EU Regional School - Eisfeld Seminar
Dr. Bernhard Eisfeld - Introduction to Statistical Turbulence Modeling
Most engineering flow problems are turbulent, i.e. all involved flow quantities exhibit random fluctuations in space and time, involving a large spectrum of scales. In so-called Direct Numerical Simulations (DNS) these fluctuations are fully resolved; in so-called Large Eddy Simulations (LES) the largest scales are resolved, while the smallest scales are modelled. However, since the smallest scales decrease with the Reynolds number, and despite considerable increase in computer power and method development, DNS and LES are still prohibitively expensive for most industrial applications.
On the other hand in engineering information on the average flow field, like mean forces or the pressure distribution, often suffices. For this purpose only the moments of the statistical distributions of the fluctuations, in particular of the velocity field, are required. Statistical turbulence modelling is therefore devoted to suitably expressing these moments by mean flow quantities, in order to avoid resolving any of the fluctuating scales. The resulting models yield reasonable accuracy at affordable cost and therefore constitute the backbone of today’s simulation capabilities of turbulent flows in engineering.
The lecture will introduce the method of Reynolds averaging, leading to the mean equations of flow and turbulence quantities. Characteristics of turbulent flow fields will be high-lighted that are regularly exploited in the modelling. Finally, popular models and their underlying ideas will be presented, where the focus is on external aerodynamics.