Problem with time average tangential velocity in swirl flow.
I'm working on the swirl flow and I'm not able to get desired time average tangential velocity. My inlet velocity is 10 m/s and I was expecting tangential velocity to be around 19 m/s (since tangential velocity is 1.7 to 2.5 times the inlet velocity) but I'm getting 11.5 m/s only. In swirl flow velocity is not independent and is coupled to pressure, thus simply time averaging the tangential velocity (as given in FLUENT) is not giving good results, although the nature of tangential velocity is fine. All I need to have is the xvelocity "vx" , the yvelocity "vy" and the zvelocity "vz" . The mean zvelocity "vz" is same as the mean axial velocity "vaxial" . The mean tangential velocity "vθ" is to be obtained using Fluent custom field function:
vθ = vx cos θ + vy sin θ where "vx" is the time averaged xvelocity, "vy" is the time averaged yvelocity and "θ" is the angular coordinate. Now when I open Fluent custom field function, nowhere i can find "θ". The above expression tells that the coordinate system used is the Cartesian coordinate system because tangential velocity vθ is expressed in terms of vx and vy. But how to express this "θ". Do I have to write a UDF for this? If yes, how. Suggestions will be appreciated. 
cos (theta) = x/r = x / sqrt(x^2 + y^2)
sin (theta) = y/r = y / sqrt(x^2 + y^2) where theta is measured counterclockwise with respect to the positive x axis. In this case the formula for v_theta becomes (the one you wrote is for v_r): v_theta = (x * Vy  y * Vx) / sqrt(x^2 + y^2) where Vx and Vy are the velocity components along the x and y directions. While for v_r you get: v_r = (x * Vx + y * Vy) / sqrt(x^2 + y^2) Now it's up to you to substitute the correct velocity components and cell center coordinates in a custom field functions (still, i suggest using an UDF to control possible singularities on the axis). By the way, the statistics on unsteady flows (in general, not only Fluent) are just a postprocessing step. The coupling between pressure and tangential velocity has nothing to do with the correct postprocessing or computation. 
Thanks sbaffini
I got it n I'll be trying it soon. I still have one question! Is the tangential velocity calculation made by fluent (one of its default option for velocities) different from the one given in your expression? 
I don't know this but certainly, if you agree with me on the derivation, it can't be different. What i'm sure of is that the tangential velocity is just a postprocessing quantity and not a solved one (except for 2D axysimmetric flows or some rotating frames... but that's another story)

Thanx sbaffini for your reply. Yea you are right. Even fluent uses the same expression for the tangential velocity, which I've confirmed with the one given by you, and the results are the same.
sbaffini, I've one more question. What is the procedure for time averaging of any parameter in the simulation. Shall I start averaging right from the beginning of the simulation or when the simulation is about to converge and let it run for some extra time? I'm following the former one with extra run time. 
Forget the CFD case. If you had to make some averages of some quantity varying in time... would you wait for it first reaching a statistically steady state? I think you know the answer (which, just in case, is to wait until the statistically steady state is reached before averaging)

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