## Stagger

For a given degree of reaction and value of Va or flow rate, a choice can be made of the stagger angle or setting of the blades. From the consideration of two defining equations:

Figure 6-6. An axial compressor controlled diffusion airfoil. (Courtesy of Elliott Company

g where

E = energy transfer

For fixed values of R and Va, a selection of a value of a2 (corresponding to a value of stagger angle) fixes a limiting value of (X] from cascade data. Thus the blade speed, u, is determined and then the energy transfer E is found.

To show the general effect of outlet angle or stagger, an approximate relation is used,

As the stagger angle increases, for higher values of a2, the optimum Va/u decreases and thus for a given value of Va, the blade speed, u, must

increase. Also as a2 increases, (o^ - a2) decreases, hence high stagger implies high rpm and blades of low camber.

Another important factor in design is the steepness of the characteristic curve, that is, the variation of pressure ratio with mass flow (see Figure 1-3), From consideration of the velocity diagram for 50% reaction, such as (d) of Figure 6-5, it can be shown that the symmetrical arrange ment gives tan a, =

and, substituting in Equation 6.7, this produces

Differentiating with respect to Va, and selecting the proportional variables

that show the energy transfer, E, which is head or pressure ratio change with respect to axial velocity, Va, which is mass flow at a greater rate as a^ increases. Therefore, high stagger blades tend to have a steeper characteristic curve. However, another feature of increased stagger that cannot be demonstrated simply, but requires use of cascade data, is that the design point or point of maximum efficiency on the characteristic curve is at a value of mass flow somewhat greater than that for maximum pressure ratio. As a result, the design point is further away from the surge mass flow and allows more flexibility on that part of the characteristic curve. Low stagger, on the other hand, tends to place the design point closer to the surge point. While this approach offers more flexibility for increased mass flow, some efficiency may be sacrificed to avoid operating too near surge.

Since for a given value of Va the blade speed must be greater for high stagger, the energy transfer is increased because

and thus fewer stages may be required. Because the relative velocity is higher, the Mach number may be prohibitive, or alternatively thinner blades may have to be used in order to obtain a higher critical Mach number for the drag value. Thinner blades would require larger chords in order to maintain reasonable levels of bending stress. As a net result, the overall length would not decrease in proportion to the decrease in number of stages.

Earlier, it was stated, on the basis of simplifying assumptions, that the maximum efficiency for 50% reaction blading was obtained at a value of Va/u = 0.5, requiring mean gas angles of 45°. The assumption for this result was that the drag-lift ratio was constant. In actual practice, cascade data indicate that drag-lift is not constant but increases as a2 increases. It would appear that the maximum efficiency may be close to a2 = 30°. However, the reduction in efficiency is not severe because for values of a2 of 15° and 45°, the drop is only about 1%.

Compressor performance can be changed by alteration of blade stagger. This is usually done by changes of stator stagger in preference of changes to the rotor. This can be accomplished on both process compressors and gas turbines, including the aircraft engine by use of variable stator vane control. While the mechanism is somewhat complex, it gives the axial compressor, with its inherently steep pressure-volume curve, the ability to be matched to a changing load without changing the speed. Figure 6-7 is a pressure-volume chart for an axial compressor with a partial stator vane control (only a portion of the stator blades is movable).

 140 COM» unmio -V- rCHOIHT OKI! 1H tfftamHCf / A ) / \ / 100 | 80 eo «0 'Tv " T — Y' J' 4 / ~__ ------- —-"""32. HAM. \ — TS Ml

PERCENT DESIGN VOLUME

PERCENT DESIGN VOLUME

Figure 6-7. Pressure-volume chart for an axial-flow compressor with partial stator vane control. (Courtesy ofA-C Compressor Corporation

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