CHAPTER FOUR TURBINES 4-1 Brief Description A course in Turbomachinery…………………………………..….…Lecturer: Dr.Naseer Al-Janabi 24 CHAPTER FOUR TURBINES 4-1 Brief Description Turbines have been used for centuries to convert freely available mechanical energy from rivers and wind into useful mechanical work, usually through a rotating shaft. Whereas the rotating part of a pump is called the impeller, the rotating part of a hydroturbine is called the runner. When the working fluid is water, the turbomachines are called hydraulic turbines or hydroturbines. When the working fluid is air, and energy is extracted from the wind, the machine is properly called a wind turbine. The word windmill should technically be applied only when the mechanical energy output is used to grind grain, as in ancient times. However, most people use the word windmill to describe any wind turbine, whether used to grind grain, pump water, or generate electricity. In coal or nuclear power plants, the working fluid is usually steam; hence, the turbomachines that convert energy from the steam into mechanical energy of a rotating shaft are called steam turbines. A more generic name for turbines that employ a compressible gas as the working fluid is gas turbine. (The turbine in a modern commercial jet engine is a type of gas turbine). 4-2 IMPULSE TURBINES In an impulse turbine, the fluid is sent through a nozzle so that most of its available mechanical energy is converted into kinetic energy. The high speed jet then impinges on bucket-shaped vanes that transfer energy to the turbine shaft, as sketched in Fig.4.1 . The modern and most efficient type of impulse turbine was invented by Lester A. Pelton (1829–1908) in 1878,

and the rotating wheel is now called a Pelton wheel in his honour. The A course in Turbomachinery…………………………………..….…Lecturer: Dr.Naseer Al-Janabi 25 and the rotating wheel is now called a Pelton wheel in his honour. The buckets of a Pelton wheel are designed so as to split the flow in half, and turn the flow nearly 180° around (with respect to a frame of reference moving with the bucket), as illustrated in Fig.4.1. Fig.4.1 Impulse turbine: (a) side view of wheel and jet; (b) top view of bucket; (c) typical velocity diagram.

P = pQu(vj - u)(1 - cosp) (4.2) A course in Turbomachinery…………………………………..….…Lecturer: Dr.Naseer Al-Janabi 26 The mass flow would be m = pQ = pAj Vj . P = pQ(u1vt1 - u2vt2) = pQ{uvj - u[u + (vj - u)cosp]} (4.1) Or P = pQu(vj - u)(1 - cosp) (4.2) Finally, we see from Power Eq. that the shaft power output P is zero if u= 0 (wheel not turning at all). P is also zero if u= Vj (bucket moving at the jet speed). Somewhere in between these two extremes lies the optimum wheel speed. By setting the derivative of Eq.4.2 with respect to u to zero, we find that this occurs when u= Vj /2 (bucket moving at half the jet speed, as shown in Fig.4.2 below. Fig.4.2 1 2 For a perfect nozzle, the entire available head would be converted to jet velocity: Vj = #2$% (4.3). Actually, since there are 2 to 8 percent nozzle losses, a velocity coefficient Cv is used: u* = Vj

Maximum efficiency occurs at - = 1 C � 0.47 . A course in Turbomachinery…………………………………..….…Lecturer: Dr.Naseer Al-Janabi 27 Vj = Cv J2gH 0.92 � Cv � 0.98. u J2gH Maximum efficiency occurs at - = 1 C � 0.47 . Fig.4.3 below plotted for an ideal turbine (β= 180°, Cv =1.0) and for typical working conditions (β= 160°, Cv = 0.94). The latter case predicts ηmax =85 percent at - = 0.47, but the actual data for a 24-in Pelton wheel test are somewhat less efficient due to windage, mechanical friction, back splashing, and non-uniform bucket flow. For this test ηmax =80 percent, and, generally speaking, an impulse turbine is not quite as efficient as the Francis or propeller turbines. Fig. 4.3 - = = peripheral velocity factor. 2 v

of turbine. Take velocity coefficient (Cv = 0.985). A course in Turbomachinery…………………………………..….…Lecturer: Dr.Naseer Al-Janabi 28 EX: The mean bucket speed of a Peloton wheel is 15 m/s. The rate of flow of water supplied by the jet under a head of 42 m is 1 m3/s. If the jet is deflected by the buckets at an angle of 165˚. Find the power and efficiency of turbine. Take velocity coefficient (Cv = 0.985).