  Closure models for the turbulent scalar flux are an important source of
uncertainty in Reynolds-averaged-Navier-Stokes (RANS) simulations of scalar
transport. This paper presents an approach to quantify this uncertainty in
simulations of complex engineering flows. The approach addresses the
uncertainty in modeling the pressure scrambling (PS) effect, which is the
primary mechanism balancing the productions in scalar flux dynamics. Inspired
by the two classical phenomenological theories of return-to-isotropy (RI) and
isotropization-of-production (IP), we assume that the most likely directions of
the PS term are around a fan-shaped region bounded by the RI and IP directions.
Subsequently, we propose a strategy that requires two additional simulations,
defining perturbations of the PS directions towards the RI and IP limits. The
approach is applied to simulations of forced heat convection in a complex
pin-fin array configuration, and shows favorable monotonic properties and
bounding behaviors for various quantities of interest (QoIs) relevant to heat
transfer. To conclude, the results are analyzed from the perspective of
transverse scalar transport in a shear flow; the analysis indicates that the
proposed approach is likely to exhibit monotonic behaviors in a wide range of
scalar transport problems.
