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The general formulae for determining the circulation function for a finite number of blades, as given by Go I d s t e i n, has been evaluated for si-x-. and eight-bladed propellers. The values of Bessel functions necessary for this purpose were computed, as the authors were not aware of any known tables listing them.Notation R Radius of the propeller blade. w Angular velocity of the blade. r Distance of any blade element from the axis of rotation.r* = T/R. Dimensionless radius parameter, i.e. 0 < r* < 1.v Velocity of advance of the propeller. w Velocity of the vortex screw surface, moving as a rigid body in the direction of its axis. I" = osr]»; 1"0 = wR/v. Ai = vlwR Advance ratio. I n(t) Modified Bessel function of the first kind. Kn(t) Modified Bessel function of the second kind.Z Number ot blades.r Circulation round any blade element.

Super alloy 718 finds extensive utilization, particularly in aero engine industry, due to its excellent strength, low cycle fatigue and creep resistance. The alloy was manufactured using vacuum induction melting followed by vacuum arc remelting techniques. The electrodes, after thermo-mechanical processing to hot rolled square bar and flat forms, were ultrasonically inspected prior to machining of aeroengine compressor blades. During machining, crack-like defects were noticed. Visual / Stereo microscopic examination revealed that the defect was along the length of airfoil and was located at mid airfoil width. The defects were filled with dark gray colored debris. Fractographic examination of the crack facets revealed flaky gray region containing number of cracks and bright region with dimpled rupture features covered with debris. Analysis of the debris indicated the presence of oxygen in addition to the elements present in the material, suggesting that the debris is essentially an oxide. These features were correlated with processing histories and defect morphologies.