DiSiVGT: Direct Numerical Simulation for the Development of a 4-Equation-Turbulencemodel

Project summary

Turbulence models which are more powerful than algebraic and two-equation models are of interest for the aircraft, automobile and chemical industries, to give only a few examples. The development of better models needs new concepts and the validation by complete and reliable data sets.

Direct numerical simulation (DNS) can create such data sets, that contain all informations necessary for the development of new turbulence models. Although these simulations are limited to low Reynolds number flows, the use of DNS data for the development of turbulence models makes sense, since near-wall turbulence is low Reynolds number turbulence and there is no proof yet, that high Reynolds number near wall flows exhibit new phenomena.

Aim of this project is the use of DNS data for the development of a new four-equation model. This model will overcome the main shortcomings of two-equation models and reach the potential of full Reynolds stress models, needing far less computational effort.

Theoretical work:

  • Development of closed transport equations for the two invariants of the Reynolds stress anisotropy tensor based on invariant theory and two point correlation technique.
  • Improved modeling of the k-epsilon-equation, considering turbulence anisotropy and Reynolds number.
  • Derivation of algebraic relations for the modeling of Reynolds stresses as a function of mean velocity field, turbulent kinetic energy and its dissipation rate, anisotropy and Reynolds number.

Numerical work

  • DNS of homogeneous shear flow at shear rates similar those of to wall-bounded turbulence. In this case the same coherent structures as in the near wall region are expected. Homogeneous turbulence shows a strong non-equilibrium of production and dissipation of turbulent kinetic energy.
  • DNS of wall bounded turbulent flows (channel and boundary layer flow) at different Reynolds numbers. In the log-layer these flows show an equilibrium of production and dissipation of turbulent kinetic energy.
  • Data analysis of the simulated flow fields considering the development and the validation of the new turbulence model, its general approaches and model constants.

KONWIHR funding

  • initial KONWIHR funding: 07/2001-06/2004


  • Prof. Dr. R. Friedrich, Chair for Fluid Mechanics, TU-München
  • PD Dr. J. Jovanovic, Institute of Fluid Mechanics, Uni-Erlangen

Selected publications