Large eddy simulation of the flow around an inclined prolate spheroid

Abstract

Results from a computational study of high Reynolds number (ReL=4.2-10) flow past a 6:1 prolate spheroid, based on Large Eddy Simulation (LES), are here presented. The objective is (i) to evaluate the applicability of LES for practically relevant high-Re flows, (ii) to investigate the influence of subgrid modeling and grid resolution on the quality of the results and (iii) to discuss the fluid mechanics of this flow. In order to help addressing the first issues we have also computed the subcritical flow past a circular cylinder at Re=3900. Both explicit (or conventional LES and Monotone Integrated LES (MILES) have been used. The LES-equations are solved using a parallelized finite-volume based solver, using a PISO-type method for handling the velocity pressure coupling. Concerning the subcritical flow past a circular cylinder good results are obtained when comparing with experimental and direct numerical simulation results. For the prolate spheroid case the results are qualitatively correct but quantitatively less satisfactory. Introduction Flows around aerodynamic vehicles or submersibles, such as submarines, torpedoes or Unmanned Underwater Vehicles (UUV's) are very complicated and fully three-dimensional. For optimized design, with respect to performance and signatures, detailed information is required about the flowfield under various operating conditions. For maneuvering three-dimensional flow separation becomes particularly important and this is the main focus of the present paper. The phenomenon of three-dimensional separation of the flow about a body, though quite common, is both difficult to model and poorly understood. In two-dimensional flow, the point (or line) of separation coincides with the point (line) at which the skin friction vanishes. However, in three-dimensional flow the situation is much more complicated, and flow detachment or separation is rarely associated with the Copyright © 2001 by P.-O. Hedin, M. Berglund, N. Alin & C. Fureby. Published by the American Institute of Aeronautics and Astronautics, Inc. wi th permission vanishing wall-shear stress, except in a few special cases. In order to facilitate the modeling and the subsequent understanding, of the underlying flow features Legendre, [1], and Lighthill, [2], introduced concepts equivalent of limiting streamlines and skin friction lines. Based on their work Tobak & Peake, [3], then formulated simple topological rules governing the set of nodes and saddle points contained in the flow. Further work by Wilson, [4], Wang, [5], and Han & Patel, [6], enabled the identification of two basic types of three-dimensional flow separation suggested earlier by Maskell, [7], a closed or bubble type of separation and an open or free-vortex type of separation. The former is also termed singular separation since the separation line passes through or joins singular points at which the wall shear stress vanishes. Such a separation divides flows from adjacent regions so that boundary layer theory is generally not applicable. In order to better understand three-dimensional flow separation, several groups have experimentally investigated the flow about a 6:1 prolate spheroid at various angles of attack. This flow is a well-defined, relatively simple three-dimensional flow that exhibits all the fundamental transition and separation phenomena of three-dimensional flow. The flow separating from the leeward side of the prolate spheroid rolls up into a strong vortex on each side of the body and reattaches around the top-dead center of the spheroid. This primary vortex is generally accompanied by at least one smaller vortex, which separates and reattaches high up on the body. The complex interaction between vortices is strongly dependent on the angle of attack and the Re-number, and results in a highly skewed and three-dimensional boundary layer. Much experimental work has been performed to obtain a detailed understanding of this flow and the associated flow phenomena. For example, Meier et al, [8], Kreplin et al, [9], and Volmers ct al, 110) , have documented the surface flow, surface pressure, skin friction and mean velocity at different angles of attack and different Re-numbers. Ahn & Simpson, [11], studied boundary layer transition and separation, Barber & Simpson, [12], examined the mean and fluctuating velocities in the cross-How separation region, (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. Chesnakas & Simpson, [13], documented the turbulence structure, Goody et al, [14], measured surface pressure fluctuations and pressure-velocity fluctuations, and Goody et al, [15], studied the pressure and velocity spectra. Because of the wealth of experimental data available, and the simplicity of the geometry this flowfield has made an excellent test case for computational fluid dynamic models. The flow of a linear viscous fluid is governed by the Navier-Stokes Equations (NSE) together with appropriate initial and boundary conditions. From a computational point of view the NSE can be solved directly for laminar flows whilst for turbulent flows the wide range of eddy scales present prohibits Direct Numerical Simulation (DNS). The prevalent remedy to this resolution problem involves the Reynolds Averaged Navier-Stokes (RANS) equations, [16], with averaging typically carried out over time, homogeneous directions or across an ensemble of equivalent flows, which require empirical information on the turbulence structure and its relation to the mean flow, [17]. A more viable method is Large Eddy Simulations (LES), in which only the small-scale turbulent fluctuations are modeled and the larger-scales fluctuations are computed directly, e.g. [18-19], and references therein. Before LES can be used for applications of practical relevance the influences on the quality of LES results must be understood. This includes numerical aspects such as discterization and resolution requirements, and modeling aspects such as Sub Grid Scale (SGS) or near-wall models. The present study is part of an ongoing research program with the long-term objective of developing a LES capability that is able to simulate high Renumber flows of practical relevance. A number of flows of different types and complexities have previously been computed, but the flow past a prolate spheroid at an angle of attack is considered among the most complex flows ever attempted by LES. Because of the complexity of this case it may serve as a necessary test case on the way to real world applications of LES. The present contribution considers primarily the ability to capture, qualitatively, the overall flow features, and their variation with Re-number and incidence. Furthermore, we investigate to which extent LES can be used to replicate wind tunnel experiments in understanding the surface flow pattern. This study is planed to be continued by (i) a detailed quantitative validation study, in which the first and second order statistical moments of the velocity and pressure fields are compared with experimental data at two cross-sections, and (ii) broader conceptual flow study aiming at clarifying the mechanisms behind three-dimensional separation and transition. The Conventional LES Model The fluid dynamic model used is based on the NSE, describing conservation of mass and balance of momentum of a linear viscous fluid, e.g. [20],