Flow topology and bifurcations of buoyancy and mixed convection in an elongated channel with an abrupt section variation

A forward-facing step (FFS) located half-way in an elongated duct subjected to a horizontal pressure gradient and a vertical temperature difference is considered as a simplified geometrical model to investigate numerically typical problems of internal non-isothermal flow in the presence of blunt obstacles. The sensitivity of this system to thermal buoyancy for each considered rate of fluid injection (measured through the related Richardson number, Ri) is explored by varying parametrically the corresponding Rayleigh number (Ra) over a large interval of orders of magnitude (up to the onset of chaos) and assuming two alternate paradigms for the bottom of the considered channel, namely an adiabatic or kept-at-constant temperature (hot) boundary. Through this conceptual framework, a kaleidoscope of situations are revealed in the (Ri, Ra) space, differing in terms of flow patterning behavior, thermal plume generation phenomena, intensity of heat exchange at the walls and bifurcation scenario. In particular, while for the isothermal floor case a higher Ri leads to an increase in the value of the Rayleigh number needed for transition to time-dependent flow, the corresponding trend becomes non-monotonic if the same boundary is thermally insulated. In such a case the Nusselt number (Nu) calculated for the horizontal surface of the step is always smaller than the equivalent Nu evaluated for the vertical side. The latter is significantly lowered when the hot-floor condition is assumed. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study investigates typical problems of internal non-isothermal flow using a simplified geometrical model of a forward-facing step in an elongated duct. The sensitivity of the system to thermal buoyancy is explored by varying the Rayleigh number over a large interval and assuming different bottom boundary conditions. Different flow patterning behaviors, thermal plume generation phenomena, and heat exchange intensity at the walls are revealed in the (Ri, Ra) space.