Numerical modelling and passive flow control using porous media

Abstract

The whole flow over a solid body covered by a porous layer is presented. The three main models used in the literature to compute efficiently the fluid flow are given: the reduction of the porous layer to a boundary condition, the coupling of Darcy equation with Navier-Stokes equations and the Brinkman-Navier-Stokes equations or the penalisation method. Numerical simulations on Cartesian grids using the latest model give easily accurate solutions of the flow around solid bodies with or without porous layers. Adding appropriate porous devices to the solid bodies, an efficient passive control of the two-dimensional incompressible flow is achieved. A strong regularisation of the flow is observed and a significant reduction of the vortex induced vibrations or the drag coefficient is obtained.

Navier–Stokes/Forchheimer models for filtration through porous media

“…For this reason, the so-called penalization approach has been introduced to model the flow over porous media (see, e.g., [9,34,35]). This method consists in considering a modified set of Navier-Stokes equations in the whole domain including two penalization terms associated to the resistance induced by the porous medium in the subregion Ω p .…”

“…This method, often called penalization approach (see, e.g., [9,34,35,39]), consists in considering in the whole computational domain a modified formulation of the Navier-Stokes equations which reduce to their classical form in the fluid region while they include additional resistance terms in the porous region. This approach is similar to the so-called fictitious domain method [1,39].…”

Modelling and shape optimization of an actuator

“…K is the non dimensional permeability coefficient used to represent the solid parts (see (Angot et al 1999) and (Bruneau and Mortazavi 2008) for more details), in practice this coefficient is set to 10 −8 in the solid domain and to 10 16 in the fluid domain to recover the genuine NavierStokes equations. The non-dimensional Reynolds number Re is computed using the mean velocity at the entrance sections and the width of the exit section.…”

Control of the flow in the annular region of a shrouded cylinder with splitter plate

“…An emerging approach of flow control is to attach a porous layer to the external surface of a structure. Bruneau and Mortazavi [6,7] investigated the flow control by using porous layer around a cylinder numerically. They used penalization method and found that adding a porous ring around a riser pipe can damp the vortex induced vibrations.…”