PVE-11652 LRB / CBM – May 17 2017

The validation study on flow in a straight pipe ran into difficulty determining the ultimate pressure drop.  Each time the mesh was further refined, a new pressure drop was calculated.  A final answer was not calculated even for extreme mesh sizes run over an entire weekend.  An approximate answer was possible, but without assurances that it was the final answer.  How can this CFD tool be useful?

When the ultimate pressure drop is not the goal, a way forward is available.  In this exercise, two similar designs for 180° pipe elbows are compared.  We do not need the absolute pressure drop.  The goal is to find which has the lower pressure drop.  How easy is it to get this result?  And finally, can this method be used on more complex objects?

Figure 1: Two 180° flow elbows to be compared. Section view.  Which has the lower pressure drop?  “U” configuration on left, “LR” for larger radius on right.

Like the previous validation sets, an initial very coarse mesh is used.  Flow Simulation is set to refine the mesh where required until all areas converge and no further mesh refinement is required.  Inlet velocity to both elbows is 1 m/s water at 293.2 K and 1 atmosphere.  Half symmetry on the XZ plane isused to reduce the complexity of the model.  Flow Simulation was set to monitor the pressure drop across both elbows, and compute the ratio of the pressure drop in the “U” design to that of the “LR” design (LR/U – numbers greater than 1 indicate that the pressure drop is larger in the LR case).  

The inside flow passage diameter for both elbows is 0.019 m (0.75″).  Both have a leg to leg spacing of 0.0508 m (2″).  The bend radius of the U design is 0.0254 m (1″)  with a 0.0369 m (1.45″) inlet section and a 0.1511 m (5.95″) outlet straight pipe section to allow flow to develop before and after the elbow.  The LR design has a larger bend radius of 0.0285 m (1.125″) and the inlet and outlets are reduced in length to allow for a 0.019 m (0.75″) long flow offset section.  

The initial coarse mesh (fig 1) was solved by Flow Simulation over 240 steps over which time the pressure drop ratio reached a rough convergence.  As the convergence was too rough to allow automatic refinement, the iteration for refinement was chosen by the operator during the run.  Total run time was 3 hours on a medium power computer: i7 6600U CPU @ 2.6-2.81 GHz (2 physical cores, 4 hyper threaded cores),  16 GB ram (14 GB used).

Figure 2: Initial mesh used. Results are not expected to be useful, but the program uses the results from each mesh size to determine where more refinement is required in the next mesh.

Figure 3: Final mesh (#6) detail for “LR” elbow. many areas of the mesh have reached convergence and their final mesh size, areas of turbulence and the boundary layer are still being refined (darkest areas with the smallest cells).

Figure 4: Midplane velocity profiles for the final mesh size.  The flow pattern is not simple, and the “LR” elbow (right) has a more complex pattern than the “U” elbow (left).

Figure 5: Complex flow patterns around the elbows.  This is from the final mesh size (mesh 6).

Figure 6: Pressure drop for the “U” elbow (green) and “LR” (red). The pressure drop graphs did not reach convergence before the run was stopped.  However, the results are still useful.  Refinement points are shown as “*”.

Figure 7: The ratio of the two pressure drops from figure 6. Useful and consistent information emerges that can be used to compare the two elbows.  The highlighted areas are the areas used for the averages.

From Figure 7 – mesh densities for 1 and 2 are too coarse to accurately capture the complexity of the flow going through the elbows and should be ignored.  Meshes densities 3 and 4 are typical of what is attainable in a practical flow problem.   These results are obtained after 6 minutes (362 s). Mesh sizes 5 and 6 are probably not attainable in real world problems more complicated than this simple flow example.   Taking the results from meshes 3 and 4, the “LR” elbow is expected to have a pressure drop about 7.6 to 7.8% higher than the “U” shaped elbow.

Although the pressure drop has not converged, it can clearly be seen that the “U” shaped elbow has a lower pressure loss. This calculation was easily within the reach of the medium powered computer used.