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A rotor with a constant radius and an axial velocity constant throughout can be written
2 R二 2 (W4 -W322)(9-3)
(V3 -V42)+(W4 -W32)
Fromthe previous relationship， it is obvious that for a zero-reaction turbine (impulse turbine) the relative exit velocity is equal to the relative inlet velocity. Most turbines have a degree of reaction between 0 and 1; negative reaction turbines have much lower efficiencies and are not usually used.
Utilization Factor
In a turbine， not all energy supplied can be converted into useful work-even with an ideal fluid. There must be some kinetic energy at the exit that isdischarged due to the exit velocity. Thus， the utilization factor is defined as the ratio of ideal work to the energy supplied
E二島 計2 (9-4)島 計+ V24
Z
and it can be written in terms of the velocity for a single rotor with constant radius
22 E二(V3 -V42)+(2 W4 -W32)(9-5)
V32 +(W4 -W32)
Work Factor
In addition to the degree of reaction and the utilizationfactor， another parameter used to determine the blade loading is the work factor
川he
r一u2 (9-6)
and it can be written for a constant radius turbine
Ve3 -Ve4
r二 u (9-7)
The previous equation can be further modified for the maximum utiliza-tion factor where the absolute exit velocity is axial and no exit swirl exists
r二 Vu e3 (9-8)

The value of the work factor for an impulse turbine (zero reaction) with a maximum utilization factor is two. In a 50% reaction turbine with a max-imum utilization factor the work factor is one.
In recent years the trend has been toward high work factor turbines. The high work factor indicates that the blade loading in the turbine is high. The trend in many fan engines is toward a high by-pass ratio for lower fuel consumption and lower noise levels.As the by-pass ratio increases， therelative diameter of the direct-drive fan turbine decreases， resulting in lower blade tip speeds. Lower blade tip speeds mean that with conventional workfactors， the number of turbine stages increases. Considerable research is being conducted to develop turbineswith high work factors， high bladeloadings， and high efficiencies. Figure 9-3 shows the effect of turbine stage work and efficiency. This diagram indicates that efficiency drops consider-ably as the work factor increases. There is little information on turbines with work factors over two.
.elocit .iagrams
An examination of various velocity diagrams for different degrees of reaction is shown in Figure 9-4. These types of blade arrangements withvarying degrees of reaction are all possible; however， they are not all prac-tical.

Examining the utilization factor， the discharge velocity ( V42/2)， representsthe kinetic energy loss or the unused energy part. For maximumutilization，the exit velocity should be at a minimum and， by examining the velocitydiagrams， this minimum is achieved when the exit velocity is axial. This type of a velocity diagram is considered to have zero exit swirl. Figure 9-5 shows the various velocity diagrams as a function of the work factor and the turbine type. This diagram shows that zero exit swirl can exist for any type of turbine.
Zero exit swirl diagram. In many cases the tangential angle of the exit velocity (Ve4) represents a loss in efficiency. A blade designed for zero exit swirl (Ve4二0) minimizes the exit loss. If the work parameter is less thantwo， thistype of diagram produces the highest static efficiency. Also， the total effici-ency is approximately the same as the other types of diagrams. If r is greaterthan2.0， stage reaction is usually negative， a condition best avoided.
Impulse diagram.For the impulserotor， the reaction iszero， so therelative velocity of the gas is constant， or W3二 W4. If the work factor is lessthan2.0， the exit swirl ispositive， which reduces the stage work. For thisreason， an impulse diagram should be used only if the work factor is 2.0 or greater. This type of diagram is a good choice for the last stage because for rgreater than 2.0， an impulse rotor has the highest static efficiency.
　
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本文鏈接地址：燃氣渦輪工程手冊 Gas Turbine Engineering Handbook 2(31)