Aerodynamic Optimization of Turboprop Turbine Blades Using a Response Surface Methodology Based Algorithm

Abstract

Turbomachinery blade design improvement and optimization by CFD is a time-consuming engineering challenge. Such an optimization process, which requires advanced numerical simulations, uses a large amount of computational resources to provide the required solutions. This paper presents a turbine blade optimization process which uses an algorithm based on response surface methodology (RSM) to increase the simulation speed. The main idea of RSM is to start with a lower number of sample points to generate an analytical model that describes the relationship between the pre-defined numbers of design parameters. In this study, the Kriging approximation is used to generate the surface model. The global minimum on the surface is searched by applying a gradient method. The increase in the convergence speed is achieved by using an adaptive scheme, which creates additional points around the previous minimum while reducing the solution space at each iteration step, until convergence is achieved. Each iteration step is composed of several CFD simulation runs where each point represents different designed geometries inside the n-dimensional parameter space. The process combines a Bezier-spline based airfoil-generator with a parametric meshing tool —G3DMESH— and a CFD solver —TRACE—, both developed and provided by DLR, into a MATLAB script function. A particular characteristic of this optimization method is its lower evaluation number requirement to reach convergence, as well as its capability to run multiple simultaneous RANS. The optimizer process was initially tested by using basic functions to analyze its solution behavior and its performance in comparison to a genetic algorithm (GA) type optimizer. It is observed from this comparison that RSM optimization reaches the convergence faster and more stable than the GA method applied on the test case. Preliminary optimization results show an improvement in function evaluation requirements by up to 50%, which depends on the complexity of the respective surface model of the test case. As an application, a 4-stage low pressure turbine for a turboprop engine is designed by multi-streamline analysis. 2D mid-span cross-sections from both rotor and stator are produced by the Bezier-spline based airfoil-generator. The basis tool requires input parameters as leading and trailing edge blade angles and maximum thickness position. The blade generator is further improved by the additional ability to work with high values of deviation angles between the leading and trailing edges, up to 90°. 6 control points are used to define the two curves, for pressure and suction sides, which encompass the cross-section geometry. Optimization process runs to improve these airfoil parameters. The 2D airfoils of the first stage are optimized by an objective function based on total pressure loss coefficient at the engine on-design point. The same geometry is also optimized using the GA method as a comparison case.