![12/12/2024 43
Design point efficiency
Nozzle loss coefficient , is defined as
𝜉𝑛=
𝐸𝑛𝑡h𝑎𝑙𝑝𝑦 𝑙𝑜𝑠𝑠𝑖𝑛𝑛𝑜𝑧𝑧𝑙𝑒
𝐾𝑖𝑛𝑒𝑡𝑖𝑐𝑒𝑛𝑒𝑟𝑔𝑦 𝑎𝑡 𝑛𝑜𝑧𝑧𝑙𝑒𝑒𝑥𝑖𝑡
𝜉𝑛=
h2 − h2 𝑠
0 .5 𝐶2
2 𝑇3
𝑇 2
=
h3 𝑠− h3 𝑠𝑠
0 . 5 𝐶2
2 𝑇 3
𝑇 2
𝜂𝑡𝑠 =[1+
(𝐶3
2
+ 𝑉 3
2
𝜉𝑟 +𝐶2
2
𝜉 𝑟
𝑇 3
𝑇 2
)
2𝑊 ]
−1
𝜂𝑡𝑠 =[1+
(𝐶3
2
+ 𝑉 3
2
𝜉𝑟 +𝐶2
2
𝜉 𝑛
𝑇 3
𝑇 2
)
2 (h1 −h3) ]
−1
𝜂𝑡 𝑡 =[1+
(𝑉 3
2
𝜉𝑟 +𝐶2
2
𝜉𝑛
𝑇3
𝑇2
)
2(h1 − h3 ) ]
−1
𝐶1=𝐶3](https://image.slidesharecdn.com/chapterthree-241212164526-5b812747/85/chapter-two-axial-flow-turbine-flows-parallel-to-the-axis-of-rotation-43-320.jpg)
chapter two axial flow turbine flows parallel to the axis of rotation
- 1. WOLDIA UNIVERSITY INSTITUTE OF TECHNOLOGY school of Mechanical & Chemical Engineering Department of Mechanical Engineering Chapter Three: Axial Flow Turbines By Mr. Gashaw Minaye (MSc.)
- 2. 12/12/2024 2 Contents • Stage velocity triangles • Reaction turbine stages • Radial equilibrium theory • Radial turbine stage
- 3. 12/12/2024 3 • From nature of fluid point of view, turbines are classified as Hydro, Steam, Gas and wind turbines. • In this chapter much emphasis is given for gas and steam turbines because hydro turbines will be treated in a chapter later and wind turbine also requires separate treatment. But the principles are the same. • Gas turbines can be axial or radial (centrifugal) • A high pressure and temperature combustion gas is expanded through the gas turbine blades and usually a gas turbine stage is preceded by a compressor stage.
- 4. 12/12/2024 4 • Due to the very high temperature and pressure of the working fluid in both gas and steam turbines, thermal stress is a big challenge. • Turbines can be classified as Impulse and reaction based on the extent or degree of expansion of the gas inside the rotor blades. • If no static pressure rise is undertaken in the rotor blades, it is called impulse turbine. Other wise it’s reaction turbine.
- 5. 12/12/2024 5 Velocity Triangles in Axial flow turbines
- 6. 12/12/2024 6 • Unless specified all the parameters are taken as that of the mean radius of the annulus flow area. • Work done • The swirl velocities are added because of the high deflection angle of the flow in turbine blades in order to increase the shaft power output.
- 7. 12/12/2024 7 • The stage efficiency of an axial flow turbine is calculated the same way we were doing in chapter one. • For ideal gas case • The total to total to total efficiency is used when the exit kinetic energy is utilized either in the next stage or in propelling nozzle as in jet engine.
- 8. 12/12/2024 8 Relative Stagnation enthalpy • For frictionless flow the relative stagnation enthalpy across the rotor row is constant 𝐶𝑦 3+𝑈 =𝑊 𝑦 3 h01=h02 𝑅 𝑜𝑡𝑜𝑟 𝑆𝑡𝑎𝑡𝑜𝑟 (𝑎𝑑𝑖𝑎𝑏𝑎𝑡𝑖𝑐)
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- 10. 12/12/2024 10 • If the exit velocity is lost, then total to static efficiency is used and for ideal gas Impulse Turbine stage - No static pressure change across the rotor blades - As a result of no pressure drop the relative flow velocities at inlet and exit are the same for friction less flow. - The blade angles will then be equal
- 11. 12/12/2024 11 • When the available pressure is high, it is inevitable to have more than one stage. Multi – stage velocity compounded • A single stage utilizing a large pressure drop will have an impractically high peripheral speed of its rotor. This would lead to either a larger diameter or a very high rotational speed. • One of the methods to employ multi-stage expansion in impulse turbines is to generate high velocity of the fluid by causing it to expand through a large pressure drop in the nozzle blade row. This high velocity fluid then transfers its energy in a number of stages by employing many rotor blade rows separated by rows of fixed guide blades Multi – stage pressure compounded (Rateau stages ) • The total pressure drop is divided into a number of impulse stages
- 12. 12/12/2024 12 The performance of an impulse stage turbine can alternatively described by utilization factor Velocity compounded Impulse stages Pressure compounded Impulse stages
- 13. 12/12/2024 13 Reaction Turbine stages • The gas pressure decreases continuously over both fixed and moving rows of blades • Since the pressure drop in each stage is smaller as compared to the impulse stages, the gas velocities are relatively low. Besides this the flow is accelerating throughout • These factors make the reaction stages aerodynamically more efficient though the tip leakage loss is increased on account of the relatively higher pressure difference across the rotor blades. • Degree of reaction • For ideal gas
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- 15. 12/12/2024 15 • For normal reaction stage or or • Zero reaction • 50 % reaction • 100 % reaction
- 16. 12/12/2024 16 Zero reaction stage Impulse stage 50 % reaction stage 100 % reaction stage
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- 19. 12/12/2024 19 • Blade loading coefficient: It is used to express the work capacity of the stage. It is also sometimes called temperature drop coefficient • Flow coefficient: is ratio of the inlet axial flow velocity to the blade speed. • Rewriting • Aspect ratio: is the ratio of the blade height to its span
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- 27. 12/12/2024 27 Enthalpy loss coefficient
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- 31. 12/12/2024 31 Free Vortex Design (Radial Equilibrium theory) • Velocity triangles vary from tip to hub due to variation in blade velocities at the respective radii. • Twisted blading designed to take account of the changing flow angle is called vortex blading. • Momentum equation • For constant enthalpy and entropy, the equation takes the form • For constant stagnation enthalpy and constant axial velocity for the annulus area , • It is also called radial equilibrium theory because the energy extracted at any blade radius is uniform.
- 32. 12/12/2024 32 Constant nozzle angle design • As before, we assume that the stagnation enthalpy at outlet is constant, this leads to the axial velocity distribution given by • And since is constant, then is proportional to . Therefore,
- 33. 12/12/2024 33 Radial Flow Turbines • There is no absolute reference to chose between axial and radial flow machines. One is much more convenient than the other in some particular conditions, and the selection is made based on the requirements for the particular application. • Some common comparisons are: Radial turbines have a higher pressure ratio per stage than the axial ones. Radial turbines are compact having small rotor radius which allows it to have a higher rotational speed with less risk of centrifugal stress. Multi – staging is more convenient in axial flow machines so that a higher total pressure ratio can be attained in axial flow turbines. • Radial Turbines can be Inward flow or outward flow. • Radial outward flow turbines in a single stage gives low specific work due to divergence of flow area which decreases the efficiency. A multi – stage version of this machine using steam gives it an acceptable feature because steam can achieve a tremendous increase in its specific volume.
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- 37. 12/12/2024 37 • Specific work: There is a difference in the blade velocities of the inlet and exit of the radial flow machines. This demands a slight alteration in the specific work calculation. • Inward flow Radial Turbine (IFR): covers tremendous range of power, mass flow rate and rotational speed ranging from very large Francis Turbines used hydroelectric power generation and developing hundreds of megawatts to tiny closed cycle gas turbines for space power generation of a few kilowatts. • IFR is classified as: • Cantilever : Lower strength • 900 IFR: More preferred due to high strength (e.g.: Radial Francis Turbine)
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- 41. 12/12/2024 41 900 IFR Turbine • The nominal (design) conditions for a 900 IFR are pure radial relative flow at inlet and pure axial exit. This is the most utilized design experience by many pioneer engineers in the field. Therefore, and • Then, the specific work for the nominal condition is
- 43. 12/12/2024 43 Design point efficiency Nozzle loss coefficient , is defined as 𝜉𝑛= 𝐸𝑛𝑡h𝑎𝑙𝑝𝑦 𝑙𝑜𝑠𝑠𝑖𝑛𝑛𝑜𝑧𝑧𝑙𝑒 𝐾𝑖𝑛𝑒𝑡𝑖𝑐𝑒𝑛𝑒𝑟𝑔𝑦 𝑎𝑡 𝑛𝑜𝑧𝑧𝑙𝑒𝑒𝑥𝑖𝑡 𝜉𝑛= h2 − h2 𝑠 0 .5 𝐶2 2 𝑇3 𝑇 2 = h3 𝑠− h3 𝑠𝑠 0 . 5 𝐶2 2 𝑇 3 𝑇 2 𝜂𝑡𝑠 =[1+ (𝐶3 2 + 𝑉 3 2 𝜉𝑟 +𝐶2 2 𝜉 𝑟 𝑇 3 𝑇 2 ) 2𝑊 ] −1 𝜂𝑡𝑠 =[1+ (𝐶3 2 + 𝑉 3 2 𝜉𝑟 +𝐶2 2 𝜉 𝑛 𝑇 3 𝑇 2 ) 2 (h1 −h3) ] −1 𝜂𝑡 𝑡 =[1+ (𝑉 3 2 𝜉𝑟 +𝐶2 2 𝜉𝑛 𝑇3 𝑇2 ) 2(h1 − h3 ) ] −1 𝐶1=𝐶3
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- 46. 12/12/2024 46 Specific speed • It is an extremely important dimensionless parameter in radial turbines. The working specific speed range of a turbine is limited by the acceptable values of efficiency.