turbulent energy spectrum
 

Hi

I want to calculate energy spectrum for my LES simulation. I put a point in domain and monitored u, v and w velocities. I calculated the kinetic energy from my velocities and imported the kinetic data and time into matlab. I, then, converted my time domain into frequency domain by using fft.

How do I draw energy spectrum then? In book there is E(k) on y-axis and k (wave number) on x-axis. Is E(k) same as kinetic energy which is 0.5(u^2+v^2+w^2)? How do I calculate k (wave number) on x-axis? Thanks in advance for your answer.

Re: turbulent energy spectrum
 

If you want to draw energy spectrum for LES, it means that you have to consider the energy of large eddies+the energy of subgrid scale. To find the energy for large eddies you are right, you can use the equation you've mentioned. But in order to draw complete energy spectrum you also need to know the energy of subgrid scale. This energy is derived from Kolmogorov hypothesis. Which means that for eddies much smaller than the energy containing eddies and much larger that dissipative eddies (of the order of Kolmogorov scales), turbulence is controlled solely by the dissipation rate (epsilon) and the size of the eddy (1/k), where k is the wave number and equals 1/L (L=size of eddies). In this subrange turbulent energy equals to epsilon^2/5*k^5/3. If this assumption is right then for LES, 1/k is basically your grid size, because in LES you have to define filter width, which separates the resolved scales from subgrid scales. In the finite volume discretization, the filter width is clearly related to the mesh size.

The question is, can you get separate energy parts (for Large scale and for Sub-grid scale) of the entire turbulence energy spectrum in the output data of STAR-CD? I guess in the output, STAR-CD only gives us turbulence energy and dissipation in the Sub-grid scale. Please correct me if I am wrong.

Regards