Effect of material ageing and dirt on the behaviour of greenhouse insect-proof screens

The present work examines the variations in the aerodynamic characteristics of four insect-proof screens by means of wind tunnel tests and digital image processing. The tested insect-proof screens were examined in three different conditions: (i) in their new, unused state; (ii) under conditions of accumulated dust and dirt after a period of 3 to 4 years of use; and (iii) under clean conditions after a period of 3 to 4 years of use and a cleaning treatment with high-pressure water. The deterioration of the screens caused the mesh to become less tense, therefore increasing its thickness and improving its aerodynamic behaviour despite a slight increase of the thread diameter and a subsequent decrease of the 2-dimensional porosity. The pressure drop coefficient, Fφ, of the used but clean screens was 1.5% to 8.8% lower (for u=1.0 m/s) than that of the new ones, thus increasing the discharge coefficient, Cd,φ, by between 0.8% and 4.8% as a result of the presence of the screens. On the other hand, comparison of the used screens in their clean and unclean states showed that the accumulation of dirt has a major bearing on their aerodynamic characteristics: Fφ increased by between 16.5% and 61.2% (for u=1.0 m/s) for the unclean screens, resulting in a Cd,φ reduction of between 7.5% and 21.3% and therefore a lower natural ventilation capacity of the greenhouse. A regular cleaning treatment of the insect-proof screens is a simple measure that improves the natural ventilation capacity of the greenhouse. Additional keywords: anti-insect screens; aerodynamic characterisation; accumulation of dust and dirt; deterioration. Abbreviations used: a, b and c (second-order polynomial regression coefficients); e (thickness [μm]); u (air velocity [m/s]); x (direction of airflow); Cd,φ (discharge coefficient due to the presence of insect-proof screens); CFD (computational fluid dynamics); Dh (diameter of the threads [μm]); Dhx (diameter of the weft threads [μm]); Dhy (diameter of the warp threads [μm]); Di (diameter of the inside circumference of the pore [μm]); Dr (thread density measurement [threads/cm 2]); Fφ (pressure drop coefficient due to the presence of an insect-proof screen); HDPE (high density polyethylene); Kp (screen permeability [m 2]); Lpx (length of the pore in the direction of the weft [μm]); Lpy (length of the pore in the direction of the warp [μm]); P (pressure [Pa]); R 2 (coefficient of determination); Rep (Reynolds number based on the screen’s permeability); Sp (area of the pore [mm 2]); St (reference surface area [mm 2]); Y (inertial factor). Greek letters: μ (dynamic viscosity of air [kg s–1 m–1]); φ (porosity [m–2 m–2]); φ* (estimated imaging porosity [m–2 m–2]); ρa (air density [kg m–3]); ∆P (pressure drop due to the presence of an insect-proof screen [Pa]). Authors ́ contributions: Conceived and research design: AL, FDMA, DLV. Acquisition data and statistical analysis: AL, KE, AP; Analysis and interpretation of data, and drafting the manuscript: AL. Critical revision of the manuscript for important intellectual content: FDMA, DLV, AP. Coordinating and supervising the research work: DLV. Citation: López, A.; Molina-Aiz, F. D.; Valera, D. L.; Peña, A.; Espinoza, K. (2018). Effect of material ageing and dirt on the behaviour of greenhouse insect-proof screens. Spanish Journal of Agricultural Research, Volume 16, Issue 4, e0205. https://doi. org/10.5424/sjar/2018164-11711 Received: 13 May 2017. Accepted: 13 Nov 2018. Copyright © 2018 INIA. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International (CC-by 4.0) License. Funding: Spanish Ministry of Economy and Competitiveness and European Regional Development Fund (ERDF) (grant AGL201568050-R). Competing interests: The authors have declared that no competing interests exist. Correspondence should be addressed to Diego L. Valera: dvalera@ual.es


Introduction
Insect-proof screens are a widespread means of preventing the entrance of harmful insects into greenhouses.Insect-proof screens are commonly manufactured with HDPE monofilament-woven fabrics of different densities of warp and weft threads (threads/cm 2 ).In the Mediterranean Basin, the use of insect-proof screens in greenhouse vents is a standard crop management practice; in the Province of Almería, Spain, insect-proof screens are employed in the side and roof vents in 99.1% and 95.4% of the greenhouses, respectively (Valera et al., 2016).These screens are installed to reduce the incidence of harmful insects inside the greenhouse (Baker & Jones, 1989;Teitel, 2007) and to impede the exit of biological-control insects that are beneficial for the crop (Teitel, 2007).
A number of research works have highlighted the negative effect of insect-proof screens on the greenhouse ventilation capacity and, by extension, on the greenhouse microclimate.Screens of low porosity increase both the temperature and the humidity inside the greenhouse (Fatnassi et al., 2002), decrease air velocity inside the greenhouse (Kittas et al., 2008) and increase the vertical temperature gradient (Soni et al., 2005), all of which have negative repercussions on crop growth and development (Teitel, 2010).Teitel (2007) published a review describing the negative effects of insect-proof screens in greenhouses, namely: (i) a reduction of the discharge coefficient of the vents, of the air velocity and of the turbulent kinetic energy of the air inside the greenhouse, resulting in a decrease of the capacity of the greenhouses to be cooled by natural ventilation; (ii) a reduction of light transmission; and (iii) an increase of temperature and humidity inside the greenhouse.A more detailed description of the negative effects of the use of insect-proof screens in greenhouses was presented in a previous work by López et al. (2013), where the effect of ageing and the accumulation of dirt on the geometrical characteristics of screens was studied.Other studies have analysed the geometric characteristics of insect-proof screens (Álvarez et al., 2012) and their aerodynamic behaviour by means of wind tunnel experiments (Miguel et al., 1997;Dierickx, 1998;Valera et al., 2005Valera et al., , 2006) ) or Computational Fluid Dynamics (CFD) simulations (Valera et al., 2005;Teitel, 2010).
In addition to determining the geometric and aerodynamic characteristics of the insect-proof screens, it is of great interest to quantify the influence of both the deterioration of the screens and the accumulation of dirt over time on these characteristics and thus on the natural ventilation capacity of the greenhouse.Among the few research works in this field of study, Linker et al. (2002) found that two months after installing a 50mesh screen (porosity of 0.36) in a 50 m 2 greenhouse in Israel, the pressure drop coefficient of the screen can increase by a factor of up to 20 (from 12 to 200).López et al. (2013) studied the effect of the deterioration of the screen over time and of the accumulation of dirt on the geometric characteristics of 4 insect-proof screens.The authors found that the thread diameter increased by between 2.1 and 3.9% and resulted in a reduction in the two-dimensional porosity φ of between 4.9 and 10.4% and a reduction of the porosity by up to 21.2% as a result of the accumulation of dust.
The effect of material aging and the accumulation of dirt on the geometrical and aerodynamic characteristics of insect-proof screens is of great research interest since their placement in the greenhouse vents negatively affects the ventilation capacity of the greenhouses (Kittas et al., 2008;Molina-Aiz et al., 2009) and, as a consequence, its microclimate (Fatnassi et al., 2002;Soni et al., 2005) and crop yield (Teitel, 2010).Moreover, the determination of the geometrical and aerodynamic characteristics of the insect-proof screens is necessary in energy balance models (Reyes-Rosas et al., 2017) and CFD simulations (Chu et al., 2017;Molina-Aiz et al., 2005) in order to predict climatic conditions in space and/or time in greenhouses in a variety of situations.The change of the characteristics of insect-proof screens as a result of their use over time is also a topic of interest for future research.Kitta et al. (2014) studied the effect of the optical properties of greenhouse covers on pepper productivity.Three types of screens were analysed in this study: a pearl insect-proof screen (transmittance to photosynthetically active radiation PAR of 78%), a white insect proof screen (59%) and a green shade screen (62%).The best agronomic results were obtained with the pearl insect-proof screen.Sangpradit (2014) analysed the effect of the material ageing and the accumulation of dirt on the optical characteristics of greenhouse cover materials.The influence of the accumulation of dust and dirt on the solar radiation transmissivity of polyethylene plastic films and of a variety of cleaning methods (jet cleaning, water jet cleaning and hand washing) was analysed in the study.Results showed that the average light transmissivity after 6 months decreased between 36% and 50% but that the mean transmission loss dropped to only 1% after the plastic film was cleaned.However, notable differences between cleaning methods were also apparent: the use of jet air with no additional treatment hardly improved the light transmissivity, whereas water jet cleaning improved the transmissivity drastically.
The aim of this work was to analyse the effect of material aging and the accumulation of dirt on the aerodynamic characteristics of the HDPE monofilament-woven fabrics that are employed as insect-proof screens in greenhouses.Variations in the aerodynamic behaviour of screens affect the ventilation capacity of greenhouses and therefore crop production.As a result, knowledge of the effect of material ageing and of the accumulation of dirt on the screen permeability is fundamental for an accurate estimation of ventilation capacity in greenhouse modelling.This work complements the information presented in the previous study by López et al. (2013), in which the geometric characteristics of used insectproof screens were analysed.

Material and methods
In this study, wind tunnel experiments were performed on samples from four screens with the objective of determining the effect of material aging and of the accumulation of dirt on the aerodynamic characteristics of insect-proof screens.Insect-proof screens were assessed in three different conditions: (i) newly installed, (ii) after 3 to 4 years of use with no cleaning treatment, and (iii) after 3 to 4 years of use after a high-pressure water cleaning treatment.

Experimental setup
The four insect-proof screens manufactured with HDPE monofilament-woven fabrics were installed in the side vents of two multi-span, naturally-ventilated greenhouses located at the agricultural research station of the University of Almería in south-eastern Spain (36° 51′ N, 02° 16′ W and 87 masl).Both Greenhouse 1 (24×45 m) and Greenhouse 2 (18×45 m), were divided in half by a polyethylene sheet.Natural ventilation consisted of two side vents (18×45 m) and three roof vents in Greenhouse 1, and of two side vents and two roof vents in Greenhouse 2 as described in López et al. (2013).The screen samples used for analysis were randomly taken from the side vents.The dimensions of the vents were 1.05×17.5 m and 1.05×22.5 m for the western and eastern half of the greenhouses, respectively, except for the northern side vents of Greenhouse 2, whose vents had a dimension of 1.05×15.0m and 1.05×20.0m for the western and eastern half, respectively.Screens 1 and 2 were installed in August 2007 (date of purchase July 2007), and screens 3 and 4 in September 2008 (date of purchase August 2008).The mechanisms used to hold the insect-proof screens in the side vents did not affect the integrity of the screens over time: U-shaped (omega) metal frames were attached to the vent structure, and the screen was then inserted and held in place by polyethylene stoppers, ensuring that the screens were not subjected to movements that may have affected their structure during usage, according to the method described in López et al. (2013).The four screens were removed from the greenhouses in September 2011.

Estimation of the porosity of unwashed insectproof screens
Screen 1 had a thread density of 13×30 threads/cm 2 and was designed by the Engineering Department of the University of Almería.Screens 2, 3 and 4 are commercial models with a thread density of 10×20 threads/cm 2 .The two-dimensional geometric characteristics of the new screens and the cleaned and uncleaned used screens (Table 1) were determined using specific software (Álvarez et al., 2012).For each screen, three samples of approximately 2.04 cm 2 were analysed.Twenty-four images were taken of each sample with a microscope that incorporated a Motic DMWB1-223 digital camera (MoticSpain S.L., Barcelona, Spain) with a 4× lens and a resolution of 10.5 μm/pixel.The analysis of each image included the geometric characteristics of 30 pores, 2 wefts and 9 warp threads (mesh 1) and 12 pores, 1 weft Table 1.Geometric characteristics of the new screens (New) and the clean used screens.Average value and standard deviation of: D r , thread density [threads/cm 2 ], determined with specific software; φ, porosity [m 2 /m 2 ]; L px and L py , the lengths of the pore [µm] in the direction of the weft and warp, respectively; D hx and D hy , diameter [µm] of the weft and warp threads, respectively; D h , diameter of the threads [µm]; D i , diameter of the inside circumference of the pore [µm]; S p , area of the pore [mm 2 ].N: number of the screen.Extracted from López et al. (2013).  .Further details on the methodology used for the digital image processing can be found in Álvarez et al. (2012).In addition, the effect of the deterioration of the screen and of the accumulation of dirt on its two-dimensional geometric characteristics was analysed in a previous work (López et al., 2013).Statistically significant differences were found between all the geometric parameters of the new screens and of the clean used screens, except for the D hx of the 4 mesh (Table 1).The two-dimensional geometric methodology cannot provide a complete analysis of the unclean used screens due to the fact that the dirt particles observed in the mesh (Fig. 1) are highly heterogeneous and, as such, hinder an accurate measurement of the real geometry of the pore with our specific software (López et al., 2013).This software calculates the porosity of the mesh φ (m 2 /m 2 ) by comparing the calculated surface of the pores S p and a total reference surface S t , maintaining the correct proportion between pores surface area and the solid surface area (threads) (Álvarez et al., 2012).Proportional allocation was performed by relating the surface area of every hole of the screen to a reference surface area defined by the longitudinal axes of the threads that define the associated hole (Álvarez et al., 2012).As this software could not determine the porosity φ of the unclean used screens, the imaging porosity (φ * ) was estimated based on black and white digital images of the insect-proof screens.This procedure compares the number of white pixels (corresponding to the pores) with the total number of pixels in each image, resulting in a certain degree of error due to the difficulty of maintaining the correct proportion between pores and threads (López et al., 2013).

Wind tunnel tests
The effect of time on the geometric characteristics on the insect-proof screens as described by López et al. (2013) was analysed in the present study by measuring the pressure drop caused by the screens.To this end, experiments were performed in a wind tunnel (Fig. 2) designed and developed at the University of Almería (Molina-Aiz et al., 2006;Valera et al., 2006).This wind tunnel was provided with an auto-tuning PI automatic control system and an open hardware and software platform as described in Espinoza et al. (2015).The pressure drop ΔP produced by the screen in the wind tunnel was measured by two Pitot tubes and a differential pressure transducer, whereas air velocity was measured by a hot-film anemometer.The wind tunnel had a length of 4.74 m and an experimental section diameter of 38.8 cm.Further details on the methodology for the tests and the characteristics of the wind tunnel can be found in Molina-Aiz et al. (2006), Valera et al. (2006), Espinoza et al. (2015) and López et al. (2016).The four insect-proof screens were tested under three different conditions: (i) the original, new screen, before installation in the greenhouse; (ii) the unclean screen after 3 to 4 years of use in the greenhouse; and (iii) the used screen after a cleaning treatment with a water jet.In all cases experiments were carried out on three randomly taken samples from each screen.
Although the wind tunnel allows testing at speeds of up to 10 m/s, the experiments were carried out at 0 1997 ;Dierickx, 1998;Muñoz et al., 1999) to adjust the experimental values of each pressure drop as a function of the air that passes through the porous medium (Molina-Aiz et al., 2006;Valera et al., 2006): (2) The zero-order term c can be neglected compared with the other terms a and b (Miguel et al., 1997;Molina-Aiz et al., 2009;López et al., 2014López et al., , 2016)).K p and Y is then determined by equalling the firstand second-order coefficients of Eq. ( 2 (3) (4) The thickness e of the insect-proof screens was introduced in Eqs. ( 3) and ( 4) and was determined by using a TESA-VISIO 300 non-contact optical measurement device (TESA SA, Switzerland; resolution of 0.05 μm; uncertainty in measurement of (3+10•e/1000) [μm]).For the magnitude of the measurements taken the uncertainty was <10 μm.
Bernoulli's equation provides an alternative way of describing the relationship between the pressure drop caused by the insect-proof screens and the air velocity through the screens (Kosmos et al., 1993;Montero et al., 1997;Teitel & Shklyar, 1998): (5) to 3 m/s to ensure that no damage to the sensors and wind tunnel components was caused when testing the unclean used screens.Once the screen is in place in the greenhouse, it is highly unlikely that the air velocity through it reaches the maximum tested speed of 3 m/s.In fact, the maximum air velocity registered at the vents in Greenhouse 1 with natural ventilation and with an insect-proof screen of 0.39 porosity was around 1.0 m/s in the study performed by López et al. (2012).
The wind tunnel experiments allow the determination of the pressure drop ∆P [Pa] caused by each insectproof screen as a function of the air velocity through the porous medium u [m/s].Thus, it is possible to determine the parameters that characterise the aerodynamic behaviour of the screens: K p , the screen permeability [m 2 ], a coefficient that is independent of the nature of the fluid and dependent on the geometry of the porous medium (Nield & Bejan, 1998); Y, the inertial factor, a dimensionless drag constant that is dependent on the characteristics of the porous material; F φ , the pressure drop coefficient; and, lastly, C d,φ , the discharge coefficient that results from the presence of insect-proof screens.
The airflow through the porous medium (the insectproof screen) can be described by modifying Darcy's equation (Forchheimer, 1901):  where F φ is the pressure drop coefficient as a result of the presence of an insect-proof screen, and can be obtained from Eqs. ( 1) and ( 5 The coefficient F φ can be used to predict the pressure drop caused by the screens below a certain limit of the Reynolds number (Teitel, 2001).This limit is established at Re p <10 5 (Molina-Aiz et al., 2009) when using a Reynolds number Re p based on the permeability of the screen.Re p can be obtained as follows (Nield & Bejan, 1998): A similar discharge coefficient has been used in the literature for monofilament-woven fabrics (Wang et al., 2007).

Statistical analysis
Regression analyses were carried out to study the relationship between different parameters (statistically significant for p<0.05), and in order to determine the statistical differences between geometric parameters.Multiple range tests were carried out applying Fisher's least significant difference (LSD) to determine the statistical differences between geometric parameters, establishing the confidence level at 99%.Statgraphics Plus (Manugistics Inc., Rockville, MD, USA) was used for all of these computations.

Results and discussion
The porosity values φ and the estimated imaging porosity φ * were obtained for the four analysed screens.The following results show the pressure drop curves produced by the screens under three different conditions: (i) new, unused screens, (ii) unclean used screens, and (iii) clean used screens.The pressure drop coefficient F φ , and the discharge coefficient that results from the presence of the insect-proof screens C d,φ are then presented, in both cases including an analysis of the effect of time and the accumulation of dirt on these values.

Porosity of unwashed old insect-proof screens
Table 2 presents the values of porosity φ and estimated imaging porosity φ * for the four screens analysed under the three testing conditions.Based on these data, it has been found that the two parameters are related as follows: φ = 0.941•φ * + 0.045 (R 2 = 0.85 and p = 0.001), with statistical significance at the 95% confidence level.This expression differs from the one presented in López et al. (2013), as the present work analyses porosity data (φ and φ * ) of the new screens and the clean used screens for determining this expression, whereas the latter study only used the porosity data of the clean used screens.The values of the calculated porosity φ are higher than the estimated imaging porosity φ* (Table 2) as a result of the reduction of the boundary areas of the images with incomplete pores.The interest of the above-mentioned equation that establishes the relationship between φ and φ*, is that it allows the determination of the values of φ for the unclean used screens in those cases where the geometrical analysis for the identification of the pore vertices is not possible.
Compared to the new screens, the unclean used ones caused a reduction of the porosity φ of 16.4%, 26.6%, 15.7% and 25.3% for meshes 1 to 4, respectively.N: screen number. [1]: estimated with φ = 0.941 φ * + 0.045 (R 2 = 0.85 and p = 0.001).a,b,c indicate that there were statistical differences at the 99.0% confidence level between the values of the estimated imaging porosity φ * for the new, clean used, and unclean used screens.d,e denote that there were statistical differences at the 99.0% confidence level between the values of the porosity φ for the new and clean used screens.Statistical analysis made with 3 samples of each screen with 24 images (72 data).This reduction is the result of two effects, namely, the accumulation of dust and dirt and the deterioration of the threads.The separate consideration of both effects is a more useful indicator than the total reduction of porosity.
Comparison of the new with the used screens, cleaned ones provided the following values for the reduction in porosity φ as a result of the deterioration of the screen: 4.9%, 10.4%, 5.3% and 5.3% for meshes 1 to 4, respectively.
The following values of reduction in porosity φ due to the accumulation of dust and dirt were obtained by comparing the cleaned and uncleaned used screens: 12.1%, 18.0%, 11.0% and 21.2% for meshes 1 to 4, respectively.These data differ from those presented by López et al. (2013) due to the modification of the expression [φ = 0.941 φ * + 0.045] that is used to estimate the porosity values φ of the unclean used screens.
In summary, deterioration of the screen mesh over time lead to a slight decrease in the two-dimensional porosity of the screen but the accumulation of dust and dirt produced a far greater reduction in this parameter.It could be argued that a reduction of the porosity of the screens should produce a reduction in the air permeability.However, this does not always hold true due to the fact that a variation in porosity produced by material ageing can also be associated with a modification in the tridimensional shape of the pore.This reinforces the need to perform aerodynamic analyses when determining the effect of material ageing and dirt on the screen permeability.

Variation in the pressure drop curves
Figure 3 shows the curves of pressure drop ∆P vs. air velocity u obtained from the wind tunnel experiments.Table 3 presents coefficients a, b and c of the fit obtained for Eq. ( 2), as well as parameters K p , Y and the coefficient F φ expressed as a function of Re p , for screens 1, 2, 3 and 4. Baker & Shearin (1994) provided values for the maximum pressure drop that an insect-proof screen should allow, namely, 8 Pa for a clean screen and 24.9 Pa for an unclean one.For air velocities of between 1 and 1.5 m/s, all the samples of new screens and clean and unclean used ones showed values close to the above-mentioned limit of 8 Pa, while the clean and unclean used screens were both above this limit (screens 1, 2 and 3) (Fig. 3).Linker et al. (2002) found that the pressure drop caused by a 50-mesh insect-proof screen (porosity 0.36) increased from 3 Pa (original sample) to 30 Pa (2 months after its installation in the greenhouse) for air velocity values of u=0.65 m/s, i.e. a 10-fold increase in pressure drop.In the present study, for the same air velocity, comparison of the unclean used samples and the new ones at the same air velocity revealed a maximum pressure drop increase of ×1.5 for screen 4, well below the findings of Linker et al. (2002).
The pressure drop caused by the clean used screens was slightly lower to that caused by the new ones (Figs.3b, 3c and 3d), except for screen 1 (Fig. 3a).The porosity values obtained for the new screens are higher than those  Old and dirty * 3.063 4.711 -1.347 0.999 2.163×10 -9 0.213 24.04×(Re p -1 + 0.213) N: number of the screen.*The thickness of the unclean used screens is considered the same as that of the clean ones.It was not determined independently on criteria of safety and hygiene in the metrology laboratory.a,b denote that there were statistical differences at the 99.0% confidence level between the thickness measured for the new and clean used screens.Statistical analysis made with 3 samples of each screens with 10 thickness measurements (30 data).
of the clean used ones (Table 2), which does not explain why the latter produced a lower pressure drop than the former.The aerodynamic behaviour of the insect-proof screens depends not only on their porosity, but also on the geometry and thickness of the threads (López et al., 2016).During manufacture the weft and warp threads are tensed, which may give rise to threads with an elliptic cross-section as opposed to a circular one (Wang et al., 2007).Wang et al. (2007) found that for the same value of orthogonal or two-dimensional porosity, the discharge coefficient of the screens (C d,φ ) was lower for threads with an elliptic cross-section than for those with a circular one.In the present work, the values of thread diameter and thickness were greater for the clean used screens than for the new ones, with significant statistical differences at the 99.0% confidence level (Tables 1 and  3).The initial tensing of the mesh may relax with time, and this, together with the deterioration of the threads, may cause the cross-section of the threads to increase, resulting in a more circular cross-section in the used screens, as compared to a more elliptic cross-section in the new ones.The difference in the thread cross-section and the fact that the mesh is less tense would explain the increase registered in the thickness of the screens over time (Table 3).The greater thickness and the more circular cross-section of the threads are the reasons why the pressure drop recorded is lower in the clean used screens than in the new ones.
The values determined for K p and Y do not depend solely on the screens' porosity of the screens, but also on other geometric characteristics (thread diameter, thread geometry, thickness, etc.) (López et al., 2016) which vary over time.Although Miguel et al. (1997) and Teitel (2001) indicated that K p increases with porosity, in the present study this was not the case.The permeability K p of the new screens was inferior to that of the clean used ones (Table 3), which were less porous but thicker.The accumulation of dust and dirt implied that the permeability K p of the unclean used screens was the lowest.As regards inertia Y, Teitel (2001) found that it increased with the porosity of the screen, whereas Miguel et al. (1997) did not find such a relationship.In the present study, no clear link between Y and porosity or any other of the screens' geometric parameters of the screens was found.
It should be highlighted that the passage of time, together with the exposure to environmental conditions, produces two contrasting effects on the aerodynamic behaviour of the screens.On the one hand, the deterioration of the mesh causes it to become less tense, resulting in a lower pressure drop (Figs.3b, 3c and 3d).On the other hand, the accumulation of dust and dirt in the mesh leads to a much greater pressure drop through the screen.
Comparison of the screens by analysis of the parameters K p and Y is difficult.Due to the fact that there is no clearly observable tendency, it is considered more suitable to analyse the effect of the deterioration and the accumulation of dirt in the screens on the pressure drop coefficient F d,φ and on the discharge coefficient due to the presence of insect-proof screens C d,φ as a result of the presence of insect-proof screens.

Variation in the pressure drop coefficient F φ
The pressure drop coefficient F φ was clearly greater for the unclean used screens than for the new ones and the clean used ones (Table 4).On the other hand, F φ was slightly lower for the clean used screens than for the new ones.As commented above, this difference may be due to the deterioration and the tension loss, which increase the thickness of the mesh and the spherical shape of the threads.To compare the F φ values of the different screens, the following air velocity u values were considered: 0.25, 0.5 and 1.0 m/s.It is considered that the maximum values of air velocity through the vents of a commercial greenhouse using natural ventilation are unlikely to exceed 1.0 m/s, as was observed in the literature by using sonic anemometry (López et al., 2012).
Comparison of the unclean used screens and the new ones revealed increases in F φ of between 36.0%(screen 2 for u=0.25 m/s) and 47.0% (screen 4 for u=1.0 m/s).The cleaning treatment on the used screens caused the value of F φ to decrease with respect to the new screens, although this decrease is only relevant in the case of screen 4 (8.8% for u=1.0 m/s).Studying the effect of the accumulation of dirt in isolation, comparison of the unclean and clean used screens reveals an increase in F φ of between 16.5% (screen 3) and 61.2% (screen 4), for u=1.0 m/s (Table 4).From Eqs. ( 6) and ( 7) we can deduce a linear relation between the pressure drop coefficient F φ and the inverse of air velocity, whose slope is 2eμ / (K p ρ).Since the thickness e was considered the same for the unclean and clean used screens, and the permeability of the clean used screens was always greater than that of the unclean used screens (Table 3), the above-mentioned slope was always greater for the unclean used screens than for the clean used screens.As a consequence, the difference between F φ values increases as the air velocity drops (and therefore 1/u increases), as we can observe in Fig. 4. Thus, the greater differences in F φ are produced when air velocity thought the greenhouse screens is lower than 0.3 m/s, (1/u > 3.3 s/m).This situation corresponds when greenhouse ventilation is deficient and the effect of the screen on the greenhouse microclimate is more important.

Variation in the discharge coefficient due to the presence of insect-proof screens C d,φ
Once the values of F φ are known, the values of the discharge coefficient C d,φ for each screen can be derived from Table 4 by using Eq. ( 8).Comparison of the unclean used screens with the new ones reveals a reduction in C d,φ of between 5.3% (screen 3 for u=0.25 m/s) and 17.6% (screen 4 for u=1.0 m/s).When comparing the clean used screens with the new ones to study the effect of the deterioration of the mesh in isolation, it can be noticed that there is a slight increase in C d,φ of between 0.8% (screen 3 u=1.0m/s) and 7.3% (screen 4 for u=0.25 m/s).When studying the effect of the accumulation of dirt in isolation by comparing the clean and unclean used screens, the reduction in C d,φ is between 7.5% (screen 3) and 21.3% (screen 4), in both cases for u=1.0 m/s (Table 4).
Table 4. Values of the pressure drop coefficient F φ and of the discharge coefficient due to the insect-proof screen C d,φ for u equal to 0.25, 0.5 and 1.0 m/s, for the new screens, clean used screens, and unclean used screens.Fatnassi et al. (2002) found that the ratio between the air renewal rate (h -1 ) in a greenhouse with and without insect-proof screens can be considered proportional to the ratio between the discharge coefficients at the vents.In turn, the discharge coefficient at the vents depends on the coefficient C d,φ .The reduction observed in the coefficient C d,φ due to the accumulation of dust and dirt on the insect-proof screens results in a reduction of the natural ventilation capacity of the greenhouse.

Conclusions
The comparison of clean used screens with new ones showed a reduction of the pressure drop coefficient F φ of up to 8.8% (screen 4 for u=1.0 m/s).The maximum increase in the discharge coefficient C d,φ was 7.3% (screen 4 for u=0.25 m/s).This may be due to the deterioration of the insect-proof screens over time as it causes the mesh to become less tense, therefore increasing its thickness and improving its aerodynamic behaviour.
In addition, the accumulation of dirt on the screens has a major bearing on their aerodynamic characteristics.Comparison between the clean and unclean used screens showed an increase in F φ of up to 61.2% (screen 4 for u=1.0 m/s) and a decrease in C d,φ of up to 21.3% (screen 4 for u=1.0 m/s), with a concomitant reduction of the natural ventilation capacity of the greenhouse.
In view of the results obtained in the present work, it is recommended that insect-proof screens are manufactured with geometrical and aerodynamic characteristics that avoid approaching the limit of 8 Pa established by Baker & Shearin (1994) at an air velocity of between 1 and 1.5 m/s.Furthermore, it is advisable to incorporate anti-static properties in order to avoid the accumulation of dirt as much as possible.From an experimental point of view, it is also important to take into account the differences between the aerodynamic characteristics of new insect-screen and deteriorated, unclean insectproof screens in order to avoid significant errors in the CFD simulation or in the climatic greenhouse models.
Lastly, we can conclude that the mechanical deformation of screens over time produces a reduction of the resistance to airflow throughout the insect-proof screens installed in the greenhouse openings, whereas ventilation is hindered by the dirt accumulation.A regular cleaning treatment of the insect-proof screens is a simple measure that improves ventilation inside the greenhouse and avoids major reductions in the natural ventilation capacity of the greenhouse, as quantified in the present study.Future research will focus on the study of the effect of material degradation and accumulation of dust on the optical properties of the insect-proof screens and on crop productivity.
and 5 warp threads (meshes 2, 3 and 4).The following steps were performed for each color digital image of the fabric: (i) the images were converted to grayscale; (ii) a gray colour was manually assigned to the areas of the pores to be analysed; (iii) the gray areas corresponding to the pores were converted to white by the software, leaving the rest of the image black; (iv) the vertices of each pore were automatically identified by the software; (v) the correct identification of the vertices was verified by the user, who could then correct any potential errors caused by the software; and, finally, (vi) the relevant geometric parameters were calculated by the software.The following parameters were obtained: thread density D r (weft × warp) [threads/cm 2 ]; porosity φ [m 2 /m 2 ]; weft pore length L px and warp pore length L py [m]; weft diameter D hx and warp diameter D hy [m]; mean thread diameter D h [m]; pore circumference diameter D i [m]; and pore surface area S p [mm 2 ]

Figure 1 .
Figure 1.Images corresponding to insect-proof screen 1: microscope image of the unclean used screen (a), of the clean used screen (b) and of the original new screen (c).
) with Eq. (1) (Molina-Aiz et al., 2009): P is the pressure [Pa], x the direction of airflow, u the air velocity [m/s], μ is the dynamic viscosity of air [kg s -1 m -1 ] and ρ a is the air density [kg/m 3 ].A second-degree polynomial can be used(Miguel et al.,

Table 3 .
Aerodynamic characteristics of the insect-proof screens number 1-4: e, thickness [µm]; a, b and c are the coefficients of the polynomial fit from the wind tunnel tests (Eq.[2]); R 2 , the fit determination coefficient; K p , screen permeability [m 2 ]; Y, inertial factor; F φ , pressure drop coefficient due to the presence of an insect-proof screen expressed as function of Re p .