Airfoil Shape Optimization for Transonic Flows Bethe-Zel'dovich-Thompson Fluids

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. High-performance airfoils for transonic flows of Bethe-Zel'dovich-Thompson fluids are constructed using a robust and efficient Euler flow solver coupled with a multi-objective genetic algorithm. Bethe-Zel'dovichThompson fluids are characterized by negative values of the fundamental derivative of gasdynamics for a range of temperatures and pressures in the vapor phase, which leads to nonclassical gasdynamic behaviors such as the disintegration of compression shocks. Using Bethe-Zel'dovich-Thompson gases as working fluids may result in low drag exerted on airfoils operating at high transonic speeds, due to a substantial increase in the airfoil critical Mach number. This advantage can be further improved by a proper design of the airfoil shape, also leading to the enlargement of the airfoil operation range within which Bethe-Zel'dovich-Thompson effects are significant. Such a result is of particular interest in view of the exploitation of Bethe-Zel'dovich-Thompson fluids for the development of high-efficiency turbomachinery.

Robust optimization of dense gas flows under uncertain operating conditions

“…In the second section of this study, a PCM stochastic analysis is coupled with an existing multi-objective Pareto-based genetic algorithm (MOGA), previously applied to transonic dense gas flows [27][28][29]. The robust optimization procedure generates a series of optimized 2D airfoils for dense gas flows, based on minimization of the mean and standard deviation of the drag coefficient.…”

Optimal airfoil shapes for viscous transonic flows of Bethe–Zel’dovich–Thompson fluids

“…For these reasons, in Ref. [25], the viscous behavior of optimal airfoils was only checked a posteriori for optimal airfoils derived from inviscid computations, and not directly taken into account in the optimization process.…”

“…In practice, it is especially important to ensure satisfactory aerodynamic performances of the airfoil in both regimes, since the freestream pressure is likely to change according to the turbine operating conditions. To this purpose, an optimization tool for transonic dense gas flows past airfoils has been developed [25], based on evolutionary optimization strategies, and namely multi-objective genetic algorithms (MOGA). Genetic algorithms have been successfully applied for some time now to shape optimization in aeronautics [26,27]; in spite of their high computational cost, they have gained much attention and popularity because of their flexibility and robustness in finding global optima of multi-modal problems.…”

A Review of Techniques for Handling Expensive Functions in Evolutionary Multi-Objective Optimization

“…The multi-objective genetic algorithm used in the second case was the NSGA [74]. In previous related work [18], a population size of 36 and 24 generations were used (totaling 864 objective function evaluations obtained from CFD), based on the constraint that the whole CFD calculation time had to be kept inferior to one week (the evaluation time for each individual varied from 5 to 10 min in a PC equipped with a Pentium Processor). In order to reduce the computational cost, the authors included an ANN (Artificial Neural Network) based on radial basis functions, formed by an input layer, an intermediate layer, and an output layer.…”