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REFERENCES Casey, M V and Roth, P, 1984, "A streamline curvature throughflow method for radial turbocompressors", Computational Methods in Turbomachinery, IMECHE Publications, London Choo, Y K and Civinskas, K C, 1985, "Three dimensional inviscid analysis of radial turbine flow and a limited comparison with experimental data", NASA TM-8709 Dawes, W N, 1986, "A numerical analysis of the three dimensional viscous flow in a transonic compressor rotor and comparison with experiment", ASME paper 86- GT-16 Denton, J D, 1983, "An improved time marching method for turbomachinery flow calculation", Trans ASME, J Eng for Power, vol 105, p514 Futral, S M and Holeski, D E, 1970, "Experimental results of varying the blade shroud clearance in a 6.02 inch radial inflow turbine", NASA TN D-5513 Futral, S M and Wasserbauer, C A, 1970, "Experimental performance valuation of a 4.59 inch radial inflow turbine with and without splitter blades", NASA TN-D7015 Glassman, A J, 1976, "Computer program for design analysis of radial inflow turbines", NASA TN D-8164 Herbert, M V Calvert, W J, 1982, "Description of an integral method for boundary layer calculation in use at NGTE, with special reference to compressor blades", NGTE memorandum M82019 Hiett, G F and Johnston, I H, 1963, "Experiments concerning the aerodynamic performance of inward flow radial turbines", Proc Inst Mech Eng, Vol 178, Pt 3I (ii), p28-42 Hodson, H P and Addison, J S, 1988, "Wake-boundary layer interactions in an axial turbine rotor at off design conditions", ASME paper no. 88-GT-233 Joslyn, H D, Brasz, J J and Dring, R P, 1990, "Centrifugal impeller aerodynamics (an experimental investigation)", ASME paper no. 90-GT-128 Joslyn, H D and Dring, R P, "Turbine rotor negative incidence stall", ASME paper no. 83-GT-23, 1983 Rohlik, H E, 1975, "Radial Inflow Turbines", NASA SP 290, Vol 3, Chapter 10 Stanitz, J D, 1952, "Some theoretical aerodynamic investigations of impellers in radial and mixed flow centrifugal compressors", Trans ASME, vol 74, no 4, p473- 497 Wisler, D C, 1984, "Loss reduction in axial flow compressors through low speed model testing", ASME paper no. 84-GT-184 Zangeneh-Kazemi, M Dawes, W N and Hawthorne, W R, 1988, "Three dimensional flow in radial inflow turbines", ASME paper 88- GT-103 Zangeneh-Kazemi, M, 1988, "Three dimensional design of radial inflow turbines", PhD thesis, Cambridge University Engineering Department APPENDIX A: A SIMPLE ANALYSIS OF THE EFFECTS OF INLET BLADE LEAN Figure A 1 shows a plan and meridional view of the rotor blades in the region of the leading edge together with the leading dimensions of the problem. The pressure gradient normal to curved streamlines is given by the general expression ap _ PWm2 Fb=btangArApbZ (A4) where Z is the number of blades and the blade pressure difference is given by the approximate expression 4tt APb=pWmAWb=ZpUWm( A 5 ) from equation 5. It is interesting to note here that if the two forces are equal, then the two effects cancel and so in the inducer, the flow is uniform regardless of the presence of the stream-line curvature and blade lean. This probably explains why turbochargers, which often have both lean and shroud curvature perform better than might be expected even though the shroud radius ratio is greater than the value of 0.7 recommended by the NASA design rules. When the two forces do not balance, there will be a spanwise variation in the flow properties. Where there is very little curvature, there may be significant variations in the flow properties. The difference between the forces Fc and Fb will result in a reaction force FX which will be related to the overall hub-to-shroud pressure difference Ap x and velocity difference (Vhub - Vshroud) by the expression Fx = 2mOrhpx = 2ttrAr PV(Vhub-Vshroud) = Fb — Fc (A6) so that upon substitution from equations (A3), (A4) and (A5) (Al) where rc is the radius of curvature and W m is the meridional (i.e. an rc mean) velocity. For large rc this expression can be approximated to Apc=PWm2b( A 2 ) where Apc is the pressure difference between the hub and the shroud due to streamline curvature. The axial force developed by the pressure difference is: W Fc = 2mOrMpc = 2ttrAr P 2 n'b (A3) c Leaning the blade results in a component of the blade force which acts towards the shroud. This component of force which is exerted by the fluid on the blades is given by V(Vh r) =b(2 tanO W - m\ m cl (A7) from which the effects of blade lean and shroud curvature can be estimated. e-- _L4r rc Plan view onto the rotor leading edge Figure Al: Determination of the effects of blade inlet rake r Meridional view 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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