Extension of the partially integrated transport modeling method to the simulation of passive scalar turbulent fluctuations at various Prandtl numbers

Abstract

The present work aims to extend the hybrid non zonal RANS/LES partially integrated transport modeling (PITM) method to turbulent flows in the presence of passive scalar contaminant for simulating large scales of turbulent flows. Focussing on the methodological aspects, we derive the basic transport equations both for the scalar variance of fluctuations and dissipation-rate of the variance. The basis of the method was introduced in references [R. Schiestel and A. Dejoan, “Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations ”, Theor. Comput. Fluid Dyn. 18, 443 (2005)] and [B. Chaouat and R. Schiestel, “A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows ”, Phys. Fluids 17, 065106 (2005)]. It provides a continuous approach for hybrid Reynolds averaged Navier–Stokes equations-large eddy simulation (RANS-LES) with seamless coupling between RANS and LES regions. The main motivation is to simulate accurately in LES mode performed on coarse grids, scalar fluctuation fields, in addition to mean scalar fields. As known, the knowledge of the rms scalar fluctuations is often involved in handling practical engineering and geophysical flows. Like in dynamical equations, it is found that the coefficient appearing in the destruction term of the dissipation-rate of the scalar variance is a function of the cutoff-wave number and also of the Prandtl number and the Reynolds number. Depending on the value of the Prandtl-number, different expressions of this function have been derived according to the relevant physics in the wave number space. Finally, numerical simulations of fully turbulent flows including passive scalar transport fields have been performed on several meshes of medium and coarse grid resolutions at the Reynolds number Rτ=395 for the Prandtl numbers Pr=0.1, 1 and 10, respectively associated with heat transfer of liquid metals, gas and water for illustrating the theoretical development made on PITM. As expected, the PITM method provides satisfactory results in good agreement with data of direct numerical simulations. From a general point of view, this work opens new routes of modeling and simulation of turbulent flows including a passive scalar with a drastic reduction of the computational time and memory in term of number of grid points in comparison with the demanding resources of highly resolved LES.