This paper presents a physical model and its mathematical expressions (partial differential equation group), which are to be used to calculate the optimum velocity distribution on blade surface. The method is based on the theory of boundary layer and the calculation of cascade loss, and to employ the Pontijagin maximum principle as well as the new optimum techniques in applied mathematics. In this paper, a computing method of optimum velocity distribution along the blade surface in 2-D

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... sible flow is presented by analysing and solving the equation group, and then by using the method which is presented by Zou Zixiang (1976), and through a logical analysis, a new method has been offered, which can converted from an optimum velocity distribution along the plane stream surface of incompressible fluid flow into that of an arbitrary stream surface of revolution in compressible fluid flow. NOMENCLATURE w H 12 H 32 a* e s tn p Aq) T w r Re • velocity of relative flow = .141/W o ;W o is inlet velocity = momentum thickness H 12 =6*/0 = H 32 =eh) = displacement thickness = energy thickness = thickness of outer edge • angle pitch = angle of relative flow • radius of rotation = density = local tangential strength • Buri rule function or form function = R-number based on the momentum thickness T = absolute temperature a = local sound velocity L = arc length from inlet stagnation point to outer edge point K adiabatic index = normal thickness of stream sheet on arbitrary stream surface of revolution (IC = velocity circulation of blade surface SUBSCRIPTS 1 or e = parameters at outer edge 0 = parameters at inlet or stagnation point Sgn = representant the signal (plus or minus) f = free flow at outer boundary of boundary layer t = pitch of cascade a = compressible flow on stream surface of revolution t o = normal thickness at outer edge INTRODUCTION