompressibility constraint ‘idealgasopensystem’ for Ideal Gas-Open System constraint ‘idealgasclosedsystem’ for Ideal Gas-Closed System constraint	String	IncompressibleFluid

Fluid discretization

The following inputs must be preceded by “mfix.”

Key	Description	Type	Default
advection_type	Predictor-Corrector Method of Lines (“mol”) or Godunov (“godunov”)	String	Godunov
redistribution_type	Use flux (“FluxRedist”), state (“StateRedist”) or no (“NoRedist”) redistribution	String	StateRedist
redistribute_before_nodal_proj	Redistribute the velocity field before the nodal projection	Bool	True
redistribute_nodal_proj	Redistribute the velocity field after the nodal projection	Bool	False
use_drag_coeff_in_proj_gp	Algebraically consistent p coeff in proj or (default) simplified form	Bool	False
use_drag_in_godunov	Include a drag term in the Godunov flux or (default) not	Bool	False
correction_small_volfrac	Threshold volume fraction for correcting small cell velocity at the end of the predictor and corrector	Real	1.e-4

Notes: The code was originally developed with MOL and FluxRedist. Preliminary tests show that the new single-step Godunov method is roughly twice as fast as the predictor-corrector MOL at the same time step (e.g., CFL limited to 0.5). Further, the Godunov method allows for roughly twice the time step, CFL should be limited to 0.9 for stability. Finally, it is recommended that the Godunov method be used in conjunction with StateRedist. While not fully vetted, early tests also show increased stability in complex geometries for a StateRedist- Godunov scheme compared to the previous FluxRedist-MOL scheme.

Additional constraitns

Additional constraints may be imposed on problems which are under-determined by IBCs, typically occurring in periodic domains. Currently, only particle constraints are supported. The prefix particles. should be applied to all input keywords listed below.

Description

Type

Default

constraint

Constraint type. Available options include:

‘mean_velocity’

String

None

For the mean_velocity constraint, the following inputs can be defined.

	Description	Type	Default
mean_velocity_x	mean particle velocity in dir=0	Real	Undefined
mean_velocity_y	mean particle velocity in dir=1	Real	Undefined
mean_velocity_z	mean particle velocity in dir=2	Real	Undefined

Below is an example for zero mean particle velocity in all three directions.

particles.constraint = "mean_velocity"

particles.constraint.mean_velocity_x = 0.
particles.constraint.mean_velocity_y = 0.
particles.constraint.mean_velocity_z = 0.

Deposition scheme

The following inputs must be preceded by “mfix.”

Description

Type

Default

deposition_scheme

The algorithm that will be used to deposit particles quantities to the Eulerian grid. Available methods are:

‘centroid’
‘trilinear’
‘true-dpvm’ divided particle volume method
‘trilinear-dpvm-square’ dpvm with square filter

String

‘trilinear’

deposition_scale_factor

The deposition scale factor. Only applies to ‘true-dpvm’ and ‘trilinear-dpvm-square’ methods. Its value must be in the interval [0, dx/2], where dx is the cell edge size.

Real

1.0

deposition_diffusion_coeff

If a positive value is set, a diffusion equation with this diffusion coefficient is solved to smooth deposited quantities.

Real

-1.0

In the following subsections, the four possible deposition methods are briefly described and illustrated.

Centroid

In the centroid deposition scheme, particles’ quantities are deposited only to the Eulerian grid cell to which the particle’s center belongs.

Trilinear

In the trilinear deposition scheme, particles’ quantities are deposited linearly to the eight Eulerian grid cells that surround its center.

Divided Particle Volume Method (DPVM)

In the DPVM method, particles’ quantities are deposited to the Eulerian grid cells that they intersect, and the deposition weights are equal to the percentage of the particle’ volume that intersects the given cell.

../../_images/dpvm.jpg — Fig. 7 Example of dpvm deposition.

Square DPVM

In the square DPVM method, particles’ quantities are deposited to the Eulerian grid similarly to the DPVM method, but with a filter applied to the deposition scheme.

The following inputs must be preceded by “mfix.”

Key	Description	Type	Default
deposition_redist_type	Redistribute excess solids using max packing (“MaxPack”) or state (“StateRedist”) algorithms.	String	MaxPack
deposition_redist_vfrac	The threshold cell volume fraction when using “StateRedist” for deposition redistribution.	Real	0.1

Drag models

The following inputs must be preceded by “mfix.”

	Description	Type	Default
drag_type	Which drag model to use	String	None

The options currently supported in mfix are WenYu, Gidaspow, BVK2, or UserDrag.

If one of these is not specified, the code will abort with

amrex::Abort::0::"Don't know this drag type!!!

The drag models are defined in src/src_des/des_drag_K.H

If the user wishes to use their own drag model, they must

specify mfix.drag_type = UserDrag in the inputs file

provide the code in the ComputeDragUser routine in a local usr_drag.cpp file. An example can be found in tests/DEM06-x.

With the variables defined as follows:

EPg     - gas volume fraction
Mug     - gas laminar viscosity
ROpg    - gas density * EP_g
vrel    - magnitude of gas-solids relative velocity
DPM     - particle diameter of solids phase M
DPA     - average particle diameter
PHIS    - solids volume fraction of solids phases
fvelx   - x component of the fluid velocity at the particle position
fvely   - y component of the fluid velocity at the particle position
fvelz   - z component of the fluid velocity at the particle position
i, j, k - particle cell indices
pid     - particle id number

The WenYu model is defined as

 RE = (Mug > 0.0) ? DPM*vrel*ROPg/Mug : DEMParams::large_number;

if (RE <= 1000.0)
{
    C_d = (24.0/(RE+DEMParams::small_number)) * (1.0 + 0.15*std::pow(RE, 0.687));
}
else
{
    C_d = 0.44;
}

if (RE < DEMParams::eps) return 0.0;
return 0.75 * C_d * vrel * ROPg * std::pow(EPg, -2.65) / DPM;

The Gidaspow model is defined as

ROg = ROPg / EPg;

RE = (Mug > 0.0) ? DPM*vrel*ROPg/Mug : DEMParams::large_number;

// Dense phase - EPg <= 0.8
Ergun = 150.0*(1.0 - EPg)*Mug / (EPg*DPM*DPM) + 1.75*ROg*vrel/DPM;

// Dilute phase - EPg > 0.8
if (RE <= 1000.0)
{
    C_d = (24.0/(RE+DEMParams::small_number)) * (1.0 + 0.15*std::pow(RE, 0.687));
}
else
{
    C_d = 0.44;
}

WenYu = 0.75*C_d*vrel*ROPg*std::pow(EPg, -2.65) / DPM;

// switch function
PHI_gs = atan(150.0*1.75*(EPg - 0.8))/M_PI / DPM;

// blend the models
if (RE < DEMParams::eps) return 0.0;
return (1.0 - PHI_gs)*Ergun + PHI_gs*WenYu;

The BVK2 model is defined as

amrex::Real RE = (Mug > 0.0) ? DPA*vrel*ROPg/Mug : DEMParams::large_number;

if (RE > DEMParams::eps)
{
    oEPgfour = 1.0 / EPg / EPg / EPg / EPg;

    // eq(9) BVK J. fluid. Mech. 528, 2005
    // (this F_Stokes is /= of Koch_Hill by a factor of ep_g)
    F_Stokes = 18.0*Mug*EPg/DPM/DPM;

    F = 10.0*PHIS/EPg/EPg + EPg*EPg*(1.0 + 1.5*sqrt(PHIS));

    F += RE*(0.11*PHIS*(1.0+PHIS) - 4.56e-3*oEPgfour +
         std::pow(RE, -0.343)*(0.169*EPg + 6.44e-2*oEPgfour));

    // F += 0.413*RE/(24.0*EPg*EPg) *
    //     (1.0/EPg + 3.0*EPg*PHIS + 8.4/std::pow(RE, 0.343)) /
    //     (1.0 + std::pow(10.0, 3.0*PHIS)/std::pow(RE, 0.5 + 2.0*PHIS));

    return F*F_Stokes;
}
else
{
    return 0.0;
}

Heat transfer coefficients

The following inputs must be preceded by “mfix.”

	Description	Type	Default
convection_type	Which HTC model to use	String	RanzMarshall

The options currently supported in mfix are RanzMarshall (default) and Gunn. In both models the HTC is determined from a Nusslet number correlation.

The RanzMarshall Nusselt number correlation is defined as:

amrex::Real N_Nu = 2.0 + 0.6 * std::sqrt(N_Re) * std::pow(N_Pr, 0.333);

The Gunn Nusselt number correlation is defined as:

amrex::Real N_Nu =
    (7 - 10*EPg + 5*EPg*EPg)*(1 + .7*std::pow(N_Re, 0.2)*std::cbrt(N_Pr))
    + (1.33 - 2.4*EPg + 1.2*EPg*EPg)*std::pow(N_Re, 0.7)*std::cbrt(N_Pr);