Modeling of Boundary Layer Transition in Turbulent Flows by Linear Combination Integral Method

Abstract

Transitional boundary layer parameters in zero and variable pressure gradient flows, typical of turbomachinery applications, are predicted using an integral method of the linear combination type. The code used is that of Dey and Narasimha and the turbulent layer is calculated by a lag-entrainment method. The predictions of test data represent an improvement upon earlier methods; although reasonable agreement is obtained for these low Reynolds number test cases further refinement of predictive correlations to account for free-stream turbulence effects on laminar boundary layers and transition inception is indicated. The transitional parameters are found to be particularly sensitive to the initial conditions selected for the turbulent layer. Techniques are identified for overcoming this sensitivity and for adequately representing the transition region. Free-stream turbulence effects are quite strong, particularly on the velocity profile of the laminar layer. Modifications to laminar methods are advocated to account for the strong effects on the velocity profile and the early formation of turbulent spots.

A Boundary Layer Transition Model

“…However, the experiments show a decrease in H prior to start of transition whereas the predictions maintain the Blasius value of H = 2.5. Similar reductions in H due to a raised freestream turbulence level have been observed by several researchers (e.g., Johnson (1994), Gostelow et at (1994)) and are believed to be due to enhanced mixing within the laminar boundary layer. Start of transition is predicted slightly early, but the transition length is very close to the measured value.…”

“…The recent work of Gostelow et al (1995) presented in Figures 6, 7 and 8 clearly indicates that a and a will vary greatly for boundary layers with imposed streamwise pressure gradients. Solomon et al (1995) accommodated this variation in their model whilst retaining Narasimha's assumption of concentrated breakdown.…”

“…Start of transition is predicted slightly early, but the transition length is very close to the measured value. The overshoot in the observed value of the skin friction coefficient beyond that for a fully developed turbulent boundary layer is not predicted, which is a usual failing of integral boundary layer methods (e.g., Gostelow et al (1994)).…”

“…trailing edge and leading edge velocities (U TE and U,) spreading half angle (a) and propagation parameter (o) in favourable and adverse pressure gradients as shown inFigures 6, 7 and 8 Gostelow et al (1995). have recently provided correlations for spot…”

On the Application of Transition Correlations in Turbomachinery Flow Calculation

“…approach currently employed in turbomachinery practice is still the use of experiment-based correlations (Coupland, 1995) with different numerical schemes ranging from integral boundary-layer method to full Navier-Stokes analysis (Gostelow, et al, 1994, Slimani and Kulisa, 1997, and Boyle and Jackson, 1997.…”