Problems with Turbulence Decay Calculation
I've come across a very strange FLUENT behavior when trying to solve a test problem on turbulence decay in 1D incompressible flow.
The parameters are simple: we have a 1D flow of incompressible fluid, Rho = 1.225 kg/m3, U = 1 m/s,
at the inlet I specify k=0.5, Eps = 0.1 to see how turbulence decays with distance (up to 4 m). There is no patricular reason for choosing the above values, just a test.
I specified quite a high value of laminar viscosity (Mu_l =0.01) and obtained successfully a converged solution with k, Eps and Mu_eff decaying with distance. Backward differences are used for convective terms (1st order scheme), standard k-epsilon models, symmetry conditions on side walls, no wall functions required.
PROBLEM: I tried to check the converged solution. In this "classic" flow there is no generation, and at convergence three terms must sum up to zero: convection, diffusion, and dissipation. I've exported cell centered data for k, Eps, Mu_eff and tried to estimate "by hand" each term
(taking finite-volume style differences) and see if they sum up to zero. Surprisingly, the converged to 10-8 solution does not give this consistency: say, convective term Rho*U*(k(i)-k(i-1))/dX =-0.08152, diffusive term
((k(i+1)-k(i))*Mu_eff(i+1/2)-(k(i)-k(i-1)*Mu_eff(i-1/2))/dX^2 is 0.005464935, Dissipation Rho*Eps = 0.090285. This together gives (Diss + Conv - Diff) = 0.00329614, which is nowhere near to 10-8. (Mu_eff at cell boundaries was estimated by linear interpolation).
To put it straight, I dont care for now about physical validity (too high laminar viscosity etc), but trying to figure out - what exactly equation is solved in FLUENT and why its hand calculation is inconsistent with convergence criterion.
Any help ot ideas is highly appreciated, perhaps something is wrong in my checks, so please dont hesitate to point my nose to it :)
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