Capability of CFD-tools for supersonic multiphase flows

Transcription

1 OpenFOAM Capability of CFD-tools for supersonic multiphase flows by József Nagy and Michael Harasek Simulations for both multiphase flows and supersonic single phased flows are well known, however the combination is a less investigated area of research, as the two basic approaches of CFD, the pressure and the density based approach, each describe one of the phases in a better way than the other one. Thus in either of the phases compromises have to be done. Until now compressible multiphase solver have a working range of up to bar. As mostly the pressure based approached is used for multi phase simulations, mostly the gaseous phase is the critical one. Attempts were made to simulate the interaction between a gaseous and a liquid state. Typical solver properties and capabilities were investigated and some settings proposed for further simulations. OpenFOAM is an open source software developed by OpenCFD Ltd. for computational fluid dynamic simulations with many different solvers that were programmed for general problem settings but also very special cases. The capabilities of OpenFOAM for the mentioned flows were investigated. There are four solvers for single phased highly compressible fluids and one multiphase solver for slightly and semi-compressible fluids. These solvers with their properties are listed below [1]: rhocentralfoam: Density-based compressible flow solver based on central-upwind schemes of Kurganov and Tadmor rhopsonicfoam: Pressure-density-based compressible flow solver rhosonicfoam: Density-based compressible flow solver sonicfoam: Transient solver for trans-sonic/supersonic, laminar or turbulent flow of a compressible gas (pressure based) compressibleinterfoam: Solver for 2 compressible, isothermal immiscible fluids using a VOF (volume of fluid) phase-fraction based interface capturing approach (pressure based) For comparison and the investigation of quality of the multiphase solver for highly compressible flows, the solver is used as a single phased solver by setting the same properties for both of the fluids. As the first step both the single phase solvers and the multiphase solver above were compared to the solution with FLUENT s density based solver and with the theory. Initially a certain driving pressure was patched onto the left-hand-side of zero point and 1 atm onto the right-hand side [2]. Then the driving pressure caused a shock front on the right-hand side. In picture 1 the pressure along the shock tube after 7 ms can be seen and it can be observed that all the four compressible solvers calculate the same curve, just the multiphase solver dislocates the expansion fan to the right, which doesn t have a great impact on the important facts of the place and the height of the pressure jump at the shock front. All the solvers even the multiphase predict the correct results within a small error interval. The pressure based solver sonicfoam places the shock front to the left of the solution of FLUENT. The multiphase solver calculates the shock front to the left of the shock front of FLUENT and the two density based solvers place it to the right. rhosonicfoam has a slight overshoot and rhopsonicfoam cannot depict the steepness of the jump. Out of these results rhocentralfoam seems to be the best solver for a single phase supersonic simulation.

2 Picture 1: Comparison between solvers using the shock tube example

3 Picture 2: Comparison with theory Comparing these results with the theory [2] (see picture 2), the OpenFOAM solver locates the pressure jump nearer to the theoretical location than FLUENT. Therefore it can be said, that OpenFOAM is capable of depicting supersonic flows, and even to a certain degree (up to pressures of bar) with two different phases.

4 Errors in OpenFOAM Picture 3: Prediction of the shock front by FLUENT, rhocentralfoam and compressibleinterfoam (10 bar case) For the investigation of the quality of the different solvers the simple Sod Shock example [2] was investigated. Different driving pressures of 10, 100, 500 and 1000 bar were used to check the performance at both low and very high driving pressures.

5 With the standard driving pressure of 10 bar, both FLUENT, the compressible and the multiphase solver yield very similar results. Just the expansion fan of the multiphase solver is somewhat dislocated (see picture 3). Picture 4: Prediction of the shock front by FLUENT, rhocentralfoam and compressibleinterfoam (100 bar case) At 100 bar results of the multiphase solver are overestimated by 30 %, as in picture 4 can be seen. At 500 bar this error is already at the level of 80 % (see picture 5).

6 Picture 5: Prediction of the shock front by FLUENT, rhocentralfoam and compressibleinterfoam (500 bar case) This result is due to the simplified physics in the multiphase solver. There is no energy equation solved and thus compressibility is constant for every time step at every location. However at high pressures temperature dependency of compressibility ψ (ρ=ψ(t)*p) and also other thermo physical properties has to be considered. Without it there is no calculation of the density jump along the contact surface between the driving and driven fluid.

7 Picture 6: Pressure, density and temperature at the contact surface and the shock front with the consideration of the energy equation as is done in rhocentralfoam Picture 7: Density jump

8 Picture 8: Prediction of the shock front by FLUENT, rhocentralfoam and compressibleinterfoam (1000 bar case) In picture 6 the density and temperature jump due to the compression of the driven fluid is shown. In rhocentralfoam the temperature dependent compressibility ψ(t) is implemented. However this effect is not used in the multiphase solver, thus the density here is overestimated in the driven fluid and the pressure is higher, too. However along the contact surface the density is supposed to jump (see picture 7). This is resulting in the overestimation of pressure by 100 % in the case of 1000 bar driving pressure (picture 8). Conclusion It can be said, that OpenFOAM is capable of depicting a multiphase flow, it is also is capable of handling a supersonic flow without bigger problems. The combination of these two is however assured just for slightly or semi-compressible fluids. Attempts in the future have to be done in order to integrate the energy equation into the multiphase solver of OpenFOAM for better quality in the investigation of supersonic multiphase flows. Literature [1] OpenCFD Ltd. OpenCFD Ltd., [2] Sod, G. A. A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws Journal of Computational Physics, 1978, 27, 1-31