## Posted tagged ‘gas turbine engine’

### 12. Energy Exchange with Moving Blades

September 22, 2011

# Subsections

• 12.1 Introduction
• 12.2 Conservation of Angular Momentum
• 12.3 The Euler Turbine Equation
• 12.4 Multistage Axial Compressors
• 12.5 Velocity Triangles for an Axial Compressor Stage
• 12.6 Velocity Triangles for an Axial Flow Turbine Stage

# 12.1 Introduction

So far we have only looked at the thermodynamic results of compressors and turbines ( ‘s and  ‘s). Now we will look in more detail at how the components of a gas turbine engine produce these effects. You will learn later that without heat transfer, it is only possible to change the total enthalpy of a fluid with an unsteady process (e.g. moving blades). Still we will use many of the steady flow tools that we have discussed in thermodynamics and propulsion by considering the steady flow in and out of a component as shown in Figure 12.1.

# 12.2 Conservation of Angular Momentum

[This section is excerpted from Fluid Flow: A First Course in Fluid Mechanics, Macmillan Publishing Company, 1989.]

The momentum theorem developed in Chapter 10 gives the force acting on a fixed volume in terms of linear momentum flux through the surface of the volume. In many situations we are interested in the moment or torque on the volume. For this purpose we may adapt the angular momentum law of mechanics to the flow of fluids. Our starting point is the familiar law

where  ,  , and  refer to a single particle. The torque exerted by the force  about a fixed point is

where  is the radius vector from the fixed point to the point of application of  . The symbol,  , signifies, as usual, that the vector cross-product shall be taken. Then, from Newton’s law of motion,

We now define a vector  as the vector product of the radius vector to the particle and the linear momentum, that is,

The quantity  is called angular momentum. Upon differentiating  with respect to time, we find that

However,  and the cross-product of a vector parallel to itself is zero. The first term in the right-hand side therefore vanishes and we have the result that

 (12..1)

Equation (12.1) states that the rate of change of angular momentum of a particle about a fixed point is equal to the torque applied to the particle.We now seek to modify the law as expressed by Equation (12.1) to be suitable for a fixed volume. The torque on a material volume  is

This is readily transformed into a control volume integral. We have, therefore,

where

 (12..2)

is the angular momentum contained within the control volume. Equation (12.2) represents the angular momentum theorem. [For more information about angular momentum and rotational energy, see pages 246 and 558 in Hibbeler’s Engineering Dynamics.]

# 12.3 The Euler Turbine Equation

The Euler turbine equation relates the power added to or removed from the flow, to characteristics of a rotating blade row. The equation is based on the concepts of conservation of angular momentum and conservation of energy. We will work with the model of the blade row shown in Figure 12.2.

Applying conservation of angular momentum, we note that the torque,  , must be equal to the time rate of change of angular momentum in a streamtube that flows through the device

This is true whether the blade row is rotating or not. The sign matters (i.e. angular momentum is a vector – positive means it is spinning in one direction, negative means it is spinning in the other direction). So depending on how things are defined, there can be positive and negative torques, and positive and negative angular momentum. In Figure 9.2, torque is positive when V_{textrm{tangential in}}\$” width=”207″ height=”32″ align=”MIDDLE” border=”0″ /> — the same sense as the angular velocity.If the blade row is moving, then work is done on/by the fluid. The work per unit time, or power,  , is the torque multiplied by the angular velocity,  :

If torque and angular velocity are of like sign, work is being done on the fluid (a compressor). If torque and angular velocity are of opposite sign work is being extracted from the fluid (a turbine). Here is another approach to the same idea:

• If the tangential velocity increases across a blade row (where positive tangential velocity is defined in the same direction as the rotor motion) then work is added to the flow (this happens in a compressor).
• If the tangential velocity decreases across a blade row (where positive tangential velocity is defined in the same direction as the rotor motion) then work is removed from the flow (this happens in a turbine).

From the steady flow energy equation,

with

Then equating this expression of conservation of energy with our expression from conservation of angular momentum, we arrive at:

or for a perfect gas with  ,

 (12..3)

Equation (12.3) is called the Euler Turbine Equation. It relates the temperature ratio (and hence the pressure ratio) across a turbine or compressor to the rotational speed and the change in momentum per unit mass. Note that the velocities used in this equation are what we will later call absolute frame velocities (as opposed to relative frame velocities).

• If angular momentum increases across a blade row, then  T_{Tb}\$” width=”80″ height=”32″ align=”MIDDLE” border=”0″ /> and work was done on the fluid (a compressor).
• If angular momentum decreases across a blade row, then <img src="http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/img1569.png&quot; alt="\$ T_{Tc}  and work was done by the fluid (a turbine).

# 12.4 Multistage Axial Compressors

An axial compressor is typically made up of many alternating rows of rotating and stationary blades called rotors and stators, respectively, as shown in Figures 12.3 and 12.4. The first stationary row (which comes in front of the rotor) is typically called the inlet guide vanes or IGV. Each successive rotor-stator pair is called a compressor stage. Hence compressors with many blade rows are termed multistage compressors.

One way to understand the workings of a compressor is to consider energy exchanges. We can get an approximate picture of this using the Bernoulli Equation, where  is the stagnation pressure, a measure of the total energy carried in the flow,  is the static pressure, a measure of the internal energy, and the velocity terms are a measure of the kinetic energy associated with each component of velocity ( is radial,  is tangential,  is axial).

The rotor adds swirl to the flow, thus increasing the total energy carried in the flow by increasing the angular momentum (adding to the kinetic energy associated with the tangential or swirl velocity, ).The stator removes swirl from the flow, but it is not a moving blade row and thus cannot add any net energy to the flow. Rather, the stator rather converts the kinetic energy associated with swirl to internal energy (raising the static pressure of the flow). Thus typical velocity and pressure profiles through a multistage axial compressor look like those shown in Figure 12.5.

Note that the IGV also adds no energy to the flow. It is designed to add swirl in the direction of rotor motion to lower the Mach number of the flow relative to the rotor blades, and thus improve the aerodynamic performance of the rotor.

# 12.5 Velocity Triangles for an Axial Compressor Stage

Velocity triangles are typically used to relate the flow properties and blade design parameters in the relative frame (rotating with the moving blades), to the properties in the stationary or absolute frame.

We begin by “unwrapping” the compressor. That is, we take a cutting plane at a particular radius (e.g. as shown in Figure 12.4) and unwrap it azimuthally to arrive at the diagrams shown in Figure 12.6. Here we have assumed that the area of the annulus through which the flow passes is nearly constant and the density changes are small so that the axial velocity is approximately constant.

In drawing these velocity diagrams it is important to note that the flow typically leaves the trailing edges of the blades at approximately the trailing edge angle in the coordinate frame attached to the blade (i.e. relative frame for the rotor, absolute frame for the stator).

We will now write the Euler Turbine Equation in terms of stage design parameters:  , the rotational speed, and   , the leaving angles of the blades.

From geometry,

and

so

or

So we see that the total or stagnation temperature rise across the stage increases with the tip Mach number squared, and for fixed positive blade angles, decreases with increasing mass flow. This behavior is represented schematically in Figure 12.7.

# 12.6 Velocity Triangles for an Axial Flow Turbine Stage

We can apply the same analysis techniques to a turbine, Figure 12.8. The stator, again does no work. It adds swirl to the flow, converting internal energy into kinetic energy. The turbine rotor then extracts work from the flow by removing the kinetic energy associated with the swirl velocity.

The appropriate velocity triangles are shown in Figure 12.9, where again the axial velocity was assumed to be constant for purposes of illustration. As we did for the compressor, we can write the Euler Turbine Equation in terms of useful design variables:

### Mechanical Engineering Seminar Topics List 4

September 10, 2011

1. 4 WHEEL STEERING
2. AIR_BREATHING_ROCKET_ENGINE
3. AUTOMATIC_TRANSMISSION
4. AUTOMATIC_WATER_SPRINK
5. AUTOMOTIVE_AIR_FILTRATION SYSTEM
6. CAVITATION_IN_CENTRIFUGAL PUMPS
7. “FLEXIBLE (RUBBER) FUEL TANKS
8. AIR_SUSPENSION_SYSTEM
9. SIX_STROKE_ENGINE
11. CAR BIKE COMBO
12. CRUISE CONTROL SYSTEM
13. EURO EMISSION NORMS-A
14. EURO EMISSION NORMS-B
15. FOUR_WHEEL_STEERING_SYSTEM
16. FUTURE OF DIESELS
17. FUTURE OF NUCLEAR ENERGY
18. GAS TURBINE ENGINE
19. GAS TURBINE ENGINE
20. GAS_TURBINE_ENGIN
21. HARD COATING ON TOOLS
22. HOVER- CRAFT
23. HYDRAULIC LAUNCH ASSIST
24. HYDRAULIC SYSTEMS FOR AIRCRAFTS
25. INTELIGENT VEHICLE
26. ION ENGINE
27. JATROPHA SEMINAR
28. MAGNETIC_LEVITATION
29. MAGNETICALLY LEVITATED TRAIN
30. MICROTURBINES
31. NANO-NEW
32. OPTICAL COMPUTER
33. PISTONLESS_PUMP_FOR_ROCKETS
34. PM-ENGINE
35. PNEUMATIC BIKE
36. ROBOT WELDING TECHNOLOGY
37. ROBOTA –A NEW GENERATION
38. SAAB
39. SAFETY SYSTEM IN MODERN AUTOMOBILES
40. SENSOTRONIC BRAKE
41. SIX SIGMA
42. SKY BUS 3
43. SMART_VEHICLES1
44. SOLAR AIR CRAFT
45. SOLAR POWER SATELLITE
46. SOLAR-CHIMNEY
47. STIRLING ENGINE
48. SUGARCANE HARVESTING
49. THERMOACOUSTIC STIRLING ENGINES
50. TURBO_INTERCOOLER
51. VIRTUAL REALITY SHOWROOM
52. VVTI
53. WIND ENERGY TURBINE
55. CARBON NANOTUBES11
56. DTH TV
57. EDGE
58. ELEC-HYDRO-JACK
59. ENERGY FOR TOMORROW
60. FINAL WEB CASTING
61. IMAGE ANALYSIS USING METHEMATICA MORPHOLOGY
62. NIGHT VISION
63. SEZS WORLD-CLASS HUBS FOR EXPORTERS
64. TPM
65. TURBO CODES SEMINAR
66. VIDEO PROCESSING FOR DLP DISPLAY SYSTEMS
67. ELECTRIC POWER STEERING

68. A Study Of a Displacement Amplifier
69. Optimal Design and Analysis Of Automotive Composite Drive Safety
70. 1st Types of Production
71. A case study of management…
72. A design theory based
73. A Fluid-Solid Interaction Model Of The Solid Phase Apiary in stressed silicon layers
74. A High -Torque Magneto-Theological fluid clutch
75. A Hypersonic Hybrid Vehicle
76. Abrasion Wear Characteristic Of Sand Cast
77. Abrasive water jet
78. Acoustic Emission Based Machining Tool Condition Monitoring – An Overview
79. Acoustic Emission Based Machining Tool Condition Monitoring – An Overview
80. Active Suspension System
81. Adaptive Cruise Control for Modern Automobile
83. Advance systems in two wheelers
84. Advances in automobiles (Hybrid Vehicles)
85. AGV for FMS
86. Air Bearing Next Generation Bearings
87. Air birthing Angina
88. Air car
89. Air powered car
90. Air suspension system and its…
91. Alternative abrasive to diamond
92. Alternative fuel
93. Amphibious Army Surveillance Vehicle
94. Artificial Intelligence
95. Artificial Intelligence Future Around Us
96. Artificial intelligence (Modeling air fuel ratio control)
97. Artificial Intelligence in Mechanical field
98. Artificial Intelligence-Present and Future
99. Assembly of Water Cooler
100. Atomic Battery
101. Auto Drilling With Geneva
102. Automated assembly system
103. Automated Guided Vehicles
104. Automatic braking system
105. Automatic Transmission System
106. Automation and Robotics
107. Automation of Foundry for Production quality
108. Automation of Ultrasonic Testing Procedures
109. Automobile AC by Utilizing Waste Heat & Gases
110. Automobile Ac By Utilizing Waste Heat & Gases Advance
111. Automobile Air Conditioning
112. Autonomously Generative CMM Part
113. Balance Of Tool Holder
114. Ball Piston Engine
115. Bike of the future- pneumatic bike
116. Bio diesel : A Fuel for the Future
117. Bio diesel From Jatropha
118. Biogas
119. Biomass as an Alternate Fuel for Diesel Engine
120. Biomass as an Alternate Fuel for Diesel Engine
121. Business Excellence Through Quality Circles
122. Business Process Analysis By BPR
124. CAD & CAE in Bio-Medical Field
125. Caged ball technology
126. Carbon Nano-tubes
127. carbon nanotubes (GCO)
128. Catalytic Converters
129. Centrifugal Pump
130. Ceramic Hybrid Ball Bearing
131. Challenges In Plasma Spray Assembly Of Nano particles To Near Net Shaped Bulk Nano structures
132. Chloro-fluro carbons
133. Cleaning of metal..
134. Clutch lining testing machine
135. COAL GASIFICATION
136. Coating of Carbide Inserts
137. Combing Developments & Their Significance-Mech10
138. Combustion Control Using Optical Fiber
139. Combustion Stability in I.C. Engines
140. Common Rail Injection System
141. Comparison Of Experimental And Finite Element Results For Elastic Plastic Stress
142. Complex system development
143. Compressed Air Cars Technology
144. Computational Fluid Dynamics
145. Computer Aided Production Engineering (CAPE)
146. Computer Integrated Manufacturing-Building the Factory of Future
147. Concentrating Solar Power Energy from Mirrors
148. Concept of flying train
149. Concurrent Engineering
150. Condition Monitoring Of Bearings
151. Condition Monitoring Through Vibration Measurement
152. Consolidation Behavior Of Cu-Co-Fe Pre-Alloyed Powers
153. Constitutive Modeling of Shape Memory Alloy Using Neural Networks
154. Continuous process improvement
155. Control of Cure Distribution in Polymer Composite
156. Control of Cure Distribution in Polymer Composite Parts Made by Laminated Object Fabrication (LOF)
157. Control Systems In Automobiles
158. Convection in Porous Media
159. Cost Effective Safety Instrumented Systems
160. Crop Harvesting Machine
161. Cryogenic Automotive Propulsion Zero Emission Vehicle
162. Cryogenic Processing of Wear Control
163. Cryogenic Rocket Engine & Their Propellants
164. Cummins Diesel Fuel System
165. Design of Efficient Production
166. Design, Implementation, Utilization of FEM
167. Determination of Transmission Spectra Using Ultrasonic NDE
168. Development & Application. Of New Cutting Tool Materials
169. Development in arc welding process using robot
170. Development of an AGV Material Handling System in a Flexible Manufacturing Environment
171. Development of Coated Electrodes For Welding of HSLA Steels
172. Development of hexapod Walking Robot Mechanical Design
173. Development of high performance heat sink based on screen fin tech.
174. Development of Self Lubricating Sintered Steels for Terminological Applications
175. Development of Simple Driver-friendly Electric 4WD System
176. Development of the electrostatic clutch
177. Digital Manufacturing Using STEP-NC
178. Direct Injection Process
179. Distribution Side Management for Urban Electric Utilities in India
180. Dry Sliding Wear Studies On Hybrid MMC’S – A Taguchi Technique
181. Effect of catalytic coating
182. Analysis Of Dimensionless Number For Heat Transfer Enhancements In Rectangular Channels
183. Effect Of Preload On Stability And Performance Of a Two-Lobe Journal Bearing
184. Effect of Pressure On Arc Welding Process
185. Effect Of Stacking Sequence On Notch Strength In Laminates
186. Efficiency In Boring
187. Electronically Controlled Air Suspension System
188. Embedded Applications Design Using Real-Time
189. Energy Engineering Bio diesel
190. Energy Saving Opportunity And Pollution Control In Furnaces
191. Engine & String less car
192. Enterprise Resource Planning
193. Environmental Friendly Refrigeration
194. Ethanol-Future Fuel For Indian Vehicles
195. Exert Quarts In Microprocessor Applications
196. Experimental Analysis of Modified Machine Tools
197. Experimental Stress Analysis For Pipes
198. External Nodes In Finite Element Analysis
199. Failure Analysis Of Lap And Wavy-Lap Composite Bonded Joints
200. Finite Element Analysis Of Robotic Arm For Optimal Work Space Determination
201. Flexible manufacturing system
202. Flying train
203. Frication Welding Of Austenitic Stainless Steel and Optimization of Weld Quality
204. Fuel cell technology
205. Gas Hydrates
206. GAS TURBINE
207. Genetic Algorithm Based Optimum Design Of Composite Drive Shaft
208. Geothermal Energy Utilization
209. Globalization
210. Grid Generation and Simulation Using CFD
211. Guided Missiles
212. H.C.C.I Engine
213. Heat pipe
214. By Forced Convection In Metal Foams
215. Heat transfer
216. HELIUM-A CRYGENICS FLUID
217. Hexapod machine tool
218. High Performance Heat Sink Based on Screen-Fin Technology
219. Hologram
220. Homogeneous combustion in IC engine
221. Human transporter
222. Hybrid engine
223. Hybrid Synergy Drive
224. Hydraulic analysis of hydrostatic bearing of primary sodium pump of a fast breeder reactor
225. HYDROFORMING
226. Hydrogen Car
227. hydrogen fuel cell
228. Hydro-Pneumatics
229. I-Mode
230. Improving service quality..
231. In view of the high commercial gains of a commercial place I
232. Independent Wheel Vehicle Suspension
233. Indian Manufacturing Scenario
234. Industrial Team Behavior and Management Tools
235. Innovation In Automobile Industries
236. Integrated web enabled information…
237. Integration of reinforced
238. Intelligent braking and vehicular..
239. JKJ
240. Job Scheduling Using Neural Network
241. Network Foe Rapid Manufacturing
242. JUST_IN_TIME
243. Kaizen culture
244. KANBAN-AN Integrated JIT System
245. Laser Beam Delivery through Optical Fiber in Laser Machining
246. Laser Machining
247. Laser Micromachining
248. Laser shot preening
249. Latest trends in steering systems
250. Level measurement of bulk solids
251. LEVEL
252. LEVEL MEASUREMENT OF BULK-SOLIDS
253. Liquefied natural gas
254. LNG vehicles
255. Logistics In A Competitive Milieu
256. Machine Vision
257. Machine phase fullerene
258. Machining of Advanced Composites with Abrasive
259. machining technology for….doc
260. Machining technology of leaf spring
261. Magne-gas-The Fuel of Future
262. Magnetic Bearing
263. Magnetic Refrigeration
264. magnetic refrigeration
265. Managerial
266. Manufacturing Of Leaf Spring
267. Master Planning for College Campus
268. MATERIAL BALANCES IN THE MISSILE
269. Materials of the Future
270. Materials of the Future
271. Mechanical seal
272. Mechanics of Composite Materials
273. Mechatronic
274. Mechatronic Strategies for Torque Control of Electric Powered Screwdrivers
275. Mechatronic Strategies for Torque Control of Electric Powered Screwdrivers
276. MECHATRONICS
277. Mechanical Properties Of MMC’S- An Experimental Investigation
278. Medical Application of Nano tech.
279. MEMS
280. Metal deposition
281. Metal Matrix composites
282. Methanol Vehicles
283. Micro air vehicle
284. Micro electro mechanical system
285. Microcellular Foam Technology
286. Micro finishing of rollers in roller bearings
287. Minimum Quantity Lubrication
288. Mission of mars
289. Modeling and Optimization on of Electron Beam Wealing Process Using ANOVA
290. Motronic engine management
291. Multifunction control system for robotic fire detection
292. Nano technology
293. Nano technology Binding experiment with Biosensor
294. Nano technology For Cancer Therapy
295. Nano technology – It’s Small, Small, Small, Small World
297. Near Net Shape Fabrications Via Vacuum Plasma Spray Forming
298. Near net shape memory..
299. Negative Supercharging
300. Non Destructive Testing Of Welds
301. Nuclear fuel
302. Nuclear Space Craft
303. Nuclei’s Next Generation
304. Ny-Tran – Alternative to V Belts
305. Optimizing centrifugal pump
306. Options & Accessories of Car
307. Packaging
308. Piston Ring
309. Pneumatic bike
310. Policies to overcome barriers to the spread of Bio energy technologies in India
311. Power Generation by Using Road Speed Breakers
312. Process steam generation…….
313. Processing and Tribo Behavior Of Nylon Clay Nano composites Under Abrasive Wear Mode
314. Product definition and Role of Aesthetics..
315. PTFE As Lubricant
316. PVD film method
317. Quality Function Deployment (QFD) for TQM
318. Quality in maintenance through TPM
319. Quality Function Deployment
320. Quasi turbine – Future Trends in automobile engine
321. Quieter fans for HVAC
323. Rapid prototyping
324. Rapid Prototyping – Slicing Strategies
325. Rapid Prototyping – Slicing Strategies
326. Rapid prototyping technique based on 3d welding
327. Redesign of plant layout using travel chart technique (a case study)
328. Reduction of idle time through TPM
329. Reliability Redundancy Design-Using
330. Remote engine starting..
331. Renesis Rotary Engine
332. Renewable Energy Design Application In Water Cooler
333. Research On Modified Layers Of Material Surface For Cr Mov Cold Die
334. results of test on laser ignition in internal combustion engine
335. Return of two stroke engine
336. Reverse Engineering
337. Reverse Engineering in Mechanical parts
338. Risk Management
339. Robonaut
340. Robot-by-voice- Experiments on commanding an industrial robot using the human voice
341. Robotics
342. Robotics for Performing Surgical Operations
343. Rotary Engines
344. Safe Handling Of Hc
345. Scope of MEMS in Space
346. Scramjet
347. Scrubber tech.
348. Self Activated Single Use Switch
349. Self replicating system
350. Selling price decision support system for a job order based manufacturing unit
351. Server clustering
352. Set up for Small Scale Industry
353. SEZs World-Class Hubs For Exporters
354. Simulation of Fuel Injection System of System of A Diesel Engine
355. Six – Stroke hybrid engine final
356. Six sigma
357. Six sigma – a quality control tool in industry
358. Six sigma effective process improvement
359. Six Stroke Engine
360. Size Reduction of Window Air Conditioner
361. Size Reduction of Window Air Conditioner
362. Smart tire
363. SMED
364. Software based reengineering..
365. Soil compaction
366. Solar air conditioning
367. Solar aircraft
368. Solar Chimney Power Generation System
369. Solar Energy Conservation to Hydrogen
370. Solar Power Satellite
371. Space Craft Structure
372. Space Elevator
373. Space robotics
374. Space transportation system
375. Spring gauge
376. Sterling engine
377. Sterling engine for co-generation
378. Strategies for product
379. Studies on Phosphoric Irons for Concrete Reinforcement Applications
380. Supply Chain Management
381. Synthesis of Planar Mechanism with Variable Topology – Review
382. System Improvements through TQM
383. Technical development in car
384. Technology of 21st Century Nano Technology
385. The Challenge of Intelligent Systems
386. The Design Of Cellular Manufacturing Systems And Whole Business Simulation
387. The Effects of Precipitate Distributions on HSLA Grain Structure
388. The Gyro Machine
389. Thermal Conductivity Of Poros Material
390. Thermo-electric Refrigeration System
392. Topic On Sng
393. Total Productive Maintenance (TPM)
394. Total Quality Management
395. TQM Implementation Learning form Indian Organizations
396. Transient Thermal Analysis of Railway
397. Tribological characteristics of cutting fluid groups
398. Tribology
399. Tribology of IC engine
400. Tribology of sealing
401. Tribometer
402. Tubeless Tyre Technology
403. Turbine Technology In Car
404. Types Of Bearing
405. Typre Pressure Monitoring System
406. Tyre Monitoring System
407. Ultrasonic Nondestructive Testing
408. Ultrasonic Phased Array For Defect Cartlization
409. Unmanned Aerial Vehicle Uavs
410. Vacuum Chuck
411. Value engineering
412. Variable Compression Ratio (VCR)
413. Variable Compression Ratio Engines
414. VCR
415. Vehicle Dynamics
416. Vehicular Emission Control
417. Vibration Analysis of Flywheel Using Finite Element Analysis
418. Virtual Manufacturing System
419. Virtual Reality Simulation
420. Vrb_Systems
421. Waste heat driven refrigeration and chilling systems.
422. Water Diesel Emulsion with High Injection Press
423. Water Diesel Emulsion with High Injection Press
424. Water as a fuel car
425. Water jet technology
426. What Is A Nuclear Reactor