DOCSLIB.ORG

Numerical Study of the Heat Transfer in a Miniature Joule-Thomson Cooler

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Numerical Study of the Heat Transfer in a Miniature Joule-Thomson Cooler NUMERICAL STUDY OF THE HEAT TRANSFER IN A MINIATURE JOULE-THOMSON COOLER TEO HWEE YEAN NATIONAL UNIVERSITY OF SINGAPORE 2004 NUMERICAL STUDY OF THE HEAT TRANSFER IN A MINIATURE JOULE-THOMSON COOLER TEO HWEE YEAN (B.Tech Mech. Engrg (Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2004 ACKNOWLEDGEMENTS Acknowledgements There are many friends, colleagues and lecturers as well as institutions to whom I would like to express my thanks for their contribution and helpful information. I would like to express my thanks to Prof. Ng Kim Choon for his valuable comments and useful assistance regarding the topics in heat transfer of fluids and thermodynamics. I would also like to mention thanks for the kind foreword and the ideas and discussions from Assistant Prof. Chua Hui Tong and Dr Wang Xiaolin. Last but not least let me express my warmest thanks to the National University of Singapore and A*STAR for giving me the opportunity and full support, without which this project could not have been completed. Thank you. National University of Singapore i Filename:TeoHY.pdf TABLE OF CONTENTS Table of Contents PAGE Acknowledgements i Table of Contents ii-v Summary vi Nomenclature vii-x List of Figures xi-xiii List of Tables xiv Chapter 1 Introduction 1 1.1 Background 1 1.1.1 Recuperative Heat Exchanger 1 1.1.2 Regenerative Heat Exchanger 4 1.2 Present Trend 9 1.2.1 Open Cycle Cooling Systems 9 1.2.2 Inefficiencies & Parasitic Losses in Real Cryocooler 10 1.3 Objectives and Scopes 12 Chapter 2 Joule-Thomson Cooler Fundamentals 16 2.1 Parameters & Characteristics 19 2.1.1 The Flows 19 2.1.2 Capillary Tubes 23 2.1.3 J-T Coefficients & Throttle Valves 25 2.2 Refrigeration Cycle 29 National University of Singapore ii Filename:TeoHY.pdf TABLE OF CONTENTS 2.2.1 Stage 5 to 1 31 2.2.2 Stage 1 to 2 31 2.2.3 Stage 2 to 3 31 2.2.4 Stage 3 to 4 32 2.2.5 Stage 4 to 5 32 2.3 Hampson-Type J-T Cryostat 33 2.4 Experimental Model 37 Chapter 3 Governing Differential Equations 40 3.1 Geometry Model 40 3.1.1 Helical Coil Capillary Tube 40 3.1.2 Helical Coil Fins 41 3.2 High Pressure Cryogen in the Helical Coil Capillary Tube 48 3.3 Helical Coil Capillary Tube 50 3.4 Helical Coil Fins 50 3.5 Shield 51 3.6 External Return Cryogen 51 3.7 Spacers 53 3.8 Entropy Generation for Internal Cryogen 54 National University of Singapore iii Filename:TeoHY.pdf TABLE OF CONTENTS Chapter 4 Numerical Prediction 55 4.1 Computational Fluid Dynamics 55 4.2 Dimensionless Governing Differential Equations 57 4.2.1 High Pressure Cryogen (Single Phase Flow) 58 4.2.2 High Pressure Cryogen (Two Phase Homogenous Flow) 58 4.2.3 Helical Coil Capillary Tube 58 4.2.4 Helical Coil Fins 58 4.2.5 Shield 58 4.2.6 External Return Cryogen 59 4.2.7 Entropy Generation 59 4.3 Properties and Areas 60 4.3.1 Fanning Friction Factors 60 4.3.2 Convective Heat Transfer Coefficients 61 4.3.3 Thermodynamic and Transport Properties of Argon 61 4.3.4 Thermal Conductivities of Materials 68 4.3.5 Heat Transfer Areas 69 4.4 Boiling Heat Transfer 70 4.4.1 Nucleate Pool Boiling 71 4.4.2 Pool Film Boiling 74 4.4.3 Jet Impingement Boiling 75 Chapter 5 Results & Discussion 76 5.1 Temperature-Entropy (T-s) Diagram 77 National University of Singapore iv Filename:TeoHY.pdf TABLE OF CONTENTS 5.2 Cooling Capacity 79 5.3 Coefficient of Performance and Figure of Merit 83 5.4 Effectiveness and Liquefied Yield Fractions 84 5.5 Temperature and Pressure Distributions 86 Chapter 6 Conclusions & Recommendations 88 6.1 Conclusions 88 6.2 Recommendations 90 References R-1 Appendix A – Operation Manual for Simulation Program A-1 Appendix B – Fortran 90 Source Code – Main Program B-1 Appendix C – Fortran 90 Source Code – IMSL Subroutine (DBVPFD) C-1 Appendix D – Fortran 90 Source Code – IMSL Subroutine (FDJAC) D-1 National University of Singapore v Filename:TeoHY.pdf SUMMARY Summary The miniature Joule-Thomson (J-T) cooler is widely used in the electronic industry for the thermal management of power intensive electronic components because of special features of having a short cool-down time, simple configuration and having no moving parts. In this thesis, the sophisticated geometry of the Hampson-type J-T cooler is analyzed and incorporated into the simulation, so that the model can be used as a design tool. The governing equations of the cryogen, helical tube and fins, and shield are coupled and solved numerically under the steady state conditions, and yield agreements with the published experiments to within 3%. The characteristics of flow within the capillary tube and external return gas are accurately predicted. The temperature versus entropy, cooling capacity versus load temperature, and cooling capacity versus input pressure charts are plotted and discussed. The conventional way of simulating a Hampson-type J- T cooler, which is accompanied by a host of empirical correction factors, especially vis-à-vis the heat exchanger geometry could now be superseded. The effort and time spent in designing a Hampson-type J-T cryocooler could be greatly reduced. By avoiding the use of empirical geometric correction factors, the model produces the real behavior during simulation. National University of Singapore vi Filename:TeoHY.pdf NOMENCLATURE Nomenclature A Areas of contact m2 cp Isobaric specific heat J/(kg.K) Coef Heat Transfer Coefficient W/(m2.K) cv Isochoric specific heat J/(kg.K) D,d Diameter of tubes m ds Grid length along s-axis m d s Dimensionless grid length along s-axis - f Fanning friction factor - f(T,P) f is a function of T and P - G Mass velocity kg/(m2.s) h Specific enthalpy J/kg k Thermal conductivity W/(m.K) Ls Total length of capillary tube m m& Mass flow rate kg/s M Molecular Weight g/mol Mv Volumetric flow rate SLPM p Perimeter of heat transfer area m P Pressure Pa or N/m2 Pitchm Pitch of capillary tube m Pitchfin Pitch of fins m C µ Pr Prandtl number = p - k National University of Singapore vii Filename:TeoHY.pdf NOMENCLATURE q Heat transfer per unit mass W/kg Q& Heat transfer W Ro Universal gas constant J/(kg.K) ρUD Re Reynolds number = H - µ S& Specific entropy J/kg.s T Temperature K u Average velocity of fluid m/s x Quality of fluid - y Liqufied yield fraction - Greek Letters α Helical angle β Helical angle γ Non-linear coefficient λ Dimensionless conduction parameter µ Fluid dynamic viscosity µJ-T Joule-Thomson coefficient σ Stefan-Boltzmann constant ρ Fluid density ε Emissitivity θ Dimensionless temperature Φ Dimensionless pressure for hot fluid National University of Singapore viii Filename:TeoHY.pdf NOMENCLATURE ψ Dimensionless pressure for returned fluid Superscipts & Subscripts 0 Initial state 1,2,3,4,5 State points amb Ambient or room temperature and pressure conditions f High pressure incoming fluid fa High pressure vapor state in two-phase condition fl High pressure liquid state in two-phase condition finm Contact between capillary tube & fins (Area) fin Capillary fins fm Contact between high temperature fluid and capillary tube (Area) g Saturated fluid in gas state H Hydraulic hel Helical in Inlet l Low pressure returned fluid m Capillary tube man Mandrel min Minimum ml Contact between capillary tube and returned fluid (Area) out Outlet pc Polycarbonate National University of Singapore ix Filename:TeoHY.pdf NOMENCLATURE r Radiation ref Refrigeration s Shield sh Shield si Shield inside so Shield outside ss Stainless steel National University of Singapore x Filename:TeoHY.pdf LIST OF FIGURES List of Figures Page Figure 1.1 Classification of Recuperative Cycles Heat Exchangers 2 Figure 1.2 Regenerative Cycles Heat Exchanger 4 Figure 2.1 Joule-Thomson Cycle and Temperature-Entropy Diagram 19 Figure 2.2 Contours of velocity head non-dimensionalized with ½ρU2 21 Figure 2.3 Development of the axial velocity fields at Re=104 & Pr=7 21 Figure 2.4 Development of secondary velocity fields at Re=104 & Pr=7 22 Extracted from [21] Figure 2.5 Mean axial velocity distribution and vectors of means 22 secondary flows in curved and helically coil pipes Extracted from [20] Figure 2.6 The CFD models for the ordinary helix centerline 23 Extracted from [24] Figure 2.7 The streamline patterns near the top of the arch. 23 Extracted from [24] Figure 2.8 Typical J-T Cryostat Nozzle Schematic Diagram 26 Figure 2.9 Schematic of J-T Inversion Curve 28 Figure 2.10 Basic Joule-Thomson Cycle 30 Figure 2.11 A Real Hampson-type Joule-Thomson Cryocooler 35 Figure 2.12 Schematic of Hampson-Type Joule-Thomson Cryocooler 36 Figure 2.13 Schematic of Experimental Apparatus 37 Extracted from [12] National University of Singapore xi Filename:TeoHY.pdf LIST OF FIGURES Figure 2.14 Photograph of Experimental Apparatus Extracted from [12] 39 Figure 3.1 Helical Coil Notations – Capillary Tube 43 Figure 3.2 Helical Coil Notations – Fins 44 Figure 3.3 Elevation View of Helical Coil Capillary Tube and Fin 45 Figure 3.4 Plan View of Helical Coil Capillary Tube and Fin 46 Figure 3.5 Cross-Sectional View of Helical Coil Capillary Tube and Fin 47 Figure 3.6 Tf, Tl, Tm and Tfin Relations 50 Figure 4.1 Variation of Argon Density against Temperature 63 Figure 4.2 Variation of Argon Specific Heat against Temperature 63 Figure 4.3 Variation of Argon Entropy against Temperature 64 Figure 4.4 Variation of Argon Enthalpy against Temperature 64 Figure 4.5 Variation of Argon Viscosity against Temperature 65 Figure 4.6 Variation of Argon Thermal Conductivities against 65 Temperature Figure 4.7 Temperature-Entropy Charts for Argon 67 Figure 5.1 Simulated T-s Diagram (CASE 1) 78
Load more

Recommended publications
  • High Efficiency and Large-Scale Subsurface Energy Storage with CO2
    PROCEEDINGS, 43rd Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, February 12-14, 2018 SGP-TR-213 High Efficiency and Large-scale Subsurface Energy Storage with CO2 Mark R. Fleming1, Benjamin M. Adams2, Jimmy B. Randolph1,3, Jonathan D. Ogland-Hand4, Thomas H. Kuehn1, Thomas A. Buscheck3, Jeffrey M. Bielicki4, Martin O. Saar*1,2 1University of Minnesota, Minneapolis, MN, USA; 2ETH-Zurich, Zurich, Switzerland; 3TerraCOH Inc., Minneapolis, MN, USA; 4The Ohio State University, Columbus, OH, USA; 5Lawrence Livermore National Laboratory, Livermore, CA, USA. *Corresponding Author: [email protected] Keywords: geothermal energy, multi-level geothermal systems, sedimentary basin, carbon dioxide, electricity generation, energy storage, power plot, CPG ABSTRACT Storing large amounts of intermittently produced solar or wind power for later, when there is a lack of sunlight or wind, is one of society’s biggest challenges when attempting to decarbonize energy systems. Traditional energy storage technologies tend to suffer from relatively low efficiencies, severe environmental concerns, and limited scale both in capacity and time. Subsurface energy storage can solve the drawbacks of many other energy storage approaches, as it can be large scale in capacity and time, environmentally benign, and highly efficient. When CO2 is used as the (pressure) energy storage medium in reservoirs underneath caprocks at depths of at least ~1 km (to ensure the CO2 is in its supercritical state), the energy generated after the energy storage operation can be greater than the energy stored. This is possible if reservoir temperatures and CO2 storage durations combine to result in more geothermal energy input into the CO2 at depth than what the CO2 pumps at the surface (and other machinery) consume.
    [Show full text]
  • Thermodynamics for Cryogenics
    Thermodynamics for Cryogenics Ram C. Dhuley USPAS – Cryogenic Engineering June 21 – July 2, 2021 Goals of this lecture • Revise important definitions in thermodynamics – system and surrounding, state properties, derived properties, processes • Revise laws of thermodynamics and learn how to apply them to cryogenic systems • Learn about ‘ideal’ thermodynamic processes and their application to cryogenic systems • Prepare background for analyzing real-world helium liquefaction and refrigeration cycles. 2 Ram C. Dhuley | USPAS Cryogenic Engineering (Jun 21 - Jul 2, 2021) Introduction • Thermodynamics deals with the relations between heat and other forms of energy such as mechanical, electrical, or chemical energy. • Thermodynamics has its basis in attempts to understand combustion and steam power but is still “state of the art” in terms of practical engineering issues for cryogenics, especially in process efficiency. James Dewar (invented vacuum flask in 1892) https://physicstoday.scitation.org/doi/10.1063/1.881490 3 Ram C. Dhuley | USPAS Cryogenic Engineering (Jun 21 - Jul 2, 2021) Definitions • Thermodynamic system is the specified region in which heat, work, and mass transfer are being studied. • Surrounding is everything else other than the system. • Thermodynamic boundary is a surface separating the system from the surrounding. Boundary System Surrounding 4 Ram C. Dhuley | USPAS Cryogenic Engineering (Jun 21 - Jul 2, 2021) Definitions (continued) Types of thermodynamic systems • Isolated system has no exchange of mass or energy with its surrounding • Closed system exchanges heat but not mass • Open system exchanges both heat and mass with its surrounding Thermodynamic State • Thermodynamic state is the condition of the system at a given time, defined by ‘state’ properties • More details on next slides • Two state properties define a state of a “homogenous” system • Usually, three state properties are needed to define a state of a non-homogenous system (example: two phase, mixture) 5 Ram C.
    [Show full text]
  • Chap. 2. the First Law of Thermodynamics Law of Energy Conservation
    Chap. 2. The First Law of Thermodynamics! Law of Energy Conservation! System - part of the world we are interest in ! Surroundings - region outside the system! World or Universe - system plus surroundings! Open system - transfer of matter between system and surroundings! Closed system - no transfer of matter! Isolated system - closed, no mechanical and thermal contact ! Internal energy of system work done on system! (initial)! Internal energy of system Heat transferred to system! (final)! First law holds however small the heat and work are.! Infinitesimal changes:! work on system due to expansion or contraction! electric or other work on system ! First law holds however small the heat and work are.! Infinitesimal changes:! work on system due to expansion or contraction! electric or other work on system! At constant volume,! Heat capacity at constant volume - the amount of heat transferred to the system per unit increase of temperature! First law holds however small the heat and work are.! Infinitesimal changes:! work due to expansion or contraction! electric or other work! At constant volume,! Heat capacity at constant volume - the amount of heat transferred to the system per unit increase of temperature! Most processes occur at constant pressure. What is the relation between heat absorbed at constant pressure and the energy?! Enthalpy:! heat content, a state function in the unit of energy! The heat absorbed at constant pressure is the same as enthalpy change of the system given that its pressure is the same as the external pressure.! Enthalpy:!
    [Show full text]
  • Second Law Analysis of Rankine Cycle
    Chapter 10 Lyes KADEM [Thermodynamics II] 2007 Refrigeration Cycles The objective of refrigeration cycles is to transfer the heat from a low temperature region to a high temperature region. - if the objective of the cycle is to decrease the lowest temperature, we call it: a Refrigeration cycle. - if the objective of the cycle is to increase the highest temperature, we call it: a heat pump. Carnot cycle As the Carnot cycle is the ideal cycle, let us first try to convert it to a refrigeration cycle, and then we will discuss practical limitations. Figure (10.1) shows a reversed Carnot cycle, the efficiency of this cycle will be: TL η 1−= TH However, if we try to apply the Carnot cycle, we will face some technical difficulties: 1-2: It is not advisable to compress a mixture of vapor and gas, since the liquid droplets would cause excessive wear. → shift point 1 to the right (saturated vapor). 3-4: It would be quite expensive to construct a device to be used in the expansion process that would be nearly isentropic (no losses allowed). It is much simpler to reduce the pressure irreversibly by using an expansion valve (isenthalpic process). Refrigeration cycles 44 Chapter 10 Lyes KADEM [Thermodynamics II] 2007 Figure.10.1. Reversed Carnot cycle. The Ideal vapor-compression refrigeration cycle 1-2: isentropic compression in a compressor. 2-3: isobaric heat rejection in a condenser. 3-4: throttling in an expansion device. 4-1: isobaric heat absorption in an evaporator. Figure.10.2. Ideal vapor- refrigeration cycle. Refrigeration cycles 45 Chapter 10 Lyes KADEM [Thermodynamics II] 2007 The coefficient of performance (COP) of a refrigeration cycle is: benefit Q& in COPR == Cost W&in The coefficient of performance (COP) of a heat pump is: benefit Q&out COPHP == Cost W&in COP can attain 4 for refrigerators and perhaps 5 for heat pumps.
    [Show full text]
  • Microscale Heat Transfer at Low Temperatures (2005)
    Published in: Microscale Heat Transfer- Fundamentals and Applications, S. Kakac, et al. (ed.), Kluwer Academic Publishers (2005), pp. 93-124. MICROSCALE HEAT TRANSFER AT LOW TEMPERATURES RAY RADEBAUGH Cryogenic Technologies Group National Institute of Standards and Technology Boulder, Colorado, USA 1. Introduction This paper discusses the fundamentals and applications of heat transfer in small space and time domains at low temperatures. The modern trend toward miniaturization of devices requires a better understanding of heat transfer phenomena in small dimensions. In regenerative thermal systems, such as thermoacoustic, Stirling, and pulse tube refrigerators, miniaturization is often accompanied by increased operating frequencies. Thus, this paper also covers heat transfer in small time domains involved with possible frequencies up to several hundred hertz. Simple analytical techniques are discussed for the optimization of heat exchanger and regenerator geometry at all temperatures. The results show that the optimum hydraulic diameters can become much less than 100 m at cryogenic temperatures, although slip flow is seldom a problem. The cooling of superconducting or other electronic devices in Micro-Electro-Mechanical Systems (MEMS) requires a better understanding of the heat transfer issues in very small sizes. Space applications also benefit from a reduction in the size of cryocoolers, which has brought about considerable interest in microscale heat exchangers. Some recent developments in miniature heat exchangers for Joule-Thomson and Brayton cycle cryocoolers are discussed. Both single-phase and two-phase heat transfer are covered in the paper, but the emphasis is on single-phase gas flow. Some discussion of fabrication techniques is also included. Another application discussed here is the use of high frequency Stirling and pulse tube cryocoolers in smaller sizes and lower temperatures.
    [Show full text]
  • Benchmarking a Cryogenic Code for the FREIA Helium Liquefier
    FREIA Report 2020/01 July 9, 2020 Department of Physics and Astronomy Uppsala University Benchmarking a Cryogenic Code for the FREIA Helium Liquefier Elias Waagaard Supervisor: Volker Ziemann Subject reader: Roger Ruber Bachelor Thesis, 15 credits Uppsala University Uppsala, Sweden Department of Physics and Astronomy Uppsala University Box 516 SE-75120 Uppsala Sweden Papers in the FREIA Report Series are published on internet in PDF format. Download from http://uu.diva-portal.org Abstract The thermodynamics inside the helium liquifier in the FREIA laboratory still contains many unknowns. The purpose of this project is to develop a theoretical model and im- plement it in MATLAB, with the help of the CoolProp library. This theoretical model of the FREIA liquefaction cycle aims at finding the unknown parameters not specified in the manual of the manufacturer, starting from the principle of enthalpy conservation. Inspiration was taken from the classical liquefaction cycles of Linde-Hampson, Claude and Collins. We developed a linear mathematical model for cycle components such as turboexpanders and heat exchangers, and a non-linear model for the liquefaction in the phase separator. Liquefaction yields of 10% and 6% were obtained in our model simula- tions, with and without liquid nitrogen pre-cooling respectively - similar to those in the FREIA liquefier within one percentage point. The sensors placed in FREIA showed simi- lar pressure and temperature values, even though not every point could be verified due to the lack of sensors. We observed an increase of more than 50% in yield after adjustments of the heat exchanger design in the model, especially the first one.
    [Show full text]
  • Lesson 8 Methods of Producing Low Temperatures
    Lesson 8 Methods of producing Low Temperatures 1 Version 1 ME, IIT Kharagpur The specific objectives of the lesson : In this lesson the basic concepts applicable to refrigeration is introduced. This chapter presents the various methods of producing low temperatures, viz. Sensible cooling by cold medium, Endothermic mixing of substances, Phase change processes, Expansion of liquids, Expansion of gases, Thermoelectric refrigeration, Adiabatic demagnetization. At the end of this lesson students should be able to: 1. Define refrigeration (Section 8.1) 2. Express clearly the working principles of various methods to produce low temperatures (Section 8.2) 8.1. Introduction Refrigeration is defined as “the process of cooling of bodies or fluids to temperatures lower than those available in the surroundings at a particular time and place”. It should be kept in mind that refrigeration is not same as “cooling”, even though both the terms imply a decrease in temperature. In general, cooling is a heat transfer process down a temperature gradient, it can be a natural, spontaneous process or an artificial process. However, refrigeration is not a spontaneous process, as it requires expenditure of exergy (or availability). Thus cooling of a hot cup of coffee is a spontaneous cooling process (not a refrigeration process), while converting a glass of water from room temperature to say, a block of ice, is a refrigeration process (non-spontaneous). “All refrigeration processes involve cooling, but all cooling processes need not involve refrigeration”. Refrigeration is a much more difficult process than heating, this is in accordance with the second laws of thermodynamics. This also explains the fact that people knew ‘how to heat’, much earlier than they learned ‘how to refrigerate’.
    [Show full text]
  • Second-Law Analysis
    Second-Law Analysis 9S.0 OBJECTIVES The first law of thermodynamics is widely used in design to make energy balances around equipment. Much less used are the entropy balances based on the second law of thermodynamics. Although the first law can determine energy transfer requirements in the form of heat and shaft work for specified changes to streams or batches of materials, it cannot even give a clue as to whether energy is being used efficiently. As shown in this chapter, calculations with the second law or a combined first and second law can determine energy efficiency. The calculations are difficult to do by hand, but are readily carried out with a process simulation program. When the second-law efficiency of a process is found to be low, a better process should be sought. The average second-law efficiency for chemical plants is in the range of only 20-25%. Therefore, chemical engineers need to spend more effort in improving energy efficiency. After studying this supplement, the reader should 1. Understand the limitations of the first law of thermodynamics. 2. Understand the usefulness of the second law and a combined statement of the first and second laws. 3. Be able to specify a system and surroundings for conducting a second-law analysis. 4. Be able to derive and apply a combined statement of the first and second laws for the determination of lost work or exergy. 5. Be able to determine the second-law efficiency of a process and pinpoint the major areas of inefficiency (lost work). 6. Understand the causes of lost work and how to remedy them.
    [Show full text]
  • AREN 2110 Second Law: Entropy, and Cycle Formula Summary Sheet I. CLOSED SYSTEM A. Irreversible Processes: B. Reversible Process
    AREN 2110 Second Law: Entropy, and Cycle Formula Summary Sheet ENTROPY BALANCES I. CLOSED SYSTEM A. Irreversible processes: 2 δQ ⎛ kJ ⎞ ΔSSS =2 − 1 = ∫ + S gen ⎜ ⎟ 1 T ⎝ K ⎠ B. Reversible processes: Sgen = 0 2 δQ⎛ kJ ⎞ SS2− 1 = ∫ ⎜ ⎟ 1 T ⎝ K ⎠ C. Adiabatic irreversible processes: Q = 0 ⎛ kJ ⎞ SSS2− 1 = gen ⎜ ⎟ ⎝ K ⎠ D. Adiabatic and reversible processes SS2− 1 = 0 E. Cycle δQ ⎛ kJ ⎞ Qk ⎛ kJ ⎞ 0 = ∫ + S gen ⎜ ⎟ = ∑ + S gen ⎜ ⎟ T ⎝ K ⎠ k Tsurr ⎝ K ⎠ II. OPEN SYSTEM (CONTROL VOLUME) A. Non-steady-state and irreversible control volume dS ⎛ Q& ⎞ kw cv ⎜ ⎟ ⎛ ⎞ = ∑∑⎜ ⎟ +m&&i s i −∑ me s e + S& gen ⎜ ⎟ dt kiT e K ⎝ ⎠ k ⎝ ⎠ subscript i is for inlet and e is for outlet B. Steady-State and irreversible control volume ⎛ Q& ⎞ ⎛ kw⎞ ⎜ ⎟ ∑ m&&e s e − ∑ mi s i = ∑⎜ ⎟ +S& gen ⎜ ⎟ e i k T K ⎝ ⎠ k ⎝ ⎠ C. Steady state and one inlet (1) and one outlet (2) and irreversible control volume ⎛ Q& ⎞ ⎛ kw⎞ ⎜ ⎟ m&&Δ s = m() s2 − s 1 = ∑⎜ ⎟ +S& gen ⎜ ⎟ k T K ⎝ ⎠k ⎝ ⎠ D. Steady-state, one inlet and outlet and adiabatic control volume ⎛ kw⎞ m& () s2− s 1 = S&gen ⎜ ⎟ ⎝ K ⎠ E. Steady state, one inlet and outlet and reversible control volume ⎛ Q& ⎞ ⎛ kw⎞ ⎜ ⎟ m& () s2− s 1 = ∑⎜ ⎟ ⎜ ⎟ k T K ⎝ ⎠ k ⎝ ⎠ F. Steady-state, one inlet and outlet adiabatic and reversible control volume ⎛ kw⎞ m& () s2− s 1 = 0⎜ ⎟ ⎝ K ⎠ G. Steady-state cycle comprised of open system (control volume) processes ⎛ Q& ⎞ kw ⎜ ⎟ ⎛ ⎞ 0 = ∑⎜ ⎟ +S& gen ⎜ ⎟ k T K ⎝ ⎠ k ⎝ ⎠ Can substitute specific properties (kJ/kg-K) for each term above (divide by mass or mass flow rate) CALCULATING ΔS (KJ/KG-K) ⎛ T ⎞ A.
    [Show full text]
  • Dynamic Modeling of the Two-Phase Leakage Process of Natural Gas Liquid Storage Tanks
    Article Dynamic Modeling of the Two-Phase Leakage Process of Natural Gas Liquid Storage Tanks Xia Wu 1,*, Changjun Li 1, Yufa He 2 and Wenlong Jia 1 1 School of Petroleum Engineering, Southwest Petroleum University, Chengdu 610500, China; [email protected] (C.L.); [email protected] (W.J.) 2 China National Offshore Oil Corporation (CNOOC) Research Institute, Beijing 100028, China; [email protected] * Correspondence: [email protected]; Tel.: +86-183-8237-8087 Received: 27 July 2017; Accepted: 05 September 2017; Published: 13 September 2017 Abstract: The leakage process simulation of a Natural Gas Liquid (NGL) storage tank requires the simultaneous solution of the NGL’s pressure, temperature and phase state in the tank and across the leak hole. The methods available in the literature rarely consider the liquid/vapor phase transition of the NGL during such a process. This paper provides a comprehensive pressure- temperature-phase state method to solve this problem. With this method, the phase state of the NGL is predicted by a thermodynamic model based on the volume translated Peng-Robinson equation of state (VTPR EOS). The tank’s pressure and temperature are simulated according to the pressure- volume-temperature and isenthalpic expansion principles of the NGL. The pressure, temperature, leakage mass flow rate across the leak hole are calculated from an improved Homogeneous Non- Equilibrium Diener-Schmidt (HNE-DS) model and the isentropic expansion principle. In particular, the improved HNE-DS model removes the ideal gas assumption used in the original HNE-DS model by using a new compressibility factor developed from the VTPR EOS to replace the original one derived from the Clausius-Clayperon equation.
    [Show full text]
  • Phd Thesis Optimising Thermal Energy Recovery, Utilisation And
    OPTIMISING THERMAL ENERGY RECOVERY, UTILISATION AND MANAGEMENT IN THE PROCESS INDUSTRIES MATHEW CHIDIEBERE ANEKE PhD 2012 OPTIMISING THERMAL ENERGY RECOVERY, UTILISATION AND MANAGEMENT IN THE PROCESS INDUSTRIES MATHEW CHIDIEBERE ANEKE A thesis submitted in partial fulfilment of the requirements of the University of Northumbria at Newcastle for the degree of Doctor of Philosophy Research undertaken in the School of Built and Natural Environment in collaboration with Brunel University, Newcastle University, United Biscuits, Flo-Mech Ltd, Beedes Ltd and Chemistry Innovation Network (KTN) August 2012 Abstract The persistent increase in the price of energy, the clamour to preserve our environment from the harmful effects of the anthropogenic release of greenhouse gases from the combustion of fossil fuels and the need to conserve these rapidly depleting fuels has resulted in the need for the deployment of industry best practices in energy conservation through energy efficiency improvement processes like the waste heat recovery technique. In 2006, it was estimated that approximately 20.66% of energy in the UK is consumed by industry as end-user, with the process industries (chemical industries, metal and steel industries, food and drink industries) consuming about 407 TWh, 2010 value stands at 320.28 TWh (approximately 18.35%). Due to the high number of food and drink industries in the UK, these are estimated to consume about 36% of this energy with a waste heat recovery potential of 2.8 TWh. This work presents the importance of waste heat recovery in the process industries in general, and in the UK food industry in particular, with emphasis on the fryer section of the crisps manufacturing process, which has been identified as one of the energy-intensive food industries with high waste heat recovery potential.
    [Show full text]
  • Lecture Nine Adiabatic Changes
    Lecture nine Adiabatic Changes Adiabatic changes We are now equipped to deal with the changes that occur when a perfect gas expands adiabatically. A decrease in temperature should be expected: because work is done but no heat enters the system, the internal energy falls, and therefore the temperature of the working gas also falls. In molecular terms, the kinetic energy of the molecules falls as work is done, so their average speed decreases, and hence the temperature falls. Because the expansion is adiabatic, we know that q = 0 That is, the work done during an adiabatic expansion of a perfect gas is proportional to the temperature difference between the initial and final states. That is exactly what we expect on molecular grounds, because the mean kinetic energy is proportional to T. Since Then EX) Consider the adiabatic, reversible expansion of 0.020 mol Ar, initially at 25°C, from 0.50 dm3 to 1.00 dm3. The molar heat capacity of argon at constant volume is 12.48 J mol-1 K-1. Q) When a sample of argon (for which γ =5/3) at 100 kPa expands reversibly and adiabatically to twice its initial volume, the final pressure will be? Q) Calculate the final pressure of a sample of water vapour that expands reversibly and adiabatically from 87.3 Torr and 500 cm 3 to a final volume of 3.0 dm 3. Take γ = 1.3. Joule-Thomson Effect The Joule-Thomson (JT) effect is a thermodynamic process that occurs when a fluid expands from high pressure to low pressure at constant enthalpy (an isenthalpic process).
    [Show full text]