Grid resolution impact

In this section, only synthetic turbulence method is used for the two intensity levels previously seen in Sec. 6.2.1 since in LES, one of the most important effect relates to the mesh resolution. For the MUR235 case it is naturally expected to play a key role. By refining the mesh, the increase in resolution will allow smaller structures to arrive to the leading edge. Such a be- haviour is confirmed by looking at instantaneous views issued from the use of meshes M1 and M2, Figs. 6.21a & 6.21b. Smaller turbulent structures can clearly be observed with the finer mesh. The other most noticeable effect of the grid resolution concerns the effect it has on the acoustic waves emanating from the vortex shedding from the trailing edge, see Fig. 6.21a. The strong acoustic waves that are emitted from the blade are seen to be much less intense with the refined mesh as observed in Fig. 6.21b.

To further investigate the differences issued by the use of M1 or M2 grids, local probes A and B are placed in the wake and on the blade surface for both simulations as shown in Figs. 6.21a and Fig. 6.23a. Recall that for MUR129, Fig. 6.2 represented the pressure spectra recorded at the same probes A and B. Spectrum at probe B clearly highlighted a tonal peak corresponding to the vortex shedding frequency at 43 kHz. A peak at the exact same frequency was found for probe A on the wall and which is also found when analyzing the M1 grid MUR235 simu- lation. However, performing the simulation with the M2 mesh, Fig. 6.22, a peak is no longer clearly visible in the pressure spectrum recorded in the wake at probe A nor at probe B. The reason for this is found by doing a visual comparison between the wakes for M1 and M2 grids, Fig. 6.23. The wakes issued by the two simulations are very different if looking at shear zones and coherent vortices. The M1 mesh shows a shorter shear zone accompanied by some very coherent vortices. On the other hand, the M2 mesh has a longer shear zone and the vortices

6.2 MUR235 predictions

B

(a) M1 mesh density gradient (b) M2 mesh density gradient

Figure 6.21: Density gradient comparison for 18% turbulent intensity at inlet.

are less coherent. As a consequence the spectrum recorded at probe A for M2 contains many less tonal frequencies than the M1 grid.

The presence or absence of these waves can however have a direct impact on the boundary layer and thus affect the heat transfer as shown in Fig. 6.24. Indeed, the boundary layer evo- lution of the M1 mesh shows a higher heat transfer upstream when compared to the fine mesh observed between s ⇡ 25 40 mm. Figure 6.24 also shows that the fine mesh predicts more accurately the level of heat flux downstream from the shock if compared to the M1 mesh, con- firming it is a mesh refinement effect. It is reasonable to ask then if one of the meshes (or both) might not be adequate for the capture of these waves or that the waves are generated due to the way the domain was meshed. It seems logical thus to generate a third more refined mesh M3. The first aspect to consider is the existence of these waves for the new M3 mesh. For this new mesh, acoustic waves are seen to reappear similarly to the M1 grid which suggests that the M2 mesh is not adequate for the capture of the correct trailing edge physics and thus the acoustic waves issued. The effect on fields such as the isentropic Mach number is shown in Fig. 6.25b. Small differences may be seen for the pressure side of the leading edge. The same conclusions are extracted on the suction side between s ⇡ 0 25 mm which corresponds to the leading edge region. Up to s ⇡ 40 mm, it is the impacting acoustic waves that dominate the flow, and so, the absence of acoustic waves in M2 shows differences compared to M1 and M3. Downstream from this position, M1 and M2 have a great resemblance while M3 departs from the previous one due to differences in flow physics.

Shear stress profiles show larger differences between meshes. On the pressure side, a slight increase in shear stress is found thanks to a better transport of turbulent structures in the pas-

0 2 4 6 x 104 −₄₀ −₂₀ 0 20 40 60 f (Hz) PSD pressure Probe A Probe B

Figure 6.22: Spectral composition of the pressure signal at probes A and B.

B

(a) M1 (b) M2

6.2 MUR235 predictions − 60 − 40 − 20 0 20 40 60 80 Curvilinear abscissa s (m m ) 0 200 400 600 800 1000 1200 H e a t tr a n sf e r co e ff ic ie n t W/ m 2 K

Pressure side Suct ion side Experim ent al MUR235

MUR235 18% Coarse MUR235 18% Fine

M1 M2

Figure 6.24: Heat flux comparison of MUR235 with fine mesh.

(a) (b)

Figure 6.25: Isentropic Mach number comparison of MUR235 with three meshes and 6% turbulent intensity at inlet.

Figure 6.26: Shear stress comparison of MUR235 with three meshes and 6% turbulent inten- sity at inlet.

sage upstream the blade as well as a better refinement in the near-wall region. This conclusion extends to the profile around the leading edge of the blade which is also better captured. The influence of the free-stream turbulence on these two regions was shown in Sec. 6.2.1 so it is not surprising that a more resolved free-stream leads to better results. The largest differences are seen however in the transitional area on the suction side. Both M1 and M2 meshes remain practically at the same level while the M3 mesh predicts a shear stress that is up to 50% higher at the abscissa before the shock wave. This tendency is similar to the already observed effect when increasing the turbulence at the inlet for a coarser grid (M1) seen in Fig. 6.10. It was demonstrated that this effect was due to the existence of turbulent spots along the suction side. Figure 6.27 shows the heat flux predictions obtained with the three meshes for the level of free stream turbulence indicated in the experiments, 6%. This turbulence level seems to have a different impact on heat flux for M3 if compared to the two coarser meshes. Both M2 and M3 show a better prediction on the pressure side of the blade, probably only due to refinement both at inlet and in the wall region. On the suction side, in the pre-transitioning region, the heat flux is notably different between the finer mesh M3 and the other two. The surface heat transfer after the shock is captured much more accurately for increasing the refinement even if the isentropic Mach number distributions are very similar as in Fig. 6.25a.

For all cases, an increase in shear stress is accompanied by an increase of heat flux at every curvilinear abscissa position. Both shear stress and heat transfer together suggest that the simulation with the M3 grid and a 6% turbulence at the inlet does present turbulent patches on the blade surface. The Q-criterion presented in Sec. 6.3 of this M3 grid confirms this aspect, turbulent spots appearing very early on within the flow BL: i.e. way upstream the shock around s/c_{⇡ 0.7 (s ⇡ 47 mm).}

6.2 MUR235 predictions

Figure 6.27: Heat flux comparison of MUR235 with three meshes and 6% turbulent intensity at inlet.