Variations of blade thickness from hub to casing of a turbomachine, which impose a non-uniform blockage upon the meridional flow, often give rise to significant perturbations. In the first part of this paper this effect is simulated by considering the circumferential average of the source distributions required to represent the blade profiles. In the second part the equations of fluid motion are first averaged across the blade passage and the resulting equations solved for the averaged properties.
Similarity between the differential equations obtained in these two ways is noted. A number of analytical examples are discussed and a simple experimental result is reported.
Get full access to this article
View all access options for this article.
References
1.
StanitzJ. D.‘Effect of blade-thickness taper on axial- velocity distribution at the leading edge of an entrance rotor-blade row with axial inlet, and the influence of this distribution on alignment of the rotor blade for zero angle of attack’, N.A.C.A. T.N. 2986, 1953.
SmithL. H.‘Radial-equilibrium equation of turbomachinery’, Am. Soc. Mech. Engrs Paper No. 65-WA/GTP-1, 1965.
4.
MarshH.‘A digital computer program for the through-flow fluid mechanics in an arbitrary turbomachine using a matrix method’, N.G.T.E. Report No. R282, 1966.
5.
GinsburgT.‘Investigations on the three-dimensional potential flows through axial blade lattices’, E.T.H. Mitt. Inst. Aerodynamik, Zürich, No. 22, 1956.
6.
RossowV. J.‘Analysis of the error involved in unrolling the flow field in turbine problems’, E.T.H. Mitt. Inst. Aerodynamik, Zürich, No. 23, 1959.
7.
ScholtzN.‘Advanced problems in turbomachinery’, Seminar at V.K.I., Brussels, 1965, contribution to discussion, Session 1.
8.
LewisR. I.‘Advanced problems in turbomachinery’, Seminar at V.K.I., Brussels, 1965, written contribution to discussion, Session 1.
9.
HorlockJ. H.‘Effect of radial variations in blade thickness in axial-flow turbines’, Liverpool University, ULME/B.21, 1966.
10.
AckeretJ.‘Zum Entwurf dichtstehendes Schaufelgitter’, Schweizerische Bauzeitung1942120 (No. 9) (also available as Min. of Aviation Translation RTP2007).
11.
SchlichtingH.‘Berechnung der reibungslosen inkom- pressiblen Strömung für ein vorgegebenes ebenes Schaufelgitter’, VDI-ForschHft195521 (447, edition B) (translation available as N.A.C.A. TIL Misc. 128, 1958).
12.
MartensenE.‘Berechnung der Druckverteilung an dicken Gitterprofilen mit Hilfe von Fredholmschen Integral-gleichungen zweiter Art’, Mitt. Max-Plank- Inst. Ström- Forsch.1959 (No. 23), Arch. Rat. Mech. Anal. 1959 3, 235.
13.
JacobK.RiegelsF. W.‘Berechnung der Druckverteilung endlich dicker Profile ohne mit Klappen und Vorflungeln’, Z. Flugwiss196311 (9), 357 (available as R.A.E. Library Translation No. 1101).
14.
PollardD.HorlockJ. H.‘Theoretical investigation of the effect of change in axial velocity on the potential flow through a cascade of aerofoils’, A.R.C., C.P. 619, 1963.
15.
HawthorneW. R.RingroseJ.‘Actuator disc theory of the compressible flow in free-vortex turbomachinery’, Thermodynamics and Fluid Mechanics Convention, Cambridge, Proc. Instn mech. Engrs1963–64178(Pt 3 I(ii)), 1.
16.
RudenP.‘Investigations of single stage axial fans’, N.A.C.A. T.M. 1062, 1944, 1965.
17.
SmithL. H.‘Radial equilibrium equation of turbo-machinery’, Trans. Am. Soc. mech. Engrs, J. Engng for Power196688, (Series A), 1.
18.
StanitzJ. D.‘Effect of blade thickness taper on axial- velocity distribution at the leading edge of an entrance rotor blade row’, N.A.C.A. T.N. 2986, 1953.
19.
HildebrandF. B.Advanced calculus for engineers1959 (Prentice Hall, New York).
20.
JahnkeE.EmdeF.Tables of functions1943 (Dover Press, New York).
21.
Merry-WeatherH. Private communication.
22.
WuChung Hua‘A general through flow theory of fluid flow with subsonic or supersonic velocity in turbo-machines of arbitrary hub and casing shapes’, N.A.C.A. T.N. 2302, 1951.
23.
MarshH.‘A digital computer program for the through-flow fluid mechanics in an arbitrary turbomachine using a matrix method’, N.G.T.E. Report R282, 1966.
