Revision as of 14:28, 6 April 2009

Blade tip and tip clearance vortex flow

Underlying Flow Regime 1-02 © copyright ERCOFTAC 2004

Best Practice Advice

Best Practice Advice for the UFR

Based on the conclusions from the various studies outlined above the following best practice advice is suggested for this underlying flow regime. It should be noted that the studies do not include all possible modern turbulence models and so a first conclusion is that further analysis is needed with these methods to extend the best practice advice.

Key physics

Leakage flow over a blade/wing tip which is driven by the pressure difference between pressure and suction surfaces and its subsequent roll-up into a strongly swirling vortex flow trailing downstream of the blade.

The wing tip leakage flow entrains the blade boundary layers into the primary wing tip vortex and these form secondary vortices.

Local details of the flow in the tip region are related to the geometry of the tip (flat or rounded) and the boundary layers on the blade.

Flow structure also depends on incidence of the wing.

Generality of advice given

BPA is based on a single computation of the chosen test case

The test case has not yet been the subject of any international CFD comparison exercise but is being considered with the EU project Flowmania as a test case for tip clearance flows.

4 other computations of similar wing tip test cases have been found to extend the advice given.

Numerical issues

Discretisation method

Use a higher order scheme (second or above) with as little numerical dissipation as possible.

Grid and grid resolution

Use around 1.5 million grid points for the wing and the tip region.

A solution adaptive grid is needed in the general case, with local refinement of the grid in areas of high gradients on the blade surfaces and in the location of the vortex core.

In the absence of a solution adaptive grid, then grid point clustering in the stream-wise direction at the wing leading and trailing edges, in the lateral direction at the wing surfaces and in the vertical direction towards the wing tip, and in the location of the wing tip vortex on the blade suction surface near the tip are useful.

Grid resolution of boundary layers needs to be adequate to capture details of the boundary layer flow that is entrained into vortex, as in line with other requirements for flow over blades and aerofoils. This needs control over the value of y+ at the first grid point (see other relevant BPA for UFRs).

A grid cell aspect ratio close to unity is needed in the vicinity of the core of the vortex.

Use a minimum of 15 to 20 grid points across the vortex core to resolve the high velocity gradients. A lower grid density can be used in the stream wise direction.

Computational domain & boundary conditions

Boundary conditions

Use a Neumann outflow pressure boundary condition (with specification of gradients) in preference to a Dirichlet condition as location of vortex on downstream plane is not known a priori.

In this test case, the end-wall influence (blockage due to end-wall boundary layers on the wind-tunnel walls) needs to be taken into account.

In this test case, a flow traverse from measurements needs to be used to provide inlet velocity profile for simulations of measurements as the inlet plane is relatively close to the wing

Computational domain

The computational domain needs to extend upstream and downstream of the leading and trailing edges by about two chord lengths

Physical modelling

Turbulence modelling for overall quantities

Qualitative predictions of the flow position of the primary vortex are generally independent of the turbulence model used, and can be well predicted by inviscid Euler simulations.

Details of the strength of the vortex and its dissipation are highly dependant depend on the turbulence models used.

Turbulence modelling for flow details on the blade

The detail of the shear layer detachment at the wing tip (in a region of adverse pressure gradient) is significantly affected by the choice of turbulence models as the different models produce different estimates for the boundary layer development. Here the BPA advice is similar to that recommended for other relevant UFRs for blade and wing flows.

Turbulence models for flow details in the tip vortex

The flow in the core of the vortex approaches solid body rotation, and thus the production of the turbulence is suppressed giving a strongly stabilized structure. Standard eddy viscosity models, such as the k-epsilon method, are unable to describe the turbulence in rotation dominated flows satisfactorily and Reynolds stress models are needed for this.

K-epsilon simulations closely reproduce the total pressure distribution but are less accurate with the prediction of the stream-wise velocity and static pressure in the core of the vortex. A 20% deficit in the stream-wise velocities in the vortex core was predicted by the k-epsilon model.

The k-epsilon model strongly over-predicts the vortex decay rate.

Reynolds stress transport models (differential and algebraic) successfully predict the strong suppression of the turbulence in the rotation dominated vortex core and a reasonable decay of the vortex.

Near wall model

A y+ of the first grid point above the wing surface in accordance with the general requirements of the turbulence model is needed in order to give accurate results for the boundary layers on the blade surface

Transition modelling

The surface boundary layers are affected by the transition modelling and the recommendations on this subject from other UFRs need to be followed. In the event that no transition modelling is possible then a sensitivity study on its effect should be carried out.

Application uncertainties

The key uncertainties in simulations of wing-tip vortex flows are the accurate estimation of the inlet flow condition, and the accurate definition of the blade geometry (wing plan-form, shape of wing tip, and angle of attack of the blade).

The details of the flow structure are affected by the boundary layer development on the blade (location of the position of transition) and the loading (angle of attack) of the blade.

Further work

Wing tip vortex

Further simulations of this test case are needed in order to make more generally valid statements of advice.

The inlet boundary conditions from the measurements are needed for the simulations as the inlet boundary is relatively close to the wing and this suggests that an improved test case is needed with adequate upstream distance to the measurement plane to remove this limitation.

The new simulations need to include a range of modern turbulence models, allowing the influence of the detail of the boundary layer on the blade to be assessed (Spalart-Allmaras, SST of Menter, V2F of Durbin) and allowing the influence of the strong rotation in the vortex to be assessed (algebraic and differential RSM models and non-linear or linear eddy viscosity models with curvature corrections).

Turbomachinery blade tip clearance flow

No recent well-documented tip-clearance test case was found which has been used for validation of turbulence models in turbomachinery flows. Further work should try to provide this, perhaps based on the test case published by Kang and Hirsch (1993).

Contributors: Michael Casey - Sulzer Innotec AG