The influence of wall permeability on laminar and turbulent flows: Theory and simulations

The influence of wall permeability on laminar and turbulent flows: Theory and simulations

Breugem, W.P.

Nieuwstadt, F.T.M. (promotor)
Boersma, B.J. (promotor)

Mechanical, Maritime and Materials Engineering

2005-01-11

The study of flows over permeable walls is relevant to many applications. Examples are flows over and through porous river beds, vegetation, snow, heat exchangers of foam metal, and oil wells. The main objectives of this thesis are to gain insight in the influence of wall permeability on both laminar and turbulent flows, and to develop a formalism for Direct Numerical Simulations (DNS) of turbulent flows over permeable walls. To describe flow inside a permeable wall, we use the Volume--Averaged Navier--Stokes (VANS) equations for the volume--averaged flow. The latter is defined as a weighted volume average of the microscopic flow, and is continuous throughout the porous medium. To solve the VANS equations, closures are needed for the subfilter--scale stress and the drag force. The latter is investigated in more detail in chapter 4. In chapter 3, an analysis is given of the influence of wall permeability on the laminar boundary layer over a wedge. A generalized Falkner--Skan equation is derived. Results are shown for various wedge angles. In chapter 5, a formalism is developed for DNS of turbulent flow in a plane channel with a permeable bottom wall. The VANS equations are used to simulate the flow inside the permeable wall. Results are shown from four simulations, for which only the wall porosity was changed. The influence of wall permeability can be characterized by the permeability Reynolds number. Turbulence near a highly permeable wall is dominated by relatively large vortical structures, which originate possibly from a Kelvin--Helmholtz type of instability. These structures cause an exchange of momentum between the channel and the permeable wall and consequently the skin friction increases. In chapter 6, the formalism developed in chapter 5 is validated. A DNS has been performed of turbulent channel flow over a permeable wall consisting of a Cartesian grid of 30x20x9 cubes. An Immersed Boundary Method is used to enforce a zero velocity on the cubes. The results of the DNS compares very well with a second DNS in which the VANS equations are used for the flow inside the permeable wall.

permeable / porous and rough
laminar and turbulent flows
volume averaging
boundary layer and falkner-skan
direct numerical simulations (dns)
immersed boundary method (ibm)

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doctoral thesis

(c) 2005 W.P. Breugem