Transition to turbulent flow in aerodynamics

Abstract

The difficult problem of understanding the physical mechanisms at work in the change from laminar, or smooth, flow to random turbulent flow, with its wide range of active time– and space–scales, has occupied engineers, physicists and mathematicians for the past century. When an airfoil is placed in and parallel to a current of fast–moving air, a so–called boundary layer forms on its surface as the velocity of the air at the surface must be reduced to zero. Near the front of the airfoil the boundarylayer flow is smooth and steady, but further downstream it is seen to become highly irregular, unsteady and turbulent, often at a well–defined front. Scientists working in transition prediction aim to answer the questions of where and why this transition occurs. It is a problem distinct from, but related to, that of understanding turbulent flow itself. It is of prime industrial importance. For example, a turbulent flow offers more drag resistance, and, indeed, an aircraft designed so that more of the flow over its wings is laminar can carry more passengers and much less fuel. Understanding the physical structures and flow patterns visible in the late end stage of transition and the initiation of turbulent spots, isolated patches of turbulence surrounded by laminar flow, should also throw much–needed light on the structures seen in fully developed wall turbulence and help in the equally difficult, distinct, problem of modelling turbulent flow. There are many possible routes through transition, depending on the flow configuration and geometry and the method in which transition is initiated by any of the range of possible background disturbances present, either in the free stream or in the form of roughness on the surface, for example. In the past 20 years, techniques for tracing the linear and nearly linear growth of small disturbances in the boundary layer have been developed that could form part of effective design tools for engineers. There has also been an increased theoretical understanding, made possible by the application of high Reynolds number asymptotic theories, of the myriad of possible interactions between disturbances driving this relatively slow stage of the transition process. Much important work remains to be done to include in any design tool the important processes occurring at the two ends of this process. Firstly, how do disturbances enter the boundary layer to be amplified, known as the receptivity problem, and secondly, what happens at the end stage, where the disturbances have grown so large that the nearly linear theories are no longer applicable? Recent experimental work has shown a remarkable similarity in the characteristics of this final breakdown among a variety of flows. Two–dimensional flows, such as that over a plate aligned with the flow or in a channel or pipe, gradually develop three–dimensional structures, known as lambda vortices. These then rapidly break down in two distinct ways, which are both active almost simultaneously. One gives rise to spikes: short–lived, large–amplitude pulses, which are practically deterministic in nature. The second involves a secondary instability and the initiation of random fluctuations. Three–dimensional flows, such as those on swept wings, develop cross–flow vortices, which themselves seem to break down via a secondary instability mechanism, possibly similar to that seen in lambda vortices. This article reviews recent developments in the field of transition research, concentrating on those related to the late stages of breakdown and the onset of random behaviour. It brings together results from young experimentalists, computationalists and theoreticians and looks forward to an increased understanding of this challenging and important problem.