Critical Condition for Flow Transition in a Full- Developed Annulus Flow
|
|
- Barry May
- 8 years ago
- Views:
Transcription
1 Citial Condition o Flow Tansition in a Full- Developed Annulus Flow Hua-Shu Dou,, Boo Cheong hoo, and He Mann Tsai. Temase Laboatoy, National Univesity o Singapoe, Singapoe 96. Depatment o Mehanial Engineeing, National Univesity o Singapoe, Singapoe 96 tsldh@nus.edu.sg; huashudou@yahoo.om The low tansition to tubulene still lagely emains an unsolved luid dynamis poblem. The stability o paallel lows is still a eseah subjet o the tubulent tansition o studies despite muh wos in the liteatue. In pevious wos, we have shown that the low instability in wall shea lows depends on the elative magnitude o enegy gadient and the enegy loss o a given distubane. Fo pipe and plane Poiseuille lows, we have demonstated that the subitial tansition to tubulene o wall bounded paallel lows ous at a onsistent value o the enegy gadient paamete. In this study, the itial ondition o subitial tansition in annulus low is alulated o vaious adius atios. The itial low ate and itial eynolds numbe ae given o vaious adius atios. These esults have wide impliations o many luid delivey devies. eywods: Subitial tansition; Full-developed low; Annulus; Citial low ate; adius atio. INTODUCTION Annulus low passage is widely used in aeo-engines, tubomahiney and vaious hemial industial devies. The low dynamis in the annulus has signiiant inluene on the peomane and low eiieny o the devies. The low in the annulus may be lamina o tubulent depending on the behaviou o the main low and the distubane level. Geneally, the distubane level in tubomahiney is vey high so that the low is liely to be tubulene in most iumstanes. Howeve, the low may be ept lamina i the low passage is aeully designed. The detemination o the itial ondition o the low tansition in annulus is theeoe o geat inteest. Flow instability and tubulene tansition have been hallenging topis o luid dynamists o moe than a entuy. This poblem has not been solved ully owing to the many diiulties enounted [-]. Thee exist a ew theoies o the analysis o low instabilities. These ae linea stability analysis, enegy method, weely nonlinea method, seonday instability theoy, and othes [-]. Linea stability analysis was suessul o some lows suh as Taylo-Coutte low and ayleigh-benad low. But, it is ailed o some lows suh as plane Poiseuille low, pipe Poiseuille low, and plane Couette low [-]. The pipe Poiseuille low (Hagen-Poiseuille) is stable by linea stability analysis o all the eynolds numbe e. Howeve, expeiments showed that the low would beome tubulene i e (ρud/µ) exeeds a value o about. Linea stability analysis o plane paallel low gives a itial eynolds numbe e (ρ u h/µ) o 577, while expeiments show that tansition to tubulene ous at the eynolds numbe o ode [3-4]. Fo plane Couette low, the low is stable o all e om linea theoy onsideation, but the expeiments show a itial value o e o 37. The enegy method uses the eynolds-o equation and involves the integation o enegy o the entie low domain. Using the enegy method, the itial e is 88, 6 and 4 espetively o plane Poiseuille low, pipe Poiseuille low and plane Couette low []. Theeoe, the non-uniomity in using this method to pedit the low tansition is still imminent. On the othe hand, the ouene o stability is stitly a loal behaviou and the low duing the tansition is intemittent. The ist ouene o the low instability geneally taes plae in the most dangeous positions as seen in the omation o tubulene spot, the ylinde wae, and the dynami stall on the aioil with lage atta angle. Hene, a method onsideing the loal low behaviou may be the oet appoah. The weely nonlinea method [5] and the seonday instability theoy [6] seem to give bette esults than the abovementioned othe methods and an explain some phenomena; howeve thee is still disepany with expeiments. eently, Dou [7] poposed a new appoah to study low instability and tubulent tansition. It is demonstated that the plane and the pipe Poiseuille lows have a onsistent itial ondition at the subitial tansition ondition detemined by expeiments. In this pape, ollowing the poposed piniple o enegy gadient theoy, the itial ondition o subitial tansition in annulus low is alulated o vaious adius atios. The itial low ate and itial eynolds numbe ae also obtained o vaious adius atios.
2 ENEGY GADIENT THEOY Dou [7] poposed an enegy gadient theoy with the aim to laiy the mehanism o tansition om lamina to tubulene o wall bounded shea lows. Hee, we shall give a shot disussion /desiption o a bette undestanding o the pesent wo. In the theoy, the whole low ield is teated as an enegy ield. It is suggested that the gadient o total enegy in the tansvese dietion o the main low and the visous ition in the steamwise dietion dominate the instability phenomena and hene the low tansition o a given distubane. The enegy gadient in the tansvese dietion has the potential to ampliy a veloity distubane, while the visous ition loss in the steamwise dietion an esist and absob this distubane. The low instability o the tansition to tubulene depends on the elative magnitude o these two oles o enegy gadient ampliiation and visous ition damping to the initial distubane. It is noted that the enegy loss ( H / s ) in unit length in steamwise dietion due to visous ition is equal to the gadient o total enegy ( E / s ) o unit volume luid in steamwise dietion o pessue diven lows. As suh, a new dimensionless paamete, (the atio o the enegy gadient in the tansvese dietion to that in the steamwise dietion), is deined to haateie the stability o the base low o the ase whee thee is no wo input, E / n. (a) E / s Hee, E p + ρv + ρgξ is the total enegy o inompessible lows with ξ as the oodinate in the dietion o gavitational ield, n denotes the dietion nomal to the steamwise dietion and s denotes the steamwise dietion. Futhemoe, ρ is the luid density, g is the gavity aeleation, V is the veloity, and p is the hydodynami pessue. Fo shea diven lows (thee is wo input), the alulation o an be obtained by the atio o the enegy gadient in tansvese dietion and the enegy loss in unit length along the steamline [8], E / n. (b) H / s As suh, the paamete in Eq.() is a ield vaiable. Thus, the distibution o in the low ield and the haateistis o distubane may seve as the means to desibe i thee is a distubane ampliiation o deay in the low. It is suggested that the low instability an ist ou at the position o whih is onstued to be the most dangeous position. Thus, o a given distubane, the ouene o instability depends on the magnitude o this dimensionless paamete and the itial ondition is detemined by the imum value o in the low. Fo a given low geomety and luid popeties, when the imum o in the low ield is lage than a itial value, it is expeted that instability an ou o etain initial distubane [7]. Fo a given low, is popotional to the global eynolds numbe. A lage value o has the ability to ampliy the distubane, and vie vesa. The analysis has suggested that the tansition to tubulene is due to the enegy gadient and the distubane ampliiation[7], athe than just the linea eigenvalue instability type as stated in [3,4]. Both Teethen et al. [3] and Gossmann [4] ommented that the natue o the onset-o-tubulene mehanism in paallel shea lows must be dieent om an eigenvalue instability o linea equations o small distubane. In at, inite distubane is needed o the tubulene initiation in the ange o inite e as ound in expeiments [9]. Dou [7] demonstated that the iteion obtained has a onsistent value at the subitial ondition o tansition detemined by the expeimental data o plane Poiseuille low, pipe Poiseuille low as well as plane Couette low (see Table ). The data in Table may suggest that the subitial ondition o tansition o Poiseuille lows ous at 385 and the subitial tansition in paallel lows taes plae at a value o This inding uthe suggests that the low instability is liely esulted om the ation o enegy gadients, and not due stitly to the eigenvalue instability o linea equations. Using enegy gadient theoy, it is also demonstated that the visous low with an inletional veloity poile is unstable o both twodimensional and axisymmetial lows []. Fo plane Poiseuille low, this said position whee > should then be the most dangeous loation o low beadown, whih has been onimed by Nishioa et al s expeiment []. Nishioa et al's [] expeiments o plane Poiseuille low showed details o the low beadown. The measued instantaneous veloity distibutions indiate that the ist osillation o the veloity ous at y/h.5~.6. Fo pipe low, in a eent study, Wedin and eswell [] showed that thee is the pesene o the "shoulde" in the veloity poile at about /.6 om thei solution o the taveling waves. They suggested that this oesponds to whee the ast steas o taveling waves eah om the wall. It an be onstued that this ind o veloity poile as obtained by simulation is simila to that o Nishioa et al's expeiments o hannel lows []. The loation o the "shoulde" is about the same as that o. Aoding to
3 the pesent theoy, this "shoulde" may then be intiately elated to the distibution o enegy gadient. The solution o taveling waves has been onimed by expeiments eently [3]. Flow type e expession Eigenvalue analysis, Enegy Expeiments, at e (om e method e expeiments), e Pipe Poiseuille e ρ UD / µ Stable o all e Plane Poiseuille e ρ UL / µ e ρ uh / µ Plane Couette e ρ Uh / µ Stable o all e Table Compaison o the itial eynolds numbe and the enegy gadient paamete o plane Poiseuille low and pipe Poiseuille low as well as o plane Couette low [7,8]. U is the aveaged veloity, u the veloity at the midplane o the hannel, D the diamete o the pipe, h the hal-width o the hannel o plane Poiseuille low (Lh) and plane Couette low. Fo Plane Poiseuille low and pipe Poiseuille low, the ous at y/h.5774, and /.5774, espetively. Fo Plane Couette low, the ous at y/h.. VELOCITY DISTIBUTION AND FLOW ATE IN THE ANNULUS The dieential equation o the ull-developed low in an annulus (Fig.) o an inompessible Newtonian luid (negleting gavity oe) in the ylindial oodinates (,) is p u ρ + µ () whee ρ is the luid density, u is the axial veloity, p is the hydodynami pessue, and µ is the dynami visosity o the luid. Integating the above equation and using the bounday ondition at the walls o inne and oute ylindes, the veloity distibution along the adius an be obtained as [4] u p 4µ + ln / ln u + b ln ( ), (3) whee / is the adius atio (, ), and u ylinde o the pipe Poiseuille low and b ( )/ ln( / ) The low ate an be integated as [4] Q u The aveage veloity in the annulus is. p 4µ 4 ( ) ( ). Hee, u is the veloity at the axis o the u π d π. (4) ln(/ ) U π Q π ( ) u ( ) ( + ln(/ ). (5) The eynolds numbe based on aveage veloity is theeoe 3
4 Uρ( ) ρu e µ µ ρu ( ) ( ) ( ) ( + µ ln(/ ). (6) CALCULATION OF IN THE ANNULUS The paamete o the low in an annulus is using Eq.() du du d u ρ u / µ + d. (7) d d Intoduing Eq.(3) into Eq.(7) and simpliying, the ollowing equations o paamete an be deived, Let ρu µ e + b ln b. (8) ( / ) ρu ρ( u / ) (9) µ µ be the eynolds numbe o the vitual pipe low, Eq.(8) an be uthe expessed as b e + bln. () ( / ) When b, the above equation simpliies to the pipe low expession [4]. Equation () an be also e-witten as whee e,, () b, + b ln. () ( / ) The distibutions o (, ) minimum o (, ) / vesus / o vaious ae shown in Fig.. It is ound that thee is a imum o / along / o given. Theeoe, we now om Eq.() that thee is a imum o minimum o o given e, whih oesponds to those o, espetively. Now, we ee these values to as o whih is lage in the magnitude between the imum and minimum o them. We have om Eq.() ρu e,, µ CITICAL EYNOLDS NUMBE OF THE ANNULUS. (3) As we now om enegy gadient theoy, the dominating paamete detemining the itial ondition o instability is. Dou [7] demonstated that the itial value ( ) o at subitial ondition o wall bounded paallel lows (pessue diven lows) is a onsistent quantity o 385. Given this itial value o the subitial tansition ondition, the itial values o u, U, and e an be alulated o any adius atio o the annulus. As long as the values o these paametes ae below the itial values, the low in the annulus an be maintained as a lamina low egadless o the level o distubane. Obviously, this obsevation has signiiant impliations in engineeing. 4
5 At the itial ondition, om Eq(3), we have the itial value o u given as µ u. (4) ρ Thus, at the itial ondition, the itial low ate is obtained om Eq.(4) as µ Q π. (5) ρ ln(/ ) The aveage veloity at itial low ate is om Eq.(5), 4 ( ) ( ) U π The itial eynolds numbe is om Eq.(6), Q π µ ρ ( ) ( + ln(/ ). (6) e Uρ( ) ρu µ µ ( ) ( + ln(/ ). (7) At the itial ondition, given as 385, and an be ound om Eq.() (see Fig.). Thus the itial values o Q, U and e vesus the adius atio an be obtained. The itial low ate and itial eynolds numbe ae shown in Fig.3 and Fig.4 espetively. It is ound that the itial value o the e ineases with the adius atio () o the annulus when the atio is lage than a value o.8. Below.8, the itial value o the e is less than that o the Poiseuille low o iula pipe. Theeoe, we an say that the inne ylinde initiates instability o <.8 and enhane stability o >.8. Similaly, the itial value o the Q ineases with the adius atio () o the annulus when the atio is lage than a value o.. Below., the itial value o the Q is less than that o the Poiseuille low o iula pipe. The impliation is that we an hange the itial value o e by inseting an inne ylinde at the ente o a pipe and thus ontol the ouene o tubulene. In this way, tubulene low in a pipe an be aused to elaminaise in an annulus. This hange may inease the aveaged veloity in the passage, but the dag oe is not ineased signiiantly i is small. This is beause the ition oeiient o lamina low is lowe than that o a tubulent low. As above disussed, the adius atio o the inne to the oute ylindes has impotant inluene on the subitial ondition o tansition to tubulene. This inding an be applied to many industial poesses and luid tanspotations. CONCLUSIONS The itial ondition o the instability o ull-developed low in an annulus is given. The iteion is based on the enegy gadient theoy o paallel low instability. The itial low ate and itial eynolds numbe inease with the adius atio o lage adius atio annulus, but thee is a tuning point in the ange o vey small adius atio o about <.. It is lea that inne ylinde eates instability o <.; and enhane stability o >.. Following this piniple, the low tansition an be ontolled by hanging the adius atio o a given oute adius. The idea an be employed in the design o luid low devies to ontol the low status lie dag edution (by eeping to lamina low) o inease the mixing o the luid media (by hanging to tubulent low). (Blan line : pt) EFEENCES (Blan line : pt.) [] Shmid, P.J., Henningson, D. S.: Stability and tansition in shea lows, Spinge-Velag, () [] Dain, P. G., eid, W. H.: Hydodynami Stability, Cambidge Univesity Pess, nd Ed., (4) [3] Teethen, L. N., Teethen, A. E., eddy, S. C., Disoll, T. A.: Hydodynami stability without eigenvalues, Siene, Vol.6, pp , (993) [4] Gossmann, S.: The onset o shea low tubulene, eviews o moden physis, Vol.7, pp.63-68, () [5] Stuat, J.T.: Nonlinea Stability Theoy, Annu. ev. o Fluid Meh., Vol.3, pp , (97) [6] Bayly, B. J., Osag, S. A.: Hebet Th. Instability mehanism in shea-low tansition, Annu. ev. Fluid Meh., 988, :
6 [7] Dou, H.-S.: Enegy gadient theoy o hydodynami instability, Tehnial epot o National Univesity o Singapoe,. Also, pesented at The Thid Intenational Coneene on Nonlinea Siene, Singapoe, 3 June -- July, 4. [8] Dou, H.-S., hoo, B.C., Phan-Thien, N., and Yeo,.S.: Instability o plane Couette low, [9] Dabyshie, A.G., Mullin, T.: Tansition to tubulene in onstant-mass-lux pipe low, J. Fluid Meh., Vol.89, pp.83-4, (995) [] Dou, H-S.: Visous instability o inletional veloity poile, eent Advanes in Fluid Mehanis, Po. o the 4th Inte. Con. on Fluid Meh., July ~3, 4, Dalian, China; Tsinghua Univesity Pess & Spinge-Velag, pp , (4) [] Nishioa, M., Iida, S., Ihiawa, Y.: An expeimental investigation o the stability o plane Poiseuille low, J. Fluid Meh, Vol.7, pp.73-75, (975) [] Wedin, H., eswell,..: Exat oheent stutues in pipe low: tavelling wave solutions, J. Fluid Meh., Vol.58, pp , (4) [3] Ho, B., van Doone, C.W.H., Westeweel, J., Nieuwstadt, F.T.M., Faisst, H., Ehadt, B., Wedin, H., eswell,.., Walee, F.: Expeimental obsevation o nonlinea taveling waves in tubulent pipe low, Siene, Vol.35, pp , (4) [4] Papanastasiou, T.C., Geogiou, G.C., Alexandou, A.N.: Visous luid low, CC Pess, (999) (/). Fig. Seth o the low in an annulus. ; / Fig. Funtion (/) along the adius atio / o vaious adius atios unstable.5 5 unstable e stable Q.5 stable Fig.3 eynolds numbe at itial ondition o annulus low at vaious adius atio. The out adius is ept onstant Fig.4 Flow ate at itial ondition o annulus low at vaious adius atio. The oute adius is ept onstant. 6
Solar wind speed theory and the nonextensivity of solar corona
AXiv:080.170 Sola wind speed theoy and the nonextensivity of sola oona Du Jiulin *, Song Yeli Depatment of Physis, Shool of Siene, Tianjin Univesity, Tianjin 30007, China Abstat. The sola oona is a omplex
More informationA Note on Risky Bond Valuation
A Note on Risky Bond Valuation C. H. Hui Banking Poliy Depatment Hong Kong Monetay Authoity 0th Floo,, Gaden Road, Hong Kong Email: Cho-Hoi_Hui@hkma.gov.hk C. F. Lo Physis Depatment The Chinese Univesity
More informationVISCOSITY OF BIO-DIESEL FUELS
VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationNewton s Law of Universal Gravitation and the Scale Principle
Newton s Law of Univesal avitation and the ale iniple RODOLO A. RINO July 0 Eletonis Enginee Degee fo the National Univesity of Ma del lata - Agentina (odolfo_fino@yahoo.o.a) Ealie this yea I wote a pape
More informationMulticriteria Decision Model for Information Systems Priorities Based on Business Process Management
Multiiteia Deision Model fo Infomation Systems Pioities Based on Business Poess Management Adiel Teixei de Almeida* and Mila Neves Souza** The pape pesents a multiiteia deision model fo infomation system
More informationYARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH
nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav
More informationON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS
ON THE R POLICY IN PRODUCTION-INVENTORY SYSTEMS Saifallah Benjaafa and Joon-Seok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poduction-inventoy
More informationIntroduction to Fluid Mechanics
Chapte 1 1 1.6. Solved Examples Example 1.1 Dimensions and Units A body weighs 1 Ibf when exposed to a standad eath gavity g = 3.174 ft/s. (a) What is its mass in kg? (b) What will the weight of this body
More informationThe Role of Gravity in Orbital Motion
! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State
More informationStrength Analysis and Optimization Design about the key parts of the Robot
Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Pint): 2320-9356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.25-29 Stength Analysis and Optimization Design
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationDYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES
DYNAMIS AND STRUTURAL LOADING IN WIND TURBINES M. Ragheb 12/30/2008 INTRODUTION The loading egimes to which wind tubines ae subject to ae extemely complex equiing special attention in thei design, opeation
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationGravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning
Gavitational Mechanics of the Mas-Phobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This
More informationFXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationDeflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
More informationThe transport performance evaluation system building of logistics enterprises
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
More informationSpirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
More informationStructure and evolution of circumstellar disks during the early phase of accretion from a parent cloud
Cente fo Tubulence Reseach Annual Reseach Biefs 2001 209 Stuctue and evolution of cicumstella disks duing the ealy phase of accetion fom a paent cloud By Olusola C. Idowu 1. Motivation and Backgound The
More informationVoltage ( = Electric Potential )
V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined
More informationCHIRAL FIELD IDEAS FOR A THEORY OF MATTER IDEAS DE CAMPO QUIRAL PARA UNA TEORÍA DE LA MATERIA
Ingeniae. Revista hilena de ingenieía, vol. 16 núeo espeial, 8, pp. 36-4 CHIRAL FILD IDAS FOR A THORY OF MATTR IDAS D CAMPO QUIRAL PARA UNA TORÍA D LA MATRIA H. Toes-Silva 1 Reibido el 5 de septiebe de
More informationAn Epidemic Model of Mobile Phone Virus
An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity
More informationdz + η 1 r r 2 + c 1 ln r + c 2 subject to the boundary conditions of no-slip side walls and finite force over the fluid length u z at r = 0
Poiseuille Flow Jean Louis Maie Poiseuille, a Fench physicist and physiologist, was inteested in human blood flow and aound 1840 he expeimentally deived a law fo flow though cylindical pipes. It s extemely
More informationGauss Law. Physics 231 Lecture 2-1
Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationResearch on Risk Assessment of the Transformer Based on Life Cycle Cost
ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,
More informationChapter 4: Fluid Kinematics
Oveview Fluid kinematics deals with the motion of fluids without consideing the foces and moments which ceate the motion. Items discussed in this Chapte. Mateial deivative and its elationship to Lagangian
More information1D STEADY STATE HEAT
D SEADY SAE HEA CONDUCION () Pabal alukda Aociate Pofeo Depatment of Mecanical Engineeing II Deli E-mail: pabal@mec.iitd.ac.in Palukda/Mec-IID emal Contact eitance empeatue ditibution and eat flow line
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationSELF-INDUCTANCE AND INDUCTORS
MISN-0-144 SELF-INDUCTANCE AND INDUCTORS SELF-INDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. Self-Inductance L.........................................
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationEfficient Redundancy Techniques for Latency Reduction in Cloud Systems
Efficient Redundancy Techniques fo Latency Reduction in Cloud Systems 1 Gaui Joshi, Emina Soljanin, and Gegoy Wonell Abstact In cloud computing systems, assigning a task to multiple seves and waiting fo
More informationChannel selection in e-commerce age: A strategic analysis of co-op advertising models
Jounal of Industial Engineeing and Management JIEM, 013 6(1):89-103 Online ISSN: 013-0953 Pint ISSN: 013-843 http://dx.doi.og/10.396/jiem.664 Channel selection in e-commece age: A stategic analysis of
More informationUNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -
More information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
More informationAn Analysis of Manufacturer Benefits under Vendor Managed Systems
An Analysis of Manufactue Benefits unde Vendo Managed Systems Seçil Savaşaneil Depatment of Industial Engineeing, Middle East Technical Univesity, 06531, Ankaa, TURKEY secil@ie.metu.edu.t Nesim Ekip 1
More informationUPS Virginia District Package Car Fleet Optimization
UPS Viginia Distit Pakage Ca Fleet Otimization Tavis Manning, Divaka Mehta, Stehen Sheae, Malloy Soldne, and Bian Togesen Abstat United Pael Sevie (UPS) is onstantly haged with ealigning its akage a fleet
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More informationThe effect of variable viscosity on the flow and heat transfer of a viscous Agwater and Cu-water nanofluids *
1 2013,25(1):1-9 DOI: 10.1016/S1001-6058(13)60332-7 The eect o vaiable viscosity on the low and heat tanse o a viscous Agwate and Cu-wate nanoluids * VAJRAVELU Kuppalapalle Depatment o Mathematics, Univesity
More informationConcept and Experiences on using a Wiki-based System for Software-related Seminar Papers
Concept and Expeiences on using a Wiki-based System fo Softwae-elated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wth-aachen.de,
More informationSkills Needed for Success in Calculus 1
Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell
More informationCellular network with continuum priority set
Cellla netwok with ontinm pioity set Jean-Ma Kelif Fane Teleom eseah Development 9794 ssy Molinea, Fane jeanma.kelif@oange-ftgop.om Eitan Alman A P 9 69 Sophia Antipolis, Fane Eitan.Altman@sophia.inia.f
More informationPHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013
PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0
More informationData Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation
(213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute
More informationInstituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt
FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB-30 AIRCRAFT - PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado
More informationThe Binomial Distribution
The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between
More informationPessu Behavior Analysis for Autologous Fluidations
EXPERIENCE OF USING A CFD CODE FOR ESTIMATING THE NOISE GENERATED BY GUSTS ALONG THE SUN- ROOF OF A CAR Liang S. Lai* 1, Geogi S. Djambazov 1, Choi -H. Lai 1, Koulis A. Peicleous 1, and Fédéic Magoulès
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation
More informationContinuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
More informationMagnetic Field and Magnetic Forces. Young and Freedman Chapter 27
Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field
More informationHUT, TUT, LUT, OU, ÅAU / Engineering departments Entrance examination in mathematics May 25, 2004
HUT, TUT, LUT, OU, ÅAU / Engineeing depamens Enane examinaion in mahemais May 5, 4 Insuions. Reseve a sepaae page fo eah poblem. Give you soluions in a lea fom inluding inemediae seps. Wie a lean opy of
More informationChapter 2 Modelling of Fluid Flow and Heat Transfer in Rotating-Disk Systems
Chapte 2 Modelling of Fluid Flow and Heat Tansfe in Rotating-Disk Systems 2.1 Diffeential and Integal Equations 2.1.1 Diffeential Navie Stokes and Enegy Equations We will conside hee stationay axisymmetic
More informationA Study on the Conducted Interference of Capacitor Charging Power Supply
Enegy and Powe Engineeing, 13, 5, 1134-1138 doi:1.436/epe.13.54b16 Published Online July 13 (http://www.scip.og/jounal/epe) A Study on the Conducted Inteeence o Capacito Chaging Powe Supply Xiao Han 1,
More informationCarter-Penrose diagrams and black holes
Cate-Penose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More information1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2
Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the
More informationINVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE
1 INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE ANATOLIY A. YEVTUSHENKO 1, ALEXEY N. KOCHEVSKY 1, NATALYA A. FEDOTOVA 1, ALEXANDER Y. SCHELYAEV 2, VLADIMIR N. KONSHIN 2 1 Depatment of
More informationLab #7: Energy Conservation
Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 1-4 Intoduction: Pehaps one of the most unusual
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance the availability
More informationA framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods
A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com
More informationExperiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
More information) ( )( ) ( ) ( )( ) ( ) ( ) (1)
OPEN CHANNEL FLOW Open hannel flow is haraterized by a surfae in ontat with a gas phase, allowing the fluid to take on shapes and undergo behavior that is impossible in a pipe or other filled onduit. Examples
More informationThe Impacts of Congestion on Commercial Vehicle Tours
Figliozzi 1 The Impacts of Congestion on Commecial Vehicle Tous Miguel Andes Figliozzi Potland State Univesity Maseeh College of Engineeing and Compute Science figliozzi@pdx.edu 5124 wods + 7 Tables +
More informationPAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII - SPETO - 1995. pod patronatem. Summary
PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8 - TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC
More informationFunctions of a Random Variable: Density. Math 425 Intro to Probability Lecture 30. Definition Nice Transformations. Problem
Intoduction One Function of Random Vaiables Functions of a Random Vaiable: Density Math 45 Into to Pobability Lectue 30 Let gx) = y be a one-to-one function whose deiatie is nonzeo on some egion A of the
More informationDatabase Management Systems
Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012
More informationMULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION
MULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION K.C. CHANG AND TAN ZHANG In memoy of Pofesso S.S. Chen Abstact. We combine heat flow method with Mose theoy, supe- and subsolution method with
More informationQuestions for Review. By buying bonds This period you save s, next period you get s(1+r)
MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the two-peiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume
More information2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES
. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES In ode to etend the definitions of the si tigonometic functions to geneal angles, we shall make use of the following ideas: In a Catesian coodinate sstem, an
More informationAn Approach to Optimized Resource Allocation for Cloud Simulation Platform
An Appoach to Optimized Resouce Allocation fo Cloud Simulation Platfom Haitao Yuan 1, Jing Bi 2, Bo Hu Li 1,3, Xudong Chai 3 1 School of Automation Science and Electical Engineeing, Beihang Univesity,
More informationChapte 3 Is Gavitation A Results Of Asymmetic Coulomb Chage Inteactions? Jounal of Undegaduate Reseach èjurè Univesity of Utah è1992è, Vol. 3, No. 1, pp. 56í61. Jeæey F. Gold Depatment of Physics, Depatment
More informationRisk Sensitive Portfolio Management With Cox-Ingersoll-Ross Interest Rates: the HJB Equation
Risk Sensitive Potfolio Management With Cox-Ingesoll-Ross Inteest Rates: the HJB Equation Tomasz R. Bielecki Depatment of Mathematics, The Notheasten Illinois Univesity 55 Noth St. Louis Avenue, Chicago,
More informationExplicit, analytical solution of scaling quantum graphs. Abstract
Explicit, analytical solution of scaling quantum gaphs Yu. Dabaghian and R. Blümel Depatment of Physics, Wesleyan Univesity, Middletown, CT 06459-0155, USA E-mail: ydabaghian@wesleyan.edu (Januay 6, 2003)
More informationThe impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011
The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility
More informationwww.sakshieducation.com
Viscosity. The popety of viscosity in gas is due to ) Cohesive foces between the moecues ) Coisions between the moecues ) Not having a definite voume ) Not having a definite size. When tempeatue is inceased
More informationA Capacitated Commodity Trading Model with Market Power
A Capacitated Commodity Tading Model with Maket Powe Victo Matínez-de-Albéniz Josep Maia Vendell Simón IESE Business School, Univesity of Navaa, Av. Peason 1, 08034 Bacelona, Spain VAlbeniz@iese.edu JMVendell@iese.edu
More informationNontrivial lower bounds for the least common multiple of some finite sequences of integers
J. Numbe Theoy, 15 (007), p. 393-411. Nontivial lowe bounds fo the least common multiple of some finite sequences of integes Bai FARHI bai.fahi@gmail.com Abstact We pesent hee a method which allows to
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance
More informationMean-Reverting-Ebit-Based Stock Option Evaluation: Theory and Practice
Jounal of Applied Finance & aning, vol. 3, no. 5, 03, 35-36 ISSN: 79-6580 pint vesion, 79-6599 online Scienpess Ltd, 03 Mean-Reveting-bit-ased Stoc Option valuation: Theoy and Pactice Hassan l Ibami Abstact
More informationThe Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C
Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit
More informationApproximation Algorithms for Data Management in Networks
Appoximation Algoithms fo Data Management in Netwoks Chistof Kick Heinz Nixdof Institute and Depatment of Mathematics & Compute Science adebon Univesity Gemany kueke@upb.de Haald Räcke Heinz Nixdof Institute
More informationAlignment of Buckingham Parameters to Generalized Lennard-Jones Potential Functions
Alignment of Buckingham Paametes to Genealized Lennad-Jones Potential Functions Teik-Cheng Lim School of Science and Technology SIM Univesity 535A Clementi oad S 599490 epublic of Singapoe epint equests
More informationVoltage ( = Electric Potential )
V-1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is
More informationReduced Pattern Training Based on Task Decomposition Using Pattern Distributor
> PNN05-P762 < Reduced Patten Taining Based on Task Decomposition Using Patten Distibuto Sheng-Uei Guan, Chunyu Bao, and TseNgee Neo Abstact Task Decomposition with Patten Distibuto (PD) is a new task
More information30 H. N. CHIU 1. INTRODUCTION. Recherche opérationnelle/operations Research
RAIRO Rech. Opé. (vol. 33, n 1, 1999, pp. 29-45) A GOOD APPROXIMATION OF THE INVENTORY LEVEL IN A(Q ) PERISHABLE INVENTORY SYSTEM (*) by Huan Neng CHIU ( 1 ) Communicated by Shunji OSAKI Abstact. This
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More informationCloud Service Reliability: Modeling and Analysis
Cloud Sevice eliability: Modeling and Analysis Yuan-Shun Dai * a c, Bo Yang b, Jack Dongaa a, Gewei Zhang c a Innovative Computing Laboatoy, Depatment of Electical Engineeing & Compute Science, Univesity
More informationDIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION
DIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION Mohammad Rashed Iqbal Fauque* #1, Mohammad Taiqul Islam* 2, Nobahiah Misan* #3 * Institute of Space Science
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationTracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors
Tacking/Fusion and Deghosting with Dopple Fequency fom Two Passive Acoustic Sensos Rong Yang, Gee Wah Ng DSO National Laboatoies 2 Science Pak Dive Singapoe 11823 Emails: yong@dso.og.sg, ngeewah@dso.og.sg
More information2. Orbital dynamics and tides
2. Obital dynamics and tides 2.1 The two-body poblem This efes to the mutual gavitational inteaction of two bodies. An exact mathematical solution is possible and staightfowad. In the case that one body
More informationModal Characteristics study of CEM-1 Single-Layer Printed Circuit Board Using Experimental Modal Analysis
Available online at www.sciencediect.com Pocedia Engineeing 41 (2012 ) 1360 1366 Intenational Symposium on Robotics and Intelligent Sensos 2012 (IRIS 2012) Modal Chaacteistics study of CEM-1 Single-Laye
More informationIBM Research Smarter Transportation Analytics
IBM Reseach Smate Tanspotation Analytics Laua Wynte PhD, Senio Reseach Scientist, IBM Watson Reseach Cente lwynte@us.ibm.com INSTRUMENTED We now have the ability to measue, sense and see the exact condition
More information(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of
Homewok VI Ch. 7 - Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the
More informationHow To Find The Optimal Stategy For Buying Life Insuance
Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,
More informationThe Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?
The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity
More informationGravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2
F Gm Gavitation and Keple s Laws Newton s Law of Univesal Gavitation in vectoial fom: F 12 21 Gm 1 m 2 12 2 ˆ 12 whee the hat (ˆ) denotes a unit vecto as usual. Gavity obeys the supeposition pinciple,
More information