A streamline curvature method for calculating S1 surface flow in turbines is presented. The authors propose a simple method in which a domain of calculation can be changed into an orderly rectangle without making coordinate transformations. Calculation results obtained on subsonic and transonic turbine cascades have been compared with those of experiment and another theory. Good agreement has been found. When calculating blade-to-blade flow velocity at subsonic speed, a function approximation technique can be used in lieu of iteration method in order to reduce calculation time. If the calculated flow section is of a mixed (subsonic-supersonic) flow type, a Boolean expression obtained from the truth table of flow states is proposed to judge the integrated character of the mixed flow section. Similarly, another Boolean expression is used to determine whether there exists a “choking” of the relevant section. Periodical conditions are satisfied by iterating the first-order derivative of stagnation streamline, which is formed simultaneously. It can be proved that the stagnation streamline formed in this way is unique.

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