Analysis of resolvent method for turbulence inflow generation

© 2018 Vikram RoutHigh-fidelity simulations of turbulent flows aim to accurately reproduce the statistical and structural properties of real-life turbulence. Such simulations rely on accurate inflow boundary conditions. A novel turbulent inflow generation method for high-fidelity DNS/LES has been developed which utilizes reduced order modelling (ROM) and evolutionary algorithms. The core idea behind this method is the classical view of turbulence which represents it as a collection of coherent structures. A low-rank approximation approach known as the resolvent analysis, developed by McKeon and Sharma [Journal of Fluid Mechanics, Vol. 658, 336-382 (2010)], is used to represent the governing equations as a linear input-output system. The non-linearities in the governing Navier-Stokes equations are the driving force behind the ow. This forcing of the linear system produces a response which represent the velocity perturbations. The resolvent analysis is performed at different wavenumber-frequency combinations which are selected in a manner to represent a variety of energetic coherent structures like the near-wall longitudinal streaks, hairpin vortices, Large Scale Motions (LSMs) and Very Large Scale Motions (VLSMs). A Singular Value Decomposition (SVD) of the linear operator in the input-output system is performed to generate a set of orthonormal basis functions for the forcing and response fields. A major advantage of the resolvent analysis is its reduced dependence on external data. It requires only the mean statistical quantities as an input which are readily available for various ow problems or can be easily obtained from cost-effective RANS simulations. The amplitudes of the selected modes were linearly scaled such that the turbulence kinetic energy (TKE) of the resolvent modes is equal to the target TKE. This technique successfully resulted in a fully developed turbulent field, although with a large development length. A further improvement of this method is obtained by optimizing the amplitude of each resolvent mode, which represents the energy content of the associated coherent structure. A genetic algorithm approach has been used to optimize the resolvent modes to represent the target Reynolds stress profiles. This modified process results in a significantly improved development length