Aerodynamic analysis and CFD simulation of several cellulose evaporative cooling pads used in Mediterranean greenhouses

Computers and Electronics in Agriculture 76 (2011) 218–230

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Original papers

Aerodynamic analysis and CFD simulation of several cellulose evaporative cooling pads used in Mediterranean greenhouses ˜ b , A.M. Pérez a A. Franco a , D.L. Valera b,∗ , A. Pena a b

ETSIA, Universidad de Sevilla, Ctra. Utrera km. 1, 41013 Sevilla, Spain Universidad de Almería, Ctra. Sacramento s/n, 04120 Almería, Spain

a r t i c l e

i n f o

Article history: Received 27 July 2010 Received in revised form 14 January 2011 Accepted 30 January 2011 Keywords: Greenhouse Aerodynamic analysis CFD Evaporative cooling Fan and pad Pressure drop

a b s t r a c t The present work makes an aerodynamic analysis and computational fluid dynamics (CFD) simulation of the four commercial models of corrugated cellulose evaporative cooling pads that are most widely used in Mediterranean greenhouses. The geometric characteristics of the pads have been determined as well as the volume of water they retain at different flows of water, thus obtaining the mean thickness of the sheet of water which runs down them and their porosity. By means of low velocity wind tunnel experiments, the pressure drop produced by the pads has been recorded at different wind speeds and water flows. In this way it has been possible to obtain the relationship of the permeability and the inertial factor with pad porosity using a cubic type equation. Finally, a CFD simulation with a 3D model has been carried out for both dry pads (Qw = 0 l s−1 m−2 ) and wet ones (Qw = 0.256 l s−1 m−2 ), finding good correlation between the simulated and experimental pressure drop, with maximum differences of 9.08% for dry pads and 15.53% for wet ones at an airspeed of 3 m s−1 . © 2011 Elsevier B.V. All rights reserved.

1. Introduction The surface area of greenhouses is increasing worldwide. Approximately 20% of this area is concentrated in the Mediterranean basin, consisting for the most part of only rudimentary greenhouses (Baille, 2001). The Spanish Mediterranean coast has 45,000 ha of greenhouses (Castilla and Hernández, 2005) and the southeast of the country, particularly the province of Almería, is the location of the highest concentration of greenhouses in the world, with 30,000 ha of farms, representing 4% of the global total (Molina-Aiz, 2010). The protected horticulture sector in southern Europe is currently facing strong international competition, mainly from areas such as the north of Africa, where production costs, including labour costs, are substantially lower. In order to improve the sustainability of greenhouse crops it is necessary to improve the final quality of production, increase crop yield and modify the periods of maximum production. These requirements have led to constant advances in greenhouse technology. As a result of this technification, evaporative cooling systems are being implanted in areas with high spring-summer temperatures such as the Mediterranean basin. These systems reduce the temperature inside the greenhouse by increasing the air humidity

∗ Corresponding author. Tel.: +34 950015546; fax: +34 950015491. E-mail addresses: [email protected] (A. Franco), [email protected] (D.L. Valera), ˜ [email protected] (A. Pena), [email protected] (A.M. Pérez). 0168-1699/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.compag.2011.01.019

content. Thus, by maintaining suitable hygrometric levels in the development stages of crops with little foliage and high evapotranspiration requirements, the transplant date of some autumn-winter crops can be brought forward to mid-August. As a result, the crop can be harvested at a time when the produce fetches higher prices. Evaporative refrigeration can be carried out by directly spraying water inside the greenhouse and combining it with natural ventilation (Fog/Mist Systems) or by obliging the outside air to pass into the greenhouse through moistened evaporative pads combined with mechanical ventilation (Fan–Pad Cooling Systems). Fan and pad cooling systems constitute a substantial improvement in climate control for greenhouses (Sethi and Sharma, 2007a) and poultry houses (Dagtekin et al., 2009). An evaporative pad is a permeable screen which is saturated with water by means of an irrigation system on its upper part. The temperature of the air passing through the screen drops, and these air then cools the inside air on mixing with it. The pads are located along part or all of the side of the greenhouse. They are continuously moistened by an irrigation and recirculation system. Powerful extractor fans installed on the opposite side of the greenhouse create the necessary suction to ensure that outside air passes into the greenhouse through the pads. When the cool damp air from the pad comes into contact with the mass of warm dry air inside the greenhouse, the air velocity falls, which brings about a sharp increase in the turbulence of the air flow (turbulence intensity, turbulence kinetic energy, turbulence kinetic energy dissipation rate and slope of the spectrum of energy density). This increase in turbulence is less when there is a crop in the

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Nomenclature A As e K Kf l le le /l Qw Re V Va Vl Vs VT %diff P

surface area per unit volume (m2 m−3 ) surface area of pad media (m2 ) mean thickness of the sheet of water (m) permeability (m2 ) Forchheimer’s permeability (m2 ) pad thickness (m) characteristic length of pad (m) characteristic parameter of pad geometry (adimensional) water flow applied (l s−1 m−2 ) Reynolds number (adimensional) airspeed (m s−1 ) volume of air in the pad (m3 ) retained water volume (m3 ) solid volume of the cellulose sheets (m3 ) total sample volume of pad (m3 ) percentage difference (%) pressure drop (Pa)

Greek letters ˇ factor inertial de Forchheimer (adimensional)  cubic law inertial factor (adimensional)  fluid density (kg m−3 )  dynamic viscosity (Pa s)  porosity (m3 m−3 )

greenhouse, which indicates that the crop has a dispersion effect on the air momentum, which is characteristic of porous media (Lopez et al., 2010). As the air moves from one end of the greenhouse to the other, undesirable gradients of temperature, humidity and CO2 develop throughout the greenhouse; the largest are to be expected at around midday when the intensity of solar radiation is greatest (Teitel et al., 2010), and in circumstances of low leaf area index and low drag coefficient. This system requires extremely air-tight structures to ensure that all the air entering the greenhouse does so through the pads. This fact has meant that in structures that are not so hermetic, such as Almería-type greenhouses, another system has been more widely applied, namely the fog system. Nevertheless, the saturation efficiency of the pad–fan system is greater (Katsoulas et al., 2009), it is cheaper to install and consumes less water and energy (Sethi and Sharma, 2007b) than the fog system. Moreover, the different types of greenhouses used in southeast Spain are evolving towards more hermetic multi-tunnel structures, which have increased from 0.6% of the total greenhouse area in the province of Almería in 1997, to 2.5% in 2006 (Valera and MolinaAiz, 2008). This trend is continuing at present (Molina-Aiz, 2010) and the increasing number of multi-tunnel greenhouses on the Mediterranean coast is allowing more and more pad–fan systems to be installed. Greenhouse cooling by means of the pad–fan system obviously involves higher energy and water consumption than the use of the traditional system of natural ventilation and transpiration of the crop. However, this increase in production costs can be offset by the corresponding increase in earliness, quality and yield of the crop, allowing growth in arid zones during the summer period. This allows growers to produce over a longer period and/or to commence the following season earlier, thus modifying the periods of maximum production. The water consumption of the pads increases linearly with the ventilation rate (Sabeh et al., 2007), registering values of between 3.2 and 10.3 l m2 of greenhouse for 150 mm cellulose pads in semiarid conditions. In conditions of extreme aridity the recorded values

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were between 7.9 and 16.3 l m2 of greenhouse for 100 mm corrugated cellulose pads (Al-Helal, 2007). For 100 mm pads in the province of Almería (Spain) values were recorded of 146.3 l d−1 m−2 of evaporative pad (Franco et al., 2010), with an air velocity through the pad of 1.27 m s−1 (ANSI/ASABE Standards, 2008), producing a mean reduction of 8 ◦ C compared to the outside temperature (Sethi and Sharma, 2007a) working 8 h d−1 on average. However, the crop requires less irrigation (Montero, 2006), as its transpiration rate falls by 31%. Therefore, the total increase in water requirement of a greenhouse fitted with a pad–fan cooling system is only 19% (Katsoulas et al., 2009). Moreover, if this system is combined with shading, the thermal gradient decreases (Kittas et al., 2003) and electrical consumption is reduced by around 8% (Willits and Peet, 2000). The vast majority of new greenhouses built in the Mediterranean area incorporate pad–fan cooling systems using corrugated cellulose pads. These are more costly than alternative local materials but they are a rigid porous medium that only requires a simple support structure, they are easy to maintain, do not emit particles and are durable. The present study therefore focuses on this type of pad, analyzing the most widely used commercial models. Rising energy costs, together with scant water resources in most areas of intensive production, urge the use of evaporative cooling systems that are economical and highly water and energy efficient. Choosing the most suitable evaporative pad requires knowledge of its different parameters. ANSI/ASABE Standards (2008) recommends values of airspeed through the pads, minimum water flow to be applied and other parameters for only two types of pad and two different thicknesses: Aspen fiber pads of 50 and 100 mm, and corrugated cellulose pads of 100 and 150 mm. Due to the intricate geometry of corrugated cellulose pads and the complex processes of heat and mass transfer that occur inside them, semi-empirical methods are still used for their design (Beshkani and Hosseini, 2006). Evaporative pads make it more difficult for outside air to flow into the greenhouse. Expressed as pressure drop, this resistance to air flow depends on the geometric characteristics of the pad, on the amount of water applied and on the air flow (Franco et al., 2010). Less resistance to air flow means lower energy costs, as the fans require less energy to maintain the ventilation rate. Finding a procedure to simulate new pad designs that reduce resistance to the flow of air and therefore increase their efficiency is a key factor for reducing costs. The aerodynamic characteristics of the different types of cellulose evaporative pads at different airspeeds and water flows must be known in order to analyze their pressure drop. Valera et al. (2006) carried out assays with insect-proof screens using two devices that suction air through the screens, obtaining data of pressure drop as a function of airspeed. This type of analysis allows us to obtain simple ratios between permeability and the inertial factor as a single function of porosity. On the other hand, in recent years computational fluid dynamics (CFD) has proved to be a most useful tool for simulating the interaction of liquids and gases with complex surfaces, and the many works published on the subject have achieved results that are very close to real results. Verification of the data obtained by CFD is usually carried out in a wind tunnel, in other scale models or by means of direct measures. According to Molina-Aiz et al. (2010), over the last 25 years, computational fluid dynamics (CFD) has been increasingly used to describe quantitatively and qualitatively the natural ventilation in greenhouses (Mistriotis et al., 1997; Boulard et al., 1999; MolinaAiz et al., 2004; Campen, 2006; Lee et al., 2006; Baeza et al., 2006; Tong et al., 2009; Teitel et al., 2008) and to model other systems of climatic control such as thermal screens (Montero et al., 2005), fan ventilation (Fidaros et al., 2008) or fog systems (Kim et al.,

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2008). CFD has also been used to study the distribution and deposition of fungal spores in greenhouses (Roy et al., 2006) or pesticide dispersion (Bartzanas et al., 2006). At present, simulations of CFD have achieved a high level of complexity, including the radiation exchanges between the atmosphere and the greenhouse surfaces (Ould Khaoua et al., 2006; Bournet et al., 2007) and the transfer of heat and water vapour between the crop and the air (Boulard et al., 2002; Roy et al., 2008; Majdoubi et al., 2009; Fatnassi et al., 2009). Simulation of evaporative pads using CFD provides the opportunity to improve their performance by increasing their cooling efficiency and reducing resistance to the airflow through the pad, which results in energy saving and therefore a reduction in environmental impact. The present work therefore has the following three aims: (i) to determine experimentally the influence of water flow regimes applied to evaporative pads on their porosity and on the pressure drop they produce when air passes through them, (ii) to characterize the airflow on passing through the evaporative pads by means of permeability and the inertial factor coefficient of cubic law, and (iii) to create a numeric model using CFD, and to validate these results with experimental data of the influence of air flow and volume of water on the pressure drop for the four commercial corrugated cellulose evaporative pads that are available on the market.

2. Materials and methods 2.1. Geometric characterization of the evaporative pads The pads are made up of sheets of corrugated cellulose that are stuck together alternating the angles of incidence on the horizontal so that they do not coincide (Fig. 1). In this way we achieve greater transfer surface (m2 m−3 ), greater mechanical resistance and lower resistance to the passage of air and water. The length and width of the undulation of the sheets, together with the angles of incidence and the thickness of the pad are considered the characteristic geometric parameters. Four commercial models of evaporative pads made by two different manufacturers were tested. These are the most commonly used models in the Mediterranean region. The manufacturer G&R (Gigola and Riccardi, Italy) commercializes a 100 mm thick model with angles of 45–45◦ , while Munters (Kista, Sweden) markets three models, two with angles of 60–30◦ that are 50 and 100 mm thick, and one with angles of 45–45◦ that is 100 mm thick, but with length and width of undulations different from the G&R model. Three different samples of each type were tested in the wind tunnel. These samples were 0.60 m wide by 0.65 m high, i.e., more than the minimum height of 0.60 m as recommended by ANSI and ASABE (ANSI/ASABE Standards, 2008). A detailed study was made of the geometric characteristics of the cellulose pads tested. The geometric parameters are as follows: angles of incidence of the sheets that make up the pads (◦ ), thickness of the pad (mm), number of sheets per meter of pad width (ud, m−1 ), thickness of the sheets (mm), undulation length (mm), undulation width (mm), specific area of the pad (m2 m−3 ), porosity (m3 m−3 ), and a non-dimensional geometric parameter (le /l), where le is the characteristic length (m) and l is the thickness of the panel (m). The characteristic length (m) is defined as le = V/As = A−1 , where V is the volume occupied by the porous medium (m3 ), As is the area of transfer of the pad (m2 ), and A is the specific area of the pad or the area per unit of pad volume (m2 m−3 ). For the length and width of the undulation of the sheets, the caliper and thickness were measured with a micrometer. To calculate the specific area, we used image software (Matrox Inspector v.2.2, Matrox Electronic Systems Ltd., Quebec, Canada). Finally, the dry porosity was calculated as one minus the ratio between the solid volume

and the total volume of the pad. Table 1 shows the geometric characteristics obtained in our study. This geometry is fundamental to carry out the fluid domain for the aerodynamic analysis of the pads and the CFD simulations of the evaporative pads. Prior the tests, the pads were immersed in water during 24 h and that all the flowing water remains on the pad’s surface and is not retained inside the pad’s solid matrix. The volume of water retained by the pad must be determined as a function of the flow of water applied to calculate the pad porosity and to simulate its behavior when wet. In order to determine the geometry of the fluid domain we have made a simplification by considering that the water displaced by the pad due to gravity maintaining constant the water sheet thickness over the whole transfer surface. Said mean thickness of the sheet of water is easy to calculate given the retained water volume and the transfer surface of the sample (Eq. (1)). Prior the tests, the pads were immersed in water during 24 h and that all the flowing water remains on the pad’s surface and is not retained inside the pad’s solid matrix. The sheet of water reduces the porosity of the evaporative pad, and consequently increases its resistance to the airflow. e=

Vl Vl = As AVT

(1)

where e is the mean thickness of the sheet of water (m), Vl the volume of water retained by the pad (m3 ), As the pad’s area of transfer (m2 ), A the pad’s specific area (m2 m−3 ) and VT the total volume of the pad sample (m3 ). The porosity () of the different pads under different working conditions can be correlated to the geometry (le /l) and the water flow applied (Qw ), the same as the pressure loss (Milosavljevic and Heikkilä, 2001; Franco et al., 2010), as follows: =k

 l a e

l

b (1 + Qw )

(2)

Carrying out a nonlinear regression analysis we can obtain the values of the parameters k, a and b. 2.2. Assay equipment and procedures In order to compare and validate the results of the CFD simulations regarding the influence of air and water flows and pressure drop with the experimental data, a low-speed open-circuit wind tunnel was used with a circular cross-section of 38.8 cm diameter. The wind tunnel was designed and constructed in the Department of Rural Engineering of the University of Almería (Valera et al., 2006). A uniform and stable air flow was achieved (as reported by Fang et al., 2001) under controlled conditions of temperature and humidity. To carry out tests with evaporative pads in the wind tunnel, a specific test frame was designed to incorporate the pads (Franco et al., 2010). This frame consisted of a galvanized metal structure with a water distribution system incorporated into the top part (Fig. 2). The water distribution system was constructed of a 20 mm diameter PVC pipe with 2 mm holes 65 mm apart. In the lower part of the frame, a water collection system allowed water to drain by gravity into a tank, before being recycled by a 12 V axial pump. Water flow at the entrance was controlled by varying the voltage of the continuous-current hydraulic pump and readings from the rotameter (flowmeter) with an average range of 3–22 l min−1 and an error of ±4%. The geometry of the frame was suitable to ensure that the assays with moistened pads were as similar as possible to conditions in the greenhouse. Moreover, the rectangular chassis was necessary to hold the rectangular sample of the pad, the system for applying water and distributing it uniformly and the drainage system. The pad sample assayed must be rectangular in order to ensure

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Fig. 1. Composition of the four evaporative pads analyzed: a) 45–45◦ 100 mm by G&R; b) 45–45◦ 100 mm by Munters; c) 60–30◦ 100 mm by Munters; d) 60–30◦ 50 mm by Munters. Table 1 Characteristics of the cellulose pads assayed. Manufacturer

G&R Munters Munters Munters

Pad thickness (mm) 100 100 100 50

Angles (◦ ) (units/m)

No. sheets

45–45◦ 45–45◦ 60–30◦ 60–30◦

157 142 132 208

Thickness of sheets (mm)

Length of undulation (mm)

Width of undulation (mm)

0.213–0.213 0.228–0.228 0.192–0.191 0.222–0.219

19.5–19.5 20.5–20.5 18.5–17 12–11

6.37–6.37 7.00–7.00 7.50–7.50 4.80–4.80

Fig. 2. Diagram of the water recirculation system for moistening the evaporative pad, the system for measuring the water flow applied and the weighing system.

Specific area (m2 m−3 )

le /l

Dry porosity (m3 m−3 )

391.114 347.114 361.516 556.752

2.557 × 10−2 2.888 × 10−2 2.766 × 10−2 3.592 × 10−2

0.957 0.959 0.965 0.937

uniform distribution of the water over the whole surface of the cellulose sheets it comprises. The chassis was completely airtight, only allowing the passage of air through the circular section of the chassis which coincided with the circular section of the wind tunnel. Three different samples were tested for each pad model. These samples were 0.60 m wide by 0.65 m high. The pads were immersed in water for 24 h before each test in order for them to be totally saturated. Four different water flow rates were tested, both above and below the 6.2 l min−1 m−1 minimum recommended by ANSI and ASABE (ANSI/ASABE Standards, 2008) for 100 mm thick corrugated vertical cellulose pads. These flow rates were 5, 6.6, 8.3, and 10 L min−1 per linear meter of pad mounted vertically. Expressed in terms of flow rate per exposed surface area of pad (m2 ) in the test, these numbers were 0.128, 0.171, 0.214, and 0.256 l s−1 m−2 , respectively. These flow rates were kept constant by varying the pressure of the hydraulic pump using a power source and adjusting the flow rate based on readings from the rotameter. The experiment was also repeated with a dry pad solely to test the pressure drop of the air passing through it.

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Fig. 3. Fluid domains of the tested dry pads: a) 45–45◦ 100 mm G&R; b) 45–45◦ 100 mm Munters; c) 60–30◦ 100 mm Munters; d) 60–30◦ 50 mm Munters.

Fig. 4. Thickness of the mean sheet of water of the fluid domain of the pad 45–45◦ 100 mm G&R when wet (Qw = 0.256 l s−1 m−2 ).

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The application of Darcy’s law is the standard method for characterizing the homogeneous flow through porous media. For a permanent flow in a single direction of incompressible and Newtonian fluid through a porous horizontal medium, this law is as follows: −

Fig. 5. Diagram of pad meshing 45–45◦ 100 mm G&R when dry.

The air flow through the pad was regulated by controlling the fan speed, taking continuous measurements with a hot-wire anemometer. The range of airspeed for the test was set between 0.3 and 3 m s−1 . At the start of the test, the water flow was fixed. After 10 min, the fan was started at an initial velocity of approximately 0.3 m s−1 , increasing by 0.6 m s−1 up to 3 m s−1 . Increments in speed were separated by 5 min intervals so that equilibrium could be achieved between the pad and the new air and water conditions. At each airspeed, 100 data were recorded by all the sensors at 3 s intervals. 2.3. Aerodynamic analysis of the porous medium The evaporative pad is a structured porous medium that produces resistance when air passes through it into the greenhouse. This resistance increases as the pad’s porosity decreases, usually due to high water flows moistening the pad or to incrustations of carbonates and organic remains in the pores when maintenance is deficient. This increase in resistance hampers ventilation and reduces the efficiency of the greenhouse cooling system. It also implies a higher energetic cost of the fans which make the air circulate.

 P = V K l

(3)

where P is the pressure drop (Pa), l the thickness of the porous medium (m),  the dynamic viscosity (Pa s), K the Darcy’s permeability (m2 ) and V the air velocity (m s−1 ). However, this law is only applicable for very low flow rates, since at higher ones the pressure drop is not proportional to the air velocity. The adimensional number used to characterize the start of non-linear behavior is the Reynolds number (Re). Non-linear behavior is accepted to occur for a Reynolds number of between 1 and 10. At high Reynolds numbers, a strongly inertial regime appears and Forchheimer’s empirical equation is used. This equation has been used by several authors to describe the passage of air through ˜ et al., insect-proof screens (Dierickx, 1998; Miguel, 1998a,b; Munoz 1999; Bartzanas et al., 2002; Valera et al., 2006) and is written as: −

P  = V + ˇV 2 Kf l

(4)

where Kf is Forchheimer’s permeability (m2 ),  the fluid density (kg m−3 ) and ˇ the adimensional inertial factor. This equation defines the pressure drop as the sum of two terms, one of which is viscous and the other inertial. Nevertheless, other authors (Amaral and Moyne, 1997; Fourar et al., 2004) show that the appearance of a weakly inertial regime, in which the non-linear behavior of flows begins to appear, can be described by the cubic law: −

P 2 3  V = V+ K  l

(5)

where  is the inertial factor, an adimensional parameter for weakly inertial regimes. This equation was obtained from numerical simulations in periodical two-dimensional porous media used

Fig. 6. Pressure at the inlet in the models of pads tested dry at an entrance velocity of 0.50 m s−1 : a) 45–45◦ 100 mm G&R; b) 45–45◦ 100 mm Munters; c) 60–30◦ 100 mm Munters; d) 60–30◦ 50 mm Munters.

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Fig. 7. Retained water volume per surface unit as a function of flow.

Fig. 8. Pressure drop against air velocity in the G&R 45–45◦ 100 mm pad both wet and dry (Qw = 0.256 l s−1 m−2 ).

in homogenization techniques for isotropic and homogenous media.

2.4. CFD simulation Computational fluid dynamics (CFD) is a sophisticated design and analysis tool that allows us to study different design limitations based on a computational model.

The CFD software used in the present work was ANSYS-CFX from the Workbench package. Its code uses a discretization procedure of finite volumes and it incorporates the equations that govern heat flow and transfer, such as the continuity equation, momentum conservation and energy conservation. The overall methodology used to carry out a complete study with the commercial software used in this work is summarized as follows: generating the geometry of the fluid domain, meshing, defining the boundary conditions and the physical properties of

Table 2 Mean theoretical thickness (mm) of the sheet of water and porosity (m3 m−3 ) as a function of the water flow applied. Pad model

Water flow applied 0 l s−1 m−2

G&R 45–45◦ 100 mm Munters 45–45◦ 100 mm Munters 60–30◦ 100 mm Munters 60–30◦ 50 mm

0.128 l s−1 m−2 −3

e (mm)

 (m m

0.00 0.00 0.00 0.00

0.957 0.959 0.965 0.937

3

)

0.171 l s−1 m−2 −3

e (mm)

 (m m

3.59 × 10−2 5.82 × 10−2 4.93 × 10−2 8.25 × 10−2

0.943 0.939 0.947 0.891

3

)

0.214 l s−1 m−2 −3

e (mm)

 (m m

4.26 × 10−2 6.59 × 10−2 5.54 × 10−2 9.55 × 10−2

0.940 0.937 0.945 0.884

3

)

0.256 l s−1 m−2 −3

e (mm)

 (m m

4.76 × 10−2 7.23 × 10−2 5.91 × 10−2 10.62 × 10−2

0.938 0.934 0.943 0.878

3

)

e (mm)

 (m3 m−3 )

4.93 × 10−2 7.87 × 10−2 6.60 × 10−2 12.19 × 10−2

0.938 0.932 0.941 0.869

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Table 3 Coefficients a and b for the best cubic fit (P = aV3 + bV), determination coefficient R2 , permeability K and inertial factor () calculated for the four pad models and five water flows tested (20). Qw (l s−1 m−2 )

a

b

R2

K (m2 )



G&R 45–45 100 mm

0 0.128 0.171 0.214 0.256

0.820 0.866 0.886 0.966 0.979

5.743 6.388 6.421 6.098 6.316

0.993 0.997 0.997 0.995 0.996

3.221 × 10−7 2.896 × 10−7 2.881 × 10−7 3.034 × 10−7 2.929 × 10−7

1.089 × 10−4 1.151 × 10−4 1.177 × 10−4 1.283 × 10−4 1.301 × 10−4

Munters 45–45◦ 100 mm

0 0.128 0.171 0.214 0.256

0.586 0.721 0.728 0.786 0.786

4.845 5.222 5.686 5.102 5.679

0.992 0.992 0.996 0.994 0.994

3.818 × 10−7 3.543 × 10−7 3.254 × 10−7 3.626 × 10−7 3.258 × 10−7

7.786 × 10−4 9.580 × 10−4 9.673 × 10−4 1.044 × 10−4 1.044 × 10−4

Munters 60–30◦ 100 mm

0 0.128 0.171 0.214 0.256

0.759 0.852 0.822 0.854 0.833

6.038 6.153 6.409 6.248 6.629

0.996 0.995 0.996 0.994 0.994

3.064 × 10−7 3.007 × 10−7 2.887 × 10−7 2.961 × 10−7 2.791 × 10−7

1.008 × 10−4 1.132 × 10−4 1.092 × 10−4 1.135 × 10−4 1.107 × 10−4

Munters 60–30◦ 50 mm

0 0.128 0.171 0.214 0.256

0.625 0.749 0.717 0.791 0.803

4.905 5.685 6.284 5.902 5.879

0.996 0.989 0.988 0.984 0.981

2.810 × 10−7 1.562 × 10−7 1.413 × 10−7 1.505 × 10−7 1.510 × 10−7

1.230 × 10−4 2.073 × 10−4 1.985 × 10−4 2.189 × 10−4 2.223 × 10−4

Pad ◦

Fig. 9. Permeability (K) as a function of the porosity of all the pads and water flows tested.

Fig. 10. Inertial factor () as a function of the porosity of all the pads and water flows tested.

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Fig. 11. Comparison of simulated and experimental results of pressure drop as a function of the air velocity entering dry pads (Qw = 0 l s−1 m−2 ): a) G&R 45–45◦ 100 mm; b) Munters 45–45◦ 100 mm; c) Munters 60–30◦ 100 mm; d) Munters 60–30◦ 50 mm.

the model (pre-processing), solving and finally analysis (postprocessing).

2.4.1. Geometry and meshing of the fluid domain The geometry of the fluid domain of each pad has been ascertained using computer assisted design (CAD) software by Autodesk. Using inverse engineering we obtained all the values required for drawing the geometry of the pad (thickness, curvature radius, length and width of undulation, etc.) by taking measurements on different samples of each pad model (Table 1). An axis is drawn corresponding to a sheet, and using equidistances, at the mid-point of the thickness of the sheet, on both sides of the axis we generate two new polylines made up of straight lines and circumference arcs. The two polylines are then joined at the ends to obtain a closed polygon that will be the basis for generating the solid sheet. The closed polygon is copied at the suitable distance to form the other cellulose sheet that will allow us to draw the basic unit of the model. The two polygons are extruded and we generate solid entities. The sheets are turned according to the angles of incidence of the different pads (45–45◦ or 60–30◦ ). Finally, a “mould” is constructed consisting of a solid parallelepiped with a hollow interior with the definitive dimensions of each pad. By means of Boolean operations (fusion of the sheets and difference between the solids and the mould) we obtain the geometry of the fluid domain. To obtain the air volumes, first a parallelepiped is generated with the same dimensions as the hollow interior of the first “mould” used and by measuring the difference between this solid and the one of the sheets we can obtain the air volume. It is most important that translational periodicity exists both in the upper and lower parts of the fluid domain, as it will later be applied as a boundary condition (Fig. 3). Obtaining the fluid domain of the air that passes through the wet pad is a complex task. Approximating the movement of water due to gravity over the transfer surface of the pad, we consider that

a mean theoretical sheet of water is a function of the flow applied and the geometry of the evaporative. A fluid model has been made for the four pads studied with a mean layer of water only for the maximum flow tested, i.e., 0.256 l s−1 m−2 . The model of the fluid domain of each type pad when wet was generated from the difference in solids between the two sheets making up the pad, minus twice the average layer of water running down it (Fig. 4). Once the geometry of the fluid domain was generated, it was imported and verified using the ANSYS-DesignModeler application. For the meshing we use the CFX-Mesh application from ANSYS Workbench, which generates hybrid meshes of tetrahedra and hexahedra. The meshing used was of the non-structured type with inflation on the sides of the model in contact with the sheets of the cellulose pad, and periodicity at the upper and lower parts of the solid model, to simulate continuity of the model used at a certain height (Fig. 5). 2.4.2. Boundary conditions, physical properties and solver The CFD simulations of evaporative pads carried out in the present work are steady state, with an isotherm fluid domain at 25 ◦ C and 1 atm atmospheric pressure. The physical model of turbulence is the Standard k-Epsilon Model. The boundary conditions, in CFX-Pre, were: - Inlet: Different speeds were applied to the input area of the model, with subsonic flow regime and normal speed to said area (V): 0.5, 1, 1.5, 2, 2.5, and 3 m s−1 , respectively in each simulation. - Outlet: Applied to the outlet area of the model, with subsonic flow regime and average static pressure of 0 Pa. - Wall: Applied at the sides of the model, in contact with the cellulose sheets, we refine for each limit layer of the mesh, considering it as a wall which does not slide and smooth wall. - Domain interface: Applied at the upper and lower areas of the model, in which periodicity was applied to the geometry and

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meshing of the model, creating domain interfaces, to conserve the conditions of the fluid. CFX-Solver has been made for a high resolution, with a maximum of 100 iterations, with an automatic control of the scale time and with a convergence criterion of residual type based on the residual average of all the control volumes (RMS) at a value of 10−4 . 2.4.3. Post-processor Once the CFX-Solver has been applied, we proceed to analyze the results (post-processor) generating a contour plot that shows the pressure field in the inlet area of the model, and obtaining the average value (Fig. 6). In this way, for each velocity simulated, the pressure difference between the inlet and outlet is determined for each type of evaporative pad tested. This difference will now be compared to the experimental results of the pads obtained in the wind tunnel. 3. Results and discussion 3.1. Volume of water retained by the pads The volume of water retained by the evaporative pads per surface unit has been shown to be directly related to the water flow applied to the pads’ upper part (Fig. 7). The pad which retained most water was the Munters 60–30◦ 50 mm, between 2.2 and 3.25 l m−2 with a maximum error of 3.08%, followed by the Munters 45–45◦ 100 mm (2.02 and 2.73 l m−2 and a maximum error of 7.74%), the Munters 60–30◦ 100 mm pad (1.78–2.39 l m−2 and a maximum error of 10.03%), and finally the G&R 45–45◦ 100 mm pad (1.40–1.93 l m−2 and a maximum error of 7.63%). Franco et al. (2010) studied the influence of water and air flow on the performance of corrugated cellulose pads, recommending airspeed intervals of between 1 and 1.5 m s−1 , obtaining pressure drop of between 3.9 and 11.25 Pa, depending on the pad thickness and the water applied. Air saturation efficiency was between 64 and 70% and evaporated water was between 1.8 and 2.62 kg h−1 m−2 ◦ C−1 . Increasing the flow of water applied to the pads, which is directly related to the water retained in them, did not modify their saturation efficiency or the amount of evaporated water, but it did increase their resistance to the air flow. 3.2. Mean thickness of the sheet of water and porosity of the pads Based on the results obtained regarding the retained water volume for the 4 types of pads and given the specific area of each one (Table 1), by applying Eq. (1) we obtain the values of mean theoretical thickness (e) of the sheet of water which descends the sheets of the cellulose pads for each flow applied. Knowing these values we are in a position to generate the geometric model of the fluid domain (air) that passes through the pad for each water flow applied. The porosity of the pads () can also be determined as the ratio between the volume of air (Va ) and the total volume (VT ); or more easily if we know the solid volume of the cellulose sheets that make up the pad (Vs ) and the volume of water retained by it (Vl ), previously determined for a known volume of sample (VT ). We can correlate these in the following equation: =

Va VT − Vs − Vl Vs V = =1− − l VT VT VT VT

(6)

As may be expected for any geometry, the greater the flow of water applied to the pad, the greater the volume of water it retains, the greater the mean theoretical sheet of water descending the pad, and the smaller the porosity, as Table 2 shows.

227

According to the results obtained, the porosity () is correlated with the geometry of the pads (le /l) and the water flow, using non-linear regression analysis of the data and obtaining the following expression, considering that the pad is moistened (Qw > 0 l s−1 m−2 ):

 l −0.210

 = 0.215

e

l

(1 + Qw −0.029 ),

R2 = 0.881

(7)

3.3. Permeability and inertial factor In order to determine the permeability and inertial factor, the four commercial models of evaporative pads have been tested at five different water flows. These tests were carried out in a low velocity wind tunnel which has been described above, obtaining data pairs that relate each pressure drop produced by the pads at each water flow with the velocity of the air passing through the pad. It is known that an increase in air velocity produces a greater pressure drop (Koca et al., 1991; Liao and Chiu, 2002; Hosseini et al., 2006). We have observed for all the cellulose pads tested that on increasing the water flow applied the pressure drop for a given air velocity also increases. The is due to the reduction in pad porosity (m3 m−3 ) since the increase in water flow increases the sheet of water descending over the interior transfer surface and reduces the air volume per unit of volume. This is contrary to the results obtained by El-Dessouky et al. (1996) for structured pads. Fig. 8 shows the pressure drop for the G&R 45–45◦ 100 mm pad against the air velocity both wet and dry (maximum water flow tested: 0.256 l s−1 m−2 ). It can be seen that the two variables (pressure drop an air velocity) are closely related by means of the determination coefficient (R2 ), using the following form: P = aV 3 + bV

(8)

Equalling the first and second terms of the polynomial equation (Eq. (8)), respectively with the cubic equation (Eq. (5)), the following expressions are obtained to determine permeability (K) and the inertial factor (): K=

·l , b

=

·a l · 2

(9)

where l is pad thickness (m), a and b the coefficients of the first and second terms of Eq. (8), and taking into account the density  and dynamic viscosity  of the air for the experimental conditions, the permeability and inertial factor can be calculated for the four pads and five water flows tested (Table 3). Table 3 shows that the values of permeability tend to increase as the pad porosity increases, whereas the inertial factor tends to decrease. Consequently, both parameters can be obtained as a function of porosity. Figs. 9 and 10 show the values of permeability and inertial factor, respectively, as a function of porosity. The following equations are the ones that best fit the experimental data: K= − 1.53 × 10−5  2 + 3.04 × 10−5  − 1.47 × 10−5 ,

R2 =0.8153 (10)

=9.53 × 10−3  2 − 18.95 × 10−3  − 9.509 × 10−3 ,

R2 =0.9204 (11)

For each pad, the fit is not so good, which shows that permeability and inertial factor do not only depend on porosity, but also on the geometry of the pad. This constitutes the main limitation of the global approach, and it is here that the approach based on CFD

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Fig. 12. Comparison of simulated and experimental results of pressure drop as a function of the air velocity entering wet pads (Qw = 0 l s−1 m−2 ): a) G&R 45–45◦ 100 mm; b) Munters 45–45◦ 100 mm; c) Munters 60–30◦ 100 mm; d) Munters 60–30◦ 50 mm.

modeling comes into its own, as it takes into account the detailed geometry of the pad. 3.4. CFD simulation results and verification The influence of air velocity on the pressure drop produced by the different evaporative pads assayed, both wet and dry (Qw = 0.256 l s−1 m−2 ) has been obtained experimentally using a low velocity wind tunnel and simulated by a 3D geometric model using commercial CFD software (ANSYS-CFX). Comparing the simulated and experimental values of pressure drop at different air velocities in the four evaporative pads, both wet (Fig. 11) and dry (Fig. 12), shows high similarity. The percentage difference (%diff) between the measured and simulated values proposed by Wilson et al. (2006) is determined by Eq. (12). %diff =

 MaxP − MinP  MaxP

× 100%

(12)

We should point out that for dry pads (Qw = 0 l s−1 m−2 ) these differences are under 2.19 Pa for air velocities below 2 m s−1 , finding a maximum of 3.27 Pa in the Munters 60–30◦ 50 mm pad for an air velocity of 3 m s−1 , equivalent to 9.08%diff. Although the differences remain small in wet pads (Qw = 0.256 l s−1 m−2 ), they are slightly greater than in dry ones, obtaining differences of under 2.33 Pa for air velocities of less than 2 m s−1 , and recording a maximum of 7.10 Pa for the G&R 45–45◦ 100 mm pad at a velocity of 3 m s−1 , equivalent to 15.53%diff. The simulated and experimental pressure drop data have been correlated (Fig. 13) for all the evaporative pads tested both dry and wet, obtaining very high correlation for dry pads and even higher correlation for wet ones. The comparison between experimental data and those simulated by CFD show good correlation when the pads are dry, with a slope of 1.0143, i.e., an error of 1.43%. This correlation decreased when the pads were moistened, registering an error of 8.35%. This error could be due to the fact that the thickness of the sheet of

Fig. 13. Correlation between simulated and experimental pressure drop data for all pads: a) dry (Qw = 0 l s−1 m−2 ); b) wet (Qw = 0.256 l s−1 m−2 ).

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water running over the inside surface of the pad was taken to be constant; although this hypothesis is a good approximation, it may not be completely true. In the case of higher airspeeds (2–3 m s−1 ), the differences found were greater. Nevertheless, we consider the correlation between simulated and measured data to be acceptable, as in no case did the error exceed 10%. The CFD simulation procedure carried out in the present work may prove useful to manufacturers of evaporative pads, who can improve their design using different geometries in order to enhance their performance. Indeed, many researchers are currently working on agricultural applications of CFD, a fact witnessed by the increase in publications on this topic in recent years. We believe that the methodology applied in this paper may be useful to other researchers who are interested in enhancing the performance of similar technologies. The fit between measured and computed pressure drops was indeed better when using a global modeling based on the porous medium approach with an experimental determination of permeability and inertial factors. However, this approach requires very costly experimental equipment. 4. Conclusions Determining the volume of water retained by the pads is most useful for determining the porosity and average thickness of the sheet of water that descends the cellulose pads at different water flows. Good degree of agreement has been found between porosity and both the water flow applied and the pad geometry. Based on the results obtained in the wind tunnel, we can state that at higher water flow the pressure drop produced by the pad increases, but to a lesser extent than at higher air flow.The results obtained for pressure drop against air velocity through the pad at any water flow applied fit a polynomial function known as cubic equation, with determination coefficients that are very close to the unit. For porosity of between 0.85 and 0.97 (a range that covers characteristic values of all the evaporative pads tested at different water flows), the best equation that describes the relationship between permeability and inertial factor is a second order polynomial. Comparison of simulated and experimental pressure drop values at different air velocities for the four evaporative pads, both dry and wet, show a good degree of agreement. The maximum percentage differences are 9.08% for dry pads and 15.53% for wet ones at air velocity of 3 m s−1 . Modeling of evaporative pads using CFD proves to be a good tool for optimizing their design, since good correlation was found between simulated results and those obtained experimentally in the wind tunnel for both dry and wet pads. Using this technique we can model how an evaporative pad will function for any air velocity and water flow. We can therefore predict the pressure drop that the pad will produce and optimize its design accordingly. Acknowledgement The authors wish to express their gratitude to the Junta de Andalucía (Spain) for partially financing the present work by means of the research grants P09-AGR-4593. References Al-Helal, I.M., 2007. Effects of ventilation rate on the environment of a fan–pad evaporatively cooled, shaded greenhouse in extreme arid climates. Appl. Eng. Agric. 23 (2), 221–230. Amaral, H., Moyne, C., 1997. Dispersion in two-dimensional periodic porous media. Part I. Hydrodynamics. Phys. Fluids 9 (8), 2243–2252.

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