PIMPLE convergence issue for closed-end pipe injection with Water97FluidProperties

[tanaka792]

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Question

I am trying to simulate a weakly-compressible 3D pipe injection problem using the MOOSE NavierStokes FV module with Water97FluidProperties.

The model is a straight 3D pipe with a length of a few hundred meters. Water is injected from the inlet, and my final target condition is a closed outlet with no outflow. I would like to observe the pressure evolution on the outlet boundary itself, not at an internal section upstream of the outlet. The expected fluid temperature range is about 30–80 °C.

My main question is about the formulation needed for this type of closed outlet + fixed inlet pressure buildup problem using PIMPLE. I am not mainly looking for advice such as simply reducing the timestep. I would like to understand whether something is missing in the PDE formulation, boundary conditions, pressure reference, mass storage/compressibility treatment, or coupling with Water97FluidProperties.

I also tried a fully coupled Newton solve, but for 3D flow with k-epsilon turbulence, the heat equation, and Water97, the computational cost was too high to be practical. Therefore, I would like to use PIMPLE.

Currently, even before switching to the final closed-outlet case, I am testing an open-outlet case with fixed outlet pressure. However, the PIMPLE residuals stagnate and do not decrease sufficiently. For example, they stay around values like these:

Momentum equation: Component 1 0.723904 Linear its: 1
Momentum equation: Component 2 0.610898 Linear its: 1
Momentum equation: Component 3 0.339547 Linear its: 1
Pressure equation: 1 Linear its: 7
Advected system: energy_system 0.270439 Linear its: 180
Advected system: TKE_system 0.126769 Linear its: 1
Advected system: TKED_system 0.158908 Linear its: 2

Another issue is the coupling with Water97FluidProperties. If I pass the solved pressure_total directly to Water97, the pressure during PIMPLE correction can exceed 100 MPa or become nonphysical, which easily causes Water97 range errors.

For this reason, I currently evaluate Water97 at a fixed representative pressure and the solved temperature, effectively using temperature-dependent properties:
The relevant input is:

  [water97]
    type = Water97FluidProperties
  []
[]

[FunctorMaterials]
  [to_regular_T]
    type = FunctorADConverter
    block = 'flu_in flu_mid flu_out borehole'
    ad_props_in = 'T_fluid'
    reg_props_out = 'T_fluid_nAD'
  []

  [T_water97]
    type = ParsedFunctorMaterial
    block = 'flu_in flu_mid flu_out borehole'
    property_name = T_w97
    expression = 'if(T < ${T_w97_min}, ${T_w97_min}, if(T > ${T_w97_max}, ${T_w97_max}, T))'
    functor_names = 'T_fluid_nAD'
    functor_symbols = 'T'
  []

  [water97_Tonly_props]
    type = NonADGeneralFunctorFluidProps
    block = 'flu_in flu_mid flu_out borehole'

    fp = water97
    pressure = ${p_prop_ref}
    T_fluid = T_w97

    speed = ${U_ref}
    characteristic_length = ${D_pipe}
    porosity = 1.0

    density_name = rho
    dynamic_viscosity_name = mu
    thermal_conductivity_name = k_fluid
    specific_heat_name = cp_w97
  []

  [rho_cp_from_rho]
    type = ParsedFunctorMaterial
    block = 'flu_in flu_mid flu_out borehole'
    property_name = rho_cp
    expression = 'rho * ${cp_fluid0}'
    functor_names = 'rho'
    functor_symbols = 'rho'
  []
[]

For the current open-outlet test, the flow setup is:

[FlowSegregated]
  [flow]
    block = 'flu_in flu_mid flu_out borehole'

    gravity = '0 0 -9.81'
    compressibility = 'weakly-compressible'
    transient = true

    density = rho
    dynamic_viscosity = mu

    define_variables = true

    velocity_variable = 'vel_x vel_y vel_z'
    pressure_variable = pressure_total
    system_names = 'u_system v_system w_system pressure_system'

    initial_velocity = '0 0 ${inlet_v}'
    initial_pressure = hydrostatic_pressure

    inlet_boundaries = 'inlet'
    momentum_inlet_types = 'fixed-velocity'
    momentum_inlet_functors = '0 0 ${inlet_v}'

    outlet_boundaries = 'outlet'
    momentum_outlet_types = 'fixed-pressure-zero-gradient'
    pressure_functors = '${p_outlet}'

    wall_boundaries = 'wall borehole_inlet'
    momentum_wall_types = 'noslip noslip'

    momentum_advection_interpolation = 'upwind'
    pressure_projection_method = consistent
    use_nonorthogonal_correction = false

    include_symmetrized_viscous_stress = true
  []
[]

The PIMPLE and linear solver settings are:

[Executioner]
  type = PIMPLE

  rhie_chow_user_object = 'ins_rhie_chow_interpolator'

  momentum_systems = 'u_system v_system w_system'
  pressure_system = 'pressure_system'
  energy_system = 'energy_system'
  turbulence_systems = 'TKE_system TKED_system'

  num_iterations = 150

  momentum_equation_relaxation = 0.5
  pressure_variable_relaxation = 0.2
  energy_equation_relaxation = 0.5
  turbulence_equation_relaxation = '0.2 0.2'
  turbulence_field_relaxation = '0.2 0.2'

  dtmax = 0.5
  end_time = 5.0

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.05
    optimal_iterations = 30
    iteration_window = 10
    growth_factor = 1.5
    cutback_factor = 0.5
    cutback_factor_at_failure = 0.25
  []

  momentum_l_tol = 1e-4
  pressure_l_tol = 1e-5
  energy_l_tol = 1e-5
  turbulence_l_tol = 1e-4

  momentum_absolute_tolerance = 5e-4
  pressure_absolute_tolerance = 1e-4
  energy_absolute_tolerance = 1e-4
  turbulence_absolute_tolerance = '5e-4 5e-4'

  momentum_petsc_options_iname = '-ksp_type -pc_type -pc_hypre_type -ksp_rtol -ksp_atol -ksp_max_it'
  momentum_petsc_options_value = 'gmres hypre boomeramg 1e-6 1e-10 300'

  pressure_petsc_options_iname = '-ksp_type -pc_type -pc_hypre_type -ksp_rtol -ksp_atol -ksp_max_it'
  pressure_petsc_options_value = 'gmres hypre boomeramg 1e-6 1e-10 300'

  energy_petsc_options_iname = '-ksp_type -pc_type -pc_hypre_type -ksp_rtol -ksp_atol -ksp_max_it'
  energy_petsc_options_value = 'gmres hypre boomeramg 1e-6 1e-10 300'

  turbulence_petsc_options_iname = '-ksp_type -pc_type -pc_hypre_type -ksp_rtol -ksp_atol -ksp_max_it'
  turbulence_petsc_options_value = 'gmres hypre boomeramg 1e-6 1e-12 300'
[]

My final target condition is:

inlet: fixed velocity
outlet: closed / no-slip wall
quantity of interest: pressure evolution on the outlet boundary itself

For the closed-outlet case, the injected mass must be stored through pressure buildup. Therefore, I am also considering adding a simplified pressure dependence only to the density used by the flow solver:

rho = rho_Water97(p_const, T) * (1 + beta_p * (pressure_total - p_const))

The intention is to avoid passing the raw PIMPLE-corrected pressure_total directly into Water97, while still allowing compressibility in the density used by the flow equations.

Is this formulation reasonable for a weakly-compressible PIMPLE closed-end pipe injection problem?
Or is there a more standard MOOSE approach for modeling pressure buildup on the closed outlet boundary itself, such as an additional storage term, pressure reference, density formulation, boundary treatment, Kernel, or FunctorMaterial?

I would also appreciate pointers to similar input files or GitHub discussions involving Water97FluidProperties with NavierStokes FV / PIMPLE / k-epsilon pipe flow.

Additional information

Mesh size and type:　A 3D straight pipe mesh loaded with FileMeshGenerator
The pipe diameter is 1 m, and the current simplified length is 100 m.
The mesh is approximately a 3D TET4 mesh with a characteristic element size of about 0.05 m

Reynolds number:　About 5.0e4, using rho = 1000 kg/m3, U = 0.05 m/s, D = 1 m, and mu = 1e-3 Pa s.

Discretization (finite element CG/DG, finite volume, etc):　Finite volume

Models (turbulence, porous media, etc):　Weakly-compressible Navier-Stokes, k-epsilon turbulence, fluid heat transfer, gravity, and Water97FluidProperties. At present, Water97 is evaluated at a fixed representative pressure and the solved temperature to avoid range errors during PIMPLE pressure correction.

Solver method (fully coupled, segregated, multiapps, etc):　PIMPLE solve.

Base input you started from:　There was no single official input file that I directly started from. I mainly referred to the MOOSE FlowSegregated documentation and assembled a custom NavierStokes FV input from there. I then added FluidHeatTransferSegregated, TurbulenceSegregated, PIMPLE settings, k-epsilon turbulence, and Water97FluidProperties through NonADGeneralFunctorFluidProps.

[GiudGiud]

hello

and my final target condition is a closed outlet with no outflow.

So where is the water going? Are you currently applying the pressure condition on the outlet?

This does not feel like our usual pipe problem with a fixed inlet velocity and a fixed outlet pressure.

[GiudGiud]

In the final case, the injected water does not leave the pipe. It remains inside the pipe, and the pressure rises due to mass accumulation and compressibility.

right but the discretization used is intended for weakly compressible flow for which density should not depend on pressure.
We should be missing terms in the energy equation for compressibility effects.

What I would like to observe is the pressure evolution on the pipe end opposite the inlet, where there is no outflow. For that reason, I do not want to prescribe the pressure on that boundary as in a usual outlet-pressure pipe-flow problem.

you have to prescribe the pressure at the inlet then. The pressure must be prescribed somewhere when using a weakly-compressible fluid.
If you set a fixed pressure (rather than the current pressure solution) in the fluid properties, you made it weakly-compressible, and the pressure solution field could vary by any spatially-constant amount and the equation would not change (because it only depends on the gradient of pressure).

[tanaka792]

Thank you for the explanation.

I understand that the pressure must be prescribed somewhere.

Until now, I had assumed that by using Water97FluidProperties, the fluid properties would become pressure- and temperature-dependent, and that this would directly allow the pressure buildup and density change caused by injection into a closed pipe to be represented.

Based on your explanation, is my understanding correct that Water97FluidProperties itself can provide pressure- and temperature-dependent properties, but the current weakly-compressible NavierStokes FV / PIMPLE discretization is not intended to fully handle compressibility effects through pressure-dependent density? In that case, additional compressibility-related terms, especially in the energy equation, would be required.

Also, for modeling pressure buildup due to injection into a closed pipe, would it be possible or reasonable to keep using Water97FluidProperties and add a separate mass storage or compressibility term? For example, a term based on the water compressibility or on a quantity such as drho/dp obtained from Water97, so that the injected mass is stored as an increase in pressure and density.

Or would that still be inconsistent with the current weakly-compressible PIMPLE formulation, meaning that a different formulation or model structure would be needed for this closed-volume pressure-buildup problem?

[GiudGiud]

I'm not familiar with this setup where mass flow is turned into a higher mass & pressure with no outlet.
Maybe @freiler @tanoret or @deOliveira-R has tried something similar before?

[lindsayad]

Is there support/demonstrations of using a mass time derivative term with linear FV? I don't know how this could be done otherwise

[GiudGiud]

I'm afraid not. We have time dependent cases (with a momentum time derivative) in the linearFV test suite and weakly compressible cases, but no case with both?
at least from a cursory search in OpenPgh and NS module