In solving the aerodynamic direct problem of flow on an arbitrary S_1 surface of revolution through a turbomachinery blade row with many splitter vanes, the circulation around blade is used as a nodeless independent variable and is directly computed in the numerical solution instead of as a condition imposed by means of finite-element method. Thus the iterative process for satisfying the generalized K-J condition at the trailing edges of the blades is avoided. The results calculated are with compared experimental measurements, and their agreement is satisfactory.In this paper, the flow in different cascades with splitter vanes is calculated using the program compiled by us, and a cascade of better aerodynamic performance with splitter vanes is presented for high pressure diaphragms in a steam turbine. The tunnel tests are performed on the cascades with splitter vanes and with different ribs. The experimental results illustrate that the flow losses in the cascade with splitter vanes are a lot lower than those in the cascades with ribs.