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Research Papers

# The Design of Highly Loaded Axial Compressors

[+] Author and Article Information
Tony Dickens, Ivor Day

Whittle Laboratory, Department of Engineering, 1 JJ Thomson Avenue, Cambridge CB3 0DY, UK

To achieve constant work addition across the span, the loading at the hub (i.e., $Δh0/Ulocal2$) must be greater than at the tip. This results in reduced diffusion toward the casing.

MISES was used to predict the velocity distribution around a series of low-speed airfoils. Sections were designed to give three levels of turning (equivalent to $Δh0/U2=0.40$, 0.50, and 0.60, assuming a flow coefficient of 0.50). Solidity, maximum thickness, and trailing edge thickness were varied.

In the present case, the boundary layer thicknesses at the trailing edge were calculated iteratively.

The group $σ(tmax/c)Vx,1/ΔVθ$ has been derived from nondimensional arguments and, although it is difficult to attach a physical meaning to this term, it has been shown to be valid for both low and high-speed designs (although at high Mach numbers values of the constants $k1$ and $k2$ change).

The integral boundary layer solver embedded in MISES was used for this purpose.

To allow comparison with Lieblein's data, the calculated boundary layers were also partially mixed out to a shape factor of 1.1, comparable to that measured by Lieblein.

Figs.  1415 show the predicted trailing edge momentum thickness for a series of airfoils of different loadings between 0.25 (lightly loaded) and 0.75 (very highly loaded), assuming a flow coefficient of 0.50. The inlet flow angle was held constant at 63.4 deg and the solidity varied. The Reynolds number was set to $1.0×106$ (representative of aeroengine Reynolds numbers).

J. Turbomach 133(3), 031007 (Nov 12, 2010) (10 pages) doi:10.1115/1.4001226 History: Received August 05, 2009; Revised October 04, 2009; Published November 12, 2010; Online November 12, 2010

## Abstract

Increasing compressor pressure ratios (thereby gaining a benefit in cycle efficiency), or reducing the number of stages (to reduce weight, cost, etc.), will require an increase in pressure rise per stage. One method of increasing the pressure rise per stage is by increasing the stage loading coefficient, and it is this topic, which forms the focus of the present paper. In the past, a great deal of effort has been expended in trying to design highly loaded blade rows. Most of this work has focused on optimizing a particular design, rather than looking at the fundamental problems associated with high loading. This paper looks at the flow physics behind the problem, makes proposals for a new design strategy, and explains sources of additional loss specific to highly loaded designs. Detailed experimental measurements of three highly loaded stages $(Δh0/U2≈0.65)$ have been used to validate a computational fluid dynamics (CFD) code. The calibrated CFD has then been used to show that, as the stage loading is increased, the flow in the stator passages breaks down first. This happens via a large corner separation, which significantly impairs the stage efficiency. The stator can be relieved by increasing stage reaction, thus shifting the burden to the rotor. Fortunately, the CFD calculations show that the rotor is generally more tolerant of high loading than the stator. Thus, when stage loading is increased, it is necessary to increase the reaction to achieve the optimum efficiency. However, the design exercise using the calibrated CFD also shows that the stage efficiency is inevitably reduced as the stage loading is increased (in agreement with the experimental results). In the second part of the paper, the role that the profile loss plays in the reduction in efficiency at high stage loading is considered. A simple generic velocity distribution is developed from first principles to demonstrate the hitherto neglected importance of the pressure surface losses in highly loaded compressors.

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## Figures

Figure 1

Compressor Smith chart showing contours of efficiency. Efficiency calculated from the 1D correlations of Wright and Miller (9) for a typical compressor stage.

Figure 2

Figure 3

Effect of stator loading and inlet flow angle on stator loss coefficient. Solid symbols denote the presence of large 3D separations.

Figure 4

The effect of stage loading and de Haller number on stator loss coefficient. Solid lines denote approximate contours of stator loss coefficient (interval 0.01) and solid symbols denote the presence of large 3D separations.

Figure 5

Effect of stage loading and inlet flow angle on rotor loss coefficient

Figure 6

(a) Effect of inlet flow angle on calculated contours of rotor exit relative velocity (left) and suction surface axial velocity (right). Separated regions shaded (right). (b) A typical corner separation in a stator blade row; shown here for comparative purposes.

Figure 7

Effect of stage loading and inlet flow angle on predicted stage lost efficiency

Figure 8

Comparison between CFD predictions (squares) of stator midspan loss and the 1D profile loss correlations of Wright and Miller (9) (circles)

Figure 9

Schematic diagram of the assumed velocity distribution around a compressor airfoil

Figure 10

Trailing edge velocity against trailing edge blockage for a series of low-speed airfoils

Figure 11

Leading edge velocity against correlation parameter, σ(tmax/c)Vx,1/ΔVθ, for a series of low-speed airfoils

Figure 12

Comparison between rotor velocity distributions predicted by MISES (dashed) and the generic “straight-line” velocity distribution (solid)

Figure 13

Comparison between momentum thickness predicted by a coupled generic velocity distribution/boundary layer calculation and those measured by Lieblein (1)(Re=2.5×105).

Figure 14

Total predicted momentum thickness at the trailing edge against local diffusion factor. Lines of constant Δh0/U2 shown from a blade row with α1=63.4 deg(Re=1.0×106).

Figure 15

(a) Suction surface and (b) pressure surface trailing edge momentum thickness against local diffusion factor. Lines of constant Δh0/U2 shown for a blade row with α1=63.4 deg(Re=1.0×106).

Figure 16

Effect of stage loading (Δh0/U2) on the assumed generic velocity distribution for a series of blades with constant local diffusion factor of 0.45 (α1=63.4 deg)

Figure 17

Effect of stage loading (Δh0/U2) on the assumed generic velocity distribution for a series of blades with constant local diffusion factor of 0.45 (α1=63.4 deg)

Figure 18

Total trailing edge momentum thickness against suction surface local diffusion factor for a series of high-speed blades (Min=0.74). Lines of constant Δh0/U2 shown from a blade row with α1=63.4 deg(Re=1.0×106).

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