Physical study of the non-equilibrium development of a turbulent thermal boundary layer

The direct numerical simulation of a non-equilibrium turbulent heat transfer case is performed in a channel flow, where non-equilibrium is induced by a step change in surface temperature. The domain is thus made of two parts in the streamwise direction. Upstream, the flow is turbulent, homogeneous in temperature and the channel walls are adiabatic. The inflow conditions are extracted from a recycling plane located further downstream so that a fully developed turbulent adiabatic flow reaches the second part. In the domain located downstream, isothermal boundary conditions are prescribed at the walls. The boundary layer, initially at equilibrium, is perturbed by the abrupt change of boundary conditions and a non-equilibrium transient phase is observed until, further downstream, the flow reaches a new equilibrium state presenting a fully developed thermal boundary layer. The study focuses on the spatial transient phase, identifies the main non-equilibrium effects and contrasts these results with usual assumptions of equilibrium turbulent heat transfer. Mean and root-mean-square profiles of temperature and velocity, as well as the respective energy and momentum balances, are presented and discussed along with budgets of second-order moment balance equations for the enthalpy variance and the wall-normal heat flux. For several quantities, an equilibrium near-wall region is identified even near the leading edge while the boundary layer is still developing. Finally, the evolution of the turbulent Prandtl number along the channel flow is investigated and shows that it reaches equilibrium only further downstream