jouleHeatingMultiRegion*Foam

Multi-region conjugated heat transfer solver with time-independent Joule heating consideration and temperature dependent electrical conductance in solid regions, for OpenFOAM v2.3.1.

Both PIMPLE(jouleHeatingMultiRegionFoam) and SIMPLE(jouleHeatingMultiRegionSimpleFoam) version exists.

Changes from chtMultiRegion*Foam

solid/interpolateProperties.H

Implements temperature dependent electrical conductance $\sigma$ with built-in interpolation library, interpolateXY.

solid/VEqn.H

Defines and solves continuity equation below to get electric potential distribution.

$\large \nabla\cdot \left( \sigma\nabla V \right) = 0 \boldsymbol{\longrightarrow}$ fvm::laplacian(sigma,elpot) == 0

solid/solveSolid.H

Energy equation in solid regions consider Joule heating per unit volume, $\mathbf{E} \cdot \mathbf{J} = -\nabla V \cdot \left(-\sigma \nabla V \right) = \sigma |\nabla V|^2$. This heat source term is added on the RHS of the energy equation.

$\large \sigma |\nabla V|^2 \boldsymbol{\longrightarrow}$ sigma*((fvc::grad(elpot))&(fvc::grad(elpot)))

Compiling the Solver

First, you should check files named file located in Make directory, for which the compiled solver's location is described. After checking and modifying the location, type following and you`ll get the solver.

wclean
wmake

Usage

Electrical conductance, electric potential and electric current density fields are added and named sigma, elpot, J respectively. So you'll need additional works for every solid region directory residing in following directories, in order to use the solver properly. Please refer to example directory for an example case.

• 0 directory
  Initial / boundary condition for electric conductance and potential, sigma and elpot are required. Electric conductance is calculated by interpolateXY, so calculated condition should be assigned to the field sigma.
• system directory
  fvSolution: requires solvers, preconditioners, relative and absolute tolerance of elpot, elpotFinal
fvSchemes: requires laplacian scheme for laplacian(sigma,elpot)
• constant directory
  A file named sigma is required. The file matches absolute temperature in Kelvin and corresponding electrical conductance value in S/m, so that you can get interpolated profile of electrical conductance.
  If you are going to use decomposePar, you should copy sigma to every processor directories. This can be done using copy_sigma.sh script at case root directory. The script is provided in scripts directory.
  sigma file looks like this:

  (  
  293.15 6666666.67  
  373.15 6410256.41  
  473.15 6172839.51  
  573.15 5917159.76  
  673.15 5714285.71  
  )
  

Testing with Example Case

For the given example case, meshing is already done so you'll just need to decompose domain with decomposePar and run the solver(jouleHeatingMultiRegionSimpleFoam) and reconstruct. Commands would be:

$ decomposePar -allRegions
$ jouleHeatingMultiRegionSimpleFoam
$ reconstructPar -allRegions -latestTime

References

[1] Read temperature dependent thermophysical properties from a file - boundaries false -- CFD Online Discussion Forums. (2012, June 26). CFD Online. Retrieved May 25, 2022, from https://www.cfd-online.com/Forums/openfoam-programming-development/103774-read-temperature-dependent-thermophysical-properties-file-boundaries-false.html
[2] Järvstråt, N. (2009). Adding electric conduction and Joule heating to chtMultiRegionFoam. http://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2009/NiklasJarvstrat/Project0126.pdf