Tutorial: Acoustic streaming in a DC mould

This tutorial describes how to pre-process, run and post-process an acoustic streaming case with acousticStreamingFoam.

The USDC casting geometry that is used in this tutorial.

Pre-processing

Change to the case directory.

$ cd acousticStreamingFoam/tutorials/helmholtz/acousticStreamingFoam/USDC

Mesh generation

Generate the mesh.

$ cd ..
$ blockMesh

Boundary and initial conditions

Acoustic pressure

The complex acoustic pressure \({P}\) is calculated by solving for its real and imaginary parts separately. The real and imaginary parts of the acoustic pressure, \(\Re(P)\) and \(\Im(P)\), at the sonotrode are therefore prescriped in separate files: 0/p_Re and 0/p_Im.

sonotrode
{
    type            fixedGradient;
    gradient        uniform 4e7;
}

Physical properties

Transport properties

The transport properties are prescribed in the constant/transportProperties dictionary file.

Example usage:

nu     [ 0  2 -1 0 0 0 0 ] 1e-05;
// Acoustic properties
omega  [ 0  0 -1 0 0 0 0 ] 125663.70614359173;
c      [ 0  1 -1 0 0 0 0 ] 4600.0;
rho    [ 1 -3  0 0 0 0 0 ] 2378.652;
phorn  [ 1 -1 -2 0 0 0 0 ] 5e5;
pblake [ 1 -1 -2 0 0 0 0 ] 320386.12807758985;
N      [ 0 -3  0 0 0 0 0 ] 1.0e3;

AbyN
{
  type                table;
  format              foam;
  file                "constant/AbyN";
  outOfBounds         clamp;
  interpolationScheme linear;
}

BbyN
{
  type                table;
  format              foam;
  file                "constant/BbyN";
  outOfBounds         clamp;
  interpolationScheme linear;
}

\(\frac{\mathcal{A}}{N}\) and \(\frac{\mathcal{B}}{N}\) values will be interpolated based on the acoustic pressure in the solver stage, and are therefore entered as Foam::Function1 interpolation tables.

Control

Discretization and solver settings

Discretization schemes are entered in the system/fvSchemes dictionary file.

gradSchemes
{
    ...
    grad(p_Im)      leastSquares;
    grad(p_Re)      leastSquares;
}

laplacianSchemes
{
    ...
    laplacian(p_Re) Gauss linear corrected;
    laplacian(p_Im) Gauss linear corrected;
}

The number of acoustic corrector loops is prescribed in the PIMPLE entry of the system/fvSolution dictionary file.

PIMPLE
{
    ...
    nacousticCorrectors 5;
}

\(\Re(P)\) and \(\Im(P)\) are difficult to solve and require a suitable preconditioner:

"p_(Re|Im)"
{
    preconditioner
    {
        preconditioner FDIC;
        tolerance      1e-04;
        relTol         1e-01;
        smoother       DICGaussSeidel;
        cacheAgglomeration yes;
    }
    solver           PBiCGStab;
    smoother         DILU;
    tolerance        1e-06;
    relTol           1e-02;
    minIter          1;
    maxIter          5000;
}

Run the application

In the case directory, run:

$ acousticStreamingFoam

Post-processing

Contour plots

The jet profile can be plotted from the VTK files that are saved in the postProcessing directory using the USDC.plot_jet.plot_jet() function.

LHS: Predicted acoustic pressure normalized by the atmospheric pressure \(p_{0}\). The dotted lines denote the Blake pressure threshold. The bubbles effect on sound propagation is modelled only when \(P > P_{0}\). RHS: The predicted acoustic streaming jet.