Turbulence modelling and turbulent-flow computation in aeronautics

Competitive pressures and economic constraints are driving aircraft manufacturers towards an ever-increasing exploitation of CFD for design, optimisation and prediction of off-design conditions. Such exploitation is favoured by rapid advances in meshing technology, numerical algorithms, visualisation tools and computer hardware. In contrast, the predictive capabilities of mathematical models of turbulence are limited - indeed, are often poor in regions of complex strain - and improve only slowly. The intuitive nature of turbulence modelling, its strong reliance on calibration and validation and the extreme sensitivity of model performance to seemingly minor variations in modelling details and flow conditions all conspire to make turbulence modelling an especially challenging component of CFD, but one that is crucially important for the correct prediction of complex flows. This article attempts to provide a broad review of the current status of turbulence modelling for aeronautical applications, both from physical and numerical points of view. The review is preceded and underpinned by a discussion of key fundamental issues and processes, based on the exact equations governing the Reynolds stresses. The main body of the review begins with a discussion of all important model categories, starting with algebraic models and ending with Reynolds-stress-transport closures, with emphasis placed on a discussion of the underlying principles in the context of aerodynamic flows. There followed a review of key numerical issues pertaining to the incorporation of turbulence models into advanced computational schemes for compressible and incompressible flows, based on both time-marching and pressure-Poisson solution techniques. The performance of different classes of models is then reviewed by reference to major validation studies undertaken over the past two decades. A discussion of current capabilities in modeling unsteady turbulent flows, especially in the context of dynamic stall and transonic buffet, forms the final element of the review.