In this paper, an optimum problem of supercavitating hydrofoils at nonzero cavitation number is treated by the linearized theory. Namely, the purpose of this paper is to determine the foil profile which has minimum drag coefficient under the given lift coefficient, angle of attack, foil length, and cavitation number. Optimum profiles are determined by using calculus of variation. The foil configuration is limited to the so-called two-term and four-term hydrofoils. The foil configuration and the lift-drag ratio are obtained under various given above conditions. The results obtained in this paper are summerized as follows: (1) When the lift coefficient, angle of attack, and foil length are fixed, the lift-drag ratio of the optimum hydrofoil with nonzero cavitation number is greater than that with zero cavitation number. (2) The difference of the lift-drag ratio between the two-term and four-term hydrofoil is only a few percents. Consequently, it may be seen that the results of the optimum hydrofoils are dominant in the problem of the optimum hydrofoils. (3) It is seen that the foil configurations which have the maximum lift-drag ratio in the optimum hydrofoils with same lift coefficient, attack of angle, and foil length are almost independent of the cavitation number.
A theoretical investigation on the compressible laminar mixing along a curved streamline is presented. The fundamental equations referred to the streamline coordinates are simplified by the boundary layer approximation and by applying the condition for the streamline curvature not to be over unity. Using the Crocco type particular solution of energy equation, a similar solution for the flow of isoenergy is obtained in the case of constant pressure along the stream. Effects of streamline curvature and compressibility on the distributions of velocity, density, pressure, temperature and so on are calculated.