Large eddy simulation of three-dimensional hybrid forced-buoyancy convection in channels with a step

This paper follows and integrates the work started in Inam and Lappa (2021, Int. J. of Heat and Mass Transfer, 173, 121267 and 2022, Int. J. of Heat and Mass Transfer, 194(12), 122963) for unsteady flow in a channel with either a forward facing (FFS) or a backward-facing step (BFS) by removing the constraint of two-dimensionality and allowing the flow to develop along the spanwise direction. As a novel aspect with respect to the existing literature (where buoyancy effects in these geometries have generally been ignored), mixed forced-gravitational convection is examined. The governing equations, formulated according to the Boussinesq approximation are integrated using an incompressible flow solver. Moreover, as the considered flow regime is turbulent [Ri=O(10²) and Ra=O(10⁷) for Pr=1], in order, to reduce the scale of the problem to a level where it is affordable, the analysis is developed in the framework of a large eddy simulation (LES) approach. Part of the study is devoted to a critical evaluation of the parameters required for the implementation of such a model. We show that while in some cases these may result in turbulent stress underestimation, in other cases, unphysical flow re-laminarization occurs due to excessive dissipation occurring on the small scales. The outcomes of the three-dimensional simulations are used to clarify some still poorly known aspects, especially the flow behavior in proximity to (before and after) the step, i.e. the point where the abrupt change in the channel cross-sectional area occurs. It is shown that a strong correlation exists between the regions where the horizontal flow separates and the presence of thermal plumes originating from the bottom wall. Moreover, the quantitative differences between two-dimensional (2D) and three-dimensional (3D) results are not limited to the patterning behavior at the flow macroscopic scale (where energy is injected into the system). The problem dimensionality also affects the cascading energy phenomena developing inside the inertial range of scales. In particular, while the thermal plumes in the FFS display a striking 3D nature, the BFS is characterized by a significant macroscopic component of vorticity along the main flow direction. In this specific case, the portion of the spectrum corresponding to the inertial regime is shifted towards higher or smaller amplitudes (with respect to the equivalent 2D dynamics) depending on the thermal boundary condition considered for the channel floor.