Wind Energy

12
Turbulence Modelling and Numerical Flow
Simulation of Turbulent Flows
Claus Wagner
12.1 Summary
Some popular techniques used in simulations of turbulent flows are presented
and discussed. It is shown how the (k, ω) turbulence model and two different
dynamic subgrid scale models perform in Reynolds-averaged Navier–Stokes
simulations (RANS) and Large-Eddy Simulations (LES) of turbulent channel
flow, respectively. Besides, some drawbacks of the eddy viscosity concept
which is the basis for most turbulence models are discussed.
12.2 Introduction
Phenomenologically most flows can be categorized into the laminar and the
turbulent flow regime. Any disturbance, which is damped by molecular dissipation
in a laminar flow, grows to form a turbulent, chaotic-like, timedependent,
three-dimensional flow field, if the relative impact of the molecular
dissipation is reduced. The latter is expressed by an increase of the Reynolds
number Re = u/(νl) (ν represent the kinematic viscosity, l and u the length
and velocity scales of the flow). Turbulent flows are characterized by fluctuations
on a wide range of scales the size of which decrease with increasing
Reynolds numbers. In order to properly resolve all scales in a so-called direct
numerical simulation (DNS) one has to specify extremely fine grids, resulting
in unaffordable computing times for high Reynolds number flows. To overcome
this, researchers developed turbulence models, which approximate the
effect of smaller scales. This is necessary since most environmental or technical
relevant turbulent flows are characterized by very high Reynolds numbers.
Hence, turbulence modelling is one of the key problems in numerical flow
simulation.