Scalar and joint velocity–scalar PDF modelling of near-wall turbulent heat transfer

The temperature field in a heated turbulent flow is considered as a dynamically passive scalar. The probability density function (PDF) method with down to the wall integration is explored and new modelling proposals are put forward, including the explicit account for the molecular transport terms. Two variants of the approach are considered: first, the scalar PDF method with the use of externally-provided turbulence statistics; and second, the joint (stand-alone) velocity–scalar PDF method where a near-wall model for dynamical variables is coupled with a model for temperature. The closure proposals are formulated in the Lagrangian setting and resulting stochastic evolution equations are solved with a Monte Carlo method. The near-wall region of a heated channel flow is taken as a validation case; the second-order thermal statistics are of a particular interest. The PDF computation results agree reasonably with available DNS data. The sensitivity of results to the molecular Prandtl number and to the thermal wall boundary condition is accounted for.