GeoSteamNet: 2. STEAM FLOW SIMULATION IN A PIPELINE
|
|
- Rosamund Blair
- 6 years ago
- Views:
Transcription
1 PROCEEDINGS, Thrty-Ffth Workshop on Geothermal Reservor Engneerng Stanford Unversty, Stanford, Calforna, February 1-3, 010 SGP-TR-188 GeoSteamNet:. STEAM FLOW SIMULATION IN A PIPELINE Mahendra P. Verma and Vctor Arellano G. Geoterma, Insttuto de Investgacones Eléctrcas Av. Reforma 113, Col. Palmra Cuernavaca, Morelos, 6490, Méxco e-mal: mahendra@e.org.mx ABSTRACT A computer program s developed to smulate steam flow n a ppelne as a part of GeoSteamNet: a computer package for the smulaton of steam flow n a geothermal power plant network. The flud movement s governed by the followng basc prncples: the conservaton of mass, the lnear momentum prncple (Newton s second law or Naver Stokes equatons) and the frst and second laws of thermodynamcs. The second law of thermodynamcs defnes the drecton of a spontaneous process, whch s ndrectly valdated n the algorthm as steam flows from hgh to low pressure and heat flows from hgh to low temperature. The nonlnear equatons are solved wth the Newton-Raphson method. A comparatve study on the varaton of temperature, pressure and heat loss n a ppelne of length 1000 m, nner dameter 0.3 m and thckness m s presented. Three cases are dscussed: a) no conducton-convecton heat loss, b) an nsulaton of 0.05 m thckness on the ppelne and c) maxmum heat loss (.e. no nsulaton). The change n pressure s same n the three cases whereas there s apprecable temperature drop even n the case a. Smlarly, there s 36% densty change n the case b, whch s a restrcton to use the Bernoull s equaton for steam flow smulaton. INTRODUCTION Knowledge of numercal smulaton of steam flow n a ppelne network of geothermal system s vtal for ratonalzaton and optmzaton of steam used for electrcal energy generaton (Ruíz et al. 010). Presently, we are workng on two mportant aspects of the project: a) thermodynamc data of water and b) approprate algorthm for steam flow n a ppelne. The second aspect wll be dscussed here. The flud flow s mostly analyzed by two equatons: mass-balance (contnuty equaton) and momentum balance (Newton s second law of moton or Naver Stokes equatons) n stuatons where the flud may be treated as ncompressble and temperature dfferences are small (Mazumdar, 009). Bhave and Gupta (006) presented a comprehensve textbook on the analyss of water dstrbuton n a muncpal network. The water flow n a ppelne network s successfully modeled wth the Bernoull s theorem and Hardy Cross method. In the crcumstances when flow s compressble (densty s not constant), or occurrence of heat flux (temperature s not constant), there s need of at least one more equaton: energy balance. Smth and van Ness (1975) presented the dervaton of all the three equatons for flud flow. In ths artcle an algorthm s developed to solve numercally the three equatons: mass, momentum and energy balance for steam flow n a ppelne. An example s presented for steam flow n a ppelne of 1000 m long for three cases: a) no heat loss, b) heat loss for gven characterstcs of ppe and nsulaton of t and c) maxmum heat loss (.e. no nsulaton). FUNDAMENTAL EQUATIONS The movement of flud n a system s governed by the followng basc prncples: conservaton of mass, the lnear momentum prncple (Newton s second law or Naver Stokes equatons) and the frst and second laws of thermodynamcs (smth and Van Ness, 1975). The second law of thermodynamcs defnes the drecton of a spontaneous process. In the ppelne network of geothermal power plant the steam flows from hgh to low pressure and heat flows from hgh to low temperature. Thus the second law of thermodynamcs s ndrectly valdated and wll not be consdered here. Majumdar (1999) developed a general purpose computer program Generalzed Flud System Smulaton Program (GFSSP) to compute pressure and flow dstrbuton n a complex flud network
2 dl m -1, T -1, P -1 m, T, P.. Q Z -1 Z r 1 r r 3 Fgure. 1. Schematc dagram of th control volume element of a ppelne. The steam flow rate at the node -1 and are and, respectvely. Z s elevaton. T and P represent temperature and pressure, respectvely. The cross-sectonal vew of the element shows the postve heat flux Q. r 1, r and r 3 are rad of nner and outer part of the ppelne, and outer part of the nsulaton over t, respectvely. ncludng unsteady state and angular flow. In the geothermal power plant we are nterested n undrectonal steady state steam flow. The followng equatons wll be consdered for steam flow n a ppelne (Smth and van Ness, 1975): Contnuty Equaton The contnuty equaton (conservaton of mass) for steady state flow s ρ (1) u r = 0 where ρ s densty and u r s velocty. Fgure 1 shows a schematc dagram of th control volume element between nodes -1 and. The fnte dfference dscretzaton (Patanker, 1980) of contnuty equaton s expressed as ρ u () = ρ 1u 1 The subscrpt and -1 represent the values at the respect node. Conservaton of Energy The equaton of the conservaton of energy s expressed as u H + + gz = Q W s (3) where Q s the amount of heat per unt mass gven to the element from surroundngs. W s s shaft work per unt mass. H s enthalpy per unt mass and Z s the elevaton from the reference datum lne. Fgure 1 also presents a cross-sectonal vew of ppelne. The rate of heat transfer to the control volume element from the surroundngs s gven by H T = 1 hnr1 dl( Tn Tout ) ( r r ) ln( r r ) π (4) ln k k h r A A out 3 Where r 1, r, and r 3 are rad as shown n Fgure 1. k A and k B are thermal conductvtes of ppelne and nsulaton over t, respectvely. h n s the convectve heat transfer coeffcent between steam and nner part of the ppelne. Smlarly, h out s the convectve heat transfer coeffcent between outer part of nsulaton and surroundng ar. T n and T out are the temperature of nner steam and outer ar, respectvely. We are nterested n the steady state flow. So, the heat transferred to the control element wll be transferred to the nflowng flud. Thus the heat added (gven) to per unt mass of nflowng flud s H = T dl Q 1 + m& u The dscretzaton of energy equaton s u u 1 H H g 1 = Conservaton of Lnear Momentum ( Z Z ) Q (5) (6) The conservaton of lnear momentum may be wrtten as VdP + udu + gdz + df = 0 (7) For both lamnar and turbulent flow the energy loss due to frcton s expressed wth the Fannng equaton
3 Table 1: Data used for the present modelng of steam flow n a ppelne. Parameter Value Ppelne Length (m) Inner dameter (m) 0.3 Thckness (m) Thermal conductvty (W/m K) 80. Roughness (m) x10-7 Temperature (K) No Heat Loss Gven Data Maxmum Heat loss a Insulaton Thckness (m) 0.05 Thermal conductvty (W/m K) Convectve heat transfer coeffcent Steam and ppelne (W/m K) 30.0 Insulaton and ar (W/m K) 6.0 Inflow saturated steam Temperature (K) Mass flow rate (kg/s) 10.0 Ar temperature (K) Horzontal ppelne (Z=0) Pressure (Pa) b c fu df = dl (8) D Thus the dscretzaton of momentum equaton s % Energy loss ρ ρ 1 u 1 ( p p ) + + g( Z Z ) 1 u fuu + D 1 dl = 0 1 The dealzatons mposed n the dervaton of these equatons are descrbed n the Chapter 10 of book by Smth and van Ness (1975). A comprehensve and systematc numercal soluton approach s adapted from Patanker (1980) and Majumdar (1999). The system of nonlnear equatons s solved wth Newton- Raphson method. PROGRAM DESCRIPTION The computer program, PpeCalc s wrtten n Vsual Basc 6.0. The thermodynamc data of water are calculated from an ActveX control, SteamTablesGrd (Verma, 010) nstead of ActveX component, SteamTables (Verma, 003). (9) Dstance along ppelne (m) Fgure.. Calculated values of temperature, pressure and energy loss for three cases: a) no conducton-convecton heat loss, b) an nsulaton of 0.05 m thckness on the ppelne and c) maxmum heat loss (.e. no nsulaton). Densty (kg/ m 3 ) Dstance along ppelne (m) Fgure. 3. Varaton of densty for case b, when there s nsulaton over the ppelne. The change n densty s 36% whch s a restrcton to use the Bernoull s equaton for steam flow smulaton.
4 A structured varable s defned as ppe, whch stores all the nput and calculated parameters n t. The advantage of ths approach s that t s straght forward to create ActveX control. Our fnal goal s to create ActveX controls for every component of a ppelne network of geothermal system and a graphc user nterface. Ths way the program wll be a general purpose computer code for analyzng steady state flow n any geothermal ppelne network. AN EXAMPLE To llustrate the applcablty of PpeCalc an example s presented here. A horzontal ppelne of 1000 m s consdered. All the nput parameters are gven n Table 1. The ppelne s dvded nto 100 elements (.e. the length of each segment s 10.0 m). We performed prelmnary calculatons for the segment length of 1.0, 10.0 and m. The results were n agreement for the segment length 1.0 and 10.0 m. A small segment length ncreases the accuracy n the calculated values, but t also ncreases the executon tme. So, one has to perform always some prelmnary calculaton to optmze the values of dfferent nput parameters accordng to confdence lmts of ther measured data. Ths can speed up the further calculatons to obtan relable results. Fgure shows the varaton of temperature, pressure and energy loss along the ppelne for three cases: a) no conducton-convecton heat loss, b) an nsulaton of 0.05 m thckness on the ppelne wth parameters gven n Table 1 and c) maxmum heat loss (.e. no nsulaton). The decrease n temperature s hghest for case c. There s a formaton of lqud water from the pont entrance of steam nto the ppelne and the condtons of temperature and pressure are along the saturaton curve. There s no formaton of lqud water n cases a and b and the system s n the superheated steam regon. The velocty of steam flow s approxmately 30 m/s. It means that the steam flows from one end to other wthn 35 s. Fgure c shows the loss energy for the three cases. It can be observed that there s about 3% energy loss wthn 35 s when there s no nsulaton on the ppelne (case c). One more pont to be emphaszed s that there s substantal decrease n temperature (11 K) even when there s no heat loss (case a). Ths decrease n temperature s assocated wth the expanson of vapor durng ts flow through the ppelne. Fgure 3 shows the varaton n the densty of steam for case b. It s 36 %. It means that the Bernoull s equaton has lmtatons to model steam flow n a ppelne. CONCLUSIONS The program PpeCalc s wrtten n Vsual Basc 6.0. The algorthm s based on the conservaton of mass, the lnear momentum prncple (Newton s second law or Naver Stokes equatons) and the frst law of thermodynamcs. The second law of thermodynamcs defnes the drecton of a spontaneous process. In the ppelne network of geothermal power plant the steam flows from hgh to low pressure and heat flows from hgh to low temperature. Thus the second law of thermodynamcs s ndrectly valdated. The nonlnear equatons are solved wth the Newton- Raphson method. The results obtaned from a numercal smulaton of steam flow n a ppelne for the three cases: a) no conducton-convecton heat loss, b) an nsulaton of 0.05 m thckness on the ppelne and c) maxmum heat loss (.e. no nsulaton) may be stated as: There s decrease n the temperature and pressure of steam along the ppelne even when there s no heat loss. It s assocated wth the expanson of steam durng ts flow. A decrease of 36 % n the densty of steam ndcates that the use of Bernoull s equaton for steam flow smulaton has certan lmtatons. Steam flow n ppelne s very fast. It takes about 35 s to travel 1000 m. In flud mechancs many emprcal relatons are used whch are based on the correlaton studes of expermental data. Therefore, the calbraton of a numercal model for the system to be studed s crucal. We performed the smulaton for a hypothetcal case. For a calbraton we need to consder real measurements. Presently, we are workng on the mplementaton of ths numercal approach for a geothermal ppelne network. It conssts of ncludng all the components lke valve, expanson-reducton, jont, etc. ACKNOWLEDGEMENTS Ths work was conducted under the project GeoSteamNet: a computer package for steam flow smulaton n a ppelne network, funded by our Insttute.
5 REFERENCES Bhave, P.R. and Gupta, R. (006), Analyss of Water Dstrbuton Networks Narosa Publshng House, Inda. Majumdar, A. (1999), Generalzed Flud System Smulaton Program (GFSSP) Verson 3.0, Report No. MG-99-90, NASA, USA. Patanker, S.V. (1980), Numercal Heat Transfer and Flud Flow, Hemsphere Publshng Corporaton, USA, 197p. Ruíz, A., Mendoza, A., Verma, M.P., García, A., Martínez, J.I. and Arellano, V. (010), Steam flow Balance n the Los Azufres Geothermal System, Mexco, Proc. World Geothermal Congress, n press. Smth, J.M. and Van Ness, H.C. (1975), Introducton to Chemcal Engneerng Thermodynamcs, 3 rd Ed., McGraw-Hll Kogakusha, Ltd., 63p. Verma, M. P. (003), Steam Tables for pure water as an ActveX component n Vsual Basc 6.0, Computer & Geoscences, 9, Verma, M.P. (010), GeoSteamNet: 1. Thermodynamc data for steam flow n a ppelne network of geothermal system Ths volume.
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 informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationModule 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 informationTHE 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 informationAirflow and Contaminant Simulation with CONTAM
Arflow and Contamnant Smulaton wth CONTAM George Walton, NIST CHAMPS Developers Workshop Syracuse Unversty June 19, 2006 Network Analogy Electrc Ppe, Duct & Ar Wre Ppe, Duct, or Openng Juncton Juncton
More information2 Finite difference basics
Numersche Methoden 1, WS 11/12 B.J.P. Kaus 2 Fnte dfference bascs Consder the one- The bascs of the fnte dfference method are best understood wth an example. dmensonal transent heat conducton equaton T
More informationSTUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS
Blucher Mechancal Engneerng Proceedngs May 0, vol., num. www.proceedngs.blucher.com.br/evento/0wccm STUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS Takahko Kurahash,
More informationLecture 5.8 Flux Vector Splitting
Lecture 5.8 Flux Vector Splttng 1 Flux Vector Splttng The vector E n (5.7.) can be rewrtten as E = AU (5.8.1) (wth A as gven n (5.7.4) or (5.7.6) ) whenever, the equaton of state s of the separable form
More informationONE DIMENSIONAL TRIANGULAR FIN EXPERIMENT. Technical Advisor: Dr. D.C. Look, Jr. Version: 11/03/00
ONE IMENSIONAL TRIANGULAR FIN EXPERIMENT Techncal Advsor: r..c. Look, Jr. Verson: /3/ 7. GENERAL OJECTIVES a) To understand a one-dmensonal epermental appromaton. b) To understand the art of epermental
More informationOutline. 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 informationCHAPTER 7 ENERGY BALANCES SYSTEM SYSTEM. * What is energy? * Forms of Energy. - Kinetic energy (KE) - Potential energy (PE) PE = mgz
SYSTM CHAPTR 7 NRGY BALANCS 1 7.1-7. SYSTM nergy & 1st Law of Thermodynamcs * What s energy? * Forms of nergy - Knetc energy (K) K 1 mv - Potental energy (P) P mgz - Internal energy (U) * Total nergy,
More informationA Numerical Study of Heat Transfer and Fluid Flow past Single Tube
A Numercal Study of Heat ransfer and Flud Flow past Sngle ube ZEINAB SAYED ABDEL-REHIM Mechancal Engneerng Natonal Research Center El-Bohos Street, Dokk, Gza EGYP abdelrehmz@yahoo.com Abstract: - A numercal
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More information(Online First)A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate
Internatonal Journal of Mathematcs and Systems Scence (018) Volume 1 do:10.494/jmss.v1.815 (Onlne Frst)A Lattce Boltzmann Scheme for Dffuson Equaton n Sphercal Coordnate Debabrata Datta 1 *, T K Pal 1
More informationIrregular vibrations in multi-mass discrete-continuous systems torsionally deformed
(2) 4 48 Irregular vbratons n mult-mass dscrete-contnuous systems torsonally deformed Abstract In the paper rregular vbratons of dscrete-contnuous systems consstng of an arbtrary number rgd bodes connected
More informationThe Analysis of Convection Experiment
Internatonal Conference on Appled Scence and Engneerng Innovaton (ASEI 5) The Analyss of Convecton Experment Zlong Zhang School of North Chna Electrc Power Unversty, Baodng 7, Chna 469567@qq.com Keywords:
More informationNumerical Transient Heat Conduction Experiment
Numercal ransent Heat Conducton Experment OBJECIVE 1. o demonstrate the basc prncples of conducton heat transfer.. o show how the thermal conductvty of a sold can be measured. 3. o demonstrate the use
More informationEXAMPLES of THEORETICAL PROBLEMS in the COURSE MMV031 HEAT TRANSFER, version 2017
EXAMPLES of THEORETICAL PROBLEMS n the COURSE MMV03 HEAT TRANSFER, verson 207 a) What s eant by sotropc ateral? b) What s eant by hoogeneous ateral? 2 Defne the theral dffusvty and gve the unts for the
More informationPES 1120 Spring 2014, Spendier Lecture 6/Page 1
PES 110 Sprng 014, Spender Lecture 6/Page 1 Lecture today: Chapter 1) Electrc feld due to charge dstrbutons -> charged rod -> charged rng We ntroduced the electrc feld, E. I defned t as an nvsble aura
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationHEAT TRANSFER THROUGH ANNULAR COMPOSITE FINS
Journal of Mechancal Engneerng and Technology (JMET) Volume 4, Issue 1, Jan-June 2016, pp. 01-10, Artcle ID: JMET_04_01_001 Avalable onlne at http://www.aeme.com/jmet/ssues.asp?jtype=jmet&vtype=4&itype=1
More informationPhysics 3 (PHYF144) Chap 2: Heat and the First Law of Thermodynamics System. Quantity Positive Negative
Physcs (PHYF hap : Heat and the Frst aw of hermodynamcs -. Work and Heat n hermodynamc Processes A thermodynamc system s a system that may exchange energy wth ts surroundngs by means of heat and work.
More informationInductance 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 informationThermal-Fluids I. Chapter 18 Transient heat conduction. Dr. Primal Fernando Ph: (850)
hermal-fluds I Chapter 18 ransent heat conducton Dr. Prmal Fernando prmal@eng.fsu.edu Ph: (850) 410-6323 1 ransent heat conducton In general, he temperature of a body vares wth tme as well as poston. In
More informationAdiabatic 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 informationA PROCEDURE FOR SIMULATING THE NONLINEAR CONDUCTION HEAT TRANSFER IN A BODY WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY.
Proceedngs of the th Brazlan Congress of Thermal Scences and Engneerng -- ENCIT 006 Braz. Soc. of Mechancal Scences and Engneerng -- ABCM, Curtba, Brazl,- Dec. 5-8, 006 A PROCEDURE FOR SIMULATING THE NONLINEAR
More informationComparative Studies of Law of Conservation of Energy. and Law Clusters of Conservation of Generalized Energy
Comparatve Studes of Law of Conservaton of Energy and Law Clusters of Conservaton of Generalzed Energy No.3 of Comparatve Physcs Seres Papers Fu Yuhua (CNOOC Research Insttute, E-mal:fuyh1945@sna.com)
More informationDETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM
Ganj, Z. Z., et al.: Determnaton of Temperature Dstrbuton for S111 DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM by Davood Domr GANJI
More informationEN40: 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 informationIntroduction to Computational Fluid Dynamics
Introducton to Computatonal Flud Dynamcs M. Zanub 1, T. Mahalakshm 2 1 (PG MATHS), Department of Mathematcs, St. Josephs College of Arts and Scence for Women-Hosur, Peryar Unversty 2 Assstance professor,
More informationCinChE 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 informationOpen Systems: Chemical Potential and Partial Molar Quantities Chemical Potential
Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,
More informationModule 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 informationApplication of B-Spline to Numerical Solution of a System of Singularly Perturbed Problems
Mathematca Aeterna, Vol. 1, 011, no. 06, 405 415 Applcaton of B-Splne to Numercal Soluton of a System of Sngularly Perturbed Problems Yogesh Gupta Department of Mathematcs Unted College of Engneerng &
More informationWeek3, 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 informationin a horizontal wellbore in a heavy oil reservoir
498 n a horzontal wellbore n a heavy ol reservor L Mngzhong, Wang Ypng and Wang Weyang Abstract: A novel model for dynamc temperature dstrbuton n heavy ol reservors s derved from and axal dfference equatons
More informationElectrical double layer: revisit based on boundary conditions
Electrcal double layer: revst based on boundary condtons Jong U. Km Department of Electrcal and Computer Engneerng, Texas A&M Unversty College Staton, TX 77843-318, USA Abstract The electrcal double layer
More information829. An adaptive method for inertia force identification in cantilever under moving mass
89. An adaptve method for nerta force dentfcaton n cantlever under movng mass Qang Chen 1, Mnzhuo Wang, Hao Yan 3, Haonan Ye 4, Guola Yang 5 1,, 3, 4 Department of Control and System Engneerng, Nanng Unversty,
More informationNote 10. Modeling and Simulation of Dynamic Systems
Lecture Notes of ME 475: Introducton to Mechatroncs Note 0 Modelng and Smulaton of Dynamc Systems Department of Mechancal Engneerng, Unversty Of Saskatchewan, 57 Campus Drve, Saskatoon, SK S7N 5A9, Canada
More informationA large scale tsunami run-up simulation and numerical evaluation of fluid force during tsunami by using a particle method
A large scale tsunam run-up smulaton and numercal evaluaton of flud force durng tsunam by usng a partcle method *Mtsuteru Asa 1), Shoch Tanabe 2) and Masaharu Isshk 3) 1), 2) Department of Cvl Engneerng,
More informationResearch & Reviews: Journal of Engineering and Technology
Research & Revews: Journal of Engneerng and Technology Case Study to Smulate Convectve Flows and Heat Transfer n Arcondtoned Spaces Hussen JA 1 *, Mazlan AW 1 and Hasanen MH 2 1 Department of Mechancal
More informationHigher Order Wall Boundary Conditions for Incompressible Flow Simulations
THE 5 TH ASIAN COMPUTAITIONAL FLUID DYNAMICS BUSAN KOREA OCTOBER 7-30 003 Hgher Order Wall Boundary Condtons for Incompressble Flow Smulatons Hdetosh Nshda. Department of Mechancal and System Engneerng
More informationCHAPTER 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 informationUncertainty 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 informationTHE IGNITION PARAMETER - A quantification of the probability of ignition
THE IGNITION PARAMETER - A quantfcaton of the probablty of ton INFUB9-2011 Topc: Modellng of fundamental processes Man author Nels Bjarne K. Rasmussen Dansh Gas Technology Centre (DGC) NBR@dgc.dk Co-author
More informationEnergy configuration optimization of submerged propeller in oxidation ditch based on CFD
IOP Conference Seres: Earth and Envronmental Scence Energy confguraton optmzaton of submerged propeller n oxdaton dtch based on CFD To cte ths artcle: S Y Wu et al 01 IOP Conf. Ser.: Earth Envron. Sc.
More informationFluid structure interaction analysis of a high-pressure regulating valve of a 600-MW ultra-supercritical steam turbine
Orgnal Artcle Flud structure nteracton analyss of a hgh-pressure regulatng valve of a 600-MW ultra-supercrtcal steam turbne Proc IMechE Part A: J Power and Energy 0(0) 1 10! IMechE 2015 Reprnts and permssons:
More informationmodeling of equilibrium and dynamic multi-component adsorption in a two-layered fixed bed for purification of hydrogen from methane reforming products
modelng of equlbrum and dynamc mult-component adsorpton n a two-layered fxed bed for purfcaton of hydrogen from methane reformng products Mohammad A. Ebrahm, Mahmood R. G. Arsalan, Shohreh Fatem * Laboratory
More information#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 informationFORCED CONVECTION HEAT TRANSFER FROM A RECTANGULAR CYLINDER: EFFECT OF ASPECT RATIO
ISTP-,, PRAGUE TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA FORCED CONVECTION HEAT TRANSFER FROM A RECTANGULAR CYLINDER: EFFECT OF ASPECT RATIO Mohammad Rahnama*, Seyed-Mad Hasheman*, Mousa Farhad**
More informationThe Governing Equations
The Governng Equatons L. Goodman General Physcal Oceanography MAR 555 School for Marne Scences and Technology Umass-Dartmouth Dynamcs of Oceanography The Governng Equatons- (IPO-7) Mass Conservaton and
More informationUncertainty and auto-correlation in. Measurement
Uncertanty and auto-correlaton n arxv:1707.03276v2 [physcs.data-an] 30 Dec 2017 Measurement Markus Schebl Federal Offce of Metrology and Surveyng (BEV), 1160 Venna, Austra E-mal: markus.schebl@bev.gv.at
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
More informationImplicit Integration Henyey Method
Implct Integraton Henyey Method In realstc stellar evoluton codes nstead of a drect ntegraton usng for example the Runge-Kutta method one employs an teratve mplct technque. Ths s because the structure
More informationTurbulence classification of load data by the frequency and severity of wind gusts. Oscar Moñux, DEWI GmbH Kevin Bleibler, DEWI GmbH
Turbulence classfcaton of load data by the frequency and severty of wnd gusts Introducton Oscar Moñux, DEWI GmbH Kevn Blebler, DEWI GmbH Durng the wnd turbne developng process, one of the most mportant
More informationCOMPOSITE 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 informationMMA and GCMMA two methods for nonlinear optimization
MMA and GCMMA two methods for nonlnear optmzaton Krster Svanberg Optmzaton and Systems Theory, KTH, Stockholm, Sweden. krlle@math.kth.se Ths note descrbes the algorthms used n the author s 2007 mplementatons
More informationAPPLICATION OF EDDY CURRENT PRINCIPLES FOR MEASUREMENT OF TUBE CENTERLINE
APPLICATION OF EDDY CURRENT PRINCIPLES FOR MEASUREMENT OF TUBE CENTERLINE DEFLECTION E. J. Chern Martn Maretta Laboratores 1450 South Rollng Road Baltmore, MD 21227 INTRODUCTION Tubes are a vtal component
More informationAGC Introduction
. Introducton AGC 3 The prmary controller response to a load/generaton mbalance results n generaton adjustment so as to mantan load/generaton balance. However, due to droop, t also results n a non-zero
More informationAn Improved Model for the Droplet Size Distribution in Sprays Developed From the Principle of Entropy Generation maximization
ILASS Amercas, 9 th Annual Conference on Lqud Atomzaton and Spray Systems, oronto, Canada, May 6 An Improved Model for the Droplet Sze Dstrbuton n Sprays Developed From the Prncple of Entropy Generaton
More informationTransactions of the VŠB Technical University of Ostrava, Mechanical Series. article No. 1907
Transactons of the VŠB Techncal Unversty of Ostrava, Mechancal Seres No., 0, vol. LVIII artcle No. 907 Marek NIKODÝM *, Karel FYDÝŠEK ** FINITE DIFFEENCE METHOD USED FO THE BEAMS ON ELASTIC FOUNDATION
More information2.29 Numerical Fluid Mechanics Fall 2011 Lecture 6
REVIEW of Lecture 5 2.29 Numercal Flud Mechancs Fall 2011 Lecture 6 Contnuum Hypothess and conservaton laws Macroscopc Propertes Materal covered n class: Dfferental forms of conservaton laws Materal Dervatve
More informationThe 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 informationConstitutive Modelling of Superplastic AA-5083
TECHNISCHE MECHANIK, 3, -5, (01, 1-6 submtted: September 19, 011 Consttutve Modellng of Superplastc AA-5083 G. Gulano In ths study a fast procedure for determnng the constants of superplastc 5083 Al alloy
More informationStatistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA
14 th Internatonal Users Conference Sesson: ALE-FSI Statstcal Energy Analyss for Hgh Frequency Acoustc Analyss wth Zhe Cu 1, Yun Huang 1, Mhamed Soul 2, Tayeb Zeguar 3 1 Lvermore Software Technology Corporaton
More informationAbstract. 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 informationU-Pb Geochronology Practical: Background
U-Pb Geochronology Practcal: Background Basc Concepts: accuracy: measure of the dfference between an expermental measurement and the true value precson: measure of the reproducblty of the expermental result
More informationChapter 13: Multiple Regression
Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to
More informationis 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 informationAn identification algorithm of model kinetic parameters of the interfacial layer growth in fiber composites
IOP Conference Seres: Materals Scence and Engneerng PAPER OPE ACCESS An dentfcaton algorthm of model knetc parameters of the nterfacal layer growth n fber compostes o cte ths artcle: V Zubov et al 216
More informationWeek 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 informationEntropy generation in a chemical reaction
Entropy generaton n a chemcal reacton E Mranda Área de Cencas Exactas COICET CCT Mendoza 5500 Mendoza, rgentna and Departamento de Físca Unversdad aconal de San Lus 5700 San Lus, rgentna bstract: Entropy
More informationAssessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion
Assessment of Ste Amplfcaton Effect from Input Energy Spectra of Strong Ground Moton M.S. Gong & L.L Xe Key Laboratory of Earthquake Engneerng and Engneerng Vbraton,Insttute of Engneerng Mechancs, CEA,
More informationChapter 11: Simple Linear Regression and Correlation
Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests
More informationANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)
Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of
More informationThermodynamics General
Thermodynamcs General Lecture 1 Lecture 1 s devoted to establshng buldng blocks for dscussng thermodynamcs. In addton, the equaton of state wll be establshed. I. Buldng blocks for thermodynamcs A. Dmensons,
More informationChapter 8. Potential Energy and Conservation of Energy
Chapter 8 Potental Energy and Conservaton of Energy In ths chapter we wll ntroduce the followng concepts: Potental Energy Conservatve and non-conservatve forces Mechancal Energy Conservaton of Mechancal
More informationNumerical modelization by finite differences of a thermoelectric refrigeration device of double jump". Experimental validation.
Numercal modelzaton by fnte dfferences of a thermoelectrc refrgeraton devce of double jump". Expermental valdaton. A. Rodríguez, J.G. Ván, D. Astran, Dpto. Ingenería Mecánca, Energétca y de Materales.
More informationGrid Generation around a Cylinder by Complex Potential Functions
Research Journal of Appled Scences, Engneerng and Technolog 4(): 53-535, 0 ISSN: 040-7467 Mawell Scentfc Organzaton, 0 Submtted: December 0, 0 Accepted: Januar, 0 Publshed: June 0, 0 Grd Generaton around
More informationFlow Induced Vibration
Flow Induced Vbraton Project Progress Report Date: 16 th November, 2005 Submtted by Subhrajt Bhattacharya Roll no.: 02ME101 Done under the gudance of Prof. Anrvan Dasgupta Department of Mechancal Engneerng,
More informationChapter 9: Statistical Inference and the Relationship between Two Variables
Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationSTATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION
STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros
More informationOne-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 informationTHE NEAR-WALL INFLUENCE ON THE FLOW AROUND A SINGLE SQUARE CYLINDER.
THE NEAR-WALL INFLUENCE ON THE FLOW AROUND A SINGLE SQUARE CYLINDER. Campregher, Rubens Faculty of Mechancal Engneerng, FEMEC Federal Unversty of Uberlânda, UFU 38400-902 Uberlânda - Brazl campregher@mecanca.ufu.br
More informationPressure Measurements Laboratory
Lab # Pressure Measurements Laboratory Objectves:. To get hands-on experences on how to make pressure (surface pressure, statc pressure and total pressure nsde flow) measurements usng conventonal pressuremeasurng
More informationCalculation of Aerodynamic Characteristics of NACA 2415, 23012, Airfoils Using Computational Fluid Dynamics (CFD)
Calculaton of Aerodynamc Characterstcs of NACA 2415, 23012, 23015 Arfols Usng Computatonal Flud Dynamcs (CFD) Hmanshu Parashar Abstract A method of solvng the flow over arfols of Natonal Advsory Commttee
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationChapter - 2. Distribution System Power Flow Analysis
Chapter - 2 Dstrbuton System Power Flow Analyss CHAPTER - 2 Radal Dstrbuton System Load Flow 2.1 Introducton Load flow s an mportant tool [66] for analyzng electrcal power system network performance. Load
More informationCalculating 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 informationLinear Regression Analysis: Terminology and Notation
ECON 35* -- Secton : Basc Concepts of Regresson Analyss (Page ) Lnear Regresson Analyss: Termnology and Notaton Consder the generc verson of the smple (two-varable) lnear regresson model. It s represented
More informationPhysics 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 informationBasic 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 informationTemperature. 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 informationA quote of the week (or camel of the week): There is no expedience to which a man will not go to avoid the labor of thinking. Thomas A.
A quote of the week (or camel of the week): here s no expedence to whch a man wll not go to avod the labor of thnkng. homas A. Edson Hess law. Algorthm S Select a reacton, possbly contanng specfc compounds
More informationParametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010
Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton
More informationCONTRAST ENHANCEMENT FOR MIMIMUM MEAN BRIGHTNESS ERROR FROM HISTOGRAM PARTITIONING INTRODUCTION
CONTRAST ENHANCEMENT FOR MIMIMUM MEAN BRIGHTNESS ERROR FROM HISTOGRAM PARTITIONING N. Phanthuna 1,2, F. Cheevasuvt 2 and S. Chtwong 2 1 Department of Electrcal Engneerng, Faculty of Engneerng Rajamangala
More informationThe Finite Element Method
The Fnte Element Method GENERAL INTRODUCTION Read: Chapters 1 and 2 CONTENTS Engneerng and analyss Smulaton of a physcal process Examples mathematcal model development Approxmate solutons and methods of
More informationNON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS
IJRRAS 8 (3 September 011 www.arpapress.com/volumes/vol8issue3/ijrras_8_3_08.pdf NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS H.O. Bakodah Dept. of Mathematc
More informationComputer Simulations of Parallel-to-Series Conversion in Solid State Frame Transfer Image Sensors. J. Bisschop
207 SIMULATION OF SEMICONDUCTOR DEVICES AND PROCESSES Vol. 3 Edted by G. Baccaran, M. Rudan - Bologna (Italy) September 26-28,988 - Tecnoprnt Computer Smulatons of Parallel-to-Seres Converson n Sold State
More information