CFD Uncertainty Quantification using stochastic spectral methods—Exemplary application to a buoyancy-driven mixing process

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The consideration of uncertainties is of particular importance for nuclear reactor safety, where high safety standards for example ensure the integrity of the containment. By means of Computational Fluid Dynamics (CFD), buoyancy-induced mixing processes, which can take place during a severe reactor accident, are investigated. However, the CFD models contain uncertainties, which have a large impact on the present flow and have to be analyzed. The method development for the subsequent Uncertainty Quantification of a representative reactor test containment is conducted using the Differentially Heated Cavity of aspect ratio 4 with Ra=2×109 as a generic test case from the literature. In this way, methods for the future quantification of uncertainties in large-scale industrial applications are established. Results from single-fidelity models such as Unsteady Reynolds-Averaged Navier–Stokes, Large Eddy Simulation and Direct Numerical Simulation are presented and combined to three-level multifidelity models. Stochastic representations of scalar random responses are constructed by means of Polynomial Chaos Expansions and Karhunen–Loève Expansions are derived for the representation of stochastic processes. A new approach for the description of highly dynamic transient processes called Random Field Composition (RFC) is presented, which proposes stochastic model construction through combination of multiple random fields. The presented multifidelity (MF) models achieve high accuracy in combination with a justifiable computational effort. Therefore, MF modeling serves as a promising approach for large-scale applications. Furthermore, it is found, that RFC allows for the description of highly dynamic processes with a reasonable number of simulation runs, if the complexity of the stochastic process representation can be reduced by partitioning the stochasticity into single random fields.