Abstract:
In recent papers it has been demonstrated that the so-called secondary flow which occurs when a non-uniform stream passes through a cascade of turning vanes or blades can be calculated by a consideration of tile turning of the vorticity vectors. Whenever the upstream vorticity or the angle of turn is small the perturbation method of Squire and Winter or Hawthorne ~ may be used for the calculation of the downstream vorticity component in the stream direction between the blades. Estimation of the induced velocities however requires a knowledge of the flow which would exist in the absence of the streamwise vorticity. It has been shown that this flow is not normally two-dimensional but may be calculated by an analytical technique whereby the cascade of blades is replaced by an 'actuator plane.' In certain special cases this basic flow is two-dimensional and can be used to demonstrate the applicability of the simple perturbation secondary flow theories. Many practical examples of secondary flow involve conditions which are beyond the limits of the perturbation theories and then all initial experimental approach to the problem enables suggestions to be made for the simplification of the analytical difficulties.
