Filip Bjurling TRANSIENT THERMAL MODEL OF A MINIBUS' CABIN AND OPTIMIZATION OF THE AIR-CONDITIONING CONTROL STRATEGIES

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TRANSIENT THERMAL MODEL OF A MINIBUS' CABIN AND OPTIMIZATION OF THE AIR-CONDITIONING

CONTROL STRATEGIES

Filip Bjurling

Department of Energy Technology Royal Institute of Technology

Stockholm, Sweden

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Dept. of Energy Technology

Div. of Applied Thermodynamics and Refrigeration Prof: Björn Palm

Abstract

Improving the climate system of cars is important since it is the largest auxiliary load in a standard vehicle with an increase of fuel consumption by up to 20%. In Electric Vehicles (EV) the range of the car is more limited than in a fossil fueled car;

furthermore there is a limited waste heat available from the EV, approximately 2-3kW at 40oC for heating and defogging in winter. The goals of this report have been part of an existing European project (ICE) where the climate system of an electric minibus is being investigated. The specific objectives of this project were to develop a radiation model and integrate it in the existing thermal model of the cabin, validating the new model with existing experimental data, including the thermal model in the overall model of the complete vehicle and to use the existing AC-model to optimize the control with the aim of decreasing the energy consumption maintaining thermal comfort inside the cabin. The radiation model uses total radiation on a horizontal surface in order to calculate the radiation hitting the different parts of the car body and windows, finally the total radiative power entering the minibus is calculated. After including these calculations into the thermal model it could be seen that the results from the model in terms of cabin temperatures fit the experimental values surprisingly well. The control of the AC-system was optimized for a hot and sunny summer day in Italy which resulted in the AC-system working very hard following that the best control strategy was to reduce only the speed of the compressor in order to save energy. Calculations show that in the Normal European Driving Cycle (NEDC) the potential energy savings of following this control strategy can result in an energy saving of the AC-system by up to 27% compared to an unregulated case, with a maintained thermal comfort resulting in 4,2% increase in autonomy.

Keywords: Thermal Model Experiments Validation Electric Car Vapor Vapour Compression Matlab Simulink Trnsys Excel

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INDEX OF TABLES

Table 1. Reflectance and emittance of different materials of the car. (Levinson et al., 2011) 25

Table 2. Reflectance of different asphalt shingles for different wavelengths. ... 28

Table 3. Angles that set the position of a surface in order to calculate the amount radiation hitting that surface. ... 36

Table 4. All the simulations done for the sunny case scenario. ... 53

Table 5. Simulations done to find optimum case of the radiator fans. ... 54

INDEX OF FIGURES

Figure 1. A picture of the minivan used for the experiments. ... 9

Figure 2. Detailed blueprint with dimensions of the car... 9

Figure 3. The overall model in practice. ... 10

Figure 4. The overall model in Matlab Simulink. ... 11

Figure 5. The overall model simplified scheme. ... 11

Figure 6. The Thermal Model and how the cabin temperature and humidity is affected. ... 12

Figure 7. The figure shows placement of heaters and positions of thermocouples. ... 16

Figure 8. The diagram shows the air temperature in the driver region (left) and passenger region (right) for test1. ... 18

Figure 9. The placement of the minibus during test2 and test3. (Google Maps, 2012) ... 19

Figure 10. Illustration of the minivan and specifically the position of the thermocouples. ... 19

Figure 11. Image showing thermocouples and pyranometer. ... 20

Figure 12. Important values from test2 where irradiance and T AMB can be found in the Appendix. ... 20

Figure 13. The important results from test3 where irradiance and T AMB can be found in Appendix. ... 21

Figure 14. Compressor control to the left and fan control to the right. ... 22

Figure 15. Blower control in the driving region (to the left) and in the passenger region (to the right). ... 22

Figure 16. Compressor efficiency as a function of speed and pressure ratio. ... 23

Figure 17. The position of a surface is determined using Beta and Gamma angle. ... 27

Figure 18. Reflectivity of different colors and materials. ... 30

Figure 19. Solar radiation Spectrum. ... 30

Figure 20. Transmissivity of windows with different materials... 31

Figure 21. Thermal comfort as defined by ASHRAE. ... 31

Figure 22. Validation with TRNSYS of south beam radiation. ... 35

Figure 23. Validation with TRNSYS of south diffuse radiation. ... 35

Figure 24. Validation with TRNSYS of south reflected radiation. ... 36

Figure 25. Irradiation hitting the different surfaces of the car during the first day of test2. ... 37

Figure 26. Temperature of the cabin air in the driver region for test3 without any changes to the model. ... 41

Figure 27. Cabin-air temperature in the driver region for test3, final validation. ... 41

Figure 28. Temperature of the internal masses in the driver region for test3, final validation. 43 Figure 29. Cabin-air temperature in the passenger region for test3, final validation. ... 43

Figure 30. Temperature of the internal masses in the passenger region for test3, final validation. ... 44

Figure 32. Temperature of the internal masses in the driver region for test2, final validation. 45 Figure 33. Cabin-air temperature in the passenger region for test2, final validation. ... 45

Figure 34. Temperature of the internal masses in the passenger region for test2, final validation. ... 46

Figure 36. Cabin-air temperature in the passenger region for test1, final validation. ... 47

Figure 37. Cabin-air temperature and relative humidity in the driver and passenger region using earlier control. ... 49

Figure 38. Reference case - Cabin-air temperature and relative humidity in the driver and passenger region. ... 50

Figure 39. Reference case - Total energy consumption of the AC-system. ... 50

Figure 40. Reference case - Operation of the AC-system. ... 51

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Figure 41. Reference case - Control plots for compressor, radiator fans, driver and passenger

blowers. ... 52

Figure 42. Optimum Control for the sunny case scenario. ... 54

Figure 43. Comparison between the driver temperatures for the standard and the optimum case. ... 55

Figure 44. Comparison of the energy use for the starting case and the optimum case. ... 55

Figure 45. Optimum case – operation of the AC-system. ... 56

Figure 46. Optimum case – performance of the vapor compression cycle. ... 57

Figure 47. Optimum case - supply temperatures and cabin air temperatures. ... 57

Figure 48. Two different ways of changing the compressor control. ... 58

Figure 49. Radiator case - temperature inside the cabin with the different radiator controls. . 59

Figure 50. Radiator case - total energy consumption for the different radiators controls. ... 59

Figure 51. Radiator case - the number of radiator fans turned on during the test for three of the radiator controls. ... 60

Figure 52. Radiator case - The auxiliaries’ energy consumption for the different radiator controls. ... 60

Figure 53. On/Off case vs. continuous operation showing driver temperature and relative humidity inside the cabin of the minibus. ... 61

Figure 54. On/Off case vs. continuous operation - energy consumption comparison. ... 62

Figure 55. On/Off case vs. continuous operation - compressor speed. ... 62

NOMENCLATURE

𝐴 Area 𝑚²

𝑐_𝑝 Specific heat ^𝐽

𝐶 Constant 𝑘𝑔∙𝐾

𝐸̇ Power [𝑊]

𝑔 Gravity constant �_𝑠^𝑁₂�

ℎ Enthalpy �_𝑘𝑔^𝑘𝐽�

𝐻 Height [𝑚]

𝑖 Isolation �_𝑚^𝑊₂�

𝐼 Insolation [𝑊]

𝑚 Mass [𝑘𝑔]

𝑚̇ Mass flow �^𝑘𝑔_𝑠�

𝑝 Pressure [𝑃𝑎]

𝑄 Energy [𝐽]

𝑄̇ Capacity [𝑊]

𝑡 Temperature [℃]

𝑇 Temperature [𝐾]

𝑈 Overall heat transfer coefficient �_{𝑘𝑔∙𝐾}^𝑊 �

𝑣 Velocity �^𝑚_𝑠�

𝑉 Volume [𝑚³]

𝑉̇ Volume flow �^𝑚_𝑠³�

𝑊 Water content �^kg_kg^water

air �

𝑥 Vapor content �^kg_kg^water

air �

𝛼 Heat transfer coeff., convection �_{𝑘𝑔∙𝐾}^𝑊 �

𝜌 Density �_𝑚^𝑘𝑔₃�

𝑅𝐻 Relative humidity [−]

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CF Carnot Factor

𝑃 Power [𝑊]

𝐺 Heat transfer inertia �^kW_K �

𝐶 Inertia �^𝑘𝐽_𝐾�

𝛼 Mixing ratio [−]

𝛽 Recirculation rate [−]

𝜓 Heat in cabin air [^kJ

K]

𝑆 Segment of a surface [𝑚²]

𝑛𝑝 Number of people [−]

𝑑𝑊

𝑑𝑡 Derivate of water content �

kgwater kgair

𝑠 � 𝑑𝑇

𝑑𝑡 Derivate of temperature �^𝐾_𝑠�

𝐿𝑒𝑛𝑔𝑡ℎ ^Length^[𝑚]

𝑊𝑖𝑑𝑡ℎ ^Width^[𝑚]

𝐻𝑒𝑖𝑔ℎ𝑡 ^Height^[𝑚]

𝛾𝑠 Solar azimuth angle

𝜃𝑧 Solar zenith angle

𝛽 Slope of surface [°]

𝛾 Angle of surface [°]

𝑛 Number of days [−]

𝑅 Geometric factor [−]

𝑘 Radiation ratio [−]

𝐴_𝐼 Anisotropy index [−]

𝜎 Stefan Boltzmann constant [_𝑚^𝑊₂_𝐾₄]

𝜖 Grey surface compensation [−]

𝐹 Geometric factor [−]

𝑎 Absorptivity constant [−]

𝑟 Reflectivity constant [−]

CFD Computational Fluid Dynamics

COP Coefficient of Performance

HVAC Heating Ventilation and Cooling

IT Information Technology

KTH Royal Institute of Technology

SCP Specific Cooling Power

SEK Svenska Kronor (Swedish Crowns)

U.S. United States

UV Ultra Violet

UPV Universitat Polytecnica de Valencia

CRF Centro Ricerche Fiat

GDP Global Depletion Potential

ODP Ozone Depletion Potential

EV Electric Vehicle

NEDC Normal European Driving Cycle

PMV Predicted mean vote

PPD Predicted percentage dissatisfied

ASHRAE American Society of Heating,

Refrigerating and Air-Conditioning Engineers

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1 INTRODUCTION

Today´s environmental questions have put focus on how to manage transports in the future without fossil fuel dependence. One candidate to help achieve this goal is electric cars but some big obstacles have to be addressed. The range of the car in one charge is very limited, the batteries are heavy and expensive and the energy capacity in the batteries is significantly lower than the fuel in a comparable fossil fueled car. Because of this the energy efficiency of the electric car is very important. Since an electric engine is more efficient than a fossil fueled engine the auxiliaries are using a larger percentage of the total energy use. The by far largest auxiliary is the climate system. Due to the higher efficiency of the electrical engine there is less heat in access from the motor able to heat up the cabin, only around 2- 3kW at 40℃ temperature, and because of this the AC-system in an electric car would benefit if able to work as a heat pump.

This report is part of a larger project where the AC-system of an electric minibus is being addressed in order to decrease the energy use of this auxiliary due to the reasons mentioned above. This report has focused on improving the thermal model of the minivan supplied by IVECO and improving the control strategies of the climate system used in this project.

The project was started in order to evaluate a magnetocaloric based air conditioning system in a car. The idea is that this not only would improve efficiency buy also solve the problems with poisonous refrigerants in conventional vapor compression cycles.

There are six different organizations involved in this European project. The tasks each organization has responsible for will be addressed further in the background section.

The organization this report is part of is Universitat Politecnica de Valencia (UPV) who has the responsibility for mathematical modeling and dissemination.

This report will focus on improving the thermal model and optimization of the control strategies of the AC-system. In order to do this an analytical mathematical model has been created in Matlab. Another program that has been used in the project when handling radiation and important input values is TRNSYS.

1.1 Objectives

This report has focused on the following objectives:

• Develop the thermal model in order for it to be able to take solar radiation into account

• Validate the new thermal model with existing experimental data from Fiat.

• Include the thermal model in the overall model

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• Use the overall model and optimize the control to decrease energy usage and to maintain thermal comfort in the cabin

1.2 Limitations

Due to the reason that this report is part of a larger project it is important to state what has been addressed in this subproject and what belong to the other parts. This project has not gone into the magnetocaloric cooling cycle;

instead it used the conventional vapor compression cycle already installed in the minibus. For the overall model of the minibus, only the thermal model and control system was addressed, meaning no details was presented regarding the vapor compression cycles, pumps, fans and hydraulic loops.

The thermal model has been simplified as much as possible, trying to maintain an accurate result. For example infiltration and solar reflection of internal masses has been neglected.

Tests have already been conducted by Fiat in order to validate the thermal model. There have been no possibilities to make any new experiments for further validation of specific properties such as transmittivity of the windows or other types of tests with lower temperatures, a cloudy sky or a test where the AC-system is running.

The way of controlling the AC-system has been proposed by Fiat. This type of control has been the baseline for the control used in this report where only the numbers was changed from simulation from simulation. No other types of control was investigated, example given a PID-controller for the compressor.

The optimum control is developed for one specific case. This optimum might change with different loads on the AC-system. No overall control that works for every case has been developed.

Since no complete data has been given from IVECO or Fiat regarding the heat recovery potential of the electric components this heat has not been included in the model.

The car body has been assumed to hold a uniform average temperature through the outside to the inside of the car body.

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2 BACKGROUND

In the background section the entire European project (the ICE-project) is being discussed and more details will be presented regarding UPV´s remit.

Everything presented in this section is previous done work.

2.1 ICE Project

The idea with the ICE-project is to implement a magnetocaloric heat pump in an electric minivan and investigate the potential benefits of such a system.

There are six major stakeholders in this project presented in the following list:

Universitat Politecnica de Valencia, Spain:

UPV is providing the mathematical modeling.

Centro Ricerche Fiat (CRF), Italy: CRF is the project coordinator of the project and presenting the control strategies.

Cooltech Applications, France: Cooltech Applications is responsible for the magnetocaloric heat pump, both the design and realization.

Behr, Germany: Behr is developing the heat exchangers.

INSA Strasbourg, France: INSA is providing a magnetocaloric refrigeration concept.

They are also developing and stand for the basics.

IVECO ALTRA, Italy: Iveco has the Vehicle Integration process as its concern.

The idea with a collaboration like this is that every organization can contribute with its level of expertise all from the early research and improvement of systems to the implementation.

The goal with the project is to deliver an efficient refrigeration unit with a cooling COP > 5 where the operating supply temp should be from 5℃ to 60℃.

The cooling need is set to 5kW and heating to 6kW. Other benefits are compact packaging, no refrigerant (neither GWP nor ODP problems) and a low working pressure since there is no compressor in a magnetocaloric heat pump. But there is still a liquid used to transfer heat from the heat pump to the load that uses a certain pressure < 2bar

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2.2 The Overall Model

UPV´s task in this work is manly to model the car with all of its heat transfers.

The benefit of having a model like this is that it will be a great tool for developing, implementing and improving the climate system in the minivan.

The idea is to create a simple yet powerful transient simulation tool for the minivan.

Since UPV´s work is done in parallel with the other organizations the magnetocaloric refrigeration machine has not yet been constructed. Thus the minivan delivered by IVECO contains a vapor compression cycle and the model uses as of now also a vapor compression cycle in its calculations. This was chosen because the entire model can be finalized and validated before the magnetocaloric heat pump has been constructed.

The minivan used in this project was supplied by IVECO showed in Figure 1.

Figure 1. A picture of the minivan used for the experiments.

A detailed blueprint was also delivered from IVECO displayed in Figure 2.

Figure 2. Detailed blueprint with dimensions of the car.

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Before making the model with its necessary calculations and interactions Figure 3 was made in order to get a good overview of the system:

Figure 3. The overall model in practice.

One input important to state when starting a simulation is what kind of driving cycle it should perform. In the simulations performed below the Normal European Driving Cycle (NEDC) has been used. The driving cycle is approximately 20min and has different driving modes such as urban- country- and stand stills. Other inputs are external conditions affecting the minivan such as speed of the car (v) taken from the NEDC, outside temperature (Te), relative humidity (RHe), solar insulation (I). Furthermore the control settings are also inputs. The control settings determine the compressor speed, speed of indoor fans (blowers), speed of the outdoor/radiator fans (fans) and speed of pumps. These inputs will make the model calculate other important values such as power consumption (P), supply temperature of the climate system (TAC), cabin temperature in the driver and passenger region (Tdriv) (Tpass) and the relative humidity in the driver and passenger region (RHdriv) (RHpass).

The model was later developed using Matlab Simulink as tool. With Simulink it was easy to couple different models together in order to be able to model the entire car. An overview of the Simulink scheme is found in Figure 4.

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Figure 4. The overall model in Matlab Simulink.

Every large colored box represents one standalone code where information is exchanged by connecting the boxes in different ways. This tool is very convenient to use when handling large models. For example information can easily be found in this overview and if wanted it can be plotted only by adding a box and thus exporting the values into for example an excel-file. The same model with the same information exchange but made as an easy-to-see- overview is found in Figure 5 below. Every box can be looked at as a separate sub-model such as the cabin-model, air-cooler-model, heat-pump-model and radiator-loop-model. Every sub-model needs input values and delivers output values for other sub-models or to be delivered as output values. Inputs come from the outside of the model, the control and other sub-models. Figure 3, Figure 4 and Figure 5 are all showing the same overall model but in different ways.

Figure 5. The overall model simplified scheme.

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2.2.1 Thermal Model

In this report focus has been put on the model of the cabin of the minivan (thermal model) and the control strategies, which is why these two are explained more in detail in this and the following section. The thermal model´s main task is to calculate temperature and the relative humidity inside the minivan (the cabin). The thermal model can be said to be the core of the overall model since it is affected by almost all the sub-models. In order to understand and see how the thermodynamic transfers interact, an image of the car was drawn. The image is shown in Figure 6.

Figure 6. The Thermal Model and how the cabin temperature and humidity is affected.

The explanations for radiation in the original model is not as accurate as in the final model, which will be presented later in the report, but the basics for heat balances are the same. The cabin is affected by a number of different parameters explained with arrows and text in Figure 6. The heat transfer between car body and external air in the passenger and driver region (Ge,driv)(Ge,pass), heat gains from the occupants in the car (Q), mass of air from the AC-system supplied in the driver and passenger region (mAC,driv)(mAC,pass), mass of fresh air from the outside (mv), mass of indoor air let out of the car (mpass,e), recirculated air in the driver region (mr,driv), the mixing of air between sections (𝑚𝜓), the extra air transferred to the passenger region (mdriv,pass) and the amount of air supplied from the driver blower that stays in the driver region (𝛼) all contribute together to the change in temperature and relative humidity in the cabin. There is also a heat transfer between car body and indoor air (Gdriv)(Gpass) as well as between the masses and the indoor air (Gmass,driv)(Gmass,pass) in the same way as for example Ge,pass but these did not fit in the picture. The horizontal radiation (I) heats up a calculated area in the driver and passenger region (Seq,driv) (Seq,pass) which correspond to the actual heat gain from radiation.

The cabin model consists of energy and air-humidity balances. The car body holds one energy balance equation. Heat will be transferred from the body to the ambient or vice versa depending on the temperatures and heat will also be transferred between the body and the cabin air inside the car. Finally the

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body can also be heated by radiation from the sun. From this reasoning the equation below can be formed and is valid for the driver region:

𝐶𝑏,𝑑𝑟𝑖𝑣·𝑑𝑇𝑏,𝑑𝑟𝑖𝑣

𝑑𝑡 =

𝐺𝑖,𝑑𝑟𝑖𝑣· �𝑇𝑖,𝑑𝑟𝑖𝑣− 𝑇𝑏,𝑑𝑟𝑖𝑣� − 𝐺𝑒,𝑑𝑟𝑖𝑣· �𝑇𝑏,𝑑𝑟𝑖𝑣− 𝑇𝑒� + 0.5 · 𝑎𝑏· 𝐼 · 𝑆𝑒𝑞,𝑏,𝑑𝑟𝑖𝑣

where 𝐶𝑏,𝑑𝑟𝑖𝑣 is the inertia of the car body, ^𝑑𝑇^{𝑏,𝑑𝑟𝑖𝑣}_𝑑𝑡 is the change in temperature of the car body, 𝐺𝑖,𝑑𝑟𝑖𝑣 is the heat transfer per Kelvin between indoor air and car body, 𝑇_{𝑖,𝑑𝑟𝑖𝑣} is indoor air temperature, 𝑇_{𝑏,𝑑𝑟𝑖𝑣} is the body temperature, 𝐺𝑒,𝑑𝑟𝑖𝑣 is the heat transfer per Kelvin between external air and car body, 𝑎𝑏 is the absorption coefficient of radiation of the car body, 𝐼 is the horizontal radiation and 𝑆_{𝑒𝑞,𝑏,𝑑𝑟𝑖𝑣} is the equivalent area horizontally exposed to the sun.

The car body has been simplified to hold a uniform temperature, in example the outside of the car body and the inside is assumed to have the same temperature in the model.

Apart from the car body there are other surfaces as well in the car, such as seats, instrument panel, and steering wheel. These objects have been called internal masses in the model and they have a certain mass, area and specific heat capacity. The seats in the car will be heated up or cooled down depending on the radiation hitting the masses and the convection to the indoor air. There is a heat balance for the internal masses as well presented below:

𝐶_{𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣}·𝑑𝑇𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣

𝑑𝑡 = 0.5 · 𝑎_{𝑚𝑎𝑠𝑠}· 𝐼 · 𝑆_{𝑒𝑞,𝑑𝑟𝑖𝑣}− 𝐺_{𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣}· �𝑇_{𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣}− 𝑇_{𝑖,𝑑𝑟𝑖𝑣}�

where the names of the terms are named in the same way as in the previous equation but in this equation values are for the masses, as where the 𝑆𝑒𝑞,𝑑𝑟𝑖𝑣is the equivalent area of the windows where horizontal radiation can enter and heat up the masses. 𝑇𝑖,𝑑𝑟𝑖𝑣 is the indoor air temperature.

There is one last heat balance which is for the cabin air. This equation is more advanced because more parameters affect the cabin air temperature. The full equation is stated below where the left side is the change in cabin air temperature, the 1st term on the right side symbolizes the energy in supply air flow, 2^nd term is return air flow, 3^rd term is energy exchange between indoor air and car body, 4^th term is energy exchange between internal masses and indoor air, 5^th ter is sensible load from passengers, 6^th term is air flow between driver and passenger due to stack effect, 7^th term is air flow between driver and passenger due to AC-distribution. The cabin air heat balance:

𝐶_{𝑖,𝑑𝑟𝑖𝑣}·𝑑𝑇𝑖,𝑑𝑟𝑖𝑣

𝛼 · 𝑉̇_{𝐴𝐶,𝑑𝑟𝑖𝑣}· 𝜌 · 𝑐_𝑝· 𝑇_{𝐴𝐶,𝑑𝑟𝑖𝑣}− 𝑉̇_{𝑟,𝑑𝑟𝑖𝑣}· 𝜌 · 𝑐𝑑𝑡 =_𝑝· 𝑇_{𝑖,𝑑𝑟𝑖𝑣}− 𝐺_{𝑖,𝑑𝑟𝑖𝑣}· �𝑇_{𝑖,𝑑𝑟𝑖𝑣}− 𝑇_{𝑏,𝑑𝑟𝑖𝑣}�

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+𝐺_{𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣}· �𝑇_{𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣}− 𝑇_{𝑖,𝑑𝑟𝑖𝑣}� + 𝑛𝑝 · 𝑄_𝑝,𝑠+ 𝜓 · �𝑇_{𝑖,𝑝𝑎𝑠𝑠}− 𝑇_{𝑖,𝑑𝑟𝑖𝑣}� − 𝑉̇_{𝑑𝑟𝑖𝑣,𝑝𝑎𝑠𝑠}

· 𝜌 · 𝑐_𝑝· 𝑇^∗

where 𝑉̇_{𝐴𝐶,𝑑𝑟𝑖𝑣} is supply air flow, 𝜌 is density of air, 𝑐_𝑝 is specific heat capacity of air, 𝑛𝑝_{𝑑𝑟𝑖𝑣} is the number of people in the driver region, 𝑄_𝑝,𝑠 is heat dissipated per person, 𝜓 is the energy in the air per Kelvin in the air, 𝑉̇𝑑𝑟𝑖𝑣,𝑝𝑎𝑠𝑠 is the air flow between driver and passenger region.

In addition to sensible heat exchange there is also a latent heat exchange that is needed to take into account. The balance is written belowand is similar to the energy balance of the cabin air above. The left side of the equation is mass change of water in the cabin, the 1^st term on the right side is water content in supply air, 2^nd term is water content in return air, 3^rd term is water vapor from occupants in the car, 4^th term is water content due to stack effect, 5^th term is water content due to AC-system. Water content balance:

𝑉𝑖,𝑑𝑟𝑖𝑣· 𝜌 ·𝑑𝑊_{𝑖,𝑑𝑟𝑖𝑣}

𝑑𝑡 = 𝛼 · 𝑉̇𝐴𝐶,𝑑𝑟𝑖𝑣· 𝜌 · 𝑊𝐴𝐶,𝑑𝑟𝑖𝑣− 𝑉̇𝑟,𝑑𝑟𝑖𝑣· 𝜌 · 𝑊𝑖,𝑑𝑟𝑖𝑣 + 𝑛𝑝𝑑𝑟𝑖𝑣· 𝑚̇𝑝,𝑤

+ 𝜓

𝑐_𝑝· �𝑊_{𝑖,𝑝𝑎𝑠𝑠}− 𝑊_{𝑖,𝑑𝑟𝑖𝑣}� − 𝑉̇_{𝑑𝑟𝑖𝑣,𝑝𝑎𝑠𝑠}· 𝜌 · 𝑊^∗ where ^𝑑𝑊^{𝑖,𝑑𝑟𝑖𝑣}

𝑑𝑡 is the change in water vapor per kg, 𝑊𝐴𝐶,𝑑𝑟𝑖𝑣 is the water content in the supply air, 𝑚̇𝑝,𝑤 is the water dissipated per person.

The same equations are made for the passenger region with slight changes.

These changes can be deduced from Figure 6. When all of these equations are made the problem consists of solving an equation system of eight differential equations. This task has been assigned to Matlab to solve.

In order for Matlab to be able to solve the differential equations Matlab needs values of every constant and variable in the equations. The values are presented below and their units can be found in the nomenclature:

Properties for the air were set to:

𝜌 = 1,2 𝑐𝑝 =1005

Dimensions of the vehicle was taken from Figure 2 and also calculated according to the following:

𝐿𝑒𝑛𝑔𝑡ℎ_{𝑑𝑟𝑖𝑣} = 1,8 𝑊𝑖𝑑𝑡ℎ_{𝑑𝑟𝑖𝑣}= 2 𝐻𝑒𝑖𝑔ℎ𝑡𝑑𝑟𝑖𝑣 = 2

𝐴𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣 = 1

𝑉_{𝑑𝑟𝑖𝑣} = 𝐿𝑒𝑛𝑔𝑡ℎ_{𝑑𝑟𝑖𝑣}𝑊𝑖𝑑𝑡ℎ_{𝑑𝑟𝑖𝑣}𝐻𝑒𝑖𝑔ℎ𝑡_{𝑑𝑟𝑖𝑣}

𝐴_{𝑑𝑟𝑖𝑣} = 2𝐿𝑒𝑛𝑔𝑡ℎ_{𝑑𝑟𝑖𝑣}𝑊𝑖𝑑𝑡ℎ_{𝑑𝑟𝑖𝑣}+ 2𝐿𝑒𝑛𝑔𝑡ℎ_{𝑑𝑟𝑖𝑣}𝐻𝑒𝑖𝑔ℎ𝑡_{𝑑𝑟𝑖𝑣}+ 𝑊𝑖𝑑𝑡ℎ_{𝑑𝑟𝑖𝑣}𝐻𝑒𝑖𝑔ℎ𝑡_{𝑑𝑟𝑖𝑣} 𝐿𝑒𝑛𝑔𝑡ℎ_{𝑝𝑎𝑠𝑠} = 4,4

𝑊𝑖𝑑𝑡ℎ_{𝑝𝑎𝑠𝑠} = 2 𝐻𝑒𝑖𝑔ℎ𝑡𝑝𝑎𝑠𝑠 = 2 𝐴𝑚𝑎𝑠𝑠,𝑝𝑎𝑠𝑠= 10

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𝑉𝑝𝑎𝑠𝑠 = 𝐿𝑒𝑛𝑔𝑡ℎ𝑝𝑎𝑠𝑠𝑊𝑖𝑑𝑡ℎ𝑝𝑎𝑠𝑠𝐻𝑒𝑖𝑔ℎ𝑡𝑝𝑎𝑠𝑠

𝐴_{𝑝𝑎𝑠𝑠} = 2𝐿𝑒𝑛𝑔𝑡ℎ_{𝑝𝑎𝑠𝑠}𝑊𝑖𝑑𝑡ℎ_{𝑝𝑎𝑠𝑠}+ 2𝐿𝑒𝑛𝑔𝑡ℎ_{𝑝𝑎𝑠𝑠}𝐻𝑒𝑖𝑔ℎ𝑡_{𝑝𝑎𝑠𝑠} + 𝑊𝑖𝑑𝑡ℎ_{𝑝𝑎𝑠𝑠}𝐻𝑒𝑖𝑔ℎ𝑡_{𝑝𝑎𝑠𝑠}

𝐿𝑒𝑛𝑔𝑡ℎ_{𝑑𝑟𝑖𝑣}, 𝑊𝑖𝑑𝑡ℎ_{𝑑𝑟𝑖𝑣}, 𝐻𝑒𝑖𝑔ℎ𝑡_{𝑑𝑟𝑖𝑣} are the dimensions of the car in the driver region. 𝐴_{𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣} is the surface of the internal masses in the driver region.

𝑉𝑑𝑟𝑖𝑣 is the driver region air volume. 𝐴𝑑𝑟𝑖𝑣 is the area of the body in the driver region. The same reasoning goes for the passenger region. Weights of the car have been roughly estimated:

𝑚_{𝑏𝑜𝑑𝑦,𝑑𝑟𝑖𝑣} = 650 𝑚_{𝑏𝑜𝑑,𝑝𝑎𝑠𝑠} = 1250 𝑚𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣 = 15 𝑚_{𝑚𝑎𝑠,𝑝𝑎𝑠𝑠} = 190

The numbers are for mass of the body and the internal masses in the driver and passenger region.

Thermal conductance may vary from case to case and the thermal inertias are experimentally determined which is why these values are presented when the model is validated against experimental tests. The air condition settings are the following and are the same for the three experimental tests:

𝛼 = 0,8 𝛽 = 1 𝑉_{𝐴𝐶,𝑑𝑟𝑖𝑣} = 0 𝑉𝐴𝐶,𝑝𝑎𝑠𝑠 = 0

𝛽 is the recirculation rate where 1 means full recirculation. When the air conditioning system is turned off the flow is 0 and when it is running the flow is determined from the control which decides the speed of the fans.

The thermal loads inside the car for the three tests are:

𝑛𝑝_{𝑑𝑟𝑖𝑣} = 0 𝑛𝑝_{𝑝𝑎𝑠𝑠} = 0

𝑄_𝑠 = 0 𝑚_𝑤 = 0,000014

A model needs to be validated which is why Fiat made a number of experiments with measurements for UPV to use as validation material. The model needs to fit with the experimental values. Three tests were conducted, one inside, with a heating and cooling period where electric heaters heated the air in the cabin for a period of time with a following cooling period. Two additional tests were made where the minivan was placed in a parking lot where the sun was heating the car for a number of days. The model was validated against the indoor test (that did not include any radiation) but not against the outside tests. One big task of this project has been to validate the remaining two tests that include radiation which is presented in 4.1.3 Validation of the Improved Thermal Model. The original model with its simplified inclusion of radiation was never validated.

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Test 1: Test Indoors With a Heating and Cooling Period

The minivan was placed inside a garage with two electrical heaters of 2kW each inside the car. The position of the electrical heaters can be seen in Figure 1 and Figure 7. Thermocouples to measure the air temperature were also placed in head level on different places in the car, as seen in Figure 7.

The thermocouples were placed in passenger seats and one in the driver seat (the driver thermocouple cannot be seen in the figure)

Figure 7. The figure shows placement of heaters and positions of thermocouples.

The test was divided into two parts. From 0 to 160,5 min into the test the two fan heaters were switched on. From 160,5min to the end at 336,5min, the fan heaters were switched off to let the cooling period take place. To take the heating into account in the model the following values were set:

𝑛𝑝𝑝𝑎𝑠𝑠 = 2 𝑄_𝑠 = 2000 𝑈_𝑖𝑛𝑡 = 5,6 𝑈_𝑒𝑥𝑡 = 3 𝑐_𝑝,𝑏= 600 𝑐𝑝,𝑚𝑎𝑠𝑠 = 900

𝜓 = 4000

between 0 – 160,5min. The heating power will then be 4000W. 𝑈_𝑖𝑛𝑡 is the internal heat transfer coefficient between the air and internal masses and between the air and the car body on the inside. 𝑈𝑒𝑥𝑡 is the external heat transfer coefficient between outside air and car body. The car body is estimated to have a uniform temperature, which is a mean temperature, from the inside to the outside of the car body. Since the conduction of the car body has been excluded 𝑈_𝑖𝑛𝑡 and 𝑈_𝑒𝑥𝑡 are in practice heat transfer coefficients

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that also includes a conduction part. 𝑐𝑝,𝑏 and 𝑐𝑝,𝑚𝑎𝑠𝑠 are the specific heat capacity of the car body and internal masses. 𝜓 is the coefficient for the air circulation between zones. From 160,5min to the end the values change to:

𝑛𝑝𝑝𝑎𝑠𝑠 = 0 𝑄_𝑠 = 0 𝑈_𝑖𝑛𝑡 = 1,87

𝑈_𝑒𝑥𝑡 = 3 𝑐_{𝑝 ,𝑏} = 600 𝑐_{𝑝,𝑚𝑎𝑠𝑠} = 900

𝜓 = 𝑉𝜓𝜌𝑐𝑝

Where 𝑉_𝜓 is calculated from the following:

𝑉𝜓 = (0,4 + 0,0045(𝑇𝑑𝑟𝑖𝑣− 𝑇𝑝𝑎𝑠𝑠))(𝑊𝑖𝑑𝑡ℎ𝑑𝑟𝑖𝑣𝐻𝑒𝑖𝑔ℎ𝑡𝑑𝑟𝑖𝑣) �9,8𝐻𝑒𝑖𝑔ℎ𝑡𝑑𝑟𝑖𝑣�𝑇𝑑𝑟𝑖𝑣− 𝑇𝑝𝑎𝑠𝑠�

𝑇𝑑𝑟𝑖𝑣 �

12

𝑛𝑝_{𝑝𝑎𝑠𝑠} and 𝑄_𝑠 is set to 0 due to the heating being turned off. Since the heating fans are turned off the heat transfer has changed from forced to natural convection and is thereby decreased by a factor 3. The external heat transfer coefficient remains the same throughout the simulation. Calculations affected by the values above are:

𝐺_{𝑑𝑟𝑖𝑣}= 𝑈_𝑖𝑛𝑡𝐴_{𝑑𝑟𝑖𝑣} 𝐺_{𝑒,𝑑𝑟𝑖𝑣}= 𝑈_𝑒𝑥𝑡𝐴_{𝑑𝑟𝑖𝑣} 𝐺𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣 = 𝑈𝑖𝑛𝑡𝐴𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣

𝐶_{𝑖,𝑑𝑟𝑖𝑣} = 𝜌𝑉_{𝑑𝑟𝑖𝑣}𝑐_𝑝 𝐶_{𝑏,𝑑𝑟𝑖𝑣} = 𝑚_{𝑏,𝑑𝑟𝑖𝑣}𝑐_𝑝,𝑏 𝐶_{𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣} = 𝑚_{𝑚𝑎𝑠𝑠,𝑑𝑟𝑖𝑣}𝑐_{𝑝,𝑚𝑎𝑠𝑠} The same calculations are done for the passenger region.

Starting temperatures of the car body, air and masses were set to 23,4℃ and humidity was set 0,012kgwater/kgair. Since there is no infiltration and full recirculation of air the absolute humidity is constant throughout the test. Input values changing over time can be found in Appendix. These values are:

𝑇𝑖𝑚𝑒_𝑠 and 𝑇_𝑒𝑥𝑡.

With the input values and calculations above together with solving the differential equation system, the temperature change in the cabin is calculated for the entire duration of the test. These values are compared against the experimental values for the driver and passenger region. The heat transfer coefficients are constant throughout the test even if temperature gradients increase they are estimated to be the same. The heat transfer coefficients could be different in the driver and passenger region but in the tests done in this report the heat transfer coefficient values for driver and passenger region have been set the same value. The car body is separated into segments adjacent to the driver and the passenger region. If the surface is adjacent to the driver region this surface only heats the driver region and vice versa.. The result can be found in Figure 8 for the driver and passenger region.

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0 10 20 30 40 50 60

0 1 2 3 4 5 6

Temperature (ºC)

Time (h)

Exp-driv Model-driv

0 10 20 30 40 50 60

0 1 2 3 4 5 6

Temperature (ºC)

Time (h)

Exp-pass Model-pass

In Figure 8 the model follows the experimental data well apart from the first minutes. One possible explanation to this could be due to the thermal inertia of the thermocouples.

More details as of how and why the values are set as they are can be read in the master thesis "Modelado y análisis de un sistema de aire acondicionado para vehículos basado en la refrigeración magnética" by B. Torregrosa-Jaime 2011.

Test2: Test Outdoors With the Vehicle Placed under the Sun

Two tests were conducted with the minivan placed in a parking lot in Torino, Italy. These tests had not yet been validated before this project started. The first outdoor test was conducted during the 6^th– 8^th of July. The second test was done on the 12^th – 16^th of July. The minivan was placed according to Figure 9 below:

Figure 8. The diagram shows the air temperature in the driver region (left) and passenger region (right) for test1.

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Figure 9. The placement of the minibus during test2 and test3. (Google Maps, 2012)

In Figure 10 and Figure 11 the positions of the instruments measuring values for the experiment are shown.

Figure 10. Illustration of the minivan and specifically the position of the thermocouples.

Thermocouples 1-6 are on head level measuring air temperature where 1 and 2 are in the driver region. Number 7-12 are measuring the internal masses, all except one measures temperature of the seats, number 7 measures temperature of the dashboard.

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Figure 11. Image showing thermocouples and pyranometer.

Number 13 and 14 are thermocouples measuring the car body temperature on the external surface. The ambient temperature is measured below the vehicle, right next to the tires, so that no direct radiation can impact the thermocouple.

All important values from test 2 have been plotted in Figure 12.

Figure 12. Important values from test2 where irradiance and T AMB can be found in the Appendix.

The values shown in figure 12 are: ambient temperature (T AMB), mean temperature in head level of the air inside the minibus (Mean Head Pass) (Mean Head Driv.), mean temperature of the surfaces of the materials inside the car for the driver and passenger region (Driver inner inertia) (Pass. Inner inertia), temperature of the outer surface of the car measured in driver and passenger region (Metal mass 13) (Metal mass 14) and the total horizontal irradiance (IRRADIANCE (W)). The values that will be used as inputs to the model are irradiance and ambient temperature (T AMB). These values can be found in Appendix. In the morning of the first day, around five o’clock it rained

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which is why there is a temperature drop around that time. It is also possible to see that the second day was a bit cloudy since the radiation data jumps up and down more than during the first day.

Test3: Test Outdoors With the Vehicle Placed under the Sun

Test 3 was conducted in the same manner as test2. The results are displayed in Figure 13 and the values for ambient temperature and irradiance are found in Appendix. The irradiance is displayed on a separate axis and the other values are all temperatures displayed on the first axis.

Figure 13. The important results from test3 where irradiance and T AMB can be found in Appendix.

The validation of test2 and test3 has been done in the chapter Models.

2.2.2 Climate Control System

The climate system control manages the compressor, fans, blowers and pumps. The main goal of the control is to regulate the climate system in such a way that the desired temperature is met. If the desired temperature is set to 24℃ and the starting temperature in the car cabin is for example 30℃ the climate system should deliver higher cooling power than if the starting temperature is lower, for example 26℃ and when the temperature is met the climate system should only work enough to maintain the temperature. The cooling or heating power should therefore be regulated by this difference in temperature (Δ𝑇_𝑑𝑒𝑣) which is defined according to the following equation:

Δ𝑇_{𝑑𝑒𝑣,𝑥} = 𝑇_{𝑖𝑛𝑑𝑜𝑜𝑟𝑠,𝑥}− 𝑇_𝑠𝑒𝑡

where 𝑇_{𝑖𝑛𝑑𝑜𝑜𝑟𝑠,𝑥} is the cabin air temperature with the index 𝑥 =driver region or 𝑥 =passenger region and 𝑇_𝑠𝑒𝑡 is the desired indoor cabin air temperature.

0 200 400 600 800 1000

0 10 20 30 40 50 60 70 80

-20 -10 0 10 20 30 40 50 60 70 80 90

Irradiance (W)

Temperature (oC)

Time (h)

T AMB Mean Head Pass.

Mean Head Driv.

Driver Inner Inertia Pass. Inner Inertia Metal Mass 13 Metal Mass 14 IRRADIANCE (W)

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The pumps will operate at the same speed all the time due to restrictions in the physical AC-system installed today in the minivan. The starting climate control was set according to Figure 14 and Figure 15.

Figure 14. Compressor control to the left and fan control to the right.

The compressor control is show in the diagram to the left in Figure 14. The speed of the compressor varies from its maximum (7000rpm) to the lowest possible speed (2000rpm). The compressor works at maximum speed until the Δ𝑇_𝑑𝑒𝑣 decreases below 10℃ whereupon the speed decreases linearly down to 2000rpm, at a Δ𝑇_𝑑𝑒𝑣 of 0℃, until it shuts down. In order for the compressor to start again the Δ𝑇_𝑑𝑒𝑣 needs to increase up to 0,5℃, or in other words the hysteresis is 0,5℃ for the compressor.

To the right in Figure 14 the control of the radiator fans are shown. There are two fans in front of the car cooling the radiator fluid which in turn cools the condenser; the out temperature of the radiator is the setting the value for the number of radiator fans turned on. The hysteresis of the fan control is 3℃, the first fan is turned off if the temperature decreases below 57℃ and the second is turned off at 52℃.

The blowers inside the car are divided into the ones in the driver region and in the passenger region. The control of the blowers differs from the radiator fans since these have different speed positions meaning they are not turned off like in the radiator control. The hysteresis for the blowers is 1℃. The controls of the blowers are shown in Figure 15.

Figure 15. Blower control in the driving region (to the left) and in the passenger region (to the right).

The driver blower, shown to the left in Figure 15, has four positions. It is never fully turned off; it stays at the lowest speed at its minimum. The maximum

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speed is on until the deviation temperature decreases below 9℃ and then the speed is lowered another step at 5℃ and one step more at 3℃.

The passenger blower, shown to the right in Figure 15, has only three positions and is lowered in speed at a Δ𝑇𝑑𝑒𝑣 of 9℃ and 4℃.

2.2.3 Compressor Efficiency

The calculations regarding the compressor are not included in this report since it belongs to the vapour compression cycle but as the efficiency of the compressor is needed for this project it is included below:

Figure 16. Compressor efficiency as a function of speed and pressure ratio.

3 LITERATURE SURVEY

In the Literature Survey section earlier projects similar to this project have been investigated. The difference between this section and the background section is that this section looks outside of the ICE-project and the project within UPV. What has been done before any of this work started? Since this report has been primary to investigate the cabin model this is what has been key investigated in the literature survey.

CFD simulations of car cabins are common which are helpful when evaluating thermal comfort. Evaluation of extreme behaviour for design purposes is something that has been investigated before including a validation with experimental values. Research of the effect of changing one certain property such as reflective car paint, absorptive glassing or pre-conditioning is a frequent reoccurrence.

In some projects a simple thermal model has been created for the purpose of optimizing control of the AC-system but in these cases no real case validation has been conducted. In cases where a validated thermal cabin model has been created no case has been found where it is coupled with a climate system control. No models have been found where solar radiation has been included together with an experimental validation of the entire thermal model.

Below a more extensive examination has been done separating what has been done in article by article.

ε = f(r

_p

, n)

Pressure ratio Speed (rpm)

Comp. eff.

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3.1 Summary of Earlier Works

In an article from SAE technical papers (Conceiçao et al. 1999) a CFD model has been created in order to simulate thermal behavior of the passengers compartment of vehicles. The model created can solve two different problems. The first problem it can solve is that it can calculate the heat stress that is put on the air conditioning system at given ambient conditions. The second problem it can solve is the thermal behavior inside the cabin. An additional article dealing with numerical simulations have been dealt with in (Fujita et al. 2001, 39-47), in this article infiltration was taken into account as well. In the article (Li and Sun 2013, 37-45) a CFD analysis was done with extensive validation for both the thermal model and the AC-system model. In an article from Applied thermal engineering (Mezrhab and Bouzidi 2006, 1697-1704) a computational model was created specifically to evaluate thermal comfort where the effect of many properties are investigated such as solar radiation, types of glazing, car color and radiation properties of materials. In another report (Liu et al. 2011, 1150-1162) a transient model was developed to evaluate the cooling load of a moving train during the hottest summer month. The train was traveling between three main railway lines in China where the energy use of the AC-system varied between 4,5 – 43,8kW.

There were large differences in power consumption depending on the cardinals and time of the day. One important conclusion of that project was that the recommended steady cooling load used today for the designing of AC-systems was very high. Due to the possibility of body thermal storage, the AC-system does not need to be as large as the dynamic peak cooling power.

In another article from applied energy engineering (Khayyam et al. 2011a, 750-764) the management of the vehicle air conditioning system has been developed. The system does not only coordinate but it also manages the operation of blower, evaporator and fresh air and recirculation. Three simulations were performed to show its saving capacities of energy. A report from 2011(Khayyam et al. 2011b, 3147-3160) presents a look-ahead fuzzy controller of an AC-system in order to save energy. The report also brought up a good scheme of how different forms of solar radiation affect the loads on the AC-system. Another article (Sanaye, Dehghandokht, and Fartaj 2012, 860-868) brings up the same subject with a fuzzy controller but did not investigate any look-ahead approach. In another article from Applied Thermal Engineering (Alahmer et al. 2011, 995-1002) a comprehensive review regarding thermal comfort models have been assessed. Tools typically used for these types of evaluations are Predicted Mean Value (PMV) and Predicted Percentage Dissatisfied (PPD) where advantages and disadvantages of these tools have been discussed. Furthermore the physiological and psychological perspectives have been looked at as of when a person is dissatisfied with the thermal climate. In a PHD thesis (Gado 2006) a test facility is designed, built and verified where the Mobile Air Conditioning system (MAC) can be tested independent of the vehicle, yet during realistic dynamic conditions. In order to do this a thermal model was created. A bit different yet interesting and important article (Barnitt et al. 2010) brings up the potential benefits of off- board powered thermal preconditioning of electric vehicles. The wear off the battery will decrease and if the battery is not charging the autonomy of the vehicle will decrease as well if the on board power is used for the AC-system.

A conclusion was that a preconditioning can increase the range of a 160km

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range electric vehicle by 3,9% when heating and 1,7% when cooling. If the battery pack temperature is reduced in a high ambient temperature scenario it can reduce capacity loss by up to 7%. In a report from National Renewable Energy Laboratory (Hendricks 2001) a transient air conditioning system model is presented. It incorporates all the relevant physics of the AC-system together with a simplified thermal model. In an article (Han and Huang 2002) a validation of a 3D passenger compartment for a hot soak and cool-down analysis has been done. In their model a CFD analysis is coupled with a thermal comfort model. In an article brining up virtual thermal comfort engineering (Han, Huang, and Kelly 2001) the thermal comfort evaluation uses 16 body segments where every segment has been modeled as four body layers, muscle, fat core and skin tissues. A very interesting work for future thermal comfort evaluations. Another article bringing up computerized simulations of an AC-system in vehicles (Kamar, Kamsah, and Senawi 2013, 787) did a paramedic study of the effects of varying number of occupants, the volumetric flow rate of supply air, and the fractional ventilation air intake and vehicle speed on the thermal climate in the car.

3.2 Reflectance and Emittance of the car´s surfaces

In one article (Levinson et al. 2011, 4343-4357) the benefits of solar reflective car shells was investigated. The soak temperature of air could be lowered by 5-6℃ when changed from a black to a silver car. The energy needed to cool the cabin would be 13% lower for the silver car compared to the black one and thereby reduce the fuel consumption by 0,12l/100km. Some interesting values for reflectance of short wave radiation and emittance of long wave radiation found in the article are shown in Table 1.

Table 1. Reflectance and emittance of different materials of the car. (Levinson et al., 2011)

3.3 Solar Radiation Calculations

The diffuse radiation correlation used in 4.1 Transient Thermal Model is the Reindl correlation (Reindl, Beckman, and Duffie 1990, 1) in which the influence of geometric variables of the hourly diffuse radiation was

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investigated. Data from 22000 hourly measurements from five European and North American locations were studied and from this some important equations could be created. A ratio between diffuse radiation and the total radiation on a horizontal surface was developed. The ratio is dependent on many different aspects. Three equations were developed for different cases and together they incorporate all possible cases of diffuse radiation. The final correlations created are:

Interval: 0 ≤ 𝑘𝑡 ≤ 0,3 Constraint: ^𝐼^𝑑

𝐼 ≤ 1,0 𝐼_𝑑

𝐼 = 1,02 − 0,254𝑘^𝑡+ 0,0123sin (𝛼) Interval: 0,3 ≤ 𝑘𝑡 ≤ 0,78 Constraint: ^𝐼_𝐼^𝑑 ≤ 0,97 and ^𝐼_𝐼^𝑑≥ 0,1

𝐼𝑑

𝐼 = 1,400 − 1,749𝑘^𝑡+ 0,177sin (𝛼) Interval: 0,78 ≤ 𝑘_𝑡 Constraint: ^𝐼^𝑑

𝐼 ≥ 0,1 𝐼𝑑

𝐼 = 0,486𝑘^𝑡− 0,182sin (𝛼)

𝑘𝑡 is the ratio of total radiation on a horizontal surface divided by the radiation outside the atmosphere (extraterrestrial radiation). 𝐼𝑑 is the diffuse radiation and 𝐼 is the total radiation, both on a horizontal surface. 𝛼 is the solar altitude angle which is the angle between a horizontal plane and the sun.

Similar solar model correlations are brought up in (Batlles et al. 2000, 675- 688) and in (Wong and Chow 2001, 191). Often their works refer back to the Reindl correlations which appear to be accurate enough.

In the mathematical reference of TRNSYS (Thermal Energy System Specialists ) a well-developed solar radiation model is being explained with the Reindl correlations included. The model explains how one can deduce a measured total horizontal radiation onto surfaces in other directions. All of the following has been collected from this source:

Total radiation onto a surface can be divided into beam- diffuse- and reflective radiation. The total radiation on a horizontal surface can be divided into diffuse radiation (which was explained by Reindl) and beam radiation. The beam radiation, 𝐼_𝑏, is calculated through the following:

𝐼_𝑏 = 𝐼 − 𝐼_𝑑

The position of the sun throughout the day can be determined by using the solar azimuth angle (𝛾𝑠) and solar zenith angle (𝜃𝑧). The azimuth angle, constraint 0° ≤ 𝛾𝑠 ≤ 360°, is defined as 0 when facing the equator, 90=Facing west, 180=Facing north and 270=Facing east. The zenith angle is the angle between a vertical line and the sun, in example 0 when the sun is on the top of the sky and 90 when it is just rising or setting, constraint 0° ≤ 𝜃_𝑧 ≤ 90°.

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When the radiation is divided into diffuse and beam radiation the position of the surface is set. Afterwards the beam, diffuse and reflective radiation onto that surface can be calculated. The size of the beam radiation on a tilted surface is calculated by using a geometric factor 𝑅_𝑏 which is calculated by using the following equation:

𝑅_𝑏= cos(𝜃) cos(𝜃_𝑧) where

cos(𝜃) = cos(𝜃_𝑧) cos(𝛽) + sin(𝜃𝑧) cos(𝛾𝑠− 𝛾) sin (𝛽)

In the equation above 𝛾 is the surface azimuth angle and 𝛽 is the slope of the surface, both defined in Figure 17 below.

Figure 17. The position of a surface is determined using Beta and Gamma angle.

To find the beam radiation on the tilted surface (𝐼_𝑏𝑇) the equation below is used:

𝐼_𝑏𝑇 = 𝐼_𝑏𝑅_𝑏

The reflected radiation on the tilted surface is calculated by using the following equation:

𝐼_𝑔𝑇 =𝐼𝜌_𝑔(1 − cos 𝛽 ) 2

where 𝜌_𝑔is the mean reflectance of the surrounding surfaces.

For calculating the diffuse radiation on a tilted surface the anisotropy index needs to be calculated using the equation below:

𝐴𝐼 = 𝐼𝑏𝑛

𝐼𝑜𝑛

where 𝐼_𝑏𝑛 is the beam radiation that would hit a perpendicular surface faced towards the sun (normal incidence) and 𝐼_𝑜𝑛 is the total extraterrestrial

Filip Bjurling TRANSIENT THERMAL MODEL OF A MINIBUS' CABIN AND OPTIMIZATION OF THE AIR-CONDITIONING CONTROL STRATEGIES

TRANSIENT THERMAL MODEL OF A MINIBUS' CABIN AND OPTIMIZATION OF THE AIR-CONDITIONING

CONTROL STRATEGIES

Filip Bjurling

Department of Energy Technology Royal Institute of Technology

Stockholm, Sweden

TABLE OF CONTENTS

INDEX OF TABLES

INDEX OF FIGURES

NOMENCLATURE

1 INTRODUCTION

1.1 Objectives

1.2 Limitations

2 BACKGROUND

2.1 ICE Project

2.2 The Overall Model

Test 1: Test Indoors With a Heating and Cooling Period

Test2: Test Outdoors With the Vehicle Placed under the Sun

Test3: Test Outdoors With the Vehicle Placed under the Sun

3 LITERATURE SURVEY

ε = f(r

, n)

3.1 Summary of Earlier Works

3.2 Reflectance and Emittance of the car´s surfaces

3.3 Solar Radiation Calculations