Large Eddy Simulation for Aerospace and Turbomachinery Aerodynamics

M. A. Leschziner (Imperial College)

D. R. Emerson (Daresbury Laboratory)

Figure courtesy of Prof. W. P. Jones (Imperial College)

Introduction

The vast majority of flows encountered in real applications are turbulent. The ability to more accurately represent turbulence motion in fluids is therefore critical to gaining a more comprehensive understanding and improved predictive capability. It is widely recognised that current schemes based on the Reynolds Averaged Navier Stokes (RANS) approach cannot capture or accurately represent many important flow features, particularly if the flow exhibits unsteady or transient behaviour. One approach that offers a potential solution to these difficult flow problems is Large Eddy Simulation (LES). As the name implies, this approach models the largest eddies without recourse to modelling. These large-scale motions are responsible for most turbulent transport mechanisms. The small-scale turbulent motions, which happen at the sub-grid level, can be modelled in a more traditional way.

Large Eddy Simulation is increasingly viewed as an approach that promises a greater degree of predictive realism and generality than RANS schemes, which rely heavily on the adequacy of approximate statistical models of turbulence. The principal advantage of LES lies in its ability to resolve the unsteady nature of turbulence down to an eddy size that is pre-defined by a spatial filtering process applied to the Navier-Stokes equations. This is especially advantageous in flows that feature coherent structures and periodic motion. To represent eddies below the filtered size - typically of order of one mesh interval - a Sub-Grid-Scale (SGS) model is introduced. This can be significantly simpler than the type of models used in RANS schemes, as it is only required to capture the influence of relatively small eddies which tend to have isotropic properties and often make a sub-ordinate contribution to the turbulent mixing processes.

A striking demonstration of the potential of LES for practically relevant flows was given at a recent ERCOFTAC workshop, held at UMIST [1] in May 1998, in which one test case was the turbulent flow around a surface-mounted cube. This study, and others directed towards vortex shedding from a square prism [2] and jets subjected to crossflow [3], demonstrate that LES returns a representation distinctly superior to that derived from almost any turbulence model in flows which are dominated by large-scale periodic features and in which the processes of primary interest are not influenced significantly by wall friction. Much greater challenges are posed, however, by flows where separation occurs at curved surfaces - for example, a round cylinder, a high-lift aerofoil or a highly-loaded compressor blade. A major problem here is that the gross behaviour of these flows is strongly influenced by the turbulence structure in the relatively thin boundary layer leading up to the separation line.

The difficulty of resolving influential near-wall processes together with far larger features associated with separation is one of several obstacles to LES simply replacing RANS approaches and becoming a practical engineering tool. Another major obstacle is the very high computer resources needed for what are inevitably 3D time-dependent computations over dense meshes, requiring about 10⁵ time steps to allow meaningful statistical information to be extracted. Important physical challenges include: the large disparity between the dominant length scales in different regions within the same flow; the highly anisotropic nature of near-wall eddies; the significant contribution of SGS modelling in high Reynolds number flows; and, the difficulty of prescribing time-dependent boundary conditions without corrupting the solution, due, for example, to spectral defects and artificial reflection.

To tackle these formidable problems, a new consortium has been formed that will be exploiting the Cray T3E/1200 at Manchester. This consortium is based upon the successful LES-UK consortium that was formed following an initiative by CCP12 to develop applications for the Cray T3D. A typical result from one of the LES-UK partners is shown in figure 1 and represents a turbulent diffusion flame emanating from a small jet. The proposed work programme of the new consortium is structured around four principal application areas:

1. separated flows around aerofoil at high incidence and subject of imposed oscillations;
2. flow around compressor-outlet guide vanes (OGV) and the passage of the associated wakes through the pre-diffuser leading to the combustor itself;
3. separated flow around turbomachinery blades;
4. vortex shedding phenomena in an IP turbine stage.

Experience within LES-UK has shown that credible LES computations require meshes of 0.5-2M nodes. A single run with such a mesh requires of order 10,000 T3D PE hours. For some applications, the requirements will be in excess of 20,000 per run. It is likely that non-orthogonal-mesh calculations would require 50-100% more CPU time and a memory of about 10GB. To reflect the importance of this work, EPSRC have awarded the new consortium the equivalent of 4.8M T3D PE hours. The work will be led by a number of key academic researchers from a range of institutions, which are:

• Professor W. P. Jones (Imperial College)

• Professor M. A. Leschziner (Imperial College)

• Professor J. J. McGuirk and Dr. Z. Yang (Loughborough University)

• Professor P. Voke (University of Surrey)

The Principal Investigator for the consortium is Prof. M. A. Leschziner and the consortium is supported by CCP12 at Daresbury Laboratory. The proposed work could substantially benefit many industrial companies that make extensive use of CFD for the development and design of fluid-flow equipment. Amongst these are Rolls Royce, British Aerospace, Westland Helicopters, European Gas Turbines and GEC. All invest substantially in computational methods for predicting complex turbulent flows.

Publications

1. Proc. 7th ERCOFTAC/IAHR Workshop on Refined Flow Modelling, UMIST, May 1998
2. Proc. of Workshop of Flows past Bluff Bodies, Tegernsee, June 1995
3. Jones, W.P. and Wille M., ‘Large Eddy Simulation of a plane jet in a cross flow’, Int J Heat Fluid Flow, pp. 296-306 (1996)

This proposal is part of an on-going collaborative research programme, coordinated through EPSRC.

For further information on this work please contact:

Prof. David Emerson
Daresbury Laboratory
Daresbury
Warrington WA4 4AD
England
Tel. +44 (0)1925 603221
Fax. +44 (0)1925 603634
Email: D.R.Emerson@dl.ac.uk
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