Non-intrusive semi-analytical uncertainty quantification using Bayesian quadrature with application to CFD simulations

To improve the safety, reliability, and performance of complex engineering systems, it is crucial to understand and quantify uncertainties. This paper presents a framework to non-intrusively and semi-analytically quantify the parametric uncertainty within CFD simulations using Bayesian quadrature (BQ). An in-house uncertainty quantification (UQ) code based upon this mathematical framework is developed. The code is then validated by applying it to quantify the uncertainty due to a varying parameter in a simple analytical test function. The mean and variance obtained using BQ are compared with those obtained from the analytical solution and stochastic simulation using the Latin hypercube sampling (LHS) method. The validation test case shows that BQ out-performs the LHS approach in terms of computational efficiency and accuracy. The UQ code is then utilised to characterise the uncertainty (due to the unknown inlet flow profile) of CFD predicted operating parameters of an industrial scale butterfly valve, as well as the uncertainties (due to the unknown high-wavenumber damping factor C-s) of a SAS-SST simulated bluff-body flow. It is found that the entry flow profile presents non-ignorable effects on the valve operating parameters. Meanwhile, the variance of the valve operating parameters changes with the valve opening. For the bluff-body flow, large variances of predicted flow properties exist in the region where the separate shear layer dominates because of varyingC(s). Moreover, the effect of C-s is more significant on the turbulence quantities, as it acts on the generation of turbulent eddies directly.