Performance evaluation of a novel compact humidification-dehumidification desalination system coupled with a heat pump for design and off-design conditions

Energy Conversion and Management 194 (2019) 160–172

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Performance evaluation of a novel compact humidificationdehumidification desalination system coupled with a heat pump for design and off-design conditions

T

Meysam Faegh, Mohammad Behshad Shafii

⁎

Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

ARTICLE INFO

ABSTRACT

Keywords: Desalination Humidification-dehumidification Heat pump Vapor compression refrigeration Refrigeration system balancing Characteristic method

In this study, the theoretical investigation of a novel heat pump assisted humidification-dehumidification desalination system has been carried out. The conventional dehumidifier of the humidification-dehumidification system was removed and the evaporator of the heat pump was utilized for direct dehumidification of air. Besides, the heat pump condenser was used as the saline water heater of the humidification-dehumidification cycle. First, the sizes of the components were calculated at design conditions for fixed input operational conditions namely the ambient air temperature, relative humidity, and inlet saline water temperature. However, the input operating conditions vary at off-design conditions resulting in changes in heat pump performance. Since the performance of a heat pump is a function of its refrigerant saturation temperatures, to examine the performance of the designed system at off-design conditions, the system performance balancing was carried out through the method of characteristics for a given set of fixed-size components. It was observed that the gained output ratio and hourly yield of the proposed system reach 2.476 and 0.91 kg/h, respectively. The economic analysis indicated that the cost per liter of the proposed system is 0.014 $/L.

1. Introduction The rapid growth of population and a huge surge of safe water in industrial activities resulted in a significant increase in freshwater demand. As a sustainable tool for freshwater production, desalination is an energy-intensive process. This motivates the researchers to develop novel systems to produce fresh water with lower energy consumption [1]. In particular, Humidification-dehumidification method has proven to be an efficient technique to obtain fresh water in small scales due to its simplicity in design and having moderate installation and operating costs [2]. HDH desalination systems mainly consist of a heating source, a humidifier in which the pure water diffuses from saline water into the air and a dehumidifier where the humidified air cools to produce freshwater [3]. An overwhelming majority of studies have focused on increasing the GOR of the HDH systems and reviewed in [4]. GOR is an indication of the performance of HDH systems, which is defined as the ratio of heat of evaporation of the produced water to the input energy of the system. A thorough review of the studies conducted on the influence of the type of solar heaters on increasing the performance of HDH systems was given in [5]. Recently, A review of the effect of using

⁎

different types of humidifiers and dehumidifiers in HDH systems was carried out in [6]. Furthermore, a review of the economics of solar HDH systems indicated that the HDH process does appear economically attractive, and thus, optimization of the major components in the system can lead to further commercialization of HDH system [7]. In addition to the methods proposed by many researchers to improve the performance of the main components of HDH systems, there has been a growing interest in coupling desalination systems with heat pumps to increase the GOR. The reason for this lies in the fact that the heat pump has evolved to become a prominent technology over the past years due to its superior performance of energy conversion. A comprehensive study on combining heat pumps and desalination systems was reported in [8]. The need for simultaneous heating and cooling in HDH systems has motivated the researchers to examine the integration of heat pumps with HDH systems, using either cooling effect [9] or heating effect [10] of the heat pump in an HDH cycle. Furthermore, utilizing both of the heat rejection in condenser and heat absorption in the evaporator of the heat pump has been the subject of some studies in recent years. A theoretical analysis of a coupled HDH-HP system in which the cooling effect of the HP evaporator is used to cool the incoming

Corresponding author. Tel.: +982166165675; fax: +982166000021. E-mail address: [email protected] (M.B. Shafii).

https://doi.org/10.1016/j.enconman.2019.04.079 Received 15 February 2019; Received in revised form 24 April 2019; Accepted 25 April 2019 Available online 03 May 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature A B Ci=1-18 Cp COP CPL CR d dhyd D De f GOR h Hh hfg HDH HP i k L LMTD m Me MR NTU Nu P Pr qe Q Re

RH RR S SC SH T TR U wc W

area (m2) constant basic rating coefficient (kW/°C) compressor performance coefficients specific heat capacity at constant pressure (J/kg K) coefficient of performance (COP = Qe/W) cost per liter ($/kgm2) heat capacity rate ratio diameter (m) hydraulic diameter (m) curvature diameter (m) dean number (=Re(d/D)^0.5) average slope of the saturated air enthalpy versus temperature (kJ/kg K) gained output ratio (=mfw hfg /W) heat transfer coefficient (W/m2K) humidifier height (m) latent heat of vaporization (J/kg) humidification-dehumidification heat pump enthalpy (kJ/kg) thermal conductivity (W/mK) length (m) logarithmic mean temperature difference (°C) mass flow rate (kg/s) merkel number mass flow rate ratio (= m sw /ma) number of transfer units (=UA/mC p ) Nusselt number (=hdh/k) pressure (kPa) Prandtl number(=µC p /k) refrigeration effect (=i1,r-i4,r) (kJ/kg) rate of heat transfer (W) Reynolds number (= vdhyd / µ )

relative humidity recovery ratio (= mfw /m sw ) salinity (g/kg) subcool (°C) superheat (°C) temperature (°C) temperature ratio (=Tdp-Twall/Tin-Twall) overall heat transfer coefficient (W/m2°C) work of compression (=i2,r-i1,r) (kJ/kg) power consumption of the compressor (W)

Greek symbols water flux (kg/sm2) humidifier effectiveness h ηcompressor isentropic efficiency of the compressor (=(hr1,isentropichr1)/(hr2-hr1)) µ viscosity (kg/ms) coil pitch (m) density humidity ratio (kgw/kga) Subscripts a b c dp e fw h i r sw o

seawater for effective condensation of humid air in the dehumidifier was given in [11]. Using the energy rejected in the HP condenser as the heating source of the HDH cycle, maximum GOR of 8.88 and 7.63 is obtained for air heated and water heated cycles, respectively. Furthermore, the exergo-economic analysis of the proposed system indicated that HP evaporator and compressor are the components with the largest exergy destruction. The cost of desalinated water for different configurations varies from 4.61 $/m3 to 14.95 $/m3 [12]. A combined HDH-HP system was introduced in [13] by recovering the heat from the rejected brine in the HP evaporator of the heat pump to heat the saline water in the HP condenser. Results show that an extra heater or cooler should be installed to heat the seawater or remove the extra released energy of the refrigerant in the HP condenser. Besides, the GOR of the HDH desalination system is improved and reached 5.14 after the integration of the heat pump subsystem. A thermodynamic analysis of a coupled HDH-HP system with direct contact dehumidifier was conducted in [14]. The heat released from the condensation of refrigerant is used to heat the inlet saline water to the humidifier. At the same time, the hot moist air is transferred to the dehumidifier in which the cold freshwater is sprayed on. This causes condensation of the vapor in the humid air producing freshwater. It was concluded that a fully coupled heat pump HDH cycle could be achieved only in some cases. To ensure coupled behavior, either the mass flow rate ratio of saline water to air or the mass flow rate ratio of saline water to freshwater must be changed. Recently, experimental examination of an HDH-HP system in which the heat demand of the HDH system is supplied by both the electrical heaters and condenser of the heat pump was reported in [15]. It was stated that the air dehumidifies

air brine condenser of HP dew point evaporator of HP freshwater humidifier inner refrigerant saline water outer

firstly with inlet saline water and secondly, in the evaporator of the heat pump. The maximum productivity of the unit reached 12.38 kg/ kWh when the flow rate of cooling seawater and process air were 0.3 m3/h and 450 m3/h, respectively. To reduce the number of heat exchangers, experimental investigation of a coupled HDH-HP system was carried out in [16] by recovering the released heat of condensation for inlet air heating and humidification and using the cooling effect of the HP for direct air dehumidification in the evaporator of the heat pump. The effects of different parameters such as relative humidity, volume flow rate of the air passing the dehumidification section and ambient air temperature on system performance were investigated. Results indicated that the highest yield and GOR reach 2.79 kg/h and 2.08, respectively. It was also observed that increasing the relative humidity and volume flow rate of the air passing the dehumidification section results in higher GOR values for the system. Performance of a given heat pump system i.e. a specific compressor and fixed-size heat exchangers, at off-design conditions is a function of the mass flow rate and thermophysical properties of the air/water entering the evaporator/condenser of it. In HDH-HP systems, a variation of air/water properties entering the evaporator/condenser of the heat pump affects the saturation temperature and pressure of the refrigerant on both sides of the compressor. In off-design conditions related to weather changes throughout the year, which its effect has not yet been investigated, the HDH-HP system adjusts its evaporating and condensing temperatures to reach a new balance point different from the design point of the system due to the limitation of the heat transfer caused by fixed-size of heat exchangers. It is good to mention that in an imbalanced condition caused by severe deviations from a design point, the 161

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system may fail to operate or even be damaged by unacceptable operating parameters such as heavy overloading, low evaporating temperature, or high-pressure cutout [17]. Thus, balancing the HDH-HP systems with respect to the specifications of a given set of components is an important step to predict their real performance in off-design conditions. To the best of the authors’ knowledge, theoretical study of HDH-HP systems for a given set of components considering its behavior at off-design conditions has not been investigated yet. To explain more, previous mathematical studies mainly focused on designing various HDH-HP cycles by considering a constant compressor isentropic efficiency and fixed saturation temperatures of the HP refrigerant for different operational conditions without considering the cycle performance for fixed-size components at off-design conditions. Moreover, most of the HDH-HP cycles in previous studies, are not fully coupled and require an additional heating/cooling source. The aim of this study is to implement the design and sizing procedure for a novel fully coupled heat pump based HDH cycle by considering the realistic performance of a given compressor and examine the designed fixed-size system performance at off-design conditions for the first time in these kinds of systems. In the proposed system, to reduce the number of heat exchangers, the conventional dehumidifier is removed and the air is directly cooled and dehumidified via the refrigerant at the evaporator of the heat pump while the saline water is heated by passing through the condenser of the heat pump before entering to the humidifier. First, the parametric study was done to investigate the effect of design heat pump saturation temperatures and humidifier efficiency on both the system performance and size of the components at fixed operational conditions namely the ambient air temperature, relative humidity, and inlet saline water temperature. At this stage, the sizing of the components was calculated at the design condition considering the realistic specifications of a given compressor provided by the manufacturer. Then, for the first time, the performance of the fixed-size system designed at the first part was evaluated at offdesign conditions by utilizing the method of characteristics to balance the performance of the system with fixed-size components at various ambient air conditions and inlet saline water temperatures. Finally, the economic analysis of the system was conducted and the cost per liter of the produced water was reported.

valve. The conventional dehumidifier of the HDH cycle has been omitted and the evaporator of the heat pump acts as a dehumidifier in the system reducing the number of heat exchangers. Furthermore, the conventional heater of the HDH cycle has been replaced by the condenser of the heat pump cycle. The superheated refrigerant (state r2) inside the HP condenser rejects heat to the incoming saline water (state sw1) to enter the expansion valve as a subcooled liquid (state r3). Air is drawn from ambient (state a1) to flow into the humidifier and is humidified by spraying the hot saline water coming from the condenser of the heat pump (state sw2). A portion of the sprayed water is evaporated and carried by air through the top of the humidifier and the remaining amount exits from it (state b). The saturated air leaves the humidifier (state a2) and enters the evaporator of the heat pump where the water vapor condenses over the cold HP evaporator coils producing freshwater. The refrigerant exiting the expansion valve (state r4), undergoes a phase change inside the HP evaporator and absorbs the heat released from the dehumidification of air. By reaching the desired amount of superheat, the refrigerant enters the compressor (state r1) and is compressed inside it to return to the HP condenser to complete the cycle. This is good to mention that, the OAOW-WH configuration was selected for the HDH cycle due to its superiority to CAOW-WH cycle as reported in [18]. Besides, the cold and dehumidified air leaving the HP evaporator (state a3) could be either utilized in air conditioning systems or cooling of solar photovoltaic thermal panels. In short, the heat released from the dehumidification of air is recovered by the heat pump to heat the inlet saline water. The use of the cold refrigerant instead of saline water in the dehumidifier, in contrast to what was done in the past, causes more cooling of the humid air and increases water production. 3. Mathematical modeling Mathematical modeling of the proposed system contains two major steps. Firstly, the design of the system was examined by solving the relevant energy and mass equilibrium equations for fixed operational conditions to determine both the design saturation temperatures of the heat pump and the effectiveness of the humidifier. At this step, the HP evaporator, HP condenser, and humidifier were designed and their dimensions were evaluated. In practical conditions, changing the operational conditions as mass flow rate ratios of saline water to air, ambient air temperature, relative humidity, and saline water temperature affect the saturation temperatures of the heat pump, forcing the components to operate at off-design conditions. Since evaluating the performance of any HDH-HP cycle in off-design conditions has not yet been investigated theoretically, at the second step of this study, the procedure of balancing the performance of the proposed HDH-HP at off-design conditions was described and carried out.

2. System description Parametric study of a novel compact HDH-HP system was investigated through thermodynamic modeling. A schematic diagram of the proposed system is presented in Fig. 1. The proposed system consists of a heat pump cycle and a humidifier. The heat pump cycle comprises an evaporator, a compressor, a condenser, and an expansion

Fig. 1. Schematic diagram of the proposed system. 162

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3.1. Basic design and component selection for a fixed operational condition

3.1.2. Condenser of the heat pump The energy equilibrium in the HP condenser can be written as follows:

The governing equations for different components of the proposed system are discussed below taking into account the following assumptions.

Qc = mr (ir,2

ma (

1)

2

= m sw

m b ib

= max(

ib i sw,ideal

i sw,2 ia,2 ia,1 , ) i sw,2 ia,ideal ia,1

MR. Cp,sw f

f ) MR. C p,sw

,

Uc =

Ln( 2.049(CR

1

h h CR

1

)

1)MR0.221

0.779H 0.632

m sw

D

)0.938

(13)

1 A o,c 1 Ai,c hi,c

+

Qe = mr (ir,1

(5)

mfw = ma (

A o,cln(d o,c / di,c) 2 kL c

+

1 h o,c

(14) (15)

ir,4) = ma (ia,2

ia,3)

(16)

mfw ifw

(17)

3)

2

The heat transfer coefficients for evaporating and superheating refrigerant inside the HP evaporator coils can be calculated from the following equations: [27,28]

Nur,e =

(6)

(0.79LnRe

1.64) 2 (Re

2 + 17.96(0.79LnRe

1000) Pr

1.64)

(Pr

1

2 3

)

1

Superheating coil (18)

Nur,e =

0.15Re 0.706

Pr 0.3

Evaporating coil

(19)

Calculation of the heat transfer coefficient of the air dehumidifying outside the HP evaporator coils is done according to [29]:

(7)

The amount of water flux over the packing material plays a vital role during the process of humidification. Higher water flux results in flooding of the water stream in thick layers instead of falling as small droplets. On the other hand, lower water flux leads to poor humidification of the air. It is believed that the consideration of water flux over the packing material in the range of 0.8–4 kg/sm2 results in a proper cross-section area required for humidification [23].

Ah =

(12)

3.1.3. Evaporator of the heat pump Energy equation and conservation of mass inside the heat pump evaporator is as:

Furthermore, Merkel number as a dimensionless number to characterize heat and mass exchangers is calculated from the following equation to examine the height of the humidifier:

Me h = 2.049MR

Subcooling coil

D

Thus, calculation of the required heat transfer area of the HP condenser is a summation of heat transfer areas in desuperheating, condensing and subcooling sections.

(4)

1

]( 0.632 )

(11)

Q c = Uc A c LMTDc

The required packing height for a commercial packing material (CF1200MA Cross Fluted Film Fill Media) from Brentwood manufacturer is calculated as [22]:

Hh = [

(10)

By calculating the heat transfer coefficients for different regions of the HP condenser i.e. the desuperheating, condensing and subcooling coil, the overall heat transfer coefficient, as well as required heat transfer area of the HP condenser, can be obtained from the following equations for each part of the HP condenser.

(1)

the ideal outlet brine enthalpy is calculated based on the assumption that its temperature is equal to the inlet air dry-bulb temperature, while the ideal outlet air enthalpy is found based on the assumption that it is fully saturated at a temperature equal to the water inlet temperature to the humidifier. By considering the heat capacity rate ratio as [21]:

CR = min(

Condensing coil

Nusw,c = 19.64Re 0.513 Pr 0.129 (

The effectiveness of the humidifier ( h ) is expressed as the ratio of actual change in total enthalpy rate of either water or air stream to a maximum possible change in total enthalpy rate [18]. h

Nur,c = 2.3Re 0.94 Pr 0.4

Desuperheating coil

Also, the heat transfer coefficient for incoming saline water to the HP condenser can be obtained as [26]:

(3)

m sw Ssw = mb Sb

di,c D

Nur,c = 0.152De0.431Pr 1.06

(2)

mb

0.1

Nur,c = 0.023Re 0.8 Pr 0.4

0.277

3.1.1. Humidifier The energy equation and mass conservation for saline water and air streams in the humidifier are given as:

ia,1) = m sw isw,2

(9)

i sw,1)

A helically coiled shell and tube condenser is designed due to its prominent heat transfer capabilities. As depicted in Fig. 1, the refrigerant enters the condenser of the heat pump as superheated vapor and by rejecting heat to the inlet saline water, undergoes a phase change and exits the HP condenser as a subcooled liquid. Heat transfer coefficients for each part of the HP condenser can be calculated from the following correlations [24–26].

1. The humidifier and heat pump components are taken to be adiabatic with respect to the environment. 2. Pumping and fan powers are negligible compared to compressor power input [11]. 3. Pressure loss within the components of the system is ignored. Also, Kinetic and potential energy effects are neglected in the energy balance [13]. 4. The air at the inlet and outlet of the evaporator of the heat pump (dehumidifier) is assumed to be saturated [18]. 5. The bulk temperature of the produced freshwater is assumed to be the average temperature of the air at the inlet and exit of the HP evaporator [19]. 6. The saline water properties are calculated based on the correlations given in [20].

ma (ia,2

ir,3) = m sw (i sw,2

Nua,e = 140.5Re 0.27 Pr 0.33RH24.48TR

0.5

(20)

Consequently, the overall heat transfer coefficient and the length of the coils for each section of the HP evaporator can be obtained from the following equation:

Ue =

(8)

1 A o,e 1 Ai,e hi,e

+

A o,eln(d o,e / di,e)

Q e = Ue A eLMTDe 163

2 kL e

+

1 h o,e

(21) (22)

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The summation of calculated heat transfer area of evaporating and superheating zone of the HP evaporator gives its overall required heat transfer area.

components and cost of the produced freshwater is discussed in details in this study. 3.2. Performance of the fixed-size system at off-design conditions

3.1.4. Compressor of the heat pump Performance of the combined HDH-HP systems studied for the first time here is directly dependent on the compressor of the system. A change in the air/water inlet to evaporator or condenser of the heat pump cycle influences its refrigerant evaporation or the condensation temperature. An increase in evaporating temperature or a decrease in condensing temperature results in increased refrigerating capacity [17]. Refrigeration capacity and power requirement of a compressor as functions of the evaporating and condensing temperatures can be expressed by various polynomials as [30]:

In the previous section, components of the system have been selected and sizes of the heat exchangers have been calculated and fixed. In this section, the procedure for evaluating the designed fixed-size system performance at off-design conditions (variable input operational parameters) was investigated. As discussed before, the performance of a given compressor is unique and can be estimated from its manufacturer’s catalog data. At the same time, the performance of the proposed system was constrained due to its fixed compressor, fixed heat transfer area of HP evaporator, HP condenser and humidifier obtained for design point with fixed input operational conditions. When the working conditions in the proposed combined HDH-HP system change, all of the components together will find a new operating point. The balance point of these components gives the exact and actual performance of the system. It is good to mention that the performance of the given compressor can be obtained from manufacture’s data according to Eqs. (23)–(25). Once the sizes of the HP condenser and evaporator are determined in the first part of the study for design conditions, the method of characteristics is needed to investigate their performance at off-design conditions [30]. Since the amount of temperature of the entering saline water affects the condensation temperature of the refrigerant inside HP condenser, the aim of using characteristics method is to relate the rate of condensation heat transfer of the HP refrigerant to the temperature difference between the inlet saline water and condensation temperature of the refrigerant inside it via a constant coefficient namely basic rating coefficient of HP condenser (Bc). The basic rating coefficient of a heat exchanger is a fixed amount, which is calculated at the design point of the system. Following equation is used to describe the performance of the fixed size HP condenser (more details regarding the method of characteristics can be found in [32]):

Q e = c1 + c2 Te + c3Tc + c4 Te Tc + c5 T2e + c6 T2c + c 7 T2e Tc + c8Te T2c + c 9 T2e T2c

(23)

W = c1 + c2 Te + c3Tc + c4 Te Tc + c5T2e + c6T2c + c 7 T2e Tc + c8Te T2c + c 9T2e T2c Q c = Qe + W

(24) (25)

The constants of these equations can be obtained from the manufacturer’s data for a given compressor. In this study, the compressor model of “Danfoss-BD 350GH-48v” is considered according to its ability to run directly by the photovoltaic panels in remote areas. The calculated coefficients of cooling capacity and required power of the considered compressor are reported in Appendix A. It is worth mentioning that in spite of the previous theoretical studies of HDH-HP cycles, the variations in compressor isentropic efficiency was considered in this study. 3.1.5. Expansion valve The subcooled liquid refrigerant exiting the HP condenser passes through an expansion valve in an isenthalpic process. The two-phase refrigerant at the exit of the expansion valve enters the HP evaporator and operation of the cycle continues.

Qc = Bc (Tc

Also, a superheating value of SH = 11.1 °C and subcooling value of SC = 8.3 °C is considered as recommended by ARI Standard 520-90 (USA) [31].

Tr,1 = Te + SH

(27)

Tr,3 = Tc

(28)

SC

(31)

Moreover, to analyze the performance of the fixed size HP evaporator in off-design conditions, the method of characteristics was used as a tool to indicate the effect of entering humid air temperature on saturation temperature and cooling load of the HP evaporator via the basic rating coefficient of HP evaporator (Be):

(26)

ir,3 = ir,4

Tsw,1)

Qe = Be (Ta,2

Te)

(32)

Besides, the humidifier effectiveness for a fixed height of humidifier can be calculated from Eq. (6). In Fig. 2b, the balancing procedure of the proposed HDH-HP cycle with fixed-size components for off-design conditions has been summarized. As can be seen, a preliminary values for Te and Tc are guessed and by solving the governing equations and applying the characteristic method for fixed-size HP condenser, HP evaporator, humidifier (i.e. fixed Bc, Be, Hh) and a fixed compressor model, the exact values of the heat pump saturation temperatures and humidifier effectiveness are calculated in an iterative procedure. It is good to mention that the values of Te, Tc, and Hh are obtained at offdesign conditions according to the variable operational conditions and fixed size components as opposed to the design stage (Fig. 2a) in which the values of these parameters were considered as the inputs of the calculation. A similar trend could be extended to other HDH-HP cycles in the literature to estimate the exact performance of them at off-design conditions for a fixed set of components.

As depicted in Fig. 2a, the system design was carried out for a fixed set of operational conditions by considering the different values for evaporation and condensation temperatures of the heat pump as well as the humidifier effectiveness. The main reason to investigate the impact of these values in system design lies in the fact that the COP of a heat pump varies at different evaporation/condensation temperatures. The rate of heat transfer in HP condenser and evaporator affects the amount of increase in inlet saline water temperature and air dehumidification amount, respectively. Thus, the amount of produced freshwater alters with a change in HP performance. Furthermore, choosing proper humidifier effectiveness is important in the viewpoint of better humidification with lower humidifier height. It is good to mention that there is a limitation for maximum and minimum temperatures of the refrigerant inside the heat pump evaporator according to its compressor catalog data and practical working conditions of the proposed system. According to Fig. 2a, the amount of produced freshwater, GOR, CPL as well as the size of HP evaporator, HP condenser and humidifier is calculated. To attain a proper design, the effect of HP saturation temperatures and humidifier effectiveness on system performance, size of

4. Results & discussion At the first stage of this study, to design the system for fixed input operational conditions i.e. the mass flow rate ratio of saline water to air 164

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Fig. 2. Flow chart of the solution a. for system design at fixed operational parameters, b. balancing procedure of the fixed-size system at off-design conditions.

(MR), temperature and relative humidity of the ambient air (Ta,1, RH1) and saline water temperature (Tsw,1), the effect of saturation temperatures of the heat pump (Te, Tc) as well as the humidification efficiency ( h ) on GOR and size of the system components were studied. Afterward, to examine the system performance at off-design conditions the impact of operational conditions were studied during the balancing of the system for a given set of components with fixed sizes by implementing the method of characteristics. To explain more, as described in Fig. 2a, the design saturation temperatures of the heat pump and humidifier effectiveness were assumed as the inputs at the design part (first part). By investigating the system performance at off-design conditions (Fig. 2b), the saturation temperatures of the heat pump, as well as humidification effectiveness, were obtained from the variable input operational conditions entering the fixed set of components designed at the first part of the study.

effectiveness of the humidifier on GOR and size of the components have been investigated thoroughly at a fixed operational condition. At the end of this section, moderate values were selected as design variables of the refrigerant saturation temperatures and humidifier effectiveness for a fixed operational condition considering both the GOR and size of the components. 4.1.1. Effect of design refrigerant saturation temperature of the heat pump evaporator Effect of design HP refrigerant evaporation temperature (dehumidification section) on both the system performance (GOR) and HP evaporator size (NTUe) is shown in Fig. 3 for an HP refrigerant condensation temperature of 40 °C, humidifier effectiveness of 0.85 and HP refrigerant evaporation temperature of 2–14 °C. As can be seen, designing the system at higher evaporation temperature increases the GOR of the system. This lies in the fact that increasing the evaporation temperature results in higher refrigeration effect (qe) due to the shape of the saturation curve on the P-h diagram of the refrigerant, as depicted in Fig. 4. Besides, work of compression (wc) drops as well at higher evaporation temperatures as a result of the divergent nature of

4.1. System design for fixed operational conditions In this section, the effect of the design refrigerant saturation temperatures of the heat pump evaporator and condenser as well the design 165

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4.1.2. Effect of design refrigerant saturation temperature of the heat pump condenser Fig. 5 indicates the GOR and NTUc as a function of the HP refrigerant condensation temperatures of 36–48 °C for a fixed refrigerant evaporation temperature of 8 °C and humidifier effectiveness of 0.85. By decreasing the design condensation temperature, both the GOR and size of the HP condenser (NTUc) increased. This is due to the fact that at lower condensation temperatures, the work of compression decreases whereas the refrigeration effect increases, resulting in a higher COP of the heat pump and increased freshwater and GOR of the combined system. On the contrary, reduced condensation temperature is not desirable due to the higher size of the HP condenser coil area and the lower temperature difference between the inlet saline water and the condensing refrigerant. Regarding these outcomes, the condensation temperature of Tc = 40 °C was chosen as the design saturation temperature of the HP condenser. 4.1.3. Effect of design humidifier effectiveness Fig. 6 presents the effect of the design humidifier effectiveness on the GOR and the Merkel number (Meh) as an indicator of the humidifier height. By increasing the design humidifier effectiveness, absolute humidity of the air entering the HP evaporator increases leading to more water yield and thus an increased GOR. In contrast, increasing the effectiveness of the humidifier increases the Meh and thus larger height. A summary of the design results for fixed operational conditions of MR = 1.85, Ta,1 = 26 °C, RH1 = 0.6, Tsw,1 = 26 °C is shown in Table 1, considering the effect of saturation temperatures of the heat pump and humidifier effectiveness on GOR and dimensions of the heat exchangers. This is good to mention that moderate values were selected for design parameters and it is recommended to conduct an optimization procedure in future studies so that annual energy consumption of this system is minimized in off-design conditions associated with fluctuations in saline water temperature as well as the air relative humidity and temperature.

Fig. 3. Effect of design HP evaporation temperature on the performance of the system and size of the HP evaporator for Tc = 40 °C and εh = 0.85.

4.2. Performance balancing at off-design conditions for a system with fixedsize components At the previous section, the proposed HDH-HP cycle was designed and the dimensions of the heat exchangers were calculated for fixed input operating conditions given in Table 1. GOR of the system, in this case, reached the amount of 2.476 for a humidification efficiency of

Fig. 4. P-h diagram of the HP refrigerant for evaporation temperatures of Te = 2, 8, 14 °C with Tc = 40℃ and εh = 0.85.

isentropic lines in the superheat region of P-h diagram. Thus, COP of a heat pump increases as the refrigerant evaporation temperature rises and more water produced via better dehumidification of the air inside the HP evaporator at higher evaporation temperatures due to the increased HP refrigeration effect and decreased work of compression. However, it is good to mention that there exists a maximum limit (15 °C for Danfoss BD-350GH) for the evaporation temperature as reported by the manufacturer of the compressor in order to have a properly working heat pump. On the other hand, decreasing the evaporation temperature increases the temperature difference between the dehumidifying air and evaporating refrigerant, which requires less heat transfer area (higher NTUe. as illustrated in Fig. 3) and thus less heat exchanger material and cost due to the required lower cooling capacity at lower evaporation temperatures. However, the subzero HP refrigerant evaporation temperatures were prevented in the design of the proposed system due to ice formation on HP evaporator coils. Thus, to achieve an acceptable GOR with a moderate HP evaporator size and cost in this study, Te = 8 °C is selected as the design HP refrigerant evaporation temperature.

Fig. 5. Effect of design HP condensation temperature on the performance of the system and size of the HP condenser for Te = 8 °C and h = 0.85.

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4.2.1. Effect of ambient air temperature on fixed-size system performance at off-design conditions The effect of ambient air temperature on GOR is reported for different mass flow rate ratios in Fig. 7. For constant ambient air temperature, by increasing the mass flow rate ratio, GOR reaches a maximum and drops by a further increase. This can be attributed to the fact that the humidification effectiveness, heat pump cooling capacity, HP saturation temperatures, and COP rises at higher mass flow rate ratios while the isentropic efficiency of the compressor drops by increasing the mass flow rate ratio, resulting in an optimum value for the ratio of the water production to consumed compressor power. At the optimum mass flow rate ratio of saline water to air, the recovery ratio of the system reaches a maximum, thus the mass flow rate of the output brine reaches a minimum leading to a maximum of GOR. It can be seen that at lower mass flow rate ratios the performance of the system is better at lower ambient air temperatures while at increased mass flow rate ratios, system outperforms at higher ambient temperatures. This lies in the fact that the performance of the heat pump i.e. the isentropic efficiency of the compressor, saturation temperatures of the HP refrigerant, the pressure ratio of the compressor and COP of the heat pump alter by changing the inlet air temperatures and mass flow rate ratios. At lower mass flow rate ratios, the COP and saturation temperatures of the heat pump decrease by increasing the ambient temperatures leading to lower GOR values, whereas at higher mass flow rate ratios the opposite trend occurs. As can be inferred from Fig. 7, the maximum achievable GOR rises at higher ambient air temperatures for the optimum value of the mass flow rate ratio. This occurs since the humidification efficiency rises from 74.8% to 83.9% by increasing the mass flow rate ratio from 1.4 to 2.4 for the fixed size humidifier at different ambient temperatures. Besides, by increasing the ambient air temperature from 22 °C to 30 °C, the optimum GOR for an inlet saline water temperature of 26 °C and ambient air relative humidity of 0.6 increases by 1.8% and reaches 2.49. This indicates the importance of balancing the system performance at off-design conditions for a given set of components to examine the complex realistic behavior of the heat pump integrated with an HDH desalination unit.

Fig. 6. Effect of design humidifier effectiveness on the performance of the system and size of the humidifier for Te = 8 °C and Tc = 40 °C.

Table 1 Summary of system design for fixed operational conditions.* Parameters

Value

Evaporator Te di do Le Be

8 °C 0.00278 m 0.004 m 3.727 m 0.0302 W/°C

Condenser Tc di do D Lc

40 °C 0.013 m 0.015 m 0.2 m 3.521 m 0.03 m

Humidifier

0.85 0.1291 m 1.5 kg/sm2

h

Hh

* MR = 1.85, Tsw,1 = 26 °C.

4.2.2. Effect of ambient air relative humidity on fixed-size system performance at off-design conditions Variations in GOR with respect to ambient air relative humidity and mass flow rate ratio can be seen in Fig. 8. As the relative humidity

0.07471 W/°C

Bc

Ta,1 = 26 °C,

RH1 = 0.6,

85% with refrigerant evaporation and condensation temperatures of 8 °C and 40 °C, respectively. The impact of mass flow rate ratio on achieving the maximum GOR, at different air temperature, relative humidity, and inlet saline water temperatures are provided here. The amount of mass flow rate ratio can be adjusted by fixing the saline water mass flow rate and changing the speed of air fan to control its mass flow rate. It is good to highlight that for fixed-size components, the saturation temperatures of the heat pump refrigerant and the effectiveness of the humidifier will vary and are obtained at off-design conditions with respect to the new input operational conditions according to Fig. 2b. Compared to previous studies, in which the HP evaporator and condenser saturation temperature values were assumed to be constant regardless of the change in heat pump performance under different input conditions, in this study for the first time, changes in the evaporation and condensation temperatures of the refrigerant were investigated under the influence of input conditions via the method of characteristics for a fixed set of components.

Fig. 7. Effect of mass flow rate ratio on GOR for different ambient air temperatures (Tsw,1 = 26 °C, RH1 = 0.6). 167

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GOR occurs in the case of 0.2 relative humidity. These observations highlight the importance of examining the heat pump performance at off-design conditions. 4.2.3. Effect of inlet saline water temperature on fixed-size system performance at off-design conditions The effects of the inlet saline water temperature on GOR for different mass flow rate ratios are shown in Fig. 9. It can be observed that at lower inlet saline water temperatures, by raising the mass flow rate ratio, GOR reaches a maximum value and then drops by an additional increase in mass flow rate ratio. However, at higher inlet saline water temperatures, by increasing the mass flow rate ratios no drop in GOR is observed. This lies in the fact that the maximum achievable GOR is restricted by the maximum allowable evaporation temperature of the compressor reported at its catalog data. To explain more, increasing the inlet saline water temperature results in higher saturation temperatures of the heat pump. The saturation temperature of the HP evaporator increases from 9.5 °C to 13.6 °C at inlet saline water temperature of 30 °C for mass flow rate ratios of 1.4 and 2.4, respectively. It should be mentioned that the maximum allowable temperature of the compressor in the current study was reported as 15 °C in the manufacturer’s catalog data. Moreover, it is inferred from Fig. 9 that the more the inlet saline water temperature, the higher the maximum achievable GOR. This occurs since the higher COP and evaporation temperature can be obtained at higher mass flow rate ratios due to enhanced humidification process. Higher COP results in more cooling capacity and freshwater dehumidification with less consumed compressor power i.e. enhanced GOR. The GOR increases by 26.6% and reaches a maximum value of 2.69 at inlet saline water temperature of 30 °C. Besides, a drop of GOR can be seen at lower mass flow rate ratios for higher inlet saline water temperatures due to the lower compressor isentropic efficiency and heat pump COP. The following results can also be explained in terms of the cycle top temperature, i.e. the temperature of the saline water exiting the heat pump condenser (Tsw,2). By increasing the inlet saline water temperature, the saturation temperature of the refrigerant inside the heat pump rises as well. This results in an increment in top temperature (Tsw,2) of the system. An increased top temperature (Tsw,2) leads to a higher temperature of the air exiting the humidifier (Ta,2). Due to the interconnection of the cycle components, increased temperature of the air at the entrance of the evaporator (Ta,2), results in higher evaporation temperature of the heat pump refrigerant. Thus, considering the variations in saline water temperature affects the system performance and adjusting the mass flow rate ratio at off-design conditions significantly improves the performance of the system. Table 2 summarizes the variations of compressor isentropic efficiency and heat pump evaporation and condensation temperatures for various inlet saline water and ambient temperatures of 22–30 °C as well as ambient air relative humidities of 0.2–0.9 for a mass flow rate ratio of MR = 1.85. It can be observed that the effect of saline water temperature on isentropic efficiency of the compressor, refrigerant evaporation, and condensation temperatures is much higher than the ambient air temperature and relative humidity. This may be attributed to the direct variation of the saturation temperature of the HP condenser at different saline water temperatures (24.9% increase) while the variations in ambient air/relative humidity indirectly affect the condensation temperature of the HP refrigerant, through the change in HP evaporation temperature. Variation in condensation temperature of

Fig. 8. Effect of mass flow rate ratio on GOR for different air relative humidities (Tsw,1 = 26 °C, Ta,1 = 26 °C).

Fig. 9. Effect of mass flow rate ratio on GOR for different inlet saline water temperatures.

increases, the temperature of the air outlet from the humidifier rises and by increasing the evaporation temperature of the refrigerant as well as enhancing the COP of the heat pump, better dehumidifying conditions and elevated GOR are achieved. Additionally, it is observed that at higher relative humidities, the amount of water needed to humidify the air to saturation state drops and results in reduced optimum mass flow rate ratios. The optimum GOR reaches 2.524 for a relative humidity of 0.9 with inlet saline water and ambient temperatures of 26 °C. Also, by adjusting the mass flow rate ratio, the maximum increase of 19.4% in

Table 2 Variations in heat pump saturation temperatures and compressor isentropic efficiency at different operational parameters for a mass flow rate ratio of MR = 1.85. Tsw (°C)

Ta,1 (°C)

RH1

ηcompressor (%)

Variations of ηcompressor (%)

Te (°C)

Variations of Te (%)

Tc (°C)

Variations of Tc (%)

22–30 26 26

26 22–30 26

0.6 0.6 0.2–0.9

35.8–39.1 37.7–37.8 38.1–37.7

9.2 0.3 1

6.3–12.3 9.4–8.5 7.4–10

95.2 9.6 35.1

36.1–45.1 40.4–40.1 39.8–40.4

24.9 0.7 1.5

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Table 3 Cost of the system components. Component

Price ($)

Compressor Expansion valve Humidifier Evaporator Condenser Blower Total

330 10 50 30 30 10 460

Table 4 Economic analysis of considered HDH-HP desalination system. Parameter

Unit

Value

Capital cost (P) Salvage value (S = 0.2 × P) Life (n) Interest rate (i) Capital recovery factor (CRF) Sink fund factor (SFF) First annual cost (FAC = P × CRF) Average hourly yield Average daily yield Annual salvage value (ASV = SFF × S) Annual maintenance cost (AMC = 0.15 × FAC) Annual current cost (ACC = CC × Power) Annual cost (AC = FAC + AMC + ACC − ASV) Annual yield (M = average daily yield × 365) Cost per liter (CPL = AC/M)

$ $ Year % – – $ kg/h L/day $ $ $ $ L $/L

460 92 10 12 0.177 0.056 81.42 0.91 21.84 5.15 12.21 27.33 115.81 7971.6 0.014

refrigerant directly affects the performance of humidifier by altering its inlet saline water temperature. However, the variations in inlet air temperature and relative humidity slightly affect the refrigerant condensation temperature (0.7% and 1.5% for ambient air temperature and relative humidity, respectively). Besides, the maximum increase in refrigerant evaporation temperature of 95.2% and compressor isentropic efficiency of 9.2% is reported for various inlet saline water temperatures. This highlights the importance of examination of a heat pump performance at off-design conditions, which was neglected in previous theoretical studies in the literature. 4.2.4. Effect of air mass flow rate on fixed-size system performance at offdesign conditions Fig. 10 represents the effect of saline water mass flow rate on saturation temperatures of the heat pump (Fig. 10a), GOR (Fig. 10b) and Recovery ratio of the system (Fig. 10c) at various mass flow rate ratios of saline water to air. It can be seen from fig a. that decreasing the mass flow rate of saline water rises the saturation temperature of the heat pump evaporator, while slightly raises the saturation temperature of the heat pump condenser. This lies in the fact that, for a given mass flow rate ratio of saline water to air, decreasing the mass flow rate of saline water led to a decrease in the mass flow rate of air. The reduced air mass flow rates and increased saline water temperature at the entrance of the humidifier (top temperature of the cycle), result in enhanced heat and mass transfer inside the humidifier, i.e. higher air temperature at the exit of it. Since the saturation temperature of the heat pump refrigerant in its evaporator is a function of the air entering to it (Ta,2), the evaporation temperature rises as well in this case, as depicted in Fig. 10a. Moreover, it is stated in the previous section that the COP of a heat pump as well as its cooling capacity increases at higher evaporation temperatures. As can be seen from Fig. 10b, for a given mass flow rate ratio of saline water to air, decreasing the mass flow rate of saline water increases the GOR of the system. This is due to increased cooling capacity and COP of the heat pump cycle caused by the increment in its saturation temperatures. Furthermore, it is illustrated in Fig. 10c that at lower saline water mass flow rate, higher recovery ratios can be

Fig. 10. Effect of saline water mass flow rates on a. saturation temperatures of heat pump, b. GOR and c. RR of the system at various mass flow rate ratios of saline water to air.

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Table 5 Comparison of HDH systems integrated with HPs in terms of GOR, Hourly yield, and CPL. Ref.

HP condenser

HP evaporator

Type of study

GOR

Hourly yield (kg/h)

CPL ($/L)

Amin & Hawlader [35] Shafii et al. [16] Xu et al. [15] Srithar et al. [36] Zhang et al. [37] Lawal et al. [11] He et al. [13] Dehghani et al. [14] Zhang et al. [38] Current study

SW heater Air heater SW heater Air heater SW heater SW/Air heater SW heater SW heater SW heater SW heater

Air dehumidifier Air dehumidifier 2nd stage dehumidifier External refrigerator & dehumidifier 2nd stage dehumidifier SW cooler Brine cooler FW cooler 2nd stage dehumidifier Air dehumidifier

Experimental & Theoretical Experimental Experimental Experimental Experimental Theoretical Theoretical Theoretical Theoretical Theoretical

0.43–0.88 2.08 1.24 1.2 2.05 8.88 5.14 0.76 2.532 2.476

1.38 2.79 12.75 – 22.26 – 82.12 – – 0.91

– 0.009 0.030–0.042 – 0.051 0.008–0.034 – – 0.0412 0.014

Table 6 Validation of HDH cycle results. Ta,1 (°C)

RHa,1 (%)

Ta,2 (°C)

RHa,2 (%)

Ta,3 (°C)

RHa,3 (%)

Experimental yield (kg/h) [16]

Theoretical yield (kg/h)

Error (%)

34.4 38 41.8

93.3 88 70.3

26.4 28.7 30.7

99.9 99.9 99.9

17.7 20.6 22.5

99.9 99.9 99.9

2.33 2.44 2.56

2.418 2.531 2.671

3.8 3.7 4.4

method of characteristics, the performance of the system was obtained at variable isentropic efficiencies of the compressor via considering the performance curves of the cooling load and compressor work given by the manufacturer’s data. Using compressors with higher isentropic efficiencies as assumed in the theoretical study of [13], could significantly increase the GOR of the system. Moreover, it is indicated that the CPL of the current system is modest compared to the CPL of the other reported HDH-HP systems. Moreover, it is anticipated that in future studies, by using higher efficiency compressors, the CPL of the present system could further drop. 4.4. Validation of the mathematical modeling To ensure the reliability of the acquired results for the combined HDH-HP system, the formulations of system components are confirmed by the existent data. Due to the novelty of the investigated cycle, the validation of the results was done in two steps. Firstly, the HDH subsystem was validated with experimental data of [16], which is similarly based on an OAOW HDH cycle with a packed bed humidifier and heat pump evaporator as the dehumidifier. Table 6 represents the temperatures of air in input and output of humidifier and dehumidifier as well as the experimental and theoretical yields obtained in [16] and the current study, respectively. It can be seen that a 3.7–4.4% deviation was observed for the modeling process compared to the experimental data. Moreover, the amount of COP and mass flow rate of the compressor are a function of its cooling capacity, evaporation and condensation temperatures for a fixed amount of superheat at compressor suction and subcooling at HP condenser outlet. The COP and refrigerant mass flow rate for a range of evaporation temperatures of the current study have been compared with the experimental data provided by the Danfoss Coolselector®2 software in Fig. 11. It can be concluded that the performance of the compressor is estimated properly with the manufacturer’s data. Accordingly, the overall performance of the system is in agreement with the existing data in the literature.

Fig. 11. Validation of the compressor COP and refrigerant mass flow rate with manufacturer’s data.

obtained. This occurs due to the increased air temperature at the exit of the humidifier (Ta,2) and as a result absorption of more moisture in the air exiting the humidifier i.e. the higher absolute humidity ( a,2 ) at lower saline water mass flow rates. Higher absolute humidity of the air at the exit of humidifier led to a lower mass flow rate of the brine and higher mass flow rate of the fresh water i.e. higher recovery ratio of the system. 4.3. Economic analysis The economic analysis of the current system was carried out according to [33]. As reported in Table 3, the capital cost of the system was 460 $. The water cost for the 10 years of system operation with a current cost of 0.012 $/kWh [34] is calculated in Table 4. The cost of produced freshwater was calculated to be 0.014 $/L. Table 5 summarizes the performance of HDH systems integrated with heat pumps in terms of GOR, hourly yield and CPL. It can be seen that the GOR of the current study is higher than all of the previous experimental studies. As discussed before, the performance of the proposed system was investigated and balanced for a given compressor and fixed-size heat exchangers at off-design conditions considering the realistic specifications of the system components. By utilizing the

5. Conclusions The aim of this study was to design a novel HDH cycle combined with a heat pump and examine its performance during the off-design conditions for the first time. The system mainly consists of a humidifier and an HP cycle comprised of a compressor, condenser, evaporator and an expansion valve. The conventional dehumidifier of the HDH cycle 170

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was eliminated in the proposed system by utilizing the cooling effect of the heat pump evaporator to air dehumidification. Moreover, the heating load of the heat pump was used to heat the inlet saline water of HDH cycle. First, by keeping a set of operational parameters fixed i.e. the mass flow rate ratio of saline water to air (MR), temperature and relative humidity of the ambient air (Ta,1, RH1) and saline water temperature (Tsw,1), the proposed system was first designed to obtain optimum values of heat pump saturation temperatures and humidifier effectiveness. Then, the method of characteristics was utilized to examine the realistic performance of the system for a given set of fixedsize components (fixed heat exchangers and compressor) at off-design conditions. In this method, the saturation temperatures of the heat pump were calculated based on the inlet temperatures of the fixed-size components. The following conclusions can be drawn: Increasing the design saturation temperature of the HP evaporator leads to the higher refrigeration effect of the compressor with lower compression work. This results in more dehumidification of air increasing the GOR of the system. However, there is a maximum allowable evaporation temperature for any given compressor. On the other hand, increasing the design saturation temperature of the HP evaporator requires more heat transfer area inside the HP evaporator due to the need for a higher rate of heat transfer. Furthermore, increasing the design saturation temperature of the HP condenser results in lower GOR and heat transfer area in the HP condenser. Thus, to achieve an acceptable amount of freshwater yield and GOR with lowest CPL, moderate values of 8 °C and 40 °C were considered as the saturation temperatures of the HP evaporator and condenser, respectively.

(3) (4)

(5)

(6)

set of components. Accordingly, the optimum mass flow rate ratio of inlet saline water to air decreases with a drop in ambient air temperature. By increasing the relative humidity of the ambient air, GOR rises, whereas the optimum mass flow rate ratio decreases. The saturation temperatures of the HP refrigerant as well as the humidification effectiveness rise by increasing the inlet saline water temperature. However, the amount of mass flow ratio is restricted by the maximum allowable saturation temperature of the compressor provided at its catalog data. The performance of the system at different operational parameters revealed the importance of balancing the cycle performance for a given set of fixed-size components, in spite of the previous theoretical studies which investigate the performance of HDH-HP cycles regardless of the impact of the input conditions on the compressor and system performances for fixed-size components. For a given compressor (Danfoss BD-350GH 48v) with a design evaporation temperature of 8 °C, condensation temperature of 40 °C and humidifier effectiveness of 0.85, GOR and hourly yield of the system reaches 2.476 and 0.91 kg/h, respectively. Besides, the CPL of the produced water is calculated to be 0.014 $/L.

Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

(1) The GOR of the system rises with an increase in design humidifier effectiveness. However, the large height of humidifier is needed to reach the higher effectiveness inside the humidifier. Humidifier effectiveness of 0.85 was considered as the design value. (2) As the ambient air temperature increases, the maximum achievable GOR of the system increases at off-design conditions for a fixed-size

Acknowledgments The authors would like to express their gratitude to Iran National Science Foundation (INSF) for their financial support via grant No. 96010475.

Appendix A Danfoss coolselector®2 software was used to calculate the compressor coefficients of cooling capacity and power consumption for Danfoss-BD 350GH-48v as reported in Table A1. Table A1 Constants of cooling capacity and power consumption of the compressor.

Qe W

C1

C2

C3

C4

C5

C6

C7

C8

C9

0.11 −1.253

0.4745 0.525

0.05133 0.08602

−0.02442 −0.02894

−0.0325 −0.02275

−0.001083 −0.001268

0.001583 0.001257

0.0003542 0.0004107

−0.00002083 −0.00001815

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