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Equation of State for a solid with mass transfer in a gas-solid flow

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Old   December 17, 2018, 04:43
Question Equation of State for a solid with mass transfer in a gas-solid flow
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anonymous
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Hello,


I got this question when I am simulating a dilute gas-solid flow with mass transfer using reactingTwoPhaseEulerFoam.. (Gas travels in a pipe at 18 ms-1 and solid particles are 2 mm in diameter)



Since there is a change of density in solid phase due to mass transfer from solid phase to gas phase I cannot use equation of state in the thermophysicalProperties file as rhoConst as used in reactingTwoPhaseEulerFoam tutorials for a fluidized bed without any reaction or mass transfer.



Hence I used perfectFluid as my equation of State as given below.



thermoType
{
type heRhoThermo;
mixture multiComponentMixture;
transport const;
thermo hConst;
equationOfState perfectFluid;
specie specie;
energy sensibleEnthalpy;
}


species
(
wood
H2O
);

inertSpecie wood;

"(mixture|wood)"
{
specie
{
molWeight 1000;
}
equationOfState
{
R 6000;
rho0 783;
}
thermodynamics
{
Hf 0;
Cp 2600;
}
transport
{
mu 1.0e-6;
Pr 0.0133;
}
}

H2O
{
specie
{
molWeight 18.0153;
}
equationOfState
{
R 6000;
rho0 1027;
}
thermodynamics
{
Hf -1.5879e+07;
Cp 4195;
}
transport
{
mu 1.0e-6;
Pr 0.0133;
}
}



But then I have to calculate the constant R for the perfectFluid in the equation for each of the species in solid phase.



rho = P/RT + rho 0


rho = density of the fluid
P = Pressure
T = Temperature
rho 0 = density of the fluid at 0 K



I assumed some values like R = 6000 , rho 0 = 1027 by getting some insight from the values given in the tutorials for reactingTwoPhaseEulerFoam. Simulation runs fine with this values.



But since I used the values blindly, I just want to know whether the equationofState I used is right or wrong?



Also if I am right can anyone please tell me how to calculate the R and rho 0 value? I searched the internet for days. But couldn't find anything.

Also the kinetic theory of granular flow which calculates the pressure and viscosity in the solid phase is used in the turbulentProperties.solids file.

simulationType RAS;

RAS
{
RASModel kineticTheory;

turbulence on;
printCoeffs on;

kineticTheoryCoeffs
{
equilibrium off;

e 0.5;
alphaMax 0.3;
alphaMinFriction 0.5;
residualAlpha 1e-6;

viscosityModel Syamlal;
conductivityModel Syamlal;
granularPressureModel SyamlalRogersOBrien;
frictionalStressModel Schaeffer;
radialModel CarnahanStarling;

SchaefferCoeffs
{
phi 36;
}
}
}

There is a equation of state for the solid flow given by the kinetic theroy of granualr flow, which is used in the granularPressureModel as follows.


Screenshot from 2018-12-17 20-24-07.png



Does this mean the type of equation of State I use is irrelevant or Do I have to incorporate this granularPressureModel into the thermoPhysicalProperties file?
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equation of state, gas-solid flow, perfectfluid, reactingtwophaseeulerfoam

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