a guy named kalyan in this forum have suggested the flowing solution procedure on peridic flow drived by pressure. but for a multiflow,the flow is not only driven by pressure, olso by other forces, such as drag force between particle and flow. So how to handle this kind of periodic pressure loss "DP".

for a single flow, the corresponding method( originate from Patankar's idea) ***************************** Temporal simulation :

i) No-slip walls

ii) Periodic boundary conditions for velocity components.

iii) Step periodic pressure B.C. in the axial direction, i.e., P(L+x) = P(x) + "DP" where L is the length of your duct.

The step periodic pressure B.C. means that your are simulating a pressure driven flow. The pressure gradient balances the frictional forces at the walls (which depend on Reynolds number).

iv) The bulk velocity would depend on "DP" (and shear stresses at walls). Once the flow has reached a stationary state, you can use the bulk velocity to compute the Reynolds number and if it is higher than the required Reynolds number, reduce "DP" till the bulk velocity is lowered to give you the required Re. If the Reynolds number is lower than required Re, then increase "DP" till you reach the appropriate Re. You might have to set up a Newtons iteration to change "DP" at every 10 time steps to move your flow Re to the required Re.

Once you have the turbulent flow setup at the required Re, take a single plane of this flow and use it for inflow conditions to a spatial simulation. This approach requires two simulation and so it some what expensive but quite accurate.

Also, could any guy detail the procedure of evaluation of "DP" by Newton iteration ? thanks in advance