DES and RANS simulations of delta wing vortical flows

Abstract

An understanding of the vortical structures and vortex breakdown is essential for the development of highly maneuverable and high angle of attack flight. This is primarily due to the physical limits these phenomena impose on aircraft and missiles at extreme flight conditions. Demands for more maneuverable air vehicles have pushed the limits of current CFD methods in the high Reynolds number regime. Simulation methods must be able to accurately describe the unsteady, vortical flowfields associated with fighter aircraft at Reynolds numbers more representative of fiill scale vehicles. It is the goal of this paper to demonstrate the ability of Detached-Eddy Simulation, a hybrid RANS-LES method, to accurately predict vortex breakdown at Reynolds numbers above 1 million. Very detailed experiments performed at Onera with LDV and pressure measurement are used to compare simulations utilizing both RANS and DES turbulence models. INTRODUCTION The delta wing flow field is dominated by vortical structures, the most prominent called leading-edge vortices. As angle of attack increases, these leading-edge vortices experience a sudden disorganization, known as vortex breakdown which can be described by a rapid deceleration of both the axial and swirl components of the mean velocity and, at the same time, a dramatic expansion of the vortex core. Henri Werle first photographed the vortex breakdown phenomenon in 1954, during water tunnel tests of a slender delta wing model at Onera. This work was quickly confirmed by Peckham and Atkinson, Elle and Lambourne and Bryer and spawned a large number of experimental, computational and theoretical studies which continue today. These investigations led to the development of several theories governing vortex breakdown, although none have been universally accepted. Despite this lack of a unified theoretical interpretation, several forms of vortex breakdown have been identified' (i.e. bubble, helical, etc.), and the global characteristics of the phenomena are understood. During the breakdown process, the mean axial velocity component rapidly decreases until it reaches a stagnation point and/or becomes negative on the vortex axis. This stagnation point, called the breakdown location, is unsteady and typically oscillates about some mean position along the axis of the vortex core' (see Fig. 1). As angle of attack is increased, the mean vortex breakdown location moves upstream over the delta wing (from the trailing edge toward the apex). Figure 1: Definition of the spatial location of the vortex core and the vortex breakdown location. The primary vortex over a slender delta wing at angle of attack is principally inviscid. Unfortunately, the location of the vortex is strongly affected by a secondary vortex formed by the inter-relationship between the surface boundary layer and the primary vortex. In addition, the vortex breakdown phenomenon creates turbulent kinetic energy that must be modeled properly. Many turbulence models create orders of magnitude too much turbulent edyy viscosity in the primary vortex core which significantly alters the flowfield and in some case eliminates breakdown observed experimentally at high Reynolds numbers. For these reasons, an accurate prediction of the flowfield over a slender delta wing at high angles of attack and high Reynolds numbers must model the boundary layer, primary and secondary vortex, and turbulent kinetic energy correctly. While advances have taken place in areas such as grid generation and fast algorithms for solutions of systems of equations, CFD has remained limited as a reliable tool for prediction of inherently unsteady flows at flight Reynolds numbers. Current engineering approaches to prediction of unsteady flows are based on solution of the Reynoldsaveraged Navier-Stokes (RANS) equations. The turbulence models employed in RANS methods necessarily model the entire spectrum of turbulent motions. While often adequate in steady flows with no regions of reversed flow, or possibly exhibiting shallow separations, it appears inevitable that RANS turbulence models are unable to accurately predict phenomena (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.