# How to calculate dissipation rate in OpenFOAM

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 November 3, 2021, 15:35 How to calculate dissipation rate in OpenFOAM #1 Senior Member   Farzad Faraji Join Date: Nov 2019 Posts: 127 Rep Power: 4 Hello all I hope you are well. I want to calculate dissipation rate in LES simulation and I find a good code for calculating TKE budget. https://github.com/AndreaDesan/pimpleTKEBudgetFoam But I can not use it since some definitions are different, so I decided to use the definitions in the code(tkeBudget.H); https://github.com/AndreaDesan/pimpl...er/tkeBudget.H Code: ``` volScalarField kSGS = turbulence->k(); //Instantaneous subgrid-scale tke volScalarField kRes = 0.5*(UPrime & UPrime); //Instantaneous resolved tke kTot = kRes + kSGS; volScalarField epsilonSGS = turbulence->epsilon(); volSymmTensorField SRes = symm(fvc::grad(UPrime)); //Instantaneous resolved fluctuating rate of strain volScalarField epsilonRes=-2*nuLam*(SRes && SRes); //Instantaneous resolved dissipation rate epsilonTot = mag(epsilonRes + epsilonSGS); LESResIndex = kRes/max(kSmall,kTot); //Instantaneous ratio of resolved to total (Resolved + SGS) tke``` Now, lets return to my main discussion; a) The dimension of tke is [m2s(-2)] and "tke rate" must be [m2s(-3)] b) the dimension of dissipation rate must be the same, so I calculate for both epsilonSGS and epsilonRes as below; 1- epsilonSGS = Ce*pow(k,3/2)/delta====>[Ce]*[k^3/2]/[delta]====>[1]*[m3s(-3)]/[m]====>m2s(-3) 2- epsilonRes = nu * (gradU && gradU)====>[m2s(-1)]*[?????]=== I calculate "gradU && gradU" in OpenFoam and dimension was s(-2), so we have [m2s(-1)]*[s(-2)]=m2s(-3). basically epsilonSGS and epsilonRes has the same dimension m2s(-3) which is the same as tke rate m2s(-3). From this I think I have calculated the [?????] correctly. Am I correct?

November 3, 2021, 16:28
#2
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Join Date: Nov 2019
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Maybe this question is a little stupid one. I always read and heard dissipation rate [m2s(-3)], but I never heard about TKE rate. TKE is [m2s(-2)], so TKE rate must be [m2s(-3)] which is the same as dissipation rate. am I correct?

Quote:
 Originally Posted by farzadmech Hello all I hope you are well. I want to calculate dissipation rate in LES simulation and I find a good code for calculating TKE budget. https://github.com/AndreaDesan/pimpleTKEBudgetFoam But I can not use it since some definitions are different, so I decided to use the definitions in the code(tkeBudget.H); https://github.com/AndreaDesan/pimpl...er/tkeBudget.H Code: ``` volScalarField kSGS = turbulence->k(); //Instantaneous subgrid-scale tke volScalarField kRes = 0.5*(UPrime & UPrime); //Instantaneous resolved tke kTot = kRes + kSGS; volScalarField epsilonSGS = turbulence->epsilon(); volSymmTensorField SRes = symm(fvc::grad(UPrime)); //Instantaneous resolved fluctuating rate of strain volScalarField epsilonRes=-2*nuLam*(SRes && SRes); //Instantaneous resolved dissipation rate epsilonTot = mag(epsilonRes + epsilonSGS); LESResIndex = kRes/max(kSmall,kTot); //Instantaneous ratio of resolved to total (Resolved + SGS) tke``` Now, lets return to my main discussion; a) The dimension of tke is [m2s(-2)] and "tke rate" must be [m2s(-3)] b) the dimension of dissipation rate must be the same, so I calculate for both epsilonSGS and epsilonRes as below; 1- epsilonSGS = Ce*pow(k,3/2)/delta====>[Ce]*[k^3/2]/[delta]====>[1]*[m3s(-3)]/[m]====>m2s(-3) 2- epsilonRes = nu * (gradU && gradU)====>[m2s(-1)]*[?????]=== I calculate "gradU && gradU" in OpenFoam and dimension was s(-2), so we have [m2s(-1)]*[s(-2)]=m2s(-3). basically epsilonSGS and epsilonRes has the same dimension m2s(-3) which is the same as tke rate m2s(-3). From this I think I have calculated the [?????] correctly. Am I correct?

 November 8, 2021, 07:27 #3 Senior Member   Andrea Join Date: Feb 2012 Location: Leeds, UK Posts: 179 Rep Power: 14 Not sure from where within code you got "tke rate". Andrea

January 11, 2022, 03:44
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Josh Williams
Join Date: Feb 2021
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Quote:
 Originally Posted by farzadmech Hello all I hope you are well. I want to calculate dissipation rate in LES simulation and I find a good code for calculating TKE budget. https://github.com/AndreaDesan/pimpleTKEBudgetFoam But I can not use it since some definitions are different, so I decided to use the definitions in the code(tkeBudget.H); https://github.com/AndreaDesan/pimpl...er/tkeBudget.H Code: ``` volScalarField kSGS = turbulence->k(); //Instantaneous subgrid-scale tke volScalarField kRes = 0.5*(UPrime & UPrime); //Instantaneous resolved tke kTot = kRes + kSGS; volScalarField epsilonSGS = turbulence->epsilon(); volSymmTensorField SRes = symm(fvc::grad(UPrime)); //Instantaneous resolved fluctuating rate of strain volScalarField epsilonRes=-2*nuLam*(SRes && SRes); //Instantaneous resolved dissipation rate epsilonTot = mag(epsilonRes + epsilonSGS); LESResIndex = kRes/max(kSmall,kTot); //Instantaneous ratio of resolved to total (Resolved + SGS) tke``` Now, lets return to my main discussion; a) The dimension of tke is [m2s(-2)] and "tke rate" must be [m2s(-3)] b) the dimension of dissipation rate must be the same, so I calculate for both epsilonSGS and epsilonRes as below; 1- epsilonSGS = Ce*pow(k,3/2)/delta====>[Ce]*[k^3/2]/[delta]====>[1]*[m3s(-3)]/[m]====>m2s(-3) 2- epsilonRes = nu * (gradU && gradU)====>[m2s(-1)]*[?????]=== I calculate "gradU && gradU" in OpenFoam and dimension was s(-2), so we have [m2s(-1)]*[s(-2)]=m2s(-3). basically epsilonSGS and epsilonRes has the same dimension m2s(-3) which is the same as tke rate m2s(-3). From this I think I have calculated the [?????] correctly. Am I correct?

You use UPrime to calculate epsilonRes, but from equation 14 in this paper [1], it appears this would give you epsilonSGS. Instead, based on [1], you should use epsilonRes_ij = nu * (gradU & gradU). Then you can probably get it as a scalar as you appear to have it by taking the trace?
I have also seen epsilonRes been calculated as epsilonRes = dkRes/dt [2].

[1] Wacławczyk, M., Pozorski, J. and Minier, J.P., 2004. Probability density function computation of turbulent flows with a new near-wall model. Physics of Fluids, 16(5), pp.1410-1422.
[2] Jayaram, R., Jie, Y., Zhao, L. and Andersson, H.I., 2020. Clustering of inertial spheres in evolving Taylor–Green vortex flow. Physics of Fluids, 32(4), p.043306.

 Tags dissipation rate, les, tke les