Flow around airfoils (and blades) A-airfoil (Ma=0.15,
Re/m=2x10⁶)

Underlying Flow Regime 2-05 © copyright ERCOFTAC 2004

Description

Preface

The underlying flow regime of a standard single-element airfoil at the maximum lift condition documented here is of major importance in aeronautical applications. It therefore represents the entire problem of prediction of stall by CFD. However, it is also important beyond the area of external aerodynamics of wings, representing a generic turbulent boundary-layer separating owing to convex curvature and an adverse pressure gradient.

The A-airfoil flows have been the object of major test-case studies by large groups within EU projects and as a result are unusually well studied, documented and understood. The primary experimental data was generated by ONERA/FAUGA. At least three major EU projects have studied the flows by CFD: two of these (EUROVAL and ECARP) covered a variety of angles of attack and two Reynolds numbers by closure methods, using steady and unsteady RANS, and incompressible and compressible methods. A third EU project (LESFOIL) studied one case at maximum lift by large-eddy simulation. Work is continuing on the case, for instance under the FLOMANIA project (http://cfd.mace.manchester.ac.uk/flomania/index2.html).

Introduction

The principal case of interest documented in the Knowledge Base is the airfoil at the maximum angle of attack prior to bulk separation, at which the maximum lift coefficient is measured for a nominal chord Reynolds number of 2x10⁶ (two million). The conditions are similar to the underlying conditions for a real wing during take-off or landing, just at the beginning of the dramatic drag rise associated with stall, but are idealised to two-dimensional flow about a single-element foil. (The Reynolds number is also lower than would occur on a real wing.) In this condition a weak separation is already present over the rear portion (15%) of the upper surface. This incipient stall, which at very slightly higher angles of attack leads to full stalling and bulk separation, makes the flow of particular interest but also makes it quite difficult to predict accurately by CFD. The airfoil also has a blunt trailing edge, which is known to affect the character and position of the separation. The position of onset of the upper surface separation is the primary parameter that the models try to predict, through the pressure (C_p) distributions. Since the boundary layer is turbulent from much further upstream (it transitions at 12% of chord on the upper surface) the final separation is fully turbulent.

The case is a challenge to CFD because of the interaction between turbulence developing in a region of adverse pressure gradient and curvature effects. In this respect the case is wider than the airfoil label might indicate: it is representative of all flows involving development of a turbulent boundary-layer in the presence of convex curvature and adverse pressure gradient, leading to eventual separation. In all such situations the prediction of the separation point is likely to be a focus of great interest, and difficult for turbulent models to predict for reasons that are similar to those encountered for this specific test case.

It is known that the boundary layer over the suction surface undergoes a small laminar separation at about 12% of chord on the suction surface, passes rapidly through transition and reattaches to form a turbulent boundary layer. This develops steadily over the upper airfoil surface to separate starting at about 82% of chord.

Review of UFR studies and choice of test case

The selected UFR has been widely studied since the EUROVAL (European Initiative on Validation of CFD Codes) project [1], culminating in the publication in 1993 of the results on several test cases including the A-foil and the case of maximum lift selected here. Five partners in the project tackled the case we are interested in (and also several other incidences, and a higher Reynolds number case at Re = 5.25x10⁶) but several of the partners investigated the performance of more than one model. Subsequently the case was included in the ECARP (European Computational Aerodynamics Research Project: Validation of CFD Codes and Assessment of Turbulence Models) project [2] , in which 14 partners contributed to the case, with many of them again investigating two or more models.

This airfoil, at the specified angle of attack, Mach and Reynolds numbers, is probably the most computed test case of its type in existence. The wide coverage of numerical methods and models employed, documented and published, in turn encouraged further work on the test case as groups have tried to improve the performance of particular approaches, check new models, or validate numerical methods. In particular, the maximum-lift condition at the lower Reynolds number has been studied by LES in the project LESFOIL [3], though with limited success. For this reason LES predictions are not included in the Knowledge Base.

There have been a number of further studies, of which this description picks out the work of Jirásek et al. [4,5] as of particular importance. The prediction of separation is critically dependent on the position of the initial transition point, and if this is wrong it appears that the entire CFD computation from that point onwards will be compromised.

Contributors: Peter Voke - University of Surrey