Optimal Design of ORC Turbine Blades under Geometric and Operational Uncertainties

orc2019 Tracking Number 78

Typical energy sources for Organic Rankine Cycle (ORC) power systems feature variable heat load and turbine inlet/outlet thermodynamic conditions. The use of organic compounds with heavy molecular weight introduces uncertainties in the fluid thermodynamic modeling and complexity in the turbomachinery aerodynamics, with supersonic flows and strong shocks, which grow in relevance in the aforementioned off-design conditions. These features also depend strongly on the local blade shape, which can be influenced by the geometric tolerances of the blade manufacturing. This study presents a Robust Optimization (RO) analysis on a typical supersonic nozzle cascade for ORC applications under the combined effect of uncertainties associated to operating conditions, fluid parameters, and geometric tolerances. The geometric variability is described by a finite Karhunen-Loeve expansion representing a non-stationary Gaussian random field, entirely defined by a null mean and its autocorrelation function. Real-gas effects are modeled through the use of the polytropic improved Peng-Robinson equation of state implemented within the open-source CFD solver SU2. The blade is parametrized by moving B-splines control points, allowed to be displaced in the direction locally normal to the blade. Different statistics, according to the RO formulation chosen, of the Quantity of Interest (QoI) are minimized in the framework of mono-objective optimization, constraining the mean mass flow-rate to be within a small range centered at the baseline value, at nominal conditions. Linear combination of mean and standard deviation of the QoI (equivalent to the popular Taguchi multi-objective optimization) are considered, as well a linear combination of mean and high quantile. The robust optimal blades are compared to the deterministic optimal shape. The impact of the choice of the RO formulation on the final blades is highlighted.