## 7 PIV Measurement and CFD Result Comparison of Research Engine  
Three base mesh sizes 3 mm, 4 mm, and 5 mm were evaluated through PIV validation CFD simulations under motoring conditions (without injection), both with and without a tumble plate. A total of 18 simulations were conducted, and the results were compared using GSI and GMI metrics [8] through MATLAB analyses. Each case was examined individually at crank angles of \(-180\)\({}^{\circ}\)CA, \(-140\)\({}^{\circ}\)CA, \(-130\)\({}^{\circ}\)CA, \(-120\)\({}^{\circ}\)CA, \(-110\)\({}^{\circ}\)CA, \(-100\)\({}^{\circ}\)CA, \(-85\)\({}^{\circ}\)CA, \(-70\)\({}^{\circ}\)CA, \(-55\)\({}^{\circ}\)CA, \(-40\)\({}^{\circ}\)CA, and \(-30\)\({}^{\circ}\)CA, based on PIV data sourced from Sandia National Laboratories. According to the GSI results, the match indices under motoring conditions were consistently similar across different mesh sizes, as shown in Figure 7. As the piston approached TDC, the GSI match index increased, reaching a maximum value of 0.8. A similar trend was observed for injection conditions without a tumble plate, as presented in Figure 8, although in this case, the GSI match index remained around 0.75 from the beginning of the injection until the piston reached TDC. Figure 8: Without Tumble Plate with Injection Case GSI Results. Figure 7: Without Tumble Plate and Injection Case GSI Results. Under injection conditions with a tumble plate, the 5 mm base mesh produced the highest GSI match index, achieving values up to 0.7 at \(-30\)\({}^{\circ}\)CA, outperforming the 3 mm and 4 mm cases, as illustrated in Figure 9.  
In terms of GMI analysis, slight variations were noted under motoring conditions. Specifically, for the 3 mm base mesh, the GMI match index declined to approximately 0.75 as the piston moved toward TDC, as shown in Figure 10. Nevertheless, injection cases, both with and without a tumble plate, showed consistent GMI match trends across different mesh sizes, with match indices decreasing steadily from approximately 0.97 to 0.7, as depicted in Figures 11 and 12. Overall, when considering mesh independence and flow separation accuracy, the 5 mm base mesh size provided superior results, particularly under injection and tumble plate conditions that closely resemble actual engine operation. Moreover, the 5 mm mesh setting offered significant computational efficiency, making it the preferred choice for subsequent combustion optimization studies. Figure 10: Without Tumble Plate and Injection Case GMI Results. Figure 9: With Tumble Plate and Injection Case GSI Results. Additional validation of the 5 mm mesh was observed in the injection flow distribution over the measurement plane. Near the end of the injection event at \(-110\)\({}^{\circ}\)CA, the CFD model successfully captured the tumble motion within the cylinder, as seen in Figure 13. Although the k-epsilon turbulence model predicted that the tumble core slightly shifted to the left due to its known underprediction of shear stresses, the overall tumble structure and cavity motion remained well-aligned with experimental observations after the injection event, as illustrated in Figure 14.  
Figure 11: With Tumble Plate and Injection Case GMI Results. Figure 8:0 Without Tumble Plate with Injection Case GMI Results. Figure 8:1 CFD-PIV Vector Field Result Comparison at \(-110\) [CA]. Figures 13 and 14 present comparative velocity vector fields from CFD simulations and PIV measurements at \(-\)110 \({}^{\circ}\)CA and \(-\)70 \({}^{\circ}\)CA, respectively. These phases correspond to the late injection and early compression stages, where tumble development and penetration-driven flow structures are most pronounced. Despite the RNG k-\(\varepsilon\) model's known limitations in capturing near-wall shear stresses and anisotropic turbulence, both figures reveal strong consistency in large-scale flow structures. In Figure 13, the tumble vortex core is reproduced with reasonable fidelity in terms of orientation, shape, and recirculation zone dimensions.