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 which 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, Melwani and Walker (1995). Recent experimental correlations of Gostelow, Blunden and Walker (1994) 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 which 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.

Transition Models for Turbomachinery Boundary Layer Flows: A Review

“…These parameters can be obtained from correlations. For example, detailed correlations for α, σ, and N were constructed by Gostelow et al [67] and Solomon et al [68]. The factor Nσ/U in (1) has the dimension 1/m 2 .…”

A bypass transition model based on the intermittency function

“…There are many other algebraic models for intermittency and these are usually based on properties like turbulent spot production and propagation rate. Examples include Gostelow et al (1994) and Solomon et al (1996). Steelant and Dick (1996) provided the following correlations ofnσ versus T u and K,…”

Simplified Approach to Predicting Rough Surface Transition

“…The transition length model is the one detailed by Boyle and Simon [32]. It is a modification of the transition length model of Solomon et al [33] to account for Mach number effects. It was shown to give good agreement with smooth blade heat transfer data for both stator, (Arts et al [1] and Hylton et al [34]), and rotor test cases, (Arts et al [35] ).…”