The pitch Sbof a cascade is the distance betweenblades， usually measured between the camberlines at the leading or trailing edges of the blades. The ratio of the chord length to the pitch is the solidity σ of the cascade. The solidity measures the relative interference effects of one blade with another.If the solidity is on the order of 0.5-0.7， the single or isolated airfoil test data，from which there are a profusion of shapes tochoose， can be applied with considerable accuracy. The same methods can be applied up to a solidity of about 1.0 but with reduced accuracy. When the solidity is on the order of
1.0-1.5， cascade data are necessary. For solidity in excess of1.5， the channel theory can be employed. The majority of present designs are in the cascade region.
The blade inlet angle .1 is the angle formed by a line drawn tangent to the forward end of the camber line and the axis of the compressor. The blade outlet angle .2 is the angle of a line drawn tangent to the rear of the camberline. Subtracting .2 from .1 gives the blade camber angle. The angle that the chordline makes with the axis of the compressor is寸， the setting or stagger angle of the blade. High-aspect ratio blades are often pretwisted so that at full operational speed the centrifugal forces acting on the blades will untwist the blades to the designed aerodynamic angle. The pretwist angle at the tip for blades with AR ratios of about four is between two and four degrees.
The air inlet angle α1， the angle at which incoming air approaches theblade， is different from .1. The difference between these two angles is the incidence angle i. The angle of attack α is the angle between the inlet airdirection and the blade chord. As the air is turned by theblade， it offers resistance to turning and leaves the blade at an angle greater than .2. The angle at which the air does leave the blade is the air outlet angle α2. The difference between .2 and α2 is the deviation angle 8. The air turning angle is the difference between α1 and α2 and is sometimes called the deflection angle.
The original work by NACA and NASA is the basis on which mostmodern axial-flow compressors are designed. Under NACA， a large number of blade profiles were tested. The test data on these blade profiles is pub-lished. The cascade data conducted by NACA is the most extensive work of its kind. In most commercial axial-flow compressors NACA 65 series blades are used. These blades are usually specified by notation similar to the following: 65-(1.) 10. This notation means that the blade has a lift coefficientof1..， aprofile shape65， and a thickness.chord ratio of 10.. The lift coefficient can be directly related to the blade camber angle by the following relationship for 65 series blades:
。何 25 CL (7-1)
Elementar叩 AirfoilTheor叩
When a single airfoil is parallel to the velocity of a flowinggas， the air flows over the airfoil as shown in Figure 7-5a. The air divides around thebody， separates at the leadingedge， and joins again at the trailing edge of the body. The main stream itself suffers no permanent deflection from the presence of the airfoil. Forces are applied to the foil by the local distribution of the stream and the friction of the fluid on the surface. If the airfoil is welldesigned， the flow is streamlined with little or no turbulence.
If the airfoil is set at the angle of attack to the air stream (as in Figure7-5b)， a greater disturbance is created by itspresence， and the streamlinepattern will change. The air undergoes a localdeflection， though at some distance ahead of and behind the body the flow is still parallel and uniform. The upstream disturbance is minor compared to the downstream distur-bance. The local deflection of the air streamcan，by Newton"slaws， becreated only if the blade exerts a force on the air;thus， the reaction of the air must produce an equal and opposite force on the airfoil. These forces can appear only in the form of a pressure stream on the airfoil. The presence of the airfoil has changed the local pressure distributionand， by the Bernoulliequation， the local velocities. Examination of the streamlines about the bodyshows that over the top of theairfoil， the lines approach eachother， indi-cating an increase of velocity and a reduction in static pressure. On theunderside of the airfoil， the action separates the streamlines， resulting in a static pressure increase.
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