Subgrid-scale helicity equation model for large-eddy simulation of turbulent flows

A new one-equation eddy-viscosity model based on subgrid-scale (SGS) helicity is introduced in this paper for large-eddy simulation (LES) of turbulent flows. First, the governing equation of SGS helicity is deduced from the incompressible Navier-Stokes equations, and it reflects the transfer of the small-scale helicity that has been filtered out. We deduce a certain functional relation between the eddy viscosity and SGS helicity based on the kinetic energy and helicity spectra in the homogeneous and isotropic helical turbulence. For improving the accuracy, each unclosed term in the governing equation of SGS helicity is modeled independently, and the coefficients of these unclosed terms are constants or are determined dynamically. The new one-equation eddy-viscosity model is first tested and validated in the simulation of the homogeneous and isotropic helical turbulence. The a priori tests from the direct numerical simulation of forced homogeneous and isotropic turbulence show that the energy and helicity fluxes exhibit scale invariance in the inertial subrange. Additionally, the a posteriori tests demonstrate that the constant-coefficient and dynamic SGS helicity equation models can predict both the energy and helicity spectra more precisely than the common SGS models. For the LES of channel flow, the SGS helicity equation model can accurately predict the mean velocity, the turbulent stress, and the viscous shear stress and supply more abundant flow structures than the compared SGS model under the same grid resolution.