Starting from the basic Fredholm integral equations, a surface vorticity theory is developed for the prediction of annular aerofoil performance in three-dimensional flow. A mathematical model is proposed for the general case of the axisymmetric body in non-axisymmetric flow, using a Fourier series to represent circumferential variations in bound vorticity strength. Using the pure incidence case as an example, it is indicated how an economical solution of the flow may be arrived at by use of a digital computer. The theoretical pressure distributions obtained are compared with the results of wind-tunnel tests on an annular aerofoil model.
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References
1.
MartensenE.‘Die Berechnung der Druckverteilung an dicken Gitterprofilen mit Hilfe von Fredholmschen Integralgleichungen Zwieter Art’, Arch. Rat. Math. Anal.1959 (3), 235–270.
2.
WilkinsonD. H.‘A numerical solution of the analysis and design problems for the flow past one or more aerofoils or cascades’, ARC R & M No. 3545 1968.
3.
RyanP. G.LewisR. I.‘Surface vorticity theory for axi-symmetric potential flow past annular aerofoils and bodies of revolution with application to ducted propellers and cowls’, J. mech. Engng Sci.197214 (No. 4).
4.
RyanP. G.Surface vorticity distribution techniques applied to ducted propeller flows. Ph D Thesis, University of Newcastle-upon-Tyne, Nov. 1970.
5.
KüchemannD.WeberJ.Aerodynamics of propulsion1963 (McGraw-Hill Book Company Inc.).
6.
LambH.Hydrodynamics1953, 6th Edition (C.U.P.).
7.
HillV. P.Surface vorticity techniques applied to the annular aerofoil in non-axisymmetric flow Ph D Thesis, University of Newcastle-upon-Tyne, Sept. 1975.
8.
JahnkeH.EmdeF.Tables of higher functions1948, 4th edition (B. G. Teubner, Leipzig).
9.
ByrdF.FriedmanM. D.Handbook of elliptic integrals for engineers and physicists1954 (Springer—Verlag, Berlin/Heidelberg/Göttingen).
10.
GibsonI. S.Application of vortex singularities to ducted propellers Ph D Thesis, University of Newcastle-upon-Tyne, Oct. 1972.
11.
BagleyJ. A.PurvisH. G. F.‘Experimental pressure distributions on an annular aerofoil in cross-flow’, RAE TR 72098 June 1972.
12.
GibsonI. S.‘On the velocity induced by a semi-infinite vortex cylinder’, Report No. Tb 26 (Department of Mechanical Engineering, University of Newcastle-upon-Tyne).
