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HP3 HEAT PROCESSES Application of Ts,hs,ph diagrams in refrigeration and cryogenic cycles. Enthalpy, entropy, exergy Balances Isobaric and isoenthalpic processes, choking and Joule Thomson effect in real gases (derivation of JT coefficient). Application of JT effect for liquefaction of gases in Linde process (kryogenics). Enthalpic balances (example: two stage compressor refrigeration, ph diagrams). Entropy and exergy balances. Exergetic losses: choking and heat exchangers. Heat processes design based upon entropy generation minimization EGM Rudolf Žitný, Ústav procesní a (derivation ds/dt). Process integration. zpracovatelské techniky ČVUT FS 2010 HP3 TZ2 T-s, h-s, p-h diagrams (application for refrigeration and cryogenic cycles) Vapor compression refrigeration uses reverse Rankine cycle. Compressor increases pressure of refrigerant vapour (ammonia, freons…). Hot vapours are cooled down in condenser. Liquefied refrigerant expands in the expansion valve (throttle valve) – flash evaporation consumes enthalpy of evaporation that is removed from the cooled media. Absorption refrigeration operates also with the reverse Rankine cycle, but compressor is replaced by an absorber. Refrigerant vapours (e.g. ammonia) are absorbed in liquid (e.g.water) and their pressure is increased by pump (power of pump is very small because it is only liquid). At this elevated pressure the refrigerant vapours are desorbed from liquid by supplied heat. Cryogenics and liquefaction of gases utilise also the expansion valve for temperature decrease, but unlike the refrigeration techniques the refrigerant vapour and not liquid expands in the throttle valve (resulting temperature decrease is caused by the Joule Thomson effect that will be described later). What happened with the refrigerant liquid or vapours when passing through the throttle valve will be discussed next HP3 TZ2 Throttling h=0 Let us assume 1 kg of fluid that flows through a porous plug (or expansion valve), that reduces pressure from p1 to p2 The duct is thermally insulated therefore q = 0. 1 kg of fluid is in front of a plug p1,T1,u1,v1 1 kg of fluid is displaced behind the plug p2,T2,u2,v2 The first law of thermodynamic describes energy balance of this 1 kg of fluid taking into account mechanical work done by the fictive pistons displacing fluid through the plug 0 u2 u1 p1v1 p2 v2 h2 h1 Internal energy change Mechanical work done by pistons HP3 TZ2 Compressor refrigeration This is the way how your household refrigerator or air conditioning (heat pumpwith exchanged roles of condenser and evaporator) operates 3 T 3 Condenser 2 Compressor 2 Throttle valve 4 1 1 s 4 Evaporator p-h diagrams are usually used for the compressor refrigeration design Throttling is represented by vertical line in the ph diagram p 2 3 1 4 h HP3 TZ2 Multistage compr. refrigeration 6 7 m 1 Two stage system with medium pressure vessel and common refrigerant. Thermal efficiency is increased. 5 6 4 p 3 2 m 3 7 4 2 2 8 8 5 1 1 h Flowrates in first and second stage are different. Ratio of mass flowrates follows from the enthalpy balance of the medium pressure vessel. 2 (h2 h3 ) m 1 (h7 h4 ) Q ztraty 0m For thermally insulated vessel (Q=0) holds m 2 h4 h7 m 1 h2 h3 HP3 TZ2 Refrigerants Both the temperature in evaporator and condenser must be between the triple point and the critical temperatures Ttp< T < Tcrit Refrigerant Ttp oC Ammonia NH3 -78 CO2 -80 R12 -158 Tcrit Tbp pcrit oC oC MPa 132 -33 11 31 sublimate at atmospheric pressure 112 -30 4 Cooling capacity kJ/m3 determines compressor size (capacity should be as high as possible). Working pressures are usually between 100 kPa and 2 MPa (according to compressor used). Freons are prohibited (R12 is CCl2F2, and aggressive radicals of Fluor destroy ozonosphere). Properties of refrigerants are available in databases. HP3 TZ2 Cryogenics Production, transport and storage of liquefied gases. Gas Boiling point oC at He -270 H2 -250 N2 -200 O2 -180 CH4 -160 atmospheric pressure Such low temperatures can be achieved by using Joule Thomson effect, cooling of a real gas during expansions from very high pressure through throttle valve. HP3 TZ2 Joule Thomson effect What is the temperature of gas after throttling: higher, lower or remains unchanged? Answer depends upon properties of gas and inlet temperature (Joule Thomson effect) dh 0 c p dT (T ( v ) p v)dp T From this equation the Joule Thomson coefficient JT can be expressed as JT ( T v T v v ) h ( ( ) p 1) (T 1) p c p v T cp JT coefficient is positive if T>1 (-coefficient of temperature expansion) and only then the temperature decreases with the pressure release. Dependence of the JT coefficient upon temperature is shown in Fig. It is seen that JT is positive at room temperature for most gases with the exception of hydrogen and helium (for them preliminary cooling is necessary). High values of JT are achieved at low temperatures therefore it is always desirable to to cool down gases before expansion. For ideal gas α=1/T and temperature remains constant Cryogenics - Linde HP3 TZ2 Linde-Hampson cycle – final cool down using throttling of precooled gas Liquefactrion of air 1 2 1 Multistage compressor with 2 intercoolers p=200 bar 3 Throttle valve p=1 bar 4 5 T 3 Separator 6 6 5 4 s HP3 TZ2 Cryogenics -Kapica Kapica cycle – expansion in turbodetander 1 2 Compressor 2 3 Detander 3 T 4 8 9 5 Throttle valve 4 7 8 6 5 Separátor 7 s 6 1 HP3 TZ2 Continuous system-balances Hockney HP3 TZ2 Continuous system-balance Design of thermal units operating in continuous mode is always based upon balances Mass balances (this is quite easy) Enthalpy balances (power consumption, temperatures… sizing equipment) Exergetic balances (enable to estimate measure of irreversibility) HP3 TZ2 Enthalpy balance Similar analysis as in throttling. We assume constant volume of system V. During the time increment dt the heat dQ is delivered to the system and the technical work dW is done by the system. Mass flowrate at inlet p1,u1,dV1 1 m dQ u, V, 2 m State at time t dW u+du, V, p2, u2,dV2 +d State at time t+dt Technical work of turbine (e.g.) dQ dW V (u du)( d ) Vu dV11u1 dV2 2u2 p1dV1 p2 dV2 Internal energy change (mass m) Mechanical work for inlet/outlet dQ dW d (u ) V m 2 (u2 p2 v2 ) m 1 (u1 p1v1 ) dt dt dt d (u ) Q W V m 2 h2 m 1h1 dt Exergetic balances HP3 TZ2 Exergy e [J/kg] is maximum technical work obtainable by transition to the state of environment having infinitely large thermal capacity (e.g. an ocean having temperature Te that remains constant even if heat is supplied or removed from the ocean) . Steady state enthalpy balance (for 1 kg of matter) T 0 hin hout q w 1 Isoentropic expansion 0 h1 he T e( s1 se ) e Exergy e Heat absorbed in ocean s Exergetic loss analysis of continuous systems enables to find out “weak points” from the point of view of large irreversible losses. e h1 he T e( s1 se ) ein eout hin hout T e( sin sout ) losses due to irreversibility HP3 TZ2 Exergetic balances examples Throttle valve h1 h2 e Te s Tds dh vdp vdp dp ds R T p e Te R ln p2 p1 Heat exchanger T1 Heat dq is removed from hot stream at temperature T1 and transferred to cold stream at T2. Entropy of the hot stream decreases and entropy of the cold stream increases ds1 dq T2 Heat transfer surface dq T1 ds2 dq T2 ds ds1 ds2 dq T1 T2 T1T2 Assuming no heat losses (dh=0) the exergy losses are T T de1 Te ds Te dq 1 T1T2 2 Exergetic balances example HP3 TZ2 Heat exchanger water/water, mass flowrate in both streams 1 kg/s, hot stream is cooled down from 95 to 900C, cold stream is heated from 40 to 450C. Heat exchanger can be substituted by HEAT PUMP and TURBINE Carnot cycles T 0C T 0C 95 95 90 90 T [0C] 3.7kW 1kW 45 45 40 40 h [kJ/kg] s[kJ/kg/K] 40 167.45 0.5721 45 188.35 0.6383 90 376.94 1.1925 95 397.99 1.25 Te=27 Te=27 0.58 0.64 H=21kW 1.2 1.25 s Net profit would be 2.7kW of mechanical energy, the same as the exergetic loss of heat exchanger T T 50 E QTe H TH TC C 21 300 365 315 2.7kW HP3 TZ2 EGM Entropy Generation Minimization There are always many different design parameters of apparatuses for thermal unit operations (diameters of pipes, fins,…) satisfying specification, e.g. required duty, maximal pressures, temperatures… Optimum is always a compromise, typically trade off between heat transfer and pressure drop (if you increase velocity in a heat exchanger the heat transfer coefficients increase, but at the same time also pressure loss increases). And it is difficult to balance quite different phenomena: thermodynamics and hydraulics. Frequently the specification of free design parameters is a matter of experience, but… HP3 TZ2 EGM Entropy Generation Minimization EGM is a design concept based upon minimization of irreversible processes. It is a new philosophy: reversible processes are good, irreversible wrong. As a measure of irreversibility the rate of entropy generation in a system is considered. Entropy increase is caused by heat transfer from high to low temperatures (this is always irreversible process) and also by hydrodynamics, by frictional losses (conversion of mechanical energy to heat by friction is also irreversible). These two causes can be summarized for the case of continuous fluid flow (general temperature and flow velocity distribution in space) as S gen Rate of entropy increase in unit volume W 3 mK T 2 : u ( ) T T Irreversibility due to heat conduction. is thermal conductivity. See also previous expression T T ds dq 1 2 T1T2 Scalar product of viscous stress tensor and gradient of velocity u is power dissipated to heat in unit volume HP3 TZ2 EGM Entropy Generation Minimization Previous equation needs explanation. Let us assume a rod of cross section A, thickness dx, made from material with thermal conductivity . T T+dT Q AT A Sin x x+dx A dT dSvolumeAdx Sout A dT T dT dx dT 1 1 Sout Sin A ( ) dx T T dT Adx dT 2 dT 2 ( ) dS ( ) gen 2 2 T dx T dx T dx dSvolumeAdx dT dx Heat flux is directly proportional to temperature gradient HP3 TZ2 EGM Entropy Generation Minimization Example: Internal flow in a heat exchanger pipe: Given fluid (viscosity , thermal conductivity …), mass flowrate through a pipe ( m ), and heat flux q’ corresponding to 1 meter of pipe, find out the diameter of pipe D giving minimum generated entropy. Rate of entropy generation related to unit length of a pipe is the sum of entropy changes in fluid and environment (in the pipe wall): q’ m D T+T wall temperature Tfluid temperature x Entropy increase in fluid Entropy decrease of environment Entropy production in system: pipe+environment ds q' S 'gen m dx T T Enthalpy balance mdh q ' dx Tds dh vdp ds 1 dh v dp q ' 1 dp dx T dx T dx mT T dx S 'gen Remark: You can alternatively derive the same result from previous EGM expression, knowing that the p / dissipated power [W] Vp m q ' m dp q' q ' T m dp T T dx T T T (T T ) T dx HP3 TZ2 EGM Entropy Generation Minimization For circular pipe (q’ is related to unit length of pipe) q' q' T D Nu dp u2 4m 2 m2 2f 2f( ) 32 f dx D D2 D 2 D5 Nusselt number Fanning friction factor And substituting to the previous equation S 'gen Nusselt number Nu and Fanning friction factor f must be evaluated for laminar/turbulent flow regime q '2 32m3 f 2 2 5 2 T Nu TD Minimisation of Sgen gives the optimal value of Reynolds number Reopt uD 2.02 Pr 0.07 ( mq ' 5T See the paper Exergy analysis… by A.Bejan )0.36 This result holds for turbulent flow 2500<Re<1e6 and Pr>0.5 (almost any fluids) HP3 TZ2 EGM Entropy Generation Minimization Similar analysis can be applied for external flows (flows around sphere, cylinder, fins…). Assuming constant temperature of body TB and constant temperature T and velocity u of fluid far from the surface, the total entropy generation rate can be expressed as S gen Q(TB T ) FDu TBT T FD is drag force therefore FDu is power dissipated to heat Need to know more about EGM? Read the book Entropy Generation Minimization by Adrian Bejan, Frank A. Kulacki (Editor) Crc Press (Oct 1995) HP3 TZ2 EGM Entropy Generation Minimization Papers Susan W. Stewart, Samuel V. Shelton: Finned-tube condenser design optimization using thermoeconomic isolation. Applied Thermal Engineering 30 (2010) 2096-2102 Using a detailed system model as a comparison, this study shows that isolating the condenser component and optimizing it independently by minimizing the entropy generation in the condenser component alone, also known as thermoeconomic isolation, can be a practical way to design the condenser for optimum air-conditioning system efficiency. This study is accomplished by comparing the optimum design determined by maximizing the entire system’s COP, an undisputed method, with the optimum design determined by minimizing the entropy generation in the isolated condenser component, with consistent constraints used for the two methods. The resulting optimum designs from the isolated model produced a COP within 0.6%e1.7% of the designs found by optimizing the COP using an entire system model. A good review of EGM applications (references on papers applying entropy minimization to counter flow HE, cross flow HE, shell&tube HE, finned tube condensers, wavy plate HE, offset strip HE) A model of an air-conditioning system using R-410a as the working fluid was developed in EngineeringEquation Solver (EES) [33]. This model includes a detailed simulation of the components of the air-conditioning system for various designs, including the compressor, finned-tube condenser, evaporator, and expansion valve. The paper doesn’t discuss details of EGM, for me it is only an indicator of the fact that the EGM concept gives similar results as the analysis based upon COP method. Optimized geometrical parameters HP3 TZ2 EGM Entropy Generation Minimization Papers Jiangfeng Guo, Lin Cheng, Mingtian Xu:Optimization design of shell-and-tube heat exchanger by entropy generation minimization and genetic algorithm. Applied Thermal Engineering 29 (2009) 2954– 2960 In the present work, a new shell-and-tube heat exchanger optimization design approach is developed, wherein the dimensionless entropy generation rate obtained by scaling the entropy generation on the ratio of the heat transfer rate to the inlet temperature of cold fluid is employed as the objective function, some geometrical parameters of the shell-and-tube heat exchanger are taken as the design variables and the genetic algorithm is applied to solve the associated optimization problem. It is shown that for the case that the heat duty is given, not only can the optimization design increase the heat exchanger effectiveness significantly, but also decrease the pumping power dramatically. In the case that the heat transfer area is fixed, the benefit from the increase of the heat exchanger effectiveness is much more than the increasing cost of the pumping power. the entropy increase by heat transfer the entropy generation number defined by Bejan suffers from the ‘entropy generation paradox’, while the modified entropy generation number avoids such a paradox. the entropy increase by friction HP3 TZ2 EGM Entropy Generation Minimization Papers Lina Zhang,Chun xin Yang, Jian hui Zhou : A distributed parameter model and its application in optimizing the plate-fin heat exchanger based on the minimum entropy generation. International Journal of Thermal Sciences 49(2010) 1427-1436 Temperatures and pressures are calculated in each 3D cell numerically Different optimization methods, for example genetic algorithms are used in the EGM (multi variable minimization of Sgen). HP3 TZ2 Process Integration Pinch Analysis and Targeting Exergetic analysis enables to identify units (boilers, reactors, heat exchangers, furnaces,…) responsible for major irreversible losses in complicated systems (e.g. processing plants of chemical industry). EGM is concentrated to the engineering design of individual apparatuses. Process integration is technology of a preliminary design of complicated systems (network of heat exchangers) aimed to “optimal” arrangement of thermal units from the point of view of process heat utilisation (internal heat transfer between sources and sinks) and minimization of irreversible heat transfer. Key feature is PINCH analysis (it has nothing to do with dogs). Pinch is a critical point in the network of heat exchanger characterised by the smallest temperature difference (approach) between the hot and cold streams. Tells nothing to you, is it confusing? Read e.g. the short and easy paper Gavin P. Towler: Integrated process design for improved energy efficiency. Renewable Energy, Volume 9, Issues 1-4, September-December 1996, Pages 1076-1080 Need to know more about the process integration? Read papers from Bodo Linnhoff, father of this technology (UMIST Manchester) or the paper of his colleague Klemesh HP3 TZ2 Process Integration Pinch Analysis and Targeting System is described as a list of apparatuses (reactors, separators, distillation columns, furnaces,…, so far without heat exchangers) connected by streams. Temperatures and flowrates at entries and outlets of apparatuses are specified according to process requirements. First step of process integration consists in generation of a table of process streams. Each stream is characterized by mass flowrate [kg/s], heat capacity, inlet and outlet temperatures and enthalpy flows H [W] which must be added to heated cold streams or rejected from hot streams. Streams are plotted in graph T,H as vectors (lines if the heat capacity of stream is constant). Vectors of hot streams are added together (by adding enthalpy flow changes) giving composite curve T T 1 2 1+2 H H HP3 TZ2 Process Integration Pinch Analysis and Targeting Composite curve of hot and cold streams in T-H diagram (plot of composite curves is obtained by summing enthalpy changes in the table of process streams) Hot service requirement T [C] Pinch point Streams below pinch H C Streams above pinch Heat utilised by heat exchangers Cold service requirement H [W] The composite curves can be freely shifted in horizontal direction because H represents only enthalpy flow changes. Moving for example the composite curve of cold streams to the right increases temperature difference between the streams (heat transfer surface of the heat exchangers transferring enthalpy from hot to cold streams will be smaller), but at the same time demands on hot and cold service increases. Process integration aims to find out a compromise between the amount of utilised processed heat and investment (heat transfer surface of HE). This optimum determines position of pinch point. Pinch point divides process streams to streams above and bellow pinch and according to this the following simple design rules can be expressed: 1. Never use hot service bellow pinch 2. Never use cold service above pinch 3. Never transfer heat across the pinch HP3 TZ2 Process Integration Pinch Analysis and Targeting Grand Composite Curve (GCC). GCC serves for alocation of hot/cold services to different utility levels (with the aim to satisfy the process requirement by the lowest possible quality of heat, e.g. using cooling water instead of refrigeration). GCC is created from the composite curve by increasing the cold composite temperature by ½ DTmin and decreasing the hot composite temperature by ½ DTmin Hot service requirement T [C] T [C] DTmin Only a part of hot service is supplied by high pressure steam Part of hot service delivered by medium pressure steam H [W] Cold service requirement HP3 TZ2 Process Integration Pinch Analysis and Targeting Try on line web application (written by undergraduate student J.S.Umbach university of Illinois, Chicago 2010) Composite curves Grand composite curves (exchanged axis – enthalpy flow vertical, temperatures and shifted temperatures on horizontal axis, please note that the GCC are simplified – only the composite cold curve is shifted up by DTmin=10)