Nusselt number and friction factor in thermally stratified turbulent channel flow under Non-Oberbeck–Boussinesq conditions

Abstract

In stably stratified turbulence, computations under Oberbeck–Boussinesq (OB) hypothesis of temperature-independent fluid properties may lead to inaccurate representation of the flow field and to wrong estimates of momentum/heat transfer coefficients. This is clearly assessed here comparing direct numerical simulations of stratified turbulence under OB conditions to simulations under NOB (Non-Oberbeck–Boussinesq) conditions of temperature-dependent fluid viscosity and thermal expansion coefficient. Compared to the OB case, NOB conditions may induce local flow relaminarization with significant variations (up to 30%) of heat and momentum transfer coefficients. Together with DNS results, we propose a phenomenological model (based on turbulent bursts) for heat transfer prediction in stratified turbulence under OB and NOB conditions. Implications of NOB assumptions on mixing efficiency (i.e. flux Richardson number Rif) and turbulent Prandtl number (Prt) are also discussed. These results are of specific importance in RANS modelling, where the condition Prt=1 is usually assumed (Reynolds analogy). Although this assumption is valid in some situations (i.e. boundary layer, pipe flow) there is uncertainty about its validity for stably-stratified turbulence. We demonstrate that this assumption is inaccurate when NOB effects become significant.