A compressible three-dimensional implicit Euler solution method for turbomachinery flows has been developed. The goal of the present study is to develop an efficient and reliable method that can be used to replace the semi-empirical, semi-analytical quasi-three-dimensional turbomachinery flow prediction method currently being used for multi-stage turbomachinery design at early design stages. Currently, a methodology has been developed based on an inviscid flow model (Euler solver) and tested on single blade rows for validation. The method presented here is derived from the Beam and Warming implicit approximate factorization (AF) finite difference algorithm. To avoid high frequency numerical instabilities associated with the use of central differencing schemes to obtain a spatial second order accuracy, a combined explicit and implicit artificial dissipation model is adopted. This model consists of a second order implicit dissipation and mixed second/fourth order explicit dissipation terms. A Cartesian coordinate H-grid generated by a three-dimensional interactive grid generator developed by Beach is used. Results for SSME High Pressure Fuel Turbine are presented and the comparison with experimental data is discussed. The use of the present implicit Euler method and the three-dimensional turbomachinery interactive grid generator shows that turnaround time could be as short as one day using a workstation. This allows the designers to explore optimal design configurations at minimum cost.
Discrete-Time Implementation of Continuous Terminal Algorithm With Implicit-Euler Method