燃气涡轮工程手册 Gas Turbine Engineering Handbook 2(33)

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The power developed by the flow in an impulse turbine is given by the Euler equation
P二mu.(Ve3 -Ve4)二u(Ve3 -.e4)(9-12)
This equation， rewritten in terms of the absolute velocity and the nozzle angle αfor maximum utilization， can be shown as
P二 .(9-13)
mu(Ve3 cos α3)
The relative velocity Wremains unchanged in a pure impulse turbine， except for frictional and turbulence effect. This loss varies from about 20% for very high-velocity turbines (3000 ft/sec) to about 8% for low-velocity turbines (500 ft/sec). Since the blade speed ratio is equal to ( cos α)/2 formaximum utilization， the energy transferred in an impulse turbine can be written
P二 .mu2
mu(2u)二2 .(9-14)
T.e Reaction Turbine
The axial-flow reaction turbine is the most widely used turbine. In a reaction turbine both the nozzles and blades act as expanding nozzles.Therefore， the static pressure decreases in both the fixed and moving blades. The fixed blades act as nozzles and direct the flow to the moving blades at a velocity slightly higher than the moving blade velocity. In the reactionturbine， the velocities are usually much lower， and the entering blade relative velocities are nearly axial. Figure 9-10 shows a schematic view of a reaction turbine.

In most designs， the reaction of the turbine varies from hub to shroud. The impulse turbine is a reaction turbine with a reaction of zero (R二 0). The utilization factor for a fixed nozzle angle will increase as the reaction approaches 100%. For R二1， the utilization factor does not reach unity but reaches some maximum finite value. The 100% reaction turbine is not practical because of the high rotor speed necessary for a good utilizationfactor. For reaction less than zero， the rotor has a diffusing action. Diffusingaction in the rotor is undesirable， since it leads to flow losses.
The 50% reaction turbine has been used widely and has special significance.The velocity diagram for a 50% reaction is symmetrical and， for the maximumutilization factor， the exit velocity ( V4) must be axial. Figure 9-11 shows a velocity diagram of a 50% reaction turbine and the effect on the utilization factor. From the diagram W3二 V4， the angles of both the stationary androtating blades are identical. Therefore， for maximum utilization，
u 二 cos α (9-15)
V3
The 50% reaction turbine has the highest efficiency of all the various types of turbines. Equation (9-15) shows the effect on efficiency is relatively small for a wide range of blade speed ratios (0.6-1.3).

The power developed by the flow in a reaction turbine is also given by the general Euler equation. This equation can be modified for maximum utilization
P二 .mu(V3 cos α3)  (9-16)
For a 50% reactionturbine， Equation (9-16) reduces to 
P二 .mu(u)二 .mu2  (9-17) 

The work produced in an impulse turbine with a single stage running atthe same blade speed is twice that of a reaction turbine.Hence， the cost of a reaction turbine for the same amountof work is muchhigher， since it requires more stages. It is a common practice to design multistage turbines with impulse stages in the first few stages to maximize the pressure decrease and to follow it with 50% reaction turbines. The reaction turbine has a higher efficiency due to blade suction effects. This type of combination leadsto an excellent compromise， since otherwise an all-impulse turbine would have avery low efficiency， and an all-reaction turbine would have an excessive number of stages.
Turbine .lade .ooling.oncepts
The turbine inlet temperatures of gas turbines have increased considerably over the past years and will continue to do so. This trend has been made possible by advancement in materials andtechnology， and the use of advanced turbine blade cooling techniques. The development of new mater-ials as well as cooling schemes has seen the rapid growth of the turbine firing temperature leading to high turbine efficiencies. The stage 1 blade mustwithstand the most severe combination of temperature，stress， and environ-ment; it is generally the limiting component in the machine. Figure 9-12 shows the trend of firing temperature and blade alloy capability.
　
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