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After the extraordinary diffusion that we have observed over the last ten years, Organic Rankine Cycles (ORCs) are nowadays widely recognized as “the unrivalled technical solution for generating electricity from low-medium temperature heat sources of limited capacity” [1]. Despite the high level of confidence and know-how reached about ORCs, they still remain a delicate technology, hiding a great amount of technical difficulties which sometimes still make them a risky investment. Most of these complexities are originated from manifold sources of uncertainty which impact on almost the whole life of the ORC project, from their design to the commissioning and operation steps, with heavy consequences in terms of performance and costs. In this work we present the proof of concept assessing and validating an innovative technique for the robust design optimization (RDO) of ORC under uncertainty. The approach allows to deal with both aleatory and epistemic uncertainty in order to avoid an over-optimization of the system that can result in a high sensitivity to small changes. Because of the large number of sources of uncertainty, the design problem must be solved in a highly multi-dimensional space, spanned by the uncertain and design variables. In such a situation, the “brute-force” Monte-carlo approach [2] is not a viable technique, since it is limited to cheap and excessively simplified models. Consequently, in the present work we consider a more efficient design methodology relying on two nested Bayesian Kriging surrogates.

Efficient Robust Design Optimization (RDO) strategies coupling a parsimonious uncertainty quantification (UQ) method with a surrogate-based multi-objective genetic algorithm (SMOGA) are investigated for a test problem in computational fluid dynamics (CFD), namely the inverse robust design of an expansion nozzle. The low-order statistics (mean and variance) of the stochastic cost function are computed through either a gradient-enhanced kriging (GEK) surrogate or through the less expensive, lower fidelity, first-order method of moments (MoM). Both the continuous (non-intrusive) and discrete (intrusive) adjoint methods are evaluated for computing the gradients required for GEK and MoM. In all cases, the results are assessed against a reference kriging UQ surrogate not using gradient information. Subsequently, the GEK and MoM UQ solvers are fused together to build a multi-fidelity surrogate with adaptive infill enrichment for the SMOGA optimizer. The resulting hybrid multi-fidelity SMOGA RDO strategy ensures a good tradeoff between cost and accuracy, thus representing an efficient approach for complex RDO problems.

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