Transition Length Prediction for Flows With Rapidly Changing Pressure Gradients

Abstract

A new method for calculating intermittency in transitional boundary layers with changing pressure gradients is proposed and tested against standard turbomachinery flow cases. It is based on recent experimental studies, which show the local pressure gradient parameter to have a significant effect on turbulent spot spreading angles and propagation velocities (and hence transition length). This can be very important for some turbomachinery flows. On a turbine blade suction surface, for example, it is possible for transition to start in a region of favorable pressure gradient and finish in a region of adverse pressure gradient. Calculation methods that estimate the transition length from the local pressure gradient parameter at the start of transition will seriously overestimate the transition length under these conditions. Conventional methods based on correlations of zero pressure gradient transition data are similarly inaccurate. The new calculation method continuously adjusts the spot growth parameters in response to changes in the local pressure gradient through transition using correlations based on data given in the companion paper by Gostelow et al. (1996). Recent Experimental Correlations of Gostelow et al. (1994a) are used to estimate the turbulent spot generation rate at the start of transition. The method has been incorporated in a linear combination integral computation and tested with good results on cases that report both the intermittency and surface pressure distribution data. It has resulted in a much reduced sensitivity to errors in predicting the start of the transition zone, and can be recommended for engineering use in calculating boundary layer development on axial turbomachine blades.

Modelling of natural and bypass transition in aerodynamics

“…The length of the transition region given by the spot generation rate and the spot propagation rate ı is expressed by the parameter N introduced by Narasimha [20]. The effect of the free-stream turbulence and the pressure gradient on the parameter N is correlated by an empirical relation N = f (Tu, O t ) proposed for the attached flow by Solomon et al [21]. This correlation agrees with experiments Schubauer and Skramstad [18] at low freestream turbulence as well.…”

Simulation of transonic flows through a turbine blade cascade with various prescription of outlet boundary conditions

“…The transition length is expressed using the parameter N = n Re t 3 where n is the spot generation rate and σ is the spot propagation rate introduced by Narasimha [10]. The parameter N for the attached flow is similarly given by the empirical relation N = g (Tu,  t ) proposed by Solomon et al [11]. The onset of transition in separated flow is given by the correlation according to Mayle [12] in the form 0 7 300…”

Extension of the algebraic transition model for the wall roughness effect

“…where the transition onset on the flat plate without pressure gradient is given by the relation 11 The length of the transition region given by the spot generation rate n and the spot propagation rate ı is expressed using the parameter N = nσ Re θt 3 introduced by Narasimha [23]. The effect of the free-stream turbulence and the pressure gradient on the parameter N is correlated by an empirical relation N = f(Tu, λ t ) proposed for the attached flow by Solomon et al [24].…”