Three-Dimensional Rotational Flow in Transonic Turbomachines: Part I—Solution Obtained Using a Number of S₁ Stream Filaments of Revolution and a Central S₂ Stream Filament

The general theory of three-dimensional flow in subsonic and supersonic turbo-machines (Wu, 1952a) is extended to the three-dimensional rotational flow in transonic turbomachines. In Part I of this paper, an approximation that the S₁ stream filaments are filaments of revolution is made. Then, the three-dimensional solution is obtained by an iterative solution between a number of S₁ stream filaments and a single S₂ stream filament. A recently developed relatively simple and quick method of solving the transonic S₁ flow is utilized. The complete procedure is illustrated with the solution of the three-dimensional flow in the DFVLR rotor operating at the design point. The solution is presented in detail, special emphasis being placed on the fulfillment of the convergence requirement. The character of the three-dimensional field obtained is examined with the three-dimensional structure of the passage shock, the relative Mach number contours on a number of S₁ surfaces, S₂ surfaces, and cross surfaces, and the variations of the thickness of S₁ and S₂ filaments. Comparison between the calculated three-dimensional field with the DFVLR measured data shows that the character of the flow field and the streamwise variation of the flow variables in the middle of the flow channel are in good agreement. It is recommended that the method presented herein can be used for three-dimensional design of transonic turbomachines.