Observation and Computation of Vortex and/or Reverse Flow Development in Mixed Convection of Air in a Slightly Inclined Rectangular Duct

Combined flow visualization and conjugated numerical heat transfer analysis were carried out to study the axial evolution of the buoyancy induced secondary vortex and reverse flow in a mixed convective air flow through a bottom heated, slightly inclined rectangular duct. Results were obtained for the Grashof number Gr ranging from 1.6 × 10³ to 2.8 × 10⁵, inclined angle φ from −20 deg to 26 deg and the Reynolds number Re below 102 covering the steady and time dependent flows. For the buoyancy-opposing case, at a certain critical buoyancy-to-inertia ratio depending on the Re and φ both the experimental and numerical results clearly showed the generation of the longitudinal vortex rolls in the entry half of the duct and a slender reverse flow zone was induced near the exit end of the duct. At a higher buoyancy-to-inertia ratio the stronger reverse flow moves upstream and is in a time periodic snaking motion which is considered to result from the Kelvin-Helmholtz instability associated with the two counter flow streams, namely, the downstream moving longitudinal vortex rolls and the upstream moving reverse flow. Through the viscous shearing effects the strong snaking reverse flow induces a number of eddies moving along it and the longitudinal rolls are pushed towards the duct sides. This strong interaction between the vortex flow and reverse flow leads to an earlier transition to turbulence. A correlation equation was proposed for the penetration length of the reverse flow. However, for buoyancy-assisting flow no reverse flow is induced and the longitudinal vortex rolls prevail for the buoyancy-to-inertia ratio up to 2.8 × 10⁵. Significant conjugated heat transfer effects were noted from the numerical results.