Shape optimization of an airfoil in a BZT flow with multiple-source uncertainties

Bethe-Zel'dovich-Thompson fluids (BZT) 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 non-classical gasdynamic behaviors such as the disintegration of compression shocks. These non-classical phenomena can be exploited, when using these fluids in Organic Rankine Cycles (ORCs), to increase isentropic efficiency. A predictive numerical simulation of these flows must account for two main sources of physical uncertainties: the BZT fluid properties often difficult to measure accurately and the usually fluctuating turbine inlet conditions. For taking full advantage of the BZT properties, the turbine geometry must also be specifically designed, keeping in mind the geometry achieved in practice after machining always slightly differs from the theoretical shape. This paper investigates some efficient procedures to perform shape optimization in a 2D BZT flow with multiple-source uncertainties (thermodynamic model, operating conditions and geometry). To demonstrate the feasibility of the proposed efficient strategies for shape optimization in the presence of multiple-source uncertainties, a zero incidence symmetric airfoil wave-drag minimization problem is retained as a case-study. This simplified configuration encompasses most of the features associated with a turbine design problem, as far the uncertainty quantification is concerned. A preliminary analysis of the contributions to the variance of the wave-drag allows to select the most significant sources of uncertainties using a reduced number of flow computations. The resulting mean value and variance of the objective are next turned into metamodels. The optimal Pareto sets corresponding to the minimization of various substitute functions are obtained using a genetic algorithm as optimizer and their differences are discussed.