A 3D COMPRESSIBLE EULER SOLVER FOR TURBOMACHINERY CASCADES Carlo CRAVERO, Martino MARINI. Antonio SATTA A94- 31950 Istituto di Macchine e Sistemi Energetici Universiti di Genova Via Montallegro 1, 16145 Genova - ITALIA Abstract The paper describes a three-dimensional Euler solver, based on a cell vertex finite volume explicit method, for calculating cascade flows. The features of the adopted algorithm, such as finite volume discretization, artificial dissipation and boundary condition implementation, are examined. Comparisons with experimental and theoretical data about a low pressure turbine cascade enable the solver to be validated. A good agreement with the results of other authors is found. Introduction In recent years a considerable number of computational methods to solve three-dimensional flows have been reported by various researchers. The application of such numerical methods to 3D compressible flows in axial turbomachinery blade rows is a matter of great interest since it contributes to the improvement of the aerodynamic performance of turbines and compressors. Central difference finite-volume techniques based on elplicit Runge-Kutta pseudotime integration with the addition of second and fourth order dissipation terms for stability and shock capturing have been shown to be particularly efficent in the solution of inviscid flows1. They are suitable for turbomachinery calculations because of their relevant robustness and of their flexibility with the smoothing under the user's control. The paper deals with an Euler solver developed by the authors to calculate the transonic flows in axial turbomachinery cascades. The main features of the solver, based on a first two-dimensional version successfully applied to rectilinear cascades2, are here discussed pointing out the contribution of the authors. Governiw E~uations We consider the three-dimensional unsteady Euler equations In an absolute Cartesian reference frame : I\ hcrc and p, u, v, w, e, p denote nondimensional density, velocity components, energy and pressure referred to inlet total temperature and pressure. The perfect gas law and the definition of internal energy give: Outline of the Numerical Techniaue Many factors play a role and must be taken into account in developing a fluid machinery numerical solver. The choices that have been especially important for the success of it are now exposed. Vertex based spatial discretization The physical domain is subdivided into a large number of hemedral control volumes and the flow variables are stored in the vertices of such a volume. An integral form of the governing equations (1) is the following : where R denotes a given volum and dR is its boundary. The time rates of change of mass, momentum and energy within the control volume is equal to the flux of the quantity through the boundary of the volume. The control volume is sketched in fig.1: the ei ht cells surrounding 5 the vertex (i,k,l) form a "super-cell" . Fig1 Control volume around point (i,k,l) The surface integral in eq. (6) is evaluated for each componcn( cell. then thc resultant convective flow of 6 74 "Copyright c 1994 by the .4merican Institute of Aeronautics and Astronautics, Inc. All fight rese~d."