Numerical study of laminar mixed convection in a square open cavity

• Critical Richardson number rules the transition to unsteady regime in 2D mixed convection in a channel.
• Development of the upstream corner vortex with the Richardson number reverses flow at the bottom of the square cavity.
• A pseudo-periodic regime emerges characterized by emission of travelling dual counter-rotating vortices.

The Lattice Boltzmann Method (LBM) is used to study steady and unsteady laminar flow in a channel with an open square cavity and a heated bottom wall in two dimensions, under mixed convection flow conditions. LBM is compared to results obtained by ANSYS-FLUENT for validation. Temperature, velocity and Nusselt number agree very well in the range of Reynolds and Richardson numbers studied, i.e. 50⩽Re⩽100050⩽Re⩽1000 and 0.01⩽Ri⩽100.01⩽Ri⩽10. Our observations indicate that the effect of the buoyancy force is negligible for Ri⩽0.1Ri⩽0.1, for all values of the Reynolds number considered. For Ri = 1, 10 buoyancy effects are important, which combined with a high enough Re (≳≳200 in our study), causes the development of the upstream secondary vortex and the stratification of the flow into two main recirculating cells. As previously observed in earlier studies, for high enough Ri the recirculation is no longer encapsulated, the flow becomes unsteady, and an oscillatory instability develops. This is observed in our simulations starting from Re = 500, Ri = 10. The analysis of the unsteady regime reveals a very rich phenomenology where the geometry of the problem couples with the oscillatory thermal instability. This regime is characterized by the periodic emission of pairs of vortices generated from the upper downstream vertex of the square cavity, and pseudoperiodic variations of the Nusselt number which persist at least up to Re = 1500, while the two main vortices remain in the cavity. Our observations extend previous studies and shed a new light on the characteristics of the oscillatory instability and the role of the Reynolds and Richardson numbers.