Simulation of a heat pump model using SIMAN

Transcription

1 Rohester Institute of Tehnology RIT Sholar Works Theses Thesis/Dissertation olletions 1993 Simulation of a heat pump model using SIMAN Venkatesh Sundarraj Follow this and additional works at: Reommended itation Sundarraj, Venkatesh, "Simulation of a heat pump model using SIMAN" (1993). Thesis. Rohester Institute of Tehnology. Aessed from This Thesis is brought to you for free and open aess by the Thesis/Dissertation olletions at RIT Sholar Works. It has been aepted for inlusion in Theses by an authorized administrator of RIT Sholar Works. For more information, please ontat ritsholarworks@rit.edu.

2 Rohester Institute of Tehnology Shool of Information Tehnology Simulation of a Heat Pump model using SIMAN. by Venkatesh Sundarraj A thesis, submitted to The faulty of the shool of Information Tehnology, in partial fulfillment of the requirements for the degree of Master of Siene in omputer Integrated Manufaturing. Approved by: "' _ Thesis Advisor: _ May 17,1993

3 PERMISSION TO REPRODUE Title of Thesis : Simulation of a Heat pump model using SIMAN I, Venkatesh Sundarraj, hereby grant permission to the Wallae Library, of R.I.T, to reprodue my thesis in whole or in part. reprodution will not Any be for ommerial use or profit. May 17, 1993

4 ABSTRAT A Heat pump is a system that follows the vapor ompression yle in whih a vapor is ompressed, then ondensed to a liquid, following whih the pressure is dropped so that fluid an evaporate at a low pressure. The system is onsidered to be a ontinuous system as there is a refrigerant whose state hanges ontinuously throughout the system. This thesis work presents the appliation of the Simulation program SIMAN in a ontinuous modeling environment. The Refrigeration yle was hosen as the Heat Pump as there is a ontinuous flow of the refrigerant through the system and hene was an exellent system for a ontinuous simulation problem. The Variables in the Heat Pump model were written as State variables in Fortran and was linked with SIMAN and the whole proess was then ontrolled by the SIMAN proessor. KEYWORDS : ompressor, ondenser, Evaporator, Pressure, Enthalpy, Mass flow rate, State Variables, Enthalpy, Entropy, Volumetri Effiieny, Universal Gas onstant.

5 TABLE OF ONTENTS 1. Introdution and bakground The simulation proess Heat pump Importane of a Heat pump simulation 4 2. Historial review Introdution Review of earlier models Simulation using SIMTool EVSIM program omponent based simulator Projet Desription Problem Definition Introdution to SIMAN State and Rate Equations definitions in Subroutine State SIMAN software organization for Disrete and ontinuous models Introdution to the heat pump yle Model Building ondenser module Evaporator module ompressor module Data aquisition and speifiation Model Translation using SIMAN subroutines Model verifiation Model validation Experimental onditions Experimentation Desription of SIMAN ommands DISRETE Element ONTINUOUS Hement STAT Element EVENTS Element 35

6 4.5 REPLIATE Element 5. Results and onlusions 5. 1 Analysis of Results 5.2 onlusions 6. Bibliography

7 FIGURES 3. 1 SIMAN file struture 3.2 Shemati of the Heat pump model investigated under Refrigeration mode 3.3 Ph Diagram 3.4 Ts Diagram 3.5 Shemati of ondenser with the flow of refrigerant R Shemati of evaporator with refrigerant flow 5. la Tank Temperature for Qload = 2000 J/se, Temp, range = 280 k 5. lb Tank Temperature for Qload = 4000 J/se, Temp, range = 280 k 5. l Tank Temperature for Qload = 5000 J/se, Temp, range = k 5. Id Tank Temperature for Qload = 8000 J/se, Temp, range = 280 k 5.2a Tank Temperature for Qload = 2000 J/se, Temp, range = k 5.2b Tank Temperature for Qload = 4000 J/se, Temp, range = k 5.2 Tank Temperature for Qload = 5000 J/se, Temp, range = k 5.2d Tank Temperature for Qload = 8000 J/se, Temp, range = k 5.3a Tank Temperature for Qload = 2000 J/se, Temp, range = k 5.3b Tank Temperature for Qload = 4000 J/se, Temp, range = k 5.3 Tank Temperature for Qload = 5000 J/se, Temp, range = k

8 5.3d Tank Temperature for Qload = 8000 J/se, Temp, range = k TABLES 2. 1 omponents used in MARK III, HPSIM & HN model 5. 1 Three ases onsidered for analysis

9 AKNOWLEDGMENTS I would like to reognize the members of my ommittee for their assistane in the ompletion of my thesis. Their diretion, help and ideas were invaluable throughout the projet. I wish to thank Dr. Satish G. Kandlikar for having given me an exellent opportunity to work in the refrigeration modeling aspets and the simulation using SIMAN whih were two totally different fields, and pointing me in the diretion of the researh in both the areas. He has given me a great amount of enouragement, interest and ideas to approah the problem in the right diretion. I also owe a debt of gratitude to Prof. Paul Stiebitz for his ideas and assistane in the area of simulation and for giving me the right diretion on using the simulation language SIMAN for a ontinuous modeling environment. My hairman, Prof. Guy Johnson, deserves speial thanks for the suggestions he has made, and also for his time and efforts in guiding me from beginning to end through my thesis projet.

10 HAPTER 1 Introdution and Bakground Simulation has beome an extremely powerful analysis tool in an inreasingly ompetitive world. It is being used in planning, design, and ontrol of systems. Simulation however gives us the essene, and not the reality, whih may allow us to fous on important features of the system rather than the onfounding details. It involves the modeling system in suh a way of a proess or a that the model mimis the response of the atual system under a given set of onditions to events that take plae over time. The problems faing industry, ommere, government, and soiety in general ontinue to grow in size and omplexity. A need for proedures and tehniques for resolving suh problems are apparent. Simulation models have proved to be the ideal tools to study the real world. In the broadest sense, omputer simulation is the proess of designing mathematiallogial model of a real system and experimenting with this model on a omputer. Thus simulation enompasses a model building of an appropriate experiment involving that model. proess as well as the design and implementation Simulation modeling assumes that we an desribe a system in terms aeptable to a omputing system. In this regard, a key onept is that of a system state desription. If the system an be haraterized by a set of variables, with eah ombination of variable values representing a unique state or ondition of the system, then manipulation of the variable values simulated movement of the system from state to state. These hanges an our ontinuously over time or at disrete instants of time. established deterministially or stohastially depending The disrete instants an be on the nature of model inputs. Though the proedures for disrete and ontinuous models vary, the basi onept of simulating a system over time remains the same. The term "system", used in the world of simulation refers to a olletion of items from a irumsribed setor of reality that is the objet of study or interest. To onsider the sope of the system, one must ontemplate its boundaries and ontents. The term models refer to the desriptions of the systems. Model building is a omplex proess, and in most fields, is an art.

11 omputer simulation is the proess of designing a mathematiallogial model of a real system whih an be "experimented" on a omputer. 1.1 The simulation proess : A simulation proess involves the following ten steps. In modeling the heat pump system, this simulation proess is arefully followed. steps are also indiated. This setion numbers overing eah of the 1. Problem Formulation The definition of the problem inluding a statement of the problemsolving objetives. [Setion 3.1 Problem Definition] 2. Model building The abstration of the system into mathematiallogial relationships in aordane with the problem formulation. [Setion 3.4 Model Building] 3. Data Aquisition The identifiation, speifiation, and olletion of data. [Setion 3.5 Data aquisition and speifiation] 4. Model Translation The preparation of the model for omputer proessing. [Setion 3.6 Model Translation using SIMAN Subroutines] 5. Verifiation The proess of establishing that the omputer program exeutes as intended. [Setion 3.7 Model Verifiation] 6. Validation The proess of establishing that a desired auray or orrespondene exists between the simulation model and the real system. [Setion 3.8 Model validation]

12 7. Strategi and tatial planning The proess of establishing the experimental onditions for using the model. [Setion 3.9 Experimental onditions] 8. Experimentation The exeution of the simulation model to obtain output values. [Setion 3.10 Experimentation] 9. Analysis of Results The proess of analyzing the simulation to draw inferenes and make reommendations for problem resolution. [Setion 5. 1 Results] Analysis of 10. Implementation and doumentation The proess of implementing deisions resulting from the simulation and doumenting the model and its use. 1.2 Heat Pump Any power produing yle, whose proess an be performed in the reverse diretion and in the reverse order, will serve as a Heat Pump yle. arnot yle is the ideal yle. A Heat pump model an be used both in ooling (Refrigeration) & Heating yles. The purpose of a heat pump is to pump heat from a low temperature reservoir to a higher temperature reservoir. A heat pump thermodynami yle an be explained onsidering the proesses that the refrigerant undergoes in the four omponents namely ondenser, Throttle valve, Evaporator and ompressor. A heat pump yle provides an exellent example for a ontinuous as well as a disrete event simulation. The proesses involved in a heat pump yle are dependent on a number of interdependent variables. Besides the basi four omponents there are, for pratial reasons, many other omponents in an atual heat pump system suh as tubes onneting basi elements, 4way valve enabling refrigerant flow reversal for the unit t^operate in the heating and ooling mode, aumulator

13 whih ats as a protetive devie for the ompressor by storing exess refrigerant from entering the ompressor. All the above mentioned omponents make up an atual vapor ompression system. 1.3 Importane of a Heat pump simulation Simulation of a heat pump performane is important in pratial appliations where the omponent performane needs to be mathed in a system, or where the operating parameters need to be seleted to obtain optimum performane. Tools available in simulating a ontinuous as well as disrete event model are employed to provide an effiient model for studying the heat pump performane. The flow of a refrigerant in a heat pump, being ontinuous requires the hanging of its state to be defined very preisely and this is one of the areas where the ontinuous modeling aspet in simulations ome into play. In the same note if there are sudden hanges ourring due to external fators we need the disrete aspet of simulation.

14 HAPTER 2 HISTORIAL REVIEW 2.1 Introdution The performane of a heat pump depends not only on the individual omponents but also on their interation with eah other. The performane in atual systems further depends on the amount of refrigerant and operating onditions. These intriate relations are linked to the amount of refrigerant in the system, as well as operating and design onditions. The first heat pump omputer model publily available was developed by Hiller and Gliksman (1976). Their model was intended to simulate a heat pump in the heating mode, and it beame the basis for later models with more adaptability. Following their work, many other omputer models have been developed and used by manufaturers and researhers. 2.2 Review of earlier models Damaseno (1990) ompared three software programs used for modeling a heat pump. He used Mark III, HPSIM, and HN and for eah of these programs a set of input data are to be speified based on the requirement of the model. The omponents of the heat pump were modeled individually in eah of the three languages. For example as seen in Table 2. 1 the basi input routines for modeling the ompressor are shown and it an be seen that the input data is different for eah of them. MARK III language has two options for the ompressor. One is to use a model inluding effets of different ompressor parameters on the heat pump performane, based on losses and effiienies and aounted for in the internal energy balanes. Heat losses related to heat transfer from the disharge tube to the low side refrigerant gas and from the ompressor shell. These losses may be speified diretly or as a fration of the power input to the ompressor. The seond option is to use a routine where the ompressor power onsumption and the mass flow rate are determined through funtions of the form f(t, Te) = a bt T2 dte ete2 f TTe

15 where Te and T are saturation temperatures at the evaporator and ondenser respetively. The bivariate oeffiients "a" through "f" are obtained from urve fitting experimental performane urves generated from alorimeter measurements, whih are provided by manufaturers. Suh models are alled map based models. The first ompressor model used the ompressor maps speified by the manufaturers data for speifi ompressor types. These maps are,generated for speifi refrigerant onditions a orretion is made during the alulations to adjust the onditions enountered during simulations (Dabiri and Rie 1981). Fisher and Rie (1983) found that the alorimeter map based models predited the performane more aurately than the first option over the same range of operating onditions. The seond model was the loss and effiienybased ompressor model. This model had drawbaks as it ould not predit the ompressor performane as aurately over the same range of operating onditions as the map based model. These models were however well suited for studying internal ompressor improvements and interations and their effet on the system performane. MARK III program features subroutines for short orifies and thermostati expansion valves. omponents of the heat pump, suh as reversing valve, fans, and aumulator reeive some or no attention in the studied models. The program is divided into a high side and a low side. The high side inludes the ompressor, ondenser, and the expansion devie, while the low side ontains the evaporator. In the MARK III program, pressure drop in the air side due to the oils, inluding fins and/or air dut effets are aounted for and in addition the user an speify whether or not the heat generated by the fan is to be inluded in the energy balane. Also in the MARK III program line losses are aounted for, by the speifiation of the rate of heat lost by the liquid line. MARK III is divided into two main parts namely, the high side and the low side. The high side inludes models for the ompressor, ondenser, and the expansion devie, while the low side ontains the evaporator. The heat pump model designed using MARK III was developed to provide a general tool for the predition of the steadystate performane of existing and new designs of eletrially driven airto air heat pumps.

16 The logi of onvergene in the MARK III program is well desribed in Fisher and Rie (1983). The organization and iteration proedure follow losely the logi of the general algorithm featured in the earlier versions of the MARK III program. HPSIM adopted a tubebytube method, in whih the performane of the heat exhanger is simulated by doing alulations over isolated tubes independently. The HPSIM model simulates a heat pump system in whih the expansion devie is of onstant flow area (either a apillary tube or a short orifie). The simulation starts with the ompressor model making use of guessed refrigerant pressure to determine the mass flow rate. The HPSIM model aounts for heat transfer and pressure drop in a reversing valve empirially from a simplified assumption of flow in a tube with some sort of expansion or ontration. The ompressor model used in HN was a mapbased model from Fisher and Rie (1983). The reversing valve aounted for in the HN program inlude haraterizing parameters for mass leakage, heat transfer losses and pressure drops at the valve. Aording to Nguyen (1986), Damaseno et al. (1986, 1987, 1988) the above mentioned parameters may be determined from laboratory tests. In MARK III and HN programs the energy balane is applied separately to the regions of the oil with either single or two phase flow ondition, and the both differed in the proess of iteration, in speifis of modeling the omponents.

17 omponents HPSIM MARK III HN OMPRESSOR Map based X X X Design parameters X X HEAT EXHANGERS Global Analysis X Tube by Tube X EXPANSION DEVIE apillary tube Short orifie X X X X X (Aurator) Thermo Valve REVERSING X VALVE AUMULATOR FAN Table 2.1 omponents used in MARK III, HPSIM & HN models 8

18 2.3 Simulation using SimTool Bukman (1990), has reviewed the urrent status of a general user friendly fluid/thermal systems simulation program alled SimTool. It is a general purpose omputer program for simulating omplex fluid/thermal systems. The user speifies the omponents of the system in an Englishlike model file. The system flow path is established by speifying the interonnetions between the system omponents. Numerous omponent models are inluded in the standard omponent libraries and additional omponent models an be reated by writing soure ode in Fortran or. The available omponent models in simulating advaned thermal systems inlude pumps, ompressors, turbines, storage tanks, gas harged tanks, ondensers, evaporators, throttling valves, pipes, tees, and many other system elements. The simulator ontains fluid property routines to alulate the enthalpy, entropy, speifi volume, absolute visosity, thermal ondutivity, and surfae tension. 2.4 EVSIM program Domanski (1991), disusses the simulation program alled EVSIM that is based on a tubebytube approah, for the simulation of an evaporator with Non uniform OneDimensional Air distribution. The program is written in Fortran 77 and makes use of standard Fortran mathematial funtions. oneptually EVSIM is said to onsist of two different funtional parts. One part for evaluating the performane of a finned tube and the other part to selet tubes for evaluation in a proper order assigning the values of inlet parameters of the refrigerant and air needed for alulations. EVSIM an also simulate a singleslab evaporator equipped with on expansion devie and a twoslab evaporator equipped with either one or two expansion devies.

19 2.5 omponent based simulator Silver (1989), desribes the general features of BS/IE (omponentbased simulator). The program has a omponent based struture whih makes it a flexible tool that aommodates a variety of system onfigurations with a minimum ode. omponents Many have been added to the BS omponent library suh as ompressors, Refrigerant reeiver tanks, ondensers, Evaporators, and Expansion valves. The advantage of maintaining suh a omponent library is the flexibility and ease with whih the omponents an be interonneted. 10

20 HAPTER 3 Projet Desription 3.1 Problem Definition : The heat pump yle is to be investigated under a refrigeration mode and the whole proess is to be simulated using SIMAN's Disrete and ontinuous simulation apablities. The variables that keep hanging ontinuously within the Heat pump yle are defined as state variables in SIMAN whih monitors the hanging state of eah variable. The ontinuous event of SIMAN is the flow of refrigerant through the liquid, while the disrete part is the turning on and turning off the heat pump depending on the temperature in the tank that supplies water for heat transfer in the evaporator. 3.2 Introdution to SIMAN SIMAN is a ombined disreteontinuous simulation analysis language for modeling general systems. The language ontains a number of features that make it partiularly useful for modeling manufaturing systems. SIMAN is a Fortran based simulation language. The language is designed to allow simulation programs to be entered using either bath input statements or in an iterative mode. In SIMAN, we model ontinuous systems by oding the state and differential equations in Fortran or. These equations, whih define the model's state variables, are inserted into subroutine STATE, whih is alled by SIMAN during the simulation's exeution. The subroutine omputes the urrent value of either the state variable or the orresponding derivative value for eah state variable in the model and returns these values to SIMAN. For those variables defined by derivatives, SIMAN automatially numerially integrates the derivative values by using a RungeKutta method, whih yields values for the state variables over time. While modeling a ontinuous system the models would onsist of a relationship for the state of the system over time. If we denote the state of the system by x, then our objetive is to find a funtion f suh that: 11

21 x = f(t, A,xo) where: t denotes time. A xo denotes parameters of the model, and denotes the initial onditions of the system. This relationship is known as a state equation. Also it is possible to develop a relationship for the rate of hange of x with respet to time. This quantity is alled the derivative of x with respet to time. For the Heat pump model there is a ontinuous flow of refrigerant through the system over time. The pressures & temperatures hange ontinuously at different stages in the system. These would be the state variables applied to SIMAN. The objetive of this work is to develop a ontinuous simulation model of a Heat pump model using SIMAN with State variables delared in Fortran and finally test the model for sample ases & generate graphs for the different variables with respet to time State and Rate Equation definitions in Subroutine State The Subroutine STATE must have numbers assigned to eah of the ontinuous state variable in the model. For state variables defined diretly by a state equation, the urrent value for the state variable is returned in S(n), where n is the state variable's number. For those state variables defined by differential equations, the urrent value of the derivative is returned in D(n), where n is the state variable's number. In addition to the D(Derivative) and the S (State) variable, SIMAN provides an array named X, whih is in the OMMON blok alled "SIM " and an be used for storing oeffiients or flags assoiated with differential equation. Although userdefined variables an be used for the same purpose, the X array provides an effiient method for passing data between the disrete and ontinuous omponents of the model. 12

22 3.2.2 SIMAN software organization for Disrete and ontinuous models As shown in Figure 3.1, a SIMAN simulation is divided into distint ativities suh as the System Model Frame development, Experimental Frame development, and analysis of data. The software is further subdivided into five individual proessors whih interat through four data files. The model proessor is used to onstrut a blok diagram, the Experimental proessor that is used to define the experimental frame for the system model, the link pressor that ombines the model and the experimental files, the user written Fortran subroutines like the PRIME, EVENT, STATE and WRAPUP, and finally the output proessor that is used to analyze, format and display the data ontained in the output file. 13

23 f~ Interative ~\ f Input I Input j ( ommand I V ommands J V File V Jser j Subroutines Written Figure. 3.1 Siman file struture 14

24 For the Heat pump model a dummy model frame was written with a Begin and End statements. An experimental frame ontained that defines the experimental onditions (run length, initial onditions, et.) under whih the model is exerised to generate speifi output data. 3.3 Introdution to the Heat pump yle A Heat pump performs the pumping of heat from a low temperature environment (evaporator) to a high temperature environment (generally atmosphere). The working fluid in a Heat pump is alled refrigerant, and it undergoes a thermodynami yle, alled vapor ompression yle as it passes through various omponents. The basi omponents of a Heat Pump yle are shown in Figure 3.2. It onsists of a ondenser whih is a Heat exhanger that has a high pressure refrigerant vapor oming its inlet and gets ondensed into liquid refrigerant at the outlet. The next omponent is the throttle valve whih is a pressure reduing devie. Following in at the throttle valve is the Evaporator whih is similar to the ondenser exept that it onverts the liquid refrigerant to vapor at its outlet. The ompressor is the next devie following inreases the Temperature and pressure of the refrigerant vapor. the evaporator whih A Heat pump thermodynami yle an be explained onsidering the proesses that the refrigerant undergoes in the four basi omponents. The most onvenient diagram for suh explanation and performane analysis is that of a pressure vs. enthalpy oordinate system, as shown in Figure 3.3. The ompressor reeives low pressure and temperature refrigerant at state 1 and ompresses it to a high pressure. This ompression proess is assoiated with an inrease of refrigerant temperature. At state 2, the high pressure and high temperature vapor enters the ondenser. The refrigerant passing through the ondenser rejets heat to the high temperature reservoir and hanges, to a subooled liquid at state 3. Then, the refrigerant flows through the expansion devie undergoing a drop in pressure and temperature. 15

25 Finally, the low pressure, low temperature refrigerant at state 4 enters the evaporator, where it piks up heat from the low temperature reservoir, reahing a superheated vapor state 1 at the evaporator exit. The above mentioned explanation on low and high temperature Water in Water out ondenser Throttle Valve Evaporator Qload Water out 7 Q_ t Water in _2!***lJ*F^rz 3" t Figure. 3.2 Shemati of the Heat Pump model investigated under Refrigeration mode 16

26 reservoirs are the indoor and outdoor environment, when the heat pump is operating in the ooling mode. The Ts (TemperatureSpeifi entropy) diagram shown in figure 3.4 shows that the temperature rises from state point 1 whih is the inlet of the ompressor, to state point 2 whih is the outlet of the ompressor relatively in the Ph (PressureEnthalpy) diagram shown in Figure 3.3 an inrease in pressure is seen from state point 1 to 2. Similarly the temperature drops down from a superheated state 2, to a lower temperature before entering the ondenser and remains a onstant in the ondenser. The refrigerant then undergoes a drop in temperature and pressure in the throttle valve and finally in the evaporator a onstant temperature is maintained with only a hange in entropy. The most onvenient diagram for explaining the overall heat pump yle is the pressure vs. enthalpy diagram. The ompressor reeives low pressure and temperature refrigerant at state 1 and ompresses it to a high pressure. This ompression proess is assoiated with an inrease of refrigerant temperature. The high pressure and high temperature vapor enters the ondenser at state 2. The refrigerant passing through the ondenser rejets heat to high temperature reservoir and hanges, usually to a subooled liquid at state 3. The refrigerant then flows through the expansion devie undergoing a drop in pressure and temperature. Finally the refrigerant enters the evaporator, where it piks up water tank and reahing a super heated vapor state 1 at the evaporator exit. heat from the low temperature 17

27 Enthalpy Figure. 3.3 Ph Diagram (2 Entropy Fig. 3.4 TfrDiagram

28 3.4 Model Building ondenser module The ondenser is basially a heat exhanger inside whih refrigerant gas flows and gets ondensed to liquid. The ondenser module was hosen to be the start point of the whole simulation. As a first step temperature at inlet of the ondenser is initialized. A all to the subroutine ondenser from subroutine STATE, swithes the ontrol to the subroutine program where the following variables like the Overall Heat transfer oeffiient * Area (UA), Enthalpy at ondenser inlet (h2), Mass flow rate (m), ondenser temperature (T) The Heat transfer rate is obtained as a funtion of UA and DT. Saturated liquid enthalpy at the ondenser outlet is obtained as a funtion of assumed value of the outlet temperature. Newton Raphson method has been used in order to optimize the assumed value of temperature at ondenser outlet T3. Water out h3,t3,p3 i ondenser Refrigerant out T Water in h2,t2,p2 Refrigerant in Figure 3.5 Shemati of ondenser with the flow of refrigerant R12 Nomenlature : h2 I13 or hi T2 = Enthalpy = at ondenser inlet. Enthalpy at ondenser outlet. = Temperature at ondenser inlet. 19

29 T3 P2 P3 m Q = Temperature at ondenser outlet. = Pressure at ondenser inlet. = Pressure at ondenser outlet. = Mass flow rate of the refrigerant. = Heat removed from the ondenser. Refrigerant used = R12 Input speifiations : U* A ( Overall Heat transfer oeffiient * Effetive heat transfer surfae area of the ondenser) h2 T (ondenser temperature) T3OLD m (Mass flow rate) Governing equation : Q =m(h3 h2) also Q =U*A(T3T) Equation development : Q = m (I13 h2) also Q = U*A (T3 T) (3.1) From the governing equation : I13 = h2 Q/m 20

30 Substituting the value of Q from equation 3. 1 we get h3 = h2 U*A(T3T)/m Sine h_ is obtained as a funtion of temperature at the ondenser outlet (T3) we have f(t3) = h2 h3 (U*A(T3 T)/m) = 0 (3.2) Taking the derivative of equation 3.2 we get f(t3) = (DI13/DT3) (U*A/m) Using NewtonRaphson onvergene tehnique T3NEW = T3 OLD (f(t3)/f(t3)) Evaporator module : The evaporator is also a heat exhanger inside whih a low pressure refrigerant flows at the inlet. Water out h4,t4,p4 1T, Refrigerant Evaporator 7 J " hl,tl,pl Refrigerant out / A in Water in Figure 3.6 Shemati of evaporator with refrigerant flow 21

31 Nomenlature h4 = Enthalpy at evaporator inlet. hi = Enthalpy at evaporator outlet. T4 = Temperature at evaporator inlet. T 1 P4 Pi Qe = Temperature at evaporator outlet. = Pressure at evaporator inlet. = Pressure at evaporator outlet. = Heat added to the evaporator. Input speifiations : U* Ae ( Overall Heat transfer oeffiient * Effetive heat transfer surfae area of the evaporator) h4 Te (ondenser temperature) TiOLD me (Mass flow rate) Governing equation : Q =m_(hi h4) also Q =U*A(TeTD Equation development : Qe = m (hi 114) also Qe = U*Ae ( Te T_OLD ) (3.3) From the governing equation : hi = I14 Qe / me 22

32 Substituting the value of Qe from equation 3.3 we get h i = h4 U*Ae ( Te TiOLD ) / me Sine hi is obtained as a funtion of temperature at the evaporator outlet (Ti) f (TD = hi h4 ( U*Ae ( Te TiOLD ) / me ) = 0 (3.4) Taking the derivative of equation 3.4 we get f(ti) = ( Dhi / DTi ) ( U*Ae / me ) Using NewtonRaphson onvergene tehnique TiNEW = Ti OLD ( f(ti) / f (Ti) ) ompressor module : The ompressor is one of the four essential parts of a vapor ompression yle and may be of the reiproating, rotary, helial rotary, or entrifugal type. Nomenlature : = hi Enthalpy at ompressor inlet. h2 = Enthalpy at evaporator outlet. T i = Temperature at evaporator inlet T2 Pi P2 PD ti W = Temperature at evaporator outlet. = Pressure at evaporator inlet. = Pressure at evaporator outlet. = Piston Displaement. = Volumetri effiieny. = Work done on the ompressor. 23

33 = hi at Enthalpy ompressor inlet. h2 = Enthalpy at ompressor outlet. h2i = Ideal Enthalpy at ompressor outlet. Y r\[ = p/v = onstant. = learane fator. = Effiieny. Input speifiations : hi Y ei PD Pi (ompressor inlet pressure) P2 (ompressor outlet pressure) Governing equation : W = [ Y / (1v) ] * Pi*Vi*[ (P_/P_)Y1 1) ] Equation development : The value of y is obtained from the following expression y = p / v where n is the Speifi heat at onstant pressure and v is the Speifi heat at onstant Volume. The value of p was obtained from the Steam Tables orresponding to the outlet temperature of the ompressor and the value of v was found from the following equation y n R where R is the Universal Gas onstant. 24

34 The value of R is obtained from the equation R = R/M where M is the Molar weight of the R 12 refrigerant From the Governing equatioh it is known that W =[y/(l Y)]*Pl*Vl*[(P2/Pl)Y"1l)] Using the equation QW = (hih2i) sine Q = 0 as there is no Heat Transfer tanking plae we get h2i = hi W From the Effiieny equation Tli = ( h2i hi we obtain ) / ( h2 hi ) h2 = hi (h2ihi)/ej The volumetri effiieny of the ompressor is obtained by the equation r\ = (1 (* (P2 / Pi) 1/Y) The mass flow rate of the refrigerant liquid is obtained from m = (tl * PD) / Vi 25

35 m3/kg Work done on the ompressor is finally obtained from the equation W = m * ( h2 hi) 3.5 Data aquisition and speifiation Data olletion for the heat pump model was ahieved from the " Thermodynami properties in SI " hand book. The properties of the refrigerant 12 was hosen and various polynomial urve fits were setup in order to form the relationships between the various parameters. The urve fit shown in Appendix B.l represents the pressure temperature urve whih is obtained for a temperature range of 200 F to F and a pressure range of 9957 Pa to Pa. The urvefit equation obtained was y = x X E E4x E4X E7X5 where y represents pressure and x represents the orresponding temperature. Appendix B.2 presents the relationship between Inverse of temperature vs. the natural logarithm of pressure and the ranges are similar to the values in Appendix B.l The urvefit equation obtained was y = E E4x E6x2 where y represents Inverse value of temperature and x represents natural logarithm of pressure. The volume vs. pressure urvefit is presented in Appendix B.3 whih relates a volume in the range of m3/kg to and the urvefit equation was y = E E10x E16x E23x E29X4 where represents volume and x represents the pressure. y Appendix B.4 gives the temperature vs. enthalpy relationship for whih the enthalpy range is between 0 kj/kg to kj/kg. The urvefit equation is given by 26

36 y = x E4x E5x E8x E10X5 where y represents the temperature, x represents liquid enthalpy. Enthalpy vs. temperature urvefit graph is shown in Appendix B.5 and the urvefit equation for that relationship is given by y = E E4x x x E3X* E6x5 where y represents iiquid enthalpy and x the orresponding temperature. The Appendix B.5 shows the relationship between the enthalpy in the liquidvapor region vs. the temperature and the equation for urvefit is given by y = E x x E2x3 where y represents enthalpy in the liquid vapor region and x represents the temperature. Finally Appendix B.6 shows the vapor enthalpy vs. temperature and the range for the vapor enthalpy is from J/kg to 241 J/kg. The urvefit equation for this relationship by y = E x x E3x3 is given where y represents vapor enthalpy and x represents temperature. Eah of the above mentioned equations are used in order to obtain relationships between variables and these are stored as state variables by SIMAN and used in proessing the ontinuous hange in the values and optimizing the values for running the yle. 3.6 Model Translation using SIMAN Subroutines The SIMAN subroutine was modeled as a ombined Disrete and ontinuous model. The refrigerant flow through the various modules (ondenser, Evaporator, ompressor) was modeled as a ontinuous simulation and the flow of water from an external tank into the Evaporator was modeled as a disrete simulation. 27

37 The subroutine STATE as mentioned in the earlier hapters is alled by SIMAN only for the ontinuous modeling onstruts. The state variables involved in the Heat pump yle were defined in this subroutine. All the state variables in the Heat pump yle were defined in the initializing phase, using the "EQUIVALENE" statement in Fortran. The "OMMON/SIM" statement was used for passing SIMAN variables between the various subroutines. Similarly " OMMON/ ATTRIB" statement was used to pass the Fortran variables between the subroutines. The first step in the Subroutine STATE was to all the ompressor module and obtain a mass flow rate value for the refrigerant R12, used in the system. One the mass flow rate was determined the next step was to initialize a ondenser outlet temperature that was assumed and using that value the ondenser module was alled next to obtain the new outlet onverged outlet temperature value and for ahieving that Newton Raphson method was used. Using the Funtion subprogram "P3(Ti)" that was obtained from the graph shown in Appendix B.l the Pressure at the ondenser outlet was alulated orresponding to the ondenser outlet temperature. Following the ondenser, the next all was to the Evaporator module for whih the input variables like the enthalpy, evaporator temperature, mass flow rate and an assumed evaporator outlet temperature are speified and the new evaporator outlet temperature is returned after the onvergene in the evaporator module. Using the new temperature value the Funtion subprogram "PVAP (Tv)" is alled to return a evaporator outlet pressure value orresponding to the evaporator outlet temperature. The equation for the funtion subprogram is obtained from the urvefit graph shown in Appendix B.l. As a part of the disrete event modeling the evaporator surrounded by a water jaket and the water was pumped from a reirulating water bath. The water bath was given a ertain amount of heat load (Qload) and was ontrolled within a speified upper and lower temperature limit. It is speified that if the Qload inreases and reahes the upper temperature limit then the Heat pump is turned on and one the yle begins the Qload starts to derease and runs till the lower temperature limit is reahed and one that ondition is ahieved the heat pump is turned off. The subroutine "Event" written in SIMAN speifies the swithing off the heat pump or turning it on, depending on the ondition given in the experimental frame of SIMAN. ^g

38 The next module is ompressor and the Work done on the ompressor is alulated. The input variables used in this module are the enthalpy at the ompressor inlet, the ratio of speifi heat, ompressor effiieny, piston displaement and pressure. The funtion subprogram TEMP (P2) was used to alulate the ompressor outlet temperature orresponding to the ompressor outlet pressure. Using the ompressor outlet temperature obtained from the previous equation the funtion subprogram HVSAT(TV) is alled to obtain the ehthalpy at ompressor outlet. To obtain the inlet temperature value the funtion subprogram TEMP (P2) was used and orresponding to the ompressor inlet temperature the enthalpy at ompressor inlet is alulated from the funtion subprogram HVSAT (Tv). 3.7 Model Verifiation The output file obtained from SIMAN is presented in Appendix A.3. Based on the state variable numbers speified in the subroutine STATE, the first state variable is T3 for whih the onverged value obtained is K. The initial value supplied for T3 was 345 K and the new value of T3 was obtained by the NewtonRaphson onvergene riteria and the SIMAN proessor was used for error heking. The similar proedure was adopted for obtaining the outlet temperature of the evaporator and the output value was K. The assumed value for initialization was 282 K. It an also be seen in Figure 3.4 that the temperature T3 whih is the ondenser outlet temperature, is higher than Ti whih is the evaporator outlet temperature. For obtaining the value of P2 and Pi the equations obtained from the urvefit graphs shown in Appendix B. The pressure values are obtained as a funtion of the orresponding temperature values. The work done on the ompressor W, was found to be 4865 Joules. This was obtained from the subroutine ompressor and the optimization done by SIMAN. Similarly the other outputs Q (Heat released by the ondenser) and Qe (Heat gained by the evaporator) were found to be J/se and J/se respetively. These output values obtained are speifi to Refrigerant 12 (R 12). 29

39 The flow of water from the tank to the evaporator as mentioned earlier was applied as a disrete event. The Qload that is applied to the water tank was varied for different test ases and the orresponding tank temperatures were obtained. 3.8 Model validation The relationships used in the heat pump model were related to the work done by Domanski (1983) and Didion (1983). For the ompressor, in modeling the ylinder proess, both ompression and the expansion proess are assumed to be polytropi with the same polytropi index y, following the equation : P.VY = onstant where Y = polytropi index P = pressure V = refrigerant vapor speifi volume All the equations used for modeling the ompressor have been obtained from previous work and the equations have already been validated and aepted. The urve fit graphs shown in temperaturepressure et., were obtained from property tables and hene are aurate in their Appendix B for relationships between pressureenthalpy, pressurevolume, results. For the ondenser and the evaporator model the NewtonRaphson's tehnique was used and the error heking done by SIMAN. The ondenser and the evaporator have similar working priniples and hene the basi equations used for the two modules were almost the same. For the disrete event taking plae in the evaporator, the Qload values were varied and the tank temperatures were plotted. 3.9 Experimental onditions The heat pump model has been analyzed for various test onditions by varying some of the input parameters. In the evaporator for example we have a ontinuous and a disrete event taking plae. transfer, the Qload For the disrete ase were a water tank is used for irulating water for heat ondition was varied from a value of 2000 to 8000 J/Se. The graphs 30

40 obtained are shown in Appendix. Similarly the evaporator temperature Te an be varied and various output ases an be obtained. For the ondenser the temperature T (ondenser temperature) an be varied for obtaining various test ase results. Also by varying the input parameters like the Piston displaement and the mass flow rate we an obtain a number of test ase results. Elements Ranges Te K T K Qload Watts Note : The refrigerant used for this model is R Experimentation The SIMAN struture as shown in Figure 3.1 explains the relationship between the Experimental frame, Model Frame and the Userwritten subroutines. The experimental frame for SIMAN has a ".EXP " extension for the file and the model frame uses a ".MOD " extension. On ompilation of the model and experimental frames SIMAN generates a file with a ".MLS " and a ".ELS " extension files respetively. The User written subroutines are put in a fortran format with a ".FOR " extension. This file is ompiled separately using the Fortran ompiler and a ".OBJ " (objet) file is generated. One this is done the next step would be to link the ".MLS ", ".ELS " and the ".OBJ " files. Upon doing the SIMAN proessor generates an output file with a ".OUT " extension ontaining the results from the simulation. 31

41 HAPTER 4 Desription of SIMAN ommands 4.1 DISRETE Element DISRETE element defines the variables assoiated with disrete systems. In the Heat pump model the tank temperature is the disrete element and hene the speifiation inludes the maximum number of onurrent entities in the system and the maximum number of general purpose attributes assoiated with the entity. Format : DISRETE,MENT,MATB,NFIL,NSTA; Operand Desription Default MENT The maximum number of onurrent entities in the 0 system, speified as an integer onstant; MATB The maximum number of general purpose attributes 0 assoiated with an entity, speified as an integer onstant. NFIL The number of files in the system, speified as an integer 0 onstant. NSTA The number of stations in the system, speified as an 0 integer onstant. 4.2 ONTINUOUS Element ONTINUOUS element speifies the integration parameters of a ontinuous model. This element has been inluded in the experimental frame for all the ontinuous variables in the heat pump model. The ONTINUOUS element must follow the PROJET element and preede all other elements exept the DISRETE element. 32

42 Format ONTINUOUS, NEQD, NEQS, DTMIN, DTMAX, DTSAVE, AERR, RERR, SERR; Operand Desription Default NEQD The number of differential equations, speified as an integer. 0 NEQS The number of state and differene equations, speified as an integer. 0 DTMIN The minimum allowable step size, speified as a real 1. onstant. DTMAX The maximum allowable step size, speified as a real 1. onstant. DTSAVE The time between save points for reording the values of STAT variables, speified as a real onstant AERR The absolute single step trunation error of the RKF algorithm, speified as a real onstant RERR The relative single step trunation error for the RKF algorithm, speified as a real onstant SERR The severity of the auray error when a step size smaller than DTMIN is required. The options are: F Fatal error terminating the simulation; W Warning message with the simulation ontinued; or N No W message and the simulation ontinued. 33

43 The first operand of the element speifies the number of differential equations involved in the model. For the heat pump there are no differential equations and hene the value is zero. The NEQS operand speifies the number of State variables used in the model. There are 17 state variables speified for the heat pump model. The next five operands ontrol the integration time step size, DTFUL. SIMAN uses a variable step size algorithm that ontinuously adjusts DTFUL based on the auray ahieved on the previous step. The value of DTFUL is always seleted in the range from DTMIN to DTMAX. For the heat pump model sine we have no differential equations (NEQD equals 0), a fixed step size is used and DTFUL is set to DTMAX. The operand DTSAVE speifies the time between save points for reording the values of ontinuous variables. 4.3 STAT Element The STAT element is used to reord timepersistent statistis on ontinuous hange variables. In the heat pump model the statistis are to be maintained for 17 variables and these observations are automatially reorded on all the ontinuous variables speified in the STAT element every DTSAVE time units. Format STAT:N, VAR, ID, NUNIT:...; Operand Desription Default N The STAT variable number speified as an integer. The variables should be numbered onseutively beginning with 1. None VAR The ontinuous variable to be reorded, speified as S(K) or D(K), where K is an integer. None ID The variable identifier used to label the output statistis in the SIMAN Summary Report. The identifier must begin with a letter and be a maximum of 16 haraters long. Blank 34

44 NUNIT The output unit number for saving observations, No values speified as a positive integer. This value is saved automatially inremented by runs. one on subsequent The observations reorded for eah STAT variable event onsist of a pair of values (z,t), where z is the value of the variable and.t is the time when the value was reorded. These observation pairs are used to ompute the mean, standard deviation, minimum value and maximum value that appear on the SIMAN summary report. The alulation of the mean and standard deviation require the area under the urve of the variable. internally by the SIMAN proessor. This is alulated 4.4 EVENTS Element The EVENTS element is used to define the interfae in a ombined disrete/ontinuous model between the ontinuous omponent and the useroded disreteevent subroutines. This element speifies the event numbers to be exeuted at eah ourrene of the speified state event. Whenever the state event ours, SIMAN proesses the event by alling the userwritten subroutine EVENT(L,N) where N represents the number of the event to be exeuted. Format EVENTS:N, XV, XD, THRES, TOL:...; Operand Desription Default N The event number, speified as an integer onstant None XV The rossing variable, speified as S(K) or D(K), where K is an integer. None XD The rossing diretion, speified as P, N or E. None THRES The threshold value, speified as S(K), D(K) onstant, where K is an integer. 35 or a real None

45 TOL The rossing tolerane, speified as a real onstant 0.0 For the heat pump model the subroutine EVENT ontrols the turning off or turning on of the heat pump depending on the tank temperature. The EVENTS element in the experimental frame speifies an upper and a lower bound temperature within whih the tank temperature should lie in order for the heat pump to be turned on or off. 4.5 REPLIATE Element The REPLIATE element speifies the number of simulation runs. The element speifies the beginning time of the first run, the maximum length of eah run, and the initialization to be performed between runs. Format REPLIATE, NRUNS, TBEG, DTRUN, ISYS, ISTAT; Operand Desription Default NRUN The number of simulation runs to exeute, speified as an integer onstant TBEG The beginning time of the first run, speified as a real 0.0 onstant. DTRUN The maximum length of eah run, speified as a real Infinite onstant. ISYS Option for initializing the system status between runs, speified as YES or NO. Yes ISTAT Option for disarding runs, speified as YES or NO. previous observations between Yes 36

46 HAPTER 5 RESULTS AND ONLUSIONS 5.1 Analysis of Results : The heat pump model was modeled for running as a ombined disrete and ontinuous simulation. The results were generated using the SIMAN general proessor and the graphs were obtained using the SIMAN output proessor. For all the results generated by SIMAN the minimum, maximum, mean and the standard deviations were speified whih learly verifies the range of values generated by the SIMAN proessor after performing the iterations for eah of the variables speified. The analysis of the whole system was done in three ases as shown in table For the tank temperature ut off range between , and with the Qload value at 2000 J/se, it was seen that the heat pump was kept in an idle state (off ondition) for a time span of about 5.75 hrs. The running time was lose to 2.5 hrs. When the Qload was inreased from 2000 to 4000 J/se, the idle time was 5.25 hrs. while the running time of the heat pump was around 2.75 hrs. Upon inreasing the Qload to 5000 J/se with the same tank temperature ut off range, the idle time was 4.75 hrs. and the running time was 5.25 hrs. Finally for a Qload of 8000 J/se, the idle time the idle time dropped from 4.75 hrs. to 3 hrs., while the running time went up from 5.25 hrs. to 5.50 hrs. The results obtained from the first test ase showed that the Qload was diretly proportional to the running time of the heat pump and inversely proportional to the idle time. A similar proedure was arried out for varying tank temperature ranges for turning on the heat pump and turning it off. The new range of 5 degree temperature range for ut off was hosen. The first Qload value hosen for ase 2 was 2000 J/se as shown in Figure 5.2a. For this ase it turned out that the idle time was lose to hrs. while the running time was 6.75 hrs. The seond Qload value hosen was 4000 J/se for whih the idle time was 11.5 hrs. and running time about 7 hrs. When the Qload was inreased to 5000 J/se the idle time 37