Entropy Generation in a Boundary Layer Transitioning Under the Influence of Freestream Turbulence

Abstract

The objective of the present research is to develop new fundamental knowledge of the entropy generation process in laminar flow with significant fluctuations (called pre-transition) and during transition prematurely induced by strong freestream turbulence (bypass transition). Results of direct numerical simulations are employed. In the pre-transitional boundary layer, the perturbations by the streaky structures modify the mean velocity profile and induce a “quasi-turbulent” contribution to indirect dissipation. Application of classical laminar theory leads to underprediction of the entropy generated. In the transition region the pointwise entropy generation rate (S′′′)+ initially increases near the wall and then decreases to correspond to the distribution predicted for a fully-turbulent boundary layer as the flow progresses downstream. In contrast to a developed turbulent flow, the term for turbulent convection in the turbulence kinetic energy balance is significant and can play an important role in some regions of the transitioning boundary layer. More turbulent energy is produced than dissipated and the excess is convected downstream as the boundary layer grows. Since it is difficult to measure and predict true turbulent dissipation rates (and hence, entropy generation rates) exactly other than by expensive direct numerical simulations, a motivation for this research is to evaluate approximate methods for possible use in experiments and design. These new results demonstrate that an approximate technique, used by many investigators, overestimates the dissipation coefficient Cd by up to seventeen per cent. For better predictions and measurements, an integral approach accounting for the important turbulent energy flux is proposed and validated for the case studied.