Direct simulation of transition in a differentially heated vertical channel

Transition to turbulence of natural convection flows ensuing in a fluid layer between two differentially heated vertical plates is a topic of substantial interest for many applications. Among these, notable examples are the air gaps in double-glazing panes or in ventilated façades, and passive heat exchangers. The correct prediction and control of flow regimes, air flow rates and heat transfer coefficients has a significant impact in the correct design of such elements and, in turn, on their efficiency. In recent studies the early stages of transition have been explored by means of Direct Numerical Simulation (DNS) with high-accuracy pseudospectral codes. While all these studies correctly capture the first bifurcation from the so-called laminar conduction regime to steady convection, the detection of the subsequent transition to turbulence appears to be accompanied by a great sensitivity to some fundamental numerical choices, such as domain size, spectral resolution and amplitude of the imposed perturbations. In turn, these aspects become of crucial importance for the prediction of the heat transfer performance of the system. In this work, the problem is tackled by means of a second-order, Finite-Volume based Direct Numerical Simulation technique, specifically devised for convection problems, and which already proved successful in the simulation of transitional scenarios. Results reveal the occurrence of a bifurcation branch which leads the system to chaos via a second bifurcation to a steady-state, a Hopf bifurcation and, seemingly, a period-doubling cascade. Such a scenario compares well with previous findings, except for minor discrepancies. All in all, though, some doubts persist upon the possible pitfalls in the use of DNS for the study of transition in this kind of systems.