Scale-resolving simulations of the flow in internal combustion engines
Paper in proceedings, 2018
The common practice in predicting engine flows is to use the Reynolds-averaged Navier-Stokes (RANS) models. However, the RANS models are single point closures relying on the assumption of self-similarity of the turbulence spectrum, the fact leading to only one characteristic turbulence length scale, defining the entire spectrum. Consequently, the complex physics of the flow in engines could not be captured well in such a way. In the case of running RANS model for multi-cycle engine calculations, calculation results will converge to one cycle results (the first 3-4 cycles are different due to different cycle starting fields, but then the results of the each next cycle will be the same) without predicting cycle-to cycle variations (CCV). Some of reported CCV results with RANS models, are probably due to numerical artefacts rather than physical background of the RANS models. In order to correctly capture all engine related flow phenomena, Large-Eddy Simulation (LES) has been recently more often used, but due to high computational costs, mainly as a research but not as a productive tool. An alternative approach could be found in the use of hybrid LES/RANS (HLR) models. Therefore, we use here a seamless HLR method denoted as Partial-Averaged Navier-Stokes (PANS) in conjunction with the universal wall treatment (Basara, 2006) in order to provide the optimum regarding the accuracy and computational costs. This turbulence bridging method, which supports any filter width or scale resolution, is derived from the Reynolds-Averaged Navier-Stokes (RANS) model equations. It inevitably improves results when compared with its corresponding RANS model if more scales of motions are resolved. The PANS (Girimaji, 2006) variant derived from the four equation near-wall eddy viscosity transport model (see Basara et al. 2011), namely k-ε-ζ-f turbulence model is used here (commercial software AVL FIRE®). This is done by varying the unresolved-to-total ratios of kinetic energy and dissipation given as (euqacation presented) This procedure is applied here on the full engine case. First, Figure 1 shows the resolution parameter fk which is based on RANS results and Eq. (2). This roughly shows that the mesh is in general coarse, for example for LES calculations, but fine enough to try PANS model (note that fk = 1 is in the 'RANS region' and fk = 0.4 is the minimum value). One could propose such mesh analysis prior to LES calculations in order to avoid long calculations, an assessment of the resolved energy and then again new meshing etc. Following the SSV approach applied on the same mesh, an instantaneous fk, which is different than one based on the RANS calculations, is shown in Figure 2, but overall, there are a lot of similarities. This is of course also due to different turbulence level predicted by two approaches. Calculations are performed here also by using spray and combustion modules. Predicted flame front propagation is shown in Figure 3, so the variations are visible for two neighbour cycles N and N+1. One can see that at the top most position of the piston towards head side of position (top dead center - TDC) and few degrees after TDC, the flame front is very different. This can be also seen at different cross-section as shown in Figure 4. This of course causes the pressure variations. It should be also reported that for this particular mesh, cycle to cycle variations obtained by LES are double larger than obtained with PANS calculations (20% vs. 10%) and measurements provided the value of 30%. However, having in mind Figures (1) and (2), and knowing that for proper LES calculations fk should be at least less than 0.2, those variations of 20% could be more addressed to the calculation error. The results presented here show the advantage of the variable resolution PANS method when compared to RANS models. With the help of the computational mesh and the resolution parameters incorporated used in PANS, cycle-to-cycle variations could be predicted. These results approve the PANS basic idea of providing the optimum fidelity on the given numerical mesh. It is also clear that in order to get the most accurate results, meshes should be further refine. However, many engine cases can be calculated with coarser meshes and the then last investigations could be made with refined meshes.
Engine cycle-to-cycle variations