Pressure scrambling effects and the quantification of turbulent scalar flux model uncertainties

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 toward 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.

Figure 1

The strategy of perturbing the PS direction in the UQ approach.

Figure 2

Computational domain and mesh for the pin-fin array configuration.

Figure 3

Definition of the metrics $m_1$ and $m_2$, indicating the relation between the estimated PS direction and the RI ($m_1=0$, $m_2=-1/2$) and IP ($m_1=0$, $m_2=+1/2$) directions.

Figure 4

Joint distribution of $(m_1,m_2)$ to visualize the estimated PS directions, weighted by their magnitude, relative to the RI and IP directions over the entire test section of the pin-fin array.

Figure 5

Globally averaged Nusselt numbers on the fins changed with the uncertain parameter.

Figure 6

Temperature counters on the middle plane of the pin-fin array.

Figure 7

Locally averaged Nusselt numbers on the fins (left) and the pins (right).

Figure 8

Nusselt number distributions on the pin surface (row 5).

Figure 9

Sketch of a typical scalar flux budget in a parallel shear flow with $\partial U_x/\partial y>0$ and $\partial \mathrm{\Theta }/\partial y>0$.