Potential flow solution and incompressible boundary layer for a two-dimensional cascade

Abstract

A blade-to-blade computer program, using the method of finite differences has been written to calculate the velocity distributions on the rotor blade of an axial-flow compressor. The shape of the blade has been approximated in two different ways employing a rather elaborate method and one whose primary goal was simplicity. The ensuing velocity distributions were compared and can be judged to be satisfactory in that they follow the expectations and show a reasonable behavior, even close to the leading and trailing stagnation point. The latter fact represents an improvement to results obtained from a previous work [ref. 3], however the calculations still need to be confirmed by the experiment.

In the second part of this thesis, following a recommendation of reference 3, the blade boundary layer effects have been calculated from the velocity distributions of the first part. Considering certain assumptions, these results also may be judged as satisfactory and the rather important conclusion may be drawn that turbulent separation, if it occurs at all, takes place close to the rear stagnation point of the blade for the applied range of upstream velocities. Another conclusion may be drawn from the displacement thickness distribution in that the flow values would not affect greatly the potential flow calculation and hence an iterative procedure between the potential flow field and the blade boundary layer should converge rapidly. The results from the second part also require a confirmation by the experiment.