a general mathematical model for a turbo-machine p m v subbarao professor mechanical engineering...
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A General Mathematical model for A Turbo-Machine
P M V SubbaraoProfessor
Mechanical Engineering Department
Mathematical Tools for Development !!!
The Superiority of Vector Parameters
kVjViVV zrˆˆˆ
Euler’s Work Equation
Torque exerted by flow on blade row = shaft output torque = Rate of change of Angular momentum of fluid =
Euler Theory:
kVjViVV zrˆˆˆ
Define, L as Angular momentum
Angular momentum is moment of linear momentum of angular velocity, V
The Boeing 747 Cruising at an Altitude of 10 km
Turbo-jet Engine
Even for a steady flow through a turbo-machine:
Inlet rate of angular momentum :
Exit rate of angular momentum at exit:
Change in Rate of angular momentum:
Euler Theory: 1122 rVrVm
Power :
A change in Whirl Velocity of fluid can only establish Power Exchange between fluid and rotor in a turbo-machine !
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
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.
The Variations : Principle of torque Generation
Centrifugal/Centripetal
Impulse Reaction
Power Generating Machines
Radial flow turbines
Pelton wheelDe Laval Turbine
Curtis Wheel
Steam turbines & Gas
TurbinesKaplan Turbine
Power Consuming Machines
Centrifugal pumps/compre
ssors
Axial flow pumps/
compressors
The Variations : Direction of Flow
Radial Mixed Axial
Power Generating Machines
Turbine of a Turbocharger
Francis Turbine
Kaplan Turbine
Power Consuming Machines
Centrifugal pump/
compressors
Pumps fan
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
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.
Attendance Policy
• Below 80% -- One grade less.
• Below 70% -- Two grades less.
• Below 60% -- Three grades less.
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.
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.
• 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 18th 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.
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.
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 .
• 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.