UFR 2-01 Best Practice Advice
Flow behind a blunt trailing edge
Underlying Flow Regime 2-01 © copyright ERCOFTAC 2004
Best Practice Advice
Best Practice Advice for the UFR
The key physics is represented by:
- the unsteadiness related to the large coherent structures, known as von Karman vortices,
- the different conditions for the boundary layers on the pressure and suction sides.
Numerical modelling issues
The mathematical model represented by the Navier-Stokes equations accompanied by a simple turbulent model support numerical models that give pretty accurate estimations of the steady base pressure and velocity profiles.
During grid generation, especially at the case of blades with non sharp trailing edge we have to be careful choosing the correct mesh type to avoid skewness and distortions. The best advice is to used O-type meshes because this eliminate grid distortion and skewness which are closely related with large (possible local) discretization error linked to validity of the computed solution. An important issues is related to maintaining the point-to-point correspondence on the periodic boundaries as well as on the mesh block connecting boundaries of the computation domain, in order to keep conservation and avoid complicated interpolation treatments.
The grid refinement in the near wall region should be sufficiently fine in order to capture the von Karman vortex street behind the trailing edge. A mesh spacing in the transversal direction to the wall is necessarily characterized by , because the different characteristics of the pressure and suction boundary layers contribute to the generation of the wake-like effects.
Regarding the turbulence modeling, use an algebraic mixing length turbulence model if one is interested in capturing steady state velocity and pressure profiles. Also, this simple turbulence modeling allows capturing the vortex shedding frequency, and it is in the fairly good agreement with the experiment. The turbulent viscosity μtis computed with an algebraic mixing length model (Baldwin-Lomax turbulent model). Constant turbulent Prandtl number of 0.9 was assumed throughout the whole domain. Regarding the time discretization, the time step computation is based on positive conditions for the non linear scalar convection equation whose speed is given by largest eigenvalue of the Euler system. No viscous time step restriction was employed.
Recommendations for Future Work
Currently computational requirements for the unsteady problem proved to be too severe. Future work will therefore be concerned with the development of implicit time accurate methods. The recommendation for future work accounts for the fact that no statements can be given about the flow inside the unsteady wake at present. This will require usage of the second order moment closure, in order to deal with the strong anisotropy effects and the production/destruction of the individual Reynolds stress tensor, which is associated to the vortex motion and the streamline curvature. The CFD approach has to deal with the full 3D, unsteady flow field.
The authors express our gratitude to Prof. C. Sieverding from von Karmam Institute of Fluid Dynamics for the support and cooperation that he has provided to preparing this UFR document.
© copyright ERCOFTAC 2004
Contributors: Charles Hirsch - Vrije Universiteit Brussel