Models for unsteady wake-induced transition in axial turbomachines

(Received 20 September 1991, revised 2 December 1991, accepted 3 December 1991)

Abstract
In turbomachinery, a considerable proportion of the blade surface area can be covered transitional boundary layers. This may occur particularly when transition is periodically induced by the passing of wakes shed by upstream blade rows. Accurate prediction of the profile loss and heat transfer depens on the successful modeling of these transitional boundary layers. This paper considers the effects of wake interactions on the transition process. As a consequence of experimental observations, a physical model of unsteady transition is put forward. Based on the fact the intermittency of steady boundary layers cans be calculated from a knowledge of the behaviour of turbulent spots, a theoretical treatment of the unsteady problem is presented. Two models, each based on different hypotheses concerning the origin of the turbulent spots are described. Numerical integration of the resulting equations provides results for comparison with experimental data. In the case of high Reynolds numbers, the results are consistent with those obtained using a much simplified model which shows that a functional relationship exists between the time-averaged behaviour of the boundary layer and a new form of reduced frequency. Favorable comparisons are made with the measured intermittency and integral boundary layer parameters and the equivalent predicted values for a number of test configurations and operating conditions. It is shown that the spot-based transition models successfully predict the boundary layer development aver a wide range of circumstances providing that an adequate escription of the unsteady location of spot-formation is available.