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Research Papers

# A Criterion for Axial Compressor Hub-Corner Stall

[+] Author and Article Information
V.-M. Lei, Z. S. Spakovszky, E. M. Greitzer

Gas Turbine Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139

For example, separation, with boundary layer fluid moving off the wall, occurs along the symmetry line on the end wall of a rectangular nozzle, where the streamwise pressure gradient is favorable (Greitzer et al. (1)). This type of three-dimensional separation, however, is associated with the confluence of boundary layer fluid due to cross-flow (Lighthill (2)) rather than by the inability of low stagnation pressure fluid to negotiate a pressure rise. In addition, there is no stagnation of the separating fluid, and the primary effect is rather a change of direction as the fluid leaves the wall.

We are indebted to Professor N. A. Cumpsty for his clarifying comments on this point.

We have found this phrase, due to Professor N. A. Cumpsty, useful in dispelling ambiguity surrounding discussions of the qualitative definition of compressor stall.

As shown later, the stall indicator $S$ correlates best with the diffusion parameter if the loading near the end wall is evaluated at a spanwise location of 10% chord. This is within the end wall boundary layer thickness in multistage compressors but sufficiently away from the end wall surface to avoid interference with localized low pressure regions associated with spanwise turning of the cross-flow in the hub corner. To generalize different blade passage geometries, the calculations suggest nondimensionalizing the spanwise distance by chord.

Vorticity of the opposite sign to the inviscid part of the flow, which is associated with the cross-stream pressure gradient, is created at the wall and diffused into the end wall region. Since $u∕U$ is almost always monotonic with distance from the wall, the opposite sign of the vorticity can be inferred from the opposite slopes of the two sides of the triangle.

This and the insensitivity to inlet blockage are reminiscent of the situation with straight diffusers where the flow regimes are not much affected by Reynolds number (Johnston (28)).

An aspect ratio of 0.5 was also considered but for such low values, the two end wall flows tend to merge developing full span stall and, under these circumstances, the separation indicator is no longer applicable.

We thank Dr. L. H. Smith for pointing this out.

This information, and the analysis, has been provided by Wellborn (31).

The assessment was based on CFD analysis.

J. Turbomach 130(3), 031006 (May 02, 2008) (10 pages) doi:10.1115/1.2775492 History: Received July 28, 2006; Revised February 12, 2007; Published May 02, 2008

## Abstract

This paper presents a new criterion for estimating the onset of three-dimensional hub-corner stall in axial compressor rotors and shrouded stators. A simple first-of-a-kind description of hub-corner stall formation is developed which consists of (i) a stall indicator, which quantifies the extent of the separated region via the local blade loading and thus indicates whether hub-corner stall occurs, and (ii) a diffusion parameter, which defines the diffusion limit for unstalled operation. The stall indicator can be cast in terms of a Zweifel loading coefficient. The diffusion parameter is based on preliminary design flow variables and geometry. Computational simulations and single and multistage compressor data are used to show the applicability of the criterion over a range of blade design parameters. The criterion also enables determination of specific flow control actions to mitigate hub-corner stall. As an illustration, a flow control blade, designed using the ideas developed, is seen to produce a substantial reduction in the flow nonuniformity associated with hub-corner stall.

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## Figures

Figure 1

Basic processes governing the formation of hub-corner stall together with limiting streamlines and separation lines

Figure 2

Definition of the Zweifel loading coefficient and relation to the stall indicator S

Figure 3

Cross-flow in the end wall region

Figure 4

Incoming end wall region skew due to moving end wall surfaces (i.e., rotor hubs or rotor drums underneath hub platforms in shrouded stators)

Figure 5

Comparison between the Lieblein DF and the diffusion parameter D. Squares denote cascades with skewed incoming end wall boundary layer.

Figure 6

Stagnation pressure loss coefficient ω (squares) and static pressure rise coefficient Cp (diamonds) as a function of diffusion parameter D for cascades with zero incidence. Solid symbols indicate hub-corner stall.

Figure 7

Formation of hub-corner stall for diffusion parameters D>0.4 (upper branch, S>0.12)

Figure 8

Limiting streamlines for two different compressor cascades: without (left) and with (right) hub-corner stall

Figure 9

Effects of blade aspect ratio, Reynolds number and incoming boundary layer thickness on hub-corner stall criterion

Figure 10

Evaluation of the hub-corner stall criterion for rotor and stator blade rows of five different production and research compressors (data courtesy of Rolls-Royce, Wellborn (31)).

Figure 11

Flow control of hub-corner stall via cross-flow of opposite sign to blade passage secondary flow: (a) upstream hub cavity leakage flow and (b) air injection in the blade passage

Figure 12

Effect of flow control on stall indicator and diffusion parameter: (a) hub cavity leakage flows and (b) suction surface air injection (squares)

Figure 13

Contours of computed stagnation pressure at cascade exit for (A) datum case, (B) streamwise air injection, and (C) streamwise plus spanwise air injection

Figure 14

Contours of stagnation pressure at compressor cascade exit: (A) datum case, (B) flow control with 0.4% of passage mass flow, and (C) flow control with 0.8% of passage mass flow. Top: Linear compressor cascade experiment; bottom: numerical simulation results.

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