RANS predictions for high-speed flows using enveloping models

In this investigation, we outline an enveloping models methodology for estimating structural uncertainty bounds on RANS closures. This methodology incorporates both eigenvalue and eigenvector perturbations in the spectral representation of the Reynolds stress tensor. The underlying rationale of this enveloping models methodology are explicated in detail and the mathematical nuances are outlined. This methodology is validated via its application to a canonical case of separated turbulent flow, while contrasted against numerical data. It is exhibited that this procedure is able to provide prudent estimates on the uncertainty of quantities of interest. Furthermore, uncertainty bounds of engineering utility can be engendered using just two specific RANS simulations, minimizing the computational overheads associated with uncertainty estimation. Thence, this methodology is applied to a supersonic axisymmetric "submerged" jet flow. The epistemic uncertainty envelopes are contrasted against the aleatoric uncertainty bounds predicated upon the predictions of the RANS closure. The methodology is able to provide satisfactory results for this high-speed flow.