Under-relaxation is used in MpCCI to stabilize the coupled simulations. Both quantities — the relative wall force and the displacements of the coordinates — are under-relaxed with a value of 0.8. The under-relaxed displacement is then added to the old coordinates to get the new position of the nodes. Additionally, in Abaqus/Explicit, the applied load is ramped linearly over the time step.
To get a better understanding of the structural problem, a solid model consisting of C3D8 hexahedron elements was also built and simulated using Abaqus/Explicit (see Figure 4).
The simulation results showed the necessity of a coupled simulation for this application. The simulation, including the fluid-structure interaction at the elastic wall, agrees significantly better with the experimental findings than the standalone CFD simulation.
For an easy comparison of simulation results and experimental data during the simulation, the pressure at three discrete points of the pump is monitored: one point located in the center of the upper chamber, one in the lower chamber, and the last point in the center of the compensation chamber. The pressure at these points is monitored during the simulations and can be compared for different pump parameters or simulation variations.
The pressure contours of the fluid on the moving geometry can also be visualized to get a general idea of the working pump and the quality of the simulation, but the slight differences between the standalone CFD solution and the fluid-structure interaction (FSI) solution cannot be perceived visually on these contour plots. The big negative pressure peaks that were observed for all simulations (CFD standalone and FSI) are probably due to cavitation occurring at the small passages between the different chambers. The oil reaches high velocities when flowing from a cylinder chamber to the compensation chamber. Highvelocity narrow passages and high pressure both point towards cavitation.
The negative pressure peaks are much less pronounced in the FSI solution. Furthermore, the pressure in the compensation chamber shows a different behavior in the two cases. The values during the “high-pressure phase” are higher for the FSI solution. Also, a qualitative difference can be observed when investigating how the pressure rises or falls in the compensation chamber.
The FSI simulations showed a very good agreement with the experiments that were conducted. The CFD model on its own is not capable of catching the pressure behavior — especially in the compensation chamber — in a satisfactory way. The elastic behavior of the wall cannot be integrated into a CFD model without coupling with a structural mechanics solver like Abaqus/Explicit.
Summary and Outlook
The FSI simulation for the simplified symmetric PWK pump model with two chambers produced results that coincide with experimental data in a very satisfactory way. Several configurations and settings for the simple pump model can now be checked with the help of numerical fluid-structure interaction simulation with the aim of finding an optimal configuration.
Simultaneously, the full model of the pump should be investigated with a FSI simulation. This model is quite complex — for seven chambers, the motion of the pistons and the motion of the bridges has to be defined — and therefore will only be simulated for relevant cases that were identified using the symmetric half models. Furthermore, the cavitation that supposedly occurs could be integrated into the CFD model in the future. This might reduce the negative pressure peaks further and lead to a more physical behavior of the fluid.
Another interesting aspect of the pump development is the leakage of hydraulic oil through small gaps. To capture such a phenomenon in a CFD simulation is a challenging task, but would clearly lead to more realistic simulations.
This article was written by Bettina Landvogt of Fraunhofer SCAI in Germany; Leszek Osiecki of Gdansk University of Technology in Poland; Tomasz Zawistowski of Space Research Center of the Polish Academy of Sciences in Poland; and Bartek Zylinski of Bandak Engineering in Norway. For more information on the software used in this work, visit Dassault Systèmes SIMULIA at http://info.hotims.com/40438-321.