Treatment of the Annulus Wall Boundary Layer Using a Secondary Flow Hypothesis Available to Purchase

Hitherto, theories of annulus wall boundary layer development in axial compressors have assumed an axially-symmetric flow in which the blade action has been replaced by a force field. A more rigorous treatment of the momentum equations in the annulus boundary layer by Mellor and Wood demonstrated the presence of certain terms, after the equations had been averaged in the pitch-wise direction, which arise from the truly three-dimensional character of the flow. These terms, which may be described as the gradients of apparent stresses, were not regarded by them (apart from a discussion of tip clearance) as having importance for the problem. In the present work a second equation of the annulus wall boundary layer is obtained by consideration of the work of these apparent stresses. By integration of the system of equations over a single blade row, two equations are obtained relating various integral quantities at inlet to and exit from the row. Each equation contains terms which depend upon apparent stresses connected with the relative velocity field at the exit plane. An experiment is described in which the six turbulent stresses in the stationary frame downstream of a single rotor, determined by means of a multiple hot wire array, are used to evaluate each term of the aforementioned equations. The integral quantities thus determined are shown to be reasonably consistent with the predictions from the two equations, in particular, for the case of the hub boundary layer. Theoretical solutions of the two integral equations require a secondary flow hypothesis so that the departure from collateral flow at blade row exit is determined by the solution.