Exergoeconomic analysis and multi-objective optimization of a semi-solar greenhouse with experimental validation

Journal Pre-proofs Exergoeconomic Analysis and Multi-Objective Optimization of a Semi-Solar Greenhouse with Experimental Validation Behzad Mohammadi, Faramarz Ranjbar, Yahya Ajabshirchi PII: DOI: Reference:

S1359-4311(19)33443-X https://doi.org/10.1016/j.applthermaleng.2019.114563 ATE 114563

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

19 May 2019 5 October 2019 17 October 2019

Please cite this article as: B. Mohammadi, F. Ranjbar, Y. Ajabshirchi, Exergoeconomic Analysis and MultiObjective Optimization of a Semi-Solar Greenhouse with Experimental Validation, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/j.applthermaleng.2019.114563

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Published by Elsevier Ltd.

Exergoeconomic Analysis and Multi-Objective Optimization of a Semi-Solar Greenhouse with Experimental Validation Behzad Mohammadi a, Faramarz Ranjbar a,*, Yahya Ajabshirchi b a

Department of Mechanical Engineering, Mechanical Engineering Faculty, University of Tabriz, Iran

b

Department of Biosystems Engineering, Faculty of Agriculture, University of Tabriz, Iran

Abstract Fossil fuels limitation and environmental pollution have justified using renewable energy resources. Utilization of the solar energy as a promising method to supply the heat required for a greenhouse with the aim of endurable agriculture has been an interesting subject for many researchers. In the present work, using MATLAB software, a dynamic model is developed to investigate an innovative semi-solar greenhouse from the thermodynamic and exergoeconomic viewpoints, which, to our knowledge, has not yet been performed for Iran conditions. This simulation is used to estimate the temperature in four different points of the semi-solar greenhouse, considering the crop evapotranspiration. In addition, the total exergy destruction values associated with different processes are inspected. Providing an appropriate thermal condition for the air inside was considered as the aim of the present study. In this regard, the air unit cost of the greenhouse for each time step is analyzed. A multi-objective optimization is conducted considering the total exergy destruction and mean air unit cost as the objective functions. To validate the simulation, the results of the proposed thermodynamic analysis are compared with the measured data recorded every one minute from the constructed typical semi-solar greenhouse. Temperature difference of 19.5 ℃ between the indoor and outdoor air is obtained during the experiment. The mean values of 6.08 % and 2.1 ℃ for MAPE (Mean Absolute Percentage Error) and RMSE (Root Mean Squared Error) indicate the accuracy of the thermal simulation. The results show that using doublelayer glass separated with air-filled space as the greenhouse cover decreases the overall exergy destruction about 45.36%. The multi-objective optimization results obtained from the Pareto frontier also shows total exergy destruction of 8.8623 MJ and mean air unit cost of 15.9164 $/MJ at the optimum point.

Key words: Dynamic model; Semi-solar greenhouse; Evapotranspiration; Exergy destruction; Air unit cost; Multi-objective optimization Nomenclature A

Surface Area (m2)

𝛼

Convection Heat transfer rate coefficient ( 𝑊 𝑚2𝐾

AIR

Energy transfer rate by dry air (W)

C 𝐶

Cost ($)

c

) 𝑘𝑔

𝜌

Density (𝑚3)

𝜆

Conduction Heat transfer rate coefficient (

Cost of air unit ( 𝐽 )

𝜂𝑟𝑑

Shortwave radiation absorption coefficient (-)

CD

Energy transfer rate by conduction (W)

𝜙

Volume flow air ( 𝑠 )

𝐶𝑅𝐹

Capital recovery factor (-)

𝜙𝑚

Mass flow rate ( 𝑠 )

CV 𝐶𝐻2𝑂,𝑎

Energy transfer rate by convection (W) Water vapor concentration at inside air

𝑣

𝐶𝐻2𝑂,𝑜

temperature ( 𝑚3 ) Water vapor concentration at outside air

Wind speed ( 𝑠 )

𝛽𝑔 ― 𝐼𝑠

𝐶𝐻2𝑂𝑠,𝑝

temperature ( 𝑚3 ) Water vapor saturation concentration at

Shortwave reflection coefficient by ground (-)

∆𝑝𝑝 ― 𝐻2𝑂𝑚

Saturation deficit of plant (mbar)

𝐶𝐻2𝑂𝑠,𝑐𝑜𝑖

plant temperature ( 𝑚3 ) Water vapor saturation concentration at

𝜂𝑣ℎ𝑟

Efficiency of ventilation heat recovery (-)

d

inside cover temperature ( Thickness (m)

𝜔

E 𝐸𝑋𝑎,𝑑𝑖𝑓 𝐸𝑋𝑎,𝑡ℎ 𝐸𝑋𝑑 F 𝑓 𝑓𝑎 H 2O I

Emission coefficient (-) Diffusional exergy of inside air (W) Thermal exergy of inside air (W) Exergy destruction (W) View factor (-) Dependency factor for 𝑅𝑠 ― 𝐻2𝑂 (-) Infiltration factor (-) Energy transfer rate by vapor (W) Absorbed shortwave solar radiation on

Φ𝑟

Absolute humidity (kg H2O vapor/kg dry air) Maintenance factor (-)

Subscripts a air coi coo De

Inside air Air Inside cover Outside cover Destruction

dg dif

Deep ground Diffusional

e

Environment

g

Inside ground

$

Cost rate (𝑠) $

𝑘𝑔𝐻2𝑂

𝑘𝑔𝐻2𝑂

𝑘𝑔𝐻2𝑂

𝑘𝑔𝐻2𝑂 𝑚3

𝑊 𝑚𝐾)

𝑚3

𝑘𝑔

𝑚

)

𝑊

i IL IS

area unit (𝑚2) Interest rate (-) Energy transfer rate by long wave radiation (W) Energy transfer rate by short wave radiation (W) 𝑊

𝐼𝑝 ― 𝑔

Heat flow rate absorbed by canopy (𝑚2)

𝑀𝑎𝑖𝑟

Molar mass of dry air (𝑚𝑜𝑙)

H2O

Water

Molar mass of water Mass flow of species (mol)

in

Inlet

leak

Leakage

𝑀𝐻2𝑂 n

𝑘𝑔

𝑘𝑔 (𝑚𝑜𝑙)

𝑜𝑝𝑣ℎ𝑟 P 𝑃𝐻2𝑂𝑠,𝑝

Option ventilation heat recovery (-) Pressure (Pa)

𝑃𝐻2𝑂,𝑎

Vapor pressure of indoor air (𝑚2) Partial pressure (Pa) Heat transfer rate (W)

𝑝𝑖 Q 𝑅

𝑁

Saturation vapor pressure for plant (𝑚2) 𝑁

𝑠

Resistance (𝑚) 𝐽

m nw nwi

Mass North wall Inside north wall

nwo

Outside north wall

o p q

Outdoor air Plant Heat

rd

Radiation

𝑅𝑎

Gas constant of dry air (𝐾.𝑚𝑜𝑙)

𝑅𝑣

Gas constant of H2O vapour (𝐾.𝑚𝑜𝑙)

sc

Screen

Water evaporation heat Temperature (K) Time (s) Volume (m3) Capital investment ($)

sk

Sky

th out vhr w

Thermal Outlet Ventilation heat recovery Work

𝑟𝑤 T t V 𝑍𝑘 𝑍𝑘

𝐽 (𝑘𝑔)

𝐽

$

Capital investment rate (𝑠)

1. Introduction One of the necessities of endurable agriculture is utilization of the energy, economically and productively. Due to the growth in the population of world, a great appetite for higher standards of living and lack of the fertile farmlands, the energy consumption in agriculture has been increased remarkably in the last decades. Increasing the use of fossil fuels for energy generation all over the world has many unwilling effects on the natural resources and environment. In this regard, the solar energy as an abundant, clean and sound source can be considered as a promising energy source instead of the traditional ones. In addition, the solar energy plays a noteworthy role in greenhouse heating with more energy saving and diminished environmental problems. In recent years, many studies on the utilization of the solar energy for the greenhouse heating have been conducted by researchers. Kondili and Kaldellis [1] proposed an integrated geothermal-solar greenhouse. They reported that the proposed system minimized the fossil fuel consumption and led to the improved technical and economical efficiencies. Kiyan et al [2] investigated the thermal behavior of a greenhouse heated by a hybrid solar collector system using a mathematical simulation. They reported that the conventional fossil fuel based systems coupled to the proposed solar collectors are more economically; however somewhat longer payback period should be expected. Joudi and Farhan [3] investigated a solar air heater experimentally for heating a novel greenhouse in winter. The results revealed that the air mass flow rate through the collectors varies from 0.006 to 0.012 kg/s.m2. In addition, the air mass flow rate of 0.012 kg/s./m2 could cover about 84 % of the daily heat consumption to maintain the greenhouse at temperature of 18oC. The closed greenhouses are moving to use maximum amount of solar and other renewable energies to produce more efficient and economic products. It can be seen some significant differences in heating requirement and payback period between the ideal closed and conventional greenhouse layout [4]. Ziapour and Hashtroudi [5] used a curved glass roof for a greenhouse equipped with a thin cover and a PCM tubular collector for saving the energy. The Optimization results using an evolutionary algorithm indicated the optimum values of 7.5 cm and 17 liters for the collector pipe radius and PCM volume, respectively. Performance of Straw block north wall in solar greenhouses investigated by Zhang et al [6]. Improved thermal characteristics such as thermal storage coefficient of storage layer, the total thermal inertia index and the total thermal resistance of the storage wall inspected. By applying this method, the system showed a better performance from the view points of the economic and the environmental. Chen et al [7] recommended an active-passive ventilation wall using PCM monitoring key factors such as performance of middle layer of the wall, the inside thermal condition and the plants’ growth. The proposed methodology showed an increase in the wall’s heat storage capacity, the heat release capacity, plant height and fruit yield. Ozturk [8] provided the thermal energy needed for a greenhouse of 180 m2 using

paraffin wax as a PCM based on the latent heat storage procedure. He examined the effects of various factors on the net energy and exergy efficiencies. It was found that the energy and exergy efficiencies were 40.4 % and 4.2 %, respectively. Hepbasli [9] studied and compared the performance of a greenhouse with three different heating methods involving a solar assisted vertical ground-source heat pump, a wood biomass boiler and a natural gas boiler. The overall exergy efficiency values for the mentioned cases were obtained 0.83 %, 2.90 % and 0.79 %, respectively. Exergy analysis by discussing the energy quality can offer clear and extensive view in costs and complicated processes management to obtain effective method in crop production greenhouses. Yildizhan and Taki [10] used cumulative exergy approach to improve efficiency of tomato production process. They claimed that this method could improve the crop production, energy use and CO2 emissions in different regions of Turkey. The mentioned studies prove that the capability of solar greenhouses to use maximum amount of free solar energy to produce more efficient and economic products and also storing solar energy in warm seasons in order to consume in cold seasons with no need for auxiliary heating systems make the solar greenhouse system be an attractive system to produce agricultural crops. However, the performed literature review reveals that, the comprehensive analysis of semi-solar greenhouse including energy, exergy and exergoeconomic aspects using dynamic model has not yet been performed under Iran’s conditions, to our knowledge. In particular there is little known on the experimental assessment of these systems from the viewpoint of energy and mass transfer. The present work is an attempt to fulfill this lack of information. An innovative dynamic modelling is performed to analysis heat and vapor transfer between components, inspect exergy destruction through heat and mass transfer processes and offer some economic recommendations based on exergoeconomic results. An interesting feature of this study is the use of multi-objective optimization with decision variables of the north wall and soil properties and the length/width of the greenhouse in order to determine the optimal values of total exergy destruction and mean air unit cost. A greenhouse of 15 𝑚2 floor area is constructed and modeling results are validated with measured values of the experimental setting. Furthermore, to assess the accuracy and performance of the greenhouse simulation, some statistical functions have been applied. Authors believe that these simulation results validated by experimental observations will hasten the commercialization of these environmentally benign greenhouses alternatives to conventional systems in Iran. The main novelties and objectives of the present work can be summarized as: To propose a dynamic model to predict the thermodynamic parameters of a semi-solar greenhouse. To apply some statistical functions to assess the accuracy and performance of the greenhouse simulation. To validate the developed model results using the measured data recorded every one minute from the constructed typical semi-solar greenhouse. To perform the exergoeconomic analysis of the semi-solar greenhouse. To use a double layer glass separated with air-filled space as the greenhouse cover to reduce the overall exergy destruction. To perform a multi-objective optimization to determine the optimal total exergy destruction and mean air unit cost. 2. Materials and Methods 2.1 Description of the semi-solar greenhouse A semi-solar greenhouse equipped by thermal screen system was designed and installed at the NorthWest of Iran in Azerbaijan Province: Latitude 38𝑜100′N and Longitude 46𝑜180′E with the elevation of 1364 m above the sea level. Researchers have attempted to evaluate the significant factors, which play a role in designing solar greenhouses in order to maximize the captured solar energy which involves lower environmental impact rather than the conventional energy technologies and decreases the energy lost. The studies on greenhouse heating strategies indicated that heating cost in conventional greenhouses exceeds the 30% of the overall operational cost of the greenhouse [11]. In addition, the shape and orientation of a greenhouse are highly considered as the factors in solar greenhouses to use clean solar energy sources

more than others. In the present study, the experimental structure was based on ‘semi-solar’ greenhouse in order to select the most appropriate shape and orientation of greenhouse. Further, six of the most commonly used shapes of greenhouses such as even, uneven, vinery, single, arch, and quonset types were investigated to increase its solar radiation absorption and thermal efficiency. For this purpose, the meteorological data recorded by Iran Meteorological Office during 1995–2016 were used and accordingly the greenhouse structure was selected after some assessments, as shown in Fig. 1. These greenhouses were evaluated for both east–west and north–south orientation, which were built in the same length, width and height. The selected structure in the orientation of east–west and perpendicular to the direction of the wind prevailing can receive highest amounts of solar radiation among other structures. Furthermore, internal thermal screen (cloth type) and cement north wall were used to store and prevent from losing heat during the cold season of the year. The experimental greenhouse occupies a floor area equal to 15 m2, and the volume of 24 m3 is covered with glass (4mm thickness). The experimental validation was done in this semi-solar greenhouse, where cabbages were grown.

Fig. 1: Selected greenhouse structure for present study

2.2. Experimental procedure In data recording experiments, cabbages were used as the test samples in the greenhouse from 9:00 to 17:00. During the experiments, the weather was generally semi-sunny, without any rain. First, eleven SHT11 sensors were fixed at different locations of the greenhouse and at the outside to measure the temperature and relative humidity. Two sensors were installed for each greenhouse components (air, cover, plant and ground) in different points. Then, the average of values measured at these two points was considered as the components temperature and humidity to reduce unfavorable measuring errors. In addition, the solar radiation

incident on a horizontal surface and wind speed was measured with pyranometre type TES1333 and an anemometer. Fig. 2 illustrates the location of SHT11 sensors and TES1333. All climatic and measured parameters of the sample were recorded every 1 min by using a CR5000 data logger. Technical properties of the measurement devices were given in Table 1. Table 1 Technical properties of the measurement devices Device Measuring Parameters SHT11 Temperature Relative Humidity TES1333 Solar Radiation ST8894 Wind Speed CR5000 Data Logger

Property 14 bit analog to digital Not light sensitive 400–1110 nm 0 to 20 m/s 16-bit resolution 5000 measurements per

Sensibility ± 0.4𝑜𝐶 ± 3 %𝑅𝐻 ± 5% W/𝑚2 ± 0.3 m/s Accurate time

second.

Plant

SHT11 sensor

TES1333

Fig. 2: Location of SHT11 sensors and TES1333 installed at the greenhouse

2.3 Statistical evaluation criteria Statistical analysis was used to confirm the accuracy of the simulation. Errors and uncertainties in the modeling can change from heat and mass equations, assumptions, initial temperature and relative humidity values, environment, and modeling simplifications. Some statistical functions were applied to assess the performance of a greenhouse modeling in some scientific references such as coefficient of determination (R2), Model Efficiency (EF), Mean Absolute Percentage Error (MAPE), Total Sum of Squared Error (TSSE) and Root Mean Squared Error (RMSE) [12]: 𝑅2 =

[

∑𝑛

(𝑑 ― 𝑑)(𝑝𝑗 ― 𝑝) 𝑗=1 𝑗

∑𝑛 (𝑑𝑗 𝑗=1

∑𝑛 𝐸𝐹 =

― 𝑑) ×

∑𝑛 (𝑝𝑗 𝑗=1

― 𝑝)

𝑇𝑆𝑆𝐸 =

∑𝑛 (𝑑𝑗 𝑗=1 1 𝑛

∑

∑

𝑅𝑀𝑆𝐸 =

1

𝑛

(𝑑𝑗 ― 𝑑)2 ― ∑𝑗 = 1(𝑝𝑗 ― 𝑑𝑗)2

𝑗=1

𝑀𝐴𝑃𝐸 =

]

2

𝑛

𝑛

|

― 𝑑)2

𝑑𝑗 ― 𝑝𝑗

𝑗=1

𝑑𝑗

|

(𝑑𝑗 ― 𝑝𝑗)2

𝑗=1 ∑𝑛 (𝑑𝑗 𝑗=1

2

― 𝑝𝑗)2

× 100

3

4 5

𝑛 where 𝑑𝑗 represents the 𝑗𝑡ℎ component of the actual output for the 𝑗𝑡ℎ sample, 𝑝𝑗 indicates the component of the predicted output produced by the network for the 𝑗𝑡ℎ sample, n is the number of variable outputs,

and d and p are considered as the average of the whole desired and predicted output, respectively. The best model is achieved when the RMSE, MAPE and ESSE are minimized and EF and R2 are maximized. Furthermore, the experiments of the constructed semi-solar greenhouse were conducted on three consecutive days of 28/11/2017 to 30/11/2017 from 9:00 to 17:0 and the measurements were evaluated with the uncertainty analysis. The measured values average is given by [13]: ∑𝑋𝑚 6 𝑋= 𝑛 where n; the numbers of the measurement and Xm; the measured value. Standard deviation is given by Eq. (7) [13]. 7 ∑𝑛 (𝑋𝑚 ― 𝑋)2 𝑚=1 𝑆𝐷 = (𝑛 ― 1) Therefore, uncertainty is determined by [13]: 𝑆𝐷 8 𝑈= 𝑛 2.4 Modeling and analysis Fig. 3 summarizes the thermodynamics of a typical semi-solar greenhouse system, including the enthalpy/mass flows (1st law) and exergy destruction processes (2nd law). Only the most important fluxes are shown thermodynamically. As shown in Fig. 3, the processes inside the greenhouse consist of long wave radiation (IL), short wave radiation (IS), convection (CV), conduction (CD), heat transfer by vapor such as transpiration and condensation (H2O), heat transfer by dry air (AIR). Accordingly, the energy balance equations derived for semi-solar greenhouse and exergy and economic analysis were solved by using a computer program in MATLAB software within each one minute time step. Table 2 indicates the design and operating parameters, which are used as the input data for the developed mathematical model. The data were recorded for the experimental set and computer simulation for the greenhouse between 9:00 am to 17:00 pm on 30 November, 2017. In this dynamic model, the following assumptions were made: - Greenhouse components as lumped systems and uniform temperature are regarded. - Soil has not any evaporation. - Inside air doesn’t absorb and doesn’t emit the solar energy. - The windows in all test period are closed and the greenhouse has not any ventilation except leakages. - The effect of CO2 emission is neglected. - The evaporation of crop is considered. Table 2 Input parameter values [14-21] Parameter Value Ag 15 Ap 15 Asc 15 Acoi 17 Acoo 17 cp,a 1000 cp,H2O 4186 cp,sc 1500 cp,g 800 cp,coi 840 cp,coo 840 dco 0.004

Parameter Ecoi Ecoo Enw Esk Fg ― p Fg ― sc Fg ― coi Fg ― nwi Fp ― sc Fp ― nwi Fp ― coi Fsc ― nwi

Value 0.95 0.95 0.7 0.8 0.472 0.528 0.8 0.528 0.472 0.472 0.528 0.528

Parameter 𝑙𝑓 Rmin Va Vg Vsc Vco 𝑣𝑎 𝜂𝑣ℎ𝑟 𝜂𝑟𝑑,𝑐𝑜𝑖 𝜂𝑟𝑑,𝑔 𝜂𝑟𝑑,𝑝 𝜎

Value 0.004 82.003 24 9.75 0.03 0.06 0.09 0.9 0.017 0.331 0.258 5.67051 × 10 ―8

0.65 0.002 0.25 0.7 0.472 0.9

dg dsc dnw Eg Ep Esc

Fsc ― coi Fnwi ― coi Fcoo ― sk fa LAI Le

1 0.528 0.86 1 1.04 0.89

𝑟𝑤 𝜌𝑠𝑐 𝜌𝑔 𝜌𝑐𝑜

2.26 × 106 200 1400 2500

Fig. 3: Thermodynamic scheme of a typical greenhouse system with different entities and flows. The physical entities are framed and their abbreviations (small letters) are given inside brackets. The flows are abbreviated by capitals with subscript letters to indicate the source entity and the destiny entity.

2.4.1 Heat and mass transfer First-order differential equations for inside air (𝑇𝑎), inside ground (𝑇𝑔), plant (𝑇𝑝) and inside cover (𝑇𝑐𝑜𝑖) are written as [12, 14, 15]: 𝑑𝑇𝑎 𝑑𝑡 𝑑𝑇𝑔 𝑑𝑡 𝑑𝑇𝑝 𝑑𝑡

=

=

=

𝑑𝑇𝑐𝑜𝑖

𝑄𝑎 ― 𝑔 ― 𝑄𝑎 ― 𝑝 ― 𝑄𝑎 ― 𝑐𝑜𝑖 ― 𝑄𝑛𝑤𝑖 ― 𝑛𝑤𝑜

9

𝜌𝑎 × 𝑐𝑝 ― 𝑎 × 𝑉𝑎 𝑄𝑟𝑑,𝑔 + 𝑄𝑎 ― 𝑔 ― 𝑄𝑔 ― 𝑝 ― 𝑄𝑔 ― 𝑐𝑜𝑖 ― 𝑄𝑔 ― 𝑑𝑔 (0.7 × 𝜌𝑔 × 𝑐𝑝 ― 𝑔 + 0.2 × 𝜌𝐻2𝑂 × 𝑐𝑝 ― 𝐻2𝑂 + 0.1 × 𝜌𝑎 × 𝑐𝑝 ― 𝑎) × 𝑉𝑔 𝑄𝑟𝑑,𝑝 + 𝑄𝑎 ― 𝑝 + 𝑄𝑐𝑜𝑖 ― 𝑝 + 𝑄𝑔 ― 𝑝 ― 𝑄𝐻2𝑂,𝑝 ― 𝑎

=

𝜌𝑝 × 𝑐𝑝 ― 𝑝 × 𝑉𝑝 𝑄𝑟𝑑,𝑐𝑜𝑖 + 𝑄𝑎 ― 𝑐𝑜𝑖 +𝑄𝐻2𝑂,𝑎 ― 𝑐𝑜𝑖 + 𝑄𝑔 ― 𝑐𝑜𝑖 ― 𝑄𝑐𝑜𝑖 ― 𝑝 ― 𝑄𝑐𝑜𝑜 ― 𝑂 ― 𝑄𝑐𝑜𝑜 ― 𝑠𝑘𝑦

𝑑𝑡 𝜌𝑐𝑜𝑖 × 𝑐𝑝 ― 𝑐𝑜𝑖 × 𝑉𝑐𝑜𝑖 The transferred heat between greenhouse components by convection is given by [15]:

10

11

12

13

𝑄𝐴 ― 𝐵 = 𝐴𝐴𝐵 × 𝛼𝐴 ― 𝐵(𝑇𝐴 ― 𝑇𝐵)

Then, the convection heat transferred in a greenhouse (Qa ― p, Qa ― g, Qa ― coi and Qcoo ― o) are obtained based on the above equation. Insulating glass (IG), more commonly known as double layer glass separated by a vacuum or a gas filled space is used in some structures to reduce the heat transfer across the windows. Insulating glass units (IGUs) are manufactured with glass in range of thickness from 3 mm to 10 mm. In present dynamic model, a kind of IGU was performed as cover of greenhouse, and its performance was compared with one layer glass performance. A standard IGU consisting of clear glass with air filled space typically has an W

overall U-value of 0.35 m2K [22, 23]. The transferred heat between greenhouse components by conduction (Qg ― dg and Qnwi ― nwo) is given by [15]: 14 𝑄 = 𝐴 × 𝜆 /𝑑 (𝑇 ― 𝑇 ) 𝐶―𝐷

𝐶

𝐶

𝐶

𝐶

𝐷

The heat transfer coefficients between the different surfaces in a greenhouse (𝛼𝐴 ― 𝐵) can be calculated from given relationships in the literatures [14]. In addition, deep ground temperature (𝑇𝑑𝑔) is obtained by [15]: 15 𝑇 = 𝑇 + 15 + 2.5sin (0.0172(𝑑𝑎𝑦 ― 140)) 𝑑𝑔

𝑜

𝑁𝑅

where 𝑑𝑎𝑦𝑁𝑅 represents the day number of the year. The long wave radiation absorbed by inside cover (𝑄𝑟𝑑 ― 𝑐𝑜𝑖), inside ground (𝑄𝑟𝑑 ― 𝑔) and plant (𝑄𝑟𝑑 ― 𝑝) are determined by [15]: 16 𝑄 =𝐴 ×𝜂 ×𝐼 𝑟𝑑 ― 𝑥

𝑥

𝑟𝑑,𝑥

𝑖𝑛

The transferred heat between all parts of inside and outside of the greenhouse by radiation (𝑄𝑔 ― 𝑝, 𝑄𝑐𝑜𝑜 ― 𝑠𝑘𝑦, 𝑄𝑐𝑜𝑜 ― 𝑠𝑘𝑦, 𝑄𝑐𝑜𝑖 ― 𝑝, 𝑄𝑔 ― 𝑐𝑜𝑖) is obtained by [14]: 17 𝑄𝐸 ― 𝐹 = 𝐴𝐸 × 𝐸𝐸 × 𝐸𝐹 × 𝐹𝐸 ― 𝐹 × 𝜎(𝑇4𝐸 ― 𝑇4𝐹) 𝑇𝑠𝑘𝑦 is obtained by [24]: 18

𝑇𝑠𝑘𝑦 = 0.0552(𝑇𝑜)1.5

Evapotranspiration accounts for most of the water lost from the leaf surface during the growth of a crop. Thus, estimating the evapotranspiration rates is important in planning irrigation schemes. Stanghellini [25] achieved a relation for the mass flow rate of water vapor from crop to indoor air in canopy transpiration process: where 𝐴𝑝 represents the total surface area of the leaves, 𝜅𝐻2𝑂,𝑝 ― 𝑎indicates the mass transfer coefficient of water vapor from the plant to the inside air, as given by Eq. (18) [25]. In addition, 𝐶𝐻2𝑂𝑠,𝑝is considered as the saturation concentration of water vapor at the plant temperature and 𝐶𝐻2𝑂,𝑎 is the concentration water vapor at the inside air temperature. 1 𝜅𝐻2𝑂,𝑝 ― 𝑎 = 19 𝑅𝑐𝑢𝑡 × 𝑅𝑠 ― 𝐻2𝑂 𝑅𝑏 ― 𝐻2𝑂 + 𝑅𝑐𝑢𝑡 + 𝑅𝑠 ― 𝐻2𝑂 where Rcut = 2000 indicates the leaf cuticular resistance, 𝑅𝑠 ― 𝐻2𝑂 represents the stomata resistance to diffusion of water, which is defined by Eq. (19). Further, 𝑅𝑏 ― 𝐻2𝑂 is regarded as the boundary layer resistance to diffusion of water as shown in Eq. (20) [25]: 20 𝑅 =𝑅 ×𝑓 ×𝑓 ×𝑓 ×𝑓 𝑠 ― 𝐻2𝑂

𝑚𝑖𝑛

𝐼

𝑇𝑐

𝐶𝑂2

𝐻2𝑂

where Rmin = 82.003 and fCO2 = 1 are minimum internal plant resistance and the CO2 dependency, respectively and fI, fTc, fCO2, and fH2O represent the radiation dependency, temperature dependency, H2O dependency, respectively. These factors are defined in Table 3.

Table 3 Formulation of dependency factors for stomata resistance calculation 𝐼𝑝 ― 𝑔 + 4.3 fI 2𝐿𝐴𝐼 𝐼𝑝 ― 𝑔 + 0.54 2𝐿𝐴𝐼 [𝐼𝑝 ― 𝑔 = (0.0089 ― 0.023𝛽𝑔 ― 𝐼𝑠)𝐼𝑖𝑛 𝛽𝑔 ― 𝐼𝑠 = 0.58] 1 + 0.005(𝑇𝑝 ― 𝑇0 ― 33.6)2

fTc

[𝑇0 = 273.15] fH2O

4 4

―0.5427∆𝑝𝑝 ― 𝐻2𝑂𝑚

1 + 255𝑒 [∆𝑝𝑝 ― 𝐻2𝑂𝑚 = 0.01(𝑝𝑝 ― 𝐻2𝑂𝑠 ― 𝑝𝑎 ― 𝐻2𝑂)]

1174 𝑙𝑓

𝑅𝑏 ― 𝐻2𝑂 =

21

1/4 207𝑣2𝑎)

(𝑙𝑓 × |𝑇𝑝 ― 𝑇𝑎| + 𝑙 where 𝑓 and 𝑣𝑎 indicate mean leaf width and inside wind speed respectively. Condensation process causes water vapor from the indoor air to be converted to water drops at the inside of the cover, where its mass flow rate is defined by [14]: where 𝐴𝑐𝑜𝑖 means the inside cover surface area, 𝜅𝐻2𝑂,𝑎 ― 𝑐𝑜𝑖indicates the mass transfer coefficient of water vapor from the inside air to the indoor side of the cover, as given by the Eq. (21) [19], 𝐶𝐻2𝑂𝑠,𝑐𝑜𝑖 is considered as the saturation concentration of water vapor at the cover temperature and 𝐶𝐻2𝑂,𝑎 shows the concentration of water vapor at the indoor air above the screen temperature. 𝛼𝑎 ― 𝑐𝑜𝑖 22 𝜅𝐻2𝑂,𝑎 ― 𝑐𝑜𝑖 = 𝜌𝑎 × 𝑐𝑝 ― 𝑎 × 𝐿𝑒2/3 where Le= 0.89 is regarded as the Lewis number for water vapor and 𝛼𝑎 ― 𝑐𝑜𝑖 indicates the convection heat transfer coefficient from the inside air to the inside cover [14]: 23 α𝑎 ― 𝑐𝑜𝑖 = 3 × |𝑇𝑎 ― 𝑇𝑐𝑜𝑖|1/3 The latent heat transfer from the canopy to the indoor air due to canopy transpiration, and the latent heat transfer from indoor air to the indoor side of the roof are calculated as [14, 25]: 24 𝑄 =𝑟 ×𝜙 𝐻2𝑂,𝑝 ― 𝑎

𝑤

𝑚𝐻2𝑂,𝑝 ― 𝑎

𝑄𝐻2𝑂,𝑎 ― 𝑐𝑜𝑖 = 𝑟𝑤 × 𝜙𝑚𝐻2𝑂,𝑎 ― 𝑐𝑜𝑖 𝑗

where 𝑟𝑤 = 2.26 × 106 𝑘𝑔 is water evaporation heat.

25

The windows were closed in all test periods and the greenhouse had no ventilation by windows or fans. However, there is always some leakage from doors and windows. The volume of flow from inside to outside air due to leakage is obtained as follows [26]: 26 𝜙𝑙𝑒𝑎𝑘,𝑎 ― 𝑜 = 𝐴𝑠(8.3 × 10 ―5 + 3.5 × 10 ―5𝑣𝑜 × 𝑓𝑎) where 𝐴𝑠, 𝑣𝑜 , and 𝑓𝑎 represent the side area, wind speed, and dimensionless infiltration factor, respectively. Infiltration factor for a new greenhouse is one [26]. The heat transfer from the inside air to outside due to leakage ventilation is calculated as [20]: 27 𝑄 = (1 ― 𝑜𝑝 × 𝜂 ) × 𝜌 × 𝑐 ×𝜙 (𝑇 ― 𝑇 ) 𝑎―𝑜

𝑣ℎ𝑟

𝑣ℎ𝑟

𝑎

𝑝―𝑎

𝑙𝑒𝑎𝑘,𝑎 ― 𝑜

𝑎

𝑜

where 𝑜𝑝𝑣ℎ𝑟, 𝜂𝑣ℎ𝑟, 𝜌𝑎 and 𝑐𝑝,𝑎 indicate option ventilation heat recovery, efficiency factor ventilation with heat recovery, air density, and air specific heat capacity, respectively. The mass flow rate of water vapor from crop to indoor air due to leakage ventilation is calculated as follows [15]: 28 𝜙 =𝜙 (𝐶 ―𝐶 ) 𝑚𝐻2𝑂,𝑎 ― 𝑜

𝑙𝑒𝑎𝑘,𝑎 ― 𝑜

𝐻2𝑂,𝑎

𝐻2𝑂,𝑜

where 𝐶𝐻2𝑂,𝑎 and 𝐶𝐻2𝑂,𝑜 represent the vapour concentration of inside and outdoor air, respectively. The latent heat transfer from the inside air to outside due to leakage ventilation is calculated as follows [15]: 29 𝑄 =𝑟 ×𝜙 𝐻2𝑂,𝑎 ― 𝑜

𝑤

𝑚𝐻2𝑂,𝑎 ― 𝑜

To solve differential equations of 9-12, all heat and mass transfers throughout the test were calculated using equations 13-28 at first time step, t=0s to t=60s (n=1). Therefore, new values of 𝑇𝑎, 𝑇𝑔, 𝑇𝑝 and 𝑇𝑐𝑜𝑖 were obtained which were used calculating the new values of heat and mass transfers. Then, this process continued consecutively to calculating final values of greenhouse components temperature (n=480). 2.4.2 Exergy Exergy is described as the maximum potential work produced by interacting a system with its environment when moving toward equilibrium with the environment (the dead state) [16]. The expression for exergy destruction in heat exchange from A to B throw convection, conduction, mass flow of air from inside to outside in the greenhouse and long wave radiation processes are written as below [27]: 1 1 30 𝐸𝑋𝑑 = ―𝑄𝑇𝑒( ― ) 𝑇𝐵 𝑇𝐴 where Q, 𝑇𝐴, 𝑇𝐵 and 𝑇𝑒 indicate the heat transferred from 𝑇𝐴 to 𝑇𝐵, temperatures of part A, part B, and temperature of environment, respectively. Exergy destruction through water condensation on the inside cover of the greenhouse and exergy destruction of transpiration are defined as follows [27]: 𝑝𝑖,𝐴 31 𝐸𝑋𝑑 = ― 𝑛𝑖𝑅𝑇𝑒ln 𝑝𝑖,𝐵

( )

where 𝑛𝑖, 𝑝𝑖,𝐴 and 𝑝𝑖,𝐵 indicate the quantity of species i, partial pressure of species A, and B, respectively. In this experimental set up, windows and doors are supposed to be closed although some unwanted airflow occurs with different water vapor concentration from inside to outside, and vice versa. Due to this water vapor inside the air flow, the exergy destruction is determined by [27]: 𝑝𝑖,𝐴 32 𝐸𝑋𝑑 = ―𝑅𝑇𝑒(𝑛𝑖,𝐴 ― 𝑛𝑖,𝐵)ln 𝑝𝑖,𝐵

( )

The water vapor concepts in air conditioning are especially used for calculating the exergy of the greenhouse air. In this case, inside air is usually assumed to be a binary mixture composed of dry air and water vapor. Thus, the exergy related to the inside air of greenhouse is obtained by calculating the thermal and diffusional exergy of the air during one-minute step [28]:

𝐸𝑋𝑎,𝑡ℎ = 𝑐𝑝∗ (𝑇𝑎 ― 𝑇𝑜) ― 𝑇𝑜(𝑐𝑝∗ log 𝐸𝑋𝑎,𝑑𝑖𝑓 = 𝑇𝑜[𝑅 ∗ log

(1 + 𝑌𝜔𝑜)

(

1 + 𝑌𝜔

)

() 𝑇𝑎 𝑇𝑜

𝑃𝑎

― 𝑅 ∗ log (

+ 𝐶𝑅𝑎𝜔log (

𝑃𝑜

)

𝜔 ) 𝜔𝑜

33 34

where 𝑐𝑝∗ , 𝑅 ∗ , 𝐶 and 𝜔 are defined as: 𝑐𝑝∗ = 𝑐𝑝 ― 𝑎 + 𝜔𝑐𝑝 ― 𝑣

35

𝑅 ∗ = 𝑅𝑎 + 𝜔𝑅𝑣

36

𝑌=

𝑀𝑎𝑖𝑟 𝑀𝐻2𝑂

𝜔 = 0.622(

37 𝑃𝐻2𝑂,𝑎

)

38

𝑃𝑎 ― 𝑃𝐻2𝑂,𝑎 The reference conditions selected here are the outside air temperature (Te) and pressure (Pe). According to Bronchart et al [27], the selected reference of outside conditions has only a slight impact on the results of the exergy evaluations. 2.4.3 Economic view An economically designed system aims to evaluate the highest possible technical efficiency at a minimum cost under the prevailing technical, economic and legal conditions with regard to ethical, ecological and social consequences. Exergoeconomic analysis could assess the cost of this irreversibility. Actually, evaluating the amount of exergy destruction of the components in a system by their costs can offer a reliable way for optimizing a system [29]. The following parameters were considered to perform the economic analysis of the greenhouse.    

Life of the greenhouse components except cover is 10 years; The life of the greenhouse cover is 5 years; The semi-solar greenhouse operated during all hours of day and night; Among the 15 m2 area, planting is done on 50% of the area (7.5 m2), which is equivalent to 9.36 plants per m2, and the remaining area is used for movement in the greenhouse and other heating equipment;  40 % of the initial investment is regarded as the salvage value of the greenhouse and the auxiliary equipment [30]. 2.4.3.1 Cost equations In the present study, the reference cost data updated to the year 2012 were used for the components of the semi-solar greenhouse system. Table 4 indicates the construction cost, axillary equipment (such as data recording equipment, heating system) cost, labor cost, test samples (cabbages) cost and non-solar energy cost [31]. Table 4 The reference cost data for construction, axillary equipment, labor, test samples and non-solar energy Components Reference cost at 2012 ($) Construction 6510 Axillary equipment Data recording equipment 1780 Heating system 350 Others 180 Labor 2300 Test samples 110

Non-solar energy Total

0 11230

In the exergoeconomic analysis, the cost data calculated at the reference year should be updated to the original year by using the following equation [29]: 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑐𝑜𝑠𝑡 =

𝑐𝑜𝑠𝑡 𝑖𝑛𝑑𝑒𝑥 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑦𝑒𝑎𝑟 𝑤ℎ𝑒𝑛 𝑡ℎ𝑒 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑐𝑜𝑠𝑡 𝑤𝑎𝑠 𝑜𝑏𝑡𝑎𝑖𝑛𝑒𝑑 × 𝑐𝑜𝑠𝑡 𝑎𝑡 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑦𝑒𝑎𝑟 𝑐𝑜𝑠𝑡 𝑖𝑛𝑑𝑒𝑥 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑦𝑒𝑎𝑟

39

In the present study, Marshall and Swift equipment cost index [32] was used to bring all the components and service costs together. Based on the cost index of this reference equipment, the indices 1889.4 and 2411.4 were used as the cost indices for the reference year, and autumn 2017, respectively. The capital investment of each component is converted to cost rate per time unit by the following equation [33]: Φ𝑟 40 × 𝑍𝑘 𝑍𝑘 = 𝐶𝑅𝐹 × 𝑁 × 3600 where N represents the annual number of hours when the greenhouse operates, 𝑍𝑘 indicates original capital investment of the greenhouse, Φ𝑟 = 1.06 means the maintenance factor, and 𝐶𝑅𝐹 is considered as the capital recovery factor obtained by the following equation: 𝑖(1 + 𝑖)𝑛 41 𝐶𝑅𝐹 = 𝑛 (1 + 𝑖) ― 1 where i=0.10-0.20 indicates the interest rate and n=20 years is regarded as the expected life of greenhouse system. 2.4.3.2 Cost balance equations and exergoeconomic evaluation Fig. 4 illustrates a schematic diagram of the cost flow in the greenhouse control mass in each time step of one minute.

Fig. 4: Schematic diagram of the cost flow of the greenhouse control mass in each time step

The cost balance equation for the greenhouse system is defined as follows: Cin + Cq,in + Zk = Cw + Cout

42

Based on this equation, the sum of cost rates of all exiting exergies (Cout) and outlet work (Cw) is equal to the sum of cost rates in all entering exergies (Cin) plus the capital investment rate (Zk) plus the cost rate of inlet exergy by heat (Cq,in). In the data recording experiments, the greenhouse was tested from 9:00 to 17:00. In addition, the energy, exergy balance equations, and economic analysis were evaluated during the same time. Thus, it was not used for any electrical heat source. Further, no work transfer was available at the greenhouse. Cq,in = 0 43 44 C =0 w

Therefore, the Eq. (41) is summarized as follows: Cin + Zk = Cout If Eq. (41) is used for each time step of one minute, then: Cn,in + Zk = Cn,out

45 46

Considering Cn ― 1,out = Cn,in (outlet cost rate of (n-1)th step is equal to the inlet cost rate of nth step); so: 47

Cn ― 1,out + Zk = Cn,out

Since the present study aimed to create conditional air with suitable temperature and moisture for exergoeconomic analysis, the inside air of greenhouse were considered as mass control. Therefore, by cancelling the time unit, Eq. (46) is expressed as follows: 48 C +Z =C n ― 1,out

k,n

n,out

where Cn and Cn ― 1 denote the total cost of nth and (n-1)th time step and Zk,n indicates the total cost of one time step; 49 Z = 60 × Z k,n

k

The inlet cost is zero for the first time step (n=1; t=0s to t=60s), because the inlet air of the greenhouse is free atmosphere air; so: 50 Z =C k,1

1,out

Further, the exergy of inside wet air in each time step is calculated at section 2.4.2. Therefore, the cost of air unit for the first time step is calculated as follows: 60𝑍𝑘 51 60 × Zk = 𝑐1,𝑜𝑢𝑡𝐸𝑋1 → 𝑐1,𝑜𝑢𝑡 = 𝐸𝑋1 Generally, the cost of air unit for each time step (n=2 to n=480) is calculated as follows by using Eq. (46): 𝐶𝑛 ― 1,𝑜𝑢𝑡 + 60𝑍𝑘 52 𝑐𝑛,𝑜𝑢𝑡 = 𝐸𝑋𝑛 2.4.4 Optimization The system performance is optimized regarding the total exergy destruction and mean air unit cost as two criteria. Considering the north wall and soil properties and the length/width of the greenhouse as design parameters, the multi-objective optimization is applied using the genetic algorithm whose flowchart is illustrated in Fig. 5. In this regard, MATLAB software optimization toolbox is employed. The restrictions of decision variables and the primary setting values of optimization toolbox in the genetic algorithm optimization process are tabulated in Tables 5 and 6, respectively.

Fig. 5 : Genetic algorithm flowchart Table 5 List of decision variables and restrictions for the multi-objective optimization process Parameter Representing Reason of restriction 3.87 ≤ 𝑙𝑔 ≤ 6 Greenhouse Length (m) Greenhouse area limitation 2.5 ≤ 𝑤𝑔 ≤ 3.87 Greenhouse width (m) Greenhouse area limitation

Conduction heat transfer

0.5 ≤ 𝜆𝑔 ≤ 2

Soil properties limitation

𝑊 (𝑚𝐾)

0.35 ≤ 𝑑𝑔 ≤ 1 1000 ≤ 𝜌𝑔 ≤ 1600

coefficient of soil Thickness of greenhouse soil (m) 𝑘𝑔

700 ≤ 𝑐𝑝,𝑔 ≤ 900

Density of soil (𝑚3) Specific heat capacity of soil (

0.05 ≤ 𝜆𝑛𝑤 ≤ 0.2

Conduction heat transfer

0.1 ≤ 𝑑𝑛𝑤 ≤ 0.5

coefficient of north wall Thickness of north wall (m)

Common used soil thickness in greenhouses Soil properties limitation Soil properties limitation

𝐽 𝑘𝑔.𝐾)

Common used materials for north wall 𝑊 (𝑚𝐾)

Common used north wall thickness in greenhouses

Table 6 List of the primary setting values of optimization toolbox parameters in the genetic algorithm optimization process Optimization toolbox parameter Value Solver Gamultiobj-Multiobjective optimization using Genetic Algorithm Number of Variables 8 Population size 500 Maximum generation number 600 Probability of cross over 85% Mutation function 0.01 Selection function Tournament Tournament size 2

3. Results and Discussion 3.1 Energy and Exergy analysis results In this section, the performance of the proposed semi-solar greenhouse system is investigated from the viewpoints of energy, exergy and exergoeconomics. Fig. 6 shows the changes in the measured temperatures of the greenhouse components as well as the surrounding air from 9:00 to 17:00 on 30/11/2017 in Tabriz city using the data recording methodology every minute.

323

Ta

Tg

Tcoi

To

Tp

Temperature (K)

313

303

293

283

273 1

51 101 151 201 251 301 351 401 451 Time (Minute)

Fig. 6: Variations of the measured temperatures of the greenhouse components and surrounding air

320

320

310

310

300 Ta-thermal Ta-experimental

290

Temperature (K)

Temperature (K)

In the present constructed semi-solar greenhouse, because of using a one layer glass cover as the greenhouse roof, the temperature difference between the two sides of the glass was negligible. Therefore, using a one layer glass cover as the greenhouse roof led to considerable temperature difference between the air inside the greenhouse and the inner side of the glass. This temperature difference caused an increase in the energy loss due to regular convection and radiation heat transfer between the inside cover and other components of the greenhouse. As discussed before, an ideal greenhouse is one that provides a better thermal condition for raising the crops. In this regard, the present constructed greenhouse was an appropriate one, because it provided a mean temperature of 33 ℃ for the inside air which was almost 19.5 ℃ more than the surrounding air temperature. This considerable temperature difference between the air inside and outside the greenhouse indicated that the selected structure for the semi-solar greenhouse had an efficient performance; obtaining the required solar energy on autumn days, even decreasing the energy loss at cold nights. The low temperature difference between the crops, soil and inside air showed that the heat transfer between the greenhouse components occurs appropriately. Therefore, the proposed structure was beneficial for the crops arising due to the temperature uniformity at different points of the greenhouse. Fig. 6 shows that plant temperature is mainly higher than the air temperature inside the greenhouse. This temperature difference prevents the water vapor condensation of the inside air on the plants at cold nights which is so effective to avoid some vegetal diseases such as Botrytis and Late blight. The thermal modeling of the proposed semi-solar greenhouse was developed by MATLAB software for each one minute time step. Fig. 7 shows comparison between the results obtained from the thermal simulation and experimental data for semi-solar greenhouse on 30/11/2017 in Tabriz city based on data recording every one minute.

300 Tg-experimental Tg-thermal

290

280

280 1

51 101 151 201 251 301 351 401 451 Time (Minute)

1

51

101 151 201 251 301 351 401 451 Time (Minute)

320

320

310

300 Tp-thermal Tp-experimental

290

Temperature (K)

Temperature (K)

310

300 Tcoi-thermal 290

Tcoi-experimental

280 280

1 1

51 101 151 201 251 301 351 401 451

51 101 151 201 251 301 351 401 451 Time (Minute)

Time (Minute)

Fig. 7: comparison between the results obtained from the thermal simulation and experimental data

Referring to Fig. 7, there was a good agreement between the thermal simulation results and experimental measured data. In this regard, a statistical analysis has been performed to prove the simulation accuracy which is represented in Table 7. Table 7 Statistical analysis results to evaluate the dynamic simulation accuracy with experimental data Temperature 𝑅2(%) 𝐸𝐹(%) 𝑀𝐴𝑃𝐸(%) 𝑇𝑆𝑆𝐸(℃2) 𝑇𝑎 97.62 92.42 4.98 121.65 𝑇𝑔 98.24 85.64 6.68 258.36 𝑇𝑝 97.51 82.35 7.12 294.32 𝑇𝑐𝑜𝑖 96.43 87.58 5.54 179.29

𝑅𝑀𝑆𝐸(℃) 1.64 1.84 2.36 2.21

An experimental study comparing to a dynamic greenhouse climate model to predict the greenhouse air temperature and relative humidity, in a naturally ventilated Zimbabwean greenhouse containing a rose crop was carried out by Mashonjowa et al. [34]. The simulation results showed a good agreement with the measured values during the day. The related data was recorded during the period of May 2007 to April 2008. In addition, the mean standard errors between the simulation results and experimental data for the inside air temperature and relative humidity and canopy temperature were calculated. Root Mean Squared Error (RMSE) of 1.8℃ and 1.3℃ for the inside air temperature and 1.9℃ and 1.6℃ for the canopy temperature were obtained in winter and summer, respectively. As it can be observed from Table 7, the values of RMSE in this study vary from 1.64℃ to 2.36℃. Sharma et al. [35] developed a dynamic model to predict the inside air as well as the plant temperatures through different zones of a greenhouse at December in Delhi, India. The behavior of such vital parameters as, the infiltration effects, the plants heat capacity, the greenhouse relative humidity and the room air temperature were investigated. The absolute error of 10% between the theoretical and experimental observations of the room air temperature was calculated. Du et al. [36] studied the performance of a greenhouse heated using a heat-pipe system, both experimentally and theoretically. They showed that the height, the heating power and the heat losses from the greenhouse have significant effects on the greenhouse performance. The absolute error of about ±20% was calculated between predicted and experimental data. Referring to two last mentioned articles [35, 36] and comparing the calculated errors listed in Table 7, it can be concluded that the present modeling of the semi-solar greenhouse was reliable.

Furthermore, results of the uncertainty analysis (Table 8) show that the recorded data during the measurements was acceptable to evaluate the accuracy of the thermal simulation. Table 8 The uncertainties of the measurements Measurement Devices Uncertainty (U) SHT11 (𝑇𝑎) ± 0.243 𝐾 SHT11 (𝑇𝑔) ± 0.425 𝐾 SHT11 (𝑇𝑝) ± 0.387 𝐾 SHT11 (𝑇𝑐𝑜𝑖) ± 0.311 𝐾 SHT11 (𝑅𝐻𝑎) ± 0.263 𝑅𝐻 SHT11 (𝑅𝐻𝑜) ± 0.314 𝑅𝐻 𝑊 TES1333 (𝐼𝑖𝑛) ± 1.23 2 𝑚 ST8894 (𝑣𝑜) ± 0.098 𝑚/𝑠

The total exergy destruction values associated with the processes of heat and mass transfer during 9:00 to 17:00 is illustrated in Fig. 8. Exergy Destruction Through Different Processes 5 Exergy Destruction (MJ)

g-a p-a 4

coi-p

a-coi

g-p

nwi-p nwi-g

3

g-coi

nwi-a 2

1

0

g-dg

coo-o a-p

nwi-nwo CD

CV

nwi-coi

a-coi coo-sk a-o

a-o

H2O

AIR

IL

Processes

Fig. 8: Total exergy destruction values associated with the processes of heat and mass transfer

As it is seen from Fig. 8, the exergy destruction value related to the convection heat transfer is more than that of the other processes. This is because of the high temperature difference between the air outside the greenhouse and the out layer of the glass cover. Therefore, in order to decrease the exergy destruction value associated with the convection heat transfer between greenhouse cover and outside air ( 𝐸𝑋𝑑,𝐶𝑉,𝑐𝑜𝑜 ― 𝑜), this temperature difference should be decreased. In this regard, a double layer glass separated with air filled space was used as cover of greenhouse to reduce the heat transfer across the roof. Applied insulating glass unit (IGU) with thickness of 4 mm for each layer and air filled space of 12 mm showed acceptable performance. The results indicated that exergy destruction of 𝐸𝑋𝑑,𝐶𝑉,𝑐𝑜𝑜 ― 𝑜 decreased 52 % by this technique. This is because; using this procedure leads to a law temperature difference between the air outside the greenhouse and out layer of the glass cover. Additionally, using IGU led to decrease the exergy destruction through convection between the inside air and inside cover (𝐸𝑋𝑑,𝐶𝑉,𝑎 ― 𝑐𝑜𝑖) as well as the exergy destruction through long wave radiation between

outside cover and sky (𝐸𝑋𝑑,𝐼𝐿,𝑐𝑜𝑜 ― 𝑠𝑘). This is justified because; the two glass layer cover with air filled distance acted as an isolator between the air inside and outside of the greenhouse. Therefore, the inside cover was kept warmer and the outside one remains colder. Performance of IGU in decreasing of exergy destructions in different processes are shown in Table 9. Table 9 Performance of IGU in decreasing of exergy destructions Exergy destructions Reduction percent with IGU as cover 𝐸𝑋𝑑,𝑐𝑜𝑜 ― 𝑜 52.0 % 𝐸𝑋𝑑,𝑎 ― 𝑐𝑜𝑖 51.5 % 𝐸𝑋𝑑,𝑐𝑜𝑜 ― 𝑠𝑘 47.1 % 𝐸𝑋𝑑,𝑛𝑤𝑖 ― 𝑐𝑜𝑖 35.3 % 𝐸𝑋𝑑,𝑔 ― 𝑐𝑜𝑖 32.2 % 𝐸𝑋𝑑,𝑝 ― 𝑐𝑜𝑖 31.7 %

During ventilation, two exergy flows leave the inside air: loss of exergy in heat and in vapor [27]. In addition, as depicted in Fig. 8, the exergy losses associated with the air and vapor is occurred due to the ventilation process through the leakage from the doors and windows. Therefore, caulking all the holes and cracks of the windows, doors and walls could be very helpful for decreasing the exergy loss. Finally, Fig. 8 demonstrates that the exergy destruction related to the condensation (𝐸𝑋𝑑,𝐻2𝑂,𝑎 ― 𝑐𝑜𝑖) and evapotranspiration (𝐸𝑋𝑑,𝐻2𝑂,𝑎 ― 𝑝) processes were only 0.1 % of the whole exergy destruction of the system which is a negligible value. 3.2 Economic analysis results Using Eq. (51), the unit cost of the air inside the greenhouse for the time steps of 1 to 480 minutes in different interest rates is illustrated in Fig. 9. Referring to this figure, the air unit cost diagram is ascendant for the most time steps. This is because; the total outlet cost of (𝑛 ― 1)𝑡ℎ time step was considered as the total inlet cost of 𝑛𝑡ℎ time step. However, for the time steps of 50 to 100 minutes, the air unit cost is descending due to remarkable increase in the air temperature and so the air exergy flow rate as shown in Fig.6. Moreover, for the time steps of 100 to 300 minutes, the air unit cost diagram is almost flat which indicates that during this period none of the investment cost and air exergy flow rate is dominant. Furthermore, the diagram is extremely ascendant for the time steps of 400 to 480. This is justified because; despite the increase in the total investment cost of the system with the time, the air temperature and so its exergy flow rate decreases. Depending on economic conditions, applying different interest rates of 10 % to 20 % can make remarkable changes in unit cost of the air inside the greenhouse. Fig. 9 shows that air unit cost increases from 64 $/MJ to 112 $/MJ by raising interest rate from 10 % to 20 %. Therefore, interest rate has significant effect on cost of agricultural crops.

120 i=0.20

Air Unit Cost ( $ / MJ )

100

i=0.15 i=0.10

80 60 40 20 0 1

51

101 151 201 251 301 351 401 451 Time (Minute)

Fig. 9: Air unit cost at time steps of n=1 to n=480 for different interest rates

3.3 Optimization results Considering the total exergy destruction and mean air unit cost as the objective functions, Pareto frontier is represented in Fig. 10. Referring to Fig. 10, the minimum value of mean air unit cost is obtained at design point A (14.4651 $/MJ); while the total exergy destruction takes on its highest value (10.9247 MJ). Furthermore, the minimum value of total exergy destruction is obtained at design point B (6.0736 MJ); where the mean air unit cost is the maximum value (21.9017 $/MJ). Then, taking into account the importance of total exergy destruction and mean air unit cost and based on optimization algorithm procedure, points A or B are chosen as the final optimum design point when the mean air unit cost or total exergy destruction is regarded as a sole objective function, respectively. Greenhouse designers choose the final optimal point depending on their preference. Equilibrium point can help designers selecting the most optimal point based on the objective functions [5]. The equilibrium point is described as unreal point on the Pareto plot where the objective functions get their ideal amounts. As illustrated in Fig. 10, the nearest point to the equilibrium point is selected as the final optimum point (point C). The objective functions of total exergy destruction and mean air unit cost take on their optimal values of 8.8623 MJ and 15.9164 $/MJ, respectively. Optimum values of decision variables/objective functions and exergoeconomic analysis parameters of the greenhouse at the optimal point C compared to values obtained from current experimental setting are listed in Tables 10 and 11, respectively.

Fig. 10: Pareto optimal solution frontier obtained by multi-objective optimization

Table 10 Optimum values of decision variables and objective functions at the final optimum design point selected from the Pareto frontier

Parameter 𝑙𝑔 (m) 𝑤𝑔 (m) 𝑊

𝜆𝑔 (𝑚𝐾) 𝑑𝑔 (m) 𝑘𝑔

𝜌𝑔 (𝑚3) 𝐽

𝑐𝑝,𝑔 (𝑘𝑔.𝐾)

Value 4.9821 3.0108 0.6710 0.8537 1280.6 727.58

𝑊 𝜆𝑛𝑤 (𝑚𝐾)

0.0626

𝑑𝑛𝑤 (m) Total exergy destruction (MJ) Mean air unit cost ($/MJ)

0.4208 8.8623 15.9164

Table 11 Optimum values of exergoeconomic analysis parameters from the multiobjective optimization compared to values obtained from current experimental setting Parameter Values from multiValues from objective optimization experimental setting 𝐸𝑋𝑑,𝐶𝐷,𝑔 ― 𝑑𝑔 (MJ) 0.2074 0.3841 𝐸𝑋𝑑,𝐶𝐷,𝑛𝑤𝑖 ― 𝑛𝑤𝑜 (MJ) 0.3761 0.5574 𝐸𝑋𝑑,𝐶𝑉,𝑎 ― 𝑐𝑜𝑖 (MJ) 0.9455 0.8864 𝐸𝑋𝑑,𝐶𝑉,𝑝 ― 𝑎 (MJ) 0.4708 0.0487 𝐸𝑋𝑑,𝐶𝑉,𝑛𝑤𝑖 ― 𝑎 (MJ) 1.2561 1.3142

𝐸𝑋𝑑,𝐶𝑉,𝑐𝑜𝑜 ― 𝑜 (MJ) 𝐸𝑋𝑑,𝐶𝑉,𝑔 ― 𝑎 (MJ) 𝐸𝑋𝑑,𝐻2𝑂,𝑎 ― 𝑝 (m) 𝐸𝑋𝑑,𝐻2𝑂,𝑎 ― 𝑜 (MJ) 𝐸𝑋𝑑,𝐻2𝑂,𝑎 ― 𝑐𝑜𝑖 (MJ) 𝐸𝑋𝑑,𝐼𝐿,𝑛𝑤𝑖 ― 𝑝 (MJ) 𝐸𝑋𝑑,𝐼𝐿,𝑛𝑤𝑖 ― 𝑐𝑜𝑖 (MJ) 𝐸𝑋𝑑,𝐼𝐿,𝑛𝑤𝑖 ― 𝑔 (MJ) 𝐸𝑋𝑑,𝐼𝐿,𝑐𝑜𝑜 ― 𝑠𝑘 (MJ) 𝐸𝑋𝑑,𝐼𝐿,𝑔 ― 𝑝 (MJ) 𝐸𝑋𝑑,𝐼𝐿,𝑔 ― 𝑐𝑜𝑖 (MJ) 𝐸𝑋𝑑,𝐴𝐼𝑅,𝑎 ― 𝑜 Total

2.0773 0.0149 0.0161 0.5877 0.0010 0.1139 0.9503 0.1540 1.3355 0.0011 0.2015 0.5331 8.8623

1.9782 0.0083 0.0157 0.5472 0.0012 0.1235 0.9874 0.1365 1.7615 0.0072 0.2143 0.6687 9.6404

4. Conclusion An innovative dynamic model was performed to analysis of a semi-solar greenhouse from the viewpoints of thermodynamics and economics. The proposed model was able to predict the temperature of the inside air, plant, soil and inside cover. The influences on such vital indicators as the inside air temperature; the exergy destruction and the air unit cost were investigated of several environmental parameters including the outside temperature, solar radiation and outside wind velocity. Considering the total exergy destruction and mean air unit cost as the objective functions a multi-objective optimization was performed. The north wall and soil thermal properties and the length/width of the greenhouse were regarded as decision variables. All the results obtained by the proposed thermodynamic model were compared to the experimental data recorded from the constructed typical semi-solar greenhouse at the North-West of Iran, Azerbaijan Province. The experiment was conducted on 30/11/2017 from 9:00 to 17:0 and cabbages were used as the test samples. It was observed that: - The considerable temperature difference of 19.5 ℃ between the air inside and outside the semisolar greenhouse showed that a thermally efficient design and structure was applied for the greenhouse, obtaining the required solar energy on autumn days. - The air inside the greenhouse with a uniformly distributed temperature provided appropriate thermal condition for cultivating crops. - A comparison between the experimental data and the results achieved by the proposed dynamic model proved that there was a good agreement between them. In this regard, the mean values of 𝑀𝐴𝑃𝐸 and RMSE were calculated as 6.08 % and 2.1 ℃, respectively. - It was observed that the convection heat transfer and the shortwave radiation heat transfer, among the other heat and mass transfer processes, had the highest exergy destruction. - Using double layer glass separated with air filled space as the greenhouse cover reduced the heat transfer from the inside air to outside as well as the exergy destruction. By this technique, total exergy destruction of the semi-solar greenhouse decreased about 45.36 %. - Exergy destruction by condensation and evapotranspiration processes were negligible. - The thermoeconomic analysis demonstrated that the unit cost of the air inside the greenhouse often increased as the time elapsed. - Providing an appropriate thermal condition for the air inside the greenhouse to raise the crop was considered as the aim of the present study. In this way, the capital investments associated with the greenhouse construction materials and the data recording equipment’s had the largest contribution to the total air unit cost; because it had not been used any other non-solar heating source. - A close look at the air unit cost diagram revealed that an increase of 36 % in the air unit cost was achieved at the interest rate of 50 % increase from 10 % to 15 %.

-

The values of 8.8623 MJ and 15.9164 $/MJ were obtained for objective functions of total exergy destruction and mean air unit cost on their optimal point, respectively. Conflict of interest The authors declare that there is no conflict of interest. Acknowledgments The authors would like to thank the editor in chief and the anonymous referees for their valuable suggestions and useful comments that improved the paper content substantially. References [1] E. Kondili, J. Kaldellis, Optimal design of geothermal–solar greenhouses for the minimisation of fossil fuel consumption, Applied Thermal Engineering, 26(8-9) (2006) 905-915. [2] M. Kıyan, E. Bingöl, M. Melikoğlu, A. Albostan, Modelling and simulation of a hybrid solar heating system for greenhouse applications using Matlab/Simulink, Energy Conversion and Management, 72 (2013) 147-155. [3] K.A. Joudi, A.A. Farhan, Greenhouse heating by solar air heaters on the roof, Renewable energy, 72 (2014) 406-414. [4] A. Vadiee, V. Martin, Energy analysis and thermoeconomic assessment of the closed greenhouse–The largest commercial solar building, Applied Energy, 102 (2013) 1256-1266. [5] B.M. Ziapour, A. Hashtroudi, Performance study of an enhanced solar greenhouse combined with the phase change material using genetic algorithm optimization method, Applied Thermal Engineering, 110 (2017) 253-264. [6] J. Zhang, J. Wang, S. Guo, B. Wei, X. He, J. Sun, S. Shu, Study on heat transfer characteristics of straw block wall in solar greenhouse, Energy and Buildings, 139 (2017) 91-100. [7] C. Chen, H. Ling, Z.J. Zhai, Y. Li, F. Yang, F. Han, S. Wei, Thermal performance of an active-passive ventilation wall with phase change material in solar greenhouses, Applied energy, 216 (2018) 602-612. [8] H.H. Öztürk, Experimental evaluation of energy and exergy efficiency of a seasonal latent heat storage system for greenhouse heating, Energy Conversion and Management, 46(9-10) (2005) 1523-1542. [9] A. Hepbasli, A comparative investigation of various greenhouse heating options using exergy analysis method, Applied Energy, 88(12) (2011) 4411-4423. [10] H. Yildizhan, M. Taki, Assessment of tomato production process by cumulative exergy consumption approach in greenhouse and open field conditions: Case study of Turkey, Energy, 156 (2018) 401-408. [11] M.J. Gupta, P. Chandra, Effect of greenhouse design parameters on conservation of energy for greenhouse environmental control, Energy, 27(8) (2002) 777-794. [12] S. Zarifneshat, A. Rohani, H.R. Ghassemzadeh, M. Sadeghi, E. Ahmadi, M. Zarifneshat, Predictions of apple bruise volume using artificial neural network, Computers and electronics in agriculture, 82 (2012) 75-86. [13] S. Bell, A beginner's guide to uncertainty of measurement, Measurement good practice guide, 11 (1999) 1. [14] G. Van Straten, G. van Willigenburg, E. van Henten, R. van Ooteghem, Optimal control of greenhouse cultivation, CRC press, 2010. [15] R. Van Ooteghem, Optimal control design for a solar greenhouse, systems and control, Wageningen: Wageningen University, (2007). [16] M.J. Moran, H.N. Shapiro, D.D. Boettner, M.B. Bailey, Fundamentals of engineering thermodynamics, John Wiley & Sons, 2010. [17] C. Von Zabeltitz, Heating, in: Integrated Greenhouse Systems for Mild Climates, Springer, 2011, pp. 285-311. [18] H. De Zwart, Analyzing energy-saving options in greenhouse cultivation using a simulation model, De Zwart, 1996. [19] G.P. Bot, Greenhouse climate: from physical processes to a dynamic model, Landbouwhogeschool te Wageningen, 1983. [20] J. Stoffers, Tuinbouwtechnische aspecten van de druppelprofilering bij kasverwarmings-buis, Intern rapport IMAG_DLO, Wageningen, (1989).

[21] A. Defant, F. Defant, Physikalische Dynamik der Atmosphäre, Akad. Verl.-Ges., 1958. [22] M. Glover, G. Reichert, Convective gas-flow inhibitors, in, Google Patents, 1994. [23] T.C. Jester, Twentieth-century building materials: History and conservation, Getty Publications, 2014. [24] K.A. Joudi, A.A. Farhan, A dynamic model and an experimental study for the internal air and soil temperatures in an innovative greenhouse, Energy Conversion and Management, 91 (2015) 76-82. [25] C. Stanghellini, Transpiration of greenhouse crops: an aid to climate management, IMAG, 1987. [26] T. De Jong, Natural ventilation of large multi-span greenhouses, De Jong, 1990. [27] F. Bronchart, M. De Paepe, J. Dewulf, E. Schrevens, P. Demeyer, Thermodynamics of greenhouse systems for the northern latitudes: Analysis, evaluation and prospects for primary energy saving, Journal of environmental management, 119 (2013) 121-133. [28] D.E.R. Kenneth Wark, Thermodynamics McGraw-Hill series in mechanical engineering, ISBN-13: 978-0071168533 (1999) 954 [29] A. Bejan, G. Tsatsaronis, M. Moran, M.J. Moran, Thermal design and optimization, John Wiley & Sons, 1996. [30] V. Sethi, S. Sharma, Experimental and economic study of a greenhouse thermal control system using aquifer water, Energy Conversion and Management, 48(1) (2007) 306-319. [31] D.P. Lambe, S.A. Adams, E.T. Paparozzi, Estimating construction costs for a low-cost Quonset-style greenhouse, DigitalCommons, University of Nebraska, Lincoln (2012). [32] E. Indicators, Marshall&Swift equipment cost index, Chemical engineering, 72 (2011). [33] P. Ahmadi, I. Dincer, Thermodynamic and exergoenvironmental analyses, and multi-objective optimization of a gas turbine power plant, Applied Thermal Engineering, 31(14-15) (2011) 2529-2540. [34] E. Mashonjowa, F. Ronsse, J.R. Milford, J. Pieters, Modelling the thermal performance of a naturally ventilated greenhouse in Zimbabwe using a dynamic greenhouse climate model, Solar Energy, 91 (2013) 381-393. [35] P. Sharma, G. Tiwari, V. Sorayan, Temperature distribution in different zones of the micro-climate of a greenhouse: a dynamic model, Energy conversion and management, 40(3) (1999) 335-348. [36] J. Du, P. Bansal, B. Huang, Simulation model of a greenhouse with a heat-pipe heating system, Applied energy, 93 (2012) 268-276.

Conflict of interests

The authors declare that there is no conflict of interest.