# Fluid model

The following inputs are defined using the prefix `fluid`:

| Description | Type | Default
--- | --- | --- | ---
solve | Specify the name of the fluid or set to `None` to disable the fluid solver. The name assigned to the fluid solver is used to specify fluid properties and initial and boundary conditions. It is common to use the name `fluid`. | String | `None`

The root prefix for the following inputs is the name defined using the `fluid.solve` keyword. For example, if the fluid solver is named `myfluid`, then the following keywords are preceded with `myfluid` and a period. Currently, MFIX-Exa only supports a single fluid; therefore, it is common to name the fluid `fluid`. This is illustrated later in example input snippets.

| Description | Type | Default
--- | --- | --- | ---
viscosity.molecular | Specify which molecular viscosity model to use. Options: `None` - no viscosity model. `constant` - constant viscosity `Sutherland` [Sut93] - \(\mu(T) = \mu_{ref}\left(\frac{T}{T_{ref}}\right)^{3/2}\frac{T_{ref} + S}{T+S}\) `Reid` [RPP87] - \(\mu(T) = Ae^{\left(\frac{B}{T} + CT + DT^2 \right)}\) `mixture` - a mixture viscosity is computed from species viscosities and local species mass fractions [BSL06] \(\mu_{mix} = \sum_{\alpha=1}^{N} \frac{X_{\alpha} \mu_{\alpha}}{\sum_{\beta} X_{\beta} \phi_{\alpha \beta}}\) A viscosity model is required if the fluid solver is enabled. | String | None
viscosity.molecular.constant | Constant fluid viscosity. A value is required for `constant` viscosity model. | Real | 0
viscosity.molecular.Sutherland.T_ref | Sutherland model reference temperature. A value is required for `Sutherland` viscosity model. | Real | 0
viscosity.molecular.Sutherland.mu_ref | Sutherland model reference viscosity at T_ref. A value is required for `Sutherland` viscosity model. | Real | 0
viscosity.molecular.Sutherland.S | Sutherland model temperature. A value is required for `Sutherland` viscosity model. | Real | 0
viscosity.molecular.Reid.A viscosity.molecular.Reid.B viscosity.molecular.Reid.C viscosity.molecular.Reid.D | Reid model constants. Values are required for `Reid` viscosity model. | Real | 0
viscosity.eddy | Specify eddy viscosity model. Options: `None` - No eddy viscosity model `Smagorinsky-Lilly` [Lil66, Sma63] `WALE` [DNP98] `usr` | String | None
viscosity.eddy.Smagorinsky-Lilly.constant | Smagorinsky-Lilly constant which usually has values between 0.1 and 0.2. A value is required when using the `Smagorinsky-Lilly` eddy viscosity model. | Real | None
viscosity.eddy.WALE.constant | WALE eddy viscosity model constant. | Real | 0.325
viscosity.suspension | Specify suspension viscosity model of the form \(\mu_{susp} = \mu_{mol}(\mu^* - 1)\) Options: `None` - No eddy suspension model \(\mu^* = 1\) `Einstein` [Ein11] \(\mu^* = 1 + 2.5\varepsilon_s\) `Brinkman` [Bri52, GLGP07] \(\mu^* = (1-\varepsilon_s)^{-c}\) `Roscoe` [KD59, MP56, Ros52] \(\mu^* = (1-\varepsilon_s/c_1)^{-c_2}\) `ChengLaw` [CL03] \(\mu^* = e^{2.5(1/(1-\varepsilon_s)^c-1)/c}\) `Sato` [SS81] \(\mu_{pit} = C d_s \rho \left|\boldsymbol{u} - \boldsymbol{u_s}\right|\) `Subramaniam` [MTGS15] \(\mu_{pit} = C_\mu k_f^2 / \epsilon_f\) | String | None
viscosity.suspension.Brinkman.constant | Constant for exponent in Brinkman suspension expression. A value is required when using the `Brinkman` model. | Real | None
viscosity.suspension.Roscoe.c1 | Constant for max packing in Roscoe suspension expression. A value is required when using the `Roscoe` model. | Real | None
viscosity.suspension.Roscoe.c2 | Constant for exponent in Roscoe suspension expression. A value is required when using the `Roscoe` model. | Real | None
viscosity.suspension.ChengLaw.constant | Constant for exponent in ChengLaw suspension expression. A value is required when using the `ChengLaw` model. | Real | None
viscosity.suspension.Sato.constant | Constant for Sato suspension expression. | Real | 0.65
viscosity.suspension.Subramaniam.constant | Constant for Subramaniam suspension expression. | Real | 0.09
viscosity.max_effective_factor | Max limit of the effective viscosity as a factor of the molecular viscosity \(\mu_{eff} < fac*\mu_{mol}\), where \(\mu_{eff} = \mu_{mol} + \mu_{eddy} + \mu_{susp} + \mu_{pit}\) | Real | 1.e6
species | Specify the species that constitute the fluid. All listed species must be properly defined. See the species definition documentation for additional details. | String | None
molecular_weight | Constant fluid molecular weight. A molecular weight should only be defined when using one of the ideal gas constraints and the species equations are not solved. | Real | 0
specific_heat | Specify which specific heat model to use for the fluid. Options: `constant` - the fluid has a constant specific heat `NASA7-poly` the fluid specific heat is defined by NASA-7 polynomials. NASA7 polynomial format: \(c_p(T)/R = \sum_{i=0}^4 a_{i}T^{i}\) Additional information on NASA-7 polynomials is provided in species specific heats. `mixture` - a mixture specific heat is computed from species specific heats and local species mass fractions. \(c_{p,\mathrm{mixture}} = \sum_n X_n c_{p,n}\) A specific heat model is required if advecting enthalpy. Furthermore, the model must be `mixture` if species equations are solved. | String | None
specific_heat.constant | Constant fluid specific heat A value is required for `constant` specific heat model. | Real | 0
specific_heat.NASA7.a[i] | Specific heat polynomial coefficients. Polynomial coefficients are required if the fluid specific heat model is `NASA7-poly`. Additional information on NASA-7 polynomials is provided in species specific heats. | Real | None
thermal_conductivity | Specify which thermal conductivity model to use for fluid. Options: `constant` - the fluid has a constant thermal conductivity model A thermal conductivity model is required if advecting enthalpy. | String | None
thermal_conductivity.constant | Constant fluid thermal conductivity. A value is required for `constant` thermal conductivity model. | Real | 0
thermodynamic_pressure | Thermodynamic pressure. A value is required when using the `IdealGasClosedSystem` constraint. If using the `IdealGasOpenSystem` constraint, then the value must match all specified outflow pressures. | Real | 0
reference_temperature | Reference temperature used to compute specific enthalpy | Real |

## Example inputs

### Incompressible fluid

The following setup shows how to define the most basic fluid model where the only required physical property is fluid viscosity. We are using the `IncompressibleFluid` constraint; therefore, the constant fluid density is defined by the initial and boundary conditions. The fluid energy and species equations are not solved.

Listing 5 Snippet of inputs defining a simple incompressible fluid. This is not a complete input file.

    mfix.constraint = IncompressibleFluid

    mfix.advect_density  = 0
    mfix.advect_enthalpy = 0
    mfix.solve_species   = 0

    # Fluid model settings
    # -----------------------------------------------------------------------
    fluid.solve = fluid0

    fluid0.viscosity.molecular = constant
    fluid0.viscosity.molecular.constant = 1.8e-5

    # Initial Conditions
    # -----------------------------------------------------------------------
    ic.regions = full-domain

    ic.full-domain.fluid0.volfrac   =  1.0
    ic.full-domain.fluid0.density   =  1.0

    ic.full-domain.fluid0.velocity  =  0.0  0.0  0.0

    # Boundary Conditions
    # -----------------------------------------------------------------------
    bc.regions = inlet  outlet

    bc.inlet = mi
    bc.inlet.fluid0.volfrac  =  1.0
    bc.inlet.fluid0.density  =  1.0

    bc.inlet.fluid0.velocity =  1.0e-8  0.0  0.0

    bc.outlet = po
    bc.outlet.fluid0.pressure =  0.

### Simple ideal gas

In the following example, we use the `IdealGasOpenSystem` so that the fluid density is calculated from the ideal gas equation of state. In addition to viscosity, we must also provide the fluid molecular weight. The fluid energy and species equations are not solved, but the constant fluid temperature is required in the initial and boundary conditions to fully specify the equation of state. Lastly, the outflow boundary pressure is taken as the thermodynamic pressure when evaluating the equation of state.

Listing 6 Snippet of inputs defining a simple ideal gas. This is not a complete input file.

    mfix.constraint = IdealGasOpenSystem

    mfix.advect_density  = 1
    mfix.advect_enthalpy = 0
    mfix.solve_species   = 0

    # Fluid model settings
    # -----------------------------------------------------------------------
    fluid.solve = fluid0

    fluid0.viscosity.molecular = constant
    fluid0.viscosity.molecular.constant = 1.8e-5

    fluid0.molecular_weight = 29.0e-3

    # Initial Conditions
    # -----------------------------------------------------------------------
    ic.regions = full-domain

    ic.full-domain.fluid0.volfrac   =  1.0

    ic.full-domain.fluid0.velocity  =  0.0  0.0  0.0

    ic.full-domain.fluid0.temperature = 300.0

    # Boundary Conditions
    # -----------------------------------------------------------------------
    bc.regions = inlet  outlet

    bc.inlet = mi
    bc.inlet.fluid0.volfrac  =  1.0

    bc.inlet.fluid0.velocity =  1.0e-8  0.0  0.0

    bc.inlet.fluid0.temperature = 300.0

    bc.outlet = po
    bc.outlet.fluid0.pressure =  101325.

### Ideal gas with energy

In the last example, we use the `IdealGasOpenSystem`, however unlike the previous demonstration, the energy equation is solved. Therefore, we must define the fluid viscosity, molecular weight, thermal conductivity, and specific heat. Again, the fluid temperature is required in the initial and boundary conditions, and the outflow boundary pressure is taken as the thermodynamic pressure for the system.

Listing 7 Snippet of inputs defining an idea gas with energy. This is not a complete input file.

    mfix.constraint = IdealGasOpenSystem

    mfix.advect_density  = 1
    mfix.advect_enthalpy = 1
    mfix.solve_species   = 0

    # Fluid model settings
    # -----------------------------------------------------------------------
    fluid.solve = fluid0

    fluid0.viscosity.molecular = constant
    fluid0.viscosity.molecular.constant = 2.0e-5

    fluid0.thermal_conductivity = constant
    fluid0.thermal_conductivity.constant = 0.026

    fluid0.molecular_weight = 28.96518e-3

    fluid0.specific_heat = NASA7-poly

    fluid0.specific_heat.NASA7.a0 =  5.95960930E+00   3.08792717E+00
    fluid0.specific_heat.NASA7.a1 =  3.56839620E+00   1.24597184E-03
    fluid0.specific_heat.NASA7.a2 = -6.78729429E-04  -4.23718945E-07
    fluid0.specific_heat.NASA7.a3 =  1.55371476E-06   6.74774789E-11
    fluid0.specific_heat.NASA7.a4 = -3.29937060E-12  -3.97076972E-15
    fluid0.specific_heat.NASA7.a5 = -4.66395387E-13  -9.95262755E+02

    # Initial Conditions
    # -----------------------------------------------------------------------
    ic.regions = full-domain

    ic.full-domain.fluid0.volfrac   =  1.0

    ic.full-domain.fluid0.velocity  =  0.0  0.0  0.0

    ic.full-domain.fluid0.temperature = 300.0

    # Boundary Conditions
    # -----------------------------------------------------------------------
    bc.regions = inlet  outlet

    bc.inlet = mi
    bc.inlet.fluid0.volfrac  =  1.0

    bc.inlet.fluid0.velocity =  1.0e-8  0.0  0.0

    bc.inlet.fluid0.temperature = 300.0

    bc.outlet = po
    bc.outlet.fluid0.pressure =  101325.

The following inputs are defined using the prefix `fluid` and control the convergence criteria of the damped Newton solver used to compute temperature from enthalpy and specific heat.

| Description | Type | Default
--- | --- | --- | ---
newton_solver.absolute_tol | Define absolute tolerance for the Newton solver | Real | 1.e-8
newton_solver.relative_tol | Define relative tolerance for the Newton solver | Real | 1.e-8
newton_solver.max_iterations | Define max number of iterations for the Newton solver | Int | 500