The Use of Transition Region Characteristics to Improve the Numerical Simulation of Heat Transfer in Bypass Transitional Flows

Abstract

A method is presented for improving the numerical prediction of bypass transition heat transfer on a flat plate in a high-disturbance environment with zero or favorable pressure gradient. The method utilizes low Reynolds number k-e turbulence models in combination with the characteristic parameters of the transition region. The parameters representing the characteristics of the transition region used are the intermittency, transition length and turbulent spot properties. An analysis is made of the transition length in terms of turbulent spot variables. The nondimensional spot formation rate, required for the prediction of the transition length, is shown by the analysis to be a function of the spot spreading angle, the dimensionless spot velocity ratio and the dimensionless spot area ratio. The intermittency form of the k-e equations was derived from conditionally averaged equations which have been shown to be an improvement over global-time-averaged equations for the numerical calculation of the transition region. The numerical predictions are in general good agreement with the experimental data and indicate the potential use of the method in accelerating flows. Turbulence models of the k-e type are known to underpredict the transition length. The present work demonstrates how incorporating transition region characteristics improves the ability of two-equation turbulence models to simulate bypass transition for flat plates with potential application to turbine vanes and blades.

Mach Number Effects on Turbine Blade Transition Length Prediction

“…Different approaches have been used to determine the value of intermittency, 7. Two recent approaches to calculating the value of 7 are those of Simon (1995), and Solomon et al (1995). In both methods the intermittency, 7, is a function of the pressure gradient A.…”

“…In the model of Solomon et al the intermittency is also a function of the turbulence intensity, Tu. Simon's (1995) method utilizes an analytically developed value for the spot production rate, while the method of Solomon et al (1995) utilizes a experimentally derived correlation for the spot production rate.…”

“…Two different approaches have been used to account for the effects of turbulence intensity and pressure gradient on the length of transition. Simon (1995), Gostelow et al (1994), andFrazer et al (1994) accounted for these effects by assuming that the flow conditions at transition onset were the dominant influences. Solomon et al (1995) extended the approach of Chen and Thyson (1971) to account for free stream flow variations on the length of transition.…”

“…The transition spot data of Clark (1993), and the frequency results of Mack (1969) were used to derive modifications to account for the effect of Mach number on the length of transition. The modifications were incorporated into the models proposed by Simon (1995), and Solomon et al (1995). These models were then implemented in a Navier-Stokes code.…”

Grid Orthogonality Effects on Predicted Turbine Midspan Heat Transfer and Performance

“…Heat transfer predictions are shown for two additional transition length models. These are the transition length models of Simon and Stephens(1991) and Simon(1994). The model of Simon and Stephens was developed for zero pressure gradient flows, while Simon's model was developed for flows with favorable pressure gradient.…”