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DEVELOPMENT OF AN EFFICIENT AND ROBUST LINEARISED NAVIER-STOKES FLOW SOLVER
Paul Petrie-Repar
Institute ofAeroelasticity, German Aerospace Center Bunsenstrasse 10, 37073 Gottingen, Germany.
Email: Paul. Petrie-Repar@dlr. de
Abstract A time-linearised Navier-Stokes flaw solver is presented. The turbulence model of Spalart & Allmaras has been included in the fOw model. The main feature of the current method is that GMRES with preconditioning is used to solve the linearised equations in a robust and efficient manner. The method is verified by the presentation of solutions of test cases from Standard Configuration 10 and 11. The use of various upwind schemes is also examined.
Keywords: linearised Navier-Stokes, Spalart and Allmaras turbulence model, GMRES, pre
conditioning
1. Introduction
Blade flitter in turbomachinery is highly undesirable as it can lead to dramatic blade failure. In order to design blading that will be free of flitter, the design engineer requires a tool that is capable of accurately predicting blade flitter. Unsteady fl»w simulation is an essential component of flitter analysis. For transonic fl>w or separated fl>w, it is necessary to consider viscous effects. Time-marching of the Navier-Stokes equations [1] is one method of simulating the unsteady flow, however this is computationally expensive and hence has a limited use in real design. An alternative to the time-marching method is the so called time-linearised method [2]. Here the unsteady fl)w is assumed to be small harmonic linear perturbations about the steady flow. This assumption allows the equations to be transformed to the frequency domain. The resulting linear equations require significantly less computational effort to solve (1 to 2 orders of magnitude faster than time-marching methods). Here, an efficient and robust method for solving the time-linearised Navier-Stokes equations is presented. The formulation of the linearised equations is similar to the methods presented by Clark & Hall [2] and Sbardella & Imregun [3].
437
K. C. Hall et al. (eds.),
Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 437-448. © 2006 Springer. Printed in the Netherlands.
The main difference between the current method and the previous methods is the use of GMRES with preconditioning instead of pseudo-time-stepping to solve the linearised equations. This was found to be a very efficient and robust method.
