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The leading-edge region was of particular-concern in this effort. Unlike an axial turbine which has a slightly negative optimum incidence, a 12-bladed radial rotor achieves optimum incidence at a much higher negative incidence (at -36.70 relative inlet flow angle for this design). This implies a region of very rapid flow adjustment and large velocity gradients in the leading-edge region of a radial turbine. The blade loadings reach their maxima in this region where the incoming negatively incident streamlines are turned toward zero incidence at the rotor inducer tip. The varying radius in this region also contributes to the rapidly varying flow field. To complicate matters further, the subject rotor was designed for a higher-than-optimum work factor of1.126resultinginanonoptimumpositiveincidenceof16.50. Anoptimum workfactorforthisrotoris0.833(ref.11). Besidesthegridpackingnear the leading edge, cusps were extended inthis region to eliminate singularity and to minimize discontinuities in the grid slope. The cusps carry no load, and, therefore, periodicity is automatically satisfied. Figure 6 shows two types of leading-edge cusps that were used. Inthe blunt leading edge on the left, the cusps were extended over three grid spaces. Inthe rounded leading edge on the right, the cusps were extended over one grid space. This rounded leading-edge geometry more closely approximates the circular leading edge of the real hardware. It should be noted that Denton presents results for a radial turbine geometry in reference 7. The blade geometry shown there, how ever, differs substantially from the rotor considered here. Denton's geometry shows a more rounded leading edge (resembling an axial turbine blade) rather than a typical highly stressed radial turbine blade. Since the blades were originally designed to have internal cooling pas sages, they are exceptionally thick, which results in the large blockage at the trailing edge as indicated in the previous section. The use of cusps at the trailing edges was necessary to get convergent solutions. The cusp at the trailing edge needed to be extended over six grid spaces. As mentioned earlier, the input data obtained from reference 11 to run the code included the blade geometry, absolute flow angle at the rotor inlet shown in figure 3, total pressure and temperature at the rotor inlet, the hub static pressure at the rotor exit, and rotational speed (table I). The actual input dataset for the DENTON code was generated by using an input generator code (ref. 13). A user of the DENTON code has an option to specify absolute swirl angle at the inlet and to allow swirl velocity to vary. This option was used, since inlet absolute swirl angle data were available from the experiment (ref. 11). With this option and the computational grids shown in figures 4 and 5, the authors had no problem in getting convergent solutions. Convergence was taken to occur when the average change in meridional velocity per cycle was less than the value of 2xlO - times an average velocity for the whole flow. Smaller time increments (time multiplier value of approximately 0.1) were required because of the fine grid spacings used. Both the average constant value and the measured profile of the absolute swirl angle shown in figure.2 were tried. Since computed results of both cases at station 4 were about the same, only the results based on the average absolute flow angle of 73.60 are now presented. Convergence of an initial computation was obtained using a computational domain which extended between two data monitoring stations,of the experimental work (i.e., between station 3 and 4 shown in fig. 5). It should be pointed 4PDF Image | 3-D Inviscid Analysis of Radial Turbine Flow
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