buoyantPimpleFoam General Assumptions (thermophysical model, energy equation, etc)

AMK53 · October 7, 2017, 03:37

I am trying to use buoyantPimpleFoam to simulate Rayleigh-Taylor instability of a gas (eventually a reacting simulation). I was looking through the source files and I had some general questions on the assumptions that the solver takes, and hope that someone can shed some light on it for me.

1. The energy equation is states as

Code:

fvScalarMatrix EEqn    (        fvm::ddt(rho, he) + fvm::div(phi, he)      + fvc::ddt(rho, K) + fvc::div(phi, K)      + (            he.name() == "e"          ? fvc::div            (                fvc::absolute(phi/fvc::interpolate(rho), U),                p,                "div(phiv,p)"            )          : -dpdt        )      - fvm::laplacian(turbulence->alphaEff(), he)     ==        rho*(U&g)      + radiation->Sh(thermo, he)      + fvOptions(rho, he)    );

All the terms look correct (though it is missing mechanical stress term), but the thermal diffusion term seems a bit odd to me. If we use Fourier's law of heat diffusion, we would have:

$\nabla \cdot (-k\nabla T) = \nabla \cdot (-\frac{k}{C_p} [\nabla(C_pT) - T \nabla C_p] = \nabla \cdot (-\alpha [\nabla h - T \nabla C_p])$

But in the solver energy equation, this is simply states as $\nabla \cdot (-\alpha \nabla h)$ . Obviously this does not matter for a thermally perfect gas as the specific heat is constant, but for gases with varying specific heats, there should be a gradient there. I have never seen the form used in buoyantPimpleFoam. Is this additional gradient term simply just ignored because it is negligible?

2. The divergence of gradients in OpenFoam (e.g. $\nabla \cdot (\mu (\nabla U + \nabla U^T))$ or $\nabla \cdot (\alpha \nabla h)$ ) are simply written as laplacians, i.e. laplacian(mu,D(U)). Again, this is only true if the transport properties do not vary. This is definitely not the case for reacting flows. Is this simply ignored in OpenFoam calculations or is this handled behind the scenes?

3. The thermophysical properties for gases seem to me to be overdefined. For example, a sample thermophysical model could be:

Code:

thermoType
{
    type            heRhoThermo;  //Thermophysical Model Based on h/e and rho
    mixture         pureMixture; // Passive Gas Mixtures
    transport       const; // Constant transport properties (mu, Pr, etc.)
    thermo          hConst; // Constant Cp and heat of fusion
    equationOfState perfectGas; // Ideal Gas Law
    specie          specie;
    energy          sensibleEnthalpy; // Solve Energy Eqn. In Terms of Enthalpy
}

From my understanding, heRhoThermo calculates the enthalpy and density, but the density and the enthalpy are already defined by the perfect gas and 'hConst' assumptions. What additional things is the thermophysical type doing to calculate these? Is the type even necessary at this point?

4. Why is $P_{rgh} \equiv P - \rho g \cdot x$ read from the initial conditions and then re-defined, i.e. in createFields.H

Code:

#include "readGravitationalAcceleration.H"
#include "readhRef.H"
#include "gh.H"

Info<< "Reading field p_rgh\n" << endl;
volScalarField p_rgh
(
    IOobject
    (
        "p_rgh",
        runTime.timeName(),
        mesh,
        IOobject::MUST_READ,
        IOobject::AUTO_WRITE
    ),
    mesh
);

// Force p_rgh to be consistent with p
p_rgh = p - rho*gh;

If you've correctly defined Prgh, then it should be consistent already. I'm not quite sure what they are doing here.

Thank you in advance.

calf.Z · October 23, 2018, 05:30

Hello,I am also confused about these questions above.

Have you found the answer of it?

Any idea will be appreciated.

October 7, 2017, 03:37	buoyantPimpleFoam General Assumptions (thermophysical model, energy equation, etc)	#1
AMK53 New Member Join Date: Oct 2017 Posts: 12 Rep Power: 8	I am trying to use buoyantPimpleFoam to simulate Rayleigh-Taylor instability of a gas (eventually a reacting simulation). I was looking through the source files and I had some general questions on the assumptions that the solver takes, and hope that someone can shed some light on it for me. 1. The energy equation is states as Code: fvScalarMatrix EEqn ( fvm::ddt(rho, he) + fvm::div(phi, he) + fvc::ddt(rho, K) + fvc::div(phi, K) + ( he.name() == "e" ? fvc::div ( fvc::absolute(phi/fvc::interpolate(rho), U), p, "div(phiv,p)" ) : -dpdt ) - fvm::laplacian(turbulence->alphaEff(), he) == rho(U&g) + radiation->Sh(thermo, he) + fvOptions(rho, he) ); All the terms look correct (though it is missing mechanical stress term), but the thermal diffusion term seems a bit odd to me. If we use Fourier's law of heat diffusion, we would have: $\nabla \cdot (-k\nabla T) = \nabla \cdot (-\frac{k}{C_p} [\nabla(C_pT) - T \nabla C_p] = \nabla \cdot (-\alpha [\nabla h - T \nabla C_p])$ But in the solver energy equation, this is simply states as $\nabla \cdot (-\alpha \nabla h)$ . Obviously this does not matter for a thermally perfect gas as the specific heat is constant, but for gases with varying specific heats, there should be a gradient there. I have never seen the form used in buoyantPimpleFoam. Is this additional gradient term simply just ignored because it is negligible? 2. The divergence of gradients in OpenFoam (e.g. $\nabla \cdot (\mu (\nabla U + \nabla U^T))$ or $\nabla \cdot (\alpha \nabla h)$ ) are simply written as laplacians, i.e. laplacian(mu,D(U)). Again, this is only true if the transport properties do not vary. This is definitely not the case for reacting flows. Is this simply ignored in OpenFoam calculations or is this handled behind the scenes? 3. The thermophysical properties for gases seem to me to be overdefined. For example, a sample thermophysical model could be: Code: thermoType { type heRhoThermo; //Thermophysical Model Based on h/e and rho mixture pureMixture; // Passive Gas Mixtures transport const; // Constant transport properties (mu, Pr, etc.) thermo hConst; // Constant Cp and heat of fusion equationOfState perfectGas; // Ideal Gas Law specie specie; energy sensibleEnthalpy; // Solve Energy Eqn. In Terms of Enthalpy } From my understanding, heRhoThermo calculates the enthalpy and density, but the density and the enthalpy are already defined by the perfect gas and 'hConst' assumptions. What additional things is the thermophysical type doing to calculate these? Is the type even necessary at this point? 4. Why is $P_{rgh} \equiv P - \rho g \cdot x$ read from the initial conditions and then re-defined, i.e. in createFields.H Code: #include "readGravitationalAcceleration.H" #include "readhRef.H" #include "gh.H" Info<< "Reading field p_rgh\n" << endl; volScalarField p_rgh ( IOobject ( "p_rgh", runTime.timeName(), mesh, IOobject::MUST_READ, IOobject::AUTO_WRITE ), mesh ); // Force p_rgh to be consistent with p p_rgh = p - rhogh; If you've correctly defined Prgh, then it should be consistent already. I'm not quite sure what they are doing here. Thank you in advance.

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October 23, 2018, 05:30		#2
calf.Z Senior Member Jianrui Zeng Join Date: May 2018 Location: China Posts: 157 Rep Power: 7	Hello,I am also confused about these questions above. Have you found the answer of it? Any idea will be appreciated.