QATAR UNIVERSITY. Graduate Studies. College of Engineering INVESTIGATION OF A REGENERATIVE INDIRECT EVAPORATIVE COOLING SYSTEM.

Transcription

1 QATAR UNIVERSITY Graduate Studies College of Engineering INVESTIGATION OF A REGENERATIVE INDIRECT EVAPORATIVE COOLING SYSTEM A Thesis in Mechanical Engineering By Ali Pakari 2015 Ali Pakari Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science January 2015

2 Declaration To the best of my knowledge, this thesis contains no material previously published or written by another person or institution, except where due reference is made in the text of the thesis. This thesis contains no material which has been accepted for the award of any other degree in any university or other institution. Name Ali Pakari Signature Date ii

3 Committee The thesis of Ali Pakari was reviewed and approved by the following: We, the committee members listed below, accept and approve the Thesis/Dissertation of the student named above. To the best of this committee s knowledge, the Thesis/Dissertation conforms the requirements of Qatar University, and we endorse this Thesis for examination. Supervisor Saud Ghani Signature Date Name Signature Date iii

4 Abstract In this study a regenerative indirect evaporative cooling system has been designed, and constructed. A regenerative evaporative cooler is a modified indirect evaporative cooler, comprised of multiple pairs of dry and wet channels. Like an indirect evaporative cooler, the air flowing through the dry channels is cooled without changing its humidity but at the outlet of the dry channels a portion of the air is extracted and directed to the wet channels where it is cooled by direct evaporative cooling. The evaporative cooling system constructed in this study consists of multiple pairs of dry and wet channels made out of plastic sheets. In order to optimize the design and find the effect of various factors on the performance of the cooling system, a mathematical model of the heat exchanger was developed and numerically simulated. Based on the simulation results, a prototype of the cooling system was constructed. The prototype was tested and a comparison between the numerical and experimental results was carried out which showed that the model can predict the experiments with a relative error between 4 to 10%. Based on the conducted experimental and numerical analysis, it was concluded that the performance of the cooling system significantly depends on the channel spacing and length of the heat exchanger, inlet air flow rate, and the extraction ratio. The constructed prototype achieved wet bulb effectiveness values as high as 1.3. iv

5 Contents Nomenclature... ix List of Tables... xii List of Figures... xiii Acknowledgement... xvi Chapter 1. Introduction Background Research description Objectives Thesis structure... 6 Chapter 2. Literature review Introduction Operational principles of EC systems DEC systems IEC systems Combination of DEC and IEC systems REC systems Performance evaluation parameters v

6 2.3.1 Wet bulb effectiveness Cooling capacity Efficiency Types of DEC systems Air washers Evaporative pads Rigid media Rotary wheel Types of IEC systems Tubular IEC system Plate type IEC system Studies conducted on EC systems IEC systems material Summary Chapter 3. Modeling Introduction Model development Transport coefficients Boundary conditions vi

7 3.2.3 Discretized model Numerical solution method Model results Effect of different parameters on the performance of the system Effect of channel spacing on performance Effect of channel length on performance Effect of inlet mass flow rate on performance Effect of extraction ratio on performance Summary Chapter 4. Experimental work Introduction Prototype description Prototype construction The heat exchanger Other components The experimental setup Experimental procedure Experimental results Effect of inlet air volume flow rate on performance vii

8 4.6.2 Effect of extraction ratio on performance Effect of inlet air temperature on performance Effect of inlet air humidity ratio on performance Comparison between model and experimental results Summary Chapter 5. Conclusions and future work Conclusions Recommendations for future work References Appendix viii

9 Nomenclature C Specific heat of air, kj/kg K dh Hydraulic diameter, m Dva Binary diffusion coefficient of water vapor in air, m 2 /s h Convective heat transfer coefficient, W/m 2 K hm Mass transfer coefficient, kg/m 2 s Hw,fg Latent heat of water, J/kg k M Nu Sh T t U W y Thermal conductivity, W/m K Mass flow rate, kg/s Number of nodes Nusselt number Sherwood number Temperature, C Thickness, m Overall heat transfer coefficient, W/m 2 K Width of the heat exchanger, m Power input, kw Channel spacing, m ix

10 Distant between adjacent nodes Effectiveness ρ Density, kg/m 3 ω Humidity ratio of air, kg water/kg dry air Subscripts d w WB wf Dry channel Wet channel Wet bulb Water film Abbreviations COP HVAC CAD DEC EC EES Coefficient of Performance Heating, Ventilation and Air Conditioning Computer Aided Design Direct Evaporative Cooling Evaporative Cooling Engineering Equation Solver x

11 IEC NTU REC RH VCAC Indirect Evaporative Cooling Number of Transfer Units Regenerative Evaporative Cooling Relative Humidity Vapor Compression Air Conditioning xi

12 List of Tables Table 1: Heat exchanger specifications Table 2: Reference operating conditions Table 3: Specifications of the measuring equipment xii

13 List of Figures Figure 1: The average low and high temperature profile [3], and domestic electricity demand during the 2013 year in Qatar... 2 Figure 2: A schematic diagram of the regenerative counter flow heat exchanger... 5 Figure 3: REC shown schematically and on a psychrometric chart... 5 Figure 4: (a) Schematic diagram of DEC. (b) DEC shown on a psychrometric chart.. 9 Figure 5: (a) Schematic diagram of IEC. (b) IEC shown on a psychrometric chart Figure 6: A schematic diagram of a typical air washer Figure 7: (a) aspen wood fibers, (b) a schematic of a DEC with evaporative pads Figure 8: DEC system with rigid media Figure 9: DEC system with rotary wheel Figure 10: A schematic of a typical tubular IEC system Figure 11: A schematic of a typical plate type IEC system Figure 12: (a) A schematic of the cooling system (three stacked channel pairs). (b) top view of a pair of channels Figure 13: The computational domain of a pair of dry and wet channels and the evenly spaced nodes used to obtain the numerical model Figure 14: The model outlet temperature as a function of the number of the nodes.. 32 Figure 15: Temperature profile of air in the dry and wet channels, and the water film Figure 16: Properties of air and water in the wet channel xiii

14 Figure 17: Effect of channel spacing on wet bulb effectiveness and outlet temperature (Inlet air temperature = 38 C, Inlet air humidity ratio = 9 g water/kg dry air) Figure 18: Effect of channel length on wet bulb effectiveness and outlet temperature (Inlet air temperature = 38 C, Inlet air humidity ratio = 9 g water/kg dry air) Figure 19: Effect of inlet air mass flow rate on wet bulb effectiveness and outlet temperature (Inlet air temperature = 38 C, Inlet air humidity ratio = 9 g water/kg dry air) Figure 20: Effect of extraction ratio on wet bulb effectiveness and outlet temperature (Inlet air temperature = 38 C, Inlet air humidity ratio = 9 g water/kg dry air) Figure 21: A CAD model of the counter flow regenerative heat exchanger Figure 22: A stack of corrugated plastic sheets Figure 23: The side of a dry channel sheet showing the wicking paper and the extraction openings Figure 24: The side of a dry channel, showing the spacers that form the wet channels Figure 25: The stack of the plastic sheets forming the heat exchanger Figure 26: The heat exchanger placed in an acrylic frame Figure 27: Top view of the heat exchanger showing the perforated sheet used to distribute water into the wet channels Figure 28: A schematic diagram of the experimental setup Figure 29: A picture of the experimental setup xiv

15 Figure 30: Wet bulb effectiveness as a function of the inlet air volume flow rate (Inlet air temperature = 30 C, Inlet air humidity ratio = 8 g water/kg dry air and extraction ratio = 41%) Figure 31: Wet bulb effectiveness versus extraction ratio (Inlet air temperature = 30 C, Inlet air humidity ratio = 8 g water/kg dry air, and Inlet air volume flow rate = 2.16 m 3 /min) Figure 32: Wet bulb effectiveness versus inlet air temperature (Inlet air volume flow rate = 2.04 m 3 /min, Inlet air humidity ratio = 9.11 g water/kg dry air, and extraction ratio = 40%) Figure 33: Wet bulb effectiveness versus inlet air humidity ratio (Inlet air temperature = 35 C, Inlet air volume flow rate = 2.15 m 3 /min, and extraction ratio = 37%) Figure 34: Comparison between model and experimental results-outlet air temperature versus inlet air temperature (Inlet air volume flow rate = 2.04 m 3 /min, Inlet air humidity ratio = 9.11 g water/kg dry air, and extraction ratio = 40%) Figure 35: Comparison between model and experimental results- outlet air temperature versus extraction ratio (Inlet temperature = 30 C, Inlet air humidity ratio = 8 g water/kg dry air, and Inlet air volume flow rate = 2.16 m 3 /min) Figure 36: A screenshot of the EES program solution window Figure 37: A screenshot of a portion of the array table obtained from the EES code above xv

16 Acknowledgement I would like to thank the staff of the Mechanical and Industrial Engineering department, particularly the staff of the mechanical workshop for their technical support throughout the project. xvi

17 Chapter 1. Introduction 1.1 Background The depletion of energy resources, global warming and climate change are just few consequences of the fast growth of energy use in the world. Population growth, demands for better comfort levels, and spending more time indoors, have all contributed to the increased energy consumption specifically in the building sector which have reached the levels of transportation and industry sectors [1]. In developed countries about 50% of the energy use in buildings is consumed by Heating, Ventilation and Air Conditioning (HVAC) systems, which is about 20% of the total nationwide energy use [1], [2]. Many countries are facing increasing electrical demand during the hot months of the year. Figure 1 shows the domestic electricity demand and average low and high temperatures during the 2013 year in Qatar. As illustrated in the figure, the electricity demand starts increasing sharply from March to August, along with the rise in temperatures, due to the increased use of air conditioning equipment. 1

18 Figure 1: The average low and high temperature profile [3], and domestic electricity demand during the 2013 year in Qatar Vapor Compression Air Conditioning (VCAC) is the dominant technology that serves the HVAC needs. But other than being energy intensive, the refrigerants used in VCAC equipment harm the environment when released to the atmosphere. Therefore it is necessary to develop cooling systems that are environmentally friendly, and energy efficient. An efficient alternative for providing thermal comfort is Evaporative Cooling (EC). The advantages of using EC systems [4] include energy and cost savings, reduction in the use of harmful refrigerants, and improved indoor air quality. EC systems have high energy saving potentials. Generally, they consume less amount of energy compared to VCAC. Overall, EC systems are 75% more efficient than VCAC systems [5]. 2

19 There are two main types of EC, direct and indirect cooling. When air is blown through a medium that is wetted with water; the water absorbs the heat from the air and evaporates; as a result the air is cooled and moistened, this type of cooling is called Direct Evaporative Cooling (DEC). Current DEC systems have an efficiency of 70 95% in terms of reaching the wet bulb temperature of the incoming air [6]. In Indirect Evaporative Cooling (IEC) air is cooled without contacting the water and therefore not adding moisture to the air. In this type of systems there are two streams of air that passes through it but they do not contact each other. They are usually called primary and secondary air streams, the primary air is the one supplied to the rooms. Indirect evaporative cooling systems are air to air heat exchangers where the primary air is cooled by the secondary air. The secondary air is either cooled by DEC before entering the air to air heat exchanger or it is cooled in the air to air heat exchanger by wetting the secondary air stream side [7]. IEC systems can achieve 50% energy savings over VCAC systems [8]. The conventional direct and indirect evaporative cooling systems have a limiting drawback. This limit is the wet bulb temperature of the ambient air, i.e. the lowest possible temperature that can be delivered by this kind of cooling systems is the wet bulb temperature of the ambient air entering the system. By modifying the structure of an IEC system a new process called Regenerative Evaporative Cooling (REC) is produced. This type of cooling can lower the ambient temperature of the air entering the system below its wet bulb and approach its dew 3

20 point temperature. This type of cooling system is identical to an IEC system with the difference that at the end of the primary air channels a portion of the air is extracted and returned through the wet passages (secondary air channels). As a result, the wet bulb temperature of the air entering the wet passages is lower than the wet bulb temperature of the ambient air. 1.2 Research description The cooling system proposed for this project is an indirect evaporative cooling system in the form of a counter flow heat exchanger. A schematic diagram of the regenerative counter flow heat exchanger is displayed in Figure 2. The heat exchanger is formed by stacking corrugated plastic sheets forming the wet and dry channels. The air enters the dry channel and is divided at the end of the channel into two parts where a part of the air is delivered to the space where cooling is required, and the other part of the air stream is extracted and diverted into the wet channel where its surface is wetted by water. Heat is absorbed in the wet channel by vaporization of the water on the walls. The air in the wet channels flows in a reverse direction to the primary air stream where it is exhausted from the bottom side of the heat exchanger. The processes of the air streams in the heat exchangers are shown schematically and on a psychrometric chart in Figure 3. Air enters the system at state 1 and passes through the dry channel. At the end of the dry channel a fraction of the primary air that leaves the system is directed to the wet side of the heat exchanger. The air in the 4

21 dry side is cooled sensibly by losing heat to the wet side and leaves the system at state 2. The secondary air passes through the channel were water is being sprayed and leaves the system at state 3. Figure 2: A schematic diagram of the regenerative counter flow heat exchanger Figure 3: REC shown schematically and on a psychrometric chart 5

22 1.3 Objectives The objectives of this study are: To investigate the design of the proposed heat exchanger by developing a numerical model of its cooling process To construct a prototype and test it under various climatic conditions 1.4 Thesis structure Chapter 1 introduces a brief background, the significance of the problem, the objectives and the structure of the thesis. Chapter 2 presents a literature review of the evaporative cooling technologies, including their working principle, materials, structure, and performance. The features and problems relevant to the EC systems are identified. Modelling and performance analysis of a regenerative counter flow heat exchanger is discussed in Chapter 3. Based on a number of assumptions and approximations the governing differential equations of the heat exchanger are established. The developed model is analyzed to find the effect of various parameters on its performance in order to optimize its design. In Chapter 4, the experimental work including, the construction of the prototype, the experimental setup, and procedure are presented. The results of the experiments and the effects of different parameters on the performance of the constructed prototype 6

23 are studied. The validity of the model developed in the previous chapter is assessed by comparing its predictions by the experimental results. Chapter 5 presents the conclusions derived from the study, and a number of recommendations for future work. 7

24 Chapter 2. Literature review 2.1 Introduction In this chapter the relevant literatures are studied and essential information regarding evaporative cooling including theory, evaporative medium, types of equipment, performance, and characteristics of various system types have been identified. 2.2 Operational principles of EC systems DEC systems A schematic diagram of DEC is shown in Figure 4-a. In direct evaporative coolers, hot and dry air enters the system at state 1, after being sprayed with water, the temperature of the air decreases and its humidity increases at state 2. In an ideal evaporative cooler, air will become saturated and reach the wet bulb temperature of the incoming air which is the lowest temperature that can be achieved by this process (state 2'). Ideal evaporative cooling is an adiabatic process; i.e., it occurs without a significant change in enthalpy. Therefore, the direct evaporative cooling process follows a line of constant enthalpy or wet bulb temperature on a psychrometric chart (Figure 4-b). 8

25 Figure 4: (a) Schematic diagram of DEC. (b) DEC shown on a psychrometric chart IEC systems The difference between DEC and IEC is that in the latter, air is cooled by the evaporation of water without contacting it therefore the air is cooled but its moisture content is kept constant. In an IEC system (Figure 5-a) air enters the system at state 1 and passes through two channels. The primary air passes through the dry channel, and the secondary air passes through the channel were water is being sprayed (wet channel). The air in the wet channel is cooled by DEC and leaves the system at state 3. The air in the dry side is cooled sensibly by losing heat to the wet channel and leaves the system at state 2. On a psychrometric chart, the cooling process of the air on the dry side follows a line of constant specific humidity since the moisture content of the air remains constant (Figure 5-b). 9

26 Figure 5: (a) Schematic diagram of IEC. (b) IEC shown on a psychrometric chart Combination of DEC and IEC systems When a DEC is added to an IEC as a second stage of cooling, it increases the effectiveness of the overall system. Since the indirect stage lowers the dry and wet bulb temperatures of the air, the direct second stage usually achieve comfort levels with much damper ambient air than do direct coolers alone. The psychrometric processes of such a system are a combination of a DEC and IEC systems. The first stage follows a constant specific humidity line since the moisture content of the air remains constant and the second stage follows a constant enthalpy line REC systems REC systems are a modified version of IEC systems. Like IEC systems, REC have a primary and a secondary stream but in REC ambient air is not used as a secondary air stream; instead, at the end of the dry channel a portion of the primary is extracted, and diverted into the wet channel and used as a secondary stream. Figure 3 shows a 10

27 schematic of REC system working principle along with its cooling processes on a psychrometric chart. The lowest temperature that can be achieved by this process is the dew point temperature of the ambient air. 2.3 Performance evaluation parameters The performance of EC systems are usually evaluated by the following parameters Wet bulb effectiveness Cooling capacity Efficiency Wet bulb effectiveness The wet bulb effectiveness is dependent on the inlet and outlet air temperatures of the evaporative cooling system. The wet bulb effectiveness is the ratio of the difference between inlet and outlet air temperature to the difference between inlet air temperature and its wet bulb temperature. The wet bulb effectiveness is defined as (1) Cooling capacity The cooling capacity of a cooling system is equal to the rate of heat removal from the cooled space, and it is expressed as: (2) Where is the mass flow rate of air, and C is the specific heat of air. 11

28 2.3.3 Efficiency The efficiency of a cooling system is expressed in terms of the Coefficient of Performance (COP). The COP of a cooling system which is a measure of its performance is expressed in terms of the heat removed from the cooled space divided by the power input: (3) The performance of cooling systems are also expressed in terms of the Energy Efficiency Ratio (EER) [9], which is defined as the ratio of heat absorbed from the cooled air in Btu/h (British thermal unit per hour) to the power usage in W (watt). Since 1 W is equal to Btu/h, the relation between EER and COP is (4) 2.4 Types of DEC systems DEC systems can be categorized according to their wetted medium to air washers, evaporative pads, rigid media, and rotary wheel Air washers In 1904, Carrier developed the air washer as the first air conditioning equipment. Still, the air washer is being used in many factories to humidify, cool, and clean the air. Typical air washers are enclosed chambers where air is drawn into and sprayed with water (Figure 6 [10]). The wet bulb effectiveness values of air washers usually range between 0.8 and 0.9 [10]. 12

29 Figure 6: A schematic diagram of a typical air washer Evaporative pads Evaporative pads are usually made of about 2 inch thick aspen wood fibers (Figure 7- a) that are treated chemically to prevent the growth of microorganisms and to increase their wettability. Evaporative pads are fitted into removable plastic or steel frames. A schematic of a DEC with evaporative pads is shown in Figure 7-b [10]. 13

30 Figure 7: (a) aspen wood fibers, (b) a schematic of a DEC with evaporative pads Rigid media Rigid media are sheets of corrugated material made from plastic, impregnated cellulose, or fiberglass, as shown in Figure 8 [10]. Typically, air flows in horizontal channels and water flows in vertical channels, making a cross flow arrangement. Rigid media have a low air pressure drop and are easily cleaned by water flushing, and they have slightly higher wet bulb effectiveness values than evaporative aspen pads [10]. 14

31 Figure 8: DEC system with rigid media Rotary wheel As seen in Figure 9 [10], rotary wheel is a wetted medium in the shape of a wheel which is made of materials that resist corrosion such as plastic, impregnated cellulose, fiberglass, or copper alloy. 15

32 Figure 9: DEC system with rotary wheel 2.5 Types of IEC systems There are two main types of IEC systems, tubular and plate type IEC systems [11], [12] Tubular IEC system In tubular IEC systems, the primary air passes through the tubes that are wetted by water from the outside, and the secondary air passes over the tubes to evaporate the water and cool the primary air, then the secondary air is exhausted out of the system. Any extra water left from spraying the tubes is collected and is sprayed again over the tubes [12]. Figure 10 Shows a schematic of a typical tubular IEC system [13]. 16

33 Figure 10: A schematic of a typical tubular IEC system Plate type IEC system The other common type of IEC systems is plate type IEC system. These systems are usually made of plastic plates. The plastic plates are very thin in order to reduce their thermal resistance. The spacing between the plates is normally between 2 to 3 mm. The plates are placed in a manner to form horizontal and vertical passages. Typically, the primary air passes through the horizontal passages and the secondary air that is sprayed with water flows in the vertical passages. The sprayed water in the vertical passages evaporates by absorbing heat from the primary air flowing in the horizontal passages. The secondary air is eventually exhausted to the outside, and excess water from the vertical passages is collected and recirculated [10]. A schematic of a typical plate type IEC system is shown in Figure 11 [14]. 17

34 Figure 11: A schematic of a typical plate type IEC system 2.6 Studies conducted on EC systems In this section an overview of the related studies is presented, starting with earlier research until most recent ones. Pescod [15] studied IEC by developing a cross flow plate heat exchanger made of parallel plastic plates. He used pin projections on the plates in order to create turbulence in the air stream which enhances the heat and mass transfer coefficients in the heat exchanger. He showed that by extracting a portion of the primary air that is cooled through the heat exchanger and returning it through the wet passages of the heat exchanger, the ambient air temperature can be lowered below temperatures achieved by normal systems. 18

35 Maclaine-cross and Banks [16] proposed a linear approximate heat and mass transfer model for the analysis of IEC systems. They referred to extracting a portion of the primary air and returning it through the wet passage as regenerative cooling, and they predicted that this process can lower the ambient air temperature below its wet bulb and approach its dew point temperature by choosing appropriate mass flows and Number of Transfer Units (NTU). They compared their model predictions with published experimental measurements. The predictions were 10 to 20% higher than the measurements. They suggested that this difference might be due to excessive or low use of water in the wet channels of the heat exchanger. Crum et al. [17] showed that the ambient inlet air can be cooled to temperatures approaching the inlet dew point temperature by using multistage IEC units, a combination of a heat exchanger and an EC system, and a combination of a cooling tower and a heat exchanger. Hsu et al. [18] studied counter flow and cross flow regenerative wet surface heat exchangers. They found that temperatures considerably lower than the inlet wet bulb temperature can be achieved with moderate flow rates and simple geometries. Erens and Dreyer [19] discussed the modeling of IEC systems by describing three calculation models. They found that the optimum extraction ratio in REC systems is dependent on the plate spacing used. For optimum REC system performances, they suggested an extraction ratio of 36% for plate spacing of 3 mm. 19

36 A two stage air conditioning unit that consists of indirect and direct evaporative cooling units was built and tested by El-Dessouky et al. [20]. They reported wet bulb effectiveness over the range of 0.9 to 1.2 which shows that the temperature of the outlet air can be lower than the wet bulb temperature of the inlet air. A numerical investigation of a counter flow IEC system that can achieve temperatures below the wet bulb temperature of the intake air was conducted by Zhao et al. [21]. They concluded that the intake air velocity, amount of primary air extraction, and the dimensions of the flow passages of the heat exchanger are the primary factors that affect the overall effectiveness of the cooling system while the temperature of the feeding water is not an important factor. Heidarinejad et al. [7] investigated the performance of a combination of IEC and DEC systems under different operational conditions. They reported wet bulb effectiveness values for the combination system in the range of 1.08 to 1.11 which is higher than the wet bulb effectiveness of a single IEC system that is between 0.55 and They showed that the average water consumption of the combination system is 55% higher than a DEC system. Also, the power consumption of the combination system is about 33% of a typical VCAC system. Riangvilaikul and Kumar [22], [23] constructed a REC system, and they tested the performance of the system under various inlet operating conditions. Their results showed that the wet bulb effectiveness of the system ranged over They 20

37 suggested coupling their system with a desiccant dehumidifier to make its use commercially feasible in hot and humid climates. The performance of a regenerative cross flow IEC system was analyzed numerically by Zhan et al. [24]. They established a model that simulates the thermal performance of the cooling system. Published experimental data was used to validate the developed model. They found that the performance of the cooling system is significantly affected by the height and length of its channels. They reported wet bulb effectiveness values as high as Lee and Lee [25], built a REC system with finned channels and tested its performance experimentally. The fins and plates of the heat exchanger were made of aluminum. They reported a wet bulb effectiveness of 1.2 for inlet air conditions of 32 C and 50% RH. For a maximum cooling capacity, they suggested an extraction ratio of 30%, for dry and wet channel plate spacing of 2 and 1 cm, respectively. Also, they concluded that the pressure drop in the wet channels is not affected by the spray of water IEC systems material The air to air heat exchangers of the first IEC systems were made of metal sheets usually aluminum sheets. Later on, thin plastic plates were used instead of metals. They used plastic sheets with a thickness of about 0.28 mm or less which reduced the conductivity advantage of metals over plastics [14]. Other advantages of the plastic sheets were light weight and corrosion resistance. 21

38 A study into several IEC materials, including metals, fibers, ceramics, zeolite, and carbon was conducted by Zhao et al. [6]. They compared the performance of these materials based on thermal conductivity, porosity, hardness, compatibility to coating material, contamination risk, and cost. They found that thermal conductivity and porosity have little influence on the performance relative to the other characteristics. The ability of the materials to retain their shape (hardness) in a descending order is ceramic, metals, carbon, zeolite, and fiber. All the materials are compatible to coating. Except for metals, all the materials are at the risk of getting contaminated. The cost of the materials in an ascending order is fiber, carbon, metal, ceramics, and zeolites. Considering all the mentioned features, they suggested that wick attained metals are the most suitable material for IEC systems. 2.7 Summary This chapter presented a review on EC including working principals, indicative parameters, and types. A summary was presented of the related studies on EC including experimental work, analytical work on heat and mass transfer, assessment of flow patterns, the selection of suitable materials, and preferred operating conditions. The review of related studies showed that EC is capable of providing comfortable indoor air conditions while consuming less energy than VCAC equipment. 22

39 Chapter 3. Modeling 3.1 Introduction This chapter presents the modeling of a counter flow regenerative heat exchanger. First, the governing heat and mass transfer equations are obtained. Then, the numerical methods used to solve the equations are introduced. Finally, using the developed model, the effect of different factors on the performance of the heat exchanger is examined. 3.2 Model development The governing equations that describe the flow within the heat exchanger are the simultaneous steady state energy and continuity equations. The differential control volume used for deriving the conservation equations is shown in Figure 12. A number of assumptions have been made to develop the model, and they are as follows: 1. The device is well insulated (there is no heat transfer between the device and the surrounding) 2. Channel heights are very small relative to their width, therefore the problem is treated as one dimensional and the temperature change normal to the flow is neglected 3. The flow inside the channels is laminar and fully developed 4. Viscous dissipation and body forces are negligible 5. Flow is steady and incompressible and there is no internal heat generation in the channels 23

40 6. Mass flow rate is constant in each channel 7. The specific heat of the dry air and water vapor are constant 8. The heat and mass transfer coefficients are constant 9. The temperature of the water film and the wall are equal Figure 12: (a) A schematic of the cooling system (three stacked channel pairs). (b) Top view of a pair of channels 24

41 Given the stated assumptions, the conservation of energy equation in the dry channel along the x direction for the control volume shown in Figure 12 can be written as: (5) Where Cd is the specific heat of dry air, and U is the overall heat transfer coefficient in the dry channel and is obtained by: 1 (6) Where hd is the convective heat transfer coefficient in the dry channel, and is estimated in section 3.2.1, and kplate and kpaper are the thermal conductivity of the plastic plate and wicking paper, respectively. In a similar manner the conservation of energy equation in the wet channel is: (7) Where Cw is the specific heat of water vapor, and hw is the heat transfer coefficient in the wet channel, and it is estimated in section The conservation of mass for the differential control volume in the wet channel can be written as: (8) Where hm is the mass transfer coefficient in the wet channel, and it is estimated in section

42 The conservation of energy at the wall separating the wet and dry channel can be expressed as:, 0 Where Hw,fg is the latent heat of water. (9) In the above equations subscripts d and w refer to the dry and wet channels, and wf refer to the water film. W and L are the width and length of the channels, respectively (Figure 12-a). Therefore, equations 5, 7, 8 and 9 describe the heat and mass transfer in the cooling system under the stated assumptions Transport coefficients The convective heat transfer coefficient in the dry and wet channel can be approximated by the equation: (10) Where Nu is the Nusselt number, kair is the thermal conductivity of air, and dh is the hydraulic diameter of the channel and is defined as [26]: 4 (11) To find the heat transfer coefficient, the Nusselt number has to be approximated in the dry and wet channels. In the dry channel the air that is assumed to be laminar and 26

43 fully developed flows through rectangular flutes, and the heat transfer is occurring through one wall, the wall where the wicking paper is attached. The Nusselt number for fully developed laminar flow in rectangular ducts with one wall experiencing heat transfer, and with an aspect ratio of 3/2 (the flutes of the plastic sheets have a 3/2 aspect ratio), according to [27], is Nud = The convective heat transfer coefficient in the dry channel is then, (12) In the wet channel air flows between parallel plates, and it is experiencing heat transfer through one wall. The Nusselt number for fully developed laminar flow between parallel plates with one wall experiencing heat transfer, according to [27], is Nuw = In order to find the mass transfer coefficient in the wet channel, the heat and mass transfer analogy is assumed to be applicable. Accordingly, heat and mass transfer relations are interchangeable for a specific surface shape which means that, where is the Sherwood number and it represents the dimensionless mass transfer coefficient [28]. Therefore, the heat and mass transfer coefficients in the wet channel are, (13), (14) 27

44 Where Dva is the binary diffusion coefficient of water vapor in air Boundary conditions The temperature and humidity ratio of the air in the inlet of the dry channel (x = L) are specified: at (15) at (16) The temperature and humidity ratio at the dry channel outlet and the wet channel inlet (x = 0) are set as equal since at this point a portion of the air of the dry channel is extracted and directed to the wet channel. at 0 (17) at 0 (18) The plastic plate separating the dry and wet channels is assumed to be insulated at the inlet and outlet of the cooling system (x = 0 and x = L) therefore 0 at x = 0 (19) 0 at x = L (20) Equations 15 to 20 are the boundary conditions of the cooling system Discretized model In order to numerically solve the governing differential equations of the cooling system (equations 5, 7, 8 and 9), the first and second derivatives are approximated 28

45 using backward and centered finite divided difference formulas, respectively. The finite difference formulas used are [29]: (21) Where h is the step size. 2 (22) The computational domain of a pair of dry and wet channels is depicted in Figure 13. To obtain the numerical model, nodes (nodes are the positions where the temperatures are calculated) are positioned throughout the computational domain. As shown in the figure, the position of any node i along x is given by: 1 1 (23) Where M is the number of nodes used in the x direction. The distance between adjacent nodes is: 1 (24) 29

46 Figure 13: The computational domain of a pair of dry and wet channels and the evenly spaced nodes used to obtain the numerical model Using the above equations the finite difference version of the governing equations, i.e., the numerical model, is obtained as follows: Energy balance in the dry channel,, Energy balance in the wet channel,, (25),, Conservation of mass in the wet channel,, (26) Energy balance in the wall,,,, (27) 30

47 ,,,,,,,,, 2,, 0 (28) 3.3 Numerical solution method The finite difference equations (Equations 25 to 28) derived from the differential equations of the mass and energy balances of the heat exchanger are implemented in the Engineering Equation Solver (EES) framework [30]. EES is a powerful tool for solving engineering problems particularly thermodynamic and heat transfer problems since it contains several built in libraries comprising of thermodynamic and thermophysical properties. All air, water, and water vapor properties are calculated with internal functions in the EES framework. Systems of equations are solved using a variation of Newton s method by EES. In this method, the process begins by a guess value for each variable, and then these values are iteratively adjusted until the set of equations are satisfied with a relative residual of It is important to choose an appropriate number of nodes to ensure that the numerical solution has sufficient accuracy. The general approach for choosing the number of nodes [31], is to select a key aspect of the solution and examine its behavior as the number of nodes in the computational domain is increased. The selected aspect of the solution, in this case, is the outlet temperature of the dry channel. The outlet 31

48 temperature as a function of the number of nodes is shown in Figure 14. It can be noted from the figure that the solution has converged after about 100 nodes. Figure 14: The model outlet temperature as a function of the number of the nodes The EES code used to simulate the heat and mass transfer in the heat exchanger is shown in the Appendix, comments are provided to explain the symbols and make the code understandable. The results obtained from the code are also shown in the Appendix. By solving the systems of equations, the distributions of temperature and humidity inside the dry and wet channels of the heat exchanger, and the outlet temperature and humidity are calculated. The dimensions of the heat exchanger are tabulated in Table 1. Reference operating conditions used in the simulation study are shown in Table 2. 32

49 Table 1: Heat exchanger specifications Parameter Symbol Value (m) Units Dry channel spacing ydry 2 mm Wet channel spacing ywet 2 mm Channel length L 50 cm Channel width W 30 cm Plate thickness tplate 0.2 mm Paper thickness tpaper 0.15 mm Table 2: Reference operating conditions Parameter Symbol Value Units Inlet air temperature Tinlet 38 C Inlet air humidity ratio ωinlet 9 g water/kg dry air Inlet air mass flow rate 0.6 g/s Extraction ratio / 35 % 3.4 Model results In this section the predicted results of the model are presented, illustrating how the temperature and humidity ratio of the inlet air changes as it moves through the heat exchanger. The temperature profiles of the air flowing in the dry and wet channels and the water film along the heat exchanger are shown in Figure 15. The directions of the air flow in the channels are indicated by arrows in the figure. It can be noted that the air in the dry channel loses its heat to the water film because its temperature (Td) is higher than that of the water film (Twf). Also, the water film temperature is higher 33

50 than the air temperature in the wet channel (Tw) for most of the length of the channel except for a small portion near the extraction point. Figure 15: Temperature profile of air in the dry and wet channels, and the water film In Figure 16, the local profile of the air humidity in the wet channel of the heat exchanger is shown. The wet air humidity ratio and relative humidity increase along the direction of its flow, starting from the branching point until it exits at a saturation state. 34

51 Figure 16: Properties of air and water in the wet channel 3.5 Effect of different parameters on the performance of the system Using the developed model, the effect of different factors, including channel spacing, length and extraction ratio, on the performance of the cooling system is investigated. The inlet and outlet air temperatures of the evaporative cooling system are used to indicate the cooling performance using the wet bulb effectiveness. The dimensions and operating conditions used are shown in Table 1 and Table Effect of channel spacing on performance The corrugated plastic sheets have flutes with an aspect ratio of 3/2 (height to width). The channel spacing (the width of the flutes) between the plastic sheets is varied from 2 to 10 mm, in order to determine its effect on the thermal performance of the heat exchanger. The result is presented in Figure 17. In this figure the channel spacing is 35

52 plotted against the wet bulb effectiveness and the outlet temperature. As shown in the figure, for fixed reference values, the outlet air temperature increases and the wet bulb effectiveness decreases when the channel spacing is increased. The reason for this behavior is that the coefficients of heat and mass transfer increases as the channel spacing decreases (from equation 10). It can be noted that a wet bulb effectiveness of more than unity is achieved when the channel spacing is smaller than about 5 mm. Figure 17: Effect of channel spacing on wet bulb effectiveness and outlet temperature (Inlet air temperature = 38 C, Inlet air humidity ratio = 9 g water/kg dry air) Effect of channel length on performance The wet bulb effectiveness value shows a significant relationship with channel length as shown in Figure 18. For fixed reference values, wet bulb effectiveness increases as the length of the channel is increased. The reason for this behavior is that increasing the length of the channel, leads to the enhancement of heat and mass transfer process by increasing the time and contact area between the air and water in the wet channel. 36

53 However, the cost of selecting a larger size and operation cost due to more friction losses should be considered for the optimization of the system. A length higher than about 0.3 m can provide wet bulb effectiveness greater than unity. Figure 18: Effect of channel length on wet bulb effectiveness and outlet temperature (Inlet air temperature = 38 C, Inlet air humidity ratio = 9 g water/kg dry air) Effect of inlet mass flow rate on performance The variation of the effectiveness and outlet temperature of the model with changing the inlet air mass flow rate is shown in Figure 19. Similar to the channel spacing, the wet bulb effectiveness is inversely proportional to the inlet mass flow rate. The reason for this behavior is that: as the mass flow rate increases, the air flows faster in the channels, therefore, reducing the contact time between the air and water in the wet channels, leading to a decrease in the wet bulb effectiveness. Wet bulb effectiveness values above unity are achieved when the inlet air mass flow rate is below about 1.2 g/s. 37

54 Figure 19: Effect of inlet air mass flow rate on wet bulb effectiveness and outlet temperature (Inlet air temperature = 38 C, Inlet air humidity ratio = 9 g water/kg dry air) Effect of extraction ratio on performance The extraction ratio represents the ratio of the mass flow rate of air in the wet channel to the mass flow rate of air in the dry channel. As seen from Figure 20, higher extraction ratios results in an increase of the wet bulb effectiveness values. This relation may be explained as follows: the entire cooling load in the dry channel is carried out by the air in the wet channel which basically acts as a heat sink in the system. This means that the total load removed in the dry channel is determined by the available amount of air in the wet channel to absorb it. So, the higher the amount of air in the wet channel (the higher the extraction ratio) the higher the wet bulb effectiveness. However, it should be noted that the greater the extraction ratio the smaller the amount of air delivered to the conditioned space. In order to achieve a wet 38

55 bulb effectiveness value greater than unity, the extraction ratio should be greater than about 25%. Figure 20: Effect of extraction ratio on wet bulb effectiveness and outlet temperature (Inlet air temperature = 38 C, Inlet air humidity ratio = 9 g water/kg dry air) 3.6 Summary In this chapter a mathematical model was developed to predict the cooling performance of a counter flow regenerative heat exchanger. The developed model was approximated using numerical analysis. From the performance predictions of the model, it was determined that the heat and mass transfer performance of the proposed cooling system strongly depends on the physical size (channel spacing and length), inlet air mass flow rate, and the extraction ratio. 39

56 Chapter 4. Experimental work 4.1 Introduction In this chapter the construction of the cooling system prototype, the experimental setup, and procedure are presented. The experimental results and the effects of various factors on the performance of the prototype are also investigated in this chapter. Furthermore, a comparison is conducted between the developed model in the previous chapter and experimental results obtained from testing the prototype. 4.2 Prototype description A computer aided design (CAD) model of the counter flow regenerative heat exchanger is shown in Figure 21. The locations of air inlet, supply air (the air that is delivered to the conditioned space) outlet, exhausted air outlet (wet channels exit), and feed water inlet are illustrated in the figure. 40

57 Figure 21: A CAD model of the counter flow regenerative heat exchanger 4.3 Prototype construction The heat exchanger The main component of the prototype is the heat exchanger, which is placed in an acrylic frame (Figure 21). The construction of the prototype is mainly based on corrugated plastic sheets, shown in Figure 22. The dry channels are made of these sheets which have 2 by 3 mm flutes. The construction of the prototype went on as follows: first, Wicking paper was attached to one side of the plastic sheets to ensure that the wet channels are continuously wet, next openings were made at the end of theses sheets as shown in Figure 23. These openings are the locations were a portion of the air in the dry 41

58 channel is extracted and directed to the wet channel. Then, these sheets were stacked together with a spacing of 2 mm between each, forming the wet channels (Figure 24). The heat exchanger consists of 50 channel pairs (one pair consist of a dry and wet channel) with the dimensions specified in Table 1.The finished stack of the sheets forming the heat exchanger is shown in Figure 25. The heat exchanger is then placed in a frame made out of acrylic as shown in Figure 26. Figure 22: A stack of corrugated plastic sheets 42

59 Wicking paper Openings Figure 23: The side of a dry channel sheet showing the wicking paper and the extraction openings Spacers Figure 24: The side of a dry channel, showing the spacers that form the wet channels 43

60 Figure 25: The stack of the plastic sheets forming the heat exchanger Figure 26: The heat exchanger placed in an acrylic frame 44

61 4.3.2 Other components Other components used in the construction of the prototype include a water pump which is used to feed water into the heat exchanger. Water is distributed into the wet channels from the top through a perforated sheet (Figure 27). A perforated sheet is used above the heat exchanger to distribute water instead of sprays to insure more even water distribution and with much less pump pressure. The wicking paper used in the wet channels helps to hold the feed water longer and as a result reduce the amount of water used. Extra water is collected at the bottom of the heat exchanger and recirculated back into the heat exchanger. A fan is placed at the secondary exit of the heat exchanger as shown in Figure 21, to extract air form the dry channels into the wet channels and eventually exhaust the air to outside. Insulated ducts are used to connect the preconditioning unit to the inlet of the prototype and to connect the secondary exit to the exhaust fan. The prototype is covered by insulation materials to limit heat transfer between the prototype and the surrounding. 45

62 Figure 27: Top view of the heat exchanger showing the perforated sheet used to distribute water into the wet channels 4.4 The experimental setup The prototype was tested in a laboratory were the inlet air was conditioned by an air conditioning unit that contain heating and humidifying elements (Hilton air conditioning laboratory apparatus, P.A. Hilton Ltd., United Kingdom). A schematic illustration of the experimental setup is shown in Figure 28. As seen in the figure, air is drawn from outside into the air conditioning unit, then the conditioned air enters the heat exchanger. The velocity, temperature and humidity of the air entering and exiting the heat exchanger were measured. Inlet and outlet air flow rates and humidities were measured with thermal velocity probes (Testo Limited, United Kingdom), and inlet and outlet temperatures were measured with type K thermocouples. The accuracy and range of measurement of the equipment used are listed in Table 3. A picture of the experimental setup is shown in Figure

63 Figure 28: A schematic diagram of the experimental setup Table 3: Specifications of the measuring equipment Parameter Instruments Measurement range Accuracy Temperature Thermocouple type K 0 to 100 C ±0.2 C Air velocity Thermal velocity probe 0 to +20 m/s ±0.03 m/s Humidity Thermal velocity probe 0 to +100 %RH ±2 %RH 47

64 Figure 29: A picture of the experimental setup 4.5 Experimental procedure All measuring instruments are connected to a computer were the data are recorded. Before starting each experiment, the ambient temperature and humidity were recorded. The fans were turned on to allow sufficient amounts of air into the dry and wet channels of the heat exchanger at the lowest rate of 1.8 m 3 /min (velocity = 1 m/s). The water pump was then turned on, and then the measurements were recorded when the system reached a steady state condition. 4.6 Experimental results The prototype has been tested by conducting a number of experiments in order to study the effect of various factors on its performance. 48

65 4.6.1 Effect of inlet air volume flow rate on performance To find the effect of the inlet air volume flow rate on the performance of the prototype, a set of experiments were conducted. By controlling the inlet fan power, the inlet air volume flow rate was changed while keeping the inlet air temperature, inlet air humidity ratio, and the extraction ratio constant. The results of the experiments are shown in Figure 30. As seen in the figure, the wet bulb effectiveness of the heat exchanger decreases as the inlet air volume flow rate increases. This behavior can be interpreted in the following way: as the volume flow rate increases, the contact time between the air and the wet surfaces is reduced which reduces the evaporation rate and consequently, decreases the effectiveness. Figure 30: Wet bulb effectiveness as a function of the inlet air volume flow rate (Inlet air temperature = 30 C, Inlet air humidity ratio = 8 g water/kg dry air and extraction ratio = 41%) 49

66 4.6.2 Effect of extraction ratio on performance By adjusting the speed of the exhaust fan, the amount of air extracted from the dry channels and diverted into the wet channels was increased while keeping the other parameters unchanged. As seen from Figure 31, the wet bulb effectiveness of the heat exchanger increases with increasing the extraction ratio. The reason for this behavior can explained as follows: the heat load removed from the dry channels is dependent on the amount of air available in the wet channels. Therefore, when the extraction ratio increases more air is in the wet channels and more heat is removed from the air in the dry channels. As a result, the temperature of the outlet air is decreased and consequently the wet bulb effectiveness is increased. Figure 31: Wet bulb effectiveness versus extraction ratio (Inlet air temperature = 30 C, Inlet air humidity ratio = 8 g water/kg dry air, and Inlet air volume flow rate = 2.16 m 3 /min) 50

67 4.6.3 Effect of inlet air temperature on performance To study the effect of raising the inlet air temperature on the performance of the heat exchanger, a set of experiments were conducted. By controlling the heating elements in the preconditioning unit, the inlet air temperature was raised while keeping the inlet air volume flow rate, inlet air humidity ratio, and the extraction ratio constant. Figure 32 shows the wet bulb effectiveness as a function of the inlet air temperature. As seen in the figure, the wet bulb effectiveness of the heat exchanger is slightly affected as the inlet air temperature increases. This shows that unlike inlet mass flow rate and extraction ratio, the inlet air temperature has little effect on the effectiveness of the prototype. Figure 32: Wet bulb effectiveness versus inlet air temperature (Inlet air volume flow rate = 2.04 m 3 /min, Inlet air humidity ratio = 9.11 g water/kg dry air, and extraction ratio = 40%) 51

68 4.6.4 Effect of inlet air humidity ratio on performance By controlling the humidifier in the preconditioning unit, the inlet air humidity ratio was increased while keeping the inlet air volume flow rate, inlet air temperature, and the extraction ratio constant. As seen in Figure 33, the wet bulb effectiveness of the heat exchanger is almost not affected by the change of the inlet humidity ratio. In a similar manner to inlet air temperature, the inlet air humidity has a little effect on the effectiveness of the prototype. Figure 33: Wet bulb effectiveness versus inlet air humidity ratio (Inlet air temperature = 35 C, Inlet air volume flow rate = 2.15 m 3 /min, and extraction ratio = 37%) 4.7 Comparison between model and experimental results To assess the validity of the model, the experimental results of the prototype were compared with the simulation results derived from the numerical model. The two results are compared while having identical operating conditions and heat exchanger dimensions. 52

69 Figure 34 shows the predicted and experimental outlet air temperature as a function of inlet air temperature. The difference between predicted and measured outlet temperatures is 1 to 1.5 C which represents 5 to 6 % relative difference. The predicted and experimental outlet air temperature as a function of the extraction ratio is shown in Figure 35. The difference between the predicted and measured outlet temperatures is between 0.5 and 2 C which is about 4 to 10 % relative difference. As seen in the figure, the discrepancy between the model and experimental results reduces at higher extraction ratios. The model results match the trend of the experimental results but it predicted lower outlet temperatures than those obtained by the prototype. However, the discrepancy is at most 10%. Therefore, the model is considered to provide good approximates of the prototype outlet conditions. The higher outlet temperatures obtained from the experiments relative to the model predictions can be due to several factors including, uneven water distribution in the wet channels, and non-uniform flow of air in the wet channels. 53

70 Figure 34: Comparison between model and experimental results-outlet air temperature versus inlet air temperature (Inlet air volume flow rate = 2.04 m 3 /min, Inlet air humidity ratio = 9.11 g water/kg dry air, and extraction ratio = 40%) Figure 35: Comparison between model and experimental results- outlet air temperature versus extraction ratio (Inlet temperature = 30 C, Inlet air humidity ratio = 8 g water/kg dry air, and Inlet air volume flow rate = 2.16 m 3 /min) 54

71 4.8 Summary The performance of the developed prototype was investigated experimentally in this chapter. The results of the experiments showed that the cooling system performs well with a wet bulb effectiveness reaching as high as 1.3. Experimental results showed that the inlet air mass flow rate and the extraction ratio have a significant effect on the performance of the cooling system. The experimental results were used to validate the developed model for the heat exchanger. The comparison showed a reasonable agreement between the experimental results and the predictions of the model, with the differences being between 4 and 10%. 55

72 Chapter 5. Conclusions and future work 5.1 Conclusions The aims of this project were to develop a model of the proposed evaporative cooling system, and use the outcomes of the model to build a prototype, and evaluate it under different operating conditions. As a result of this research, a numerical model was developed that is capable of predicting the performance and outlet conditions of the proposed cooling system. The model was validated by experimental results gathered from testing a working prototype. It was found that the cooling system is capable of cooling the ambient inlet air temperature below its wet bulb temperature. From the conducted parametric analysis in Chapter 3 and Chapter 4, it was concluded that the performance of the cooling system significantly depends on the dimensions of the heat exchanger, namely channel spacing and length, inlet air flow rate, and the amount of air extracted from the dry channels and diverted to the wet channels (extraction ratio). The performance of the cooling system was investigated experimentally by conducting different experiments. The results of the experiments indicate that a wet bulb effectiveness of about 1.2 could be achieved with an air volume flow rate of 2.16 m 3 /min and an extraction ratio of 40%. A comparison of the obtained experimental results with the developed model revealed that the experiments were in reasonable agreement with the predictions of the model. 56

73 The differences between the predicted and measured outlet temperatures were between 0.5 and 2 C which is about 4 to 10 % relative difference. It is concluded that the proposed evaporative cooling system can cool the temperature of the ambient air significantly below its wet bulb temperature and by that overcoming the limitations of the typical evaporative cooling systems. This suggests that the proposed cooling system has the potential to replace VCAC systems. 5.2 Recommendations for future work Some recommendations for future works are presented below: To further investigate the performance of the proposed cooling system, a stand-alone prototype should be constructed. To examine the daylong operation of the system, a filed installation and monitoring of the prototype is recommended. An experimental comparison in power consumption savings between the stand-alone prototype and VCAC equipment should be conducted. 57

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77 Appendix Sample EES program code Counter flow regenerative heat exchanger simulation code "Operating conditions" T_in=38[C] omega_in=0.009[kg/kg] m_d=0.0006[kg/s] Ex_ratio=0.35 m_w=m_d*ex_ratio "Inlet temperature of the air in the wet channel" "Inlet humidity ratio of the air in the wet channel" "mass flow rate of dry channel" "extraction ratio" "mass flow rate of wet channel" "Heat exchanger specifications" y=0.002[m] z=0.003[m] d_h_dry=4*(z*y)/(2*(z+y)) d_h_wet=2*y W=0.3[m] L=0.5[m] "spacing of wet and dry channel" "width of dry channel flutes" "hydraulic diameter dry channel" "hydraulic diameter wet channel" "width of wet and dry channels" "length of wet and dry channel" "Properties" Nu_dry=2.811[-] Nu_wet=5.385[-] "Nusselt number of dry channel" "Nusselt number of wet channel" k_air=0.0264[w/m-k] "conductivity of air at 30 C" k_plate=0.1[w/m-k] k_paper=0.05[w/m-k] "conductivity of polypropylene" "conductivity of paper" 61

78 h_d=nu_dry*k_air/d_h_dry h_w=nu_wet*k_air/d_h_wet t_plate=0.2[mm]*convert(mm,m) t_paper=0.15[mm]*convert(mm,m) "heat transfer coefficient of dry channel" "heat transfer coefficient of wet channel" "thickness of polypropylene sheet" "thickness of wick paper" U=1/(1/h_d+t_plate/k_plate+t_paper/k_paper) rho_air=density(air,t=t_in,p= ) D_v= [m^2/s] "overall heat transfer coefficient" "density of the inlet air" "binary diffusion coefficient of water vapor in air" h_m=(nu_wet*d_v*rho_air)/d_h_wet "mass transfer coefficient of wet channel" C_d=1004[J/kg-K] "specific heat of dry air" "Grid setup" M=101 [-] "number of nodes" duplicate i=1,m x[i]=(i-1)*l/(m-1) x_bar[i]=x[i]/l "position of each node" "dimensionless position of each node" end DELTAx=L/(M-1) "distance between adjacent nodes" duplicate i=2,(m) governing equations -m_d*c_d*(t_d[i]-t_d[i-1])/deltax=u*w*(t_wf[i]-t_d[i]) m_w*(omega_w[i]-omega_w[i-1])/deltax=h_m*w*(omega_wf[i]-omega_w[i]) m_w*c_w[i]*(t_w[i]-t_w[i-1])/deltax=h_w*w*(t_wf[i]-t_w[i]) 62

79 h_w*w*(t_w[i]-t_wf[i])+u*w*(t_d[i]-t_wf[i])+h_uwfg[i]*h_m*w*(omega_w[i]- omega_wf[i])+k_plate*w*l*(t_wf[i+1]-2*t_wf[i]+t_wf[i-1])/(deltax^2)=0 C_w[i]=SpecHeat(AirH2O,T=T_w[i],w=omega_w[i],P= )*1000 "specific heat of air in the wet channel" H_uwfg[i]=(Enthalpy(Water,T=T_wf[i],x=1)-Enthalpy(Water,T=T_wf[i],x=0))*1000 "latent heat of water" omega_wf[i]=humrat(airh2o,t=t_wf[i],r=1,p= ) "humidity ratio of saturated air in the wet channel" end "Boundary conditions" T_w[1]=T_d[1] T_d[101]=T_in omega_w[1]=omega_in (T_wf[2]-T_wf[1])/DELTAx=0 (T_wf[101]-T_wf[100])/DELTAx=0 "Results" T_out=T_d[1] "outlet temperature" T_wb=WetBulb(AirH2O,T=T_in,w=omega_in,P=101.32) "inlet wet bulb temperature" epsilon_wb=(t_in-t_out)/(t_in-t_wb) "the dry channel wet bulb effectiveness" NTU=(h_d*W*L)/(C_d*m_d) "number of transfer units of the dry channel" 63

80 The results obtained from the EES code above are shown in Figure 36 and Figure 37. Figure 36: A screenshot of the EES program solution window. Figure 37: A screenshot of a portion of the array table obtained from the EES code above 64