IncompressibleEnergySPScalarKernel

Overview

This class implements the steady-state residual of the energy equation for the Path-integrated incompressible flow model, the right-hand side of Path-Integrated Incompressible Flow Model, Eq. (5). It requires a coupled variable mass flow rate, a coupled variable upstream fluid temperature, a coupled variable downstream fluid temperature, and a coupled variable wall temperature, all given as coupled ScalarVariables. It operates on the segment temperature, $var element = document.getElementById("moose-equation-911ae4ab-8d5e-49a5-bd8f-a5f1c88ae299");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ :

var element = document.getElementById("moose-equation-6333d278-bd7f-4a5a-b0a6-524805a6c526");katex.render("0 = F + \\frac{\\dot{m}}{2 L A \\rho} \\left(1 - \\frac{|\\dot{m}|}{\\dot{m}}\\right) T_d - \\frac{\\dot{m}}{2 L A \\rho} \\left(1 + \\frac{|\\dot{m}|}{\\dot{m}}\\right) T_u + \\frac{|\\dot{m}|}{L A \\rho} T - \\frac{h P_w}{2 A \\rho c_p} \\left[ 2 T_w - T - \\frac{1}{2} \\left( 1 - \\frac{|\\dot{m}|}{\\dot{m}} \\right) T_d - \\frac{1}{2} \\left( 1 + \\frac{|\\dot{m}|}{\\dot{m}} \\right) T_u \\right] \\,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Note, use of this kernel with transient problems also necessitates the use of a ODETimeDerivative, which includes the time derivative term, $var element = document.getElementById("moose-equation-289869c4-45af-4747-89b5-d8f1a549367c");katex.render("\\frac{du}{dt}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , with $var element = document.getElementById("moose-equation-eab292b1-51f8-4170-bb87-068655886296");katex.render("u", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ being the segment temperature, which adds the time derivative of the segment temperature to the residual:

This kernel takes a fluid properties object based on the SinglePhaseFluidProperties base class. It also takes functor inputs for flow area, perimeter, and length. All parameters are defined as functors, which should allow versatility in accepting a variety of input arguments. Furthermore, being functors, it is possible for them to be controlled via Controls as supplied Postprocessors, for example.

Some consideration should be given to the "is_implicit" parameter. This term allows the user to select whether the solve should be done with the current or the previous state values of functor properties. This may allow the system to evolve more slowly which may avoid some issues with respect to divergence of particularly unstable systems.

As a reminder, the system of variables should be defined with the "family" attribute set to SCALAR for each variable.

Input Parameters

areaSegment/Component flow area [m^2]. 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:Segment/Component flow area [m^2]. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
fpThe name of the user object for fluid properties
C++ Type:UserObjectName
Controllable:No
Description:The name of the user object for fluid properties
lengthSegment/Component length [m]. 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:Segment/Component length [m]. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
perimeterSegment/Component wetted perimeter [m]. 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:Segment/Component wetted perimeter [m]. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
reference_pressuresystem reference pressure [Pa]. 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:system reference pressure [Pa]. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

inlet_temperatureFluid temperature of nominal inlet segment/component (N-1). Takes a scalar variable name
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Fluid temperature of nominal inlet segment/component (N-1). Takes a scalar variable name
is_implicitFalseWhether an explicit (previous value calculation) or implicit (current value) is used
Default:False
C++ Type:bool
Controllable:No
Description:Whether an explicit (previous value calculation) or implicit (current value) is used
mass_flow_rateMass flow rate in component. Takes a scalar variable name
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Mass flow rate in component. Takes a scalar variable name
outlet_temperatureFluid temperature of nominal outlet segment/component (N+1). Takes a scalar variable name
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Fluid temperature of nominal outlet segment/component (N+1). Takes a scalar variable name
wall_temperatureWall temperature adjacent to fluid. Takes a scalar variable name
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Wall temperature adjacent to fluid. Takes a scalar variable name

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data 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
use_displaced_meshFalseWhether 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:False
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

Input Files

(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/heatreverse.i)
(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/ADheat_twoseg.i)
(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/ADheat_exp.i)
(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/heat_threeseg.i)
(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/ADheatreverse.i)
(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/ADheat_threeseg.i)
(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/ADheat.i)

(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/heatreverse.i)



length = 1.0
R = 0.025
min = 1.0
Pin = 101300
dP = -10130
Tin = 323.15
Tout = 293.15
mu = 0.001002
cp = 4185.0
k = 0.598
alpha = 0.0
epsilon = 0.0001
forms = 0.0
pump = 0.0
gravity = 0.0
area = '${fparse 3.14159* ${R}^2}'

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = ${length}
  nx = 1
[]

[Variables]
  [m1]
    family = SCALAR
    initial_condition = ${min}
  []
  [dPc]
    family = SCALAR
    initial_condition = ${dP}
  []
  [T0]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [T1]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [Tw]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [T2]
    family = SCALAR
    initial_condition = ${Tout}
  []
[]

[FluidProperties]
  [water]
    type = Water97FluidProperties
  []
[]

[ScalarKernels]
  [pipe1_mom]
    type = IncompressibleMomentumSPScalarKernel
    variable = 'm1'
    reference_pressure_drop = 'dPc'
    temperatures = 'T1'
    reference_pressure = ${Pin}
    fp = 'water'
    areas = '${area}'
    perimeters = '${fparse 2*3.14159* ${R}}'
    lengths = '${length}'
    alphas = '${alpha}'
    forms_losses = '${forms}'
    pump_pressures = '${pump}'
    roughnesses = '${epsilon}'
    g = ${gravity}
    is_implicit = True
  []
  [pipe1_DT]
    type = ODETimeDerivative
    variable = 'm1'
  []
  [temp1]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T0'
    outlet_temperature = 'T2'
    wall_temperature = 'Tw'
    area = ${area}
    fp = water
    length = ${length}
    perimeter = '${fparse 2*3.14159* ${R}}'
    reference_pressure = ${Pin}
    variable = T1
    is_implicit = True
  []
  [temp1_DT]
    type = ODETimeDerivative
    variable = 'T1'
  []
  [temp0]
    type = ParsedODEKernel
    expression = 'T0 - ${Tin}'
    variable = T0
  []
  [temp2]
    type = ParsedODEKernel
    expression = 'T2 - ${Tout}'
    variable = T2
  []
  [walltemp]
    type = ParsedODEKernel
    expression = 'Tw - ${Tin}'
    variable = Tw
  []
  [dPk]
    type = ParsedODEKernel
    expression = 'dPc - ${dP}'
    variable = dPc
  []
[]

[Postprocessors]
  [T]
    type = ScalarVariable
    variable = T1
    execute_on = 'TIMESTEP_END'
  []
  [M]
    type = ScalarVariable
    variable = m1
    execute_on = 'TIMESTEP_END'
  []
  [Re]
    type = ParsedPostprocessor
    expression = 'abs(M) / ${area} * 2 * ${R} / ${mu}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [Pr]
    type = ParsedPostprocessor
    expression = '${cp} * ${mu} / ${k}'
    execute_on = 'TIMESTEP_END'
  []
  [h]
    type = ParsedPostprocessor
    expression = '0.023 * Re^0.8 * Pr^0.4'
    pp_names = 'Re Pr'
    execute_on = 'TIMESTEP_END'
  []
  [in]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * ${Tout}
                  + 1 / 2 * (1 + abs(M)/M) * ${Tin}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [q]
    type = ParsedPostprocessor
    expression = 'h * ${fparse 2*3.14159* ${R}} / 2 * ( 2 * ${Tin} - T - in)'
    pp_names = 'T h in'
    execute_on = 'TIMESTEP_END'
  []
  [analytical_T]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q * ${length} - M / 2 * (1 - abs(M)/M) * ${cp} * ${Tout}
                  + M / 2 * (1 + abs(M)/M) * ${cp} * ${Tin}) '
    pp_names = 'T q M'
  []
  [relative_error]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T - T)/analytical_T)'
    pp_names = 'analytical_T T'
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  end_time = 100.0
  line_search = 'none'
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.4
    dt = 5
  []
  solve_type = 'PJFNK'
  nl_abs_tol = 1e-08
  l_tol = 1e-07
[]

[Outputs]
  perf_graph = true
  [out]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/ADheat_twoseg.i)



length1 = 1.0
length2 = 2.0
R1 = 0.025
R2 = 0.05
min = 1.0
Pin = 101300
dP = -10130
Tin = 293.15
Tout = 343.15
mu = 0.001002
cp = 4185.0
k = 0.598
alpha1 = 0.0
alpha2 = '${fparse 3.14159/2}'
epsilon1 = 0.0001
epsilon2 = 0.0002
forms1 = 0.0
forms2 = 1.0
pump1 = '${fparse - ${dP}}'
pump2 = 0.0
gravity = 9.81
area1 = '${fparse 3.14159* ${R1}^2}'
area2 = '${fparse 3.14159* ${R2}^2}'

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = ${length1}
  nx = 1
[]

[Variables]
  [m1]
    family = SCALAR
    initial_condition = ${min}
  []
  [dPc]
    family = SCALAR
    initial_condition = ${dP}
  []
  [T0]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [T1]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [Tw1]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [T2]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [Tw2]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [T3]
    family = SCALAR
    initial_condition = ${Tout}
  []
[]

[FluidProperties]
  [water]
    type = Water97FluidProperties
  []
[]

[ScalarKernels]
  [pipe1_mom]
    type = IncompressibleMomentumSPScalarKernel
    variable = 'm1'
    reference_pressure_drop = 'dPc'
    temperatures = 'T1 T2'
    reference_pressure = ${Pin}
    fp = 'water'
    areas = '${area1} ${area2}'
    perimeters = '${fparse 2*3.14159* ${R1}} ${fparse 2*3.14159* ${R2}}'
    lengths = '${length1} ${length2}'
    alphas = '${alpha1} ${alpha2}'
    forms_losses = '${forms1} ${forms2}'
    pump_pressures = '${pump1} ${pump2}'
    roughnesses = '${epsilon1} ${epsilon2}'
    g = ${gravity}
    is_implicit = True
  []
  [pipe1_DT]
    type = ODETimeDerivative
    variable = 'm1'
  []
  [temp1]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T0'
    outlet_temperature = 'T2'
    wall_temperature = 'Tw1'
    area = ${area1}
    fp = water
    length = ${length1}
    perimeter = '${fparse 2*3.14159* ${R1}}'
    reference_pressure = ${Pin}
    variable = T1
    is_implicit = True
  []
  [temp1_DT]
    type = ODETimeDerivative
    variable = 'T1'
  []
  [temp0]
    type = ParsedODEKernel
    expression = 'T0 - ${Tin}'
    variable = T0
  []
  [temp2]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T1'
    outlet_temperature = 'T3'
    wall_temperature = 'Tw2'
    area = ${area2}
    fp = water
    length = ${length2}
    perimeter = '${fparse 2*3.14159* ${R2}}'
    reference_pressure = ${Pin}
    variable = T2
    is_implicit = True
  []
  [temp2_DT]
    type = ODETimeDerivative
    variable = 'T2'
  []
  [temp3]
    type = ParsedODEKernel
    expression = 'T3 - ${Tout}'
    variable = T3
  []
  [walltemp1]
    type = ParsedODEKernel
    expression = 'Tw1 - ${Tout}'
    variable = Tw1
  []
  [walltemp2]
    type = ParsedODEKernel
    expression = 'Tw2 - ${Tout}'
    variable = Tw2
  []
  [dPk]
    type = ParsedODEKernel
    expression = 'dPc - ${dP}'
    variable = dPc
  []
[]

[Postprocessors]
  [Tone]
    type = ScalarVariable
    variable = T1
    execute_on = 'TIMESTEP_END'
  []
  [Ttwo]
    type = ScalarVariable
    variable = T2
    execute_on = 'TIMESTEP_END'
  []
  [M]
    type = ScalarVariable
    variable = m1
    execute_on = 'TIMESTEP_END'
  []
  [Re1]
    type = ParsedPostprocessor
    expression = 'abs(M) / ${area1} * 2 * ${R1} / ${mu}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [Re2]
    type = ParsedPostprocessor
    expression = 'abs(M) / ${area2} * 2 * ${R2} / ${mu}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [Pr]
    type = ParsedPostprocessor
    expression = '${cp} * ${mu} / ${k}'
    execute_on = 'TIMESTEP_END'
  []
  [h1]
    type = ParsedPostprocessor
    expression = '0.023 * Re1^0.8 * Pr^0.4'
    pp_names = 'Re1 Pr'
    execute_on = 'TIMESTEP_END'
  []
  [h2]
    type = ParsedPostprocessor
    expression = '0.023 * Re2^0.8 * Pr^0.4'
    pp_names = 'Re2 Pr'
    execute_on = 'TIMESTEP_END'
  []
  [in1]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * Ttwo
                  + 1 / 2 * (1 + abs(M)/M) * ${Tin}'
    pp_names = 'Ttwo M'
    execute_on = 'TIMESTEP_END'
  []
  [in2]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * ${Tout}
                  + 1 / 2 * (1 + abs(M)/M) * Tone'
    pp_names = 'Tone M'
    execute_on = 'TIMESTEP_END'
  []
  [q1]
    type = ParsedPostprocessor
    expression = 'h1 * ${fparse 2*3.14159* ${R1}} / 2 * ( 2 * ${Tout} - Tone - in1)'
    pp_names = 'Tone h1 in1'
    execute_on = 'TIMESTEP_END'
  []
  [q2]
    type = ParsedPostprocessor
    expression = 'h2 * ${fparse 2*3.14159* ${R2}} / 2 * ( 2 * ${Tout} - Ttwo - in2)'
    pp_names = 'Ttwo h2 in2'
    execute_on = 'TIMESTEP_END'
  []
  [analytical_T1]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q1 * ${length1} - M / 2 * (1 - abs(M)/M) * ${cp} * Ttwo
                  + M / 2 * (1 + abs(M)/M) * ${cp} * ${Tin})'
    pp_names = 'Ttwo q1 M'
  []
  [analytical_T2]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q2 * ${length2} - M / 2 * (1 - abs(M)/M) * ${cp} * ${Tout}
                  + M / 2 * (1 + abs(M)/M) * ${cp} * Tone)'
    pp_names = 'Tone q2 M'
  []
  [relative_error1]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T1 - Tone)/analytical_T1)'
    pp_names = 'analytical_T1 Tone'
    execute_on = 'TIMESTEP_END'
  []
  [relative_error2]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T2 - Ttwo)/analytical_T2)'
    pp_names = 'analytical_T2 Ttwo'
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  end_time = 100.0
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.4
    dt = 5
  []
  solve_type = 'PJFNK'
  nl_abs_tol = 1e-09
  l_tol = 1e-07
[]

[Outputs]
  perf_graph = true
  [out]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/ADheat_exp.i)



length = 1.0
R = 0.025
min = 1.0
Pin = 101300
dP = -10130
Tin = 293.15
Tout = 323.15
mu = 0.001002
cp = 4185.0
k = 0.598
alpha = 0.0
epsilon = 0.0001
forms = 0.0
pump = 0.0
gravity = 0.0
area = '${fparse 3.14159* ${R}^2}'

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = ${length}
  nx = 1
[]

[Variables]
  [m1]
    family = SCALAR
    initial_condition = ${min}
  []
  [dPc]
    family = SCALAR
    initial_condition = ${dP}
  []
  [T0]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [T1]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [Tw]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [T2]
    family = SCALAR
    initial_condition = ${Tout}
  []
[]

[FluidProperties]
  [water]
    type = Water97FluidProperties
  []
[]

[ScalarKernels]
  [pipe1_mom]
    type = IncompressibleMomentumSPScalarKernel
    variable = 'm1'
    reference_pressure_drop = 'dPc'
    temperatures = 'T1'
    reference_pressure = ${Pin}
    fp = 'water'
    areas = '${area}'
    perimeters = '${fparse 2*3.14159* ${R}}'
    lengths = '${length}'
    alphas = '${alpha}'
    forms_losses = '${forms}'
    pump_pressures = '${pump}'
    roughnesses = '${epsilon}'
    g = ${gravity}
    is_implicit = True
  []
  [pipe1_DT]
    type = ODETimeDerivative
    variable = 'm1'
  []
  [temp1]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T0'
    outlet_temperature = 'T2'
    wall_temperature = 'Tw'
    area = ${area}
    fp = water
    length = ${length}
    perimeter = '${fparse 2*3.14159* ${R}}'
    reference_pressure = ${Pin}
    variable = T1
    is_implicit = True
  []
  [temp1_DT]
    type = ODETimeDerivative
    variable = 'T1'
  []
  [temp0]
    type = ParsedODEKernel
    expression = 'T0 - ${Tin}'
    variable = T0
  []
  [temp2]
    type = ParsedODEKernel
    expression = 'T2 - ${Tout}'
    variable = T2
  []
  [walltemp]
    type = ParsedODEKernel
    expression = 'Tw - ${Tout}'
    variable = Tw
  []
  [dPk]
    type = ParsedODEKernel
    expression = 'dPc - ${dP}'
    variable = dPc
  []
[]

[Postprocessors]
  [T]
    type = ScalarVariable
    variable = T1
    execute_on = 'TIMESTEP_END'
  []
  [M]
    type = ScalarVariable
    variable = m1
    execute_on = 'TIMESTEP_END'
  []
  [Re]
    type = ParsedPostprocessor
    expression = 'abs(M) / ${area} * 2 * ${R} / ${mu}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [Pr]
    type = ParsedPostprocessor
    expression = '${cp} * ${mu} / ${k}'
    execute_on = 'TIMESTEP_END'
  []
  [h]
    type = ParsedPostprocessor
    expression = '0.023 * Re^0.8 * Pr^0.4'
    pp_names = 'Re Pr'
    execute_on = 'TIMESTEP_END'
  []
  [in]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * ${Tout}
                  + 1 / 2 * (1 + abs(M)/M) * ${Tin}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [q]
    type = ParsedPostprocessor
    expression = 'h * ${fparse 2*3.14159* ${R}} / 2 * ( 2 * ${Tout} - T - in)'
    pp_names = 'T h in'
    execute_on = 'TIMESTEP_END'
  []
  [analytical_T]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q * ${length} - M / 2 * (1 - abs(M)/M) * ${cp} * ${Tout}
                  + M / 2 * (1 + abs(M)/M) * ${cp} * ${Tin}) '
    pp_names = 'T q M'
  []
  [relative_error]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T - T)/analytical_T)'
    pp_names = 'analytical_T T'
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  end_time = 100.0
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.4
    dt = 5
  []
  solve_type = 'PJFNK'
  nl_abs_tol = 1e-08
  l_tol = 1e-07
[]

[Outputs]
  perf_graph = true
  [out]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/heat_threeseg.i)



length1 = 1.0
length2 = 1.0
length3 = 1.0
R1 = 0.025
R2 = 0.05
min = 1.0
Pin = 101300
dP = -10130
Tin = 293.15
Tout = 343.15
mu = 0.001002
cp = 4185.0
k = 0.598
alpha1 = 0.0
alpha2 = '${fparse 3.14159/2}'
epsilon1 = 0.0001
epsilon2 = 0.0002
forms1 = 0.0
forms2 = 1.0
pump1 = '${fparse - ${dP}}'
pump2 = 0.0
gravity = 9.81
area1 = '${fparse 3.14159* ${R1}^2}'
area2 = '${fparse 3.14159* ${R2}^2}'

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = ${length1}
  nx = 1
[]

[Variables]
  [m1]
    family = SCALAR
    initial_condition = ${min}
  []
  [dPc]
    family = SCALAR
    initial_condition = ${dP}
  []
  [T0]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [T1]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [Tw1]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [T2]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [Tw2]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [T3]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [Tw3]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [T4]
    family = SCALAR
    initial_condition = ${Tout}
  []
[]

[FluidProperties]
  [water]
    type = Water97FluidProperties
  []
[]

[ScalarKernels]
  [pipe1_mom]
    type = IncompressibleMomentumSPScalarKernel
    variable = 'm1'
    reference_pressure_drop = 'dPc'
    temperatures = 'T1 T2 T3'
    reference_pressure = ${Pin}
    fp = 'water'
    areas = '${area1} ${area2} ${area2}'
    perimeters = '${fparse 2*3.14159* ${R1}} ${fparse 2*3.14159* ${R2}} ${fparse 2*3.14159* ${R2}}'
    lengths = '${length1} ${length2} ${length2}'
    alphas = '${alpha1} ${alpha2} ${alpha2}'
    forms_losses = '${forms1} ${forms2} ${forms2}'
    pump_pressures = '${pump1} ${pump2} ${pump2}'
    roughnesses = '${epsilon1} ${epsilon2} ${epsilon2}'
    g = ${gravity}
    is_implicit = True
  []
  [pipe1_DT]
    type = ODETimeDerivative
    variable = 'm1'
  []
  [temp0]
    type = ParsedODEKernel
    expression = 'T0 - ${Tin}'
    variable = T0
  []
  [temp1]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T0'
    outlet_temperature = 'T2'
    wall_temperature = 'Tw1'
    area = ${area1}
    fp = water
    length = ${length1}
    perimeter = '${fparse 2*3.14159* ${R1}}'
    reference_pressure = ${Pin}
    variable = T1
    is_implicit = True
  []
  [temp1_DT]
    type = ODETimeDerivative
    variable = 'T1'
  []
  [temp2]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T1'
    outlet_temperature = 'T3'
    wall_temperature = 'Tw2'
    area = ${area2}
    fp = water
    length = ${length2}
    perimeter = '${fparse 2*3.14159* ${R2}}'
    reference_pressure = ${Pin}
    variable = T2
    is_implicit = True
  []
  [temp2_DT]
    type = ODETimeDerivative
    variable = 'T2'
  []
  [temp3]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T2'
    outlet_temperature = 'T4'
    wall_temperature = 'Tw3'
    area = ${area2}
    fp = water
    length = ${length3}
    perimeter = '${fparse 2*3.14159* ${R2}}'
    reference_pressure = ${Pin}
    variable = T3
    is_implicit = True
  []
  [temp3_DT]
    type = ODETimeDerivative
    variable = 'T3'
  []
  [temp4]
    type = ParsedODEKernel
    expression = 'T4 - ${Tout}'
    variable = T4
  []
  [walltemp1]
    type = ParsedODEKernel
    expression = 'Tw1 - ${Tout}'
    variable = Tw1
  []
  [walltemp2]
    type = ParsedODEKernel
    expression = 'Tw2 - ${Tout}'
    variable = Tw2
  []
  [walltemp3]
    type = ParsedODEKernel
    expression = 'Tw3 - ${Tout}'
    variable = Tw3
  []
  [dPk]
    type = ParsedODEKernel
    expression = 'dPc - ${dP}'
    variable = dPc
  []
[]

[Postprocessors]
  [Tone]
    type = ScalarVariable
    variable = T1
    execute_on = 'TIMESTEP_END'
  []
  [Ttwo]
    type = ScalarVariable
    variable = T2
    execute_on = 'TIMESTEP_END'
  []
  [Tthree]
    type = ScalarVariable
    variable = T3
    execute_on = 'TIMESTEP_END'
  []
  [M]
    type = ScalarVariable
    variable = m1
    execute_on = 'TIMESTEP_END'
  []
  [Re1]
    type = ParsedPostprocessor
    expression = 'abs(M) / ${area1} * 2 * ${R1} / ${mu}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [Re2]
    type = ParsedPostprocessor
    expression = 'abs(M) / ${area2} * 2 * ${R2} / ${mu}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [Pr]
    type = ParsedPostprocessor
    expression = '${cp} * ${mu} / ${k}'
    execute_on = 'TIMESTEP_END'
  []
  [h1]
    type = ParsedPostprocessor
    expression = '0.023 * Re1^0.8 * Pr^0.4'
    pp_names = 'Re1 Pr'
    execute_on = 'TIMESTEP_END'
  []
  [h2]
    type = ParsedPostprocessor
    expression = '0.023 * Re2^0.8 * Pr^0.4'
    pp_names = 'Re2 Pr'
    execute_on = 'TIMESTEP_END'
  []
  [in1]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * Ttwo
                  + 1 / 2 * (1 + abs(M)/M) * ${Tin}'
    pp_names = 'Ttwo M'
    execute_on = 'TIMESTEP_END'
  []
  [in2]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * Tthree
                  + 1 / 2 * (1 + abs(M)/M) * Tone'
    pp_names = 'Tone Tthree M'
    execute_on = 'TIMESTEP_END'
  []
  [in3]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * ${Tout}
                  + 1 / 2 * (1 + abs(M)/M) * Ttwo'
    pp_names = 'Ttwo M'
    execute_on = 'TIMESTEP_END'
  []
  [q1]
    type = ParsedPostprocessor
    expression = 'h1 * ${fparse 2*3.14159* ${R1}} / 2 * ( 2 * ${Tout} - Tone - in1)'
    pp_names = 'Tone h1 in1'
    execute_on = 'TIMESTEP_END'
  []
  [q2]
    type = ParsedPostprocessor
    expression = 'h2 * ${fparse 2*3.14159* ${R2}} / 2 * ( 2 * ${Tout} - Ttwo - in2)'
    pp_names = 'Ttwo h2 in2'
    execute_on = 'TIMESTEP_END'
  []
  [q3]
    type = ParsedPostprocessor
    expression = 'h2 * ${fparse 2*3.14159* ${R2}} / 2 * ( 2 * ${Tout} - Tthree - in3)'
    pp_names = 'Tthree h2 in3'
    execute_on = 'TIMESTEP_END'
  []
  [analytical_T1]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q1 * ${length1} - M / 2 * (1 - abs(M)/M) * ${cp} * Ttwo
                  + M / 2 * (1 + abs(M)/M) * ${cp} * ${Tin})'
    pp_names = 'Ttwo q1 M'
  []
  [analytical_T2]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q2 * ${length2} - M / 2 * (1 - abs(M)/M) * ${cp} * Tthree
                  + M / 2 * (1 + abs(M)/M) * ${cp} * Tone)'
    pp_names = 'Tone Tthree q2 M'
  []
  [analytical_T3]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q3 * ${length3} - M / 2 * (1 - abs(M)/M) * ${cp} * ${Tout}
                  + M / 2 * (1 + abs(M)/M) * ${cp} * Ttwo)'
    pp_names = 'Ttwo q3 M'
  []
  [relative_error1]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T1 - Tone)/analytical_T1)'
    pp_names = 'analytical_T1 Tone'
    execute_on = 'TIMESTEP_END'
  []
  [relative_error2]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T2 - Ttwo)/analytical_T2)'
    pp_names = 'analytical_T2 Ttwo'
    execute_on = 'TIMESTEP_END'
  []
  [relative_error3]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T3 - Tthree)/analytical_T3)'
    pp_names = 'analytical_T3 Tthree'
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  end_time = 100.0
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.4
    dt = 5
  []
  solve_type = 'PJFNK'
  nl_abs_tol = 1e-08
  l_tol = 1e-07
[]

[Outputs]
  perf_graph = true
  [out]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/ADheatreverse.i)



length = 1.0
R = 0.025
min = 1.0
Pin = 101300
dP = -10130
Tin = 323.15
Tout = 293.15
mu = 0.001002
cp = 4185.0
k = 0.598
alpha = 0.0
epsilon = 0.0001
forms = 0.0
pump = 0.0
gravity = 0.0
area = '${fparse 3.14159* ${R}^2}'

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = ${length}
  nx = 1
[]

[Variables]
  [m1]
    family = SCALAR
    initial_condition = ${min}
  []
  [dPc]
    family = SCALAR
    initial_condition = ${dP}
  []
  [T0]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [T1]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [Tw]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [T2]
    family = SCALAR
    initial_condition = ${Tout}
  []
[]

[FluidProperties]
  [water]
    type = Water97FluidProperties
  []
[]

[ScalarKernels]
  [pipe1_mom]
    type = IncompressibleMomentumSPScalarKernel
    variable = 'm1'
    reference_pressure_drop = 'dPc'
    temperatures = 'T1'
    reference_pressure = ${Pin}
    fp = 'water'
    areas = '${area}'
    perimeters = '${fparse 2*3.14159* ${R}}'
    lengths = '${length}'
    alphas = '${alpha}'
    forms_losses = '${forms}'
    pump_pressures = '${pump}'
    roughnesses = '${epsilon}'
    g = ${gravity}
    is_implicit = True
  []
  [pipe1_DT]
    type = ODETimeDerivative
    variable = 'm1'
  []
  [temp1]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T0'
    outlet_temperature = 'T2'
    wall_temperature = 'Tw'
    area = ${area}
    fp = water
    length = ${length}
    perimeter = '${fparse 2*3.14159* ${R}}'
    reference_pressure = ${Pin}
    variable = T1
    is_implicit = True
  []
  [temp1_DT]
    type = ODETimeDerivative
    variable = 'T1'
  []
  [temp0]
    type = ParsedODEKernel
    expression = 'T0 - ${Tin}'
    variable = T0
  []
  [temp2]
    type = ParsedODEKernel
    expression = 'T2 - ${Tout}'
    variable = T2
  []
  [walltemp]
    type = ParsedODEKernel
    expression = 'Tw - ${Tin}'
    variable = Tw
  []
  [dPk]
    type = ParsedODEKernel
    expression = 'dPc - ${dP}'
    variable = dPc
  []
[]

[Postprocessors]
  [T]
    type = ScalarVariable
    variable = T1
    execute_on = 'TIMESTEP_END'
  []
  [M]
    type = ScalarVariable
    variable = m1
    execute_on = 'TIMESTEP_END'
  []
  [Re]
    type = ParsedPostprocessor
    expression = 'abs(M) / ${area} * 2 * ${R} / ${mu}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [Pr]
    type = ParsedPostprocessor
    expression = '${cp} * ${mu} / ${k}'
    execute_on = 'TIMESTEP_END'
  []
  [h]
    type = ParsedPostprocessor
    expression = '0.023 * Re^0.8 * Pr^0.4'
    pp_names = 'Re Pr'
    execute_on = 'TIMESTEP_END'
  []
  [in]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * ${Tout}
                  + 1 / 2 * (1 + abs(M)/M) * ${Tin}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [q]
    type = ParsedPostprocessor
    expression = 'h * ${fparse 2*3.14159* ${R}} / 2 * ( 2 * ${Tin} - T - in)'
    pp_names = 'T h in'
    execute_on = 'TIMESTEP_END'
  []
  [analytical_T]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q * ${length} - M / 2 * (1 - abs(M)/M) * ${cp} * ${Tout}
                  + M / 2 * (1 + abs(M)/M) * ${cp} * ${Tin}) '
    pp_names = 'T q M'
  []
  [relative_error]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T - T)/analytical_T)'
    pp_names = 'analytical_T T'
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  end_time = 100.0
  line_search = 'none'
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.4
    dt = 5
  []
  solve_type = 'PJFNK'
  nl_abs_tol = 1e-08
  l_tol = 1e-07
[]

[Outputs]
  perf_graph = true
  [out]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/ADheat_threeseg.i)



length1 = 1.0
length2 = 1.0
length3 = 1.0
R1 = 0.025
R2 = 0.05
min = 1.0
Pin = 101300
dP = -10130
Tin = 293.15
Tout = 343.15
mu = 0.001002
cp = 4185.0
k = 0.598
alpha1 = 0.0
alpha2 = '${fparse 3.14159/2}'
epsilon1 = 0.0001
epsilon2 = 0.0002
forms1 = 0.0
forms2 = 1.0
pump1 = '${fparse - ${dP}}'
pump2 = 0.0
gravity = 9.81
area1 = '${fparse 3.14159* ${R1}^2}'
area2 = '${fparse 3.14159* ${R2}^2}'

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = ${length1}
  nx = 1
[]

[Variables]
  [m1]
    family = SCALAR
    initial_condition = ${min}
  []
  [dPc]
    family = SCALAR
    initial_condition = ${dP}
  []
  [T0]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [T1]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [Tw1]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [T2]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [Tw2]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [T3]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [Tw3]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [T4]
    family = SCALAR
    initial_condition = ${Tout}
  []
[]

[FluidProperties]
  [water]
    type = Water97FluidProperties
  []
[]

[ScalarKernels]
  [pipe1_mom]
    type = IncompressibleMomentumSPScalarKernel
    variable = 'm1'
    reference_pressure_drop = 'dPc'
    temperatures = 'T1 T2 T3'
    reference_pressure = ${Pin}
    fp = 'water'
    areas = '${area1} ${area2} ${area2}'
    perimeters = '${fparse 2*3.14159* ${R1}} ${fparse 2*3.14159* ${R2}} ${fparse 2*3.14159* ${R2}}'
    lengths = '${length1} ${length2} ${length2}'
    alphas = '${alpha1} ${alpha2} ${alpha2}'
    forms_losses = '${forms1} ${forms2} ${forms2}'
    pump_pressures = '${pump1} ${pump2} ${pump2}'
    roughnesses = '${epsilon1} ${epsilon2} ${epsilon2}'
    g = ${gravity}
    is_implicit = True
  []
  [pipe1_DT]
    type = ODETimeDerivative
    variable = 'm1'
  []
  [temp0]
    type = ParsedODEKernel
    expression = 'T0 - ${Tin}'
    variable = T0
  []
  [temp1]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T0'
    outlet_temperature = 'T2'
    wall_temperature = 'Tw1'
    area = ${area1}
    fp = water
    length = ${length1}
    perimeter = '${fparse 2*3.14159* ${R1}}'
    reference_pressure = ${Pin}
    variable = T1
    is_implicit = True
  []
  [temp1_DT]
    type = ODETimeDerivative
    variable = 'T1'
  []
  [temp2]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T1'
    outlet_temperature = 'T3'
    wall_temperature = 'Tw2'
    area = ${area2}
    fp = water
    length = ${length2}
    perimeter = '${fparse 2*3.14159* ${R2}}'
    reference_pressure = ${Pin}
    variable = T2
    is_implicit = True
  []
  [temp2_DT]
    type = ODETimeDerivative
    variable = 'T2'
  []
  [temp3]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T2'
    outlet_temperature = 'T4'
    wall_temperature = 'Tw3'
    area = ${area2}
    fp = water
    length = ${length3}
    perimeter = '${fparse 2*3.14159* ${R2}}'
    reference_pressure = ${Pin}
    variable = T3
    is_implicit = True
  []
  [temp3_DT]
    type = ODETimeDerivative
    variable = 'T3'
  []
  [temp4]
    type = ParsedODEKernel
    expression = 'T4 - ${Tout}'
    variable = T4
  []
  [walltemp1]
    type = ParsedODEKernel
    expression = 'Tw1 - ${Tout}'
    variable = Tw1
  []
  [walltemp2]
    type = ParsedODEKernel
    expression = 'Tw2 - ${Tout}'
    variable = Tw2
  []
  [walltemp3]
    type = ParsedODEKernel
    expression = 'Tw3 - ${Tout}'
    variable = Tw3
  []
  [dPk]
    type = ParsedODEKernel
    expression = 'dPc - ${dP}'
    variable = dPc
  []
[]

[Postprocessors]
  [Tone]
    type = ScalarVariable
    variable = T1
    execute_on = 'TIMESTEP_END'
  []
  [Ttwo]
    type = ScalarVariable
    variable = T2
    execute_on = 'TIMESTEP_END'
  []
  [Tthree]
    type = ScalarVariable
    variable = T3
    execute_on = 'TIMESTEP_END'
  []
  [M]
    type = ScalarVariable
    variable = m1
    execute_on = 'TIMESTEP_END'
  []
  [Re1]
    type = ParsedPostprocessor
    expression = 'abs(M) / ${area1} * 2 * ${R1} / ${mu}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [Re2]
    type = ParsedPostprocessor
    expression = 'abs(M) / ${area2} * 2 * ${R2} / ${mu}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [Pr]
    type = ParsedPostprocessor
    expression = '${cp} * ${mu} / ${k}'
    execute_on = 'TIMESTEP_END'
  []
  [h1]
    type = ParsedPostprocessor
    expression = '0.023 * Re1^0.8 * Pr^0.4'
    pp_names = 'Re1 Pr'
    execute_on = 'TIMESTEP_END'
  []
  [h2]
    type = ParsedPostprocessor
    expression = '0.023 * Re2^0.8 * Pr^0.4'
    pp_names = 'Re2 Pr'
    execute_on = 'TIMESTEP_END'
  []
  [in1]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * Ttwo
                  + 1 / 2 * (1 + abs(M)/M) * ${Tin}'
    pp_names = 'Ttwo M'
    execute_on = 'TIMESTEP_END'
  []
  [in2]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * Tthree
                  + 1 / 2 * (1 + abs(M)/M) * Tone'
    pp_names = 'Tone Tthree M'
    execute_on = 'TIMESTEP_END'
  []
  [in3]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * ${Tout}
                  + 1 / 2 * (1 + abs(M)/M) * Ttwo'
    pp_names = 'Ttwo M'
    execute_on = 'TIMESTEP_END'
  []
  [q1]
    type = ParsedPostprocessor
    expression = 'h1 * ${fparse 2*3.14159* ${R1}} / 2 * ( 2 * ${Tout} - Tone - in1)'
    pp_names = 'Tone h1 in1'
    execute_on = 'TIMESTEP_END'
  []
  [q2]
    type = ParsedPostprocessor
    expression = 'h2 * ${fparse 2*3.14159* ${R2}} / 2 * ( 2 * ${Tout} - Ttwo - in2)'
    pp_names = 'Ttwo h2 in2'
    execute_on = 'TIMESTEP_END'
  []
  [q3]
    type = ParsedPostprocessor
    expression = 'h2 * ${fparse 2*3.14159* ${R2}} / 2 * ( 2 * ${Tout} - Tthree - in3)'
    pp_names = 'Tthree h2 in3'
    execute_on = 'TIMESTEP_END'
  []
  [analytical_T1]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q1 * ${length1} - M / 2 * (1 - abs(M)/M) * ${cp} * Ttwo
                  + M / 2 * (1 + abs(M)/M) * ${cp} * ${Tin})'
    pp_names = 'Ttwo q1 M'
  []
  [analytical_T2]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q2 * ${length2} - M / 2 * (1 - abs(M)/M) * ${cp} * Tthree
                  + M / 2 * (1 + abs(M)/M) * ${cp} * Tone)'
    pp_names = 'Tone Tthree q2 M'
  []
  [analytical_T3]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q3 * ${length3} - M / 2 * (1 - abs(M)/M) * ${cp} * ${Tout}
                  + M / 2 * (1 + abs(M)/M) * ${cp} * Ttwo)'
    pp_names = 'Ttwo q3 M'
  []
  [relative_error1]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T1 - Tone)/analytical_T1)'
    pp_names = 'analytical_T1 Tone'
    execute_on = 'TIMESTEP_END'
  []
  [relative_error2]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T2 - Ttwo)/analytical_T2)'
    pp_names = 'analytical_T2 Ttwo'
    execute_on = 'TIMESTEP_END'
  []
  [relative_error3]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T3 - Tthree)/analytical_T3)'
    pp_names = 'analytical_T3 Tthree'
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  end_time = 100.0
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.4
    dt = 5
  []
  solve_type = 'PJFNK'
  nl_abs_tol = 1e-09
  l_tol = 1e-07
[]

[Outputs]
  perf_graph = true
  [out]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(modules/thermal_hydraulics/test/tests/scalarkernels/IncompressibleVerification/ADheat.i)



length = 1.0
R = 0.025
min = 1.0
Pin = 101300
dP = -10130
Tin = 293.15
Tout = 323.15
mu = 0.001002
cp = 4185.0
k = 0.598
alpha = 0.0
epsilon = 0.0001
forms = 0.0
pump = 0.0
gravity = 0.0
area = '${fparse 3.14159* ${R}^2}'

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = ${length}
  nx = 1
[]

[Variables]
  [m1]
    family = SCALAR
    initial_condition = ${min}
  []
  [dPc]
    family = SCALAR
    initial_condition = ${dP}
  []
  [T0]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [T1]
    family = SCALAR
    initial_condition = ${Tin}
  []
  [Tw]
    family = SCALAR
    initial_condition = ${Tout}
  []
  [T2]
    family = SCALAR
    initial_condition = ${Tout}
  []
[]

[FluidProperties]
  [water]
    type = Water97FluidProperties
  []
[]

[ScalarKernels]
  [pipe1_mom]
    type = IncompressibleMomentumSPScalarKernel
    variable = 'm1'
    reference_pressure_drop = 'dPc'
    temperatures = 'T1'
    reference_pressure = ${Pin}
    fp = 'water'
    areas = '${area}'
    perimeters = '${fparse 2*3.14159* ${R}}'
    lengths = '${length}'
    alphas = '${alpha}'
    forms_losses = '${forms}'
    pump_pressures = '${pump}'
    roughnesses = '${epsilon}'
    g = ${gravity}
    is_implicit = True
  []
  [pipe1_DT]
    type = ODETimeDerivative
    variable = 'm1'
  []
  [temp1]
    type = IncompressibleEnergySPScalarKernel
    mass_flow_rate = 'm1'
    inlet_temperature = 'T0'
    outlet_temperature = 'T2'
    wall_temperature = 'Tw'
    area = ${area}
    fp = water
    length = ${length}
    perimeter = '${fparse 2*3.14159* ${R}}'
    reference_pressure = ${Pin}
    variable = T1
    is_implicit = True
  []
  [temp1_DT]
    type = ODETimeDerivative
    variable = 'T1'
  []
  [temp0]
    type = ParsedODEKernel
    expression = 'T0 - ${Tin}'
    variable = T0
  []
  [temp2]
    type = ParsedODEKernel
    expression = 'T2 - ${Tout}'
    variable = T2
  []
  [walltemp]
    type = ParsedODEKernel
    expression = 'Tw - ${Tout}'
    variable = Tw
  []
  [dPk]
    type = ParsedODEKernel
    expression = 'dPc - ${dP}'
    variable = dPc
  []
[]

[Postprocessors]
  [T]
    type = ScalarVariable
    variable = T1
    execute_on = 'TIMESTEP_END'
  []
  [M]
    type = ScalarVariable
    variable = m1
    execute_on = 'TIMESTEP_END'
  []
  [Re]
    type = ParsedPostprocessor
    expression = 'abs(M) / ${area} * 2 * ${R} / ${mu}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [Pr]
    type = ParsedPostprocessor
    expression = '${cp} * ${mu} / ${k}'
    execute_on = 'TIMESTEP_END'
  []
  [h]
    type = ParsedPostprocessor
    expression = '0.023 * Re^0.8 * Pr^0.4'
    pp_names = 'Re Pr'
    execute_on = 'TIMESTEP_END'
  []
  [in]
    type = ParsedPostprocessor
    expression = '1 / 2 * (1 - abs(M)/M) * ${Tout}
                  + 1 / 2 * (1 + abs(M)/M) * ${Tin}'
    pp_names = 'M'
    execute_on = 'TIMESTEP_END'
  []
  [q]
    type = ParsedPostprocessor
    expression = 'h * ${fparse 2*3.14159* ${R}} / 2 * ( 2 * ${Tout} - T - in)'
    pp_names = 'T h in'
    execute_on = 'TIMESTEP_END'
  []
  [analytical_T]
    type = ParsedPostprocessor
    expression = '1 / abs(M) / ${cp} * (q * ${length} - M / 2 * (1 - abs(M)/M) * ${cp} * ${Tout}
                  + M / 2 * (1 + abs(M)/M) * ${cp} * ${Tin}) '
    pp_names = 'T q M'
  []
  [relative_error]
    type = ParsedPostprocessor
    expression = 'abs((analytical_T - T)/analytical_T)'
    pp_names = 'analytical_T T'
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  start_time = 0
  end_time = 100.0
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.4
    dt = 5
  []
  solve_type = 'PJFNK'
  nl_abs_tol = 1e-08
  l_tol = 1e-07
[]

[Outputs]
  perf_graph = true
  [out]
    type = CSV
    execute_on = 'FINAL'
  []
[]

Overview
Input Parameters
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