Uncertainty quantification and global sensitivity analysis of double-diffusive natural convection in a porous enclosure

Abstract

In this paper, detailed uncertainty propagation analysis (UPA) and variance-based global sensitivity analysis (GSA) are performed on the widely adopted double-diffuse convection (DDC) benchmark problem of a square porous cavity with horizontal temperature and concentration gradients. The objective is to understand the impact of uncertainties related to model parameters on metrics characterizing flow, heat and mass transfer processes, and to derive spatial maps of uncertainty and sensitivity indices which can provide physical insights and a better understanding of DDC processes in porous media. DDC simulations are computationally expensive and UPA and GSA require large number of simulations, so an appropriate strategy is developed to reduce the computational burden. The approach is built on two pillars: (a) an efficient numerical simulator based on the Fourier series method that generates training data, and (b) polynomial chaos expansion (PCE) meta-models that are trained using the simulator data, and then replace the numerical model in UPA and GSA. Assuming that the Rayleigh number (Ra), the solutal to thermal buoyancy ratio (Nb) and the Lewis number (Le) are the uncertain input variables, the results of UPA show that the zones of high temperature and concentration variability are located in the regions where the flow is mainly driven by the buoyancy effects. GSA indicates that Nb is the most influential parameter affecting the temperature and concentration fields, followed respectively by Ra and Le. For the heat-driven flow case (Nb>−1), the concentration field is more influenced by Le than Ra. For deeper understanding of uncertainty propagation, we estimate the bias introduced by replacing uncertain parameters by deterministic values. The resulting spatial maps of the difference between deterministic output and stochastic mean show that a deterministic approach leads to different zones where the temperature, concentration and velocity fields can be either overestimated or underestimated. The conclusions drawn in this work are likely to be helpful in different applications involving DDC in porous enclosures leading to convective circulation cells.