Figure 8 Dependence on number of points on the airfoil.
Related Figures (14)
Fig. 1 Performance at design speed - Predicted and measured exi survey data near peak efficiency (NASA Rotor 67) The grids topologies developed along with the TRAF codes are of non-periodic C- and H-types (Amone et al., 1992). The removal of mesh periodicity allows the generation of grids with a low level of skewness even in blade rows with large camber (turbine blades) or high stagger (compressor). <A bdlade-to-blade view of a 225xd/ viscous grid originally used for the NASA Rotor 37 blind test case is shown in fig. 2. In the same figure, enlargements near leading end trailing edge of the airfoil are also given. Fig. 2. Blade-to-blade grid for the NASA Rotor 37 (blind test case). Flg. 3 Regions considered on a blade-to-blade surface for the grid dependency study. To quantify the influence of the grid variations, it was found effective to use the rotor operating characteristics in terms of total pressure ratio versus normalized mass flow. The choice of the total pressure ratio is related to the fact that total pressure was found to have larger variations with respect to efficiency. Leading Edge Reglon Fig. 5. Fine grid with 40 cells on the leading edge circle. Fig. 4. Relative Mach number contours near leading edge. The impact of the leading edge grid density on the rotor operating characteristic is summarized in fig. 6. The solution becomes grid independent starting from the case with 20 cells on the leading edge circle. With few cells, differences grow when going towards low mass flow rates. In such conditions, the bow shock is detached and moves away from the leading edge in a region where the grid is relatively coarse so that the associated total pressure rise is not properly predicted. Fig. 7. Influence of grid density in the inlet region. Fig. 6. Dependence on number of cells on leading edge circle. Fig. 9. Dependence on y* (blade boundary layer). Figure 9 shows the results of the calculations and indicates how a near-wall y* close to 2.0 should be sufficient for a good prediction of the profile loss in compressor rows, (oo. Tralling Edge Region In compressor blades, the trailing edge ts often rounded and thinner than the leading edge. Downstream of the passage shock, the flow is rather uniform and as far as unsteady losses are concerned, those associated with shock buffeting, shock boundary layer interaction and boundary layer thickening are suspected of dominating possible trailing edge vortex shedding. For compressors, it is generally accepted that the grid at the trailing edge can be relatively coarse (Strazisar and Denton, 1995). A series of calculations has been performed increasing the number of cells located on the trailing edge circle. To compensate for the impact of the grid clustering in the trailing edge area, the mesh size has been progressively increased to obtain meshes as similar as possible except near the trailing edge. Good independence of the calculations from the number of cells located on the trailing edge According to the results of figs. 5-6, 20 uniformly spaced cells were located on the leading edge circle, and 53 points were introduced in the normal-like direction. The grid spacing at the wall in the normal-like direction was selected to have an averaged near-wall y* of about 2.0 (see fig. 9). Two cells were used to model the trailing edge (see fig. 10) and 57 points were introduced to stack the grid in the radial direction. The final mesh is therefore close to 800,000 grid points (265x53x57) and more than twice as big as the one employed in the blind test case (225x4/x41). The predicted operating characteristics in terms of total pressure ratio and adiabatic efficiency are compared to experiments in fig. 13. To quantify the impact due to the grid improvement, the original results of the blind test case are also reported. Because of memory restrictions at that time, the blind test case results were obtained on a 225x41x41 grid with roughly /0 cells on the leading edge circle and an averaged near-wall y* of 4.0. The improvement in the prediction of the rotor total pressure rise is appreciable but not substantial with a mean overestimation of about 3%. On the contrary, the computed efficiency on the refined grid exhibits good agreement with measurements. Only very close to the choke does the underprediction reach 1%. Fig. 14. (a,b,¢,d) Predicted and measured exit survey data - M/mehake=0.98 (NASA Rotor 37) Fig. 15. Total pressure exit survey - m/m.p542=0.995 (NASA Rotor 37). Fig. 16. Measured and predicted relative Mach number contours - n/mchoke=0.98 (NASA Rotor 37). Fig. 17. Dependence on point distribution in the spanwise direction.
