Stagnation point flow

Underlying Flow Regime 3-12 © copyright ERCOFTAC 2004

Best Practice Advice

Best Practice Advice for the UFR

Based on the given example and the examined turbulence models the following best practice advice is proposed for the underlying flow regime "Flow in Stagnation Point":

Key physics

Fluid impinging on a solid surface results in a stagnation point, i.e. the fluid is decelerated. This results in an adverse pressure gradient which may lead to separation. The stagnation point is in any case the starting point of the boundary layer growth. For technical relevant applications the flow is turbulent. Therefore, the development of the boundary layer depends strongly on the turbulence intensity.

Generality of advice given

The BPA is based on the consideration of the theoretical background of two-equation turbulence models. Furthermore, this BPA is supported by the results gained form calculations with the original k-e and different modifications thereof (k-ε with T bound, Kato-Launders k-e, v²-f) which are all applied to a single test case.

Numerical issues

Discretisation method

§ In order to minimise numerical diffusion a higher order discretisation scheme should be used.

§ With the given considerations of the turbulent flow an elliptic solver should be used.

Grid and grid resolution

§ Grid cell aspect ratio close to unity around the stagnation point area.

§ Grid point distribution according to the recommended standard values for two-equation models.

Computational domain & boundary conditions

§ Inlet and outlet of the grid have to be placed sufficiently far away of the stagnation point, although through the (almost) parabolic nature of this flow problem the upstream boundary can be placed closer to the stagnation point than the downstream boundary.

§ The outflow should be described as a Neumann boundary condition.

Physical modelling

Turbulence modelling

§ Instead of using the standard k-ε or k-ω model, the v²-f model could be used. Other possibilities would be a bound on the time scale or a modification of the production term.

Near wall modelling

§ The first grid point above the solid surface should be placed appropriate to the requirement of the model.

Application uncertainties

§ The heat transfer at the leading edge was obviously affected by the cooling wholes even without coolant flow.

§ Since the turbulence level has a major impact on the heat transfer its correct value is of utmost importance.

Further work

Application of a Reynolds Stress Transport Model (RSTM) on the same test case.

Contributors: Beat Ribi - MAN Turbomaschinen AG Schweiz