Can anybody explain how it is possible for a low Reynolds number turbulence model (Launder & Sharma, 1974) to accurately predict the friction velocity in turbulent pipe flow, yet underpredict the pressure gradient? My simulation results are definitely grid independent and the pressure gradient was obtained from the calculated pressure field near the pipe exit, where the flow is fully developed. I would greatly appreciate any comments.

Richard Carroni

It is really nice to hear the word "grid independent solution". Since you have obtained a solution for the turbulent pipe flow, it shouldn't be difficult for you to compute a laminar flow case. In this way, you can isolate the problem. You can increase the Reynolds number systematically to make sure that you are not in the turbulent flow regime. It's likely that the source of error is from the code your using or the algorithm in the code. Run a fully developed laminar pipe flow case (1-D problem) using a 2-D code is a good way to check out the numerics of your algorithm. Once you have done that, try to use hand calculation to computate the pressure gradient from the velocity profile and double check the pressure gradient from the code. There are three posibilities:1). you made the mistake, 2). the code was not checked out properly, 3). the algorithm used in the code was not good enough. You must past the laminar flow test, otherwise, it's hopeless. ( In this business, you can not trust anybody including yourself. I mean, CFD is not just running a code. )

John, thanks a lot for replying. Please ignore the second message I posted (I thought the first one had gone missing since I was looking at the wrong index).

After posting my initial call for help, I had done exactly as you suggested, i.e. a laminar pipe flow simulation (Re=1000). The returned pressure gradient was only 1 percent less than the theoretical value, so I guess this indicates that my code is not to be faulted (phew). It might interest you to know that in the turbulent case, the predicted radial profiles for mean velocity and turbulence energy are spot on with other people's predictions using the Launder & Sharma model; the results also compare very favourably with experimental data. All this leads me to extend my original plea for help!!!

Well, I am no sure whether you have resolve your problem or not. Since you have checked out your code for the laminar flow case, the problem ( if it's still there ) is related to your turbulent flow calculation. In addition to the velocity plot, it's also very important to check the radial distributions of the turbulent kinetic energy, the dissipation function, the eddy viscosity and the total shear stress. If you are still having problem with the axial pressure gradient value, then the total shear stress distribution must be off. For the pressure gradient to be a constant there ( in the fully developed flow region), the total shear stress distribution must be linear from the wall to the centerline. It's quite possible that the slope of the total shear stress is off. I had similar problem almost 25 years ago. I solved that problem with 100 mesh points. It's related to the numerical formulation and the evaluation of transformation factors, basically the numerical errors associated with high gradients. Some formulation will give you linear total shear stress distribution, but the numerical will be shifted toward the primitive variables, such as the velocity distribution.