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Meridional Geometry Velocity triangles. The work-mass flow characteristics of any turbine are effectively prescribed by the velocity triangles at inlet to and at exit from the rotor blade. This means that it is essential that any model of the full-size turbine must have equivalent if not identical velocity triangles. The rotor inlet radius (r3) is constant across the span so that the angular momentum entering the rotor is also constant. This is not generally true at rotor exit. If the flow conditions and work-mass flow characteristics of the model are to be matched to those of the full- size turbine at all flow coefficients along fl streamlines, then the shroud inlet to shroud exit radius ratio (r4shroud/r3), the hub-shroud radius ratio at rotor exit (r4hubh'4shroud) and the radial variation of the swirl velocity V(r) must be scaled exactly. Matching the exit flow field of the model rotor in all its details to the flow field behind the full-size rotor means that true matching can only occur at this location. Both the full-size and the model turbine operate at the same nominal specific speed, N s, of 0.6 which corresponds to the optimum value given by the NASA correlations and design rules (see Rohlik (1975)). Variation of streamtube height. The variation of density is negligible at low-speed. Thus, in order to produce meridional velocity variations and, therefore, velocity triangles which are correctly scaled, the heights of the streamtubes would need to vary much less in the low-speed model than in the high-speed turbine. This meant that true geometric similarity could not be maintained. Given that the exit hub- to-shroud radius ratio (r4hub/r4shroud) was already prescribed, the desired variation in streamtube thickness could only be achieved by increasing the width (b3) of the inducer. The width of the inducer in the model turbine was increased by a factor of about two relative to the scaled dimension. Although this is a large increase, the design is not significantly compromised. At rotor inlet, for example, the effects of secondary flow (see Zangeneh et al (1988))) and of tip clearance (see Futral and Holeski (1970)) are not as significant as in the the exducer at the design point, since large scale incidence induced separations will not occur. Rotor hub and shroud profiles. The importance of streamline (meridional) curvature in the generation of secondary flows may be characterised by reference to the Rossby number Ro=Mr(2) where rc is the local radius of curvature and W is the local relative velocity of the flow. Since the radius of curvature is significantly smaller and the loading significantly greater at the shroud than at the hub, it is not unreasonable to find that the secondary flows are more significant near the rotor shroud (see, for example, Zangeneh et al (1988)). Given the desire to obtain similar secondary flow patterns in both the model and the full-size turbine and with the above observations in mind, the less critical hub profile was altered to compensate for the increased width of the inducer. The same shroud contour was employed in the model as in the high-speed turbine. Reynolds numbers. Hiett and Johnston (1963) have reported the effect of changes in Reynolds number on the performance of radial inflow turbine rotors. The investigations showed that at Reynolds numbers, defined as model turbine and maintaining the nozzle radius ratio (rl/r2) would mean that the Reynolds number of the stator blades would be lower in the model by a factor of 0.6. In addition, the aspect ratio of the stator blades would also be greater by about the same factor due to the increased streamtube thickness at the rotor inlet. In an attempt to offset some of the effects of these potential changes, the chord and therefore the radius ratio (rl/r2) of the stator blades was increased while maintaining the same radius ratio (r2/r3) for the vaneless space and lift coefficient for the stator blades (equation 1). Increasing the radius ratio of the stator blades also reduces the impact of using parallel as opposed to converging endwalls in the model since the velocity ratio V2/V1 is increased. The Reynolds number of the stator blades, when defined as p2V2cradial (4) N2 6. 315 x10 -2 7 Re=U3b(3) E^b vi above 1.25x105, there is very little change in efficiency with Reynolds number. Even though the flow accelerates over much of the rotor blade surfaces, consideration of the high magnitude of the surface length based Reynolds number shows that turbulent flow is already well established over much of the blade when operating above the limits established by Hiett and Johnston. The full-size turbine has a Reynolds number of 2.4x10 5 which indicates that its operation is within the turbulent boundary layer regime. The absence of a variation in density (and viscosity) through the L.E. r 0 . 884 l Irn 0.88411 S IT.E. 0.8841-{ Figure 3: Meridional view of stator suction surface Mach number contours (Denton) showing the effect of wall curvature Restator= has a value of 2.8x10 5 in the full-size turbine. When based on true chord, the value is 4.5x105. This means that these stator blades are operating at conditions where the laminar-turbulent transition may well occur. Because the rotor of the full-size turbine operates well within the turbulent flow regime, the model turbine can be operated with the correct stator Reynolds number but with a higher rotor Reynolds number without significantly affecting the flow conditions in the rotor. Nozzle Guide Vanes There are 23 NGV's in the model turbine which represents a reduction of six from the original 29 in the full-size. The majority of this decrease is simply due to the change in radial chord. The rotor inlet flow angle is the same in both cases. The effect of contouring the endwall in the full-size turbine can be seen by examining figure 3. This shows the meridional projection of the predicted suction surface Mach number contours obtained using the method of Denton (1983). The extent of the effects of the wall curvature is limited to less than one half of the span and that rather than being advantageous, the convex curvature of the curved endwall results in a greater amount of diffusion beginning near 75 percent c radj . The parallel endwall has, by contrast, very little back-surface diffusion. These observations further support the original decision to employ parallel endwalls in the model turbine where the blade surface velocity distributions were matched to the Mach number distributions of the straight endwall of the full-size turbine. It may, of course, be argued that altering the endwall contours will lead to substantially different secondary flow fields in the model turbine. Figure 4 shows the predicted secondary flow patterns obtained using the flow prediction method of Dawes (1986). The figure shows that there is very little secondary flow in the model turbine so any changes that might occur will be very small. Integral boundary layer calculations were carried out using the method of Herbert and Calvert (1982) for the Mach number distributions of the straight endwall of the full-size turbine and for the model turbine. These calculations showed that the momentum thickness based Reynolds number (Reg=AV/v) was everywhere less than the critical value of 163 (see Herbert and Calvert (1982)), so that transition to turbulent flow would not occur. Because there was little or no diffusion, the boundary layers would also remain attached. Downloaded from http://asmedigitalcollection.asme.org/GT/proceedings-pdf/GT1991/78989/V001T01A077/2400491/v001t01a077-91-gt-220.pdf by guest on 23 January 2021PDF Image | Design and Testing of a Radial Flow Turbine for Aerodynamic Research
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