Axial Turbine Analysis

Size: px
Start display at page:

Download "Axial Turbine Analysis"

Transcription

1 Axal Turbne Analyss From Euler turbomachnery (conservaton) equatons need to Nole understand change n tangental velocty to relate to forces on blades and power m W m rc e rc uc uc e Analye flow n a plane normal to rotatonal axs (cascade plane) to fnd c Rotor Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Cascade Analyss You may have prevously analyed flow over a blade (arfol) but n blade s reference frame Here there are movng (e.g. rotor) and statonary blades e.g., for turbne nole (stator) rotor se velocty trangles to swtch between frames Nole r Mechancs and Thermodynamcs of Propulson, Hll and Peterson Rotor Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved.

2 Velocty Trangles Two reference frames to use for flud velocty engne s c blade s w Dfference due to blade moton c c w u u u w For cascade flow u s n drecton defne angles (,) for each ref. frame c w u Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved., Rotor Velocty Trangles Blade moves n drecton, and n cascade flow for fxed r, let u = w c w c Also have general geometrc relatons e.g., c c sn c tan Therefore c c tan c c w c tan Mechancs and Thermodynamcs of Propulson, Hll and Peterson Nole Rotor c w c w u Turbomachnery - 4 Copyrght 0,07 by Jerry M. Setman. All rghts reserved.

3 Sngle-Stage Characterstcs (Axal Turbne) Goal - determne how turbne performance, e.g., Pr T, affected by changes n operatng condtons Start by analyng sngle-stage turbne Rotor () Euler W R m u c uc m h o ho at fxed W R m c c m h o ho radal locaton c h, o, Nole () W h h So for stage h S h 0 o o c o, o,, Turbomachnery - 5 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Axal Turbne Stage Combnng c c tan ho h, o c,, results c c tan ho, stage c tan c tan assumng constant axal velocty, stage loadng coeff. h o, stage, flow coeffcent c tan tan Hgh output power: W T, produced A nlet c nletc tan tan Turbomachnery - 6 Copyrght 0,07 by Jerry M. Setman. All rghts reserved.

4 Turbne Stage Pressure Rato For adabatc turbne wth TPG/CPG po To To ho, PrT p0 st T o st RTo > as wrtten c h o,, p p o st RT o c o, M blade Stage pressure rato depends on. = f(= r, c, ). blade Mach number M blade =f(r, T o ). st <0 for turbne Turbomachnery - 7 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Turbne Characterstcs For gven M b, blade desgn,, T c PrT M b st tan tan c PrT C C As ncrease flowrate through turbne (at fxed rpm), larger pressure drop (more expanson) s produced more work extracted per unt mass Pr T Hgher M b c Turbomachnery - 8 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. 4

5 Axal Turbne Maps Typcally presented as separate curves for each rpm (M b ) x-axs - replace flow coeffcent wth corrected mass flow rate, recall m A p o RT o at hgh corrected mass flowrate, nole becomes choked Peak effcency around desgn pont Turbomachnery - 9 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. T Pr T /Pr T Mechancs and Thermodynamcs of Propulson, Hll and Peterson Turbomachnery - 0 Blade Desgn: Degree of Reacton We have TWO blade parameters to desgn rotor tralng edge (match ) nole tralng edge (match ) How to do ths?.degree of reacton, R c c.stage ext condton constrant ( ) tan tan c c w w Copyrght 0,07 by Jerry M. Setman. All rghts reserved. c, c tan tan c tan c c w,, c tan c Mechancs and Thermodynamcs of Propulson, Hll and Peterson 5

6 Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Degree of Reacton Recall R h rotor h stage allows us to dstrbute load (statc pressure change) between rotor and nole (or stator) how to relate statc enthalpy change to amuthal velocty changes? KE!! h h v o for statonary blade, no work done h o 0 h KE e.g., nole blade h f c constant, and neglgble c r h c c c c c c c Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Degree of Reacton (Turbne) Rotor blades?? are statonary n rotor s reference frame h h w w Reacton h h h h R h h ho c ho c h w w h h o h o c c R f c c, c tan tan relates desgn blade angles to amuthal KE change c c c w w c tan tan 6

7 R = 0 w w c w,, c tan c, c tan Impulse Turbne h R h all the pressure change occurs across the nole, or the nole creates hgh KE 0 w c tan c tan w w w, w w c tan tan Mechancs and Thermodynamcs of Propulson, Hll and Peterson Turbomachnery - Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Impulse Turbne So for mpulse turbne, blade loadng coeff. Relates blade loadng to nole ext angle tan ho c <0 stage From prevous & velocty trangles, rotor angles gven by tan tan tan c hostage c c tan Mechancs and Thermodynamcs of Propulson, Hll and Peterson Turbomachnery - 4 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. 7

8 Impulse Turbne To let largest power per unt mass flow rate large tends to produce hgh veloctes and p o losses practcal lmt, ~70-75 Further possble constrant no ext swrl (c =0) c c c c c,, c c h o stage tan, tan c c c c c tan Mechancs and Thermodynamcs of Propulson, Hll and Peterson Turbomachnery - 5 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. R 0.5 c 50% Reacton Turbne balanced p drop across stage w w, w w w w c tan c c tan tan h c ostage, c tan f no ext swrl ho stage tan, c c tan, c less convergence n nole w w vs mpulse turbne R c, c, c tan tan Mechancs and Thermodynamcs of Propulson, Hll and Peterson Turbomachnery - 6 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. 8

9 Rocket Turbnes Can combne results for no ext swrl condton to show R ho stage as reacton decreases, power per stage ncreases To mnme se/weght, rocket turbopumps often employ mpulse or low reacton turbnes but effcences typcally lower (<70%) for mpulse turbnes compared to hgher reacton turbnes (~90%) Can mprove effcency by decreasng flow coeffcent (c /) for gven flowrate, requres hgher blade speed, RPM hgher RPM = hgher stresses = heaver, and larger gear rato f geared to pump Turbomachnery - 7 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. Velocty-Compound Impulse Turbne Can ncrease stage power even more usng velocty-compoundng multple nole/rotors n seres Example, two-row compounded mpulse turbne all p n st nole st rotor exts wth hgh swrl (so large allowed) nd nole redrects flow wthout p nd rotor extracts more work and reduces swrl stage loadng s 4x that of sngle-row mpulse stage From Sutton Turbomachnery - 8 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. 9

10 Hghly-Loaded Turbne Effcences Can provde effcency mprovement over sngle row mpulse stage stll lower than hgh reacton turbnes From Hll and Peterson Turbomachnery - 9 Copyrght 0,07 by Jerry M. Setman. All rghts reserved. 0

#64. ΔS for Isothermal Mixing of Ideal Gases

#64. ΔS for Isothermal Mixing of Ideal Gases #64 Carnot Heat Engne ΔS for Isothermal Mxng of Ideal Gases ds = S dt + S T V V S = P V T T V PV = nrt, P T ds = v T = nr V dv V nr V V = nrln V V = - nrln V V ΔS ΔS ΔS for Isothermal Mxng for Ideal Gases

More information

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle

More information

Turbomachinery. Turbines

Turbomachinery. Turbines Turboachinery Turbines Turboachinery -40 Copyright 04,05 by Jerry M. Seitan. ll rights reserved. Turbine Overview Configurations (aial, radial, ied), analysis and other issues siilar to copressors Copared

More information

Outline. Unit Eight Calculations with Entropy. The Second Law. Second Law Notes. Uses of Entropy. Entropy is a Property.

Outline. Unit Eight Calculations with Entropy. The Second Law. Second Law Notes. Uses of Entropy. Entropy is a Property. Unt Eght Calculatons wth Entropy Mechancal Engneerng 370 Thermodynamcs Larry Caretto October 6, 010 Outlne Quz Seven Solutons Second law revew Goals for unt eght Usng entropy to calculate the maxmum work

More information

Week 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2

Week 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2 Lnear omentum Week 8: Chapter 9 Lnear omentum and Collsons The lnear momentum of a partcle, or an object that can be modeled as a partcle, of mass m movng wth a velocty v s defned to be the product of

More information

CHAPTER 6. LAGRANGE S EQUATIONS (Analytical Mechanics)

CHAPTER 6. LAGRANGE S EQUATIONS (Analytical Mechanics) CHAPTER 6 LAGRANGE S EQUATIONS (Analytcal Mechancs) 1 Ex. 1: Consder a partcle movng on a fxed horzontal surface. r P Let, be the poston and F be the total force on the partcle. The FBD s: -mgk F 1 x O

More information

= 1.23 m/s 2 [W] Required: t. Solution:!t = = 17 m/s [W]! m/s [W] (two extra digits carried) = 2.1 m/s [W]

= 1.23 m/s 2 [W] Required: t. Solution:!t = = 17 m/s [W]! m/s [W] (two extra digits carried) = 2.1 m/s [W] Secton 1.3: Acceleraton Tutoral 1 Practce, page 24 1. Gven: 0 m/s; 15.0 m/s [S]; t 12.5 s Requred: Analyss: a av v t v f v t a v av f v t 15.0 m/s [S] 0 m/s 12.5 s 15.0 m/s [S] 12.5 s 1.20 m/s 2 [S] Statement:

More information

Rotor Noise Modeling Kenneth S. Brentner Penn State University

Rotor Noise Modeling Kenneth S. Brentner Penn State University Rotor Nose Modelng Kenneth S. Brentner Penn State Unversty Joby Avaton S4 www.jobyavaton.com 2018 Kenneth S. Brentner. All rghts reserved. 5 th Transformatve Vertcal Flght Workshop, January 18-19, 2018

More information

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force. Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act

More information

Physics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1

Physics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1 P. Guterrez Physcs 5153 Classcal Mechancs D Alembert s Prncple and The Lagrangan 1 Introducton The prncple of vrtual work provdes a method of solvng problems of statc equlbrum wthout havng to consder the

More information

ME 440 Aerospace Engineering Fundamentals

ME 440 Aerospace Engineering Fundamentals Fall 006 ME 440 Aerosace Engneerng Fundamentals roulson hrust Jet Engne F m( & Rocket Engne F m & F ρ A - n ) ρ A he basc rncle nsde the engne s to convert the ressure and thermal energy of the workng

More information

STATISTICAL MECHANICS

STATISTICAL MECHANICS STATISTICAL MECHANICS Thermal Energy Recall that KE can always be separated nto 2 terms: KE system = 1 2 M 2 total v CM KE nternal Rgd-body rotaton and elastc / sound waves Use smplfyng assumptons KE of

More information

PHYS 705: Classical Mechanics. Calculus of Variations II

PHYS 705: Classical Mechanics. Calculus of Variations II 1 PHYS 705: Classcal Mechancs Calculus of Varatons II 2 Calculus of Varatons: Generalzaton (no constrant yet) Suppose now that F depends on several dependent varables : We need to fnd such that has a statonary

More information

Temperature. Chapter Heat Engine

Temperature. Chapter Heat Engine Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the

More information

Conservation of Angular Momentum = "Spin"

Conservation of Angular Momentum = Spin Page 1 of 6 Conservaton of Angular Momentum = "Spn" We can assgn a drecton to the angular velocty: drecton of = drecton of axs + rght hand rule (wth rght hand, curl fngers n drecton of rotaton, thumb ponts

More information

Chapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods

Chapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods Chapter Eght Energy Method 8. Introducton 8. Stran energy expressons 8.3 Prncpal of statonary potental energy; several degrees of freedom ------ Castglano s frst theorem ---- Examples 8.4 Prncpal of statonary

More information

One-sided finite-difference approximations suitable for use with Richardson extrapolation

One-sided finite-difference approximations suitable for use with Richardson extrapolation Journal of Computatonal Physcs 219 (2006) 13 20 Short note One-sded fnte-dfference approxmatons sutable for use wth Rchardson extrapolaton Kumar Rahul, S.N. Bhattacharyya * Department of Mechancal Engneerng,

More information

Chapter 11 Angular Momentum

Chapter 11 Angular Momentum Chapter 11 Angular Momentum Analyss Model: Nonsolated System (Angular Momentum) Angular Momentum of a Rotatng Rgd Object Analyss Model: Isolated System (Angular Momentum) Angular Momentum of a Partcle

More information

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Fall 2012 Fnal Exam Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem

More information

1. Int In e t rnal Losses: tak ta e k place plac in the inner passages adding heat to the flow medium 2. External losses:

1. Int In e t rnal Losses: tak ta e k place plac in the inner passages adding heat to the flow medium 2. External losses: he Losses of urbomachnes 1. Internal Losses: Losses whch take place n the nner passages of the machne and drectly connected wth rotor or flow of the medum and whch are addng heat to the flow medum 2. External

More information

Name: SID: Discussion Session:

Name: SID: Discussion Session: Name: SID: Dscusson Sesson: Chemcal Engneerng Thermodynamcs 141 -- Fall 007 Thursday, November 15, 007 Mdterm II SOLUTIONS - 70 mnutes 110 Ponts Total Closed Book and Notes (0 ponts) 1. Evaluate whether

More information

SWITCHING PROCESS IN LIMITED SLIP DIFFERENTIAL

SWITCHING PROCESS IN LIMITED SLIP DIFFERENTIAL 6th Internatonal DAAAM Baltc Conference INDUSTRIAL ENGINEERING 24-26 Aprl 2008, Tallnn, Estona SWITCHING PROCESS IN LIMITED SLIP DIFFERENTIAL Resev, J.; Roosmölder, L.; Stas, M. Abstract: The energy flow

More information

THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD

THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD Journal of Appled Mathematcs and Computatonal Mechancs 7, 6(3), 7- www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.3. e-issn 353-588 THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS

More information

Calculating the Quasi-static Pressures of Confined Explosions Considering Chemical Reactions under the Constant Entropy Assumption

Calculating the Quasi-static Pressures of Confined Explosions Considering Chemical Reactions under the Constant Entropy Assumption Appled Mechancs and Materals Onlne: 202-04-20 ISS: 662-7482, ol. 64, pp 396-400 do:0.4028/www.scentfc.net/amm.64.396 202 Trans Tech Publcatons, Swtzerland Calculatng the Quas-statc Pressures of Confned

More information

Problem Points Score Total 100

Problem Points Score Total 100 Physcs 450 Solutons of Sample Exam I Problem Ponts Score 1 8 15 3 17 4 0 5 0 Total 100 All wor must be shown n order to receve full credt. Wor must be legble and comprehensble wth answers clearly ndcated.

More information

So far: simple (planar) geometries

So far: simple (planar) geometries Physcs 06 ecture 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap. to 3 Rotatonal quanttes as vectors Cross product Torque epressed as a vector Angular momentum defned Angular momentum as a vector

More information

GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE

GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE Prof. J. N. Mandal Department of cvl engneerng, IIT Bombay, Powa, Mumba 400076, Inda. Tel.022-25767328 emal: cejnm@cvl.tb.ac.n Module - 9 LECTURE - 48

More information

Finite Wings Steady, incompressible flow

Finite Wings Steady, incompressible flow Steady, ncompressble flow Geometrc propertes of a wng - Fnte thckness much smaller than the span and the chord - Defnton of wng geometry: a) Planform (varaton of chord and sweep angle) b) Secton/Arfol

More information

If the solution does not follow a logical thought process, it will be assumed in error.

If the solution does not follow a logical thought process, it will be assumed in error. Group # Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem n the space provded

More information

Week 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product

Week 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product The Vector Product Week 11: Chapter 11 Angular Momentum There are nstances where the product of two vectors s another vector Earler we saw where the product of two vectors was a scalar Ths was called the

More information

COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD

COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,

More information

Chapter 11: Angular Momentum

Chapter 11: Angular Momentum Chapter 11: ngular Momentum Statc Equlbrum In Chap. 4 we studed the equlbrum of pontobjects (mass m) wth the applcaton of Newton s aws F 0 F x y, 0 Therefore, no lnear (translatonal) acceleraton, a0 For

More information

Indeterminate pin-jointed frames (trusses)

Indeterminate pin-jointed frames (trusses) Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all

More information

Frame element resists external loads or disturbances by developing internal axial forces, shear forces, and bending moments.

Frame element resists external loads or disturbances by developing internal axial forces, shear forces, and bending moments. CE7 Structural Analyss II PAAR FRAE EEET y 5 x E, A, I, Each node can translate and rotate n plane. The fnal dsplaced shape has ndependent generalzed dsplacements (.e. translatons and rotatons) noled.

More information

Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1

Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Frank L. H. Wolfs Department of Physcs and Astronomy, Unversty of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Course Informaton: Lab report # 3. Exam # 2. Mult-Partcle

More information

Part C Dynamics and Statics of Rigid Body. Chapter 5 Rotation of a Rigid Body About a Fixed Axis

Part C Dynamics and Statics of Rigid Body. Chapter 5 Rotation of a Rigid Body About a Fixed Axis Part C Dynamcs and Statcs of Rgd Body Chapter 5 Rotaton of a Rgd Body About a Fxed Axs 5.. Rotatonal Varables 5.. Rotaton wth Constant Angular Acceleraton 5.3. Knetc Energy of Rotaton, Rotatonal Inerta

More information

Lecture 16. Chapter 11. Energy Dissipation Linear Momentum. Physics I. Department of Physics and Applied Physics

Lecture 16. Chapter 11. Energy Dissipation Linear Momentum. Physics I. Department of Physics and Applied Physics Lecture 16 Chapter 11 Physcs I Energy Dsspaton Lnear Momentum Course webste: http://aculty.uml.edu/andry_danylov/teachng/physcsi Department o Physcs and Appled Physcs IN IN THIS CHAPTER, you wll learn

More information

PART I: MULTIPLE CHOICE (32 questions, each multiple choice question has a 2-point value, 64 points total).

PART I: MULTIPLE CHOICE (32 questions, each multiple choice question has a 2-point value, 64 points total). CHEMISTRY 123-07 Mdterm #2 answer key November 04, 2010 Statstcs: Average: 68 p (68%); Hghest: 91 p (91%); Lowest: 37 p (37%) Number of students performng at or above average: 58 (53%) Number of students

More information

Study Guide For Exam Two

Study Guide For Exam Two Study Gude For Exam Two Physcs 2210 Albretsen Updated: 08/02/2018 All Other Prevous Study Gudes Modules 01-06 Module 07 Work Work done by a constant force F over a dstance s : Work done by varyng force

More information

Inductance Calculation for Conductors of Arbitrary Shape

Inductance Calculation for Conductors of Arbitrary Shape CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name

More information

EN40: Dynamics and Vibrations. Homework 7: Rigid Body Kinematics

EN40: Dynamics and Vibrations. Homework 7: Rigid Body Kinematics N40: ynamcs and Vbratons Homewor 7: Rgd Body Knematcs School of ngneerng Brown Unversty 1. In the fgure below, bar AB rotates counterclocwse at 4 rad/s. What are the angular veloctes of bars BC and C?.

More information

Module 3: The Whole-Process Perspective for Thermochemical Hydrogen

Module 3: The Whole-Process Perspective for Thermochemical Hydrogen "Thermodynamc Analyss of Processes for Hydrogen Generaton by Decomposton of Water" by John P. O'Connell Department of Chemcal Engneerng Unversty of Vrgna Charlottesvlle, VA 2294-4741 A Set of Energy Educaton

More information

I have not received unauthorized aid in the completion of this exam.

I have not received unauthorized aid in the completion of this exam. ME 270 Sprng 2013 Fnal Examnaton Please read and respond to the followng statement, I have not receved unauthorzed ad n the completon of ths exam. Agree Dsagree Sgnature INSTRUCTIONS Begn each problem

More information

Week 9 Chapter 10 Section 1-5

Week 9 Chapter 10 Section 1-5 Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,

More information

is the calculated value of the dependent variable at point i. The best parameters have values that minimize the squares of the errors

is the calculated value of the dependent variable at point i. The best parameters have values that minimize the squares of the errors Multple Lnear and Polynomal Regresson wth Statstcal Analyss Gven a set of data of measured (or observed) values of a dependent varable: y versus n ndependent varables x 1, x, x n, multple lnear regresson

More information

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS

More information

Increase Decrease Remain the Same (Circle one) (2 pts)

Increase Decrease Remain the Same (Circle one) (2 pts) ME 270 Sample Fnal Eam PROBLEM 1 (25 ponts) Prob. 1 questons are all or nothng. PROBLEM 1A. (5 ponts) FIND: A 2000 N crate (D) s suspended usng ropes AB and AC and s n statc equlbrum. If θ = 53.13, determne

More information

Chapter 3. r r. Position, Velocity, and Acceleration Revisited

Chapter 3. r r. Position, Velocity, and Acceleration Revisited Chapter 3 Poston, Velocty, and Acceleraton Revsted The poston vector of a partcle s a vector drawn from the orgn to the locaton of the partcle. In two dmensons: r = x ˆ+ yj ˆ (1) The dsplacement vector

More information

Vehicle Propulsion Systems Lecture 2. Energy System Overview. W2M Energy Paths. Evaluating the integral. Mechanical Energy Demand of a Cycle

Vehicle Propulsion Systems Lecture 2. Energy System Overview. W2M Energy Paths. Evaluating the integral. Mechanical Energy Demand of a Cycle Vehcle Propulson Systems Lecture 2 Fuel Consumpton Estmaton & ICE Powertrans Lars Erksson Professor Vehcular Systems Lnköpng Unversty March 21, 2017 2 / 51 3 / 51 W2M Energy Paths Energy System Overvew

More information

Design and Analysis of Landing Gear Mechanic Structure for the Mine Rescue Carrier Robot

Design and Analysis of Landing Gear Mechanic Structure for the Mine Rescue Carrier Robot Sensors & Transducers 214 by IFSA Publshng, S. L. http://www.sensorsportal.com Desgn and Analyss of Landng Gear Mechanc Structure for the Mne Rescue Carrer Robot We Juan, Wu Ja-Long X an Unversty of Scence

More information

Optimization of the thermodynamic model of a solar driven Aqua - ammonia absorption refrigeration system

Optimization of the thermodynamic model of a solar driven Aqua - ammonia absorption refrigeration system nd WSEAS/IASME Internatonal Conference on RENEWABLE ENERGY SOURCES (RES') Corfu, Greece, October -, Optmzaton of the thermodynamc model of a solar drven Aqua - ammona absorpton refrgeraton system J. ABDULATEEF,

More information

MEEM 3700 Mechanical Vibrations

MEEM 3700 Mechanical Vibrations MEEM 700 Mechancal Vbratons Mohan D. Rao Chuck Van Karsen Mechancal Engneerng-Engneerng Mechancs Mchgan echnologcal Unversty Copyrght 00 Lecture & MEEM 700 Multple Degree of Freedom Systems (ext: S.S.

More information

Adiabatic Sorption of Ammonia-Water System and Depicting in p-t-x Diagram

Adiabatic Sorption of Ammonia-Water System and Depicting in p-t-x Diagram Adabatc Sorpton of Ammona-Water System and Depctng n p-t-x Dagram J. POSPISIL, Z. SKALA Faculty of Mechancal Engneerng Brno Unversty of Technology Techncka 2, Brno 61669 CZECH REPUBLIC Abstract: - Absorpton

More information

Physics 5153 Classical Mechanics. Principle of Virtual Work-1

Physics 5153 Classical Mechanics. Principle of Virtual Work-1 P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal

More information

Description of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t

Description of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set

More information

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15 NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound

More information

A Tale of Friction Basic Rollercoaster Physics. Fahrenheit Rollercoaster, Hershey, PA max height = 121 ft max speed = 58 mph

A Tale of Friction Basic Rollercoaster Physics. Fahrenheit Rollercoaster, Hershey, PA max height = 121 ft max speed = 58 mph A Tale o Frcton Basc Rollercoaster Physcs Fahrenhet Rollercoaster, Hershey, PA max heght = 11 t max speed = 58 mph PLAY PLAY PLAY PLAY Rotatonal Movement Knematcs Smlar to how lnear velocty s dened, angular

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem n the space

More information

ONE-DIMENSIONAL COLLISIONS

ONE-DIMENSIONAL COLLISIONS Purpose Theory ONE-DIMENSIONAL COLLISIONS a. To very the law o conservaton o lnear momentum n one-dmensonal collsons. b. To study conservaton o energy and lnear momentum n both elastc and nelastc onedmensonal

More information

Pivot-Wheel Drive Crab with a Twist! Clem McKown Team November-2009 (eq 1 edited 29-March-2010)

Pivot-Wheel Drive Crab with a Twist! Clem McKown Team November-2009 (eq 1 edited 29-March-2010) Pvot-Wheel Drve Crab wth a Twst! Clem McKown Team 1640 13-November-2009 (eq 1 edted 29-March-2010) 4-Wheel Independent Pvot-Wheel Drve descrbes a 4wd drve-tran n whch each of the (4) wheels are ndependently

More information

Tensor Analysis. For orthogonal curvilinear coordinates, ˆ ˆ (98) Expanding the derivative, we have, ˆ. h q. . h q h q

Tensor Analysis. For orthogonal curvilinear coordinates, ˆ ˆ (98) Expanding the derivative, we have, ˆ. h q. . h q h q For orthogonal curvlnear coordnates, eˆ grad a a= ( aˆ ˆ e). h q (98) Expandng the dervatve, we have, eˆ aˆ ˆ e a= ˆ ˆ a h e + q q 1 aˆ ˆ ˆ a e = ee ˆˆ ˆ + e. h q h q Now expandng eˆ / q (some of the detals

More information

Uncertainty in measurements of power and energy on power networks

Uncertainty in measurements of power and energy on power networks Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:

More information

Ground Rules. PC1221 Fundamentals of Physics I. Linear Momentum, cont. Linear Momentum. Lectures 17 and 18. Linear Momentum and Collisions

Ground Rules. PC1221 Fundamentals of Physics I. Linear Momentum, cont. Linear Momentum. Lectures 17 and 18. Linear Momentum and Collisions PC Fundamentals of Physcs I Lectures 7 and 8 Lnear omentum and Collsons Dr Tay Seng Chuan Ground Rules Swtch off your handphone and pager Swtch off your laptop computer and keep t No talkng whle lecture

More information

LAGRANGIAN MECHANICS

LAGRANGIAN MECHANICS LAGRANGIAN MECHANICS Generalzed Coordnates State of system of N partcles (Newtonan vew): PE, KE, Momentum, L calculated from m, r, ṙ Subscrpt covers: 1) partcles N 2) dmensons 2, 3, etc. PE U r = U x 1,

More information

Basic concept of reactive flows. Basic concept of reactive flows Combustion Mixing and reaction in high viscous fluid Application of Chaos

Basic concept of reactive flows. Basic concept of reactive flows Combustion Mixing and reaction in high viscous fluid Application of Chaos Introducton to Toshhsa Ueda School of Scence for Open and Envronmental Systems Keo Unversty, Japan Combuston Mxng and reacton n hgh vscous flud Applcaton of Chaos Keo Unversty 1 Keo Unversty 2 What s reactve

More information

Modeling of Dynamic Systems

Modeling of Dynamic Systems Modelng of Dynamc Systems Ref: Control System Engneerng Norman Nse : Chapters & 3 Chapter objectves : Revew the Laplace transform Learn how to fnd a mathematcal model, called a transfer functon Learn how

More information

Formal solvers of the RT equation

Formal solvers of the RT equation Formal solvers of the RT equaton Formal RT solvers Runge- Kutta (reference solver) Pskunov N.: 979, Master Thess Long characterstcs (Feautrer scheme) Cannon C.J.: 970, ApJ 6, 55 Short characterstcs (Hermtan

More information

Abstract. 1 Introduction

Abstract. 1 Introduction Numercal models for unsteady flow n ppe dvdng systems R. Klasnc," H. Knoblauch," R. Mader* ^ Department of Hydraulc Structures and Water Resources Management, Graz Unversty of Technology, A-8010, Graz,

More information

Second Order Analysis

Second Order Analysis Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to

More information

Angular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004

Angular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004 Angular Momentum and Fxed Axs Rotaton 8.01t Nov 10, 2004 Dynamcs: Translatonal and Rotatonal Moton Translatonal Dynamcs Total Force Torque Angular Momentum about Dynamcs of Rotaton F ext Momentum of a

More information

PY2101 Classical Mechanics Dr. Síle Nic Chormaic, Room 215 D Kane Bldg

PY2101 Classical Mechanics Dr. Síle Nic Chormaic, Room 215 D Kane Bldg PY2101 Classcal Mechancs Dr. Síle Nc Chormac, Room 215 D Kane Bldg s.ncchormac@ucc.e Lectures stll some ssues to resolve. Slots shared between PY2101 and PY2104. Hope to have t fnalsed by tomorrow. Mondays

More information

PHYS 705: Classical Mechanics. Newtonian Mechanics

PHYS 705: Classical Mechanics. Newtonian Mechanics 1 PHYS 705: Classcal Mechancs Newtonan Mechancs Quck Revew of Newtonan Mechancs Basc Descrpton: -An dealzed pont partcle or a system of pont partcles n an nertal reference frame [Rgd bodes (ch. 5 later)]

More information

NUMERICAL DIFFERENTIATION

NUMERICAL DIFFERENTIATION NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the

More information

Physics 181. Particle Systems

Physics 181. Particle Systems Physcs 181 Partcle Systems Overvew In these notes we dscuss the varables approprate to the descrpton of systems of partcles, ther defntons, ther relatons, and ther conservatons laws. We consder a system

More information

Module 1 : The equation of continuity. Lecture 1: Equation of Continuity

Module 1 : The equation of continuity. Lecture 1: Equation of Continuity 1 Module 1 : The equaton of contnuty Lecture 1: Equaton of Contnuty 2 Advanced Heat and Mass Transfer: Modules 1. THE EQUATION OF CONTINUITY : Lectures 1-6 () () () (v) (v) Overall Mass Balance Momentum

More information

Elshaboury SM et al.; Sch. J. Phys. Math. Stat., 2015; Vol-2; Issue-2B (Mar-May); pp

Elshaboury SM et al.; Sch. J. Phys. Math. Stat., 2015; Vol-2; Issue-2B (Mar-May); pp Elshabour SM et al.; Sch. J. Phs. Math. Stat. 5; Vol-; Issue-B (Mar-Ma); pp-69-75 Scholars Journal of Phscs Mathematcs Statstcs Sch. J. Phs. Math. Stat. 5; (B):69-75 Scholars Academc Scentfc Publshers

More information

Estimation of Natural Frequency of the Bearing System under Periodic Force Based on Principal of Hydrodynamic Mass of Fluid

Estimation of Natural Frequency of the Bearing System under Periodic Force Based on Principal of Hydrodynamic Mass of Fluid Internatonal Journal o Mechancal and Mechatroncs Engneerng Vol:, No:7, 009 Estmaton o Natural Frequency o the Bearng System under Perodc Force Based on Prncpal o Hydrodynamc Mass o Flud M. H. Pol, A. Bd,

More information

AP Physics 1 & 2 Summer Assignment

AP Physics 1 & 2 Summer Assignment AP Physcs 1 & 2 Summer Assgnment AP Physcs 1 requres an exceptonal profcency n algebra, trgonometry, and geometry. It was desgned by a select group of college professors and hgh school scence teachers

More information

Equilibrium and stability of toroidal plasmas with flow in high-beta reduced MHD

Equilibrium and stability of toroidal plasmas with flow in high-beta reduced MHD Equlbrum and stablty of torodal plasmas wth flow n hgh-beta reduced MHD Atsush Ito and Noryosh Nakajma Natonal Insttute for Fuson Scence Equlbrum wth flow n extended MHD models of fuson plasmas Equlbrum

More information

More metrics on cartesian products

More metrics on cartesian products More metrcs on cartesan products If (X, d ) are metrc spaces for 1 n, then n Secton II4 of the lecture notes we defned three metrcs on X whose underlyng topologes are the product topology The purpose of

More information

Comparison of Novel Identification Method of Suspension Force Parameters and the Conventional Identification Method in Bearingless Motors

Comparison of Novel Identification Method of Suspension Force Parameters and the Conventional Identification Method in Bearingless Motors Comparson of Novel Identfcaton ethod of Suspenson orce Parameters and the Conventonal Identfcaton ethod n Bearngless otors Yuma Otsu, Kouk Nakaya, Kmo Hjkata and Yasuhro Tanaka Department of echancal Systems

More information

Chapter 3 Thermochemistry of Fuel Air Mixtures

Chapter 3 Thermochemistry of Fuel Air Mixtures Chapter 3 Thermochemstry of Fuel Ar Mxtures 3-1 Thermochemstry 3- Ideal Gas Model 3-3 Composton of Ar and Fuels 3-4 Combuston Stochometry t 3-5 The1 st Law of Thermodynamcs and Combuston 3-6 Thermal converson

More information

Energy, Entropy, and Availability Balances Phase Equilibria. Nonideal Thermodynamic Property Models. Selecting an Appropriate Model

Energy, Entropy, and Availability Balances Phase Equilibria. Nonideal Thermodynamic Property Models. Selecting an Appropriate Model Lecture 4. Thermodynamcs [Ch. 2] Energy, Entropy, and Avalablty Balances Phase Equlbra - Fugactes and actvty coeffcents -K-values Nondeal Thermodynamc Property Models - P-v-T equaton-of-state models -

More information

The Design and Analysis of Helium Turbine Expander Impeller with a Given All-Over-Controlled Vortex Distribution

The Design and Analysis of Helium Turbine Expander Impeller with a Given All-Over-Controlled Vortex Distribution Plasma Scence and Technology, Vol.16, No.3, Mar. 214 The Desgn and Analyss of Helum Turbne Expander Impeller wth a Gven All-Over-Controlled Vortex Dstrbuton LIU Xaodong ( ), FU Bao ( ), ZHUANG Mng ( )

More information

( ) = ( ) + ( 0) ) ( )

( ) = ( ) + ( 0) ) ( ) EETOMAGNETI OMPATIBIITY HANDBOOK 1 hapter 9: Transent Behavor n the Tme Doman 9.1 Desgn a crcut usng reasonable values for the components that s capable of provdng a tme delay of 100 ms to a dgtal sgnal.

More information

Structure and Drive Paul A. Jensen Copyright July 20, 2003

Structure and Drive Paul A. Jensen Copyright July 20, 2003 Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.

More information

Principles of Food and Bioprocess Engineering (FS 231) Solutions to Example Problems on Heat Transfer

Principles of Food and Bioprocess Engineering (FS 231) Solutions to Example Problems on Heat Transfer Prncples of Food and Boprocess Engneerng (FS 31) Solutons to Example Problems on Heat Transfer 1. We start wth Fourer s law of heat conducton: Q = k A ( T/ x) Rearrangng, we get: Q/A = k ( T/ x) Here,

More information

Report on Image warping

Report on Image warping Report on Image warpng Xuan Ne, Dec. 20, 2004 Ths document summarzed the algorthms of our mage warpng soluton for further study, and there s a detaled descrpton about the mplementaton of these algorthms.

More information

Finite Element Modelling of truss/cable structures

Finite Element Modelling of truss/cable structures Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures

More information

The equation of motion of a dynamical system is given by a set of differential equations. That is (1)

The equation of motion of a dynamical system is given by a set of differential equations. That is (1) Dynamcal Systems Many engneerng and natural systems are dynamcal systems. For example a pendulum s a dynamcal system. State l The state of the dynamcal system specfes t condtons. For a pendulum n the absence

More information

Physics 111: Mechanics Lecture 11

Physics 111: Mechanics Lecture 11 Physcs 111: Mechancs Lecture 11 Bn Chen NJIT Physcs Department Textbook Chapter 10: Dynamcs of Rotatonal Moton q 10.1 Torque q 10. Torque and Angular Acceleraton for a Rgd Body q 10.3 Rgd-Body Rotaton

More information

EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st

EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to

More information

JJMIE Jordan Journal of Mechanical and Industrial Engineering

JJMIE Jordan Journal of Mechanical and Industrial Engineering JJMIE Jordan Journal of Mechancal and Industral Engneerng Volume 11 Number 4, December. 2017 ISSN 1995-6665 Pages 235-243 Modelng and Smulaton of Shrouded Horzontal Axs Wnd Turbne Usng RANS Method C. Ghena

More information

and Statistical Mechanics Material Properties

and Statistical Mechanics Material Properties Statstcal Mechancs and Materal Propertes By Kuno TAKAHASHI Tokyo Insttute of Technology, Tokyo 15-855, JAPA Phone/Fax +81-3-5734-3915 takahak@de.ttech.ac.jp http://www.de.ttech.ac.jp/~kt-lab/ Only for

More information

Rotordynamic coe cients for labyrinth gas seals: single control volume model

Rotordynamic coe cients for labyrinth gas seals: single control volume model Rotordynamc coe cents for labyrnth gas seals: sngle control volume model R. MALVANO C.N.R. Centro Stud Dnamca Flud F. VATTA and A. VIGLIANI (alessandro.vglan@polto.t) Poltecnco d Torno Dpartmento d Meccanca

More information

Page 1. SPH4U: Lecture 7. New Topic: Friction. Today s Agenda. Surface Friction... Surface Friction...

Page 1. SPH4U: Lecture 7. New Topic: Friction. Today s Agenda. Surface Friction... Surface Friction... SPH4U: Lecture 7 Today s Agenda rcton What s t? Systeatc catagores of forces How do we characterze t? Model of frcton Statc & Knetc frcton (knetc = dynac n soe languages) Soe probles nvolvng frcton ew

More information

Physics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.

Physics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding. Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays

More information

CinChE Problem-Solving Strategy Chapter 4 Development of a Mathematical Model. formulation. procedure

CinChE Problem-Solving Strategy Chapter 4 Development of a Mathematical Model. formulation. procedure nhe roblem-solvng Strategy hapter 4 Transformaton rocess onceptual Model formulaton procedure Mathematcal Model The mathematcal model s an abstracton that represents the engneerng phenomena occurrng n

More information