TKE budget estimation by k-epsilon model

pd.iiest · March 12, 2016, 09:38

Hi
I am working on turbulent pipe flow problems, three dimensional and I want to plot total turbulent kinetic energy budget in different axial and redial direction in a pipe bend flow. Reynolds stress transport equation can be defined as: ∂k/∂t= Pk + εk + πk + Dk + Tk − Ck
where
(i) Production (Pk) = −<uiuj> ∂Ui/∂xj
(ii) Dissipation (εk) = −ν <∂ui/∂xj∂ui/∂xj>
(iii) Pressure diffusion (πk) = −1/ρ ∂(<pui>)/∂xi
(iv) Viscous diffusion (Dk) = (ν/2) ∂^2(<uiui>)/∂xj^2
(v) Turbulent diffusion (Tk) = −(1/2) ∂<uiuiuj>/∂xj
(vi) Convection (Ck) = <uj>/2 ∂(<uiui>)/∂xj
Now due to lack of computations resources I can not affort LES. So if I perform transient simulation with k-epsilon model and using the fluctuation data (ui, uj, uk) is it logical to get TKE budget because it is well known that k-epsilon turbulent model is solving the turbulent kinetic energy (k) and turbulent dissipation (ε) using its modeled transport equations and coefficients.

Thanks ..

LuckyTran · March 12, 2016, 12:25

Why can't you solve the k-epsilon model in steady state and just get the turbulent kinetic energy from that? I am not sure what you hope to achieve by running a transient k-epsilon model.

I also don't get where velocity fluctuations come into play. Are you sure you can get fluctuations from a k-epsilon model? You've written down a time-averaged equation (a RANS/URANS equation). Because of separate of time-scales you wouldn't be able to get velocity fluctuations from RANS.

A time-accurate k-epsilon is slightly more expensive than a time-accurate LES because of the additional transport equations being solved (for k and epsilon) whereas LES solves only the three momentum equations.

March 12, 2016, 09:38	TKE budget estimation by k-epsilon model	#1
pd.iiest New Member Prasun Dutta Join Date: Aug 2014 Posts: 13 Rep Power: 12	Hi I am working on turbulent pipe flow problems, three dimensional and I want to plot total turbulent kinetic energy budget in different axial and redial direction in a pipe bend flow. Reynolds stress transport equation can be defined as: ∂k/∂t= Pk + εk + πk + Dk + Tk − Ck where (i) Production (Pk) = −<uiuj> ∂Ui/∂xj (ii) Dissipation (εk) = −ν <∂ui/∂xj∂ui/∂xj> (iii) Pressure diffusion (πk) = −1/ρ ∂(<pui>)/∂xi (iv) Viscous diffusion (Dk) = (ν/2) ∂^2(<uiui>)/∂xj^2 (v) Turbulent diffusion (Tk) = −(1/2) ∂<uiuiuj>/∂xj (vi) Convection (Ck) = <uj>/2 ∂(<uiui>)/∂xj Now due to lack of computations resources I can not affort LES. So if I perform transient simulation with k-epsilon model and using the fluctuation data (ui, uj, uk) is it logical to get TKE budget because it is well known that k-epsilon turbulent model is solving the turbulent kinetic energy (k) and turbulent dissipation (ε) using its modeled transport equations and coefficients. Thanks ..

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March 12, 2016, 12:25		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,762 Rep Power: 66	Why can't you solve the k-epsilon model in steady state and just get the turbulent kinetic energy from that? I am not sure what you hope to achieve by running a transient k-epsilon model. I also don't get where velocity fluctuations come into play. Are you sure you can get fluctuations from a k-epsilon model? You've written down a time-averaged equation (a RANS/URANS equation). Because of separate of time-scales you wouldn't be able to get velocity fluctuations from RANS. A time-accurate k-epsilon is slightly more expensive than a time-accurate LES because of the additional transport equations being solved (for k and epsilon) whereas LES solves only the three momentum equations.