FLOW: Wall-bounded turbulence: Re-visit using numerical experiments

In our everyday live, we are constantly surrounded by fluids, be it gaseous air or liquid water. Most of these fluids are in the so-called turbulent state, i.e. characterised by a seemingly random, highly unsteady and swirly motion of the fluid, extending from very large scales (on the order of the considered domain) down to extremely small scales (smaller than micrometers on, for instance, a commercial airplane at cruising speed). The dynamics of turbulent flows (and also laminar ones) are essentially governed by the highly non-linear Navier-Stokes equations. The most important parameter entering these equations is the so-called Reynolds number Re, which can be viewed as the ratio between inertial and viscous effects. The Re of a flow crucially determines its properties and is therefore of central importance when studying turbulent flows.

Since no complete theory of turbulence is available, basic research in turbulence relies heavily on either experimental studies in wind tunnels or the direct numerical simulation (DNS) of turbulent flows. DNS bears many advantages compared to experiments, e.g. that the full time-dependent velocity field with many statistics is available for analysis, and that boundary conditions can be specified accurately. However, the number of degrees of freedom necessary for realistic flow setups is extremely large, in particular as the Reynolds number is large.

In the present context, we study a turbulent boundary layer, as e.g. arising on airplane wings, via large-scale simulations. During the last years, a growing interest in such canonical turbulent boundary layers could be observed, with new experimental and numerical data being obtained. KTH Mechanics has been an active player in this development: With up to 7.5 billion grid points we have reached Re_\theta=4300. Among the specific project goals are:

  • Demonstrating that numerical simulations can indeed predict flows at high Re with excellent accuracy, cross- validating numerical and experimental approaches: “Numerical Experiments”.
  • Provide increased diagnostic possibilities due to the availability of whole velocity fields (in particular also quantities impossible to measure experimentally) in an effort to single out dominant dynamic properties of turbulent flows.
  • Contributing to the development of numerical methods, parallel algorithms and postprocessing tools (visualisation) for present and future computer architectures.
  • Develop and test engineering methods that can eventually be used in actual industrial application, e.g. flow control to reduce drag of turbulent flow close to surfaces.