  Aerospace design is increasingly incorporating Design Under Uncertainty based
approaches to lead to more robust and reliable optimal designs. These
approaches require dependable estimates of uncertainty in simulations for their
success. The key contributor of predictive uncertainty in Computational Fluid
Dynamics (CFD) simulations of turbulent flows are the structural limitations of
Reynolds-averaged Navier-Stokes models, termed model-form uncertainty.
Currently, the common procedure to estimate turbulence model-form uncertainty
is the Eigenspace Perturbation Framework (EPF), involving perturbations to the
modeled Reynolds stress tensor within physical limits. The EPF has been applied
with success in design and analysis tasks in numerous prior works from the
industry and academia. Owing to its rapid success and adoption in several
commercial and open-source CFD solvers, in depth Verification and Validation of
the EPF is critical. In this work, we show that under certain conditions, the
perturbations in the EPF can lead to Reynolds stress dynamics that are not
physically realizable. This analysis enables us to propose a set of necessary
physics-based constraints, leading to a realizable EPF. We apply this
constrained procedure to the illustrative test case of a converging-diverging
channel, and we demonstrate that these constraints limit physically implausible
dynamics of the Reynolds stress tensor, while enhancing the accuracy and
stability of the uncertainty estimation procedure.
