Applying the Euler turbine equation
H二 1 [U1Ve1 -U2Ve2l(7-.)于句
and assuming that the blade speeds at the inlet and exit of the compressorAssuming that the axial component (Vz) remains unchanged，
are the same and noting the relationships，
Ve1二 Vz1 tan α1 Ve2二 Vz2 tan α3 (7-.)(7-10)
Equation (7-1) can be written
H二 U1 于句 (Vz1 tan α2 -Vz2 tan α3) (7-11)
H二 UVz(tan α1 -tan α3) (7-12)
于句
The previous relationship is in terms of the absolute inlet and outlet vel-ocities. By rewriting the previous equation in terms of the blade angles or therelative air angles， the following relationship is obtained:
U1二U2二 Vz1 tan α1二 Vz1 tan α2
二 Vz2 tan α3 + Vz2 tan α4
Therefore，
H二 UVz(tan α2 -tan α4) (7-13)
于句
The previous relationship can be written to calculate the pressure rise in the stage
寸 -1
寸
P2 UV2
句几 in P1-1二 于(tan α2 -tan α4) (7-14)
句
which can be rewritten
寸寸
( ì
+1
P2 UVz
P1二 于句句几 in [tan α2 -tan α4l+ 1 (7-15)
The velocity triangles can be joined together in several different ways to help visualize the changes in velocity. One of the methods is to simply join these triangles into a connected series. The two triangles can also be joinedand superimposed using the sides formed by either the axial velocity， whichis assumed to remain constant as shown in Figure7-1.a， or the blade speedas a commonside， assuming that the inlet and exit blade speed are the same as shown in Figure 7-1.b.
Degree of Reaction
The degree of reaction in an axial-flow compressor is defined as the ratio of the change of static head in the rotor to the head generated in the stage
Hrotor
R二 Hstage (7-16)
The change in static head in the rotor is equal to the change in relative kinetic energy:
Hr二 1 (W12 -W12)(7-17)
2于句 and
W12二Vz12 +(Vz1 tan α2)2 (7-1 )
W22二Vz22 +(Vz2 tan α4)2 (7-1.)
Therefore，
Hr二 Vz 2 (tan2 α2 -tan2 α4)
2于句
Thus， the reaction of the stage can be written
R二 Vz tan2 α2 -tan2 α4 (7-20)
2U tan α2 -tan α4
Simplifying the previous equation，
R二 2VUz (tan α2 +tan α4)(7-21)
In the symmetrical axial-flow stage， the blades and their orientation in therotor and stator are reflected images of each other. Thus， a symmetrical axial-flow stage where V1二W2 and V2二W1as seen in Figure7-1.， the head delivered in velocity as given by the Euler turbine equation can be expressed
H二 1 [(U12 -U22)+(V12 -V22)+(W22 -W12)l (7-22)
2于句
H二 21 于句 (W22 -W12)(7-23)
The reaction for a symmetrical stage is 50.
The 50.reaction stage is widelyused， since an adverse pressure rise on either the rotor or stator blade surfaces is minimized for a given stagepressure rise. When designing a compressor with this type of blading， thefirst stage must be preceded by inlet guide vanes to provide prewhirl， and the correct velocity entrance angle to the first-stage rotor. With a high tangential velocity component maintained by each succeeding stationaryrow， the magnitude of W1is decreased. Thus， higher blade speeds and axial-velocity components are possible without exceeding the limiting value of .70-.75 for the inlet Mach number. Higher blade speeds result in compressors of smaller diameter and less weight.
Another advantage of the symmetrical stage comes from the equality ofstatic pressure rises in the stationary and moving blades， resulting in a maxi-mum static pressure rise for the stage. Therefore， a given pressure ratio canbe achieved with a minimum number of stages， a factor in the lightness of this type of compressor. The serious disadvantage of the symmetrical stage isthe high exit loss resulting from the high axial velocity component. However， the advantages are of such importance in aircraft applications that thesymmetrical compressor is normally used. In stationary applications， whereweight and frontal area are of lesser importance， one of the other stage types is used.
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本文链接地址：燃气涡轮工程手册 Gas Turbine Engineering Handbook 2(17)
