2. A General Mathematical model for A Turbo-Machine P M V Subbarao Professor Mechanical Engineering Department Mathematical Tools for Development !!!

3. The Superiority of Vector Parameters

4. Euler’s Work Equation Torque exerted by flow on blade row = shaft output torque = Rate of change of Angular momentum of fluid =  Euler Theory:

5. Define, L as Angular momentum Angular momentum is moment of linear momentum of angular velocity, V 

6. The Boeing 747 Cruising at an Altitude of 10 km

7. Turbo-jet Engine

8. Even for a steady flow through a turbo-machine: Inlet rate of angular momentum :

9. Exit rate of angular momentum at exit: Change in Rate of angular momentum: Euler Theory:

10. Power : A change in Whirl Velocity of fluid can only establish Power Exchange between fluid and rotor in a turbo-machine !

11. This is known as Euler Turbo-machinery Equation. First Law for Steady Flow Steady State Turbo Machine: Avoid heat transfer across surface of a turbo-machine. Conservation of Energy

12. Read Through Euler Turbo-machinery Equation A Change in total enthalpy is proportional to change in tangential flow speed or tangential engine speed. For engines with little change in mean radius (inlet to exit), the change in total enthalpy is due to change in tangential flow velocity of the fluid. Creates a small change in enthalpy of fluid. For engines with large change in radius, the change in enthalpy is to a large degree due to the change in radius. The centrifugal/centripetal effect. Creates Large change in enthalpy of fluid. How to select a suitable type of action for a resource/demand.

13. The Variations : Principle of torque Generation Centrifugal/ Centripetal ImpulseReaction Power Generating Machines Radial flow turbines Pelton wheel De Laval Turbine Curtis Wheel Steam turbines & Gas Turbines Kaplan Turbine Power Consuming Machines Centrifugal pumps/compre ssors Axial flow pumps/ compressors

14. The Variations : Direction of Flow RadialMixedAxial Power Generating Machines Turbine of a Turbocharger Francis Turbine Kaplan Turbine Power Consuming Machines Centrifugal pump/ compressors Pumpsfan

15. MEL346 : Syllabus Introduction: turbo-machinery / history / types / classification. Euler equation for turbo-machines. Thermodynamics and fluid mechanics of turbo-machinery Mass, momentum and energy. Radial equilibrium theory and design of blades for a turbo- machine. Design of Hydraulic turbines. Axial flow turbines and compressors: theory and design Centrifugal compressors & Pumps Wind Turbines Micro Turbines

16. References Fluid Mechanics, Thermodynamics of Turbomachinery : S.L. Dixon. Principles of Turbomachinery: R.K. TURTON. Handbook of Turbomachineryedited by Earl Logan, Jr. & Ramendra Roy. The Design of High-Efficiency Turbomachinery and Gas Turbines – David G Wilson & T Korakianitis. Principles of Turbomachinery in Air Breathing Engines – E A Baskharone. Steam Turbines for Modern Fossil-Fuel Power Plants; Alexander S Leyzerovich.

17. Attendance Policy Below 80% -- One grade less. Below 70% -- Two grades less. Below 60% -- Three grades less.

18. No Break Through Just A Natural Evolution Knowledge of turbo-machines has evolved slowly over centuries without the benefit of sudden and dramatic breakthrough for more than 41500 yrs! Turbo-machines, such as windmills and waterwheels, are millenniums old.

19. An Evolution from Water Wheel to Hydraulic Turbine Waterwheels, which dip their vanes into moving water, were employed in ancient Egypt, China, and Assyria. Waterwheels appeared in Greece in the second century B.C. and in the Roman Empire during the first century B.C. A seven-ft-diameter waterwheel at Monte Cassino was used by the Romans to grind corn at the rate of 150 kg of corn per hour, Waterwheels at Arles ground 320 kg of corn per hour. The Doomsday Book, based on a survey ordered by William the Conqueror, indicates the there were 5,624 water mills in England in 1086. Besides the grinding of grain, waterwheels were used to drive water pumps and to operate machinery.

20. Agricola (1494–1555) showed by illustrations how water wheels were used to pump water from mines and to crush metallic ores in the 16th century. The pumps were driven by 14 waterwheels, each 12m in diameter, that were turned by the currents of the Seine. The undershot waterwheel, which had an efficiency of only 30%, were used up until the end of the 18 th century. It was replaced in the 19th century by the overshot waterwheel with an efficiency of 70 to 90%. By 1850, hydraulic turbines began to replace waterwheels. The first hydroelectric power plant was built in Germany in 1891 and utilized waterwheels and direct-current power generation. However, the waterwheels were soon replaced with hydraulic turbines and alternating-current electric power.

21. Evolution of Wind Turbines Although the use of wind power in sailing vessels appeared in antiquity, the widespread use of wind power for grinding grain and pumping water was delayed until –the 7th century in Persia, –the 12th century in England, and –the 15th century in Holland. 17th century, Leibniz proposed using windmills and waterwheels together to pump water from mines in the Harz Mountains. Dutch settlers brought Dutch mills to America in the 18th century. This led to the development of a multiblade wind turbine that was used to pump water for livestock. Wind turbines were used in Denmark in 1890 to generate electric power. Early in the 20th century American farms began to use wind turbines to drive electricity generators for charging storage batteries.

22. Discovery of Steam and Gas Turbines In the second century B.C. Hero of Alexandria invented rotors driven by steam and by gas, but these machines produced insignificant amounts of power. During the 18th and 19th centuries the reciprocating steam engine was developed and became the predominant prime mover for manufacturing and transportation industries. In 1883 the first steam turbines were constructed by de Laval whose turbines achieved speeds of 26,000 rpm. In 1884 a steam turbine, which ran at 17,000 rpm and comprised 15 wheels on the same shaft, was designed and built by Charlie Parsons. The gas turbine was conceived by John Barber in 1791, and the first gas turbine was built and tested in 1900 by Stolze.

23. Sanford Moss built a gas turbine in 1902 at Cornell University. At Brown Boveri in 1903, Armenguad and Lemale combined an axial-flow turbine and centrifugal compressor to produce a thermal efficiency of 3%. In 1905 Holzwarth designed a gas turbine that utilized constant-volume combustion. This turbine was manufactured by Boveri and Thyssen until the 1930s. In 1911 the turbocharger was built and installed in diesel engines by Sulzer Brothers, and in 1918 the turbocharger was utilized to increase the power of military aircraft engines. In 1939 the first combustion gas turbine was installed by Brown Boveri in Switzerland. A similar turbine was used in Swiss locomotives in 1942. The aircraft gas turbine engine (turbojet) was developed by Junkers in Germany around 1940.