Figure 7-1.. Details of the various casing treatments. Each treatment was on a separate disc.
treatment used. The third disc used is ablank， representing the present type of casing. The results indicate that the radial casing treatment is most effective in reducing leakage and also in increasing the surge-to-stall margin. Figure 7-15 shows the leakage at the tips for the various casing treatments. Figure 7-16 shows the velocity patterns observed by the use of various casingtreatments. Note that for the treatment along the chord (radial)， the flow is maximum at the tip. This flow maximum at the tip indicates that the chance of rotor tip stall is greatly reduced.
Energ叩 Increases
In an axial flow compressor air passes from one stage to the next with each stage raising the pressure and temperature slightly. By producing low-pressure increases on the order of 1.1:1-1.4:1， very high efficiencies can be obtained. The use of multiple stages permits overall pressure increases up to
FPO
Figure 7-14. Two discs with casing treatment.
Figure 7-15. .ass flow leakage at tips for various casing treatments.
40:1. Figure 7-3 shows the pressure，velocity， and total enthalpy variation for flow through several stages of an axial flow compressor. It is important to note here that the changes in the totalconditions for pressure， temperature， and enthalpy occur only in the rotating component where energy is inputtedinto the system. As seen also in Figure7-3， the length of theblades， and theannulusarea， which is the area between the shaft and shroud， decreases through the length of the compressor. This reduction in flow area compen-sates for the increase in fluid density asit is compressed， permitting a constant axial velocity. In most preliminary calculations used in the designof a compressor， the average blade height is used as the blade height for the stage.
The rule of thumb for a multiple stage gas turbine compressor would bethat the energy rise per stage would be constant， rather than the commonly held perception that the pressure rise per stage is constant. The energy rise per stage can be written as:
H二[H2 -H1l(7-6)
NS
where: H1， H2二 Inlet and Exit Enthalpy Btujlbm (k.jkg)
N，二 number of stages
Assuming that the gas is thermally and calorically perfect (句 ， and寸 are constant) equation 7-1 can be rewritten as:
[]寸-1
几in PP12 寸 -1
几stage二N， (7-7)
where:几in二 Inlet Temperature (oF， oC)
P1， P2二 Inlet and Exit Pressure (psia， bar)
Velocit叩 Triangles
As stated earlier， an axial-flow compressor operates on the principle of putting work into the incoming air by acceleration and diffusion. Air enters the rotor as shown in Figure 7-17 with an absolute velocity (V ) and an angle α1， which combines vectorially with the tangential velocity of the blade ( U ) to produce the resultant relative velocity W1 at an angle α2. Air flowing through the passages formed by the rotor blades is given a relative velocity W2 at an angle α4， which is less than α2 because of the camber of the blades. Note that W2 is less than W1， resulting from an increase in the passage widthas the blades become thinner toward the trailing edges. Therefore， some diffusion will take place in the rotor section of the stage. The combination of the relative exit velocity and blade velocity produce an absolute velocity V2at the exit of the rotor. The air then passes through the stator， where it is turned through an angle so that the air is directed into the rotor of the next stage with a minimum incidence angle. The air entering the rotor has an axial component at an absolute velocity Vz1 and a tangential component Ve1.
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