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fork = 1,2.....NWN, where NZ is the number of blade passages in which no measurements were acquired in window k. ment grid (refer to fig. 15). The measurement grid used in this investigation divided the streamwise blade length into a series of quasi-orlhogonal, or near-normal, cross-channel planes. The secondary velocity vector 17Vs(k) for any given window k (hereafter we shall drop the k denoting window number) is given by l_s - I_ - Wst, where W is the total relative velocity vector and Wst =(W.,_st ) *gst is the projection of ffin the After looking at the normalized difference +0 -l), NWN] v(k) where V(k) is the passage-averaged location k, and V[k + (j- I)*NWN] is the ensemble- averaged velocity in blade passage j at the same pitchwise location, we found this difference to be a maximum of I per- cent. This indicates that the passage-averaging process does not appreciably alter any details of the blade-to-blade velocity profile. Velocity triangle components.--Values of Vr, ¢o' and _z were used as follows to calculate passage-averaged absolute, relative, and meridional velocities, and swirl and pitch angles: flrel(k) = arctan|- -_----- | = 2 q2_2 where gsp and _p are unit vectors in the local spanwise and pitchwise grid directions. When secondary flow results are pre- sented in the form of vector plots in a quasi-orthogonal plane, Wsp and Wp are used to determine the magnitude and direction of the plotted secondary velocity vectors. The procedure just described was applied at each measure- ment grid node. Thus, in a cross-channel vector plot of second- ary velocity components, a flow field with no secondary flow components appears as a point at each grid node, indicating that the flow is following the streamwise grid direction. Since the local streamwise grid direction was parallel to the blade, hub, and shroud surfaces, the aforementioned definition of sec- ondary flow also ensured that the secondary velocity was zero at all solid surfaces. The throughflow velocity comlmnent VT is the vector projec- tion of the meridional velocity vector I_rain the local streamwise meridional-plane grid direction: VT = Vm "g'm" Since a quasi-orthogonal plane is nearly normal to the streamwise grid direction at any station in the iml_ller, VT is a close approxi- mation to the throughflow velocity that crosses a quasi- orthogonal plane. It is also a close approximation to the streamwise velocity component measured by Krain (1988), Ahmed and Elder (1990), and Fagan and Fleeter (1991) in la- LJ a(k) = arctanl =-------| Lvs, J for k = 1,2 ..... NWN, where r is the local radius and w is the rotor rotational speed in radians per second. Hereafter, all velocity components will be assumed to be the passage-average of ensemble-averaged results, and therefore, velocity at any pitchwise local streamwise grid pitchwise components and Wp, respectively, direction _st(r,O,z). of the secondary are the projections The spanwise and velocity vector, Wsp of the secondary (13) (14) the overbar and tilde will be dropped from subsequent velocity ser anemometer investigations. In these investigations, the component designations. Through flow and secondary velocity calculations.--In order to visualize secondary flow, we must view the total rela- tive velocity vector along the streamwise direction. However, in a geometrically complex channel such as a centrifugal im- peller blade passage, the streamwise direction can be defined in several different ways, each of which yields a slightly differ- ent result for the secondary flow. This problem has been pointed out by many previous authors. The following discus- sion will document the procedure used to generate the second- ary flow field results presented in this report. The secondary flows presented herein are defined as the departure of the local relative velocity vector from the local streamwise grid direction as defined by a body-filled measure- streamwise velocity component was defined as the velocity component normal to the azimuthal angle _ of the laser an- emometer optical axis, where _ was chosen to be normal to the local shroud direction. velocity directions: vector in the local spanwise and pitchwise grid (15) Results and Discussion Performance Measurements Figure 16 is a plot of the impeller inlet axial velocity distri- butions normalized by the impeller exit tip speed U t at design and off-design conditions. The distributions of impeller inlet total and static pressures (normalized by the reference pressurePDF Image | Laser anemometer measurements of the three-dimensional rotor flow
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