Flow around (airfoils and) blades (subsonic)

Underlying Flow Regime 2-04 © copyright ERCOFTAC 2004

Description

Preface

The Underlying Flow Regime entitled "Flow Around (Airfoils and) Blades" is of major importance in both the turbomachinery and the aeronautical industry. A quick literature review would reveal at least ten test cases that have been measured around the world, in order to provide data for both better comprehension of the related physics and validation of computational methods. In particular, and confining the review to turbomachinery applications, the ASME, Journal of Turbomachinery has accepted for publication three papers in a row reporting on a single test case (a highly loaded compressor cascade, see Deutsch and Zierke 1987), accompanied by a fourth one, two years later (Zierke and Deutsch 1989). The importance of this kind of flow is also reflected in Scientific Coordinator’s decision to split this UFR into four separate UFRs: one dealing with three-dimensional blades, and another three dealing with two-dimensional blades (subsonic and transonic), as well as airfoils. This document will focus upon the low-speed (subsonic) two-dimensional flow around blades in turbomachinery applications.

The turbomachinery sector is obviously very interested in flows around blades since they constitute the primitive element of turbomachinery. The following key-reasons are identified:

Improved Loss Prediction: Profile losses are one of the major sources of losses in turbomachinery. Along with secondary flow and tip-clearance losses, they contribute to the total losses of a row and determine its performance and its efficiency. Any attempt to diminish losses involves among others and the improvement of the viscous behaviour of the flow around the blade. In addition, in three-dimensional applications the sources of losses must be easily identified and accounted for.

Improved Blade Profiles: Current design trends include the use of customised blade designs, as opposed to the use of standard airfoils. This demands the effective control of the chord-wise pressure distribution and the boundary layer behaviour in order to increase the efficiency of the designed blade. Since, even the simplest boundary layer parameters can not be extracted from three-dimensional results in a straightforward manner, and thereby the assessment of a three-dimensional flow/simulation is extremely complex in its fine details, a lot of turbomachinery design is still carried out by means of a quasi-three-dimensional approach that combines blade-to-blade calculations (in the so-called S-1 surface) with through-flow calculations in the S-2 surface.

Facilitated Flow Analysis: Performing experimental measurements in a rotating blade passages is always fraught with problems and measurements are facilitated if conducted for cascade flows. Most of the turbulence modelling was conducted by analysing simple two-dimensional experiments.

Facilitated Development of Computational Methods: Flow around blades includes most of the essential physics that arise in turbomachinery flows, without the extreme complexity of the actual, three-dimensional geometry. Being two-dimensional, the equations that model the flow are reduced and allow for new computational methods to be developed, the effects of the boundary conditions at the upstream and downstream boundaries to be assessed, different discretization schemes and numerical procedures to be tested and evaluated, grid dependency studies to be carried out and turbulence models to be assessed and/or tuned, without the large computational resources that the equivalent three-dimensional cases would demand.

Essential Understanding of the Flow Physics: Flow around blades provides the essential physics behind Turbomachinery.

The essential physics behind the low-speed flow past blades include the development of a two-dimensional boundary layer under pressure gradient. As simple as it might sound, especially when compared to the complex three-dimensional boundary layer development, the development of any two-dimensional boundary layer includes:

A laminar part that is formed at the leading edge stagnation point region of the blade in both the pressure and the suction side.
A transition region, where the boundary layer becomes turbulent. The onset of this region is affected by the adverse pressure gradients, the free stream turbulence, etc.
The evolution of the turbulent part of the boundary layer until the trailing edge. At high incidence angles the last part of the boundary layer in the suction side can be separated. The extent of this part is mainly affected by the flow angle.

Downstream of the blade, the main feature of the flow is the development of the wake and its interaction (mixing) with the main flow.

Despite their simplicity, these features are more complex than any computational method can afford. For example the incorporation of any turbulence model in a computational algorithm renders the method incapable of capturing the laminar parts of the boundary layers. On the other hand a convenient way to computationally simulate transition is to switch on either the turbulence model or the turbulent eddy viscosity at an experimentally predetermined location. This method is ad hoc and ignores the transition physics and the importance of the transitional zone completely. Especially for flows, where the transitional region covers a large portion of the flow field as observed in many low-pressure turbine experiments, this practice can lead to severe errors in the solution.

Of course, the prediction of transition is a major problem not only in turbomachinery (see Mayle, 1991) since direct simulation is still computationally not viable and there are no general models covering transitional flows. Transition occurs due to the following reasons:

The growth of Tollmien-Schlichting waves in a laminar boundary layer that eventually break down (natural transition). This mode of transition appears in flows around isolated airfoils (aeronautical applications) and past first stage compressor bladings (turbomachinery applications).
The growth of turbulence that is caused by the presence of ‘external’ disturbances, such as the free-stream turbulence intensity and/or roughness, streamline curvature (bypass transition). This is the most common mode of transition appearing in turbomachinery applications.
Laminar separation bubbles that occur near the leading edge of the blade. In these cases the suction side boundary layer is reattached turbulent after the laminar separation.
Relaminarization of the flow (reverse transition) that occurs in cases with very strong acceleration of the flow.

Periodic-unsteady transition, caused by the periodic passing of wakes from upstream blades in multi-row turbomachines.

The prevailing mechanisms in natural transition are not modelled by any turbulence model at all, since they are related to instability mechanisms. This is a serious weakness of the computational models that these models are incorporated. So, in flow around turbine blade calculations, where the pressure side boundary layer may remain laminar at 70-80% of the chord, these methods will fail to accurately predicting pressure losses. Both natural and bypass transition have been analysed in depth. Emmons (1951) was the first to identify transition as a stochastic, unsteady process where laminar and turbulent regions coexist in the same boundary layer. He introduced the intermittency function, ã (0<ã<1), as the probability of the flow to be turbulent at a given position of the flow. This work that provides a valid description of the last stage of the natural transition and the principle stage of bypass transition has been the corner stone of all methods dealing with transition. Nevertheless, all methods that sprung from it are better suited for inclusion to boundary layer codes rather than to turbulence models. Only, in recent years, ‘advanced’ methods for transition modelling have been reported (see Steelant and Dick, 1996 and Suzen and Huang, 2000), but despite solving a transport-type equation for the intermittency function in the cost of additional computational requirements, no significant improvement in transition prediction is reported.

**Table 1.** Main features of the test cascade.
Parameter	Value
Chord	12.73cm
Solidity	1.67
Leading Edge Radius	0.114m
Trailing Edge Radius	0.157m
Thickness	7%
Section Angle	14.2°
Stagger Angle	14.4°
Span	25.4cm

Review of UFR studies and choice of test case

The selected UFR test case is described in full detail in a couple of ASME, Journal of Turbomachinery articles (Elazar and Shreeve, 1990 and Shreeve et al., 1991). It embodies the measurements in a controlled diffusion compressor cascade at a low Mach number. In the literature review that was conducted, an additional very interesting low-speed test case was found. It corresponds to the measurements on another low-speed compressor blade in cascade (see Deutsch and Zierke, 1997). The reason for selecting the former to the latter is that it combines more key-elements of the physics related to the flow around blades, such as the laminar separation bubble formation at suction side near the leading edge and the separation of the flow at the rear part of the same side in the near-stall flow conditions (see Figure 1). On the other side the second cascade is less separated but more highly loaded. Finally, the measurements of Elazar and Shreeve (1990) are accompanied by a greater number of papers reporting on computational results.

Contributors: E. S. Politis - NTUA