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Low-Order Models for Turbulent Flows over Complex Walls

Mitul Luhar
Graduate Aerospace Laboratories California Institute of Technology Pasadena, CA 91125, USA; Aerospace and Mechanical Engineering University of Southern California Los Angeles, CA 90089, USA

Abstract

Porous and patterned surfaces appear in many turbulent flows of engineering and scientific interest. Yet, there are few computationally efficient models that can predict how such complex walls alter spectral and structural features of the turbulent flow field. The present effort seeks to address this limitation by extending the resolvent formulation proposed by McKeon & Sharma (2010). Under the resolvent formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes, identified via a gainbased decomposition of the governing Navier-Stokes equations. To account for porous and patterned surfaces, the resolvent framework is extended to the volume-averaged Navier-Stokes equations, such that the effect of the complex substrate appears explicitly as an additional body force: a generalized version of Darcy's law. The permeability is infinite within the fluid domain so that the body force is zero. Solid domains are modeled as regions with (near) zero permeability. For a complex porous substrate, the permeability depends on the specific microstructure i.e. the size, distribution, and alignment of pores. Preliminary results show that a gain-based decomposition of the volume-averaged Navier-Stokes equations is able to reproduce many key observations from previous simulations of flow over streamwise-constant riblets (Garcia-Mayoral & Jimenez, 2011) as well as homogeneous porous media (Breugem et al., 2006).