Dear all. I'm going to perform direct numeriacl simulation of the fully developed turbulent flow through square duct. I want to make efficient initial condition of velocity field in order to get fully developed turbulent profile faster. Could you tell me how to make initial velocity of turbulent flow.

Hi there,

A way of initializing the field would be to superimpose some random fluctuation to the typical turbulent average velocity profile for channel flow. you would get something like (in fortran):

flct= 0.1 u= uaverage(y) + flct*( rand(0) - rand(0) ) v= flct*( rand(0) - rand(0) ) w= flct*( rand(0) - rand(0) )

Where the expression for uaverage(y) is known and can easily be found in the litterature. Check the book: "Viscous Fluid Flow" by Frank M. White, McGraw-Hill, 1991.

Sincerely,

Frederic Felten.

(1). There was some discussions here, long time ago. So, you may want to do the old messages search for the related topics.

You can temporally evolve the solution using a pressure-driven periodic flow in a square duct. They are a couple of points to note.

i) You can not estimate the pressure gradient needed to evolve the flow to the Reynolds number you want unless you know the wall shear stress distribution (in the fully developed state) in the cross-sectional plane. You would know the stress distribution if you know the velocity profiles (at least near the walls). If you already know the velocity profile, you might not want to solve the problem unless you want the turbulence characteristics. To solve this problem, assume a pressure gradient, solve the periodic problem and if the bulk flow Re is lower than what you need, increase the pressure gradient or else decrease it. You can use Newtons method to arrive at the pressure gradient at each step (or every few time steps). Once you have the Re you want, you also have at hand the pressure gradient that is needed to drive the flow.

ii) When you solve the periodic problem, you need to make sure that length of the domain in the periodic direction is much larger than the longitudinal integral length scale and the size of the largest longitudinal structure you want.

iii) Temporal evolution to a fully developed state might take a long time when using DNS. So use coarser resolution (about four times coarser along each direction than the DNS) ans use LES to obtain a quick approximate solution. Then map this LES solution to the fine mesh and then start the DNS.