January 21, 2015
Report internship AeronamicModeling a Vapor Compression Cycle
By: Martin GoossensSupervisor Aeronamic: R. HeukersSupervisor University of Twente: Prof. dr. ir. H.W.M. Hoeijmakers
VCC Test rig
PREFACE
This is the report of my internship at Aeronamic BV as part of my master Mechanical Engineering atthe department Engineering Fluid Dynamics from prof. dr. ir. H.W.M. Hoeijmakers and later on fromprof. dr. ir. C.H. Venner. The report is written to give the University of Twente an indication about myactivities done during my internship.
My internship originally ran from the 15th of September 2014 until the 19th of December 2014, howeverthe internship was extended to the 16th of January 2015. The reason for this was a software changewithin my internship (SciLab to Matlab) at the start of December, so at that moment I only had a coupleof weeks to simulate the whole model in Simulink (toolbox of Matlab). In consultation with my supervisorat Aeronamic we concluded it was nearly impossible to come over with a good simulation model in thatfew weeks, so we decided to extend the internship period to the 16th of January 2015. An additionaladvantage of extending my internship was the fact that at the start of January 2015 the test rig for testingscroll compressors was arrived and installed, whereby it was possible for me to do a performance test ofa scroll compressor. Finally, these test results where very useful for me to validate my simulation model.
In particular I would like to thank my supervisor at Aeronamic Reinder Heukers for assisting me withhelpful suggestions, advice and constructive comments. I am also grateful for Aeronamic offering myinternship.
January 2015,
Martin GoossensMaster student Mechanical EngineeringDepartment Engineering Fluid Dynamicss1082612
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CONTENTS
Preface i
List of abbreviations 3
List of symbols 5
1 Introduction 71.1 Aeronamic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 Assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Structure of the report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Theoretical analysis scroll compressor 92.1 Principle scroll compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Geometry scroll compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Leakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Axial leakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.2 Tangential leakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Pressure ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.1 Static-static pressure ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.2 Total-total pressure ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.3 Total-total pressure ratio (constant static-static efficiency) . . . . . . . . . . . . . . 15
3 Vapor Compression Cycle 173.1 Theoretical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 Description of the coolant medium phases . . . . . . . . . . . . . . . . . . . . . . . 173.2 Mollier diagram in Mathcad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Structure of the simulation models 214.1 Process description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Principle of control loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2.1 Different types of valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.2 Signal converter equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.2.3 Calculating the delays between control actions and measurements . . . . . . . . . 24
5 Simulation model xCos 275.1 Limitation/ error in xCos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2 Conclusions and recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6 Simulation model Simulink 296.1 A roadmap how to open and run the simulink model . . . . . . . . . . . . . . . . . . . . . 296.2 Block definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.2.1 Thermosys and Refprop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306.3 Structure of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.3.1 Defined time steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.3.2 Input parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.3.3 The different control loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7 Test rig test results and a comparison with the Simulink simulation model 397.1 Test rig test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
7.1.1 Pressures in condenser and at the in- and outlet of the compressor . . . . . . . . 397.1.2 Temperatures at the in- and outlet of the compressor . . . . . . . . . . . . . . . . . 407.1.3 Superheat at the inlet of the compressor . . . . . . . . . . . . . . . . . . . . . . . . 407.1.4 Mass flow through the compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
7.2 Comparison of the test rig test results with the Simulinksimulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427.2.1 Inlet conditions compressor (pressure and temperature) . . . . . . . . . . . . . . . 427.2.2 Amount of superheat going into the compressor . . . . . . . . . . . . . . . . . . . 427.2.3 Mass flow through the condenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
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7.2.4 Pressure in the condenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437.2.5 Controller settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
8 Conclusions and recommendations 458.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
References 47
Appendices 49
A Mollier diagram 51A.1 Ph-diagram 4000 RPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51A.2 Ts- diagram 4000 RPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
B Process scheme 53B.1 Process scheme VCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54B.2 Process scheme VCC (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
C Test measurement 57C.1 Test measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
D Technical data of a valve 59D.1 Technical data of the valve: Sporlan SER-A-3/8x1/2-ODF-10-S . . . . . . . . . . . . . . . 59
E Simulation model 61E.1 Simulation model xCos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61E.2 Simulation model Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
F User manual xCos simulation model 63F.1 Block definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63F.2 Main differences between the Simulink model . . . . . . . . . . . . . . . . . . . . . . . . . 63F.3 Description of the different block loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
F.3.1 Input parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64F.3.2 Compressor exit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65F.3.3 Mixing vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66F.3.4 Condenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
F.4 Interaction between loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
G Matlab files 71
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LIST OF ABBREVIATIONS
ATP - Acceptance Test ProcedureDPCV - Discharge Pressure Control ValveLPCV - Liquid Pressure Control ValveMRO - Maintenance, Repair and OperationsNIST - The National Institute of Standards and Technology (NIST) is a measurement standards labora-tory which is a non-regulatory agency of the United States Department of Commerce. [1]PH diagram- Pressure Enthalpy diagramRPM- Revolutions Per MinuteSPCV - Suction Pressure Control ValveSTCV - Suction Temperature Control ValveSV - Suction ValveTS diagram- Temperature Entropy diagramVCC- Vapor Compression Cycle
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LIST OF SYMBOLS
Symbol Subscript* Unit MeaningA - m2 Areacp water kJ/kgK Specific heat waterd ax m Axial clearance between vane tip and the base of the opposite
scrollrad m Radial clearance between orbiting and fixed scroll
dh latentheat kJ/kg Difference in enthalpy between point 4 and the enthalpy on thesaturated vapor line (same pressures)
vapor kJ/kg Difference in enthalpy between the enthalpy on the saturated va-por line and point 3 (same pressures)
subc kJ/kg Difference in enthalpy between point 4 and 5dT water K Difference between in- and outlet water temperature of the con-
denserh 1-7 kJ/kg Enthalpy points 1-7
2s kJ/kg Isentropic enthalpy point 2s m Height of the scrolls
sat.liq kJ/kg Enthalpy on saturated liquid linesat.vap kJ/kg Enthalpy on saturated vapor line
H 1 kJ/kg Total enthalpy point 1l pipe m Length of a pipelinem 1-7 kg/s Mass flow points 1-7
water kg/s Mass flow waterR134a kg/s Mass flow R134a
N - RPM Speed compressorp - m perimeterP 1-7 bar Pressure points 1-7
in bar Pressure point 1
Q 1-2 m3/s Volume flow points 1-2
Q water J/s Heat of waterR134a J/s Heat of R134a
r - m (radial) Polar coordinates out kJ/kgK Entropy point 2T 1-7 K Temperature points 1-7
in K Temperature point 1u - m/s Velocity
in m/s Velocity point 1V chamber1 m3 Volume of the first compression chamberx piston - Position of the piston of a valve in a pipeline (amount of steps)η - Efficiencyθ - - (angular) Polar coordinate
port - Position of the port of a ball valve in a pipeline (in degrees rota-tion)
τ d s Time delayρ 1-7 kg/m3 Density points 1-7
chamber1 kg/m3 Density R134a in the first compression chamber
Table 1: Symbols. *Sometimes additional subscripts are used: ref (reference values) or act (actualvalues)
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CHAPTER 1
INTRODUCTION
1.1 Aeronamic
The assignment is given by Aeronamic - Aircraft Subsystems, Almelo. For 25 years Aeronamic hasbeen and still is on the cutting edge of high technology to design, produce and provide full service Main-tenance, Repair and Operations (MRO) for airflow valves, air turbine starters, centrifugal load compres-sors, cooling turbines, scroll compressors and re-circulation fans for commercial and military aircraft.
Aeronamic focuses on single source production and development of critical (sub)systems and compo-nents, investing highly in innovative research, future proof, cleaner and greener ways of power and airmanagement on-board aircraft.
Aeronamic is the single source supplier for the scroll compressor system used for cooling the galleysand avionics for all versions of Airbus A350XWB with deliveries starting in 2013. The aircraft made itsmaiden flight on June 14th 2014 and so far records 764 aircraft orders.
1.2 Assignment
The assignment was to make a computer simulation model of a Vapor Compressions Cycle (VCC)where the compression part will be realized by a scroll compressor. In the near future, Aeronamic isgoing to deliver scroll compressors for the Airbus A350. Aeronamic received some conflicted measure-ment data of the test installation of the VCC, which at that moment was placed in the USA. At the startof December 2014 the test installation of the VCC was shipped to Aeronamic Almelo. It is useful to havea theoretical model of the cycle for a better understanding of the VCC. The goal of this model is to makeit possible to explain the inexplicable measurement data from the test rig and come up with solutions byfor example changing controller settings. Finally, in the future it may be possible to use the model as anappliance to make it easier to build test rigs for testing other types of scroll compressors.
The first task was to make a calculation sheet of the scroll compressor using the computer programMathcad. For example the volume and pressure ratio between in- and outlet of the compressor wherecalculated and also the efficiency and thermodynamic quantities at important locations where calcu-lated. The second task was to research the entire VCC. Hereafter, a simulation model is made tosimulate the entire VCC. Finally, the reliability of the simulation model is reviewed and conclusions andrecommendations are given.
1.3 Structure of the report
First a scroll compressor analysis is done in chapter 2. The geometry of the scrolls of the scroll com-pressor is obtained from a point cloud from the original CAD-model and is transformed into analyticalfunctions. Second areas and volumes of the compressions chambers and thermodynamic quantitiessuch as pressure and temperature are calculated. Also the influence of two types of leakage are inves-tigated. Finally pressure ratios from the inlet to the outlet of the compressor are calculated.
In chapter 3 the working principle of the test rig of the VCC is explained. All components within theVCC test rig are given schematically in process schemes (given in Appendix B). Hereafter a descriptionof the coolant medium phases is given. The last section explains how the entire VCC is displayed in aMollier diagram with the use of Mathcad.
In chapter 4 the structure of the simulation model based on the Simulink simulation model is explained.Section 4.1 gives a process description of the VCC. Section 4.2 gives the principle of the control loopbased on the Simulink simulation model. In the associated subsections are the different types of controlvalves, the ’signal converter equations’ and the time delays between control action and measurement
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explained, respectively.
Simulating the VCC in Mathcad proved to be virtually impossible and cumbersome, so finding a freesoftware with the same options as Simulink (toolbox of Matlab) was necessary. The software Scilab incombination with the toolbox Xcos was found. The simulation done with this toolbox can be found inChapter 5. However, some limitations and errors were found in xCos and it appears not to be a goodprogram for such a complex model as the VCC. A User manual for the xCos simulation model was atthat moment already made, it can be found in appendix F.
Through consultation with some employees of Aeronamic, Aeronamic decided to buy licenses of Matlabwith the toolbox Simulink. Chapter 6 gives the entire description of the Simulink simulation model. Insection 6.1 a roadmap is given to instruct how to open and run a simulation in Simulink. Section 6.2gives an overview of the meaning of the used blocks in Simulink. The subsequent section (section 6.3)gives the structure of the model: defining the time steps, the input parameters and finally an explanationof the different loops.
In chapter 7 the test results of a performance test of a scroll compressor on the test rig (see section7.1) are given, which was meanwhile arrived and installed at Aeronamic Almelo. In section 7.2 is acomparison between the test rig test results and the Simulink simulation results made.
Chapter 8 gives the conclusions and recommendations.
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CHAPTER 2
THEORETICAL ANALYSIS SCROLLCOMPRESSOR
The compressor used in the VCC (explained in chapter 3) is a scroll compressor. This is shortly ex-plained in section 2.1. A view of the exterior of the scroll compressor and how it is placed in the test rigis given in figure 2.1a. A cross-section view of the scroll compressor is given in figure 2.1b.
(a) Scroll compressor placed in the test rig (b) Cross-section scroll compressor
Figure 2.1: Scroll compressor
The refrigerant that is used in the cycle is R134a, which is not an ideal gas. With the use of the thermo-dynamic state principle a thermodynamic quantity can be found if two other thermodynamic quantitiesare known. A Mathcad sheet is made which loads the thermodynamic properties of R134a [2] and itcan interpolate the value of a thermodynamic quantity with the use of the thermodynamic state principle.
The starting point is the determination of the analytical function of the geometry of the scroll compressor,resulting in areas and volumes of different chambers. With that information it is possible to calculate themass flow and volume flow at both the inlet and outlet of the compressor (section 2.2). The calculationsare made in the software Mathcad.
Two types of leakage occur during the operation of a scroll compressor: axial and tangential leakage.These are elaborated in section 2.3.
An important parameter for the performance of a scroll is compressor is the pressure ratio; which isthe outflow pressure divided by the inflow pressure. Different types of pressure ratios are calculated insection 2.4, dependent on rotational speed, an entropy loss model and efficiency.
NOTE: Because of confidentiality, no geometry values are given during calculations on the scroll com-pressor.
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2.1 Principle scroll compressor
A scroll compressor consists of two interleaving spiral scrolls: a fixed and an orbiting scroll. The orbitingscroll orbits eccentrically without rotating, wherein three processes occur simultaneously: suction (blueregion), compression (violet region) and discharge (red region). This is graphically displayed in figure2.2.
Figure 2.2: Working principle of a scroll compressor [3]
2.2 Geometry scroll compressor
The geometry of the fixed and orbiting scroll is known from a point cloud, which is obtained from theoriginal CAD-model of the orbiting and fixed scroll by the software ’NX’. The point cloud exists of 150points, which leads to a low resolution representation of the scrolls (see figure 2.3).
Figure 2.3: Orbiting and fixed scroll of the scroll compressor (obtained from a point cloud)
An analytic function must be made to calculate areas of different chambers. The Cartesian coordinatesof the point cloud is transformed in polar coordinates with the following equations:
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r =√x2 + y2
tan θ =y
x
Plotting the values of θ against the values of r gives us a straight line. The constants C1 − C13 (thatdescribe the linear line) are approximated with the ’genfit’ function of Mathcad:
rAorb(θAorb) = C1θAorb − C2 with θAorb = [C3, C4]
rBorb(θBorb) = C1θBorb − C5 with θBorb = [C6, C7]
rAfix(θAfix) = C1θAfix − C8 with θAorb = [C9, C10]
rBfix(θBfix) = C1θBfix − C11 with θBorb = [C12, C13]
where the subscript A represents the inner curve of a scroll and the subscript B the outer curve, seefigure 2.3. If the constants would be calculated exactly the form of the function would be exact, becauseit is known that the scrolls are described by an Archimedes spiral.
A surface integral with the correct boundaries gives the area of a chamber (enclosed by the fixed andorbiting scroll and determined by the position of the orbiting scroll). The height of the scrolls hs isobtained by the assembly drawing of the scroll compressor. The volume of chamber 1 is equal to twotimes the initial inlet volume (see figure 2.4) multiplied by the height of the scrolls:
Vchamber1 =2hs
∫ θ2
θ1
∫ r2
r1
r(θ)drdθ
=2hs
∫ θ2
θ1
1
2
[r2(θ)2 − r1(θ)2
]dθ
=2hs
∫ 8π
6π
1
2[rAorb(θAorb)]
2dθ −
∫ 8π
6π
1
2
[rBfix(θBfix)
]2dθ
(2.1)
Figure 2.4: Inlet volume of the scroll compressor (both scrolls are drawn with the analytical functions).NB: The inner part is missing, because this part of both scrolls is not part of the Archimedes spiral andthus could not exactly be determined
The volume flow at the inlet of the compressor Q1 can be calculated by multiplying the known rotationalspeedN by the volume of chamber 1. When the inlet pressure P1 and temperature T1 of the compressorare known the associated density ρ1 can be found with the Mollier diagram of R134a. Finally the massflow of the refrigerant m can be calculated:
m1 = Q1ρchamber1 = Vchamber1Nρchamber1 [kg/s] (2.2)
The mass flow is constant throughout the scroll compressor: m1 = m2. The volume flow at the outlet ofthe compressor can be calculated using the following equation:
Q2 =m2
ρ2(P2, T2)[m
3/s] (2.3)
Where again ρ2 can be interpolated with the Mathcad interpolation sheet of the Mollier diagram, be-cause the pressure P2 is a set-point regulated by a PID-controller and the temperature T2 can be foundby assuming an entropy-loss or an efficiency of the scroll compressor.
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2.3 Leakage
Leakage is an important phenomena in a scroll compressor, because it increases power consumption,reduces compressor capacity and diminishes efficiency. It results in a higher discharge temperature. Arough estimate is made to indicate the order of magnitudes of the leakages.
From literature [4] it is known that the gap between two chambers is typically around 1 µm across. Thisgap may be increased by wear and/or poor machining. It is known that if the gap between two neigh-boring chambers reaches around eight microns, the compressor becomes useless.
There are two types of leakages: axial leakage and tangential leakage, which are discussed in the nextsections.
2.3.1 Axial leakage
Axial leakage occurs between the vane tips and the base of the opposite scroll. The refrigerant R134awill leak from a high pressure chamber to a lower pressure chamber. A visual display of axial leakageis given in figure 2.5
Figure 2.5: A visual display of axial leakage [5] (side view of a scroll compressor)
Ideally there are no gaps between the scrolls and the housing. There is a spring present to ensure thatthe leakage is minimized. In reality it is not practical to reduce the gap to a minimum with a high springstiffness, because this results in a high friction and a high wear. There is a coating layer of manganesephosphate applied which serves as a wear layer.
The axial leakage can be calculated with the following equation:
Leakageax = u ∗ ρ ∗ dax ∗ p [kg/s] (2.4)
where u [m/s] is the velocity and ρ [kg/m3] is the density of R134a in the associated chamber, dax [m]is the axial clearance between the vane tip and the base of the opposite scroll (see figure 2.5) and p[m] is the perimeter. These variables are directly or indirectly known from the input variables or knowngeometry. It is known from drawing specification that the axial clearance will be around 0.3 µm.
Dividing the axial leakage by the mass flow gives the percentage of the total amount of leaking mass.From the calculation it is known that the percentage of the total mass flow that leaks is independentof both the inlet conditions and the rotational speed. It is in the order of 1 percent (≈ 0.235g/s
19g/s ≈ 1.2%,where Pin = 1.83 bar, Tin = 268.15 K and N = 1800 RPM). Of course, the absolute mass flow that’leaks’ is higher in case a higher rotational speed and/or inlet pressure is applied.
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2.3.2 Tangential leakage
Tangential leakage (also called radial leakage) is the leakage between the orbiting and the fixed scroll.The leakage is going from the high pressure chamber to the low pressure chamber.
From tangential leakage point of view, ideally there are no gaps between the orbiting and fixed scroll. Inreality there will be a certain amount of eccentricity. To reduce the gap width as a result of the eccen-tricity, a coating layer of manganese phosphate has been applied serving as a wear layer.
A visual display of tangential leakage is given in figure 2.6:
Figure 2.6: A visual display of tangential leakage [5]
The tangential leakage between two chambers can be calculated with the following equation:
Leakagetan = u ∗ ρ ∗ hs ∗ drad [kg/s] (2.5)
where u [m/s] is the velocity and ρ [kg/m3] is the density of R134a in the associated chamber, drad [m] isthe radial clearance between the fixed and the orbiting scroll (see figure 2.6) and hs [m] is the height ofa scroll. These variables are directly or indirectly known from the input variables or known geometry. Itis also known that the radial clearance will be around 2 µm.
From the calculation it is known that the percentage of the total mass flow that leaks is also independentof both the inlet conditions and the rotational speed. It is in the order of 0.3 percent (≈ 0.049g/s
19g/s ≈ 0.25%
, where Pin = 1.83 bar, Tin = 268.15 K and N = 1800 RPM). Of course, the absolute mass flow that’leaks’ is higher in case a higher rotational speed and/or inlet pressure is applied.
2.4 Pressure ratio
In the VCC the pressure ratio will be substantially constant in time, because both the inlet and the outletpressure (which is hard imposed) will be regulated by PID-controllers. At the discharge of the scrollcompressor there is a mechanical valve which will open at a certain pressure difference between thelast chamber of the scroll compressor and the discharge pipeline of the scroll compressor. Dependingof the pressure in the discharge pipeline, the volume of the last compression chamber in the scroll com-pressor will change. It is convenient to know something about the relation between different pressureratios, mass flows, entropy loss, efficiency, etc. This will be discussed in this section. Calculating thepressure ratios the assumption is made that there are no leakages.
Two models that describe losses in the compressor are investigated:
• A constant entropy loss (section 2.4.1 and 2.4.2)
• A constant efficiency (section 2.4.3)
In both models the volume of the last compression chamber is set to a fixed value, which in reality isnot the case. The reason to do this is to make it possible to investigate the relationship between thepressure ratio, rotational speed, efficiency and the mass flow. Setting the last compression chamberto a fixed value leads to maximum ’static to static’ and total to total pressure ratios, which are not themaximum achievable pressure ratios. In reality the last compression chamber may be smaller, whichleads to higher pressure ratios. The volume flow of the outlet of the compressor can be calculated bymultiplying the volume of the last compression chamber by the rotational speed of the compressor (Hz).
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2.4.1 Static-static pressure ratio
First, there is a ’static to static’ pressure ratio found. The entropy at the inlet is calculated for differentpressures and temperatures. The entropy at the outlet is taken constant and estimated on 1.8 kJ/kgK.The density at the outlet of the compressor can be calculated through dividing the mass flow by thevolume flow of the outlet. The outlet pressure can be obtained with the use of entropy and density.
The pressure ratios are plotted in figure 2.7 and one can see that the pressure ratio with a certain massflow is increasing when increasing rotational speed. In other words: to reach a certain pressure ratiothere is more mass flow needed with a higher rotational speed.
Figure 2.7: Static-static pressure ratio for different rotational speeds. sout is taken constant on 1.8 kJ/kgK
2.4.2 Total-total pressure ratio
The two thermodynamic quantities which are required to find the stagnation pressure are the total en-thalpy (for example: H1 = h1+0.5u2in ) and the entropy at both the in- and outlet. The speed is calculatedby dividing the associated volume flow by the associated chamber area.
The pressure ratios are plotted in figure 2.8. The biggest difference with figure 2.7 is that the maximumpressure ratio is decreasing for increasing rotational speeds. Changing the rotational speed results indifferent velocities at both the discharge and suction pipeline and thus different total enthalpies and adifferent pressure ratio.
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Figure 2.8: Total-total pressure ratio for different rotational speeds. sout is taken constant on 1.8 kJ/kgK
2.4.3 Total-total pressure ratio (constant static-static efficiency)
It is also possible to calculate the total-total pressure ratio, considering that the static-static efficiencywill be constant (η = 0.65). If the efficiency is known the enthalpy at the outlet h2 can be calculated:
h2 =h2s − h1
η+ h1 (2.6)
where η is the efficiency, h1 is the enthalpy at the inlet of the compressor (obtained by the inlet pressureand temperature) and h2s is the isentropic enthalpy (’the enthalpy if the compression was an isentropicprocess’) at the outlet of the compressor .
The pressure ratios are plotted in figure 2.9. Again the pressure ratio is decreasing for increasing massflow.
Figure 2.9: Total-total pressure ratio for different rotational speeds. sout and η are taken constant
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CHAPTER 3
VAPOR COMPRESSION CYCLE
The VCC is a refrigeration cycle, which uses a circulating refrigerant (R134a) as the medium whichabsorbs heat from the space to be cooled and subsequently ejects the heat elsewhere. The refrigerantenters the scroll compressor as a slightly superheated vapor and it will be compressed to a higher pres-sure, resulting in a higher temperature, density, enthalpy and entropy as well.
Section 3.1 gives the theoretical model and the associated description of the coolant medium phasesof the VCC.
Section 3.2 explains how the entire VCC model is displayed in a Mollier diagram with the use of Mathcad.
3.1 Theoretical model
A description of the coolant medium phases in the test rig is given in section 3.1.1. Locations in theVCC are represented by points or lines between points in the Mollier diagram. All the points (1 − 7)mentioned in this chapter are given in figure 3.1. The process scheme is given in two parts: appendixB.1 and appendix B.2. The most important components within the VCC test rig are given schematicallyin these process schemes (less important components are left out to make the model clearer).
Figure 3.1: Graphical display of the VCC in a Mollier diagram
3.1.1 Description of the coolant medium phases
The main components of the VCC are: scroll compressor, hot gas bypass valve, condenser, expansionvalve and the mixing vessel (described sequentially in this section).
During the Acceptance Test Procedure (ATP) of the scroll compressor there is no cooling load (asopposed to when it is operating), which is an important design idea behind the test rig. Therefore onlythe heat added by the scroll compressor has to be extracted. There is no need for a separate evaporatorin the circuit, because the heat extraction takes place in the condenser.
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Scroll compressor 1→ 2
From point 1 to point 2 the scroll compressor compresses the (slightly) superheated coolant resulting ina higher pressure and temperature. The motorized Discharge Pressure Control Valve (DPCV-1B) in thedischarge line of the compressor is PID-controlled (PID-102B) by the measured discharge pressure ofthe compressor. The pressure control valve sets the desired pressure in the discharge pipeline quickly(point 2) by changing the valve position. This pressure is hard imposed, which is possible through thevariable volume of the last compression chamber (as explained before in chapter 2).
Hot gas bypass valve 2→ 3→ 7
The coolant gas coming from the DPCV-1B is divided through an isenthalpic process into a flow to thecondenser (point 3) and a flow to the hot gas bypass valve (point 7). The hot gas bypass valve willcontrol the inlet pressure of the VCC, by changing the mass flow from point 7 and thus the mass flowthrough the condenser. The difference between the mass flows of point 2 and 7 is of course equal tothe mass flow through the condenser (m3).
Condenser 3→ 4→ 5
From point 3 to point 5 the coolant is condensed over an isobar (theoretically) to a liquid coolant. Thereis a cold and a hot flow in the condenser. If it is assumed that there is no heat loss to surroundings theheat of the hot flow is equal to the heat of the cold flow: Qwater = QR134a.
The water flow (cold) through the condenser (CD-1B) is maintained at a constant value with its ownwater pump (P-1B). To reach a fixed temperature difference between the refrigerant and the water inthe condenser, the water flow will mix with the chilled water to maintain the set point. This flow loopwill extract cooling water from the built-in chilled water system through a motorized control valve (SV-1)regulated by the cooling water temperature control loop (PID-101C). So the amount of sub-cooling iscontrolled with this loop. The equilibrium temperature remain basically constant for any given test. Inthe simulation model there has been chosen to set the amount of sub-cooling to a constant value, whichis acceptable because of less variations in the amount of sub-cooling. It leads to a less complex simu-lation model, because the model will be independent from the PID-101C controller. However, in the realtest rig the SV-1 must be controlled, because the flow of point 5 must be pure liquid.
Assuming there is a constant heat capacity coefficient cp for the water (no heat loss to surroundings)the following energy balance is as follows:
Qwater =QR134a
(mcpdT )water =mR134a [dhsubc + dhlatentheat(P3) + dhvapor(P3)]
(mcpdT )water =mR134a [dhsubc + hsat.vap(P3)− hsat.liq(P3) + h3(P3)− hsat.vap(P3)]
mwater =m3 [dhsubc + h3(P3)− hsat.liq(P3)]
(cpdT )water
(3.1)
The desired mass flow of the water loop can now be calculated, because the mass flow of therefrigerant is known (m3), cpdT can be approximated, the amount of sub-cooling can be set and theenthalpy at both point 3 and 4 can be calculated using the reference pressure of the condenser.
The pressure of the liquid coolant is measured and the PID-103B controller controls the mass flowof water with the Liquid Pressure Control Valve (LPCV-1B). So the pressure of point 3 (and thus thepressure of point 4 and 5 because of assuming an isobaric process) can be regulated with the liquidpressure control loop by changing the mass flow of the glycol loop.
Expansion valve 5→ 6
The expansion valve (Suction Temperature Control Valve, STCV-1B) is controlled by the PID-controllerPID-101B. The liquid coolant (point 5) passes the valve. The flow will be a mixture of a gas and a liquid(point 6). The expansion valve will be used to control the inlet gas temperature.
Mixing vessel 6, 7→ 1
To get a homogeneous and fully vaporized refrigerant from the hot gas bypass- and the expansion valve,a mixing vessel has been added. The coolant gas (point 6) and the hot gas (point 7) are purged to-
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gether. The suction loop PID-controllers PID-104B and PID-101B control the hot gas bypass valve andthe expansion valve respectively. These valves work closely together to get the correct temperature andpressure at the compressor inlet (point 1). Very important is that the flow at the inlet of the compressoris pure vapor and absolutely not a liquid.
From the inlet conditions the associated inlet enthalpy h1 with for example the aforementioned Mathcadinterpolation sheet of the Mollier diagram can be calculated. The enthalpy h6 from point 6 and enthalpyh7 from point 7 are known from the output quantities from the condenser and the compressor respec-tively (because of isenthalpic processes in the expansion valve and the hot gas bypass valve). Themass flow at the inlet of the compressor m1 is known due to the compressor analysis (chapter 2). Theenergy balance of the mixing vessel is given in equation 3.2:
m6h6 + m7h7 = m1h1 (3.2)
From the mass balance it is known that the mass flow of point 1 is equal to the sum of the mass flowsfrom point 6 and 7: m1 = m6 + m7. So an expression for the ratio m7
m6can be found:
m6h6 + m7h7 = (m6 + m7)h1
m7
m6=
h6 − h1h1 − h7
(3.3)
Rewriting the equation above leads to expressions for expressions for m6 and m7:
m6 =1
1 + h6−h1
h1−h7
m1
m7 =h6−h1
h1−h7
1 + h6−h1
h1−h7
m1
(3.4)
For example, to get a more superheated coolant with the same pressure (h1 will increase) the fractionm7
m6has to increase, which means more fraction of hot gas and less fraction of cold mix.
3.2 Mollier diagram in Mathcad
A scroll compressor model is made in Mathcad which uses the geometry calculations explained in sec-tion 2.2. It can calculate the pressures and temperatures between point 1 and point 2 with as inputs:speed of the compressor, inlet thermodynamic quantities compressor (pressure and temperature), outletpressure compressor and an efficiency model (or an entropy loss model). With the use of the charac-teristics of the condenser (isobaric process), valves (isenthalpic processes) and mixing vessel (isobaricprocess), the entire VCC model is displayed in a Mollier diagram. Again the Mathcad interpolation sheetis used to interpolate a value of a thermodynamic quantity with the use of the thermodynamic state prin-ciple.
To get more insight into the changes of thermodynamic quantities of the entire VCC, the first thoughtwas to make an entire Mollier diagram of the VCC. There are some Pressure Enthalpy (PH)- and Tem-perature Entropy (TS) - diagrams made with different conditions. In appendix A a PH- and a TS- diagramcan be seen with the following input conditions:
1. P1 = 1.83 bar
2. T1 = 268 K
3. P2 = 16 bar
4. N = 4000 RPM
5. η = 0.7
Finally, there are some animations made with the Mathcad script using the data from the simulationmodels. It was possible to see what was happening with the thermodynamic quantities (pressure,enthalpy, entropy and temperature) during a simulation.
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CHAPTER 4
STRUCTURE OF THE SIMULATIONMODELS
Section 4.1 gives the process description of the simulation models made in both xCos and Simulink.
The simulation model of the VCC was initially made with xCos (a toolbox of the software Scilab). Be-cause of limitations and some errors in xCos, later on, it was made with Simulink (a toolbox of thesoftware Matlab). At the time of the software switch there a User manual of the xCos simulation modelwas already made. So it has been decided to place the xCos User manuals in appendix F. The prin-ciple of the control loops of both models are broadly equal to each other. However Simulink has a lotmore modeling possibilities. Therefore, the Simulink model is much more extensive and detailed. Theprinciple of a control loop based on the Simulink model is explained in section 4.2. In the associatedsubsections are the different types of valves, the ’signal converter equations’ and the delays betweencontrol action and measurement explained, respectively. The main differences of the principle of a con-trol loop between the Simulink and the xCos model are given in appendix F.2.
4.1 Process description
The task is to make a model that describes the VCC (explained in chapter 3) as accurate as possible.It has to be a model which is well comparable with the test rig test results. The functions included in thetest rig will drive and control the rpm, condition the temperature, pressure and flow of inlet and outletof the VCC and at the same time, it can read, record and evaluate the parameters. So the simulationmodel must include the same functions to control the VCC.
The test rig has 5 controllers, which regulates 5 motorized control valves in total. The controller PID-101C in combination with valve SV-1 is not modeled in the simulation model for convenience, which isexplained in section 3.1.1. The simulation model of the VCC consists of 4 PID controllers which regulate4 motorized control valves.
From the ATP of the scroll compressor it becomes clear that the performance test is done with 4 differentspeeds, including a heat up rotation speed of the compressor at 1800 RPM. In the simulation modelthere are step functions made that vary the speed of the compressor from 1800 RPM, to 6000 RPM,to 4000 RPM and to 1800 RPM subsequently, which results in different PID-settings and variable timedelay.
4.2 Principle of control loop
The basic principle of a control loop is given in figure 4.1:
Figure 4.1: Principle of the closed loop system
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The control loop consists of an input reference value, a PID controller with a saturation setting, a ’ratelimiter’ block, a signal converter function (for example from an amount of steps and thus position of thevalve to pressure), a time delay and a feedback signal.
The PID controller must be adjustable for each compressor speed to reach a stable system (also truefor the real test rig), so there are ’switch’ blocks introduced. An example of this principle is given infigure 4.2. The value of ’A’ (block ’From2’ and ’From 3’ in figure 4.2) is (dependent of the time) zero ornonzero. It determines the moment of the switch between two loops. For example if the value of ’A’ isonly the first 300 seconds nonzero: only the first 300 seconds the loop is using ’PID Controller 1’ and’Variable Time Delay 1’ in combination with ’Constant 1’.
Figure 4.2: Principle of the closed loop system with the different adjustable PID controllers and differenttime delays
Settings used in the PID-controllers are: P-, I- and D- action, an anti-windup mechanism (’limited in-tegrator’), signal tracking (for bumpless control transfer and multiloop control) and an output saturationsetting (limits the output values).
The different types of valves and the associated values for the ’rate limiter’ block and the ’saturation’block are given in section 4.2.1. The rate limiter limits the speed of opening or closing of the valve,which means that the valve can not open or close faster than possible due to mechanical limits. Thesaturation setting in the PID-controller limits the total amount of steps. For example a ball valve canrotate between 0 and 90◦ (fully opened or fully closed).
The signal converter function converts for example an amount of steps (position of the valve) to a pres-sure with an approximated relation between the two signals. All the signal converter equations are givenin section 4.2.2. There are some test measurements done with different mass flows to find a relationshipbetween the position of a ball valve and the associated pressure drop, see appendix C.1. From thesemeasurements it is decided to approximate the relation between the position of the plug of the valve inthe pipeline and the associated pressure drop with a third order curve.
The feedback signal has a certain time delay, which is the delay between a control action and a mea-surement by a sensor. This time delay is important for the settings of the PID-controller. For exampleif the time delay is relatively large the controller may not be too ’aggressive’, because it will lead tounstable behaviour. The time delay depends on the length of the pipeline between the valve and thesensor. It is also depending on of the speed of the refrigerant in the pipelines, which is dependent of thevolume flow and the associated sectional area. The time delays for different control loops and differentcompressor speeds are given in section 4.2.3.
4.2.1 Different types of valves
There are different types of motorized control valves used in the VCC: Sporlan SDR-3X 5 ODF-20-S[6], Sporlan SER-A-3/8x1/2-ODF-10-S [7] and a ball valve with a Bray DMS24-27(A) actuator. Reasonsfor different control valves are mainly the different required control speeds (reducing the risk of unstablebehavior) and different working conditions (mainly pressure and temperature). The different valves canbe seen in figure 4.3 and are described in the next sections.
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(a) Sporlan SDR-3X 5 ODF-20-S (b) Sporlan SER-A-3/8x1/2-ODF-10-S (c) An example of a ball valve
Figure 4.3: Three types of used motorized control valves
Sporlan SDR-3X 5 ODF-20-S
This type of valve is used in the SPCV-1B and the DPCV-1B. At these positions in the VCC the pressureand the temperature are relatively high (discharge gas), so the used materials in the valve must be ratedfor discharge gas temperature and pressures.
The SDR3-3x valve is modulated by the electronically controlled rotation of a step motor (a two phase,bipolar, 12 volt DC, permanent magnet rotor style with a step angle of 3.6°) , which drives a gearingtrain. The output of the gear train rotates a threaded screw. The plunger converts the rotational motionto a linear motion. The piston is directly connected to the plunger. So, when the proper signal stream issupplied, the motor will rotate, driving a gear train to position the piston.
The shaft of the motor moves in distinct step increments when electrical control pulses are applied. Themotor takes 3193 steps to go from fully opened to fully closed with a recommended step rate of 200steps/s. So the full motor transit time is approximately 16 seconds. The current polarity and frequencyof the applied pulses determines the direction and speed of the shaft’s movement, respectively.
In the simulation model a so-called ’rate limiter’ block must be present, which limits the speed of stepincrements to ±200 steps/s. So the valve can not close or open faster than possible is by mechanicallimits. There also must be a ’saturation’ block present, which limits the total amount of steps from 0 to3193 steps. [8]
Sporlan SER-A-3/8x1/2-ODF-10-S
This type of valve is used in the STCV-1B. The valve is intended for the precise control of liquid refrig-erant flow.
The SER-A valve is controlled in the same way and in the same order of accuracy as the SDR3-3xvalve. So the valve is also modulated by the electronically controlled rotation of a step motor (a twophase, bipolar, 12 volt DC, permanent magnet rotor style with a step angle of 3.6°), which finally resultsin a position of the piston.
The shaft of the motor moves in distinct step increments when electrical control pulses are applied. Themotor takes 2500 steps to go from fully opened to fully closed with a recommended step rate of 200steps/s. So the full motor transit time is 12.5 seconds. The current polarity and frequency of the appliedpulses determines the direction and speed of the shaft’s movement, respectively.
In the simulation model a so-called ’rate limiter’ block must be present, which limits the speed of stepincrements to ±200 steps/s. So the valve can not close or open faster than possible due to mechanicallimits. There must also be a ’saturation’ block present, which limits the total amount of steps from 0to 2500 steps. These technical data and other technical information of the certain valve is given in
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appendix D (type of the valve is indicated by the black arrows: ”SER(I) G,J,K”) [9]
Ball valve with a DMS24-27(-A) actuator
This type valve is used in the LPCV-1B.
A ball valve is a valve with a spherical disk. This part of the valve controls the flow within. The spherehas a port right through the middle so when the port is in line with the flow there is no pressure drop. Theport is perpendicular to the flow when the valve is closed. So the flow is then fully blocked (assuming noleakage); maximum pressure drop. The chosen valve is a linear ball valve: the port of the valve has aV-form (see figure 4.4), which leads to a linear relation between pressure drop and position of the port.
Figure 4.4: Spherical disk with a V-form in it: a linear ball valve
The ball valve is a relatively slow valve: the rotation time for 90 degrees of travel is 150 seconds, whichmeans that the valve can rotate with 0.6 ◦/s [10].
Again, the ’rate limiter’ block and the ’saturation’ setting the PID-controllers must be set, respectively to±0.6◦/s and between 0◦ and 90 ◦.
4.2.2 Signal converter equations
Some measurements on a globe valve are done to predict the relation between the position of the valveand the associated pressure drop of the valve. One measurement is elaborated in appendix C.1. Withthe use of these measurements the relation between the position of the valve and the associated pres-sure drop is approximated as a third order curve.
For example, the calculation of the signal converter equation of the DPCV-1B is outlined here: Fromsection 4.2.1 it is known that the motor makes 3193 steps to go from fully opened to fully close. It isroughly estimated that, if the valve is fully closed, the maximum pressure drop is around 30 bar. Sowe get: P = Constant ∗ 31933 = 30 bar (for convenience the pressure drop ∆P is changed into thepressure at the discharge of the compressor P2). So we get: P = 9.2 ∗ 10−10 ∗ N3, where N is theamount of steps made by the motor.
To simplify, there is chosen to approximate also the relations between the axial position of the pistonand both the mass flow (STCV-1B) and another pressure (SPCV-1B) with a third order curve, which ofcourse is not always the right assumption. The ball valve (LPCV-1B) is linear, so the relation betweenthe radial position of the piston and mass flow of water through the valve is linear. Finally, the followingsignal converter equations for the different loops are found:
Valve Conversion EquationDPCV-1B xpiston → P (bar) P = 9.2 ∗ 10−10 ∗N3
SPCV-1B xpiston → P (kPa) P = 2.56 ∗ 10−7 ∗N3
LPCV-1B θport → mwater (kg/s) mwater = 0.2/90 ∗NSTCV-1B xpiston → m6 (kg/s) m6 = 3.84 ∗ 10−12 ∗N3
Table 4.1: Signal converter equation for the different control valves
4.2.3 Calculating the delays between control actions and measurements
As written before, from the ATP it becomes clear that the performance test must be done with 3 differentspeeds (excluding the heat-up speed of the compressor) with associated pressures at the discharge of
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the compressor(P2), given in the first two lines of table 4.2. The time delay between a control action andthe associated measurement signal by a sensor depends on these values.
The time delay is calculated as follows:
τd =lpipeQA
(4.1)
Where lpipe is the approximated distance between the sensor and the associated controlled valve, Q isthe volume flow (calculation of Q2 is given in equation 2.3, other volume flows are assumed fractions ofQ2) and A is the sectional area (dependent on the diameter of the associated pipeline (1/2”, 3/4”, 5/8”or 7/8”, see appendix B.1).
Assumptions that are made:
• The fraction mass flow through valve SPCV-1B is set on 23 of the mass flow through the compres-
sor m1, resulting in a fraction of 13 through valve STCV-1B. These fractions are approximated with
a calculation of reference values (known from the ATP and the measurement results).
• A pressure and a temperature are needed to calculate the density at a point. Most of the time thetemperature is not known exactly, so it is approximated by using a Mollier diagram.
• The length of the pipelines are assumingly based on the existing pictures of the test setup andwith the help of an employee of Aeronamic who has seen the test setup in real life.
• The inlet pressure and temperature are set constant (P = 1.83 bar and T = 268.15 K).
• The densities used to calculate the volume flows at different locations are calculated with referenceor assumed thermodynamic quantities and are taken constant.
For example, calculating the delay between SPVC-1B and sensor PE-01XB (see appendix B.1) in thecase of a speed of 1800 RPM gives us an equation existing of 2 parts (see equation 4.2): the flow inthe pipeline between SPCV-1B to the mixing vessel (’Part 1’) and the flow in the pipeline between themixing vessel and the sensor (’Part 2’). Different parts of the pipelines have different diameters, whichcan also be seen in appendix B.1.
τd,SPCV−1B =
[lpipeQA
]Part1
+
[lpipeQA
]Part2
≈ 1.5mm1∗ 2
3ρ(P7,T7)
m3/s14π∗(0.015875)2m2
+9.0mm1
ρ(P1,T1)m3/s
14π∗(0.015875)2m2
≈ 13.8s (4.2)
All the time delays for different speeds and different valves are given in the table below.
Speed (RPM) 1800 4000 6000P2 (bar) 17 19 14
DPCV - 1B τd (s) 2.4 1.3 0.6SPCV - 1B τd (s) 13.8 7.6 3.5LPCV - 1B τd (s) 5.4 3.0 1.4STCV - 1B τd (s) 22.6 11.5 6.4
Table 4.2: Time delays associated to the different valves by different speeds
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CHAPTER 5
SIMULATION MODEL XCOS
The simulation model made in xCos is given in appendix E.1. The associated User manual is given inappendix F. Section 5.1 gives a limitation (error) in xCos. Finally the conclusions and recommendationsare given in 5.2. The most important decision made in that section is that the xCos model is rejectedbecause of unreliability and a less detailed model.
5.1 Limitation/ error in xCos
If there is more than one closed loops on the same sheet (even if they are not connected to each other)they influence each other, such that the results are no longer reliable. This has most likely somethingto do with a memory limit of the free software xCos, whereby the step size of the model will changeautomatically by adding an additional loop. Examples are the very simple closed loop models given inthe figure 5.1 and figure 5.2. In the first figure one can see the output of the upper closed loop (loop 1)displayed by the associated scope. In the second figure the reference value of loop 2 has changed andnothing changed at the first loop, however the result of scope 1 strongly differs.
Figure 5.1: Two independent closed loops both with the same reference values. The figure on the rightside gives the output of the scope of loop 1
Figure 5.2: Two independent closed loops with a modified reference value of loop 2. The figure on theright side gives the output of the scope of loop 1 as well
5.2 Conclusions and recommendations
• The simulation model has given insight in the principle of the entire system and how to model it.However, no reliable conclusion can be drawn, because of, for example, the unreliability of the
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software xCos and the lack of detail in the model. The decision is made to reject to model andlook for another simulation software.
• xCos can not handle complex models (as well as long computation times occur), such as VCC,very well. However, xCos may be a useful toolbox in case of an easier single loop model.
• Adding more detail to the simulation model is a strong recommendation. For example inserting atool which can calculate thermodynamic quantities with the use of a Mollier diagram (such as thetoolbox Thermosys, which will be discussed later on in the report) will be very important.
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CHAPTER 6
SIMULATION MODEL SIMULINK
In this chapter the Simulink simulation model is explained. In section 6.1 is a roadmap given to make itclear to open and run a simulation in Simulink. Section 6.2 gives an overview of the meaning of the usedblocks in Simulink. In this section the importance of the use of two additional programs (Thermosys andRefprop) is explained as well. The subsequent section (section 6.3) gives the structure of the Simulinkmodel: first the defined time steps, then the input parameters and finally an explanation and someresults of the different control loops.
6.1 A roadmap how to open and run the simulink model
Before running the Simulink model the current directory in Matlab must be set to the right folder andsome Matlab data must be loaded in. A roadmap is given below to start a simulation:
• Start Matlab R2014b
• In the taskbar select ’browse for folder’ and select:’S: \Afdelingen \Engineering \Model li-brary \Scroll compressor A350 \1. Test model Matlab Simulink’
• Open from ’current folder’ two Matlab data files: ’R134a.mat’ and ’S PT’
• Open Simulink by typing ’Simulink’ in the ’Command window’
• In the Simulink menu click on ’Open model or library’ from the taskbar and open the file:’S: \Afdelingen \Engineering \Model library \Scroll compressor A350 \1. Test model MatlabSimulink \Endmodel’
• A simulation can be done by clicking on the ’run’ button in the taskbar
6.2 Block definitions
The definition of the used blocks in het simulation model are given in table 6.1.
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CONSTANT: This block is a constantvalue generator
CLOCK: Display and provide simula-tion time
FROM: The main role of the GO-TO/FROM blocks is to transport signalsfrom a block to another block withoutconnecting them
GOTO: The main role of the GO-TO/FROM blocks is to transport signalsfrom a block to another block withoutconnecting them
GAIN: The Gain block multiplies the in-put by a constant value (gain)
Add or subtract inputs
The Bus Creator block combines a setof signals into a bus
The Bus Selector block outputs a spec-ified subset of the elements of the busat its input. The block can output thespecified elements as separate signalsor as a new bus
SCOPE: Display signals generatedduring simulation
SUBSYSTEM: This block opens up anew Simulink window for editing a newblock diagram in order to keep the mainscreen more clear
Approximate 1D look-up table. Thedata comes from the software Ther-mosys (see section 6.2.1)
Approximate 2D look-up table. Thedata comes from the software Ther-mosys or from the software Thermosysin combination with the program Ref-prop (see section 6.2.1)
Include MATLAB code in models thatgenerate embeddable C code
The Rate Limiter block limits the firstderivative of the signal passing throughit. The output changes no faster thanthe specified limit
Create input port for subsystem or ex-ternal input
Switch output between first input andthird input based on value of secondinput
Create output port for subsystem or ex-ternal output
The output at the current time stepequals the value of its data input at aprevious time step. This time step isthe current simulation time minus a de-lay time specified by the time delay in-put
This block finds the minimum or maxi-mum values from the input values (pa-rameter Min or Max)
This block implements a PID(Proportional-Integral-Differential)controller. Used configurable optionsin the PID controllers in the modelare: Signal tracking for bumplesscontrol transfer and multiloop control,output saturation limits and built-inanti-windup mechanism
Table 6.1: Block descriptions Simulink
6.2.1 Thermosys and Refprop
A free (and limited) toolbox is found which has a built-in thermodynamic properties database for R134a:Thermosys. Thermosys is a toolbox for Matlab/Simulink and it is a suite of simulation tools for analyzingthe behaviour of air-conditioning and refrigeration systems. It was developed at the University of Illinoisat Urbana- Champaign through sponsorship by the Air-Conditioning and Refrigeration Center (ACRC)and is distrubited by CU Aerospace [11]. Most of the 1D and 2D look-up tables are made with the datafrom Thermosys. However, the conversion of a pressure and a temperature to an entropy is not includedin the toolbox. To expand the possibilities of Thermosys, another program is bought from the NationalInstitute of Standars and Technology (NIST): Refprop.
The Refprop ’database’ is actually a program and does not contain any experimental information, apartfrom the critical and triple points of the pure fluids. The program uses equations for the thermodynamicand transport properties to calculate the thermodynamic state of the fluid or mixture [12]. There is aMatlab code made that connects Matlab with Refprop, it is called: ’refpropm.m’. Furthermore, a Matlabcode is written that can connect to ’refpropm.m’ and can calculate the entropy with the use of a pressureand a temperature. This information is saved to a 100x100 Matlab Data file (see Appendix G.1) and canbe imported in a 2D look-up table from Thermosys.
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6.3 Structure of the model
There is an underlying function which is also called in other functions: ’StepReponse end2.m’. Thisfunction defines the switch between different compressor speeds and different compressor and con-denser pressures. The explanation including an example is given in section 6.3.1. The input parame-ters are adjustable in the function ’Inputs.m’, see section 6.3.2. The different control loops are given insection 6.3.3. The entire main model is given in appendix E.2.
6.3.1 Defined time steps
There is one underlying function which is also called in other functions: ’StepResponse end2.m’, seeAppendix G.2. It is important to place the function in the right folder (’S: \Afdelingen \Engineering\Projecten\Aviation \Scroll Compressor Honeywell \3. Test model Matlab Simulink \StepReponseend2.m’), see section 6.1. This function determines the time transitions between different compressorspeeds and different pressures of both the compressor and condenser. The different transitions arespread over 3000 seconds, but are adjustable via the ’Factor’ value (which is equal to one in the re-mainder of the report).
The output values of the function ’StepResponse end2.m’ are used as inputs of other functions in themodel. An example: the value of ’step 1800RPM comp cond’ is only between 400 and 700 secondsequal to 1, otherwise it is 0. Via ’GOTO’ and ’FROM’ blocks the signal is sent to the second input valueof a ’Switch’ block (the if-condition). So between 400 and 700 seconds the if-statement is true and theoutput of the ’Switch’ block is equal to the first input, otherwise the output of the block is equal to thethird input value. In this way it is possible to use different PID-controllers (and thus PID-settings) andother time delays for different compressor speeds and different set-point compressor and condenserpressures.
All the output signals from the function ’timespan’ are sent to ’GOTO’ blocks, as can be seen in figure6.2a.
6.3.2 Input parameters
The density at the inlet, the speed and the volume of the first compression chamber of the compressorare needed to calculate the mass flow at the inlet of the compressor m1. The density at the inletof the compressor is during the start-up equal to 8.862 kg/m3, calculated with the inlet pressure andtemperature known from the ATP. Hereafter the density is determined with a look-up table with as inputthe regulated pressure P1 and temperature T1. It is possible to reduce simulation time by eliminating ’rho
in = rho in startup’ in the equation, however this gives less accurate results (no feedback from theregulated input conditions of the compressor). The different speeds of the compressor at different timesteps is defined with the use of step functions (see Appendix G.2). The volume of the first compressionchamber is calculated with the use of a compressor model made in Mathcad. Because of confidentiality,this value is hidden in Appendix G.2. The mass flow of point 1 is given in figure 6.1.
Figure 6.1: Mass flow through the compressor
Page 31
The pressure at the outlet of the compressor Pcompout is hard imposed and is regulated to differentset-point values for different time steps. The pressure of the compressor changes from 0 bar to 12 bar,to 14 bar, to 19 bar and eventually changes back to 17 bar (known from the ATP).
As written before in section 3.1.1 the amount of sub-cooling is set to a constant value, which is accept-able because of the lesser variations in the amount of sub-cooling. The amount of sub-cooling is notregulated and fixed at 5 K. From a Mollier diagram the enthalpy as function of the temperature on thesaturated liquid line in the temperature range from 293 K to 333 K can be approximated with a linear line.The enthalpy increase per degree Kelvin is equal to approximately 1.4 kJ/kg. hsubc Is the approximateddifference in enthalpy between the points 4 and 5 (see 3.1). So with 5 K subcooling hsubc is equal to7 kJ/kg.
For the heat balance of the condenser the value of CpdT of the water loop must be approximated. TheCp of the cold loop of the condenser is approximated to 4.2 kJ/kgK [13] and there is approximated a fixedtemperature difference dT of 10 K (which is in the real test rig regulated by a fifth controller). So thevalue of CpdT is approximated to 42 kJ/kg.
The inlet pressure P1ref and temperature T1ref of the compressor are known from the ATP and equalto respectively 183 kPa and −5.15◦C. Some simulation problems occur at the start up of the mixing ves-sel, because the mass flows are zero if the compressor is not working yet. Therefore another variablewith a value zero during the start-up of the compressor is introduced: P1ref tot. This variable goes intothe mixing vessel, which will be discussed later on.
Finally, from the test rig test results it is known that the pressure of the condenser is equal to 7 bar atthe start-up and equal to 10 bar otherwise. This is implemented in the simulation as well.
All the output signals from the function ’Inputs’ are sent to ’GOTO’ blocks, as can be seen in figure 6.2b.
PID-104B and SPCV PID-101B and STCV
PID-103B and LPCV
mwater
Mass flow (linear with compressor speed) PID-102B and DPCV
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[Pcomp]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_0RPM_cond]
[clock]
Scope13
timespantime
step_0RPM_cond
step_1800RPM_N
step_1800RPM_comp_cond
step_6000RPM_N
step_6000RPM_comp
step_4000RPM_N
step_4000RPM_comp
step_1900RPM_N
step_1900RPM_comp
[clock]
In1 Out1Scope6
[step_0RPM_cond]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[massflow2]
[h2_act]
In1 Out1
[m1]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope3
mwater
h2_act
hsubc
h4
m6act
CpdT
time
mwater
[h2_act]
[hsubc]
[h4]
[CpdT]
Scope8
glycolstartup
CpdT
m6act
mwater
h2_act
h4_7bar
dhsubc
time
dhrefr
h4_act
[CpdT]
[clock]
[h2_act]
[hsubc]
[h4_7bar]
[h2_act][clock]
In1 Out1
H (p,s)
100
Scope1
entropymodel
Sin
timeentropy
[clock]Scope4
PstartupPcomp Pcomp2
Scope17 Scope60
Tsat (p)1
max
-30
Scope61
[superh]
In1 Out1
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
In1 Out1
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope24
Scope59
Psat (t)2
[superh]Scope64
[Pcompin_act]
[Tcompin_act]
T (Pref,hact)3Calculatingh1
m6
h7
h6_act
h6
m1_act
time
h1
[clock]
[h2_act]
[h4_act]
[h4]
[m1]
[Pfeedback]
Scope19
H (p,t)1
[Pcompin_act]
[Tcompin_act]
[Tcompin_act]
Scope42
Scope56
[clock]
[Pfeedback]
P (h_sat)1
Scope2
Scope55
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[m6_act]
[h4_act]
Scope10
Scope11
[m6_act]
[m6_act]
S (p,t)
Scope120.001
[m6_act]
[m1] Scope5
min
[m1]
Tsat (p)2
[Pcompin_act]
[Tcompin_act]Scope7
[Pcompin_act]
[Tcompin_act]
Scope14
Inputs
rho_in_act
time
massf low_1
Pcomp_out
hsubc
CpdT
P1_ref
P1_ref_tot
T1_ref
P4_ref
P4_startup
T_superheat
[massflow2]
Rho (p,t)
[rho_in]
[rho_in]
[clock]
[massflow2]
[h1_act]
[h1_act]
[h2_act]
[h4_act]Scope9
Hf (p)
Scope15
[h4_7bar]
Hf (p)1
Scope16
[h4]
[Pcomp]
[hsubc]
[CpdT]
[P1ref]
[P1ref]
From9[T1ref]
[P4startup]
[P4ref]
[P1ref_tot]
[T1ref]
[P4ref]
[P4startup]
[superh]
[P1ref_tot]
[P1ref_tot]
Scope18
Tin
(a) The output signals of the function ’timespan’ are sentto ’GOTO’ blocks
PID-104B and SPCV PID-101B and STCV
PID-103B and LPCV
mwater
Mass flow (linear with compressor speed) PID-102B and DPCV
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[Pcomp]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_0RPM_cond]
[clock]
Scope13
timespantime
step_0RPM_cond
step_1800RPM_N
step_1800RPM_comp_cond
step_6000RPM_N
step_6000RPM_comp
step_4000RPM_N
step_4000RPM_comp
step_1900RPM_N
step_1900RPM_comp
[clock]
In1 Out1Scope6
[step_0RPM_cond]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[massflow2]
[h2_act]
In1 Out1
[m1]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope3
mwater
h2_act
hsubc
h4
m6act
CpdT
time
mwater
[h2_act]
[hsubc]
[h4]
[CpdT]
Scope8
glycolstartup
CpdT
m6act
mwater
h2_act
h4_7bar
dhsubc
time
dhrefr
h4_act
[CpdT]
[clock]
[h2_act]
[hsubc]
[h4_7bar]
[h2_act][clock]
In1 Out1
H (p,s)
100
Scope1
entropymodel
Sin
timeentropy
[clock]Scope4
PstartupPcomp Pcomp2
Scope17 Scope60
Tsat (p)1
max
-30
Scope61
[superh]
In1 Out1
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
In1 Out1
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope24
Scope59
Psat (t)2
[superh]Scope64
[Pcompin_act]
[Tcompin_act]
T (Pref,hact)3Calculatingh1
m6
h7
h6_act
h6
m1_act
time
h1
[clock]
[h2_act]
[h4_act]
[h4]
[m1]
[Pfeedback]
Scope19
H (p,t)1
[Pcompin_act]
[Tcompin_act]
[Tcompin_act]
Scope42
Scope56
[clock]
[Pfeedback]
P (h_sat)1
Scope2
Scope55
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[m6_act]
[h4_act]
Scope10
Scope11
[m6_act]
[m6_act]
S (p,t)
Scope120.001
[m6_act]
[m1] Scope5
min
[m1]
Tsat (p)2
[Pcompin_act]
[Tcompin_act]Scope7
[Pcompin_act]
[Tcompin_act]
Scope14
Inputs
rho_in_act
time
massf low_1
Pcomp_out
hsubc
CpdT
P1_ref
P1_ref_tot
T1_ref
P4_ref
P4_startup
T_superheat
Rho (p,t)
[rho_in]
[rho_in]
[clock]
[massflow2]
[h1_act]
[h1_act]
[h2_act]
[h4_act]Scope9
Hf (p)
Scope15
[h4_7bar]
Hf (p)1
Scope16
[h4]
[Pcomp]
[hsubc]
[CpdT]
[P1ref]
[P1ref]
From9[T1ref]
[P4startup]
[P4ref]
[P1ref_tot]
[T1ref]
[P4ref]
[P4startup]
[superh]
[P1ref_tot]
[P1ref_tot]
Scope18
Tin
[massflow]
(b) The output signals of the function ’Inputs’ are sent to’GOTO’ blocks
Figure 6.2: Defined time steps and input parameters Simulink model
The Matlab script with all input values is given in Appendix G.3.
6.3.3 The different control loops
Compressor exit
This is the most straightforward PID-control loop, because the pressure of the discharge pipeline can bedirectly regulated to the desired value, assuming no influences of other controllers. The control schemecan be seen in figure 6.3.
Page 32
PID-104B and SPCV PID-101B and STCV
PID-103B and LPCV
mwater
Mass flow (linear with compressor speed) PID-102B and DPCV
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[Pcomp]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_0RPM_cond]
[clock]
Scope13
timespantime
step_0RPM_cond
step_1800RPM_N
step_1800RPM_comp_cond
step_6000RPM_N
step_6000RPM_comp
step_4000RPM_N
step_4000RPM_comp
step_1900RPM_N
step_1900RPM_comp
[clock]
In1 Out1Scope6
[step_0RPM_cond]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[massflow2]
[h2_act]
In1 Out1
[m1]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope3
mwater
h2_act
hsubc
h4
m6act
CpdT
time
mwater
[h2_act]
[hsubc]
[h4]
[CpdT]
Scope8
glycolstartup
CpdT
m6act
mwater
h2_act
h4_7bar
dhsubc
time
dhrefr
h4_act
[CpdT]
[clock]
[h2_act]
[hsubc]
[h4_7bar]
[h2_act][clock]
In1 Out1
H (p,s)
100
Scope1
entropymodel
Sin
timeentropy
[clock]Scope4
PstartupPcomp Pcomp2
Scope17 Scope60
Tsat (p)1
max
-30
Scope61
[superh]
In1 Out1
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
In1 Out1
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope24
Scope59
Psat (t)2
[superh]Scope64
[Pcompin_act]
[Tcompin_act]
T (Pref,hact)3Calculatingh1
m6
h7
h6_act
h6
m1_act
time
h1
[clock]
[h2_act]
[h4_act]
[h4]
[m1]
[Pfeedback]
Scope19
H (p,t)1
[Pcompin_act]
[Tcompin_act]
[Tcompin_act]
Scope42
Scope56
[clock]
[Pfeedback]
P (h_sat)1
Scope2
Scope55
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[m6_act]
[h4_act]
Scope10
Scope11
[m6_act]
[m6_act]
S (p,t)
Scope120.001
[m6_act]
[m1] Scope5
min
[m1]
Tsat (p)2
[Pcompin_act]
[Tcompin_act]Scope7
[Pcompin_act]
[Tcompin_act]
Scope14
Inputs
rho_in_act
time
massf low_1
Pcomp_out
hsubc
CpdT
P1_ref
P1_ref_tot
T1_ref
P4_ref
P4_startup
T_superheat
[massflow2]
Rho (p,t)
[rho_in]
[rho_in]
[clock]
[massflow2]
[h1_act]
[h1_act]
[h2_act]
[h4_act]Scope9
Hf (p)
Scope15
[h4_7bar]
Hf (p)1
Scope16
[h4]
[Pcomp]
[hsubc]
[CpdT]
[P1ref]
[P1ref]
From9[T1ref]
[P4startup]
[P4ref]
[P1ref_tot]
[T1ref]
[P4ref]
[P4startup]
[superh]
[P1ref_tot]
[P1ref_tot]
Scope18
Tin
Figure 6.3: Compressor control loop
The ’FROM’ block with the signal Pcomp (bar) gives the reference values of the exit pressure of thecompressor and with the step functions mentioned earlier the reference values will change at the rightmoment.
With the ’Bus Creator’ all values goes to the ’SUBSYSTEM’. In the ’SUBSYSTEM’ the signals areselected with a ’Bus Selector’. The first signal is the reference compressor exit pressure and dependson whether the ’Switch’ blocks succeed or not. Hereafter, the signal successively goes through a PID-controller, rate limiter, time delay and finally the position of valve is converted to a pressure accordingto table 4.1. The ’SUBSYTEM’ can be seen in figure 6.4.
PID-102B and DPCV-1BFactor=1; % If factor =1 :::::::: tijd_0RPM_cond=300*Factor; % 0-300 sec: Druk cond naar 7 bar % Etijd_1800RPM_N=400*Factor; % 300-400 sec: Toerental naar 1800 RPM % Etijd_1800RPM_comp_cond=700*Factor; % 400-700 sec: Druk comp naar 12 bar, druk cond naar 10 bar % Atijd_6000RPM_N=1000*Factor; % 700-1000 sec: Toerental naar 6000 RPM % Atijd_6000RPM_comp=1500*Factor; % 1000-1500 sec: Druk compressor naar 14 bar % Btijd_4000RPM_N=1800*Factor; % 1500-1800 sec: Toerental naar 4000 RPM % Btijd_4000RPM_comp=2300*Factor; % 1800-2300 sec: Druk compressor naar 19 bar % Ctijd_1900RPM_N=2600*Factor; % 2300-2600 sec: Toerental naar 1840 RPM % Ctijd_1900RPM_comp=3000*Factor; % 2600-3000 sec: Druk compressor naar 17 bar % D
Other
17 bar
19 bar
14 bar
12 bar
1
1
> 0 > 0[A] [A]
> 0[B] > 0[B]
[A]
[B]
PID(s)
PID(s)TR DPCV
N dP
To2.4
To0.6
To
1.3
[C] PID(s)TR
> 0PID(s)TR
[C]
[D]
> 0[D]
PID(s)TR
> 0
To2.4
> 0
To2.4
[C]
[D]
Figure 6.4: SUBSYSTEM with PID controllers, rate limiters, switch blocks, time delays and signal con-verter equations
Without the function ’Pstartup’ in the control scheme in figure 6.3 the pressure would be zero, whichleads to simulation problems at the start-up of the model. Therefore, there is chosen to give the pres-sure a minimum value of 1.83 bar at the start-up, see Appendix G.4.
There are two thermodynamic quantities needed to compute another thermodynamic quantity. How-ever, at the exit of the compressor, just one thermodynamic quantity is known (pressure). There ischosen to let the entropy increase linearly from reference value ( S as function of P1ref and T1ref ) to1.85 kJ/kgK during the (from test rig test results) approximated time (200 s) of increasing the pressurefrom start-up pressure to the first set-point compressor exit pressure. Hereafter the entropy remainsconstant at 1.85 kJ/kgK, which of course is not the case in reality. This Matlab script is given in AppendixG.5.
Two thermodynamic quantities at the compressor exit are known (pressure and entropy), so the asso-ciated enthalpy h2act can be calculated with look-up table ’H(p,s)’. The actual signal value of point 2 issent to the mixing vessel and the condenser. The result of h2act is given in figure 6.5. The enthalpybefore start-up of the compressor is equal to approximately 397 kJ/kg. At t = 400 s the compressor startsup and the enthalpy is increasing in time, knowing the regulated pressure and the linear increasingentropy. After t = 600 s the entropy remains constant as written before and the enthalpy only changesdue to changing pressures.
Page 33
Figure 6.5: Regulated compressor output enthalpy h2act
Mixing vessel
The block model of the control loops with the valves SPCV-1B and STCV-1B is given in figure 6.6.These two control loops must work closely together and are placed in series.
PID-104B and SPCV PID-101B and STCV
PID-103B and LPCV
mwater
Mass flow (linear with compressor speed) PID-102B and DPCV
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[Pcomp]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_0RPM_cond]
[clock]
Scope13
timespantime
step_0RPM_cond
step_1800RPM_N
step_1800RPM_comp_cond
step_6000RPM_N
step_6000RPM_comp
step_4000RPM_N
step_4000RPM_comp
step_1900RPM_N
step_1900RPM_comp
[clock]
In1 Out1Scope6
[step_0RPM_cond]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[massflow2]
[h2_act]
In1 Out1
[m1]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope3
mwater
h2_act
hsubc
h4
m6act
CpdT
time
mwater
[h2_act]
[hsubc]
[h4]
[CpdT]
Scope8
glycolstartup
CpdT
m6act
mwater
h2_act
h4_7bar
dhsubc
time
dhrefr
h4_act
[CpdT]
[clock]
[h2_act]
[hsubc]
[h4_7bar]
[h2_act][clock]
In1 Out1
H (p,s)
100
Scope1
entropymodel
Sin
timeentropy
[clock]Scope4
PstartupPcomp Pcomp2
Scope17 Scope60
Tsat (p)1
max
-30
Scope61
[superh]
In1 Out1
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
In1 Out1
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope24
Scope59
Psat (t)2
[superh]Scope64
[Pcompin_act]
[Tcompin_act]
T (Pref,hact)3Calculatingh1
m6
h7
h6_act
h6
m1_act
time
h1
[clock]
[h2_act]
[h4_act]
[h4]
[m1]
[Pfeedback]
Scope19
H (p,t)1
[Pcompin_act]
[Tcompin_act]
[Tcompin_act]
Scope42
Scope56
[clock]
[Pfeedback]
P (h_sat)1
Scope2
Scope55
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[m6_act]
[h4_act]
Scope10
Scope11
[m6_act]
[m6_act]
S (p,t)
Scope120.001
[m6_act]
[m1] Scope5
min
[m1]
Tsat (p)2
[Pcompin_act]
[Tcompin_act]Scope7
[Pcompin_act]
[Tcompin_act]
Scope14
Inputs
rho_in_act
time
massf low_1
Pcomp_out
hsubc
CpdT
P1_ref
P1_ref_tot
T1_ref
P4_ref
P4_startup
T_superheat
[massflow2]
Rho (p,t)
[rho_in]
[rho_in]
[clock]
[massflow2]
[h1_act]
[h1_act]
[h2_act]
[h4_act]Scope9
Hf (p)
Scope15
[h4_7bar]
Hf (p)1
Scope16
[h4]
[Pcomp]
[hsubc]
[CpdT]
[P1ref]
[P1ref]
From9[T1ref]
[P4startup]
[P4ref]
[P1ref_tot]
[T1ref]
[P4ref]
[P4startup]
[superh]
[P1ref_tot]
[P1ref_tot]
Scope18
Tin
Figure 6.6: Mixing vessel control loop. For a larger figure see Appendix E.2 figure E.2
The FROM block with the signal ’P1ref tot’ (kPa) gives the reference values of the inlet pressure of thecompressor and with the step functions, the reference values will change at the right moment.
With the ’Bus Creator’ all values goes to the SUBSYSTEM. This ’SUBSYTEM’ has the same structureas the earlier discussed ’SUBSYSTEM’ of the DPCV-1B in combination with PID-102B, see figure 6.4.The result of the regulated inlet pressure of the compressor is given in figure 6.8a. The first 400 secondsof the simulation the pressure is almost zero as can be seen in the figure, this is the same as in realitybecause of a Hermeticity Test just before the ATP. Hereafter, the set point pressures are given to themodel and the pressure is slowly rising to the reference value of 183 kPa.
With the 1D look-up table ’Tsat(p)1’ the pressure is transmitted to a temperature that lies on the sat-urated vapor line in the Mollier diagram. Adding the chosen amount of superheat (adjustable) to thetemperature on the saturated vapor line and the reference temperature for the second control loop isknown.
The first signal that goes to the second ’Bus Creator’ in the figure is in this case the difference betweenthe reference temperature Tin and the regulated temperature Tcompin act. The other signals that goto the second ’Bus Creator’ are of course again step values.
The ’SUBSYSTEM’ again has the same structure as the earlier discussed subsystems.
There is placed a ’min’ block just after the ’SUBSYSTEM’, because the mass flow of point 6 m6 can notbe larger than the mass flow of point 1 m1. Hereafter the mass flow m6 goes to the energy balanceof the mixing vessel, which is given in Appendix G.6. The enthalpy of point 1 h1 is calculated with therewritten form of the energy balance in combination with the mass balance given in equation 3.2.
The inlet enthalpy of the compressor is given in figure 6.7. Figure 6.7a gives the result of the 2D look-uptable with as look-up method: ’Use Input Nearest’ and figure 6.7b gives the result of the 2D look-up
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table with as look-up method: ’Interpolation-Extrapolation’. Most prominently is the outlier down in theright figure. The reason for this outlier is an insufficient amount of data points in the 2D look-up tables,resulting in an interpolation between a value on the liquid side and a value on the vapor side of theMollier diagram, which gives an enthalpy in the mixture area. Solution for this problem is adding higherresolution input Matlab Data arrays (instead of arrays of length 100) into the 2D look-up tables .
(a) h1 act. Look-up method: Use Input Nearest (b) h1 act. Look-up method: Interpolation-Extrapolation
Figure 6.7: Enthalpy at the inlet of the compressor h1 act with different settings of a 2D look-up table
Now the actual value of the enthalpy at the inlet of the compressor h1 is known and can be transmittedinto an actual temperature of the inlet of the compressor with the use of the reference inlet pressure ofthe compressor. The temperature on the saturated vapor line can be found by subtracting the amountof superheat (adjustable) from Tcompin act. So the inlet temperature of the compressor is in factregulated by giving an amount of superheat to the model. This temperature can be easily transmitted toa saturated pressure with the 1D look-up table ’Psat(t)2’. Finally, this is the feedback signal (measuredsignal by the pressure sensor ’PE-1’) to the control loop with the SPCV-1B in combination with the PID-104B in it. The regulated temperature is given in figure 6.8b. Until the pressure gets a value of about1 bar the temperature is still very low (around −12 ◦C). Hereafter it stays between −8 ◦C and −1 ◦C.
(a) Regulated compressor inlet pressure P1act (b) Regulated compressor inlet pressure T1act
Figure 6.8: Regulated inlet conditions for the compressor
A much more important question is: ’Is the coolant always superheated when it enters the compressor?’The answer to this question is in this case ’yes’ and verified by figure 6.9. The figure shows the amountof superheating at the inlet of the compressor. The first part of the figure is not important, because itis at the start-up of the compressor with a very low pressure and a limited minimum temperature. Theresult of the first part is a high amount of superheated coolant.
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Figure 6.9: superheat
Condenser
The block model with the regulated water flow in the condenser is given in figure 6.10
PID-104B and SPCV PID-101B and STCV
PID-103B and LPCV
mwater
Mass flow (linear with compressor speed) PID-102B and DPCV
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[Pcomp]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_0RPM_cond]
[clock]
Scope13
timespantime
step_0RPM_cond
step_1800RPM_N
step_1800RPM_comp_cond
step_6000RPM_N
step_6000RPM_comp
step_4000RPM_N
step_4000RPM_comp
step_1900RPM_N
step_1900RPM_comp
[clock]
In1 Out1Scope6
[step_0RPM_cond]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[massflow2]
[h2_act]
In1 Out1
[m1]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope3
mwater
h2_act
hsubc
h4
m6act
CpdT
time
mwater
[h2_act]
[hsubc]
[h4]
[CpdT]
Scope8
CpdT
m6act
mwater
h2_act
h4_7bar
dhsubc
time
dhrefr
h4_act
[CpdT]
[clock]
[h2_act]
[hsubc]
[h4_7bar]
[h2_act][clock]
In1 Out1
H (p,s)
100
Scope1
entropymodel
Sin
timeentropy
[clock]Scope4
PstartupPcomp Pcomp2
Scope17 Scope60
Tsat (p)1
max
-30
Scope61
[superh]
In1 Out1
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
In1 Out1
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope24
Scope59
Psat (t)2
[superh]Scope64
[Pcompin_act]
[Tcompin_act]
T (Pref,hact)3Calculatingh1
m6
h7
h6_act
h6
m1_act
time
h1
[clock]
[h2_act]
[h4_act]
[h4]
[m1]
[Pfeedback]
Scope19
H (p,t)1
[Pcompin_act]
[Tcompin_act]
[Tcompin_act]
Scope42
Scope56
[clock]
[Pfeedback]
P (h_sat)1
Scope2
Scope55
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[m6_act]
[h4_act]
Scope10
Scope11
[m6_act]
[m6_act]
S (p,t)
Scope120.001
[m6_act]
[m1] Scope5
min
[m1]
Tsat (p)2
[Pcompin_act]
[Tcompin_act]Scope7
[Pcompin_act]
[Tcompin_act]
Scope14
Inputs
rho_in_act
time
massf low_1
Pcomp_out
hsubc
CpdT
P1_ref
P1_ref_tot
T1_ref
P4_ref
P4_startup
T_superheat
[massflow2]
Rho (p,t)
[rho_in]
[rho_in]
[clock]
[massflow2]
[h1_act]
[h1_act]
[h2_act]
[h4_act]Scope9
Hf (p)
Scope15
[h4_7bar]
Hf (p)1
Scope16
[h4]
[Pcomp]
[hsubc]
[CpdT]
[P1ref]
[P1ref]
From9[T1ref]
[P4startup]
[P4ref]
[P1ref_tot]
[T1ref]
[P4ref]
[P4startup]
[superh]
[P1ref_tot]
[P1ref_tot]
Scope18
Tin
waterstartup
Figure 6.10: Condenser control loop
The function ’mwater’ gives the energy balance of the condenser (see Appendix G.7), which is alreadygiven in equation 3.1:
mwater =m3 [dhsubcooled + h3(P3)− hsat.liquid(P3)]
(cpdT )water(6.1)
The mass flow of point 3 is equal to the mass flow of point 6 (same branch of the pipeline, see AppendixB.1), the enthalpy of point 3 is equal to the enthalpy of point 2 (isenthalpic process) and the enthalpyof point 4 with a certain pressure is equal to the enthalpy on the saturated liquid line with the samepressure.
The signal ’mwater’ goes (again together with the step functions) to the ’Bus Creator’, then to the’SUBSYSTEM’ and the ’measured’ signal is fed back and subtracted from the signal ’mwater’. ThisSUBSYTEM has the same structure as the earlier discussed SUBSYSTEM of the DPCV-1B in combi-nation with PID-102B, see figure 6.4.
The function ’waterstartup’ again uses the energy balance of the condenser (only another form of it),in this case to calculate the saturated liquid enthalpy h4 act with the use of a regulated mass flow ofpoint 6 m6 act. This enthalpy can easily be translated to the pressure in the condenser, because point4 holds the saturated liquid pressure. The regulated pressure of the condenser is given in figure 6.11.
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Figure 6.11: Regulated pressure of the condenser
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CHAPTER 7
TEST RIG TEST RESULTS AND ACOMPARISON WITH THE SIMULINKSIMULATION MODEL
In this chapter are some test rig test results (section 7.1) given. Also there is a comparison between thetest rig test results and the results of the Simulink simulation model made, see section 7.2. The task ofthis chapter is to give an insight of the reliability and accuracy of the Simulink simulation model.
7.1 Test rig test results
There is a ’performance test’ with a scroll compressor done. The test takes approximately 13.000 s intotal (including a start-up time of 4.000 s). The test results from this test are imported to Mathcad andsome figures are made. A short explanation of these figures is given in the next sections.
NB: In all figures is the speed of the compressor placed on the secondary axis, mainly to give moreinsight in the effects of changing the compressor speed.
7.1.1 Pressures in condenser and at the in- and outlet of the compressor
Figure 7.1 gives the pressures of the in- and outlet of the compressor and the pressure in the condenser.During a change of the compressor speed the pressure set-point values remains constant. After thecompressor has reached his set-point speed, the set-point pressure values of the compressor outputchanges. This process can be seen in the figure.
The pressures at the in- and outlet of the compressor remains pretty constant, so these pressures arewell controlled to the set-point values.
Furthermore, the start-up pressure of the condenser is equal to approximately 6.5 bar. When thecompressor speeds up to 1800 RPM the flow of R134a goes through the condenser and the pressurein the condenser increases slowly to 10 bar. The changes in pressure of the condenser is a slowprocess, because the LPCV-1B is a relatively slow valve (see section 4.2.1) and the heat transfer in thecondenser (heat from from R134a to water) is also slow .
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Figure 7.1: Some pressures from the test rig test results
7.1.2 Temperatures at the in- and outlet of the compressor
Figure 7.2 gives the temperatures at the in- and outlet of the compressor. The outlet temperature isnot controlled and is only a result of changes of other thermodynamic quantities (mainly pressure). Theinlet temperature of the compressor is hard to control, which can also be seen in the figure.
Figure 7.2: Some temperatures from the test rig test results
7.1.3 Superheat at the inlet of the compressor
Most important of the inlet conditions of the compressor is that the inlet pressure and the inlet temper-ature of the compressor jointly leads to a superheat vapor. This is shown in figure 7.3. From the figurecan be concluded that during the test the amount of superheat is always higher than approximately4 ◦C. So there is no liquid going into the compressor.
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Figure 7.3: The amount of superheat at the inlet of the compressor from the test rig test results
7.1.4 Mass flow through the compressor
The mass flow through the compressor depends linearly of the speed of the compressor (see equation2.2). This can also be seen in figure 7.4. The mass flow is also proportional with the inlet density of thecompressor. The fluctuations in the mass flow are the result of the constantly changing pressures andtemperatures at the inlet of the compressor.
Figure 7.4: The mass flow values through the compressor from the test rig test results
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7.2 Comparison of the test rig test results with the Simulinksimulation model
To determine for example the accuracy, the reliability and predictive capacity of the Simulink simulationmodel a comparison of those results with the test rig test results is made. Important to note is the dif-ferent test time (3000 s and 15.500 s, respectively the Simulink simulation time and the test rig test time).Simulating 3000 s in the Simulink model takes about 200 s real time (factor 15 time reduction), which isof course a big advantage.
In the next sections a comparison between the performance test and the simulation model is done forthe inlet conditions of the compressor (pressure, temperature and superheat), the mass flow throughthe compressor and the pressure in the condenser. Finally, the settings of the controllers of both thetest rig and the simulation model are investigated in section 7.2.5.
7.2.1 Inlet conditions compressor (pressure and temperature)
An important difference between the two thermodynamic quantities (pressure and temperature) of bothtests is the start-up phase. The pressure and temperature of the test rig test results (see figures 7.1and 7.2) before speeding up the compressor are equal to respectively 6.5 bar and 22 ◦C as opposedto an inlet pressure of 0 bar (see figure 6.8a) and a limited temperature of −12 ◦C at the inlet of thecompressor (see figure 6.8b) in the Simulink simulation model.
Furthermore, the changes in pressure after the start-up of both the test rig and the simulation modelare almost the same. There are fluctuations with small amplitudes, see figure 7.1. The control of theinlet temperature of the compressor is difficult for both the simulation model and the test rig, which canbe seen by the relatively large fluctuations (see figure 7.2).
7.2.2 Amount of superheat going into the compressor
The amount of superheat going into the compressor at the start-up is in the order of 40 ◦C for both theperformance test and the simulation model (see figures 7.3 and 6.9, respectively).
Furthermore, the values of the amount of superheat during the compressor is on both the test rig andthe simulation model is approximately around 8 ◦C. However, in the test rig are more fluctuations inthe area of compressor speeds of 6000 and 4000 RPM (see figure 7.3). Perhaps the time delay is toooptimisticly approximated in the Simulink simulation model for these compressor speeds, where thecontroller gets the response on a control action too fast. This leads to less fluctuations in the simulationresults (see figure 6.9).
7.2.3 Mass flow through the condenser
The values of the mass flows of point 1 is in both the test rig and the simulation model for the differentcompressor speeds approximately equal to each other (see figures 7.4 and 6.1). A difference can befound between approximately 800 and 1200 s in the Simulink simulation model. In this part of the simula-tion result the mass flow is approximately 10 % lower than the mass flow of the test rig test results. Thisis because the pressure and temperature in the Simulink simulation model at the inlet of the compressorare both below their set-point values (see figure 6.8a and 6.8b).
Furthermore, there are much less fluctuations in the simulation results. This is because the fact thatthere is an additional control loop placed that regulates the mass flow at point 1. This was neededbecause of an insufficient amount of data points in the 2D look-up table ’Rho(p,t)’, resulting in interpo-lations between values on the liquid side and values on the vapor side of the Mollier diagram (see theoutliers in figure 7.5).
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Figure 7.5: Massflow calculated with the density of point 1
7.2.4 Pressure in the condenser
The pressures in the condenser at both tests have an overshoot to approximately 12 bar when the pres-sure set-point was changed from 7 to 10 bar (see figures 7.1 and 6.11) . Lowering the speed of thecompressor from 4000 to 1800 RPM leads in both the test rig and the simulation model to a pressuredrop in the condenser to approximately 9 bar.
The largest difference between the two test rig performance test and the simulation model is the rateof change of the condenser pressure. The reason for this is the slow heat transfer between R134aand water. This phenomenon is not included in the Simulink simulation model. The pressure in thecondenser is directly dependent on the temperature of the refrigerant. So the change of the condenserpressure of the Simulink simulation model is too fast.
7.2.5 Controller settings
In the test rig the controllers transform a error signal to a position of the valve in a percentage of how farthe valve is open. In the Simulink simulation model the controllers transform a error signal to a positionof the valve in an amount of steps made. This difference leads to another order of the P-, I- and D-values.
Furthermore, almost each controller in the test rig has during a performance test approximately tendifferent P-, I- and D- settings. At almost every change of speed of the compressor or a different set-point pressure at the outlet of the compressor the P-, I- and D- settings are changed. In the simulationmodel there are just 5 changes of P-, I- and D- settings available. This difference leads also to a hardercomparison between the P-, I- and D-action of the test rig and the Simulink simulation model controllersettings.
However, it is possible to see some trends in PID settings during a pressure set-point change or achange in compressor speed, which corresponds to both the PID settings of the test rig controllers andthe simulation model controllers. To show such a trend, the settings of the controller which controlls theSTCV-1B (PID-101B) are outlined below. Experience has shown that this controller is the most difficultcontroller to control. Table 7.1 shows the settings of controller PID-101B during a compressor pressureoutput set- point change for both the test rig controller and the Simulink simulation model controller.From the table can be seen that the P- and I- values for both the test rig controller and the simulationmodel controller are the highest at a speed of 6000 RPM and followed by the values for both the test rigcontroller and the simulation model controller at a speed of 1800 RPM.
Set-point pressures - Speed compressor 14 bar− 6000 RPM 19 bar− 4000 RPM 17 bar− 1800 RPM
PID-101B of the test rig P: 60 I: 240 D: off P: 19 I:32 D: 8 P: 20 I:140 D: offPID-101B of the simulation model P:1.8 I:0.15 D:1 P:1.2 I:0.08 D:0.5 P:1.5 I:0.12 D:0.3
Table 7.1: P-, I, and D- settings of the controller PID-101B
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Page 44
CHAPTER 8
CONCLUSIONS AND RECOMMENDATIONS
There are two simulation models of the VCC made: a simulation model in xCos and a simulation modelin Simulink. Conclusions and recommendations about the xCos model are already given in section 5.2.The most important conclusion about xCos was that it is rejected, because it is not reliable. The re-mainder conclusions and recommendations for the report are given in section 8.1 and 8.2, respectively.
8.1 Conclusions
• The Simulink simulation results show many similarities with the test rig test results (with the excep-tion of the start-up phase). Mainly the inlet conditions of the compressor (pressure, temperatureand superheat) are quite the same for both models. The biggest difference between the two mod-els is the pressure of the condenser, because of the absence of heat transfer coefficients betweenthe R134a loop and the water loop.
• The start-up phase of the Simulink model gives in most cases unreliable thermodynamic quanti-ties, because the compressor is not rotating yet. There are no mass flows present in the system,which means the used energy and mass balances in the model are not applicable.
• The Simulink simulation model is flexible in terms of changing input values and changing the sim-ulation time. In the function ’input.m’ (see Appendix G.3) all the input variables can be changedeasily. Also the total simulation time can be changed through changing the value of the called vari-able ’factor’ in the function ’StepResponse end2’ (see Appendix G.2). Also changing PID-settingsand adding position limits to valves (by changing the saturation values in the right controllers) isvery easy.
• Simulink simulates approximately 15 times faster than the real test rig, which is a big advantage.Running one simulation of a model with this complexity in xCos will take much more time thendoing the same simulation with Simulink.
8.2 Recommendations
• In the process scheme given in appendix B.1 can be seen that there is also an oil mass flowprevent in the cycle, branding together after the hot gas bypass valve. This mass flow is alsoavailable in the mixing vessel and will result into a higher inlet temperature of the compressor moil
in mixing chamber. This results in a more superheated gas at the inlet of the compressor and thusinto a less critical system.
• In the current simulation model the output pressure of the compressor is independent of the com-pressor characteristics. There is a compressor model with the software Mathcad. In this modelthe pressure ratio is calculated with among others the use of a chosen efficiency, calculated massflow and a given rotational speed. A similar model can be made in Matlab and implemented inSimulink which will improve the accuracy of the model.
• It became clear that it is very important to include limits to the extreme valve positions to get arobust simulation model. For example, limiting the STCV-1B to maximum 5 % and limiting theSPCV-1B to minimum 2 % reduces the chance that liquid refrigerant goes into the compressor.This kind of limits are also set to the valves in the real test rig.
• Some assumptions made in the Simulink simulation model are not sufficiently validated. There aretime delays calculated based on reference values and with many assumptions, given in section4.2.3. These delays are constant for each different speed. However, the only variable that changesand needed to calculate the time delay is the volume flow, which depends on the mass flow andthe associated density. These two variables are both known and can be used to calculate the timedelay dynamically. Another assumption made is the length of the pipelines, which are assumedbased on the existing pictures of the test rig and with the help of an employee of Aeronamic who
Page 45
has seen the test rig in real life. Since the test rig is arrived at Aeronamic Almelo it is possible tomeasure the length of the pipelines to get more accurate values for the time delays used in thesimulation model.
• There are some warnings (mainly algebraic loop warnings) given by Simulink Diagnostic Viewerduring a simulation. These warnings may effect for example the simulation result or the simulationspeed. It is important to remove all the warnings to make sure that the results are not influencedby them.
• The signal converter equations given in section 4.2.2 are based on the results of some experi-ments done with a valve under different operating conditions and air as a medium. It is better todo a certain amount of experiments for each valve in the test rig under the same conditions as inthe test rig to find relations between the position of a valve, the pressure drop over a valve and themass flow through a valve.
• The 2D look-up tables have an insufficient amount of data points, resulting sometimes in an inter-polation between a value on the liquid side and a value on the vapor side of the Mollier diagram. Arecommendation is adding higher resolution input Matlab Data arrays into the 2D look-up tables.
• The controller settings of the test rig and the Simulink simulation model are not directly compa-rable, mainly through different output quantities of the controller. The controller in the Simulinksimulation model must also transform the input error signal to a position of the valve in a percent-age of how far the valve is open. This will lead to the same order of P-, I- and D- values and thecontroller settings of both cases will be easier to compare.
• In the Simulink simulation model the mass flow is regulated by PID controllers to reduce the largefluctuations in the massflow values of through the compressor (see section 7.2.3). The mass flowthrough the compressor is equal to: m = Vchamber1 ∗ρ1 ∗N (see equation 2.2). Making 2D look-uptables with higher resolution input Matlab Data arrays will reduce the large fluctuations and makeit possible to use the density at the inlet of the compressor to calculate the mass flow through thecompressor. A function for the increase and decrease of the speed of the compressor comparablewith the speed of the compressor from the test results must be written. All these changes will leadto a more reliable result of the Simulink simulation model.
Page 46
REFERENCES
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[2] U.S. Secretary of Commerce on behalf of the United States of America, NIST Standard ReferenceData, http : //webbook.nist.gov/chemistry/fluid/, 2011
[3] Baulinks, Neues Planungshandbuch von Viessmann fr Wrmepumpen, http ://www.baulinks.de/webplugin/2012/0001.php4, January 2012
[4] Akpobi and Ajayi , ”Design and Construction of a Scroll Compressor of an Automobile Air Condi-tioning,” J. Appl. Sci. Environ. Manage. June, 2007, Vol. 11 (2) 33 - 41
[5] Chen Rong and Wang wen, ”Discussion on leaking characters in meso- scroll compressor,” Else-vier, October 2007
[6] Parker Hannifin Corporation, Sporlan Division, Electric Hot Gas Bypass Valves, http ://www.parker.com/ , March 2010
[7] Parker Hannifin Ltd, Refrigeration and Air Conditioning Europe, Sporlan Electric ExpansionValves Valves, https : //www.rsdtotalcontrol.com/fx/assets/item/218.pdf , September 2008
[8] LNS, commercial components, Stepper Motor Discharge Bypass Valves SDR 3, 3X,SDR4 / Pressure Regulating Valves, http : //www.lns.com.pl/en/products/commercial −components/parker − sporlan − 19/pressure − regulating − valves − 1/2stepper − motor −discharge− bypass− valves− sdr − 3− 3x− sdr4, 2012.
[9] Rsdtotalcontrol, Sporlan Electric Expansion Valves, https ://www.rsdtotalcontrol.com/fx/assets/item/218.pdf , 2008.
[10] Bray Controls Commercial Division (17 May 2011), DMS24-27 (-A) Series Proportional ElectricSpring Return Actuators, p.10-11
[11] CU Aerospace, Products, http : //www.cuaerospace.com/Products/THERMOSY S −MATLABToolbox.aspx , 2010
[12] National Institute of Standards and Technology, NIST Reference Fluid Thermo-dynamic and Transport Properties Database (REFPROP): Version 9.1, http ://www.boulder.nist.gov/div838/theory/refprop/Frequently asked questions.htm, Sept. 22,2014.
[13] GCSE Bitesize, Science, Specific heat capacity, http ://www.bbc.co.uk/schools/gcsebitesize/science/aqa/heatingandcooling/buildingsrev3.shtml, 2014
Page 47
Page 48
Appendices
Page 49
APPENDIX A
MOLLIER DIAGRAM
A.1 Ph-diagram 4000 RPM
Figure A.1: Ph- diagram
A.2 Ts- diagram 4000 RPM
Figure A.2: Ts- diagram
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Page 52
APPENDIX B
PROCESS SCHEME
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B.1 Process scheme VCC
2
3
4
5
6
7
1
Figure B.1: The process scheme of the VCC. All the points (1− 7) mentioned in this scheme are given in figure 3.1
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B.2 Process scheme VCC (2)
Figure B.2: The process scheme of the VCC
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APPENDIX C
TEST MEASUREMENT
C.1 Test measurement
There are done some test measurements with a globe valve (see figure C.1) with different mass flows.The main target of this measurement was to find a global relation between the position of the piston ina pipeline and the associated pressure drop. One of the test results is explained below.
Figure C.1: Principle of a globe valve
The used pressure sensor was able to measure pressures up to 8 bar, so the maximum available mea-sured pressure drop was approximated 7 bar. The maximum stroke of the plug is approximately 18 mm.As can be seen in figure C.2 the test was intermitted at a position of the valve equal to approximately15 mm. At this position of the pressure drop was equal to 6 bar, which comes near the limit of the sensorrange. The mass flow is set constant on 80 g/s during the test. The measured pressure drop in theworking range is approximated by a third order curve, which is the blue line in the figure below. Therecould be chosen to approximate the pressure drop by a curve which is inversely proportional, becauseof the present asymptote in it. However, in the working range of the used control valves the area in theneighbor of the asymptote is not the most interesting area.
Figure C.2: measurement results
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APPENDIX D
TECHNICAL DATA OF A VALVE
D.1 Technical data of the valve: Sporlan SER-A-3/8x1/2-ODF-10-S
Figure D.1: Technical data of the valve
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APPENDIX E
SIMULATION MODEL
E.1 Simulation model xCos
Figure E.1: Entire Xcos model
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E.2 Simulation model Simulink
PID-104B and SPCV PID-101B and STCV
PID-103B and LPCV
mwater
Mass flow (linear with compressor speed) PID-102B and DPCV
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[Pcomp]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_0RPM_cond]
[clock]
Scope13
timespantime
step_0RPM_cond
step_1800RPM_N
step_1800RPM_comp_cond
step_6000RPM_N
step_6000RPM_comp
step_4000RPM_N
step_4000RPM_comp
step_1900RPM_N
step_1900RPM_comp
[clock]
In1 Out1Scope6
[step_0RPM_cond]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[h2_act]
In1 Out1
[m1]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope3
mwater
h2_act
hsubc
h4
m6act
CpdT
time
mwater
[h2_act]
[hsubc]
[h4]
[CpdT]
Scope8
CpdT
m6act
mwater
h2_act
h4_7bar
dhsubc
time
dhrefr
h4_act
[CpdT]
[clock]
[h2_act]
[hsubc]
[h4_7bar]
[h2_act][clock]
In1 Out1
H (p,s)
100
Scope1
entropymodel
Sin
timeentropy
[clock]Scope4
PstartupPcomp Pcomp2
Scope17 Scope60
Tsat (p)1
max
-30
Scope61
[superh]
In1 Out1
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
In1 Out1
[step_1800RPM_N]
[step_1800RPM_comp_cond]
[step_6000RPM_N]
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
Scope24
Scope59
Psat (t)2
[superh]Scope64
[Pcompin_act]
[Tcompin_act]
T (Pref,hact)3Calculatingh1
m6
h7
h6_act
h6
m1_act
time
h1
[clock]
[h2_act]
[h4_act]
[h4]
[m1]
[Pfeedback]
Scope19
H (p,t)1
[Pcompin_act]
[Tcompin_act]
[Tcompin_act]
Scope42
Scope56
[clock]
[Pfeedback]
P (h_sat)1
Scope2
Scope55
[step_6000RPM_comp]
[step_4000RPM_N]
[step_4000RPM_comp]
[step_1900RPM_N]
[step_1900RPM_comp]
[m6_act]
[h4_act]
Scope10
Scope11
[m6_act]
[m6_act]
S (p,t)
Scope120.001
[m6_act]
[m1] Scope5
min
[m1]
Tsat (p)2
[Pcompin_act]
[Tcompin_act]Scope7
[Pcompin_act]
[Tcompin_act]
Scope14
Inputs
rho_in_act
time
massf low_1
Pcomp_out
hsubc
CpdT
P1_ref
P1_ref_tot
T1_ref
P4_ref
P4_startup
T_superheat
Rho (p,t)
[rho_in]
[rho_in]
[clock]
[h1_act]
[h1_act]
[h2_act]
[h4_act]Scope9
Hf (p)
Scope15
[h4_7bar]
Hf (p)1
Scope16
[h4]
[Pcomp]
[hsubc]
[CpdT]
[P1ref]
[P1ref]
From9[T1ref]
[P4startup]
[P4ref]
[P1ref_tot]
[T1ref]
[P4ref]
[P4startup]
[superh]
[P1ref_tot]
[P1ref_tot]
Scope18
Tin
waterstartup
[massflow]
[massflow]
[massflow]
Figure E.2: Entire Simulink model
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APPENDIX F
USER MANUAL XCOS SIMULATIONMODEL
F.1 Block definitions
The definition of the used blocks in het simulation model are given in table F.1.
This block is a constantvalue generator
FROM: The main role ofthe GOTO/FROM blocks isto transport signals from ablock to another block with-out connecting them physi-cally
This block performs addi-tion or subtraction on scalar,vector or matrix inputs
GOTO: The main role ofthe GOTO/FROM blocks isto transport signals from ablock to another block with-out connecting them physi-cally
This block computes theproduct of the gain parame-ter and the input value
This block finds the min-imum/maximum values(parameter Min or Max)
This block computeselement-wise multiplicationor division of its vectorinputs
Given vector valued inputsthis block merges inputs ina single output matrix
This block outputs the rightmatrix division
LOOK-UP TABLE: Thisblock realizes a non-linearfunction defined using agraphical editor (data fromMollier diagram)
This block implements aPID (Proportional-Integral-Differential) controller
The unique output of thisblock generates a regularchain of events that arescheduled in seconds
This block realizes a SISOlinear system representedby its rational transfer func-tion Numerator/Denomina-tor
SCOPE: The Scope blockdisplays its input with re-spect to simulation time
This block outputs a stepsignal between two defin-able levels: initial value andfinal value (starting at aspecified step time)
SUPER BLOCK: This blockopens up a new Xcos win-dow for editing a new blockdiagram in order to keep themain screen more clear
This block is a signal linkfrom outside of the mainsystem into a sub-system
This block is a signal linkfrom outside of a sub-system into the main system
Table F.1: Block descriptions
F.2 Main differences between the Simulink model
• The principle of a control loop in the xCos model is basic: a reference, a PID-controller, a transferfunction of the valve and the feedback signal. There are no rate limiters, transport delays andsaturation settings available.
• To find the transfer function of a valve there is looked at the conversion of a rotational speed of thestep motor of the valve to the position of the piston of the valve (translation or rotation).
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– The transfer function of the Sporlan SDR-3x 5 ODF-20-S (used in SPCV-1B and DPCV-1B)and the Sporlan SER-A-3/8*1/2-ODF-10-S (used in STCV-1B) from rotational speed of thestep motor ω to axial position of the piston x is given by: M(s) = x
ω = p2πτd∗ e−τds, where p =
pitch (mm) and τd = delay (s). This last term represents the time delay and can be linearized,which leads to the following transfer function:
M(s) =x
ω=
p2πτd
s2 + 1τds
(F.1)
The values for the time delay τd are given in table 4.2.
– The linearized transfer function of the ball valve with a DMS24-27(-A) actuator (used in LPCV-1B) from rotational speed of the step motor ω to radial position θ is given by: M(s) = θ
ω =1τd
s+ 1τd
An overview of the transfer function for the different valves with different rotational speeds is givenin the table below:
Speed (RPM) 1800 4000 6000P2 (bar) 17 19 14
DPCV - 1B M(s) = xω
6.582e−5s2+0.414s
1.209e−4s2+0.76s
2.614e−4s2+1.642s
SPCV - 1B M(s) = xω
1.151e−5s2+0.072s
2.104e−5s2+0.132s
4.598e−5s2+0.289s
LPCV - 1B M(s) = θω
0.184s+0.184
0.337s+0.337
0.732s+0.732
STCV - 1B M(s) = xω
7.056e−6s2+0.044s
1.389e−5s2+0.087s
2.468e−5s2+0.155s
Table F.2: Properties different valves at different speeds
• Because of the non-existence of a ’switch’ block in xCos and the difficulty of making a lot ofswitches with many other blocks (which would lead to an unclear model), there are less switchesmade compared to Simulink. So in the xCos model the compressor will speed up or down and theset-point values for the exit pressure of the compressor will change at the same time, which wouldin reality lead to an uncontrollable system.
• The signal converter equations used in the Simulink model (see table 4.1) are not needed in thexCos model, because of a different approach.
F.3 Description of the different block loops
F.3.1 Input parameters
(a) Inlet condition compressor (b) Outlet pressure compressor (c) Inlet stepfunction condenser
(d) Fixed amount of subcooling (e) Fixed value of CP dT(f) Mass flow compressor
Figure F.1: Different input parameters
At point 1 (the inlet of the compressor) the pressure and temperature are known from the ATP of thecompressor: P1 = 1.83 bar and T1 = 268 K. So the enthalpy at point 1 h1 is calculated with a look-uptable (pressure to enthalpy with a constant temperature) and used as reference, see figure F.1a.
The pressure at the outlet of the compressor is 14, 19 or 17 bar, dependent on the speed of the com-pressor. The compressor will start after the hermeticity test in which the pressure is less than 0.06 bar(given in the ATP). So in the step function is inserted an initial value of 0.01 bar for a certain amount ofseconds, whereupon the different pressures are described. The temperature at the outlet of the com-pressor is approximated to 360 K, which may be a poor approximation. The transformation from the
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pressure to enthalpy is done with a look-up table with a constant temperature, see figure F.1b.
The pressure in the condenser is before set-up equal to 7 bar. Hereafter, the stepfunction changes thepressure to 10 bar, independent of the compressor speed. At point 4 the pressure can easily be trans-lated into an enthalpy, because point 4 lies on the saturated liquid line. So the look-up table transformsthe pressure into an enthalpy with the use of the data from the Mollier diagram, see figure F.1c.
As written before in section 3.1.1 the amount of sub-cooling is set to a constant value, which is accept-able because of less variations in the amount of sub-cooling. From a Mollier diagram the enthalpy asfunction of the temperature on the saturated liquid line in the temperature range from 293 K to 333 K canbe approximated with a linear line. The enthalpy increase per degree Kelvin is equal to approximately1.4 kJ/kg. Figure F.1d gives the block diagram of the amount of sub-cooling and the associated changein enthalpy.
For the heat balance of the condenser the value of CpdT of the water loop must be approximated. TheCp of the cold loop of the condenser is approximated to 4.2 kJ/kgK [13] and there is approximated a fixedtemperature difference dT of 10 K. So the value of CpdT is approximated to 42 kJ/kg, see figure F.1d.
The mass flow in the compressor is dependent on the volume of the inlet chamber, the speed of thecompressor and the density of the inlet flow (see equation 2.2). However, the density of the flow at theinlet of the compressor during the process is unknown, because both the temperature and pressureare not known in the simulation model. The mass flow should change gradually by compressor speedtransitions. Therefore, there is chosen to regulate the mass flow with the same control loop as thecontrol loop of the compressor (the same P-, I- and D-action and the same motorized control valve) andas input a step function of the different mass flows. The block system with a super block in it is given infigure F.1f. As an example the mass flow m1in is graphically displayed in figure F.2.
Figure F.2: Mass flow at the inlet of the compressor (and thus at the outlet of the compressor: m1 = m2)
where:t ≤ 5 :End of hermeticity test; compressor is not running yet5 < t ≤ 40 :Speed of compressor goes to 6000 RPM40 < t ≤ 65 :Speed of compressor goes to 4000 RPMt > 65 :Speed of compressor goes to 1800 RPM
(F.2)
F.3.2 Compressor exit
This is the most straightforward PID-control loop, because the pressure of the discharge pipeline canbe directly regulated to the desired value, assuming no influences of other PID-controllers. The controlscheme can be seen in figure F.3.
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Figure F.3: Block diagram of the compressor, N = 1800RPM
The reference pressure Pcomp is set according to section F.3.1 (given in an amount of bars). The gainblocks transform the reference unit from bar to Pa and vica versa.
The transfer function of the DPCV-1B at a given speed can be found in table 4.2 and is given in thesuperblock (figure F.4).
Figure F.4: PID-102B and DPCV-1B
The position x of the valve in the pipeline is controlled by PID-102B, where the P-,I- and D- action areempirically set. By changing the x-position of the motorized control valve both the the volume flow andthe pressure will change. With some experiments there is found a relation between the position x ofthe valve and the pressure drop ∆P in the pipeline. It became clear that this relation can be roughlyapproximated as a linear curve, with a pressure drop almost equal to zero when the valve is fully openedand a maximum pressure drop when the valve is fully closed (assumed on 20 bar). With this relation theposition of the valve can be translated into a pressure drop: x = 1
20∆P .
In the following example the compressor speed is 1800 RPM. With the relation between the position xand the pressure drop ∆P it is possible to get the transfer function from ω to ∆P :
MN=1800(s) =∆P
ω=
20 ∗ 6.582e− 5
s2 + 0.414s=
0.001316
s2 + 0.414 ∗ s(F.3)
F.3.3 Mixing vessel
The block model of the regulated mass flows in the mixing vessel with the energy balance in it is givenin figure F.5. In this section the different parts of this block model are elaborated.
Figure F.5: Block diagram of the mixing vessel
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PART 1
An important parameter is the reference fraction m7
m6, according to equation 3.3. The expressions for
m6.ref and m7.ref are given in equation 3.4. The reference mass flows are calculated in part 1 of theblock scheme.
PART 2
In the test rig the loop with the PID-104B in it is the suction pressure control loop and the other loop is thesuction temperature control loop, so the feedback signals of the loops are measured with a pressure-and a temperature- sensor respectively (see appendix B.1). In the block model both PID-controllers(PID-101B and PID-104B) are regulating a mass flow (m6 and m7) and the feedback signals are also’measured’ mass flows. This change from suction pressure control loop and suction temperature con-trol loop to two mass flow loops is possible through the reference mass flows that depends on the inletpressure and temperature (h1).
The transfer functions of the motorized control valves are dependent on the speed of the compressorand can be found in table 4.2 and are given in the superblocks (figure F.6).
(a) PID-104B and SPCV-1B (b) PID-101B and STCV-1B
Figure F.6: Two superblocks
In the block scheme the feedback signal of the suction pressure control loop is directly fed back and thefeedback signal of the suction temperature control loop is not directly fed back, which will be explainedin PART 4.
PART 3
In PART 3 of the block scheme the regulated enthalpy at point 1 is calculated with the following rewrittenform of the energy balance:
h1.act =m7
m6h2.act + h6.act
1 + m7
m6
(F.4)
The scope is placed to display the reference enthalpy h1in and the regulated enthalpy h1, see figureF.7. The first part of the figure is not reliable, because of the start-up phenomena. Important is that thecoolant is slightly superheated before it enters the compressor, which means that h1in at a pressure of1.83 bar must be higher than approximately 393 kJ/kg.
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Figure F.7: Regulated enthalpy at the inlet of the compressor, compared to the reference enthalpy
PART 4
The total mass flow (m1) must be equal to the sum m6 and m7. So the controllers mentioned in PART 2must work closely together. The temperature control loop is the slow loop, which is the reason that thefeedback signal of the suction temperature control loop is not fed back directly. The mass flow of point6, m6, is calculated with the following equation:
m6 =m1
1 + m7
m6
(F.5)
where the fraction m7
m6is regulated by both PID controllers. The mass flow of point 7 m7 is calculated in
a similar manner, however it is not important for the rest of the simulation model.
The scope is placed to display the reference mass flows, the regulated mass flows and the sum of theregulated mass flows.
F.3.4 Condenser
The block model of the regulated water mass flow in the condenser with the energy balance in it is givenin figure F.8.
Figure F.8: Block diagram of the condenser
PART 5
In PART 5 is given the energy balance of the condenser, which is already given in equation 3.1:
mwater =m3 [dhsubcooled + h3(P3)− hsat.liquid(P3)]
(cpdT )water(F.6)
Important to note is that the pressure in the condenser is equal to 7 bar before the start-up of thecompressor. However, from the energy balance becomes clear if the mass flow at point 6 m6act (equal
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to point 3) is zero (which is the case before the start-up of the compressor), the mass flow of the waterloop is equal to zero. Therefore the mass flow of point 6 m6act is set manually to 0.00561 kg/s duringthe first few seconds. Finally, this value for the mass flow leads to a pressure in the condenser of 7 bar.The mass flow of point 6 is displayed in a scope, see figure F.9.
Figure F.9: Mass flow of R134a through the condenser with manually set start-up values
PART 6
In the test rig the loop with the PID-103B in it is the liquid pressure control loop, with a pressure feedbacksignal coming from the R134a loop (see appendix B.1). In the block model the PID-controller PID-103Bis regulating a mass flow (mwater) and the feedback signal is also a measured mass flow.
The transfer function of the motorized control valve is dependent on the speed of the compressor andcan be found in table 4.2 and is given in the superblock (figure F.10).
Figure F.10: PID-103B and LPCV-1B
PART 7
In PART 7 the mass flow of the water loop mwater is converted into an enthalpy difference dhR134a withthe following equation (energy balance rewritten in dhR134a):
dhR134a =mwater(CpdT )water
m6act(F.7)
PART 8
The enthalpy difference in the condenser dhR134a, the enthalpy difference due to sub-cooling dhsubcand the enthalpy at the inlet of the condenser h3 are known, so the enthalpy of point 4 h4 can becalculated. This is the enthalpy value on the saturated liquid line, which can be transformed easily intothe condenser pressure with the use of a look-up table. There is also a scope placed, which gives thedifferent enthalpy values in time.
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F.4 Interaction between loops
Regulating the output pressure of the compressor results in a constantly changing the enthalpy h2, dif-ferent mass flows m6 and m7 and finally it results in different conditions at the inlet of the compressorh1. The changing enthalpy h2 has also effect on the mass flow of the water loop, which can be seen inthe energy balance (equation 3.1).
Regulating the mass flow of the water loop results in a constantly changing pressure in the condenser,different enthalpy values h3, h4 and h5 (and thus h6, because of an isenthalpic process of the motorizedcontrol valve STCV-1B) and finally it results in different inlet conditions at the inlet of the compressor h1.
There is assumed a compressor outlet temperature (and thus compressor efficiency), which results inan enthalpy h2 knowing the pressure P2. The compressor itself is not modeled. The interaction betweendifferent inlet conditions (regulated h1) of the compressor and therefore also other outlet conditions isnot included.
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APPENDIX G
MATLAB FILES
Listing G.1: MATLAB script ’S PT.m’1 Pstart=30; % Pressure in kPa2 Pend=3000; % Pressure in kPa3 dP=Pstart:(Pend−Pstart)/99:Pend; % The pressure increases from 'Pstart' to ...
'Pend' (array of size 100x1)4
5 Tstart=−50; % Temperature in degrees Celcius6 Tend=148; % Temperature in degrees Celcius7 dT=Tstart:(Tend−Tstart)/99:Tend; % The temperature increases from 'Tstart' to ...
'Tend' (array of size 100x1)8
9 % The following 'for− loops' calculate for every pressure 'dP' and10 % temperature 'dT' the associated value of entropie 'S PT' (in case of the11 % fluidum is 'R134a') with the use of the Matlab file 'refpropm.m'. The12 % output 'S PT' is a 100x100 matrix, which can be used in look−up tables13 % from the downloaded toolbox 'Thermosys'. These tables can be used in Simulink.14
15 for P=1:length(dP)16 for T=1:length(dT)17 S PT(P,T) = refpropm('S','T',dT(T)+273.15,'P',dP(P),'R134a');18 end19 end20
21 save('S PT.mat') % Save the 100x100 matrix 'S PT' to the file ...'S PT.mat'
Listing G.2: MATLAB script ’StepResponse end2.m’1 function [step 0RPM cond , step 1800RPM N , step 1800RPM comp cond , step 6000RPM N , ...
step 6000RPM comp , step 4000RPM N , step 4000RPM comp , step 1900RPM N , ...step 1900RPM comp , time 0RPM cond , time 1800RPM N , time 1800RPM comp cond , ...time 6000RPM N , time 6000RPM comp , time 4000RPM N , time 4000RPM comp , ...time 1900RPM N , time 1900RPM comp] = StepResponse end2(time)
2
3 Factor=1;4 time 0RPM cond=300*Factor; %0−300 sec: Pressure condenser to 7 bar5 time 1800RPM N=400*Factor; %300−400 sec: Compressor speed to 1800 RPM6 time 1800RPM comp cond=700*Factor; %400−700 sec: Pressure compressor to 12 bar, ...
pressure condenser to 10 bar7 time 6000RPM N=1000*Factor; %700−1000 sec: Compressor speed to 6000 RPM8 time 6000RPM comp=1500*Factor; %1000−1500 sec: Pressure compressor to 14 bar9 time 4000RPM N=1800*Factor; %1500−1800 sec: Compressor speed to 4000 RPM
10 time 4000RPM comp=2300*Factor; %1800−2300 sec: Pressure compressor to 19 bar11 time 1900RPM N=2600*Factor; %2300−2600 sec: Compressor speed to 1840 RPM12 time 1900RPM comp=3000*Factor; %2600−3000 sec: Pressure compressor to 17 bar13
14 if time < time 0RPM cond %(0−300)*factor sec: Pressure condenser to 7 bar15 step 0RPM cond=1;16 step 1800RPM N=0;17 step 1800RPM comp cond=0;18 step 6000RPM N=0;19 step 6000RPM comp=0;20 step 4000RPM N=0;21 step 4000RPM comp=0;22 step 1900RPM N=0;23 step 1900RPM comp=0;24 elseif time < time 1800RPM N %(300−400)*factor sec: Compressor speed to 1800 RPM25 step 0RPM cond=0;26 step 1800RPM N=1;27 step 1800RPM comp cond=0;28 step 6000RPM N=0;29 step 6000RPM comp=0;30 step 4000RPM N=0;31 step 4000RPM comp=0;
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32 step 1900RPM N=0;33 step 1900RPM comp=0;34 elseif time < time 1800RPM comp cond %(400−700)*factor sec: Pressure compressor to ...
12 bar, pressure condenser to 10 bar35 step 0RPM cond=0;36 step 1800RPM N=0;37 step 1800RPM comp cond=1;38 step 6000RPM N=0;39 step 6000RPM comp=0;40 step 4000RPM N=0;41 step 4000RPM comp=0;42 step 1900RPM N=0;43 step 1900RPM comp=0;44 elseif time < time 6000RPM N; %(700−1000)*factor sec: Compressor speed to 6000 RPM45 step 0RPM cond=0;46 step 1800RPM N=0;47 step 1800RPM comp cond=0;48 step 6000RPM N=1;49 step 6000RPM comp=0;50 step 4000RPM N=0;51 step 4000RPM comp=0;52 step 1900RPM N=0;53 step 1900RPM comp=0;54 elseif time < time 6000RPM comp %(1000−1500)*factor sec: Pressure compressor to 14 bar55 step 0RPM cond=0;56 step 1800RPM N=0;57 step 1800RPM comp cond=0;58 step 6000RPM N=0;59 step 6000RPM comp=1;60 step 4000RPM N=0;61 step 4000RPM comp=0;62 step 1900RPM N=0;63 step 1900RPM comp=0;64 elseif time < time 4000RPM N; %(1500−1800)*factor sec: Compressor speed to 4000 RPM65 step 0RPM cond=0;66 step 1800RPM N=0;67 step 1800RPM comp cond=0;68 step 6000RPM N=0;69 step 6000RPM comp=0;70 step 4000RPM N=1;71 step 4000RPM comp=0;72 step 1900RPM N=0;73 step 1900RPM comp=0;74 elseif time < time 4000RPM comp; %(1800−2300)*factor sec: Pressure compressor to 19 bar75 step 0RPM cond=0;76 step 1800RPM N=0;77 step 1800RPM comp cond=0;78 step 6000RPM N=0;79 step 6000RPM comp=0;80 step 4000RPM N=0;81 step 4000RPM comp=1;82 step 1900RPM N=0;83 step 1900RPM comp=0;84 elseif time < time 1900RPM N; %(2300−2600)*factor sec: Compressor speed to 1840 RPM85 step 0RPM cond=0;86 step 1800RPM N=0;87 step 1800RPM comp cond=0;88 step 6000RPM N=0;89 step 6000RPM comp=0;90 step 4000RPM N=0;91 step 4000RPM comp=0;92 step 1900RPM N=1;93 step 1900RPM comp=0;94 else %(2600−3000)*factor sec: Pressure compressor to 17 bar95 step 0RPM cond=0;96 step 1800RPM N=0;97 step 1800RPM comp cond=0;98 step 6000RPM N=0;99 step 6000RPM comp=0;
100 step 4000RPM N=0;101 step 4000RPM comp=0;102 step 1900RPM N=0;103 step 1900RPM comp=1;104 end105
106 end
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Listing G.3: MATLAB script ’Inputs.m’1 function [massflow 1 , Pcomp out, hsubc, CpdT, P1 ref, P1 ref tot, T1 ref , P4 ref , ...
P4 startup, T superheat] = Inputs(rho in act , time)2
3 [step 0RPM cond , step 1800RPM N , step 1800RPM comp cond , step 6000RPM N , ...step 6000RPM comp , step 4000RPM N , step 4000RPM comp , step 1900RPM N , ...step 1900RPM comp , time 0RPM cond , time 1800RPM N , time 1800RPM comp cond , ...time 6000RPM N , time 6000RPM comp , time 4000RPM N , time 4000RPM comp , ...time 1900RPM N , time 1900RPM comp] = StepResponse end2(time);
4
5 %% Mass flow for different compressor speeds6
7 rho in startup = 8.862; % kg/mˆ38 V in = 6.895*10ˆ−5; % mˆ39 N 1 = 6000/60; % RPM to Hz
10 N 2 = 4000/60; % RPM to Hz11 N 3 = 1800/60; % RPM to Hz12
13 if time < 70514 rho in=rho in startup;15 else16 rho in=rho in act;17 end18
19 % rho in=rho in startup; % Use this value for 'rho in' to reduce20 % calculation time (disadvantage: No feedback of the compressor inlet21 % pressure and compressor inlet temperature).22
23 massflow 1 = 0 * (step 0RPM cond) + rho in*V in * ( (step 1800RPM N + ...step 1800RPM comp cond) * N 3 + ( step 6000RPM N + step 6000RPM comp ) *N 1 + ( ...step 4000RPM N + step 4000RPM comp) * N 2 + ( step 1900RPM N + step 1900RPM comp ...)* N 3 ) ;
24
25 %% Different pressure set−points at different time steps26
27 Pcomp out = 0 * (step 0RPM cond + step 1800RPM N) + 12 * (step 1800RPM comp cond ...+ step 6000RPM N) + 14 * (step 6000RPM comp + step 4000RPM N ) + 19 * ...(step 4000RPM comp + step 1900RPM N ) + 17 * step 1900RPM comp;
28
29 %% Other input variables30
31 hsubc=5*1.4; %Amount of subcooling [kJ/kg] (5K subcooling, approx 1.4 kJ/kg per K)32 CpdT=42; %Value of CpdT from the glycol loop (kJ/kg) (assumed: Cp =4.2 ...
kJ/(kg*K) , dT=10 K)33 P1 ref = 183; %Reference input compressor pressure (kPa)34 T1 ref = −5.15; %Reference input compressor temperature (degrees Celcius)35 if time < time 0RPM cond %Compressor is still not rotating36 P1 ref tot=0; %Inlet pressure of the compressor is set to 0 (there are still no ...
mass flows)37 else %After 'time 0RPM cond' the compressor is rotating38 P1 ref tot=183;%Reference inlet pressure of the compressor is equal to 183 kPa39 end40 P4 ref=1000; %Reference condenser pressure (kPa)41 P4 startup=700; %Condenser pressure at start−up(kPa)42 T superheat=10; %Reference value for amount of superheating (in degrees Celcius)43
44 end
Listing G.4: MATLAB script ’Pcomp.m’1 function Pcomp2 = Pstartup(Pcomp)2
3 if Pcomp < 1.834 Pcomp2 = 1.83;5 else6 Pcomp2=Pcomp;7 end8
9 end
Listing G.5: MATLAB script ’entropymodel.m’1 function entropy = entropymodel(Sin,time)2 [step 0RPM cond , step 1800RPM N , step 1800RPM comp cond , step 6000RPM N , ...
step 6000RPM comp , step 4000RPM N , step 4000RPM comp , step 1900RPM N , ...step 1900RPM comp , time 0RPM cond , time 1800RPM N , time 1800RPM comp cond , ...
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time 6000RPM N , time 6000RPM comp , time 4000RPM N , time 4000RPM comp , ...time 1900RPM N , time 1900RPM comp] = StepResponse end2(time);
3
4 dT=200; % The approximated start−up time of the pressure of the compressor (so during ...this time the entropy is increasing linear)
5
6 if time<time 1800RPM N % The first 'time 1800RPM N' seconds the pressure is ...not changed
7 entropy=Sin; % The entropy remains the same as the input entropy8 elseif time <time 1800RPM N + dT % The pressure increases, so the entropy will increase9 entropy=(1.85−Sin)/dT*time + Sin − (1.85−Sin)/dT*time 1800RPM N; % Linear increase ...
of entropy10 else11 entropy=1.85; % Entropy remains constant12 end13
14 end
Listing G.6: MATLAB script ’Calculatingh1.m’1 function h1 = Calculatingh1(m6,h7,h6 act,h6,m1 act,time)2 [step 0RPM cond , step 1800RPM N , step 1800RPM comp cond , step 6000RPM N , ...
step 6000RPM comp , step 4000RPM N , step 4000RPM comp , step 1900RPM N , ...step 1900RPM comp , time 0RPM cond , time 1800RPM N , time 1800RPM comp cond , ...time 6000RPM N , time 6000RPM comp , time 4000RPM N , time 4000RPM comp , ...time 1900RPM N , time 1900RPM comp] = StepResponse end2(time);
3
4 %Keep in mind: h2 act = h7, h4 = h6 and h4 act = h6 (because of isenthalpic processes ...from respectively point 2 to point 7 and from point 4 to point 7)
5 if time < time 0RPM cond + 13 % Start−up time6 m1 opstart=1; % Random value (import that it is not equal to 0)7 h1 = h7 + (h6 − h7) * m6 / m1 opstart; % Energy balance with start−up values for ...
h6 and m18 else9 h1 = h7 + (h6 act − h7) * m6 / m1 act; % Energy balance with regulated values
10 end11
12 end
Listing G.7: MATLAB script ’mwater.m’1 function mwater = mwater(h2 act,hsubc,h4,m6act,CpdT,time)2 [step 0RPM cond , step 1800RPM N , step 1800RPM comp cond , step 6000RPM N , ...
step 6000RPM comp , step 4000RPM N , step 4000RPM comp , step 1900RPM N , ...step 1900RPM comp , time 0RPM cond , time 1800RPM N , time 1800RPM comp cond , ...time 6000RPM N , time 6000RPM comp , time 4000RPM N , time 4000RPM comp , ...time 1900RPM N , time 1900RPM comp] = StepResponse end2(time);
3
4 if time < time 0RPM cond + 20 % Start−up time5 m6 = max(0.0165,m6act); % Before the start−up of the compressor there are no ...
mass flows, therefore m6 is given a value by hand)6 mwater = m6 * (h2 act + hsubc − h4) / (CpdT); % Energy balance of the condenser7 else8 m6=m6act; % m6 is equal to the actual (calculated) m69 mwater = m6 * (h2 act + hsubc − h4) / (CpdT); % Energy balance of the condenser
10 end11
12 end
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