Mathematical Simulation of the dehumidifier of Seawater Greenhouse Abdulrahim M. Al-Ismaili1*, Edward K. Weatherhead2, Hemantha P. Jayasuriya1 1
Department of Soils, Water and Agricultural Engineering, College of Agricultural and Marine Sciences, Sultan Qaboos University, P.O. Box. 34, P.Code 123, Muscat, Oman
2
Centre for Water Science, School of Applied Sciences, Cranfield University, United Kingdom
*Corresponding Author. E-mail:
[email protected];
[email protected] Abstract This article addresses a steady-state mathematical model developed to simulate the dehumidifier unit of the seawater greenhouse (SWGH) located in Oman. The simulation was based on the energy balance of the system. Experiments were conducted to generate two datasets; first dataset was used to develop an empirical relationship necessary to estimate freshwater production and the second dataset was used to test the accuracy of the model. The developed model follows an iterative approach predicting the outlet air temperature and humidity, the outlet water temperature and the freshwater water production (the dehumidification rate). The conducted validation experiments showed a good conformity between the predicted and measured values with significantly low predictive errors; humidity ratio less than 1.4%, outlet air and water temperatures less than 1.9% and -1.5%, respectively. The predictive error of the freshwater production reached 11.5%. Keywords simulation, seawater greenhouse, dehumidifier, Oman 1. Introduction: In agricultural practices, the main purpose of constructing greenhouses is to overcome harsh ambient conditions and hence provide a controlled environment suitable for cultivating certain crops. In hot environments, as the case in the Sultanate of Oman, greenhouses are used to provide cool environments by means of pad-and-fan evaporative cooling systems. In such environments, the use of dehumidifiers (condensers) inside greenhouses is very seldom (Stanghellini & van Meurs, 1992) however, it becomes a necessary component of the Seawater greenhouse. The aim of constructing this type of greenhouses is to provide freshwater suitable for agricultural purposes in places lacking access to affordable freshwater sources due to their nearness to the sea and/or having saline/brackish groundwater. The seawater greenhouse in Oman comes after two other versions each of which got its own peculiarities. The first one was built in 1994 in Tenerife, Spain (Paton & Davis, 1996; and Davies et al., 2004) and was able to produce an amount of water more than the greenhouse “crop water demand”. The second one was constructed in 2000 in the United Arab Emirates and, after several modifications, was able to produce almost its own crop water demand (Davies et al., 2004; and Davies & Paton, 2005). Even though the Oman greenhouse used the knowledge and techniques attained from the previous versions to make it compatible to the Omani environment, the amount of water produced was not meeting the greenhouse water requirement (Al-Ismaili, 2009). It was thought that further efforts should be made towards increasing the water yield through mathematical simulation techniques. This paper addresses a steady-state mathematical simulation of the dehumidifier used in the Oman seawater greenhouse. The developed model is capable of predicting the outlet air temperature and humidity, the outlet water temperature and the freshwater water production (dehumidification rate). The input parameters of the model, in addition to the dehumidifier design parameters, are the inlet air temperature, humidity and flow rate, and the inlet water temperature and flow rate.
2. Material and Methods: 2.1. Seawater Greenhouse in Oman The developed setup is two tunnel-type greenhouses attached together, located 50 m from the seashore. It is an airtight structure cooled by a pad-and-fan evaporative cooling system in which the pads (1st humidifier) are placed at one end of the tunnel and the fans are at the other end. As a result of the withdrawing force of the fans, warm dry ambient air is forced through the 1st humidifier wetted with saline underground water. The cooled moistened air leaving the humidifier passes through the cultivation area after which air moisture increases due to evapotranspiration. The air temperature increases due to the solar heat gain and as a result, the air capacity to hold more moisture increases. Hence, a 2nd humidifier is placed by the end of the cultivation area to further load the air with moisture. A dehumidifier is placed 1.5 m after the 2nd humidifier and before the fans to extract moisture. The greenhouse includes two water circuits; the first connects the 1st humidifier and the dehumidifier and the second connects the 2nd humidifier and the solar heater unit. In the first circuit, water flowing down the 1st humidifier is pumped as coolant to the dehumidifier. AlIsmaili (2003) and Perret et al. (2005) reported that the use of this water as the dehumidifier coolant is feasible owing to its temperature being always below the dew-point temperature of the moist air passing through the dehumidifier of their greenhouse. The coolant water gains latent heat of vaporization from the condensed water and sensible heat coming from the cross-flowing air. Water leaving the dehumidifier then flows back to the 1st humidifier. In the second circuit, water pumped to the 2nd humidifier is preheated by passing it through an array of black polyethylene tubes in order to boost up the evaporation. 2.2. Dehumidifier The dehumidifier (1.8 m high, 15 m wide and 0.8 m thick, as in Fig. 1) of the Oman seawater greenhouse was made up of 4832 vertical PVC tubes through which the moist air and the coolant are flowing in a cross-flow pattern. The thickness of the tube walls is only 200 microns to compensate for the low thermal conductivity of PVC.
FIGURE 1: The dehumidifier of the seawater greenhouse (air direction is towards camera) 2.3. Simulation Model The simulation started by formulating the following energy balance;
& w (hwo − hwi ) = m & a [(hai − hao ) − (ω ai − ω ao ) CP, w Tao ] m
(1)
& is mass flow rate (kg s-1), h is specific enthalpy (J kg-1), ω is humidity ratio where, m -1 (kg kg ), CP is specific heat capacity (J kg-1 oC-1), T is temperature (oC) and subscripts a is air, w is water, i is inlet and o is outlet. Equation 1 reveals that all the heat gained by the coolant water comes from the sensible heat lost by the flowing air as well as from the latent heat released by the condensate. The simulation aims at predicting the outlet air temperature and humidity, outlet water temperature and dehumidification rate (ml min-1), and will follow an iterative approach
because there are some parameters that cannot be solved explicitly. The steps are as follows: a) Initially, the sensible heat lost by convection from the air to the external surface of the dehumidifier tubes is calculated using the following relation;
[
Q a = m& a C p, da (T ai − T ao ) + ω ai (Lv, 0 + C p, wv T ai ) − ω ao (Lv, 0 + C p, wv T ao ) −[(ω ai − ω ao ) C P, w T ao ] (2)
where, Lv, 0 is latent heat of vaporization at 0oC (J kg-1). However, this calculation necessitates the outlet air temperature ( T ao ) and humidity ratio ( ω ao ) to be known beforehand. b) Assume an initial value for T ao or use the T ao value obtained from step (e). c) By knowing ω ai and the dehumidification rate ( R d ), the outlet humidity ratio ( ω ao ) can be calculated. Therefore, a multiple linear regression analysis was conducted to correlate the R d to the influencing inlet parameters. The analysis using half of the dataset generated through experiments resulted the following empirical relation; & a + 249.1 * VPD + 71.5 * Twi + 484287.5 * m &w Rd = - 488886.9 + 10.4 * m
(3)
where, VPD is vapor pressure deficit (kPa). d) Assume an initial value for the external surface temperature of dehumidifier tubes ( T es ) or use the T es value obtained from step (i). The T es value is needed in the next step. e) Estimate another value for T ao from Equation (4) in which the external convective heat transfer ( Qcv, ext ) is equal to Qa (assuming an adiabatic system);
k Qcv, ext = Qa = Nu ext a Dext
T + Tao Aes ai − Tes 2
(4)
where, Nuext , ka , Dext and Aes are average external Nusselt number, thermal conductivity (W m-1 oC-1), external tube diameter (m) and external surface area of dehumidifier tubes (m2), respectively. Nuext is estimated from the equation originally developed by Grimison (1937) and then clarified and modified by Hausen (1983);
s D 0.31 Nuext = 0.35 1 + 0.1 T + 0.34 ext Rea,0.57 max Pra D s ext L
(5)
where sT and sL are spacing (m) between adjacent tubes of the dehumidifier in a direction perpendicular and parallel to the direction of flow, respectively. Rea, max is maximum Reynolds’s number and Pra is Prandlt number. f) Repeat steps (a – e) until a fixed Tao value is reached. g) Calculate Two from Equation (6) by making the sensible heat transfer rate of the water ( Qw ) equal to Qa (adiabatic system);
& w Cp, w (Two − Twi ) Qw = Qa = m
(6)
h) Find the average internal surface temperature of dehumidifier tubes ( Tis ) by making the internal convective heat transfer rate ( Qcv, int ) equal to Qa (adiabatic system);
T + Two k Qcv, int = Qa = Nuint w Ais Tis − wi Dint 2
(7)
where, Nu int is calculated using the following relation that was developed by Hausen (1943) for a fully-developed laminar flow condition and a constant wall temperature T is ;
Nu int
D 0.0668 int Rew Prw Ltube = 3.66 + 23 Dint Rew Prw 1 + 0.045 Ltube
(8)
i) Find another value for T es by using the conductive heat transfer rate through the walls of the dehumidifier tubes ( Qcd ). Similarly, Qcd is made equal to Qa (adiabatic system);
Qcd =
2 π k tube Ltube (Tes − Tis ) D ln ext Dint
(9)
j) Repeat steps (d – i) until a fixed T es value is obtain. By reaching the end of this iterative process, all of the aforementioned outputs are obtained, namely; T ao , ω ao , Two and R d . 2.4. Experiments A number of experiments were conducted on the dehumidifier of the Oman seawater greenhouse for two purposes; to generate enough data to develop an empirical relation predicting the dehumidification rate as a function of some inlet weather and operating parameters and to test the accuracy of the simulation approach. It should be noted that the dataset generated through experiments was divided into two halves; one half to develop the empirical relation and the other one was to test the accuracy. The multiple linear regression analysis provided the empirical correlation mentioned earlier (see Equation 3). In the experiments, the variable parameters were airflow rate, inlet air temperature and humidity. Humidity and air temperature were measured before and after the dehumidifier using humidity/temperature sensors. Water temperature was measured at the inlet and outlet of the dehumidifier using water temperature sensors. Airflow rate was made variable using fan speed regulators. Water production (dehumidification rate) was measured using a tipping bucket raingauge. 3. Results & Discussion: It was found that the predicted dehumidification rate ( R d (P ) ), using the developed empirical relation, was in agreement with the measured values ( R d (M ) ). Consequently, the calculated outlet humidity ratio ( ω ao (P) ) was also in agreement with the measured values ( ω ao (M ) ). Figs. 2 & 3 show the conformity between measured and predicted R d & ω ao , respectively. For data shown in Fig. 2, it was found that the average percentage predictive error (i.e. predictive error = predicted value – measured value) for the freshwater production was almost 11.5%. The predictive error for the outlet humidity ratio was less than 1.4% (SD ≤ 4.4%). Similarly, the simulation model accurately predicted the outlet air and water temperatures as can be seen in Figs. 4 & 5, respectively. The average percentage predictive error for the outlet air and water temperatures was less than 1.9% (SD ≤ 5.4%) and -1.5% (SD ≤ 3.4%), respectively.
Dehumidification rate (ml min-1)
500 400 300 200 100 0 20:10
Rd (M)
01:10
06:10
14:40
Rd (P)
19:40 00:40 05:40 Time (hh:mm)
10:40
15:40
20:40
FIGURE 2: Predicted & measured dehumidification rates at low airflow rate Humidity ratio (kg kg-1)
0.030
wao (M)
wao (P)
0.025 0.020 0.015 0.010 20:10
01:10
06:10
14:40
19:40 00:40 05:40 Time (hh:mm)
10:40
15:40
20:40
FIGURE 3: Predicted & measured outlet humidity ratio at low airflow rate
Temperature (oC)
35
Tao (M)
Tao (P)
30 25 20 15 20:10
01:10
06:10
14:40
19:40 00:40 05:40 Time (hh:mm)
10:40
15:40
20:40
Temperature (oC)
FIGURE 4: Predicted & measured outlet air temperature at low airflow rate. 35 30 25 20 15 10 5 20:10
Two (M)
01:10
06:10
14:40
Two (P)
19:40 00:40 05:40 Time (hh:mm)
10:40
15:40
20:40
FIGURE 5: Predicted & measured outlet water temperature at low airflow rate. 4. Conclusions The developed iterative approach to simulate the dehumidifier of the Oman seawater greenhouse was found to have a good capability to accurately predict the dehumidification rate, air outlet temperature and humidity ratio, and outlet water temperature. The predictive error for the freshwater production reached 11.5% and was less than 1.4%, 1.9% and -1.5% for outlet humidity ratio, outlet air and water temperatures, respectively. The outcome of the research results and trends can be utilized to fine tune the existing design in order to obtain performance characteristics.
5. References Al-Ismaili, A. M. (2003). Modification of a Quonset greenhouse to a humidificationdehumidification system: Design, construction and pilot testing. Unpublished MSc. Thesis,
Sultan Qaboos University, Muscat, Oman. Al-Ismaili, A. M. (2009). Modelling of a Humidification-Dehumidification Greenhouse in Oman. Unpublished PhD. Thesis, Cranfield University, UK. Davies, P. A., & Paton, C. (2005). The seawater greenhouse in the United Arab Emirates: Thermal modelling and evaluation of design options. Desalination, 173(2), 103-111. Davies, P., Turner, K., & Paton, C. (2004). Potential of the seawater greenhouse in Middle Eastern climates. In: Proc. International Engineering Conference Mutah 2004, April 26-28, Mutah University, Jordan, 523-540. Grimson, E D (1937). Correlation and utilization of new data on flow resistance and heat transfer for cross flow of gases over tube banks. Transactions of the ASME, 59, 583-594. Hausen, H (1943). Darstellung des warmeuberganges in rohern durch verallgemeinerte potenzbeziehungen. Z. VDI-Beiheft Verfahrenstechnic, 4, 91-98. Hausen, H (1983). Heat transfer in counter flow, parallel flow and cross flow. McGraw-Hill, New York. Paton, C., & Davis, P. (1996). The seawater greenhouse for arid lands. In: Proc. Mediterranean conference on renewable energy sources for water production, June 10-12, Santorini, 163-166. Perret, J. S., Al-Ismaili, A. M., & Sablani, S. S. (2005). Development of a humidificationdehumidification system in a Quonset greenhouse for sustainable crop production in arid regions. Biosystems Engineering, 91(3), 349-359. Stanghellini, C., & van Meurs, W. T. (1992). Environmental control of greenhouse crop transpiration. Journal of Agricultural Engineering Research, 51, 297-311.
