Abstr:Stagnation point flow

Semi-Confined Flows

Underlying Flow Regime 3-12

Abstract

The underlying flow regime (UFR) considered is the flow in a stagnation point. This type of flow regime is of considerable technical relevance since it occurs whenever a flow impinges onto a solid object, typically in turbo-machinery or the leading edge of an aerofoil. Nowadays, for the determination of the flow-field in these configurations, CFD is used and hence this URF is always a part of such calculations. However, since the flow in this region is usually turbulent the predictions depend strongly on the quality of the chosen turbulence model. It is well known that the flow in stagnation point is often incorrectly predicted by the turbulence models. Even when the stagnation point region is not of interest per se, any erroneous calculation can distort the rest of the computed flow field, for example in the case for the prediction of heat transfer in the vicinity of the stagnation point. An overproduction of turbulent kinetic energy, as is typically predicted by two-equation turbulence models, results in an overestimation of heat transfer. It is evident that this failure is of strong relevance for the design of cooled turbine blades.

The choice of the turbulence model is always a compromise between accuracy of the predicted results and the numerics (i.e. stability, convergence, CPU time). In the following the focus is on the two-equation models. This type of turbulence model is widely used because of its numerical stability and relatively simple formulation. The main disadvantage of the two-equation models is their poor performance under adverse pressure gradients, which is also an important feature of stagnation point flows. In order to overcome these deficits of the model many different modifications where proposed.

For most technical relevant applications the stagnation point flow is turbulent, therefore in the following only turbulent flows are considered. Whenever the fluid impinges a solid surface a stagnation point flow occurs. The fluid is decelerated in the region ahead of the stagnation point. This condition results in an adverse pressure gradient which may result in separation. Hence, it is crucial that the simulation is able to predict the onset of the separation but unfortunately most turbulence models fail to calculate correctly this key issue. Furthermore, this UFR is often the starting point of boundary layer growth. It is obvious that the correct prediction of the turbulence is of importance since the size and development of the boundary layer depends strongly on the strength of the turbulence.

Flow in stagnation region is a URF with relevance to many Application Challenges. It is of special importance for the following AC's:

Low-Speed Centrifugal Compressor	6-02
Annular Compressor Cascade Without Clearance	6-03
Pump Turbine	6-04
Annular Compressor Cascade With Tip Clearance	6-05
Gas Turbine Nozzle Cascade	6-06
High Speed Centrifugal Compressor	6-08
High Speed Axial Compressor	6-09
Axial Compressor Cascade	6-10
Turbine Cascade With Cooling Holes	6-11
Steam Turbine Rotor Cascade	6-12

Turbulence can be regarded as a superimposition of vortices of several sizes. The largest eddies are in the order of magnitude of the dimension of the flow. On the other hand, the smallest eddies are limited in their size through the viscous forces of the fluid. The kinetic energy, hence the momentum, from the mean motion of the flow is transferred into those large eddies which subsequently feed the smaller eddies through vortex stretching. This process, the so-called energy cascade continues until the viscous effects are dominant, where the energy dissipates into heat. The rate at which the energy is extracted from the mean flow is matched to the rate of the energy transfer across the energy spectrum to small dissipating eddies, ε.

The momentum transfer by the turbulent motion generates shear stresses which is a key issue for the turbulence production. The Reynolds stresses generated in this process are much larger than the viscous stress, with the exception in the vicinity of the wall, where these two stresses are comparable in magnitude.

The structures of turbulent flow are mainly determined by the origin of the turbulence in the transition process. The effect on turbulence in a stagnation point flow is considerably different than that generated by shear. In the former case a local irrotational strain field is created with stretching in lateral direction (i.e. in direction of the surface) and compression in wall-normal direction. Furthermore, another significant feature of turbulence in the stagnation region is the ratio of production of turbulent kinetic energy k to dissipation ε. In this UFR this particular ratio is much bigger than 1, in contrast to shear layers where the ratio is approximately equal to 1.

Contributors: Beat Ribi - MAN Turbomaschinen AG Schweiz