Modern Engineering Thermodynamics

476 CHAPTER 13: Vapor and Gas Power Cycles
and that this efficiency drops off quickly when these conditions are deviated from. Similarly, it can be
shown that a reaction turbine has a maximum energy conversion efficiency when the fluid enters the rotor
blades parallel to the direction of motion of the blades and with a velocity exactly equal to the blade average
velocity. The effect of the turbine’s nozzles is to convert static pressure energy into dynamic kinetic energy,
whose momentum can then be manipulated by the turbine’s geometry to drive the rotor. Nozzles are analyzed
in Chapter 6, and the outlet velocity of an adiabatic nozzle with a negligible inlet velocity is given by
Eq. (6.16) as
p
V out =
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2g c ðh in − h out Þ
(6.16)
A nozzle receiving steam at 200. psia, 700.°F and exhausting to 1.00 psia has an enthalpy drop of, say,
400. Btu/lbm. The resulting nozzle outlet velocity is supersonic and can be calculated from Eq. (6.16) as
V out = f232:174 ½ lbm . ft/ ðlbf . ftÞŠð400: Btu/lbmÞð778:16 ft . lbf/BtuÞg 1/2
≈ 4500 ft/s
Then, a reaction turbine operating at its most efficient speed requires a blade average velocity of about 4500 ft/s.
If we assume a mean rotor radius of 1.0 ft, then the angular velocity of the rotor at its most efficient operating
speed is 4500 radians per second, or about 43,000 rpm. This is an extremely high rotational speed and is very
dangerous, due to the high centrifugal stresses and the high bearing loads produced by unbalanced forces. Also,
few auxiliary turbine driven devices (e.g., an electrical generator) could be made to operate at these speeds.
Therein was the major problem with early turbine development. How could they be slowed down while still
maintaining their good energy conversion and thermal efficiencies?
This problem remained unsolved until the end of the 19th century, when it was discovered that certain types of
turbine staging significantly decrease the turbine’s operating speed while maintaining its energy conversion efficiency.
The region between stationary nozzles in an impulse turbine is referred to as an impulse stage. It was discovered
that the effect of adding two extra rows of blades, one stationary and one moving, to each stage of an
impulse turbine reduced its most efficient operating speed by about a factor of 2. In a reaction turbine, every
other row of blades is stationary, and the combination of a stationary row and a moving row forms a reaction
stage of the turbine. Large reaction turbines typically have 30 to 100 or more stages, whereas impulse turbines,
normally, have fewer than 10 stages.
In 1883, the Swedish engineer Carl Gustaf Patrik DeLaval (1845–1913) built and ran the first practical singlestage
impulse steam turbine. It had a mean rotor diameter of 3 inches (0.076 m) and produced about 1.5 hp
with a shaft speed of 40,000 rpm. In 1889, he discovered that, if the pressure ratio across his stationary nozzles
were less than about 0.55, he could increase the nozzle exit velocity to supersonic speeds by making the nozzles
with a converging-diverging internal profile. The high shaft velocity of the DeLaval impulse turbine required a
gearbox to reduce the output rotational speed to a usable value. Since high-speed gear reduction is very inefficient,
it became necessary to find other ways of reducing the turbine’s speed effectively. The addition of multiple
stages of fixed nozzles and moving blades to the shaft of a DeLaval impulse turbine was first carried out by the
Frenchman Auguste Camille Edmond Rateau (1863–1930) in 1899. By having a sufficient number of these
stages in series, he was able to reduce the efficient rotating speed enough to allow electrical generators to be driven
directly from the output shaft. Also, in 1898, the American engineer Charles Gordon Curtis (1860–1953)
introduced multiple sets of stationary and moving blade rows downstream from a single stationary nozzle. This
technique exposed each set of moving vanes to a different mean velocity and also had the effect of slowing
down an impulse turbine while maintaining its energy conversion efficiency. Rateau staging exposes each row of
moving blades to nearly constant pressure, usually called pressure compounding or pressure staging. Curtis staging
exposes each row of stationary blades to nearly constant velocity, usually called velocity compounding or velocity
staging. Figure 13.26 illustrates these impulse turbine staging concepts.
The practice of putting several different constant pressure stages in series in a reaction turbine was introduced in
1884 by the Englishman Charles Algernon Parsons (1854–1931). His first turbine had 14 stages (14 pairs of
stationary and moving blade rows) and produced about 10 hp at 18,000 rpm. This was still too fast for direct
coupling to the existing electrical generators, so Parsons designed a new high-speed generator that could be
driven directly by his turbine.
By the early 20th century, the pressure and velocity staged DeLaval impulse turbine and the multiple pressure
staged Parsons reaction turbine became nearly equal rivals in terms of cost and efficiency. A lot was at stake at
this point in time, because electrical power generation was just coming into existence, and it was clear that it
had the potential for creating a second Industrial Revolution, based on electricity rather than steam.