Exergoeconomic analysis of a solar photovoltaic-based direct evaporative air-cooling system

Solar Energy 193 (2019) 253–266

Contents lists available at ScienceDirect

Solar Energy journal homepage: www.elsevier.com/locate/solener

Exergoeconomic analysis of a solar photovoltaic-based direct evaporative air-cooling system

T

⁎

Alireza Kiyaninia, Hajir Karimi , Vahid Madadi Avargani Department of Chemical Engineering, Faculty of Engineering, Yasouj University, P.O. Box 353, Yasouj 75918-74831, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Direct evaporative air-cooling Solar photovoltaic panel Cellulose and straw pads Mathematical modeling Exergoeconomic analysis

The target of this work is to perform the exergoeconomic analysis of a solar photovoltaic-based direct evaporative air-cooling system. The system was investigated experimentally with different thicknesses of cellulose and straw pads. For inlet air rates up to 1000 m3/h, the maximum changes in the humidity and temperature of outlet air are achieved by a pad with a thickness of 30 cm. A comprehensive mathematical model was developed for the system and the exergoeconomic analysis of the system was carried out. The influence of the effective parameter on the performance of the system was investigated. For an inlet air with a temperature of 30 °C and relative humidity of 30%, the maximum system exergy efficiency was obtained about 20%. With changes in the water temperature from 15 to 27 °C, inlet air rate from 300 to 1500 m3/h, and inlet air temperature from 26 to 34 °C, the system exergoeconomic factor changes up to 60%. The current system was compared with a conventional system and results showed that for four early years of systems lifetime, the exergoeconomic factor of the conventional system is greater than the solar system due to its lower initial investment, and for later years is lower due to its larger operating cost.

1. Introduction Today, both energy crisis and environmental pollution are the results of using conventional fossil fuels. Renewable energy resources due to their almost unlimited availability and environmental-friendliness, provide a perfect solution to the problem. Solar energy due to its even distribution, safety and serving as sources for others is widely recognized as one of the most important renewable energy resources. Air conditioning systems, including cooling and heating systems, are the only energy-consuming units (Zhao and Magoulès, 2012). Air conditioning systems account for about 20% of the world's total energy consumption, which is depended on fossil fuels and it leads to an enhancement of carbon dioxide emissions in the atmosphere. The type of air conditioning system by using chlorofluorocarbons (CFCs) will cause irreparable damage to the environment such as the destruction of the ozone layer and the warming of the planet. Global warming leads to climate change owing to the using of fossil fuels. The ending of fossil resources from one hand, and the demand for reducing air pollutants, on the other hand, has increased the focus on environmentally ecofriendly cooling technologies (Chengqin et al., 2002a). The building solar heating and cooling systems are categorized as passive and active systems. In passive systems, the integral parts of the building admit, absorb, store, and release solar energy, and therefore the auxiliary ⁎

energy for comfort heating is reduced. The direct evaporative cooling (DEC) system is one of the simplest, oldest and cheapest cooling systems. The evaporative air conditioning systems, especially DEC units, have been used in numerous arid areas of the world form many years ago. But given the dehydration problem in the world, there is a need for further investigation into the performance of these systems. In many cases, energy analysis is still used to evaluate the performance of systems. Energy analysis expresses the quantity of the energy within the system but does not provide information about the quality of energy and useful work availability, hence it cannot fully answer our needs. Therefore, the exergy analysis of systems is very important and is a suitable and powerful tool for performance evaluation of the systems. Exergy analysis uses a combination of the first and second laws of thermodynamics and is an applicable tool for analyzing the quantity and quality of energy. The exergoeconomic analysis is a new method to study and optimize the systems by combining exergy analysis with economic constraints (Enteria et al., 2015). Recently, many researchers and manufacturers take into account many important issues such as low power consumption and high efficiency with minimal cost configurations, in the designing and manufacturing of systems. Before now, several studies have been conducted on the evaporative cooling systems. Yang et al. carried out comprehensively a review of the recent developments and applications of different enhanced

Corresponding authors. E-mail addresses: [email protected] (A. Kiyaninia), [email protected] (H. Karimi), [email protected] (V. Madadi Avargani).

https://doi.org/10.1016/j.solener.2019.09.068 Received 5 July 2019; Received in revised form 23 August 2019; Accepted 20 September 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

Nomenclature

V frontal air velocity (m/s) work rate (W) Ẇ x x-direction (m) Y humidity (kg water/kg dry air) y y-direction (m) z z-direction (m) Ż capital cost rate ($/h) Greek symbols Definition ηex Exergy efficiency ρ air density (kg/m3) φ annual maintenance factor ψ maximum useful work available from the radiation source Superscript Definition CI capital investment OM operating and maintenance Subscripts Definition 0 dead state a air AB air Blower Ac air cooler c.v. control volume D destruction des, total total destruction dry dry air e exit f fuel gen generation i inlet k kth component PV photovoltaic q heat sat saturation solar, in inlet solar irradiation st, ECP the power stored by the battery t total v vapor w water wp water Pump

Alphabetical symbols Definition A surface (m2) b model data c cost per exergy rate ($/kJ) Ċ exergy cost rate ($/h) cp specific heat of the air (J/kg K) CRF capital recovery factor Deff effective mass diffusivity of vapor (m2/s) dx the thickness of the differential element (m) e specific exergy (J/kg) Ė exergy rate (W) f exergoeconomic factor h specific enthalpy of moist air (J/kg) ha annual operating hours i interest rate Ig solar Irradiation (W/m2) jv vapor diffusion mass flux (kg/ m2 s) Ka volumetric mass transfer coefficient (kg/m3. s) keff effective thermal conductivity of air (W/m K) ṁ mass flow rate (kg/s) ṁ v mass source term (kg/m3 s) MBE mean BIOS error n component lifetime (year) N total number of data o experimental data ō average values of the experimental data p pressure (Pa) heat transfer rate (W) Q̇ qv heat source term (W/m3) R specific gas constant (J/kg K) R2 determination coefficient RH relative humidity (%) RMSE mean square error s entropy (J) T temperature (°C) Ts apparent sun temperature (K) u air velocity in x-direction (m/s)

reduce the water consumption of a direct evaporative cooler for dry climates. Results showed that at 2 × 105 ppm salinity ratio, the water consumption was reduced by about 1.5 Lh−1 but the supply air temperature was increased by about 8.6% (Kabeel and Bassuoni, 2017). Dai and Sumathy developed a mathematical model and carried out laboratory experiments to analyze the efficiency of a direct evaporative air cooler with crossflow pattern, and in this study, the optimal values for some operational parameters were obtained (Dai and Sumathy, 2002). Wu et al. also provided a mathematical model for describing the heat and moisture transfer between air and water flows in a direct evaporative air cooler. In this study, the influence of some effective parameters such as inlet air velocity, air dry and wet bulb temperatures, and pad thickness on the performance of the system was investigated (Wu et al., 2009a). De Antonellis et al. investigated the effect of water nozzles and airflows arrangement on the performance of an indirect evaporative cooling system (De Antonellis et al., 2019). Wan et al. studied an evaporative air cooler under diverse climatic, operating and geometric conditions, and a new method proposed to predict and analysis of heat and mass transfer in a counter-flow configuration (Wan et al., 2018). Florides et al. reviewed the technology of solar and energy-saving cooling technologies for construction. They showed that evaporative cooling systems could be 85 to 90% effective. Also, when a direct evaporator coolant is used with a mechanical cooler, the cooling costs are reduced by 25–40% (Florides et al., 2002). Elmetenani et al.

evaporative cooling technologies (Yang et al., 2019). A passive evaporative cooling system was investigated by Belarbi et al., and a water spray evaporation system was modeled (Belarbi et al., 2006). The counter and cross-flow configurations of an indirect evaporative cooling system were compared by Pandelidis et al. and in this study, the analyses were based on the numerical simulations conducted with mathematical ε–NTU model of the heat and mass transfer (Pandelidis et al., 2019). Camargo et al. studied experimentally a direct evaporative cooling system during summer in a Brazilian city. In that study, a mathematical model was developed for the system and the experimental data were compared with model results (Camargo et al., 2005). Shukla et al. investigated the effect of an inner thermal curtain in an evaporative cooling system. It was obtained that the use of the proposed system reduces the temperature of the greenhouse by 5 °C and 8 °C in comparison to the greenhouse without a curtain in May (Shukla et al., 2008). Bishoy and Sudhakar studied a direct evaporative cooling system with Honeycomb and Aspen cooling pads. The energy efficiency ratio and cooling capacity of an air cooler with Honeycomb cooling pad are better than the Aspen cooling pad of the same surface area (Bishoyi and Sudhakar, 2017). Abohorlu Dogramac et al. studied the potential of eucalyptus fibers for evaporative cooling systems and concluded that the eucalyptus fibers at low air velocity, provides better performance in terms of cooling efficiency (Abohorlu Doğramacı et al., 2019). Kabeel et al. investigated experimentally a direct evaporative cooling system to 254

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

on exergy analysis or in other words, the exergoeconomic analysis of these systems. However, the use of solar energy in these systems has been considered after the 1973 energy crisis (Lazzarin and Noro, 2018). Therefore, the use of renewable energy resources, in particular, solar energy, in these systems and their exergy-economic assessment has not been thoroughly investigated. In this study, a direct evaporative cooling system with two cellulose and straw pads coupled to a solar photovoltaic panel was investigated both experimentally and theoretically. The novelty of the present work is to propose a comprehensive energy and exergy analysis of the system based on system economic assessment that has not been performed before now. The main purpose of this study is to propose a clear study pathway to the design and manufacture of a high-performance such cooling system with lower costs, by choosing the optimal range of system operational and structural parameters. Finally, the exergoeconomic factor of the system was compared with a conventional direct evaporative air-cooling system.

studied the performance of a solar direct evaporative under the Algerian climate. The maximum temperature drop was 18.86 °C (Elmetenani et al., 2011). Many of previous studies of the evaporative cooling system have been focused on only exergy analysis. Peng et al. performed the exergy analysis of a liquid desiccant evaporative cooling system. In this study, the effects of various parameters on the thermodynamic performance of the system were revealed and the optimal range of those parameters was obtained (Peng et al., 2017). Santos et al. performed the exergy and energy analyses of an evaporative cooling process in air washers (Santos et al., 2013). Sadighi Dizaji et al. carried out a comprehensive exergy analysis of a prototype Peltier air-cooler system (Sadighi Dizaji et al., 2019). Zhang et al. carried out the exergy analysis of parameter unmatched characteristic in coupled heat and mass transfer between humid air and water. The results indicate that when the parameter unmatched coefficient is small, the exergy destruction decreases, and flow paths show better performance (Zhang et al., 2015). Chengqin et al. investigated the performance of various evaporative cooling systems based on an exergy analysis. The results showed that in studied evaporative cooling schemes, the regenerative cooling scheme has the best performance, and to improve its exergy efficiency, the effectiveness has a great effect (Chengqin et al., 2002b). Farmahini-Farahani et al. carried out an exergy analysis of common evaporative cooling systems to obtain the optimum system for diverse climates. The results of this work revealed that the direct evaporative cooling systems are the best option for the dry climate with an exergy efficiency of 20% (FarmahiniFarahani et al., 2012). Taufiq et al. studied an exergy analysis to optimize the performance of a direct evaporative cooling process and examined the effect of relative humidity and air temperature on the process performance for building applications in Malaysia. The increase in the relative humidity from 20 to 80% enhances the exergy efficiency from 19 to 51% (Taufiq et al., 2007a). Fewer studies have been done to analyze the energy and exergy of cooling systems, taking into account the economic aspects of systems. Jaber carried out a feasibility study on the economic and environmental assessment of an indirect evaporative cooling unit under three climate conditions. The well-optimized unit can cover more than 84% of the annual cooling demand in the tested cities (Jaber, 2016). Chidambaram et al. reviewed the methods of solar cooling and heat storage options. They showed that for development of solar cooling, the factors of energy efficiency, cost, and type of thermal reservoir are very important in the economic analysis (Chidambaram et al., 2011). Mohammadi and McGowan performed a thermo-economic analysis of a combined cooling system and for the specified design and operating conditions, the annual operating cost and unit production cost of the integrated system reduced between 35.5% and 48.5% as well as between 23.4% and 34.5%, respectively (Mohammadi and McGowan, 2019). As reported in the literature, few previous studies have been focused on the economic assessment of the evaporative cooling systems based

2. Experimental setup The graphical representation and different parts of the experimental setup are shown in Fig. 1(a) and (b) respectively. The direct evaporative cooling system including an air fan and a water pump with 120 and 60 W power consumption respectively, cellulose pad (50 × 60 × 15 cm) and a solar photovoltaic panel with 200 W power generation. The water is circulated by a pump from the tank at the bottom of the cooler, and then is distributed by the water distributors on the top of the pads, which are then exposed to the blown air of the fan. The water evaporates into the warm air and gives cool and humid air. The experiments were carried out at different inlet air rates, with one, two and three cellulose pads of 0.15 m thickness, and moisture and temperature were measured at the input and output of the system. The results were repeated three times for each test. The different parts specification of the system, operational parameter values and ranges are given in Table 1. The solar energy is converted to the electrical energy in the photovoltaic panel and is stored in an electrical battery. The battery supplies the requisite electricity for the air fan and water pump embedded in the system and the excess electricity of the amount required is stored in the battery. The weather conditions, ambient temperature, and air rate through the cooler were measured by a multi-function HVAC meter model Testo 480 and a Testo vane probe, with 4″ diameter (100 mm). 3. Mathematical modeling The mathematical modeling of systems is a powerful tool to investigate the performance of systems. A good model can be used to design and optimize a system with higher performance. The only energetically modeling of systems cannot be more useful due to the lack of qualitative energy analysis and economic assessment within the

Fig. 1. Experimental setup, (a) schematic diagram of a direct evaporative cooling system coupled to a photovoltaic panel, and (b) different parts of the tested system. 255

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

Table 1 Geometrical specifications and operational parameter values and ranges in the experimental setup. Evaporative cooler (parts and specifications)

Operational range in experiments

Parts

Specifications

Parameter

Range

Cellulose pad dimensions PV panel dimensions Water pump Air fan

0.5 m × 0.6 m × 0.15 m

Inlet air humidity Irradiation intensity Air velocity Inlet air temperature Water temperature

25–35%

Electric power storage battery

2 (0.5 m × 1.0 m), 200 W DC, 60 W DC, 120 W 2 * (12 V, 7.5 Ah)

ṁ dry Y |x − ṁ dry Y |x + dx + jv A|x − jv A|x + dx + ṁ v Adx = 0, jv = −Deff d (ρdry uY ) dx

= Deff

d2Y dx 2

dY ⇒ dx

+ ṁ v (1)

where ṁ ν is the mass source term per unit volume of pad, kg water/m3 pad, Y is air humidity, kg water/kg dry air, jv is the vapor diffusion mass flux, which is transport through the pad in the x-direction, Deff is the effective mass diffusivity of vapor through the air within the pad and A is the air cross-sectional area.

200–1050 W/m2 0–5 m/s 25–35 °C

3.1.2. Momentum balance The momentum balance equation for air in the differential element gives:

25–35 °C

̇ |x − mu ̇ |x + dx + pA|x − pA|x + dx + ṁ ν Adxu = 0 ⇒ mu systems. Therefore, in this study in addition to energy analysis, the exergoeconomic analysis of the system is also carried out. The schematic of the differential element in the mathematical model is shown in Fig. 2. For the system described, a mathematical model is developed, and to simplify the formulation, the following assumptions are made (Fouda and Melikyan, 2011; Wu et al., 2009a, 2009b):

=−

d (ρu. u) dx

dp + ṁ ν u dx

(2)

In Eq. (2), u is the air velocity inside the pad. The first two terms are represented as the momentum of the inlet and outlet air flows, the second two terms are the momentum caused by the pressure forces, and the last term is the momentum of the vapor that diffuses through the air. dp is the amount of pressure drop along the pad thickness an is dx replaced based on the data of the manufacturer company.

• The system operates at the steady-state condition. • The cooler is adiabatic and no heat transfer occurs between the external surface of the cooler and ambient. • The pad material is uniformly wetted. • The transport phenomena through the pad are considered as one-

3.1.3. Energy balance The energy balance equation for the moist air through the pad can be written as Eq. (3):

dimensional.

̇ p T|x − mc ̇ p T|x + dx + qA|x − qA|x + dx + qv̇ Adx = 0, q = −keff mc

For mass, momentum and energy balances, and also for exergoeconomic analysis, all the required and auxiliary equations are given in the Appendix.

d (ρucp T ) dx

= keff

d2T dx 2

dT ⇒ dx

+ qv̇ (3)

where, cp and T are the heat capacity and temperature of moist air respectively, q̇v is the rate of the heat source term, W/m3, and keff is the effective thermal conductivity of moist air. The above equations are subject to the following boundary conditions:

3.1. Mass, momentum and energy balances 3.1.1. Mass balance The mass conservation equation for moisture transport to the air within the pad, which is shown schematically in Fig. 2, can be written as follows:

@ x = 0: u = uin , T = Tin, Y = Yin

@ x = L:

∂T ∂x

= 0, x=L

∂Y ∂x

=0 x=L

Fig. 2. The schematic of the differential element in the mathematical model with energy and mass flows. 256

(4)

(5)

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

battery capacity was equal only to the power consumption by the electrical devices in the system such as air blower and water pump, only the exergy gained by the outlet humid air must be considered in the exergy efficiency definition. The total input exergies to the system are the exergy of incident solar irradiation on the PV panel, the exergy of the inlet air and the exergy of the inlet water to the system. According to the above explanations, the exergy efficiency of the system is given by the following equation:

3.2. Exergoeconomic analysis For a better understanding of the economic assessment of an energy system, the losses within the system must be considered. The exergy analysis is a potential tool to determine the system irreversibilities that cause losses in the system. Thus, exergoeconomic analysis is a suitable method to achieve this goal. The economic assessment of a system based on exergy analysis can determine the cost of products and irreversibilities in the system. In this approach, the cost partition criteria are used, which are a function of exergy content of every energy flow that takes place within the system (De Oliveira, 2013). In the appropriate design of a high-performance evaporative air cooler, besides the consideration of technical performance, its economic assessment also should be taken into account. In the economic analysis of a system, the major costs involved such as initial capital investment, operating and maintenance expenses, fuel costs and the total final cost of the system must be considered. In mathematical modeling of an evaporative cooling system, the thermo/exergoeconomic analysis of the system gives two sets of equations: exergy-based cost partition criteria and cost rate balances. The results provided by exergoeconomic analysis give more detailed cost balances and are quite unlike that obtained by other methods such as internal rate of return, payback period and net present value.

ηex =

∑ Qċ .v. ⎛⎜1 − j=1

⎝

T0 ⎞ ̇ ⎟ − WC . V . + (∑ ṁ i ex i − Tj ⎠

̇ ∑ ṁ e exe) = T0 Sgen

N

N

∑ Cė ,k + Ċw,k = Cq̇ ,k + ∑ Ci̇ ,k + Zk̇ e

(10)

i

This equation for a system shows that the total cost of all output streams from the system equals the total cost to attain them. In this study, according to the above explanations, the exergy cost balance rates for components are summarized in Table 3. By a combination of cost rate balances in Table 3, the cost balance equation for the entire system can be written as:

̇ + ZECP ̇ ̇ + C5̇ + C7̇ − Csṫ , ECP C9̇ = ZPV + Z ̇wP + ZAC

(11)

The cost source in a system component may be grouped into two categories. The first consist of non-exergy-related costs (capital investment, operating and maintenance expenses), while the second category consists of exergy destruction and exergy loss. In evaluating the performance of a component, we want to know the relative significance of each category. This is provided by the exergoeconomic factor of the system that is defined as follows:

fex − eco =

̇ Ztotal ̇ ̇ , total Ztotal + cf Edes

(12)

4. Results and discussion In this section, at first, the experimental results are reported and finally, the results of system modeling and exergoeconomic analysis of the system are discussed. In the experiments, the effect of inlet air rate, temperature, humidity and pad types on the conditioned air was investigated. In the modeling of the system, at first, the model was validated, then the influence of effective parameters on the performance of the system was analyzed.

(6)

where, T0 is the temperature of dead state and ex is the specific exergy of flows. According to schematic representation shown in Fig. 1, the exergy rate balances and related expressions for each component of the system is given in Table 2. By a combination of exergy rate balances in Table 2, the exergy balance equation of the entire system can be written as:

̇ , in + E5̇ + E7̇ − Esṫ , ECP − E9̇ − Edes ̇ , total = 0 Esolar

(9)

3.2.2. Cost rate balances The exergy cost rate balance for the kth component of the system is expressed as the following equation:

3.2.1. Exergy balances Exergy is the maximum amount of work theoretically available by bringing a resource into equilibrium with its surrounding through a reversible process. The actual work output from a system is much smaller due to the system irreversibilities. The work loss in a continuous process is the difference in the exergy before and after the process. In contrast to energy, exergy is not conserved and decreases in irreversible processes. Exergy analysis provides an alternative and illuminating means of assessing and comparing processes and systems rationally and meaningfully. In particular, exergy analysis gives a true measure of how nearly actual performance approaches the ideal and identifies causes and locations of thermodynamic losses more clearly than energy analysis. Consequently, exergy analysis can assist in improving and optimizing designs (Dincer and Rosen, 2008). The general exergy balance equation for an open system at steadystate is expressed as follows (Bejan, 2016): n

ṁ a, out ex a, out + Esṫ , ECP ψIg APV + ṁ a, in ex a, in + ṁ v ex w

4.1. Experimental results 4.1.1. Effect of inlet air rate on the properties of outlet air The effect of inlet air rate on the temperature and relative humidity of conditioned outlet air from the system for two types of pads and three thicknesses of 15, 30 and 45 cm is shown in Fig. 3(a) and (b), respectively. As the results outlined in Fig. 3(a), the temperature of the

(7)

In Eq. (7), Esṫ , ECP is the rate of power exergy that is stored by the ̇ , in is the exergy rate of incident solar irradiation on the battery, Esolar ̇ , total is the total exergy destruction within photovoltaic panel, and Edes the system. Finally, using Eqs. (A.7)–(A.10), the exergy balance equation for the entire system, Eq. (7) can be finalized as the below equation:

Table 2 The exergy rate balances for system components.

̇ , total = 0 ψIg APV + ṁ a, in ex a, in − ṁ a, out ex a, out + ṁ v ex w − Esṫ , ECP − Edes (8)

Component

Exergy rate balance

Solar photovoltaic panel

Water pump

̇ ̇ − Edes ̇ , PV = 0 Esolar , in − PPV ̇ − ẆP − Ẇ AB − Esṫ , ECP − Edes ̇ , ECP = 0 PPV ̇ , AB = 0 Ẇ AB + E5̇ − E6̇ − Edes ̇ , wp = 0 Ẇwp + E7̇ − E8̇ − Edes

Air cooler

̇ , Ac = 0 E6̇ + E8̇ − E9̇ − Edes

Electrical control panel

The exergy efficiency of a system is defined as the ratio of the net exergy gained by the system to the total exergy input to the system. The net exergy gained by the present system is the exergy of outlet humid air and the amount of the exergy that is stored in the battery. If the

Air blower

257

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

Table 3 The cost rate balances for the system. Component

Cost rate balance

Solar photovoltaic panel Air blower

̇ C2̇ = ZPV ̇ C3̇ + C4̇ + Csṫ , ECP = ZECP + C2̇ ̇ + C4̇ + C5̇ C6̇ = ZAB

Water pump

C8̇ = Z ̇wp + C3̇ + C7̇

Air cooler

̇ + C8̇ + C6̇ C9̇ = ZAC

Electrical control panel

conditioned air increases with an increase in inlet air rate. On the other hand, the results indicate that the cellulose pad is more efficient than the straw pad. The reason for this is the higher amount of contact surface between water and air flows for the use of cellulose pads and the higher mass and heat transfer rates. Also, according to the results, the temperature reduction for the pad with a higher thickness is higher. Because for a thicker pad, the amount of heat and mass transfer between air and water within the system is greater due to the increase of contact surface that leads to achieving a conditioned air with lower temperature. By increasing the pad thickness from 15 to 30 cm, the temperature reduction is more noticeable, but for larger thicknesses, outlet temperature changes are negligible, which indicates that for more than 30 cm thickness of pads the air is almost in its saturation state. The results in Fig. 3(b) demonstrate that when the flow rate of the inlet air decreases, the heat and mass transfer between the air and the water inside the cooler decreases, and consequently the relative outlet air humidity is decreased. This reduction for the cellulose pad is more than the straw pad. Also, the results indicate that the main changes in air humidity are taken in the first 15 cm of pad thickness. For a specific flow rate, for example, a flow rate of 500 m3/h, the 68% saturation is achieved in the cellulose pad at the first 15 cm, a 21% saturation in the second 15 cm, and only 11% occurs at the last 15 cm of pad thickness. It can be explained that the higher driving force of heat and mass transfer in the first section of the pads leads to more saturation of the air.

Fig. 4. Temperature variations along the system for cellulose and straw pads and different air rates.

changes for the cellulose pad are greater than that of the straw, which demonstrates that the cellulose pad in the direct evaporating of air is more efficient than the straw pad.

4.2. Model results 4.2.1. Model validation In order to investigate the effect of different operational and structural parameters such as flow rate, temperature, velocity and humidity of the inlet air, as well as the effect of thickness and type of used pads in the system, the proposed model for the system should first be approved and validated. After the validation of the model, the effect of mentioned parameters on the performance of the system can be studied. For model validation, these criterions, the root mean square error, RMSE, coefficient of determination, R2 and mean bias error, MBE were chosen that are defined as follows (Willmott and Matsuura, 2006):

MBE =

4.1.2. Temperature changes along the pad inside the system The temperature changes along the system for two types of pads with 45 cm in thickness and for various inlet air rates are shown in Fig. 4. Based on the previous explanations, the results show that the main changes occur at the first 15 cm of pad thickness and the rate of temperature changes is higher for cellulose pad and for lower air rates. In the pad entrance, the mass driving force is higher, so, the vapor is more transferred within the air that leads to a higher reduction in the air temperature. Also, the graphs show well that, the temperature

1 N

N

∑ j=1

bj − oj oj

(13)

N

∑ (oj − bj )2 RMSE =

j=1

N

(14)

Fig. 3. Variations of outlet air properties for two types of pads at different inlet air rates (Tin = 30 °C and RH = 30%) (a) Outlet temperature, (b) Outlet humidity. 258

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al. N

described in Figs. 6 and 7. The effect of ambient air temperature on the exergy efficiency of the system is shown in Fig. 6(a). The results show that the exergy efficiency of the system is lower for hotter climate zones. As air with higher temperature enters the cooler, the exergy of inlet air increases and according to Eq. (9), the exergy efficiency of the system decreases. When the temperature of inlet air increases, its exergy increases, and these variations are greater than the increase in the exergy of the outlet air due to humidification process. Form the results in Fig. 6, the exergy efficiency of the system is higher for cellulosic pad thickness with greater thicknesses at any ambient air temperature, but most changes occur at the pad entrance and for pad thicknesses greater than 15 cm the changes in system exergy efficiency are not significant. The influence of inlet air temperature on the entropy generation and irreversibilities within the system is shown in Fig. 6(b). The results illustrate when hotter air enters the cooler, the amount of irreversibilities decreases. Since by an increase in the inlet air temperature, the temperature difference between the inlet and outlet air decreases, therefore the entropy generation within the system decreases. On the other hand, when the thicker cellulose pad is selected, the irreversibility increases due to increasing irreversible process such as air pressure drop through the pad thickness, and also the difference between humidity and temperature of inlet and outlet air increases and as a result, the entropy generation increases. This increase is more significant for pad thickness from 5 to 30 cm, and there are no significant changes for thicker pads.

∑ (oj − bj )2 R2 = 1 −

j=1 N

∑ (oj − o¯)2 j=1

(15)

where, in Eqs. (13)–(15), N is the number of data, oj and bj are the ith experimental data and corresponding model value, and o¯ is the average value of the experimental data. The value of R2 varies between 0 and 1, and the larger value shows the better corresponds to the model and the experimental data. Also, for RMSE and MBE, smaller values represent better matches. For the present system, the model results were compared with all experimental data and for some conditions with greatest deviations, the results of error analysis were reported in Table 4 for air rate in the range of 300–1500 m3/h. The results in Table 4 show that for different experimental conditions, the developed model can predict the temperature and humidity of the outlet conditioned air with good accuracy. For most conditions, the error analysis shows that the model has reasonable accuracy and its prediction for outlet humidity is more accurate than outlet temperature based on lower RMSE and higher R2. Maybe it is due to the fact that in the energy balance of the cooler, the thermal losses from the cooler were not considered, although its magnitude is so negligible. 4.2.2. Effect of water temperature on exergy efficiency and irreversibility The effect of water supply temperature on the exergy efficiency of the system for various thicknesses of the cellulose pad is shown in Fig. 5(a). By increasing the water temperature for each thickness of the pad, exergy efficiency is increasing. The reason for the increase in exergy efficiency of the system is the faster evaporation of water at higher temperatures. According to Eq. (9), although by increasing in the water temperature its exergy increases, but the increase of outlet air exergy is more significant due to the increase in the vapor transferring to the air and increase in the outlet air exergy, and as a result, the exergy efficiency of the system is increased. In addition, the results in Fig. 5(a) indicated that when a thicker pad is used in the cooler, the exergy efficiency of the system for a specified temperature is higher due to more heat and mass transfer between air and water within the system. However, the system efficiency changes are more severe for pad thicknesses less than 30 cm. For a given temperature of the incoming water, i.e. 26.85 °C, by increasing the thickness of the pad from 5 to 10, 15, 30 and 45 cm, the exergy efficiency increases as 53.7, 24.7, 20.3 and 1.3% respectively, which represents the greatest changes among of small thicknesses. The variation of irreversibility within the system versus inlet water temperature and for a pad with various thicknesses is shown in Fig. 5(b). It is clear that an increase in the water temperature for each thickness, the amount of entropy generation inside the system increases, and therefore the irreversibility is also increased. But this does not mean that as the water temperature rises, the total exergy efficiency of the whole system decreases. The increase in irreversibility is accompanied by an increase in the exergy efficiency, and when the water temperature increases both exergy efficiency and irreversibility within the system are increased. Finally, by taking into account the results of Fig. 5, it is concluded that the choice of a cellulose pad with 15 cm in thickness in the system is more suitable to achieve a high exergy efficiency and less irreversibility.

4.2.4. Effect of inlet air wet-bulb depression The evaporative cooler is suitable for hot and dry climate conditions, and by using an air dryer system such as solid and liquid desiccant system, it can be used also in warm and humid weather conditions. Thus, the inlet air conditions to the cooler have the most important effect on the performance of the system. The effect of inlet air on the exergy efficiency of the system and system irreversibilities were discussed before. The effect of inlet air humidity on the air temperature drop within the system is shown in Fig. 7. From the results in Fig. 7, the larger air temperature drop in the evaporative cooling system for inlet air flows with more humidity is obvious. The temperature difference between the dry and wet bulbs of the inlet air is introduced as wet-bulb depression. A greater wet-bulb depression indicates that the air can absorb more amount of water to reach its saturation state. For a direct evaporative cooler, to achieve a suitable conditioned air and a system with high saturation efficiency, a greater wet-bulb depression is more suitable. When an inlet air with higher wet-bulb depression enters the cooler, a thicker pad can produce more temperature drop due to the higher contact area and consequently more ability of air to absorb water. These results also show that an appropriate pad thickness must be used to achieve a suitable conditioned air and reasonable air temperature drop within the system, and for pads with more thicknesses not only will no significant changes occur in the properties of outlet air, but also the irreversibilities within the system are increased.

Table 4 The results of error analysis of model validation for various conditions.

4.2.3. Effect of inlet air temperature on exergy efficiency and irreversibility If the aim is to evaluate the efficiency of these systems in different climatic zones, for example, different climate zones in terms of temperature and humidity of the inlet air, the effects of these variables on the performance of the system are so important. The effect of supply water temperature on the exergy efficiency of the system and irreversibility within the system was investigated already, and the effect of inlet air temperature and humidity on the mentioned parameters are 259

Conditions

RMSE

R2

MBE

Outlet temperature, 15 cm thickness of cellulose pad Outlet temperature, 30 cm thickness of cellulose pad Outlet temperature, 45 cm thickness of cellulose pad Outlet humidity, 15 cm thickness of cellulose pad Outlet humidity, 30 cm thickness of cellulose pad Outlet humidity, 45 cm thickness of cellulose pad

0.0590

0.9833

−0.0025

0.0332

0.9448

0.0013

0.0240

0.9554

−0.0002

0.0042 0.0051 0.0320

0.9885 0.9695 0.9675

−0.0031 0.0028 −0.0011

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

Fig. 5. Influence of water temperature on (a) exergy efficiency of the system, and (b) system irreversibilities for various thicknesses of cellulose pad (Tin = 30 °C, Q = 1000 m3/h, RH = 30%).

Fig. 6. Influences of air temperature on (a) exergy efficiency, and (b) system irreversibilities at different thicknesses of cellulose pad (Q = 1000 m3/h, RH = 30%).

These results indicate that when a lower air rate enters the cooler, for example, 200 m3/h, a cellulose pad with a thickness of 15 cm gives the maximum system exergy efficiency, while for air rate greater than 200 m3/h, a thicker pad is needed. These results are good results that obtained in this study since for such a system, for a specified air rate, the maximum pad thickness can be selected to achieve the maximum system exergy efficiency with lower irreversibilities. The results in Fig. 8(b) show that for thinner pads, the irreversibilities within the system are greater for smaller air flow rates and for thicker pads, the irreversibilities for larger flow rates are greater than smaller rates. By increasing the thickness of pad for each air rate, the irreversibility increases until it reaches a constant value. For large flow rates at smaller thicknesses, the difference in properties between inlet and outlet airs is lesser compared to the smaller flow rates, and consequently, the entropy generation within the system is lower. For larger air rates with thicker pads, since the outlet air gains more humidity than inlet air, the entropy generation within the system increases.

Fig. 7. Influences of wet bulb depression on the air temperature drop at different thicknesses of cellulose pad (Q = 1000 m3/h).

4.2.5. Effect of inlet air rate on the system exergy efficiency The inlet air flow rate within the system can determine the capacity of the cooler. Fig. 8 shows the effect of inlet air rate on the system exergy efficiency and irreversibilities for various pad thicknesses. The results in Fig. 8(a) show that the maximum system exergy efficiency is about 20% for mentioned conditions and can achieve for lower flow rates with thinner pads and for larger flow rates with thicker pads.

4.3. Exergoeconomic analysis of the system 4.3.1. Effect of water temperature The effect of the water temperature on the exergy cost of the outlet air from the system for various thicknesses of the cellulose pad is shown in Fig. 9(a). The exergy cost of the outlet air increases with increasing 260

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

Fig. 8. Influences of inlet air rate on (a) the system exergy efficiency, (b) system irreversibilities at different pad thicknesses (Tin = 30 °C, RH = 30%).

water temperature due to more humidification of air through the system. It is also observed that, with an increase in the thickness of the pad up to 15 cm, the exergy cost of outflow air increases and for greater thicknesses, it increases with fewer rates. When warmer water exposed to contact with air, the amount of more vapor diffuses to the air, and as a result, the exergy of outlet humid air and consequently the exergy cost of outlet air increases. Fig. 9(b) shows the effect of the water temperature on the cost rate of exergy destruction for different pad thicknesses. The cost rate of exergy destruction increases with increasing water temperature. This can be explained by the fact that when warmer water is contacted by air, more vapor transfers to the air and as a result, the exergy of outlet air increases. In this condition, the difference between inlet and outlet exergy within the system increases and consequently the entropy generation is more than colder waters. Therefore, warmer water in the evaporative cooler system leads to destroying more exergy, and this destruction is higher for thicker pads due to more heat and mass transfer. The most changes in the cost rate of exergy destruction occur in the pads with a thickness of 5–30 cm and for thicker pads, no significant changes are observed. The effect of the water temperature on the exergoeconomic factor for various pad thicknesses is shown in Fig. 10. As mentioned already (see Fig. 9(b)), with increasing water temperature, the cost of exergy destruction within the system increases and consequently, according to Eq. (12), the exergoeconomic factor of the system decreases. This

Fig. 10. Influences of water temperature on the exergo-economic factor at different pad thicknesses.

means that warmer water in the evaporative air coolers increases the cost of exergy destruction and as a result, is not economically suitable for the system. Also, correspondence to the results in Fig. 10, the exergoeconomic factor of the system for pads with a smaller thickness is higher. By increasing the water temperature from 15 to 27 °C, the exergoeconomic factor of the system decreases by about 57% for all pads. At a fixed water temperature, when pad thickness increases from 5 to 15 cm, the exergoeconomic factor of the system decreases about 19%,

Fig. 9. Influences of water temperature on (a) the exergy cost rate, and (b) exergy destruction cost rate at different pad thicknesses. 261

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

while for 15 to 45 cm, this factor decreases about 15%. This result indicates that the optimum pad thickness in the system has an important effect on the exergoeconomic factor of the system, and for designing and manufacturing of a cost-effective such system, the pad thickness must be selected based on accurate calculations.

4.3.2. Effect of inlet air flow rate The effect of inlet air temperature on the cost rate of exergy and exergy destruction for different pad thicknesses is shown in Fig. 11(a) and (b) respectively. According to Eq. (11), the exergy cost of the conditioned air outlet from the system is equal to the exergy cost of inlet flows and the rate of fixed and operational investment costs. Therefore, when the inlet air rate increases, according to the results in Fig. 11(a), the exergy cost of the outlet air increases. This increase is higher for pads with a larger thickness. Because for pads with larger thicknesses, more moisture is transported within the air, and consequently its exergy cost increases. It means that when a greater air rate enters the cooler, more costs are forced to the system and its performance decreases. The rate of increase of exergy cost for thicker pads is more significant than thinner pads. Noteworthy changes are observed for pads with thicknesses of 5–30 cm, and for greater thicknesses, there are no significant changes in exergy cost rate. Fig. 11(b) shows that the cost rate of exergy destruction of the system increases with increasing inlet air rate for pads with different thicknesses. The increase in the cost rate of exergy destruction is much lower compared to the cost rate of exergy for all pads (Fig. 11(a) and (b)). It can be explained that when the greater air flows enter the system, the reduction of outlet air temperature is lower, and consequently, the entropy generation within the system and exergy destruction is lower. In other words, the increase in the cost rate of exergy due to increases in the exergy of inlet flows compared to increasing in exergy destruction cost rate due to entropy generation within the system is more significant. On the other hand, when greater air enters the system, the pressure drop through the thicker pads increases and as a result, the exergy destruction for thicker pads increases. The effect of inlet air rate on the exergoeconomic factor of the system for different pad thicknesses is shown in Fig. 12. As can be seen from the figure, with increasing the flow of inlet air, the exergoeconomic factor of the system decreases. It can be explained that when the inlet air increases, the air pressure drop within the pad and consequently the rate of exergy destruction caused by pressure drop increase. Rustles indicate that when a lower air rate enters the system for a 15 cm thick pad, for example about 200 m3/h, the exergoeconomic factor of the system increases up to about 0.8. It means that for low air rates and thinner pads about only 20% of the total cost is destructed,

Fig. 12. Influences of air rates on the exergoeconomic factor of the system for different pad thicknesses.

while for larger air rates, for example, 1400 m3/h, and thicker pads up to 70% of the total cost is destructed. Also, the results illustrate that about 60% of total cost destruction can be observed when the pad thickness is increased from 5 to 10 cm, and only 40% of the total cost is destructed with increasing in the pad thickness from 10 to 45 cm.

4.3.3. Effect of inlet air temperature The effect of the inlet air temperature on the exergy cost rate of the conditioned outlet air from the system for various thicknesses of the pad is shown in Fig. 13(a). Results demonstrate that with an increase in the temperature of the inlet air, the cost exergy of outlet air decreases. It can be explained that when a warmer air enters the system, the conditioned air is warmer and it may not stay in the comfort zone. Therefore, its cost is decreased. Although when a warmer air enters the system the exergy cost of conditioned air for all pads decreases, but the exergy cost for thicker pads is higher. It means that for zones with warmer airs, thicker pads must be selected to achieve conditioned air with higher exergy cost. When the temperature of inlet air to the system increases from 26 to 34 °C, the exergy cost rate decreases about 40 and 33% respectively for pads with thicknesses of 45 and 5 cm. Also, as previously described, when the inlet air temperature increases, the most changes for exergy cost rate is for pad thickness of 5 to 30 cm, and for thicker pads, no significant changes are observed. Fig. 13(b) shows that warmer air input to the cooler decreases the cost rate of exergy destruction. For warmer air, the system capacity to a reduction in the temperature of the air is lower, and consequently, the temperature difference between inlet and outlet airs is lower. Therefore, the exergy destruction within the system decreases. On the other hand, the cost rate of exergy destruction for pads with higher

Fig. 11. Influences of air rates on (a) exergy cost rate, and (b) exergy destruction cost rate at different pad thicknesses. 262

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

Fig. 13. Influences of inlet air temperature on (a) exergy cost rate, and (b) exergy destruction cost rate at different pad thicknesses.

The results demonstrate that in the early years of the system lifetime, the exergoeconomic factor of the PV-based air cooler is lesser than a conventional system with the same conditions. For the next years of the system lifetime, the exergoeconomic factor of the PV-based cooler is greater than the conventional system and is almost constant, while the exergoeconomic factor of the conventional system continuously decreases during system lifetime. It can be explained that the solar system has a higher initial investment for purchasing photovoltaic panel and more exergy destruction due to the conversion of solar irradiation to the electricity, while the conventional system has lower exergy destruction, and as a result, the exergoeconomic factor of the conventional system is greater than the solar system for the early years. For later years, after about four years, the exergoeconomic factor of the conventional system is lower than the solar system due to the increase in annual electricity cost. The results also show that for lower inlet air rates, the exergoeconomic factor of two systems is higher than larger flow rates. For an evaporative system with solar panel and inlet air rate of 600 m3/h during 15 yr of system lifetime, the exergoeconomic factor decreases about 38%, while for a conventional system with the same cooling capacity it decreases about 77%. The present work gives some suitable information about the PV-based evaporative air cooler systems, and it seems that for feature works, more studies must be carried out on these systems. Some other gaps such as the usage of theses system in night times, use in hot and humid weather conditions and coupling with adsorption systems can be guidelines for future works.

thicknesses is greater than thinner thicknesses due to the increase in the pressure drop and irreversibilities inside the system. The cost rate of exergy destruction compared to the exergy cost rate of conditioned air is so low, but this value for thicker pads is more considerable rather than thinner pads. The exergy destruction cost rate for thicker pads is almost twice the thinner pads. The effect of the inlet air temperature on the exergoeconomic factor of the system for different thicknesses of the pad is shown in Fig. 14. Results indicate that the exergoeconomic factor of the system is higher for warmer air flows. This can be justified that according to the results in Fig. 13(b) when a warmer air enters the system, the cost rate of exergy destruction decreases and consequently the exergoeconomic factor of the system increases. The most changes in the exergoeconomic factor of the system by increasing in the inlet air temperature occur for pad thicknesses from 5 to 30 cm, and for thicker pads no significant variation observed. By an increase in the inlet air temperature from 26 to 34 °C, the exergoeconomic factor of the system for pad thickness of 5 cm increases about 52%, while for 45 cm thickness increases about 60%.

4.4. Comparison of the performance of the studied system and conventional systems The performance of the current system is compared with a conventional direct evaporative air cooler by considering the economic and technical aspects of the systems in this section. The results of the previous studies are compared with the results of the present work. Farmahini-Farahani et al. obtained that the exergy efficiency of direct evaporative coolers are estimated 20%, while the indirect evaporative coolers are more efficient in hot and dry climate with approximate exergy efficiency of 55% (Farmahini-Farahani et al., 2012). The maximum exergy efficiency of an evaporative air cooling system installed in a Malaysian building was obtained as about 42% (Taufiq et al., 2007b). The mentioned systems used the common electricity source while for the present system with a photovoltaic panel, the maximum exergy efficiency is obtained about 20% and by accurate selection of the operating parameters and pad type and thickness, the exergy efficiency up to 45% can be obtained. The exergoeconomic factor of the current system and a conventional system versus the lifetime of the systems for 600, 1000 and 1400 m3/h inlet air rates are shown in Fig. 15. These results are for a conventional system that uses urban electricity and a PV-based evaporative air-cooling system that a photovoltaic panel supplies its required electricity. The cost of electricity consumed for the conventional system was considered as 0.04 $ per hour of operation, with an annual inflation rate of 5%.

Fig. 14. Influences of air temperature on the exergoeconomic factor at different pad thicknesses. 263

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

Fig. 15. Variation of the exergoeconomic factor during systems lifetime, for a conventional system and present system.

5. Conclusions

15 cm, and for thicker pads changes are not significant. Water temperature changes from 15 to 27 °C can enhance the exergy efficiency of the system from 12 up to 40%, and decrease the exergoeconomic factor of the system up to 55%. For an inlet air with a temperature of 30 °C and relative humidity of 30%, the maximum system exergy efficiency that can be obtained for a pad with all thicknesses is 20%. When the inlet air flow rate increases from 300 to 1500 m3/h, the exergoeconomic factor of the system decreases up to 57%. When the inlet air temperature increases from 26 to 34 °C, the exergoeconomic factor of the system is increased up to 60%. The exergoeconomic factor of the conventional system for the first four years of its lifetime is greater than solar system due to the larger initial investment of solar system and more exergy destruction due to the conversion of solar irradiation to the electricity. For later years, the exergoeconomic factor of the conventional system is lower than the solar system due to its larger operating cost especially the cost of consumable electricity.

In this work, a PV-based direct evaporative air-cooling system was investigated both experimentally and theoretically. In experiments, the effect of pad type (straw and cellulose pads), pad thickness and inlet air rate on the system performance was tested. A differential mathematical model was developed for the system and an exergoeconomic analysis was carried out to evaluate the system performance and economic aspects of the system in different operating conditions. After model validation, the effect of various parameters on the exergy cost rate of conditioned air, exergy destruction within the system, and exergoeconomic factor of the system was analyzed. Finally, the performance of the present system was compared with a conventional system with the same specifications that it uses urban electricity. The results show that the most changes in the properties of the conditioned air can achieve by a cellulose pad with a thickness of Appendix

1. Equations for mass, momentum and energy balances: According to Hawlader and Liu (Hawlader and Liu, 2002), ṁ v and q̇v can be described by the following equations:

ṁ v = K a (Ysat − Y )

(A.1)

qv̇ = K a (hsat − h)

(A.2)

where K a is the volumetric mass transfer coefficient and is estimated as follows (J. M. Wu et al., 2009a):

K a = 20.4 × V 0.65

(A.3)

In Eq. (A.3), V is the frontal velocity of air. The enthalpy of moist air for Eq. (A.2) is given by the following equation (Wu et al., 2009a): 264

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

h = cp (T − 273.15) + (2.5 × 106 + 1840) Y

(A.4)

The effective mass diffusion coefficient of water vapor in the air is expressed by the following equation (Zhang et al., 2003):

T 1.81 ⎞ × 10−5 Deff = 2.256 ⎛ 256 ⎝ ⎠

(A.5)

The air pressure drop along the pad thickness in the momentum balance equation in the location of x from the air inlet section is estimated based on the MUNTERS manufacture company data, pad model of CELdek® 7090-15 and given by the following equation:

Δp (Pa) = (15.388 ∗ u2 − 6.8702 ∗ u + 4.2326) ∗ (x /0.15)

(A.6)

where u is the velocity of air inside the pad. 2. Equations for exergy and cost balances: The exergy rate of incident solar irradiation on the photovoltaic panel is expressed as:

̇ , in = ψIg APV Esolar

(A.7)

The relative potential of the maximum useful work available from radiation ψ is defined as (Badescu, 2018, 2014, 1999):

ψ=1−

4T0 1 T + ⎛ 0⎞ Ts 3 ⎝ Ts ⎠ ⎜

4

⎟

(A.8)

where Ts is the sun temperature, which is about 5800 K. Eqs. (A.9) and (A.10) gives the total flow exergy of humid air per kg of dry air, and the specific flow exergy of liquid water respectively (Bejan, 2016)

et = (cp, a + Ycp, v ) T0

(

T T0

T

)

p

− ln T − 1 + (1 + 1.608Y ) Ra T0 Ln p +

Ra T0 ⎡ (1 + 1.608Y ) Ln ⎣

0

(

1 + 1.608Y0 1 + 1.608Y

0

)

1.608Y

+ 1.608Y Ln 1.608Y ⎤ 0⎦

(A.9)

p0, w ⎞ e w ≅ −Rv T0 ln ⎛⎜ ⎟ p ⎝ sat (T0 ) ⎠

(A.10)

The exergy cost of each stream of matter Ci̇ , the exergy cost rate associated with work as well as heat transfer through the system are given as the following equations:

Ci̇ = ci Ei̇ = ci (ṁ i ei )

(A.11)

Ċw = c w Ẇ

(A.12)

Cq̇ = cq Q̇

(A.13)

In Eqs. (A.11)–(A.13), the lowercase c denotes the average costs per unit cost of exergy ($/GJ). The Zk̇ in Eq. (10), is the sum of the capital OM CI investment rate Zk̇ and operating and maintenance cost rate Zk̇ . The kth component operating and maintenance cost rate is expressed as follows (Ahmadi and Dincer, 2011): OM

Zk̇

=

ZkOM φCRF 3600ha

(A.14) th

The purchase equipment cost of the k component in the system is in US dollars. In Eq. (A.14), the annual maintenance factor φ is considered as 1.1, the annual operating hours ha of the system, are expressed as 48 h per week or 2308 h in a year. The capital recovery factor CRF is introduced as (Bejan et al., 1996):

CRF =

i (1 + i)n (1 + i)n − 1

(A.15)

where i is the interest rate, and n is the component lifetime and are considered as 10% and 10 yr respectively. The cost rate of exergy destruction within the system is a hidden cost for a process in the system components. Therefore, the exergy destruction cost rate is defined as:

CḊ , k = cf , k EḊ

(A.16)

where cf , k is the fuel average cost per unit of exergy of the kth component in the system.

Badescu, V., 2014. How much work can be extracted from a radiation reservoir? Phys. A Stat. Mech. Its. Appl. https://doi.org/10.1016/j.physa.2014.05.024. Badescu, V., 1999. Simple upper bound efficiencies for endoreversible conversion of thermal radiation. J. Non-Equilibr. Thermodyn. https://doi.org/10.1515/JNETDY. 1999.011. Bejan, A., 2016. Advanced engineering thermodynamics. Adv. Eng. Thermodyn. https:// doi.org/10.1002/9781119245964. Bejan, A., Tsatsaronis, G., Moran, M.J., 1996. Thermal Design and Optimization. WileyInterscience publication, John Wiley. Belarbi, R., Ghiaus, C., Allard, F., 2006. Modeling of water spray evaporation: application to passive cooling of buildings. Sol. Energy. https://doi.org/10.1016/j.solener.2006.

References Abohorlu Doğramacı, P., Riffat, S., Gan, G., Aydın, D., 2019. Experimental study of the potential of eucalyptus fibres for evaporative cooling. Renew. Energy. https://doi. org/10.1016/j.renene.2018.07.005. Ahmadi, P., Dincer, I., 2011. Thermodynamic analysis and thermoeconomic optimization of a dual pressure combined cycle power plant with a supplementary firing unit. Energy Convers. Manag. https://doi.org/10.1016/j.enconman.2010.12.023. Badescu, V., 2018. How much work can be extracted from diluted solar radiation? Sol. Energy. https://doi.org/10.1016/j.solener.2018.05.094.

265

Solar Energy 193 (2019) 253–266

A. Kiyaninia, et al.

economical considerations. Sol. Energy. https://doi.org/10.1016/j.solener.2017.12. 055. Mohammadi, K., McGowan, J.G., 2019. A thermo-economic analysis of a combined cooling system for air conditioning and low to medium temperature refrigeration. J. Clean. Prod. https://doi.org/10.1016/j.jclepro.2018.09.107. Pandelidis, D., Cichoń, A., Pacak, A., Anisimov, S., Drąg, P., 2019. Performance comparison between counter- and cross-flow indirect evaporative coolers for heat recovery in air conditioning systems in the presence of condensation in the product air channels. Int. J. Heat Mass Transf. https://doi.org/10.1016/j.ijheatmasstransfer. 2018.10.134. Peng, D., Zhou, J., Luo, D., 2017. Exergy analysis of a liquid desiccant evaporative cooling system. Int. J. Refrig. https://doi.org/10.1016/j.ijrefrig.2017.06.021. Sadighi Dizaji, H., Jafarmadar, S., Khalilarya, S., Pourhedayat, S., 2019. A comprehensive exergy analysis of a prototype Peltier air-cooler; experimental investigation. Renew. Energy. https://doi.org/10.1016/j.renene.2018.07.056. Santos, J.C., Barros, G.D.T., Gurgel, J.M., Marcondes, F., 2013. Energy and exergy analysis applied to the evaporative cooling process in air washers. Int. J. Refrig. https:// doi.org/10.1016/j.ijrefrig.2012.12.012. Shukla, A., Tiwari, G.N., Sodha, M.S., 2008. Experimental study of effect of an inner thermal curtain in evaporative cooling system of a cascade greenhouse. Sol. Energy. https://doi.org/10.1016/j.solener.2007.04.003. Taufiq, B.N., Masjuki, H.H., Mahlia, T.M.I., Amalina, M.A., Faizul, M.S., Saidur, R., 2007a. Exergy analysis of evaporative cooling for reducing energy use in a Malaysian building. Desalination. https://doi.org/10.1016/j.desal.2007.04.033. Taufiq, B.N., Masjuki, H.H., Mahlia, T.M.I., Saidur, R., Faizul, M.S., Niza Mohamad, E., 2007b. Second law analysis for optimal thermal design of radial fin geometry by convection. Appl. Therm. Eng. https://doi.org/10.1016/j.applthermaleng.2006.10. 024. Wan, Y., Lin, J., Chua, K.J., Ren, C., 2018. A new method for prediction and analysis of heat and mass transfer in the counter-flow dew point evaporative cooler under diverse climatic, operating and geometric conditions. Int. J. Heat Mass Transf. https:// doi.org/10.1016/j.ijheatmasstransfer.2018.07.142. Willmott, C.J., Matsuura, K., 2006. On the use of dimensioned measures of error to evaluate the performance of spatial interpolators. Int. J. Geogr. Inf. Sci. https://doi. org/10.1080/13658810500286976. Wu, J.M., Huang, X., Zhang, H., 2009a. Theoretical analysis on heat and mass transfer in a direct evaporative cooler. Appl. Therm. Eng. https://doi.org/10.1016/j. applthermaleng.2008.05.016. Wu, J.M., Huang, X., Zhang, H., 2009b. Numerical investigation on the heat and mass transfer in a direct evaporative cooler. Appl. Therm. Eng. https://doi.org/10.1016/j. applthermaleng.2008.02.018. Yang, Y., Cui, G., Lan, C.Q., 2019. Developments in evaporative cooling and enhanced evaporative cooling. A Rev. Renew. Sustain. Energy Rev. https://doi.org/10.1016/j. rser.2019.06.037. Zhang, L., Liu, X., Jiang, Y., 2015. Exergy analysis of parameter unmatched characteristic in coupled heat and mass transfer between humid air and water. Int. J. Heat Mass Transf. https://doi.org/10.1016/j.ijheatmasstransfer.2015.01.023. Zhang, X.J., Dai, Y.J., Wang, R.Z., 2003. A simulation study of heat and mass transfer in a honeycombed rotary desiccant dehumidifier. Appl. Therm. Eng. 23, 989–1003. https://doi.org/10.1016/S1359-4311(03)00047-4. Zhao, H.X., Magoulès, F., 2012. A review on the prediction of building energy consumption. Renew. Sustain. Energy Rev. https://doi.org/10.1016/j.rser.2012.02.049.

01.004. Bishoyi, D., Sudhakar, K., 2017. Experimental performance of a direct evaporative cooler in composite climate of India. Energy Build. https://doi.org/10.1016/j.enbuild.2017. 08.014. Camargo, J.R., Ebinuma, C.D., Silveira, J.L., 2005. Experimental performance of a direct evaporative cooler operating during summer in a Brazilian city. Int. J. Refrig. https:// doi.org/10.1016/j.ijrefrig.2004.12.011. Chengqin, R., Nianping, L., Guangfa, T., 2002a. Principles of exergy analysis in HVAC and evaluation of evaporative cooling schemes. Build. Environ. https://doi.org/10.1016/ S0360-1323(01)00104-4. Chengqin, R., Nianping, L., Guangfa, T., 2002b. Principles of exergy analysis in HVAC and evaluation of evaporative cooling schemes. Build. Environ. 37, 1045–1055. https:// doi.org/10.1016/S0360-1323(01)00104-4. Chidambaram, L.A., Ramana, A.S., Kamaraj, G., Velraj, R., 2011. Review of solar cooling methods and thermal storage options. Renew. Sustain. Energy Rev. 15, 3220–3228. https://doi.org/10.1016/j.rser.2011.04.018. Dai, Y.J., Sumathy, K., 2002. Theoretical study on a cross-flow direct evaporative cooler using honeycomb paper as packing material. Appl. Therm. Eng. 22, 1417–1430. https://doi.org/10.1016/S1359-4311(02)00069-8. De Antonellis, S., Joppolo, C.M., Liberati, P., 2019. Performance measurement of a crossflow indirect evaporative cooler: Effect of water nozzles and airflows arrangement. Energy Build. https://doi.org/10.1016/j.enbuild.2018.11.049. De Oliveira, S., 2013. Exergy, exergy costing, and renewability analysis of energy conversion processes. Green Energy Technol. https://doi.org/10.1007/978-1-44714165-5_2. Dincer, I., Rosen, M.A., 2008. Exergy and energy analyses. Exergy. https://doi.org/10. 1016/b978-008044529-8.50005-7. Elmetenani, S., Yousfi, M.L., Merabeti, L., Belgroun, Z., Chikouche, A., 2011. Investigation of an evaporative air cooler using solar energy under Algerian climate. Energy Procedia 6, 573–582. https://doi.org/10.1016/j.egypro.2011.05.066. Enteria, N., Yoshino, H., Mochida, A., Satake, A., Takaki, R., 2015. Exergoeconomic performances of the desiccant-evaporative air-conditioning system at different regeneration and reference temperatures. Int. J. Refrig. https://doi.org/10.1016/j. ijrefrig.2014.11.007. Farmahini-Farahani, M., Delfani, S., Esmaeelian, J., 2012. Exergy analysis of evaporative cooling to select the optimum system in diverse climates. Energy. https://doi.org/10. 1016/j.energy.2012.01.075. Florides, G., Tassou, S., Kalogirou, S., Wrobel, L., 2002. Review of solar and low energy cooling technologies for buildings. Renew. Sustain. Energy Rev. 6, 557–572. https:// doi.org/10.1016/S1364-0321(02)00016-3. Fouda, A., Melikyan, Z., 2011. A simplified model for analysis of heat and mass transfer in a direct evaporative cooler. Appl. Therm. Eng. https://doi.org/10.1016/j. applthermaleng.2010.11.016. Hawlader, M.N., Liu, B., 2002. Numerical study of the thermal–hydraulic performance of evaporative natural draft cooling towers. Appl. Therm. Eng. 22, 41–59. https://doi. org/10.1016/S1359-4311(01)00065-5. Jaber, S., 2016. An assessment of the economic and environmental feasibility of evaporative cooling unit. Appl. Therm. Eng. 103, 564–571. https://doi.org/10.1016/j. applthermaleng.2016.04.090. Kabeel, A.E., Bassuoni, M.M., 2017. A simplified experimentally tested theoretical model to reduce water consumption of a direct evaporative cooler for dry climates. Int. J. Refrig. https://doi.org/10.1016/j.ijrefrig.2017.06.010. Lazzarin, R.M., Noro, M., 2018. Past, present, future of solar cooling: technical and

266