GapFluxModelPressureDependentConduction

Heat flux model across a closed gap to calculate the conductance between two solid materials

Description

GapFluxModelPressureDependentConduction computes a conductive heat flux across a closed gap between two solid bodies as a function of the normal mechanical pressure at the interface. The normal contact pressure is included in this calculation as a Lagrange multiplier associated with a lower-dimensional domain. This class requires the use of ModularGapConductanceConstraint.

The thermal conductance of the interface is calculated as (1) where is a scaling or fitting parameter, k is the harmonic mean of the thermal conductivities, P is the contact pressure, and H is the harmonic mean of the material hardness, following (Cincotti et al., 2007). The harmonic mean of the thermal conductivities is given as (2) where k and k are the thermal conductivities of the two materials on either side of the closed gap interface. The harmonic mean of the hardness values is calculated in a similar fashion.

Analytical Solution

Using this heat flux object alone, the temperature of the hotter material at the interface, T, is given by the analytical expression and the temperature of the cooler material at the interface, T, is where T and T are the prescribed hot and cool temperature boundary conditions, respectively, k and k are the thermal conductivities of the materials associated with the hot and cool temperatures, and C is the thermal conduction at the interface as given by Eq. (1). Note that these expressions were derived assuming no deformation and unit thickness of both materials in the direction of the temperature gradient.

Example Input File Syntax

[UserObjects<<<{"href": "../../syntax/UserObjects/index.html"}>>>]
  [closed]
    type = GapFluxModelPressureDependentConduction<<<{"description": "Heat flux model across a closed gap to calculate the conductance between two solid materials", "href": "GapFluxModelPressureDependentConduction.html"}>>>
    primary_conductivity<<<{"description": "The thermal conductivity of the primary surface solid material"}>>> = steel_thermal_conductivity
    secondary_conductivity<<<{"description": "The thermal conductivity of the secondary surface solid material"}>>> = aluminum_thermal_conductivity
    temperature<<<{"description": "The name of the temperature variable"}>>> = temperature
    contact_pressure<<<{"description": "The name of the contact pressure variable"}>>> = interface_normal_lm
    primary_hardness<<<{"description": "The hardness value of the primary surface material"}>>> = steel_hardness
    secondary_hardness<<<{"description": "The hardness of the secondary surface material"}>>> = aluminum_hardness
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = moving_block_right
  []
[]
(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/closed_gap_prescribed_pressure.i)

GapFluxModelPressureDependentConduction must be used in conjunction with the modular gap conductance constraint as shown below:

[Constraints<<<{"href": "../../syntax/Constraints/index.html"}>>>]
  [thermal_contact]
    type = ModularGapConductanceConstraint<<<{"description": "Computes the residual and Jacobian contributions for the 'Lagrange Multiplier' implementation of the thermal contact problem. For more information, see the detailed description here: http://tinyurl.com/gmmhbe9", "href": "../constraints/ModularGapConductanceConstraint.html"}>>>
    variable<<<{"description": "The name of the lagrange multiplier variable that this constraint is applied to. This parameter may not be supplied in the case of using penalty methods for example"}>>> = temperature_interface_lm
    secondary_variable<<<{"description": "Primal variable on secondary surface."}>>> = temperature
    primary_boundary<<<{"description": "The name of the primary boundary sideset."}>>> = moving_block_right
    primary_subdomain<<<{"description": "The name of the primary subdomain."}>>> = interface_primary_subdomain
    secondary_boundary<<<{"description": "The name of the secondary boundary sideset."}>>> = fixed_block_left
    secondary_subdomain<<<{"description": "The name of the secondary subdomain."}>>> = interface_secondary_subdomain
    gap_flux_models<<<{"description": "List of GapFluxModel user objects"}>>> = 'closed'
  []
[]
(modules/heat_transfer/test/tests/gap_heat_transfer_mortar/closed_gap_prescribed_pressure.i)

Input Parameters

  • boundaryThe list of boundary IDs from the mesh where this object applies

    C++ Type:std::vector<BoundaryName>

    Controllable:No

    Description:The list of boundary IDs from the mesh where this object applies

  • contact_pressureThe name of the contact pressure variable

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the contact pressure variable

  • primary_conductivityThe thermal conductivity of the primary surface solid material

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:The thermal conductivity of the primary surface solid material

  • primary_hardnessThe hardness value of the primary surface material

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:The hardness value of the primary surface material

  • secondary_conductivityThe thermal conductivity of the secondary surface solid material

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:The thermal conductivity of the secondary surface solid material

  • secondary_hardnessThe hardness of the secondary surface material

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:The hardness of the secondary surface material

  • temperatureThe name of the temperature variable

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the temperature variable

Required Parameters

  • scaling_coefficient1The leading coefficient for the closed gap conductance value; used for tuning

    Default:1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:The leading coefficient for the closed gap conductance value; used for tuning

Optional Parameters

  • allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).

    Default:False

    C++ Type:bool

    Controllable:No

    Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).

  • execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.

    Default:0

    C++ Type:int

    Controllable:No

    Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.

  • force_postauxFalseForces the UserObject to be executed in POSTAUX

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Forces the UserObject to be executed in POSTAUX

  • force_preauxFalseForces the UserObject to be executed in PREAUX

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Forces the UserObject to be executed in PREAUX

  • force_preicFalseForces the UserObject to be executed in PREIC during initial setup

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling 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

  • use_displaced_meshTrueWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

    Default:True

    C++ Type:bool

    Controllable:No

    Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

  • 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

    Unit:(no unit assumed)

    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.

Material Property Retrieval Parameters

Input Files

References

  1. Alberto Cincotti, Antonio Mario Locci, Roberto Orru, and Giacomo Cao. Modeling of sps apparatus: temperature, current and strain distribution with no powders. AIChE journal, 53(3):703–719, 2007.[BibTeX]