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Free Flows

Underlying Flow Regime 1-02

Abstract

The underlying flow regime (UFR) - wing/blade tip and tip clearance flow - documented here is of major importance in many aeronautical and turbomachinery applications. As a simple demonstration of its importance in gas turbine flows, the ASME Journal of Turbomachinery published over 60 technical papers on the subject of the aerodynamics of tip clearance flows in axial compressors and axial turbines during the decade from 1990 to 2000. If we were to extend this literature survey to applications in water turbines, radial compressors, pumps, ventilators, helicopter blades, propellers, turbochargers, wind turbines and aeroplane wings then the list would certainly extend to well over 1000 relevant publications in this period. Clearly this is not a subject where a brief review will be particularly satisfactory.

There are four main areas where this underlying flow regime - tip clearance flow and wing/blade tip flow - are important:

  • The turbomachinery industry is interested in tip clearance flows through the small clearance gaps between the rotating and stationary components. These gaps are either between the rotor blades and the casing or between the stator vanes and the shaft, and lead to a reduction in performance level (both in terms of efficiency and in operating range) and aerodynamically excited vibration and noise through the interaction of the tip clearance vortex with downstream blade rows. Tip gap related losses in turbomachinery may account for up to one third of the total losses. In the case of water turbines and pumps, additional strong interest is present in the cavitation which occurs in the low pressure core of the tip clearance vortex.
  • The aeroplane industry is interested in the formation, persistence, and motion of the trailing vortices from wings. This is partly as a source of drag (the induced drag caused by the downwash created by the trailing wake changes the direction of the force generated by each section and leads to a drag force even in an inviscid flow) and partly as a wake turbulence problem where the strength of the trailing vortices sets constraints on the nearness of aeroplanes on similar flight paths (particularly landing and take-off).
  • This is also relevant for the helicopter and propeller industry where the tip vortices generated by a rotor blade cause unfavourable aerodynamic problems, such as blade-vortex interaction, acoustic excitation, vortex-airframe interaction, ground resonance at take-off mode and so on.
  • The marine industry also has relevant applications whereby it is the cavitation in the cores of the tip clearance vortices from the propeller blades that is most important. Trailing vortices from submarine wings is also relevant in military applications.

In each of the application areas mentioned above there are numerous technical papers available where studies of tip clearance flow and wing/blade tip flow have taken place, including comparisons of measurements with CFD results. In such a large technical area it is difficult to focus upon a single study as being representative. Nevertheless, after examining the available technical literature, this UFR documentation concentrates on a specific study related to the flow over an isolated wing tip (Chow, Zilliac and Bradshaw (1997) and Dacles-Mariani et al (1995)) which is considered to be of extremely high quality and highly representative for the simplest case of a typical wing tip vortex.

The chosen UFR documentation is less representative of blade tip clearance flow in turbomachinery, but an extensive search of the literature did not produce a turbomachinery test case of the same quality as that for the isolated wing tip. It is clear that a good representative case for a rotating turbomachinery blade row is extremely difficult to set up and measure, due to the mechanical and experimental difficulties in rotating rigs, the small size of turbomachinery blades compared to aeroplane wing tips, and because of the many possible parameter variations that are possible for the turbomachinery cases. The best case found for turbomachinery applications was the work on a large-scale cascade (200 mm chord) of Kang and Hirsh (1993), where the authors give an excellent experimental study on the 3D flow in an axial compressor cascade with different tip clearance levels and a flat blade end. An interesting observation based on the literature survey carried out is that many of the R&D papers on this subject in the turbomachinery literature have not been designed solely as a source of CFD validation, but rather have tried to elucidate aspects of the basic physics of the tip clearance flow and to develop simple semi-empirical models for the effects on performance, and are not really suitable for CFD validation and turbulence model studies.

The essential physics of the underlying flow regime of a wing/blade tip and tip clearance flow is the leakage flow over a blade tip driven by the pressure difference between the pressure and the suction surfaces of the blade and its subsequent rolling up into a vortex. The flow over the wing tip tends to entrain the blade surface boundary layers which separate and become part of the vortex so that the final vortex structure can be quite complex. The interaction of the blade flow with the pressure gradients from the vortex can lead to local separation and secondary flows. The core of the vortex has an axial velocity substantially different to the free stream velocity and is of course a strongly swirling flow. Figure 1 shows some of the relevant features of this flow.

It can be seen from this short description that the wing/blade tip flow is an extremely complex problem (and in fact could be categorised as an application challenge rather than an underlying flow regime) because of the presence of large gradients of velocity and pressure in three dimensions at high Reynolds number. The CFD simulations need to capture the detail of the strong swirling flow in the vortex core and the interaction of the blade surface pressures and the thin blade boundary layers with the strong pressure gradient from the vortex. This will generally imply fine grid resolution, low numerical dissipation and no use of the law of the wall. The roll-up of the vortex from the wing-tip and the misalignment of the mean strains and Reynolds stresses make it an extremely challenging case for eddy-viscosity turbulence models and may suggest that second-moment closures will be necessary.

Even the simplest picture of the basic UFR flow given above is made more complex in reality by many issues which have an influence on this flow. The precise shape and thickness of the wing tip can be important in determining the structure of the flow (the wing planform can be rectangular straight wing, tapered straight wing, rounded or elliptical straight wing). The tip-cap shape can be rounded or flat, whereby the leakage flow over flat wing ends tend to separate as the fluid passes from the pressure to the suction surface and can generate multiple secondary vortices, Snyder and Spall (2000). The presence of any design modifications to reduce the strength of the leakage flow and the vortex may need to be considered (optimised loading distribution, winglets, flow injection at blade tip, cavitation shields, trenches in the casing, etc., etc.).

Figure 1: Flow features of the wing/tip vortex flow (courtesy of AIAA)

If the wing/tip flow seems complex then the tip clearance flow in turbomachinery should seem even more daunting. In turbomachinery, the proximity of adjacent surfaces above the blade leading to a small clearance gap is fundamentally important and dominates the motion of the tip clearance vortex that is formed. The clearance gap size in relation to the thickness of the blade is of major influence, and leads to different structures of the leakage flow (particularly in turbines which have thicker blades than compressors). At very low tip clearance gaps there is little shed vorticity and often no strong evidence of a tip clearance vortex. The presence of boundary layers on the adjacent surfaces and on the blades can cause additional vortices, separations and shear flows which interact with the tip clearance flow (scraping vortices, interactions with the casing wall boundary layer, endwall separation, rolling up of blade boundary layers into tip clearance vortex, free shear layer in the tip gap, tip separation vortex (Kang and Hirsch (1993)). The relative motion of the endwalls is also important such that in compressors the endwall motion is in a direction that tends to increase the flow through the tip gap and turbines it tends to decrease the flow through the tip gap. In fact it is possible to split this UFR for tip clearance flows into a long series of sub-UFR’s taking into account some of the different flow structures that can occur. This has not been attempted here and is another reason why a relatively simple wing/blade tip vortex is used as the UFR test case.

Contributors: Michael Casey - Sulzer Innotec AG

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