A physics-based approach for quantifying the structural uncertainties of turbulent scalar flux models

Turbulent scalar flux modeling is relevant to a variety of engineering problems, from heat transfer in cooling systems of buildings to urban pollutant dispersion. However, most practical models for turbulent scalar fluxes are known to fail in complex flows, and thus methods for quantifying model form uncertainties are necessary. This paper proposes a physics-based uncertainty quantification approach for scalar flux models to estimate plausible intervals for quantities of interest related to scalar transport. The approach introduces uncertainty in the traditional model for the pressure-scrambling terms in the scalar flux equation by adding an extra term with a time scale that blends the scales of turbulence and mean distortion. A non-dimensional coefficient in this extra term defines the one-dimensional uncertain parameter space. The approach is applied to forced heat convection simulations of a pin-fin heat exchanger, and shows promising capabilities to bound the overall heat transfer rate and the Nusselt number distributions on fin and pin surfaces.