A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows
Résumé
A new subgrid-scale turbulence model involving all the transport equations of the subgrid-scale stresses and including a dissipation rate equation is proposed for large-eddy simulation (LES) of unsteady flows which present nonequilibrium turbulence spectra. Such a situation in flow physics occurs when unsteadiness is created by forced boundary conditions, but also in more complex situations, when natural unsteadiness develops due to the existence of organized eddies. This latter phenomenon explains the instability found in a porous-walled chamber with mass injection. Due to the high value of Reynolds number, the presence of wall boundaries, and the use of relatively coarse grids, the spectral cutoff may be located before the inertial zone of the energy spectrum. The use of transport equations for all the subgrid-scale stress components allows us to take into account more precisely the turbulent processes of production, transfer, pressure redistribution effects, and dissipation, and the concept of turbulent viscosity is no longer necessary. Moreover, some backscatter effects can possibly arise. As a result of modeling in the spectral space, a formally continuous derivation of the model is obtained when the cutoff location is varied, which guaranties compatibility with the two extreme limits that are the full statistical Reynolds stress transport model of Launder and Shima and direct numerical simulation. In the present approach, due to the presence of the subgrid-scale pressure-strain correlation term in the stress equations, the new subgrid model is able to account for history and nonlocal effects of the turbulence interactions, and also to describe more accurately the anisotropy of the turbulence field. The present model is first calibrated on the well-known fully turbulent channel flow. For this test case, the LES simulation reveals that the computed velocities and Reynolds stresses agree very well with the DNS data. The application to the channel flow with wall mass injection which undergoes a transition process from laminar to turbulent regime and the development of natural unsteadiness is then considered for illustrating the potentials of the method. LES results are compared with experimental data including the velocity components, the turbulent stresses, and the transition location. A satisfactory agreement is obtained for both the mean quantities and the turbulent field. In addition, structural information of the flow is provided.