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 "Stagnation Point Flow":

Key physics

Fluid impinging on a solid surface results in a stagnation point, i.e. the fluid is decelerated with consequences on the turbulence production and hence the development of any free-stream turbulence approaching the stagnation point. This point is the starting point of the boundary layer growth. In general, the boundary layer is initially laminar and then undergoes transition to turbulence some place downstream. This boundary-layer development is quite sensitive to the turbulence prevailing in the stagnation region which is swept downstream in the free stream.

Basis 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 from calculations with the original k-ε and different modifications thereof (k-ε with T bound, Kato-Launders k-ε v²-f) which are all applied to a single test case, namely the flow around a turbine rotor blade.

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 the standard k-epsilon or k-omega model, the v2-f model should be used which gave the best results. Improvement was also achieved by using Durbin's bound on the time scale or the Kato-Launder modification of the production term. Explicit transition modelling may be necessary when using such models.

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 of the approach flow has an impact on the heat transfer, reliable knowledge of its value is of utmost importance.

Further work

Application of a Reynolds Stress Transport Model (RSTM) on the same test case. Also, consideration of transition and use of transition models. Study of different cases for which not only heat transfer has been measured.

Contributors: Beat Ribi - MAN Turbomaschinen AG Schweiz