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How to write a material derivative of ln[Tc/Ts] in Openfoam
Title
Question
Hello Everyone

I trust this finds you well,

May kindly assist me, I have  the below Stress /Constitutive Giesekus  Equation written in Openfoam

// Velocity gradient tensor
    const tmp<volTensorField> tL = fvc::grad(U());
    const volTensorField& L = tL();

    // Convected derivate term
    volTensorField C = tau_ & L;

    // Twice the rate of deformation tensor
    volSymmTensorField twoD = twoSymm(L);

// Giesekus Equation:

fvSymmTensorMatrix tauEqn
    (
        fvm::ddt(tau_)
      + fvm::div(phi(), tau_)
     ==
        etaP_/lambda_*twoD
      + twoSymm(C)
      - (alpha_/etaP_)*symm(tau_ & tau_)
      - fvm::Sp(1/lambda_, tau_)
    );
where Lambda is relaxation time.

Now , in the above equation I need to add the term
 - tau D/Dt (ln [Tc/Ts]) may you kindly assist me I do not know how to express this term in openfoam. Tc & Ts these are temperature for core and shell fluids.

Your help will so much appreciate

Thanks


OpenFOAM General None min None sec 03-08-21, 1:12 p.m. AM1

Answers:

You can write

- fvm::ddt(tau_ , log(Tc/Ts))

in your equation, but make sure you have defined values of Tc and Ts before adding here.

Regards,
Divyesh Variya
03-08-21, 5:07 p.m. divyesh7
Hi Divyesh

Thank you for your response
 
Okay thank you

Regards


03-08-21, 5:34 p.m. AM1
Hi Diveyesh

May I kindly ask another question with regard to the above,

So for this type D/Dt ln(Tc/Ts), D/Dt is not treated as a material derivative i.e D/Dt = d/dt() + U. grad()?
03-08-21, 8:57 p.m. AM1
Right, If it is material derivative then go with -tau_*(fvm::ddt(log(Tc/Ts))+(U*fvm::grad(log(Tc/Ts)))
or you can write fvm::DDt(tau_, log(Tc/Ts))
03-08-21, 9:18 p.m. divyesh7
Okay now I understand, thank you so much for clarifying this part and assisting me. Much appreciated
03-08-21, 10:48 p.m. AM1

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