[obscureed]

Hi All.

This is a basic question, sorry, but I'm having a mental block.

I would like to estimate Root-Mean-Squared (RMS) flow speed from a steady-state k-epsilon CFD simulation. (Basically, I want to distinguish between regions with low time-averaged speed but plenty of fluctuations, and regions that are genuinely stagnant.)

If U is the time-averaged x-component of velocity and u is the time-varying part, and the same for V+v and W+w, and <...> indicates time-averaging, then RMS flow speed is
sqrt(<(U+u)^2 + (V+v)^2 + (W+w)^2>)
= sqrt(<(U^2+V^2+W^2 + 2(Uu + Vv + Ww) + u^2+v^2+w^2>)
= sqrt((time-averaged-speed)^2 + 2k)

Because the time-averaged <Uu> = U<u> = 0,
and k = <u^2 + v^2 + w^2> / 2.

Is this correct? I seem to remember 2k/3 instead of 2k, but I can't see where the 3 comes in and some Googling hasn't helped. Thanks in advance.
Ed