Navier Stokes Fluid Heat Transfer / WCNSFVFluidHeatTransferPhysics

Define the Navier Stokes weakly-compressible energy equation

Equation

This Physics object creates the kernels and boundary conditions to solve the advection-diffusion equation for the fluid temperature. For free flow in a non-porous media:

var element = document.getElementById("moose-equation-6f1c64e2-7638-424a-8d64-fb94107c0463");katex.render("\\dfrac{\\partial \\rho h}{\\partial t} + \\nabla \\cdot (\\rho h \\mathbf{v}) - \\nabla \\cdot (k_f \\nabla T_f) - Q + \\alpha (T_f - T_{ambient}) = 0", element, {displayMode:true,throwOnError:false});

For flow in a porous medium:

var element = document.getElementById("moose-equation-2e51a7cc-e5a3-4577-899d-5e5f0285241f");katex.render("\\dfrac{\\partial \\epsilon \\rho h}{\\partial t} + \\nabla \\cdot (\\rho h \\mathbf{v}_D) - \\nabla \\cdot (k_f \\nabla T_f) - Q + \\alpha (T_f - T_{ambient}) = 0", element, {displayMode:true,throwOnError:false});

where:

$var element = document.getElementById("moose-equation-1e905319-3045-4ad7-ab08-e207caf78b5c");katex.render("h", element, {displayMode:false,throwOnError:false});$ is the fluid enthalpy, computed from the specific heat $var element = document.getElementById("moose-equation-f64b2464-5e11-49b1-8f87-eda40b744173");katex.render("c_p", element, {displayMode:false,throwOnError:false});$
$var element = document.getElementById("moose-equation-26b6066c-ba7f-406b-af30-091e6993de19");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ is the fluid density
$var element = document.getElementById("moose-equation-d0568ce7-e78d-4237-8f07-c9af7c67d3aa");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false});$ is the porosity
$var element = document.getElementById("moose-equation-b2911071-b85b-408c-8ca3-a9427ecc72c0");katex.render("T_f", element, {displayMode:false,throwOnError:false});$ is the fluid temperature
$var element = document.getElementById("moose-equation-bac87b31-5215-466f-877a-37f1409008c8");katex.render("\\mathbf{v}", element, {displayMode:false,throwOnError:false});$ is the advecting velocity (clean flow)
$var element = document.getElementById("moose-equation-4041c829-fddf-40a0-9ee7-529ef246b1a4");katex.render("\\mathbf{v}_D", element, {displayMode:false,throwOnError:false});$ is the advecting superficial velocity (porous media flow)
$var element = document.getElementById("moose-equation-5de939f0-c8d1-40cb-abab-139a0029beec");katex.render("\\kappa_f", element, {displayMode:false,throwOnError:false});$ the fluid effective thermal conductivity
$var element = document.getElementById("moose-equation-1cd3f4d2-01d5-43fe-be1a-87946fbc8704");katex.render("Q", element, {displayMode:false,throwOnError:false});$ is the source term, corresponding to energy deposited directly in the fluid
$var element = document.getElementById("moose-equation-771d4a9b-dcd1-455a-bc27-0c7244d60870");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ is the ambient convection volumetric heat transfer coefficient
$var element = document.getElementById("moose-equation-f86e753a-c01d-4c19-9109-6553e5e7f349");katex.render("T_{ambient}", element, {displayMode:false,throwOnError:false});$ is the ambient temperature

The enthalpy is used in lieu of $var element = document.getElementById("moose-equation-a3e6ddcd-db77-4136-9329-a093bb2310e0");katex.render("\\rho c_p T", element, {displayMode:false,throwOnError:false});$ to be able to model gases with temperature dependent specific heat.

The kernels created for flow in a non-porous medium are:

INSFVEnergyTimeDerivative for the time derivative for incompressible flow a transient solve
WCNSFVEnergyTimeDerivative for the time derivative for weakly-compressible flow a transient solve
INSFVEnergyAdvection for advection
FVDiffusion for diffusion
FVCoupledForce for the energy source term
PINSFVEnergyAmbientConvection for the volumetric ambient convection term, if present

For flow in a porous medium:

PINSFVEnergyTimeDerivative for the time derivative in a transient solve
PINSFVEnergyAdvection for energy advection
PINSFVEnergyDiffusion for energy diffusion with an isotropic thermal diffusivity
PINSFVEnergyAnisotropicDiffusion for energy diffusion with an anisotropic thermal diffusivity
FVCoupledForce for the energy source term
PINSFVEnergyAmbientConvection for the volumetric ambient convection term, if present

note

Additional details on porous media flow equations can be found on this page.

Automatically defined variables

The WCNSFVFluidHeatTransferPhysics automatically sets up the variables which are necessary for solving the energy transport equation:

Fluid temperature:
```
static const std::string T_fluid = "T_fluid";
```
(moose/modules/navier_stokes/include/base/NS.h)

For the default names of other variables used in this action, visit this site.

Coupling with other Physics

The heat advection equation can be solved concurrently with the flow equations by combining both the Navier Stokes Fluid Heat Transfer / WCNSFVFluidHeatTransferPhysics and the Navier Stokes Flow / WCNSFVFlowPhysics. The following input performs this coupling for incompressible flow in a 2D channel. No system parameters are passed, so the equations are solved in a fully coupled manner in the same nonlinear system.

[Physics<<<{"href": "../../syntax/Physics/index.html"}>>>]
  [NavierStokes<<<{"href": "../../syntax/Physics/NavierStokes/index.html"}>>>]
    [Flow<<<{"href": "../../syntax/Physics/NavierStokes/Flow/index.html"}>>>]
      [flow]
        compressibility<<<{"description": "Compressibility constraint for the Navier-Stokes equations."}>>> = 'incompressible'

        density<<<{"description": "The name of the density. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'rho'
        dynamic_viscosity<<<{"description": "The name of the dynamic viscosity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'mu'

        initial_velocity<<<{"description": "The initial velocity, assumed constant everywhere"}>>> = '${u_inlet} 1e-12 0'
        initial_pressure<<<{"description": "The initial pressure, assumed constant everywhere"}>>> = 0.0

        inlet_boundaries<<<{"description": "Names of inlet boundaries"}>>> = 'left'
        momentum_inlet_types<<<{"description": "Types of inlet boundaries for the momentum equation."}>>> = 'fixed-velocity'
        momentum_inlet_function = '${u_inlet} 0'
        wall_boundaries<<<{"description": "Names of wall boundaries"}>>> = 'bottom top'
        momentum_wall_types<<<{"description": "Types of wall boundaries for the momentum equation"}>>> = 'symmetry noslip'

        outlet_boundaries<<<{"description": "Names of outlet boundaries"}>>> = 'right'
        momentum_outlet_types<<<{"description": "Types of outlet boundaries for the momentum equation"}>>> = 'fixed-pressure-zero-gradient'
        pressure_function = '${p_outlet}'

        mass_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating density, as an advected quantity, to the face."}>>> = 'average'
        momentum_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating momentum/velocity, as an advected quantity, to the face."}>>> = 'average'
      []
    []

    [FluidHeatTransfer<<<{"href": "../../syntax/Physics/NavierStokes/FluidHeatTransfer/index.html"}>>>]
      [heat]
        thermal_conductivity<<<{"description": "The name of the fluid thermal conductivity for each block. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'k'
        specific_heat<<<{"description": "The name of the specific heat. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'cp'

        fluid_temperature_variable<<<{"description": "Name of the fluid temperature variable"}>>> = 'T_fluid'
        initial_temperature<<<{"description": "The initial temperature, assumed constant everywhere"}>>> = '${T_inlet}'
        energy_inlet_types<<<{"description": "Types for the inlet boundaries for the energy equation."}>>> = 'heatflux'
        energy_inlet_functors<<<{"description": "Functions for fixed-value boundaries in the energy equation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = '${fparse u_inlet * rho * cp * T_inlet}'

        energy_wall_types<<<{"description": "Types for the wall boundaries for the energy equation."}>>> = 'heatflux heatflux'
        energy_wall_functors<<<{"description": "Functions for Dirichlet/Neumann boundaries in the energy equation. For wall types requiring multiple functions, the syntax is <function_1>:<function_2>:... So, 'convection' types are '<Tinf_function>:<htc_function>'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = '0 0'

        ambient_convection_alpha<<<{"description": "The heat exchange coefficients for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'h_cv'
        ambient_temperature<<<{"description": "The ambient temperature for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number."}>>> = 'T_solid'

        energy_advection_interpolation<<<{"description": "The numerical scheme to use for interpolating energy/temperature, as an advected quantity, to the face."}>>> = 'average'
      []
    []
  []
[]

Input Parameters

add_energy_equationFalseWhether to add the energy equation. This parameter is not necessary if using the Physics syntax
Default:False
C++ Type:bool
Controllable:No
Description:Whether to add the energy equation. This parameter is not necessary if using the Physics syntax
blockBlocks (subdomains) that this Physics is active on.
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:Blocks (subdomains) that this Physics is active on.
effective_conductivityTrueWhether the conductivity should be multiplied by porosity, or whether the provided conductivity is an effective conductivity taking porosity effects into account
Default:True
C++ Type:bool
Controllable:No
Description:Whether the conductivity should be multiplied by porosity, or whether the provided conductivity is an effective conductivity taking porosity effects into account
energy_wall_boundariesWall boundaries to apply energy boundary conditions on. If not specified, the flow equation Physics wall boundaries will be used
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Wall boundaries to apply energy boundary conditions on. If not specified, the flow equation Physics wall boundaries will be used
fluid_temperature_variableT_fluidName of the fluid temperature variable
Default:T_fluid
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:Name of the fluid temperature variable
initial_enthalpyInitial value of the enthalpy variable, only to be used when solving for enthalpy
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Initial value of the enthalpy variable, only to be used when solving for enthalpy
initial_temperature300The initial temperature, assumed constant everywhere
Default:300
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The initial temperature, assumed constant everywhere
solve_for_enthalpyFalseWhether to solve for the enthalpy or the temperature of the fluid
Default:False
C++ Type:bool
Controllable:No
Description:Whether to solve for the enthalpy or the temperature of the fluid
system_namesnl0 Name of the solver system(s) for the variables. If a single name is specified, that system is used for all solver variables.
Default:nl0
C++ Type:std::vector<SolverSystemName>
Controllable:No
Description:Name of the solver system(s) for the variables. If a single name is specified, that system is used for all solver variables.
transientsame_as_problemWhether the physics is to be solved as a transient
Default:same_as_problem
C++ Type:MooseEnum
Options:true, false, same_as_problem
Controllable:No
Description:Whether the physics is to be solved as a transient
verboseFalseFlag to facilitate debugging a Physics
Default:False
C++ Type:bool
Controllable:No
Description:Flag to facilitate debugging a Physics

Optional Parameters

active__all__ If specified only the blocks named will be visited and made active
Default:__all__
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified only the blocks named will be visited and made active
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
define_variablesTrueWhether to define variables if the variables with the specified names do not exist. Note that if the variables are defined externally from the Physics, the initial conditions will not be created in the Physics either.
Default:True
C++ Type:bool
Controllable:No
Description:Whether to define variables if the variables with the specified names do not exist. Note that if the variables are defined externally from the Physics, the initial conditions will not be created in the Physics either.
ghost_layers2Number of layers of elements to ghost near process domain boundaries
Default:2
C++ Type:unsigned short
Controllable:No
Description:Number of layers of elements to ghost near process domain boundaries
inactiveIf specified blocks matching these identifiers will be skipped.
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified blocks matching these identifiers will be skipped.

Advanced Parameters

ambient_convection_alphaThe heat exchange coefficients for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:std::vector<MooseFunctorName>
Unit:(no unit assumed)
Controllable:No
Description:The heat exchange coefficients for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
ambient_convection_blocksThe blocks where the ambient convection is present.
C++ Type:std::vector<std::vector<SubdomainName>>
Controllable:No
Description:The blocks where the ambient convection is present.
ambient_temperatureThe ambient temperature for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:std::vector<MooseFunctorName>
Unit:(no unit assumed)
Controllable:No
Description:The ambient temperature for each block in 'ambient_convection_blocks'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.

Volumetric Heat Convection Parameters

coupled_flow_physicsWCNSFVFlowPhysics generating the velocities
C++ Type:PhysicsName
Controllable:No
Description:WCNSFVFlowPhysics generating the velocities
coupled_turbulence_physicsTurbulence Physics coupled with this Physics
C++ Type:PhysicsName
Controllable:No
Description:Turbulence Physics coupled with this Physics

Coupled Physics Parameters

dont_create_aux_kernelsFalseWhether to skip the 'add_aux_kernel' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_aux_kernel' task
dont_create_aux_variablesFalseWhether to skip the 'add_aux_variable' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_aux_variable' task
dont_create_bcsFalseWhether to skip the 'add_bc' task for each boundary condition type
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_bc' task for each boundary condition type
dont_create_correctorsFalseWhether to skip the 'add_correctors' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_correctors' task
dont_create_functionsFalseWhether to skip the 'add_function' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_function' task
dont_create_icsFalseWhether to skip the 'add_ic' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_ic' task
dont_create_kernelsFalseWhether to skip the 'add_kernel' task for each kernel type
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_kernel' task for each kernel type
dont_create_materialsFalseWhether to skip the 'add_material' task for each material type
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_material' task for each material type
dont_create_postprocessorsFalseWhether to skip the 'add_postprocessors' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_postprocessors' task
dont_create_solver_variablesFalseWhether to skip the 'add_variable' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_variable' task
dont_create_user_objectsFalseWhether to skip the 'add_user_object' task. This does not apply to UserObject derived classes being created on a different task (for example: postprocessors, VPPs, correctors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_user_object' task. This does not apply to UserObject derived classes being created on a different task (for example: postprocessors, VPPs, correctors)
dont_create_vectorpostprocessorsFalseWhether to skip the 'add_vectorpostprocessors' task
Default:False
C++ Type:bool
Controllable:No
Description:Whether to skip the 'add_vectorpostprocessors' task

Reduce Physics Object Creation Parameters

energy_advection_interpolationupwindThe numerical scheme to use for interpolating energy/temperature, as an advected quantity, to the face.
Default:upwind
C++ Type:MooseEnum
Options:average, upwind, sou, min_mod, vanLeer, quick, venkatakrishnan, skewness-corrected
Controllable:No
Description:The numerical scheme to use for interpolating energy/temperature, as an advected quantity, to the face.
energy_face_interpolationaverageThe numerical scheme to interpolate the temperature/energy to the face (separate from the advected quantity interpolation).
Default:average
C++ Type:MooseEnum
Options:average, skewness-corrected
Controllable:No
Description:The numerical scheme to interpolate the temperature/energy to the face (separate from the advected quantity interpolation).
energy_scaling1The scaling factor for the energy variable.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The scaling factor for the energy variable.
energy_two_term_bc_expansionTrueIf a two-term Taylor expansion is needed for the determination of the boundary valuesof the temperature/energy.
Default:True
C++ Type:bool
Controllable:No
Description:If a two-term Taylor expansion is needed for the determination of the boundary valuesof the temperature/energy.
preconditioningdeferWhich preconditioning to use/add for this Physics, or whether to defer to the Preconditioning block, or another Physics
Default:defer
C++ Type:MooseEnum
Options:default, defer
Controllable:No
Description:Which preconditioning to use/add for this Physics, or whether to defer to the Preconditioning block, or another Physics

Numerical Scheme Parameters

energy_inlet_functorsFunctions for fixed-value boundaries in the energy equation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:std::vector<MooseFunctorName>
Unit:(no unit assumed)
Controllable:No
Description:Functions for fixed-value boundaries in the energy equation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
energy_inlet_typesTypes for the inlet boundaries for the energy equation.
C++ Type:MultiMooseEnum
Options:fixed-temperature, flux-mass, flux-velocity, heatflux
Controllable:No
Description:Types for the inlet boundaries for the energy equation.

Inlet Boundary Conditions Parameters

energy_wall_functorsFunctions for Dirichlet/Neumann boundaries in the energy equation. For wall types requiring multiple functions, the syntax is ::... So, 'convection' types are ':'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:std::vector<MooseFunctorName>
Unit:(no unit assumed)
Controllable:No
Description:Functions for Dirichlet/Neumann boundaries in the energy equation. For wall types requiring multiple functions, the syntax is ::... So, 'convection' types are ':'. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
energy_wall_typesTypes for the wall boundaries for the energy equation.
C++ Type:MultiMooseEnum
Options:fixed-temperature, heatflux, wallfunction, convection
Controllable:No
Description:Types for the wall boundaries for the energy equation.

Wall Boundary Conditions Parameters

external_heat_sourceThe name of a functor which contains the external heat source for the energy equation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The name of a functor which contains the external heat source for the energy equation. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
external_heat_source_coeff1Multiplier for the coupled heat source term.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Multiplier for the coupled heat source term.

Heat Source Parameters

initial_from_file_timestepLATESTGives the time step number (or "LATEST") for which to read the Exodus solution
Default:LATEST
C++ Type:std::string
Controllable:No
Description:Gives the time step number (or "LATEST") for which to read the Exodus solution
initialize_variables_from_mesh_fileFalseDetermines if the variables that are added by the action are initializedfrom the mesh file (only for Exodus format)
Default:False
C++ Type:bool
Controllable:No
Description:Determines if the variables that are added by the action are initializedfrom the mesh file (only for Exodus format)

Restart From Exodus Parameters

specific_heatcpThe name of the specific heat. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
Default:cp
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the specific heat. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
thermal_conductivityk The name of the fluid thermal conductivity for each block. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
Default:k
C++ Type:std::vector<MooseFunctorName>
Unit:(no unit assumed)
Controllable:No
Description:The name of the fluid thermal conductivity for each block. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
thermal_conductivity_blocksThe blocks where the user wants define different thermal conductivities.
C++ Type:std::vector<std::vector<SubdomainName>>
Controllable:No
Description:The blocks where the user wants define different thermal conductivities.
use_external_enthalpy_materialFalseTo indicate if the enthalpy material is set up outside of the action.
Default:False
C++ Type:bool
Controllable:No
Description:To indicate if the enthalpy material is set up outside of the action.

Material Properties Parameters

(moose/modules/navier_stokes/include/base/NS.h)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include <string>
#include "MathUtils.h"
#include "MooseTypes.h"
#include "libmesh/vector_value.h"
#include "HeatConductionNames.h"

namespace NS
{
using namespace HeatConduction;

static const std::string directions[3] = {"x", "y", "z"};

// geometric quantities
static const std::string pebble_diameter = "pebble_diameter";
static const std::string infinite_porosity = "infinite_porosity";
static const std::string axis = "axis";
static const std::string center = "center";
static const std::string wall_porosity = "wall_porosity";
static const std::string wall_distance = "wall_distance";

// Names defined in Navier-Stokes
static const std::string density = "rho";
static const std::string superficial_density = "superficial_rho";
static const std::string momentum_x = "rhou";
static const std::string momentum_y = "rhov";
static const std::string momentum_z = "rhow";
static const std::string momentum_vector[3] = {momentum_x, momentum_y, momentum_z};
static const std::string superficial_momentum_x = "superficial_rhou";
static const std::string superficial_momentum_y = "superficial_rhov";
static const std::string superficial_momentum_z = "superficial_rhow";
static const std::string superficial_momentum_vector[3] = {
    superficial_momentum_x, superficial_momentum_y, superficial_momentum_z};

static const std::string velocity = "velocity";
static const std::string velocity_x = "vel_x";
static const std::string velocity_y = "vel_y";
static const std::string velocity_z = "vel_z";
const std::string velocity_vector[3] = {velocity_x, velocity_y, velocity_z};
static const std::string superficial_velocity_x = "superficial_vel_x";
static const std::string superficial_velocity_y = "superficial_vel_y";
static const std::string superficial_velocity_z = "superficial_vel_z";
static const std::string superficial_velocity = "superficial_velocity";
static const std::string superficial_velocity_vector[3] = {
    superficial_velocity_x, superficial_velocity_y, superficial_velocity_z};
static const std::string pressure = "pressure";
// Starting variable name with pressure so it is displayed next to pressure in outputs
static const std::string total_pressure = "pressure_total";
static const std::string temperature = "temperature";

static const std::string internal_energy = "internal_energy";
static const std::string specific_internal_energy = "e";
static const std::string specific_total_energy = "et";
static const std::string internal_energy_density = "rho_e";
static const std::string total_energy_density = "rho_et";
static const std::string superficial_total_energy_density = "superficial_rho_et";

static const std::string specific_enthalpy = "h";
static const std::string specific_total_enthalpy = "ht";
static const std::string enthalpy_density = "rho_h";
static const std::string total_enthalpy_density = "rho_ht";
static const std::string superficial_total_enthalpy_density = "superficial_rho_ht";

static const std::string mixing_length = "mixing_length";
static const std::string wall_shear_stress = "wall_shear_stress";
static const std::string wall_yplus = "wall_yplus";
static const std::string eddy_viscosity = "eddy_viscosity";
static const std::string total_viscosity = "total_viscosity";

static const std::string mach_number = "Mach";
static const std::string specific_volume = "specific_volume";

static const std::string momentum = "momentum";
static const std::string v = "v";
static const std::string acceleration = "acceleration";

static const std::string fluid = "fp";

// for Navier-Stokes material props representing gradients of nonlin+aux vars
inline std::string
grad(const std::string & var)
{
  return MathUtils::gradName(var);
}
// for Navier-Stokes material props representing time derivatives of nonlin+aux vars
inline std::string
time_deriv(const std::string & var)
{
  return MathUtils::timeDerivName(var);
}

// Navier-Stokes Variables
// Relating to porous media
static const std::string porosity = "porosity";
static const std::string smoothed_porosity = "smoothed_porosity";
static const std::string T_fluid = "T_fluid";
static const std::string T_solid = "T_solid";
static const std::string heat_source = "heat_source";

// Navier-Stokes Materials
static const std::string cL = "Darcy_coefficient";
static const std::string cQ = "Forchheimer_coefficient";
static const std::string alpha_boussinesq = "alpha_b";
static const std::string drhos_dTs = "drhos_dTs";
static const std::string dks_dTs = "dks_dTs";
static const std::string kappa = "kappa";
static const std::string kappa_s = "kappa_s";
static const std::string rho_s = "rho_s";
static const std::string cp_s = "cp_s";
static const std::string k_s = "k_s";
static const std::string cp = "cp";
static const std::string cv = "cv";
static const std::string mu = "mu";
// Turbulent dynamic viscosity
static const std::string mu_t = "mu_t";
// Turbulent dynamic scalar viscosity
static const std::string mu_t_passive_scalar = "mu_t_passive_scalar";
// Effective viscosity = sum of viscosities
static const std::string mu_eff = "mu_eff";
static const std::string k = "k";
// Turbulence 'conductivity'
static const std::string k_t = "k_t";
static const std::string thermal_diffusivity = "thermal_diffusivity";
static const std::string alpha = "alpha";
static const std::string alpha_wall = "alpha_wall";
static const std::string solid = "solid";
static const std::string Prandtl = "Pr";
static const std::string turbulent_Prandtl = "Pr_t";
static const std::string Reynolds = "Re";
static const std::string Reynolds_hydraulic = "Re_h";
static const std::string Reynolds_interstitial = "Re_i";
static const std::string c = "c";
static const std::string speed = "speed";
static const std::string sound_speed = "sound_speed";

// Two phase mixture materials
static const std::string latent_heat = "latent_heat";
static const std::string T_liquidus = "T_liquidus";
static const std::string T_solidus = "T_solidus";
static const std::string alpha_exchange = "alpha_exchange";

// other Navier-Stokes terms
static const std::string component = "component";
static const std::string source_scaling = "source_scaling";

// SUPG terms
static const std::string matrix_tau = "matrix_tau";
static const std::string vector_tau = "vector_tau";
static const std::string scalar_tau = "scalar_tau";
static const std::string diagonal_tau = "diagonal_tau";
static const std::string A = "A";
static const std::string R = "R";
static const std::string S = "S";
static const std::string dS_dTs = "dS_dTs";
static const std::string F = "F";
static const std::string G = "G";
static const std::string dUdt = "dUdt";
static const std::string C = "C";
static const std::string Z = "Z";
static const std::string K = "K";
static const std::string mass_flux = "mass_flux";

// Turbulence

// Turbulence variables
static const std::string TKE = "tke";
static const std::string TKED = "epsilon";

/**
 * Wall treatment options
 */
enum class WallTreatmentEnum
{
  EQ_NEWTON = 0,
  EQ_INCREMENTAL = 1,
  EQ_LINEARIZED = 2,
  NEQ = 3
};

// Turbulence constants
static constexpr Real von_karman_constant = 0.4187;
static constexpr Real E_turb_constant = 9.793;
// Lower limit for mu_t
static constexpr Real mu_t_low_limit = 1.0e-8;
// Lower limit for epsilon in the k-epsilon
static constexpr Real epsilon_low_limit = 1.0e-8;
// Lower limit for y_plus
static constexpr Real min_y_plus = 1e-10;
}

namespace NS_DEFAULT_VALUES
{
static const Real infinite_porosity = 0.4;
static const int bed_axis = 2;
static const Real wall_porosity = 1.0;

static const Real k_epsilon = 1e-6;
static const Real vel_epsilon = 1e-8;

static const RealVectorValue center(0.0, 0.0, 0.0);
static const RealVectorValue acceleration(0.0, 0.0, 0.0);

// assumed that the RZ geometry is not annular unless otherwise specified
static const Real inner_radius = 0.0;
}

namespace NS_CONSTANTS
{
using namespace HeatConduction::Constants;
}

(moose/modules/navier_stokes/include/base/NS.h)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include <string>
#include "MathUtils.h"
#include "MooseTypes.h"
#include "libmesh/vector_value.h"
#include "HeatConductionNames.h"

namespace NS
{
using namespace HeatConduction;

static const std::string directions[3] = {"x", "y", "z"};

// geometric quantities
static const std::string pebble_diameter = "pebble_diameter";
static const std::string infinite_porosity = "infinite_porosity";
static const std::string axis = "axis";
static const std::string center = "center";
static const std::string wall_porosity = "wall_porosity";
static const std::string wall_distance = "wall_distance";

// Names defined in Navier-Stokes
static const std::string density = "rho";
static const std::string superficial_density = "superficial_rho";
static const std::string momentum_x = "rhou";
static const std::string momentum_y = "rhov";
static const std::string momentum_z = "rhow";
static const std::string momentum_vector[3] = {momentum_x, momentum_y, momentum_z};
static const std::string superficial_momentum_x = "superficial_rhou";
static const std::string superficial_momentum_y = "superficial_rhov";
static const std::string superficial_momentum_z = "superficial_rhow";
static const std::string superficial_momentum_vector[3] = {
    superficial_momentum_x, superficial_momentum_y, superficial_momentum_z};

static const std::string velocity = "velocity";
static const std::string velocity_x = "vel_x";
static const std::string velocity_y = "vel_y";
static const std::string velocity_z = "vel_z";
const std::string velocity_vector[3] = {velocity_x, velocity_y, velocity_z};
static const std::string superficial_velocity_x = "superficial_vel_x";
static const std::string superficial_velocity_y = "superficial_vel_y";
static const std::string superficial_velocity_z = "superficial_vel_z";
static const std::string superficial_velocity = "superficial_velocity";
static const std::string superficial_velocity_vector[3] = {
    superficial_velocity_x, superficial_velocity_y, superficial_velocity_z};
static const std::string pressure = "pressure";
// Starting variable name with pressure so it is displayed next to pressure in outputs
static const std::string total_pressure = "pressure_total";
static const std::string temperature = "temperature";

static const std::string internal_energy = "internal_energy";
static const std::string specific_internal_energy = "e";
static const std::string specific_total_energy = "et";
static const std::string internal_energy_density = "rho_e";
static const std::string total_energy_density = "rho_et";
static const std::string superficial_total_energy_density = "superficial_rho_et";

static const std::string specific_enthalpy = "h";
static const std::string specific_total_enthalpy = "ht";
static const std::string enthalpy_density = "rho_h";
static const std::string total_enthalpy_density = "rho_ht";
static const std::string superficial_total_enthalpy_density = "superficial_rho_ht";

static const std::string mixing_length = "mixing_length";
static const std::string wall_shear_stress = "wall_shear_stress";
static const std::string wall_yplus = "wall_yplus";
static const std::string eddy_viscosity = "eddy_viscosity";
static const std::string total_viscosity = "total_viscosity";

static const std::string mach_number = "Mach";
static const std::string specific_volume = "specific_volume";

static const std::string momentum = "momentum";
static const std::string v = "v";
static const std::string acceleration = "acceleration";

static const std::string fluid = "fp";

// for Navier-Stokes material props representing gradients of nonlin+aux vars
inline std::string
grad(const std::string & var)
{
  return MathUtils::gradName(var);
}
// for Navier-Stokes material props representing time derivatives of nonlin+aux vars
inline std::string
time_deriv(const std::string & var)
{
  return MathUtils::timeDerivName(var);
}

// Navier-Stokes Variables
// Relating to porous media
static const std::string porosity = "porosity";
static const std::string smoothed_porosity = "smoothed_porosity";
static const std::string T_fluid = "T_fluid";
static const std::string T_solid = "T_solid";
static const std::string heat_source = "heat_source";

// Navier-Stokes Materials
static const std::string cL = "Darcy_coefficient";
static const std::string cQ = "Forchheimer_coefficient";
static const std::string alpha_boussinesq = "alpha_b";
static const std::string drhos_dTs = "drhos_dTs";
static const std::string dks_dTs = "dks_dTs";
static const std::string kappa = "kappa";
static const std::string kappa_s = "kappa_s";
static const std::string rho_s = "rho_s";
static const std::string cp_s = "cp_s";
static const std::string k_s = "k_s";
static const std::string cp = "cp";
static const std::string cv = "cv";
static const std::string mu = "mu";
// Turbulent dynamic viscosity
static const std::string mu_t = "mu_t";
// Turbulent dynamic scalar viscosity
static const std::string mu_t_passive_scalar = "mu_t_passive_scalar";
// Effective viscosity = sum of viscosities
static const std::string mu_eff = "mu_eff";
static const std::string k = "k";
// Turbulence 'conductivity'
static const std::string k_t = "k_t";
static const std::string thermal_diffusivity = "thermal_diffusivity";
static const std::string alpha = "alpha";
static const std::string alpha_wall = "alpha_wall";
static const std::string solid = "solid";
static const std::string Prandtl = "Pr";
static const std::string turbulent_Prandtl = "Pr_t";
static const std::string Reynolds = "Re";
static const std::string Reynolds_hydraulic = "Re_h";
static const std::string Reynolds_interstitial = "Re_i";
static const std::string c = "c";
static const std::string speed = "speed";
static const std::string sound_speed = "sound_speed";

// Two phase mixture materials
static const std::string latent_heat = "latent_heat";
static const std::string T_liquidus = "T_liquidus";
static const std::string T_solidus = "T_solidus";
static const std::string alpha_exchange = "alpha_exchange";

// other Navier-Stokes terms
static const std::string component = "component";
static const std::string source_scaling = "source_scaling";

// SUPG terms
static const std::string matrix_tau = "matrix_tau";
static const std::string vector_tau = "vector_tau";
static const std::string scalar_tau = "scalar_tau";
static const std::string diagonal_tau = "diagonal_tau";
static const std::string A = "A";
static const std::string R = "R";
static const std::string S = "S";
static const std::string dS_dTs = "dS_dTs";
static const std::string F = "F";
static const std::string G = "G";
static const std::string dUdt = "dUdt";
static const std::string C = "C";
static const std::string Z = "Z";
static const std::string K = "K";
static const std::string mass_flux = "mass_flux";

// Turbulence

// Turbulence variables
static const std::string TKE = "tke";
static const std::string TKED = "epsilon";

/**
 * Wall treatment options
 */
enum class WallTreatmentEnum
{
  EQ_NEWTON = 0,
  EQ_INCREMENTAL = 1,
  EQ_LINEARIZED = 2,
  NEQ = 3
};

// Turbulence constants
static constexpr Real von_karman_constant = 0.4187;
static constexpr Real E_turb_constant = 9.793;
// Lower limit for mu_t
static constexpr Real mu_t_low_limit = 1.0e-8;
// Lower limit for epsilon in the k-epsilon
static constexpr Real epsilon_low_limit = 1.0e-8;
// Lower limit for y_plus
static constexpr Real min_y_plus = 1e-10;
}

namespace NS_DEFAULT_VALUES
{
static const Real infinite_porosity = 0.4;
static const int bed_axis = 2;
static const Real wall_porosity = 1.0;

static const Real k_epsilon = 1e-6;
static const Real vel_epsilon = 1e-8;

static const RealVectorValue center(0.0, 0.0, 0.0);
static const RealVectorValue acceleration(0.0, 0.0, 0.0);

// assumed that the RZ geometry is not annular unless otherwise specified
static const Real inner_radius = 0.0;
}

namespace NS_CONSTANTS
{
using namespace HeatConduction::Constants;
}

(moose/modules/navier_stokes/test/tests/finite_volume/ins/channel-flow/2d-rc-transient-physics.i)

# Fluid properties
mu = 1.1
rho = 1.1
cp = 1.1
k = 1e-3

# Operating conditions
u_inlet = 1
T_inlet = 200
T_solid = 190
p_outlet = 10
h_fs = 0.01

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 5
    ymin = -1
    ymax = 1
    nx = 50
    ny = 20
  []
[]

[Physics]
  [NavierStokes]
    [Flow]
      [flow]
        compressibility = 'incompressible'

        density = 'rho'
        dynamic_viscosity = 'mu'

        initial_velocity = '${u_inlet} 1e-12 0'
        initial_pressure = 0.0

        inlet_boundaries = 'left'
        momentum_inlet_types = 'fixed-velocity'
        momentum_inlet_function = '${u_inlet} 0'
        wall_boundaries = 'bottom top'
        momentum_wall_types = 'symmetry noslip'

        outlet_boundaries = 'right'
        momentum_outlet_types = 'fixed-pressure-zero-gradient'
        pressure_function = '${p_outlet}'

        mass_advection_interpolation = 'average'
        momentum_advection_interpolation = 'average'
      []
    []
  []
[]
# This separation is introduced for documentation purposes.
# Both Physics could be nested under Physics/NavierStokes
[Physics/NavierStokes]
  [FluidHeatTransfer]
    [heat]
      thermal_conductivity = 'k'
      specific_heat = 'cp'

      fluid_temperature_variable = 'T_fluid'
      initial_temperature = '${T_inlet}'
      energy_inlet_types = 'heatflux'
      energy_inlet_functors = '${fparse u_inlet * rho * cp * T_inlet}'

      energy_wall_types = 'heatflux heatflux'
      energy_wall_functors = '0 0'

      ambient_convection_alpha = 'h_cv'
      ambient_temperature = 'T_solid'

      energy_advection_interpolation = 'average'
    []
  []
[]

[FunctorMaterials]
  [constants]
    type = ADGenericFunctorMaterial
    prop_names = 'h_cv T_solid rho mu cp k'
    prop_values = '${h_fs} ${T_solid} ${rho} ${mu} ${cp} ${k}'
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = 'none'
  nl_rel_tol = 7e-13
  dt = 0.4
  end_time = 0.8
[]

[Outputs]
  exodus = true
  csv = true
[]

Equation
Automatically defined variables
Coupling with other Physics
Input Parameters