Improved self-consistency of the Reynolds stress tensor eigenspace perturbation for uncertainty quantification

Abstract

The limitations of turbulence closure models in the context of Reynolds-averaged Navier–Stokes (RANS) simulations play a significant part in contributing to the uncertainty of computational fluid dynamics (CFD). Perturbing the spectral representation of the Reynolds stress tensor within physical limits is common practice in several commercial and open-source CFD solvers, in order to obtain estimates for the epistemic uncertainties of RANS turbulence models. Recent research revealed that there is a need for moderating the amount of perturbed Reynolds stress tensor to be considered due to upcoming stability issues of the solver. In this paper, we point out that the consequent common implementation can lead to unintended states of the resulting perturbed Reynolds stress tensor. The combination of eigenvector perturbation and moderation factor may actually result in moderated eigenvalues, which are not linearly dependent on the originally unperturbed and fully perturbed eigenvalues anymore. Hence, the computational implementation is no longer in accordance with the conceptual idea of the Eigenspace Perturbation Framework. We verify the implementation of the conceptual description with respect to its self-consistency. Adequately representing the basic concept results in formulating a computational implementation to improve self-consistency of the Reynolds stress tensor perturbation.