FunctorKappaFluid

Zero-thermal dispersion conductivity

Description

Most macroscale models neglect thermal dispersion Suikkanen et al. (2014) and Li and Ji (2016), in which case $var element = document.getElementById("moose-equation-e8193922-196a-4a85-9bde-354caad7cac2");katex.render("\\kappa_f", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is given as

$(1)var element = document.getElementById("moose-equation-5b00a283-7f18-4cc3-a413-52c805871fef");katex.render(" \\kappa_f=\\epsilon k_f\\ .", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

Neglecting thermal dispersion is expected to be a reasonable approximation for high Reynolds numbers Gunn (1978) and Littman et al. (1968), but for low Reynolds numbers more sophisticated models should be used Becker and Laurien (2002). Because thermal dispersion acts to increase the diffusive effects, neglecting thermal dispersion is (thermally) conservative in the sense that peak temperatures are usually higher Becker and Laurien (2002).

Input Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
execute_onALWAYSThe list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM.
Default:ALWAYS
C++ Type:ExecFlagEnum
Options:FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM.
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional Parameters

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.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator

Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

Input Files

(modules/navier_stokes/test/tests/finite_volume/materials/ergun/ergun.i)

References

S. Becker and E. Laurien. Three-Dimensional Numerical Simulation of Flow and Heat Transport in High-Temperature Nuclear Reactors. In High Performance Computing in Science and Engineering. 2002. doi:10.1016/S0029-5493(03)00011-6.

@InProceedings{becker,
    author = "Becker, S. and Laurien, E.",
    title = "{Three-Dimensional Numerical Simulation of Flow and Heat Transport in High-Temperature Nuclear Reactors}",
    booktitle = "{High Performance Computing in Science and Engineering}",
    year = "2002",
    DOI = "10.1016/S0029-5493(03)00011-6"
}

D.J. Gunn. Transfer of Heat or Mass to Particles in Fixed and Fluidised Beds. International Journal of Heat and Mass Transfer, 21:467–476, 1978. doi:10.1016/0017-9310(78)90080-7.

@Article{gunn1987_htc,
    author = "Gunn, D.J.",
    title = "{Transfer of Heat or Mass to Particles in Fixed and Fluidised Beds}",
    journal = "International Journal of Heat and Mass Transfer",
    year = "1978",
    volume = "21",
    pages = "467--476",
    DOI = "10.1016/0017-9310(78)90080-7"
}

Y. Li and W. Ji. Thermal Analysis of Pebble-Bed Reactors Based on a Tightly Coupled Mechanical-Thermal Model. In Proceedings of NURETH. 2016.

@InProceedings{y_li,
    author = "Li, Y. and Ji, W.",
    title = "{Thermal Analysis of Pebble-Bed Reactors Based on a Tightly Coupled Mechanical-Thermal Model}",
    booktitle = "{Proceedings of NURETH}",
    year = "2016"
}

H. Littman, R.G. Barile, and A.H. Pulsifer. Gas-Particle Heat Transfer Coefficients in Packed Beds at Low Reynolds Numbers. I & EC Technology, 7:554–561, 1968. doi:10.1021/i160028a005.

@Article{littman,
    author = "Littman, H. and Barile, R.G. and Pulsifer, A.H.",
    title = "{Gas-Particle Heat Transfer Coefficients in Packed Beds at Low {Reynolds} Numbers}",
    journal = "I \\& EC Technology",
    year = "1968",
    volume = "7",
    pages = "554--561",
    DOI = "10.1021/i160028a005"
}

H. Suikkanen, V. Rintala, and R. Kyrki-Rajamaki. Development of a Coupled Multi-Physics Code System for Pebble Bed Reactor Core Modeling. In Proceedings of the HTR 2014. 2014.

@InProceedings{suikkanen,
    author = "Suikkanen, H. and Rintala, V. and Kyrki-Rajamaki, R.",
    title = "{Development of a Coupled Multi-Physics Code System for Pebble Bed Reactor Core Modeling}",
    booktitle = "{Proceedings of the HTR 2014}",
    year = "2014"
}

(modules/navier_stokes/test/tests/finite_volume/materials/ergun/ergun.i)

# This file simulates flow of fluid in a porous elbow for the purpose of verifying
# correct implementation of the various different solution variable sets. This input
# tests correct implementation of the primitive superficial variable set. Flow enters on the top
# and exits on the right. Because the purpose is only to test the equivalence of
# different equation sets, no solid energy equation is included.

porosity_left = 0.4
porosity_right = 0.6
pebble_diameter = 0.06

mu = 1.81e-5 # This has been increased to avoid refining the mesh
M = 28.97e-3
R = 8.3144598

# inlet mass flowrate, kg/s
mdot = -10.0

# inlet mass flux (superficial)
mflux_in_superficial = ${fparse mdot / (pi * 0.5 * 0.5)}

# inlet mass flux (interstitial)
mflux_in_interstitial = ${fparse mflux_in_superficial / porosity_left}

p_initial = 201325.0
T_initial = 300.0
rho_initial = ${fparse p_initial / T_initial * M / R}

vel_y_initial = ${fparse mflux_in_interstitial / rho_initial}
vel_x_initial = 0.0

superficial_vel_y_initial = ${fparse mflux_in_superficial / rho_initial}
superficial_vel_x_initial = 1e-12

# Computation parameters
velocity_interp_method = 'rc'
advected_interp_method = 'upwind'

# ==============================================================================
# GEOMETRY AND MESH
# ==============================================================================

[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = 'ergun_in.e'
  []
  coord_type = RZ
[]

[UserObjects]
  [rc]
    type = PINSFVRhieChowInterpolator
    u = superficial_vel_x
    v = superficial_vel_y
    pressure = pressure
    porosity = porosity
  []
[]

[GlobalParams]
  porosity = porosity
  pebble_diameter = ${pebble_diameter}
  fp = fp

  # rho for the kernels. Must match fluid property!
  rho = ${rho_initial}

  fv = true
  velocity_interp_method = ${velocity_interp_method}
  advected_interp_method = ${advected_interp_method}

  # behavior at time of test creation
  two_term_boundary_expansion = false
  rhie_chow_user_object = 'rc'
[]

# ==============================================================================
# VARIABLES AND KERNELS
# ==============================================================================

[Variables]
  [pressure]
    type = INSFVPressureVariable
    initial_condition = ${p_initial}
  []
  [superficial_vel_x]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${superficial_vel_x_initial}
  []
  [superficial_vel_y]
    type = PINSFVSuperficialVelocityVariable
    initial_condition = ${superficial_vel_y_initial}
  []
[]

[FVKernels]
  # Mass Equation.
  [mass]
    type = PINSFVMassAdvection
    variable = 'pressure'
  []

  # Momentum x component equation.
  [vel_x_time]
    type = PINSFVMomentumTimeDerivative
    variable = 'superficial_vel_x'
    momentum_component = 'x'
  []
  [vel_x_advection]
    type = PINSFVMomentumAdvection
    variable = 'superficial_vel_x'
    momentum_component = 'x'
  []
  [vel_x_viscosity]
    type = PINSFVMomentumDiffusion
    variable = 'superficial_vel_x'
    momentum_component = 'x'
    mu = 'mu'
  []
  [u_pressure]
    type = PINSFVMomentumPressure
    variable = 'superficial_vel_x'
    pressure = pressure
    momentum_component = 'x'
  []
  [u_friction]
    type = PINSFVMomentumFriction
    variable = 'superficial_vel_x'
    Darcy_name = 'Darcy_coefficient'
    Forchheimer_name = 'Forchheimer_coefficient'
    momentum_component = 'x'
    speed = speed
    mu = 'mu'
  []

  # Momentum y component equation.
  [vel_y_time]
    type = PINSFVMomentumTimeDerivative
    variable = 'superficial_vel_y'
    momentum_component = 'y'
  []
  [vel_y_advection]
    type = PINSFVMomentumAdvection
    variable = 'superficial_vel_y'
    momentum_component = 'y'
  []
  [vel_y_viscosity]
    type = PINSFVMomentumDiffusion
    variable = 'superficial_vel_y'
    momentum_component = 'y'
    mu = 'mu'
  []
  [v_pressure]
    type = PINSFVMomentumPressure
    variable = 'superficial_vel_y'
    pressure = pressure
    momentum_component = 'y'
  []
  [v_friction]
    type = PINSFVMomentumFriction
    variable = 'superficial_vel_y'
    Darcy_name = 'Darcy_coefficient'
    Forchheimer_name = 'Forchheimer_coefficient'
    momentum_component = 'y'
    mu = 'mu'
    speed = speed
  []
  [gravity]
    type = PINSFVMomentumGravity
    variable = 'superficial_vel_y'
    gravity = '0 -9.81 0'
    momentum_component = 'y'
  []
[]

# ==============================================================================
# AUXVARIABLES AND AUXKERNELS
# ==============================================================================

[AuxVariables]
  [T_fluid]
    initial_condition = ${T_initial}
    order = CONSTANT
    family = MONOMIAL
  []
  [vel_x]
    initial_condition = ${fparse vel_x_initial}
    order = CONSTANT
    family = MONOMIAL
  []
  [vel_y]
    initial_condition = ${fparse vel_y_initial}
    order = CONSTANT
    family = MONOMIAL
  []
  [porosity_out]
    type = MooseVariableFVReal
  []
[]

[AuxKernels]
  [vel_x]
    type = FunctorAux
    variable = vel_x
    functor = vel_x_mat
  []
  [vel_y]
    type = FunctorAux
    variable = vel_y
    functor = vel_y_mat
  []
  [porosity_out]
    type = FunctorAux
    variable = porosity_out
    functor = porosity
  []
[]

# ==============================================================================
# FLUID PROPERTIES, MATERIALS AND USER OBJECTS
# ==============================================================================

[FluidProperties]
  [fp]
    type = IdealGasFluidProperties
    k = 0.0
    mu = ${mu}
    gamma = 1.4
    molar_mass = ${M}
  []
[]

[FunctorMaterials]
  [enthalpy]
    type = INSFVEnthalpyMaterial
    temperature = 'T_fluid'
  []
  [speed]
    type = PINSFVSpeedFunctorMaterial
    superficial_vel_x = 'superficial_vel_x'
    superficial_vel_y = 'superficial_vel_y'
    porosity = porosity
    vel_x = vel_x_mat
    vel_y = vel_y_mat
  []
  [kappa]
    type = FunctorKappaFluid
  []
  [const_Fdrags_mat]
    type = FunctorErgunDragCoefficients
    porosity = porosity
  []
  [fluidprops]
    type = GeneralFunctorFluidProps
    mu_rampdown = mu_func
    porosity = porosity
    characteristic_length = ${pebble_diameter}
    T_fluid = 'T_fluid'
    pressure = 'pressure'
    speed = 'speed'
  []
[]

d = 0.05

[Functions]
  [mu_func]
    type = PiecewiseLinear
    x = '1 3 5 10 15 20'
    y = '1e5 1e4 1e3 1e2 1e1 1'
  []
  [real_porosity_function]
    type = ParsedFunction
    expression = 'if (x < 0.6 - ${d}, ${porosity_left}, if (x > 0.6 + ${d}, ${porosity_right},
        (x-(0.6-${d}))/(2*${d})*(${porosity_right}-${porosity_left}) + ${porosity_left}))'
  []
  [porosity]
    type = ParsedFunction
    expression = 'if (x < 0.6 - ${d}, ${porosity_left}, if (x > 0.6 + ${d}, ${porosity_right},
        (x-(0.6-${d}))/(2*${d})*(${porosity_right}-${porosity_left}) + ${porosity_left}))'
  []
[]

# ==============================================================================
# BOUNDARY CONDITIONS
# ==============================================================================

[FVBCs]
  [outlet_p]
    type = INSFVOutletPressureBC
    variable = 'pressure'
    function = ${p_initial}
    boundary = 'right'
  []

  ## No or Free slip BC
  [free-slip-wall-x]
    type = INSFVNaturalFreeSlipBC
    boundary = 'bottom wall_1 wall_2 left'
    variable = superficial_vel_x
    momentum_component = 'x'
  []
  [free-slip-wall-y]
    type = INSFVNaturalFreeSlipBC
    boundary = 'bottom wall_1 wall_2 left'
    variable = superficial_vel_y
    momentum_component = 'y'
  []

  ## Symmetry
  [symmetry-x]
    type = PINSFVSymmetryVelocityBC
    boundary = 'left'
    variable = superficial_vel_x
    u = superficial_vel_x
    v = superficial_vel_y
    mu = 'mu'
    momentum_component = 'x'
  []
  [symmetry-y]
    type = PINSFVSymmetryVelocityBC
    boundary = 'left'
    variable = superficial_vel_y
    u = superficial_vel_x
    v = superficial_vel_y
    mu = 'mu'
    momentum_component = 'y'
  []
  [symmetry-p]
    type = INSFVSymmetryPressureBC
    boundary = 'left'
    variable = 'pressure'
  []

  ## inlet
  [inlet_vel_x]
    type = INSFVInletVelocityBC
    variable = 'superficial_vel_x'
    function = ${superficial_vel_x_initial}
    boundary = 'top'
  []
  [inlet_vel_y]
    type = INSFVInletVelocityBC
    variable = 'superficial_vel_y'
    function = ${superficial_vel_y_initial}
    boundary = 'top'
  []
[]
# ==============================================================================
# EXECUTION PARAMETERS
# ==============================================================================

[Executioner]
  type = Transient

  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'asm      lu           NONZERO                   200'
  line_search = 'none'

  # Problem time parameters
  dtmin = 0.01
  dtmax = 2000
  end_time = 3000
  # must be the same as the fluid

  # Iterations parameters
  l_max_its = 50
  l_tol     = 1e-8
  nl_max_its = 25
  # nl_rel_tol = 5e-7
  nl_abs_tol = 2e-7

  # Automatic scaling
  automatic_scaling = true
  verbose = true

  [TimeStepper]
    type = IterationAdaptiveDT
    dt                 = 0.025
    cutback_factor     = 0.5
    growth_factor      = 2.0
  []

  # Steady state detection.
  steady_state_detection = true
  steady_state_tolerance = 1e-7
  steady_state_start_time = 400
[]

# ==============================================================================
# POSTPROCESSORS DEBUG AND OUTPUTS
# ==============================================================================

[Postprocessors]
  [mass_flow_in]
    type = VolumetricFlowRate
    boundary = 'top'
    vel_x = 'superficial_vel_x'
    vel_y = 'superficial_vel_y'
    advected_quantity = ${rho_initial}
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [mass_flow_out]
    type = VolumetricFlowRate
    boundary = 'right'
    vel_x = 'superficial_vel_x'
    vel_y = 'superficial_vel_y'
    advected_quantity = ${rho_initial}
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [p_in]
    type = SideAverageValue
    variable = pressure
    boundary = 'top'
  []
  [dP]
    type = LinearCombinationPostprocessor
    pp_names = 'p_in'
    pp_coefs = '1.0'
    b = ${fparse -p_initial}
  []
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
[]

Description
Input Parameters
Input Files
References