Techno-Economic Analysis of Organic Rankine Cycles for a Boiler Station Energy System Modeling and Simulation Optimization
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Arxiv:2008.06405V1 [Physics.Ed-Ph] 14 Aug 2020 Fig.1 Shows Four Classical Cycles: (A) Carnot Cycle, (B) Stirling Cycle, (C) Otto Cycle and (D) Diesel Cycle
Investigating student understanding of heat engine: a case study of Stirling engine Lilin Zhu1 and Gang Xiang1, ∗ 1Department of Physics, Sichuan University, Chengdu 610064, China (Dated: August 17, 2020) We report on the study of student difficulties regarding heat engine in the context of Stirling cycle within upper-division undergraduate thermal physics course. An in-class test about a Stirling engine with a regenerator was taken by three classes, and the students were asked to perform one of the most basic activities—calculate the efficiency of the heat engine. Our data suggest that quite a few students have not developed a robust conceptual understanding of basic engineering knowledge of the heat engine, including the function of the regenerator and the influence of piston movements on the heat and work involved in the engine. Most notably, although the science error ratios of the three classes were similar (∼10%), the engineering error ratios of the three classes were high (above 50%), and the class that was given a simple tutorial of engineering knowledge of heat engine exhibited significantly smaller engineering error ratio by about 20% than the other two classes. In addition, both the written answers and post-test interviews show that most of the students can only associate Carnot’s theorem with Carnot cycle, but not with other reversible cycles working between two heat reservoirs, probably because no enough cycles except Carnot cycle were covered in the traditional Thermodynamics textbook. Our results suggest that both scientific and engineering knowledge are important and should be included in instructional approaches, especially in the Thermodynamics course taught in the countries and regions with a tradition of not paying much attention to experimental education or engineering training. -
Internal Energy in an Electric Field
Internal energy in an electric field In an electric field, if the dipole moment is changed, the change of the energy is, U E P Using Einstein notation dU Ek dP k This is part of the total derivative of U dU TdSij d ij E kK dP H l dM l Make a Legendre transformation to the Gibbs potential G(T, H, E, ) GUTSijij EP kK HM l l SGTE data for pure elements http://www.sciencedirect.com/science/article/pii/036459169190030N Gibbs free energy GUTSijij EP kK HM l l dG dU TdS SdTijij d ij d ij E kk dP P kk dE H l dM l M l dH l dU TdSij d ij E kK dP H l dM l dG SdTij d ij P k dE k M l dH l G G G G total derivative: dG dT d dE dH ij k l T ij EH k l G G ij Pk E ij k G G M l S Hl T Direct and reciprocal effects (Maxwell relations) Useful to check for errors in experiments or calculations Maxwell relations Useful to check for errors in experiments or calculations Point Groups Crystals can have symmetries: rotation, reflection, inversion,... x 1 0 0 x y 0 cos sin y z 0 sin cos z Symmetries can be represented by matrices. All such matrices that bring the crystal into itself form the group of the crystal. AB G for A, B G 32 point groups (one point remains fixed during transformation) 230 space groups Cyclic groups C2 C4 http://en.wikipedia.org/wiki/Cyclic_group 2G Pyroelectricity i Ei T Pyroelectricity is described by a rank 1 tensor Pi i T 1 0 0 x x x 0 1 0 y y y 0 0 1 z z 0 1 0 0 x x 0 0 1 0 y y 0 0 0 1 z z 0 Pyroelectricity example Turmalin: point group 3m Quartz, ZnO, LaTaO 3 for T = 1°C, E ~ 7 ·104 V/m Pyroelectrics have a spontaneous polarization. -
3. Energy, Heat, and Work
3. Energy, Heat, and Work 3.1. Energy 3.2. Potential and Kinetic Energy 3.3. Internal Energy 3.4. Relatively Effects 3.5. Heat 3.6. Work 3.7. Notation and Sign Convention In these Lecture Notes we examine the basis of thermodynamics – fundamental definitions and equations for energy, heat, and work. 3-1. Energy. Two of man's earliest observations was that: 1)useful work could be accomplished by exerting a force through a distance and that the product of force and distance was proportional to the expended effort, and 2)heat could be ‘felt’ in when close or in contact with a warm body. There were many explanations for this second observation including that of invisible particles traveling through space1. It was not until the early beginnings of modern science and molecular theory that scientists discovered a true physical understanding of ‘heat flow’. It was later that a few notable individuals, including James Prescott Joule, discovered through experiment that work and heat were the same phenomenon and that this phenomenon was energy: Energy is the capacity, either latent or apparent, to exert a force through a distance. The presence of energy is indicated by the macroscopic characteristics of the physical or chemical structure of matter such as its pressure, density, or temperature - properties of matter. The concept of hot versus cold arose in the distant past as a consequence of man's sense of touch or feel. Observations show that, when a hot and a cold substance are placed together, the hot substance gets colder as the cold substance gets hotter. -
Energy Minimum Principle
ESCI 341 – Atmospheric Thermodynamics Lesson 12 – The Energy Minimum Principle References: Thermodynamics and an Introduction to Thermostatistics, Callen Physical Chemistry, Levine THE ENTROPY MAXIMUM PRINCIPLE We’ve seen that a reversible process achieves maximum thermodynamic efficiency. Imagine that I am adding heat to a system (dQin), converting some of it to work (dW), and discarding the remaining heat (dQout). We’ve already demonstrated that dQout cannot be zero (this would violate the second law). We also have shown that dQout will be a minimum for a reversible process, since a reversible process is the most efficient. This means that the net heat for the system (dQ = dQin dQout) will be a maximum for a reversible process, dQrev dQirrev . The change in entropy of the system, dS, is defined in terms of reversible heat as dQrev/T. We can thus write the following inequality dQ dQ dS rev irrev , (1) T T Notice that for Eq. (1), if the system is reversible and adiabatic, we get dQ dS 0 irrev , T or dQirrev 0 which illustrates the following: If two states can be connected by a reversible adiabatic process, then any irreversible process connecting the two states must involve the removal of heat from the system. Eq. (1) can be written as dS dQ T (2) The equality will hold if all processes in the system are reversible. The inequality will hold if there are irreversible processes in the system. For an isolated system (dQ = 0) the inequality becomes dS 0 isolated system , which is just a restatement of the second law of thermodynamics. -
The Carnot Cycle, Reversibility and Entropy
entropy Article The Carnot Cycle, Reversibility and Entropy David Sands Department of Physics and Mathematics, University of Hull, Hull HU6 7RX, UK; [email protected] Abstract: The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be performed in a reversible process rather than the work that is actually performed in an irreversible process. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, reversibility and irreversibility are investigated by means of a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can be traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appropriately, the gas can be made to trace out a Carnot cycle in P-V space. -
The Carnot Cycle Ray Fu
The Carnot Cycle Ray Fu The Carnot Cycle We will investigate some properties of the Carnot cycle and explore the subtleties of Carnot's theorem. 1. Recall that the Carnot cycle consists of the following four reversible steps, in order: (a) isothermal expansion at TH (b) isentropic expansion at Smax (c) isothermal compression at TC (d) isentropic compression at Smin TH and TC represent the temperatures of the hot and cold thermal reservoirs; Smin and Smax represent the minimum and maximum entropy reached by the working fluid in the Carnot cycle. Draw the Carnot cycle on a TS plot and label each step of the cycle, as well as TH , TC , Smin, and Smax. 2. On the same plot, sketch the cycle that results when steps (a) and (c) are respectively replaced with irreversible isothermal expansion and compression, assuming that the resulting cycle operates between the same two entropies Smin and Smax. We will prove geometrically that the Carnot cycle is the most efficient thermodynamic cycle working between the range of temperatures bounded by TH and TC . To this end, consider an arbitrary reversible thermody- namic cycle C with working fluid having maximum and minimum temperatures TH and TC , and maximum and minimum entropies Smax and Smin. It is sufficient to consider reversible cycles, for irreversible cycles must have lower efficiencies by Clausius's inequality. 3. Define two areas A and B on the corresponding TS plot for C. A is the area enclosed by C, whereas B is the area bounded above by the bottom of C, bounded below by the S-axis, and bounded to left and right by the lines S = Smin and S = Smax. -
Thermodynamics Cycle Analysis and Numerical Modeling of Thermoelastic Cooling Systems
international journal of refrigeration 56 (2015) 65e80 Available online at www.sciencedirect.com ScienceDirect www.iifiir.org journal homepage: www.elsevier.com/locate/ijrefrig Thermodynamics cycle analysis and numerical modeling of thermoelastic cooling systems Suxin Qian, Jiazhen Ling, Yunho Hwang*, Reinhard Radermacher, Ichiro Takeuchi Center for Environmental Energy Engineering, Department of Mechanical Engineering, University of Maryland, 4164 Glenn L. Martin Hall Bldg., College Park, MD 20742, USA article info abstract Article history: To avoid global warming potential gases emission from vapor compression air- Received 3 October 2014 conditioners and water chillers, alternative cooling technologies have recently garnered Received in revised form more and more attentions. Thermoelastic cooling is among one of the alternative candi- 3 March 2015 dates, and have demonstrated promising performance improvement potential on the Accepted 2 April 2015 material level. However, a thermoelastic cooling system integrated with heat transfer fluid Available online 14 April 2015 loops have not been studied yet. This paper intends to bridge such a gap by introducing the single-stage cycle design options at the beginning. An analytical coefficient of performance Keywords: (COP) equation was then derived for one of the options using reverse Brayton cycle design. Shape memory alloy The equation provides physical insights on how the system performance behaves under Elastocaloric different conditions. The performance of the same thermoelastic cooling cycle using NiTi Efficiency alloy was then evaluated based on a dynamic model developed in this study. It was found Nitinol that the system COP was 1.7 for a baseline case considering both driving motor and Solid-state cooling parasitic pump power consumptions, while COP ranged from 5.2 to 7.7 when estimated with future improvements. -
Stirling Cycle Working Principle
Stirling Cycle In Stirling cycle, Carnot cycle’s compression and expansion isentropic processes are replaced by two constant-volume regeneration processes. During the regeneration process heat is transferred to a thermal storage device (regenerator) during one part and is transferred back to the working fluid in another part of the cycle. The regenerator can be a wire or a ceramic mesh or any kind of porous plug with a high thermal mass (mass times specific heat). The regenerator is assumed to be reversible heat transfer device. T P Qin TH 1 1 Q 2 in v = const. Q Reg. TH = const. v = const. 2 QReg. 3 4 TL 4 Qout Qout 3 T = const. s L v Fig. 3-2: T-s and P-v diagrams for Stirling cycle. 1-2 isothermal expansion heat addition from external source 2-3 const. vol. heat transfer internal heat transfer from the gas to the regenerator 3-4 isothermal compression heat rejection to the external sink 4-1 const. vol. heat transfer internal heat transfer from the regenerator to the gas The Stirling cycle was invented by Robert Stirling in 1816. The execution of the Stirling cycle requires innovative hardware. That is the main reason the Stirling cycle is not common in practice. Working Principle The system includes two pistons in a cylinder with a regenerator in the middle. Initially the left chamber houses the entire working fluid (a gas) at high pressure and high temperature TH. M. Bahrami ENSC 461 (S 11) Stirling Cycle 1 TH TL QH State 1 Regenerator Fig 3-3a: 1-2, isothermal heat transfer to the gas at TH from external source. -
Removing the Mystery of Entropy and Thermodynamics – Part IV Harvey S
Removing the Mystery of Entropy and Thermodynamics – Part IV Harvey S. Leff, Reed College, Portland, ORa,b In Part IV of this five-part series,1–3 reversibility and irreversibility are discussed. The question-answer format of Part I is continued and Key Points 4.1–4.3 are enumerated.. Questions and Answers T < TA. That energy enters through a surface, heats the matter • What is a reversible process? Recall that a near that surface to a temperature greater than T, and subse- reversible process is specified in the Clausius algorithm, quently energy spreads to other parts of the system at lower dS = đQrev /T. To appreciate this subtlety, it is important to un- temperature. The system’s temperature is nonuniform during derstand the significance of reversible processes in thermody- the ensuing energy-spreading process, nonequilibrium ther- namics. Although they are idealized processes that can only be modynamic states are reached, and the process is irreversible. approximated in real life, they are extremely useful. A revers- To approximate reversible heating, say, at constant pres- ible process is typically infinitely slow and sequential, based on sure, one can put a system in contact with many successively a large number of small steps that can be reversed in principle. hotter reservoirs. In Fig. 1 this idea is illustrated using only In the limit of an infinite number of vanishingly small steps, all initial, final, and three intermediate reservoirs, each separated thermodynamic states encountered for all subsystems and sur- by a finite temperature change. Step 1 takes the system from roundings are equilibrium states, and the process is reversible. -
Chapter 20 -- Thermodynamics
ChapterChapter 2020 -- ThermodynamicsThermodynamics AA PowerPointPowerPoint PresentationPresentation byby PaulPaul E.E. TippensTippens,, ProfessorProfessor ofof PhysicsPhysics SouthernSouthern PolytechnicPolytechnic StateState UniversityUniversity © 2007 THERMODYNAMICSTHERMODYNAMICS ThermodynamicsThermodynamics isis thethe studystudy ofof energyenergy relationshipsrelationships thatthat involveinvolve heat,heat, mechanicalmechanical work,work, andand otherother aspectsaspects ofof energyenergy andand heatheat transfer.transfer. Central Heating Objectives:Objectives: AfterAfter finishingfinishing thisthis unit,unit, youyou shouldshould bebe ableable to:to: •• StateState andand applyapply thethe first andand second laws ofof thermodynamics. •• DemonstrateDemonstrate youryour understandingunderstanding ofof adiabatic, isochoric, isothermal, and isobaric processes.processes. •• WriteWrite andand applyapply aa relationshiprelationship forfor determiningdetermining thethe ideal efficiency ofof aa heatheat engine.engine. •• WriteWrite andand applyapply aa relationshiprelationship forfor determiningdetermining coefficient of performance forfor aa refrigeratior.refrigeratior. AA THERMODYNAMICTHERMODYNAMIC SYSTEMSYSTEM •• AA systemsystem isis aa closedclosed environmentenvironment inin whichwhich heatheat transfertransfer cancan taketake place.place. (For(For example,example, thethe gas,gas, walls,walls, andand cylindercylinder ofof anan automobileautomobile engine.)engine.) WorkWork donedone onon gasgas oror workwork donedone byby gasgas INTERNALINTERNAL -
10.05.05 Fundamental Equations; Equilibrium and the Second Law
3.012 Fundamentals of Materials Science Fall 2005 Lecture 8: 10.05.05 Fundamental Equations; Equilibrium and the Second Law Today: LAST TIME ................................................................................................................................................................................ 2 THERMODYNAMIC DRIVING FORCES: WRITING A FUNDAMENTAL EQUATION ........................................................................... 3 What goes into internal energy?.......................................................................................................................................... 3 THE FUNDAMENTAL EQUATION FOR THE ENTROPY................................................................................................................... 5 INTRODUCTION TO THE SECOND LAW ....................................................................................................................................... 6 Statements of the second law ............................................................................................................................................... 6 APPLYING THE SECOND LAW .................................................................................................................................................... 8 Heat flows from hot objects to cold objects ......................................................................................................................... 8 Thermal equilibrium ........................................................................................................................................................... -
Forms of Energy: Kinetic Energy, Gravitational Potential Energy, Elastic Potential Energy, Electrical Energy, Chemical Energy, and Thermal Energy
6/3/14 Objectives Forms of • State a practical definition of energy. energy • Provide or identify an example of each of these forms of energy: kinetic energy, gravitational potential energy, elastic potential energy, electrical energy, chemical energy, and thermal energy. Assessment Assessment 1. Which of the following best illustrates the physics definition of 2. Which statement below provides a correct practical definition of energy? energy? A. “I don’t have the energy to get that done today.” A. Energy is a quantity that can be created or destroyed. B. “Our team needs to be at maximum energy for this game.” B. Energy is a measure of how much money it takes to produce a product. C. “The height of her leaps takes more energy than anyone else’s.” C. The energy of an object can never change. It depends on “ D. That performance was so exhilarating you could feel the energy the size and weight of an object. in the audience!” D. Energy is the quantity that causes matter to change and determines how much change occur. Assessment Physics terms 3. Match each event with the correct form of energy. • energy I. kinetic II. gravitational potential III. elastic potential IV. thermal • gravitational potential energy V. electrical VI. chemical • kinetic energy ___ Ice melts when placed in a cup of warm water. • elastic potential energy ___ Campers use a tank of propane gas on their trip. ___ A car travels down a level road at 25 m/s. • thermal energy ___ A bungee cord causes the jumper to bounce upward. ___ The weightlifter raises the barbell above his head.