Annular compressor cascade with tip clearance
Application Challenge 6-05 © copyright ERCOFTAC 2004
The CFD predictions are presented in Figure 13, Figure 14, Figure 15, Figure 16 and Figure 17. For each and every test case examined, results in the form of circumferential mass average span-wise distributions of the flow quantities at Stations 2, 8 (when available) and 9 of the cascade are provided. The quantities shown are the static and total pressure, the absolute yaw angle, the Mach number, the axial and peripheral velocity and the PLC. By definition PLC=0 at Station 2. The experimental curves are also included in the same figures, so that comparisons between theoretical predictions and experiments are feasible. For every value of the tip-clearance height (i.e. 2mm or 4mm), the distributions of the flow quantities when the hub is still or rotating appear in the same figure, so that the reader may readily identify the differences that the relative blade/end-wall motion introduces to the flow structure.
At Station 2 there exists a very good agreement between experiments and calculations for all flow quantities but the flow angle in the peripheral direction. For this quantity, discrepancies are found to be important in the regions near the two end-walls. They reflect the development of a boundary layer between the grid inlet plane and Station 2 in the calculations. It is appropriate to recall, in this respect, that the exact experimental curves have been imposed at a plane located 50%Cax upstream of the actual measuring plane. Imposing the experimental data in the exact measuring station is not viable computationally, since this station is located very close to the blade leading edge, where flow is by no means uniform in the circumferential direction, as the imposed boundary conditions imply. On the other hand, trying to reconstruct the boundary conditions at Station 1, in order to match the experiment at Station 2 is very difficult (time consuming) when calculations are performed using three-dimensional Navier-Stokes solvers.
The comparisons between the computational results and the experimental data for the circumferential mass average flow quantities at Station 9 reveals that the former predict the persistence of the tip-clearance vortex at a station located 119%Cax downstream of the trailing edge, whilst in the experiments a mixed out situation exists at the exit. This is a common feature for all cases examined, for both tip-clearance heights, and this is more pronounced in the distribution of the flow angle in the peripheral direction in the first 40% of the span above the hub level.
Deficits appearing on the computational distributions of the axial velocity, the total pressure and the Mach number near the hub wall, in respect to experiment, result in higher axial velocity and Mach number values away from the wall and inside the mid-span region. It must be stressed that a thinner hub boundary layer is predicted in the computations for all cases, when compared with the experimental data. On the other hand, a thicker boundary layer is predicted at the casing.
These discrepancies between experiments and calculations are identical with the ones observed in the computations of the first set of experimental data (Politis et al., 1998a, Bonhommet–Chabanel and Gerolymos, 1998 and Gregory–Smith and Crossland, 2000). In these calculations, inconsistencies were attributed to the inability of the assessed isotropic turbulence models to predict an accurate mixing of the flow downstream of the cascade. This inability is thought to be due to the prediction of too strong a tip-clearance vortex, and is a common feature of the k-ε type turbulence models, as reported in open literature. It is attributed to the fact that all such models are unable to account for departure from equilibrium conditions, which is closely related to non-isotropic behaviour. The interesting feature of the calculations for this Application Challenge is that all variants that have been used (see section “Overview of CFD Simulations” and Gregory–Smith and Crossland, 2000) fail to reproduce the correct physical processes, regardless of their ‘simplicity’ (for example the high-Reynolds-number variant presented herein) or their elaborate modelling. It would appear that a higher order turbulence model is required to capture fully the mixing of the flow downstream of the blade trailing edge.
On the other hand, despite these deficiencies, the calculations have been able to predict the correct behaviour of the flow quantities due to the tip-clearance size changes or the relative blade/end-wall motion. In this context, it is worth mentioning that the presence of a stationary hub increases the level of losses for the same value of the tip-clearance size. However, losses are overestimated in the computations. Over and above, the span-wise extent of the region occupied by the tip-clearance vortex is larger when the hub is still. Finally, the rate of the increase in losses, when the tip-clearance increases, is greater when the hub rotates, in comparison with that for a stationary hub. In this case, the ‘absolute’ values of losses are larger, as shown by both calculations and experiments.
Figure 13 : Span-wise distributions of the circumferential mass average flow quantities at Station 2. Red lines: CFD-1, red symbols: EXP-1, green lines: CFD-3, green symbols: EXP-2.
Figure 14: Span-wise distributions of the circumferential mass average flow quantities at Station 8. Red lines: CFD-1, red symbols: EXP-1, green lines: CFD-3, green symbols: EXP-2.
Figure 15: Span-wise distributions of the circumferential mass average flow quantities at Station 9. Red lines: CFD-1, red symbols: EXP-1, green lines: CFD-3, green symbols: EXP-2.
Figure 16: Span-wise distributions of the circumferential mass average flow quantities at Station 2. Red lines: CFD-4, red symbols: EXP-3, green lines: CFD-5, green symbols: EXP-4.
Figure 17: Span-wise distributions of the circumferential mass average flow quantities at Station 9. Red lines: CFD-4, red symbols: EXP-3, green lines: CFD-5, green symbols: EXP-4.
© copyright ERCOFTAC 2004
Contributors: Dr. E.S. Politis; Prof. K.D. Papailiou - NTUA