#
Analysis of Turbulent Air Flow Characteristics Due to the Presence of a 13 × 30 Threads·cm^{−2} Insect Proof Screen on the Side Windows of a Mediterranean Greenhouse

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## Abstract

**:**

^{−2}insect-proof screen on the turbulence properties of the micro and microscale airflow turbulence. Four tests have been carried out in windward-oriented side windows of a Mediterranean greenhouse. Results demonstrate that the approach of using two simultaneous 3D sonic anemometers for the first time allows one to observe that the effect is different for the three components of the velocity vector field, and there is a strong connection between the simultaneous conditions inside and outside of the greenhouse. Useful information and data on the effect of using a 13 × 30 threads·cm

^{−2}insect-proof screen are also provided. To give details on the impact of screens in the turbulent properties of ventilation is essential for any commercial distribution, as well as providing important data in the design and development of more efficient insect-proof screens.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup

^{2}three-span greenhouse as depicted in Figure 1. Furthermore, each span of the greenhouse was transversally partitioned into two halves by means of a polyethylene sheet fixed to a stainless-steel structure.

_{V}) with respect to the wintering surface (S

_{A}). The insect-proof screen (IPS) installed at the vents is a 13 × 30 threads·cm

^{−2}(Figure 2), whose geometric properties can be characterized according to Valera et al. [30]. Following the methodology, Table 1 summarizes the characteristics of the IPS under study, which is a standard IPS in greenhouses in the Mediterranean region of Almería because of its demonstrated good ventilation properties together with exclusion of most insects typical of the area [25]. The size of the greenhouse is similar to the average greenhouse that can be found in the Mediterranean region. It is then irrelevant its size as we conducted the experiments near the IPS, where convection of windward-oriented vents is dominant. The greenhouse grows a tomato crop (Solanum lycopersicum L. var. cerasiforme Hort., cv. Salomee) with an average crop height of approximately 2.0 m and a leaf area index [m

^{2}leaf/m

^{2}ground] of 2.9. The north–south oriented crop rows were orthogonal to the side windows.

#### 2.2. Equipment and Instrumentation

^{−1}and accuracy of ±0.04 m s

^{−1}were deployed for the experimental data campaign. For the record of the data, two CR3000 Micrologger (Campbell Scientific Spain S.L.) were used, with a data acquisition frequency of 10 Hz [31]. Air velocity was measured simultaneously outside and inside the greenhouse, in the center of the north side window of the western sector of the experimental greenhouse (see Figure 1 and Figure 3). An anemometer was placed at the inner face of the window and another at the outer face, measuring the air velocity at 6 cm away from the IPS for a total of 30 min (Figure 3).

^{−1}, accuracy of ±5%, and a resolution of 0.01 m s

^{−1}. Wind direction was measured with a vane with an accuracy of ±5° and resolution of 1°. Solar radiation was quantified by means of a Kipp Solari sensor (Hortimax S.L.), with a measurement range from 0 to 2000 W m

^{−2}, accuracy of ±20 W m

^{−2}, and resolution of 1 W m

^{−2}.

#### 2.3. Theoretical Foundations of Turbulence Characteristics

_{t}[38]:

_{int}, the autocorrelation should be integrated to infinity. However, this is not feasible as measurement data is finite, and thus the integral is solved only up to the first zero crossing value (t

_{0}) by [37,39,40]:

_{i}[m], can be obtained. This is also called macroscale [33] or the average size of the largest eddies [41], and can be calculated by:

^{2}s

^{−1}], which relates to the frequency f of a signal. The analysis of this quantity is very useful to understand the scale of dependence of turbulent fluctuations, especially in isotropic turbulence [43] as in insect-proof screens. To obtain the discrete power spectrum density function E(f), the Fast Fourier Transform (FFT) is used [44]:

^{*}(f) is the conjugate complex number of X(f). This quantity can be represented in terms of logarithmic scale. This logarithmic power spectrum representation allows one to observe the slope (β) of the spectrum curve. The average value of this slope, which is negative, gives an insight into the isotropy of turbulence because it provides a reference to the energy distribution of eddies of different scales. In natural ventilation, turbulence is usually isotropic with the typical value of β = 5/3, also known as Kolmogorov’s law [45,46]. Mechanically generated airflows have a smaller value of β [44]. The slope of the logarithmic power spectrum is related to E(f) [36] as below:

^{2}s

^{−2}]. This value can be obtained from the integration of the spectrum of energy density, $k={{\displaystyle \int}}_{0}^{\infty}E\left(\nu \right)d\nu $, (with $\nu $ being the wavenumber and $\nu =2\pi /\lambda $). This can also be easily calculated from the variance of the measured velocity components by the following expression [47]:

_{x}, σ

_{y}, and σ

_{z}are the standard deviations for each air velocity component. On the other hand, the turbulence energy dissipation rate ε [m

^{2}s

^{−3}] can be defined as the total amount of energy lost by viscous dissipation. Large eddies transfer energy into smaller eddies in order to achieve a very small size at which viscous forces dissipate them. This microscale is known as Taylor microscale (λ), whereas the smallest eddy size that can be achieved is the famous Kolmogorov microscale, η [48]. The turbulence energy dissipation rate ε is represented by the expression [37]:

^{3/4}ε

^{−4}. In terms of dissipation, the Taylor microscale λ [m] provides an average length for the eddies that produce most dissipation, often known as turbulence dissipation scale [41,48]. This scale can be calculated as [33]:

## 3. Results

#### 3.1. Description of Airflow throughout the Side Openings

#### 3.1.1. Airflow through the NE Window, before and after Passing through the Insect-Proof Screen

_{z}. When the airflow passes through the IPS, the vertical component is reduced, and the airflow becomes practically horizontal, which is attributed to the laminarization effect of the IPS as a porous medium. This effect is similar to the popular honeycomb effect to reduce turbulence inflows. When the side window faces windward, part of the airflow that reaches the window comes into the greenhouse, and also the amount of air that does not come in descends through the side of the greenhouse and continues to the west, following the direction of the northeast wind.

#### 3.1.2. Airflow through the Northern Side Window, before and after Passing through the Insect-Proof Screen

_{y}and vertical u

_{z}components are reduced, on average, by 76% and 88%, respectively.

_{x}, perpendicular to the side window (parallel to the normal of the window opening surface), in the first two tests, was reduced by 3% and 61% when entering the greenhouse. It is surprising that in the last two tests, the u

_{x}component on the inner face of the window was greater than on the outer face, increasing by 19% and 18%. The variations observed in u

_{x}, are mainly due to the separation of the anemometers with respect to the window and not so much to the effect of the mesh. In considering the continuity equation (equivalent to the conservation of mass), if the downstream component of airflow velocity u

_{x}is measured right before and after passing through the IPS, it should reach the same value on both faces due to symmetry and no mass-flow rate losses. However, the reality is that due to the reduction of the cross-sectional area when passing though pores rather than a screenless window, velocity may increase for energy conservation (pressure changes due to the presence of the screen) and mass conservation (the volume flow rate is kept unless strong recirculation occurs or streamlines are deviated from passing through the pores). As studied numerically by Abou-Hweij and Azizi [49], this increase in velocity past the screen is only noticed up to a certain short distance. The length of the area strongly depends on the velocity of the wind. Thus, if the sonic anemometers are placed at the same position for the four tests, it is not surprising to observe some differences. Furthermore, since in the last two tests, the outside humidity was three times the outside humidity in the first test and twice in the second, the transport of water particles has an effect on buoyancy. The effect of a large discrepancy between humidity indoors and outdoors was also noticed by Teitel et al. [16] in their measurements of turbulence inside tomato crop greenhouse, finding a higher contribution of buoyancy. The mesh should act as a filter reducing the magnitude of the fluctuations but maintaining their mean value (Figure 5).

_{y}and u

_{z}components may take a minor contribution to the mass-flow rate and may even be the consequence of rejected flow or formation of small swirls and recirculation due to the blockage effect. The reduction in the magnitude of these components of the airflow velocity field can be observed in Figure 6. This knowledge can help in the improvement of window design optimization, as one may consider introducing devices or mechanisms to ensure that most of the airflow is directed to the windows perpendicular to the plane formed by the ventilation surfaces.

#### 3.2. Influence of the Insect-Proof Screen on the Turbulence of the Airflow

_{y}and vertical i

_{z}components (shown in Table 4). The laminarization effect of the IPS is observed when analyzing the longitudinal component u

_{x}perpendicular to the window and the pore section of the IPS. The turbulence intensity i

_{x}is reduced when passing through the IPS, except in Test 2, carried out at very low wind speed. This may be due to several reasons. First, in this situation, the thermal effect plays an important role in greenhouse ventilation, and its contribution is greater to the airflow on the inner side of the window. Second, as aforesaid when describing velocity, the variations in velocity when passing through the IPS are mostly noticed in a region close to the pore, and the length of this region depends on the wind velocity [49]. Thus, if the anemometers are placed at the same distance in all tests, there may be some differences in the behavior of a parameter. Furthermore, in Tests 3 and 4, the vertical component i

_{z}has a significant increase inside the greenhouse. This is due to the buoyancy forces acting in the z-direction, which appears due to the great difference in humidity inside and outside and temperature effect, as also observed in Teitel et al. [16] in measurements inside and outside greenhouses. In addition, it must be noted that the tests have been carried out in an open system: if the airflow would be isolated, for example, in a wind tunnel, results may vary slightly, as, for instance, buoyancy effects would not take place.

_{x}component, as it reduces part of the large fluctuations, while the lower variations are kept around the mean value (see Figure 5). On the other hand, for the transversal and vertical components (see Figure 6), in addition, to eliminate part of the large fluctuations, it considerably reduces the mean value of these components. This is reasonable because the size of the pores can filter only larger velocity fluctuations, and as the size of the pore increases (and actually the porosity), the filtering may be less noticeable. Thus, the filtering effect in u

_{y}and u

_{z}is directly related to the reduction of the turbulence scales for the said components after passing through the IPS (Table 5). In this table, the macroscale (average size of the largest eddies) and microscale (average size of the smallest eddies) parameters are given (including also their three components) for the turbulence inside and outside the window sides observing a dramatical reduction in turbulence.

_{iy}and λ

_{y}) and the vertical component (L

_{iz}and λ

_{z}), while an increase in the turbulence scales of the longitudinal component (L

_{ix}and λ

_{x}) (Table 5). This increase in the turbulence scale may be the consequence of the grid-generated effect on turbulence, which is adopted in many fluid dynamics experiments to generate turbulent flows by passing laminar flows through grids [46,55]. More specifically, for u

_{y}and u

_{z}, at each pore, there are top–bottom and left–right threads contributing to the filtering. However, for u

_{x}, two scenarios take place together: small eddies can pass through the pore with minimal perturbations, and larger eddies may split or break due to the presence of the threads, leading quicker to smaller eddies entering the greenhouse. Thus, the macroscale of the longitudinal component L

_{ix}can increase up to 220% on the inner face of the window and the microscale λ

_{x}up to 429% (Test 4). On the contrary, for the other two components, the macroscale is reduced by an average of 75% and 72% for the transversal component L

_{iy}and vertical L

_{iz}, respectively. Likewise, the microscale is reduced by an average of 74% and 87% for λ

_{y}and λ

_{z}, respectively. The increase in the longitudinal component of the turbulence scale and decrease in the transversal and vertical components has also been noticed by Teitel et al. [16]. Although they characterized turbulence inside the greenhouse and not near the IPSs, they noticed the same behavior mainly due to the top bound and side bounds of the canopy. In our case, the threads also create lateral and top bounds that constrain the airflow, but not in the longitudinal motion, hence the here shown observation.

^{2}s

^{−2}, and ε greater than 1.44 m

^{2}s

^{−3}in the lateral windward ventilation openings. Similar facts were observed in the macroscale. They indicated maximum values of L

_{ix}equal to 8.37 m, L

_{iy}equal to 3.76 m, and L

_{iz}equal to 2.07 m in the windward-oriented window.

_{y}and u

_{z}, turbulence energy is reduced throughout the entire frequency range. However, in the longitudinal component u

_{x}, the energy transported in the larger scales (at low frequency) is maintained after passing through the mesh, whereas the energy transported by the smaller scales (high frequency) is dissipated or lost when passing through the porous mesh. For the total airflow velocity u, the results obtained agree with the observations made by Teitel and Tanny [27], which confirms that the turbulence energy decreases and the spectral decay rate is increased. It is obvious that this loss of energy at high frequency is what produces the reduction in the velocity fluctuations of u

_{x}(seen in Figure 5). Regarding the other two components, the turbulence energy at low and high frequencies is reduced, which results in a decrease in the average airspeed and also in fluctuations (Figure 6). The passage of air through the mesh pores also causes a generalized increase in the slope of the spectrum (see Table 6 and Figure 7) [2]. A greater slope of the spectrum indicates a greater distribution of energy in the larger scales (lower frequencies). In addition, if the three spectral density plots are matched, it can be observed that the one corresponding to u

_{x}is less energetic (Figure 8). Most of the airflow turbulence energy is transported in the transverse and vertical components. An important part of such energy is lost as discussed above, either when passing through the mesh or because of the air rejection due to the barrier created by the IPS threads, perhaps even avoiding part of the mass-flow rate to enter into the greenhouse as part of the flow may be deviated by the screen.

## 4. Conclusions

^{−2}insect-proof screen (IPS) on the turbulence properties of the airflow, as IPSs represent an important physical barrier to insects but also to efficient natural ventilation in greenhouses.

_{y}and vertical u

_{z}components are reduced by 76% and 88%, respectively. However, the observed variations of the longitudinal component u

_{x}, perpendicular to the lateral window, are mainly due to the separation of the anemometers with respect to the window placed at the same position in the four tests. Furthermore, reduction in air velocity caused by the presence of the IPS may occur, mainly due to preventing the passage of air currents or flows that are not directed perpendicular to the window cross-surface (i.e., to the pore section of the mesh).

_{x}component, eliminating part of the magnitude of the large fluctuations while keeping the lower variations around the mean value. In addition, the transverse and vertical components considerably reduce the mean value since the physical barrier created by the screen slows down the airflow velocity component that has not arrived with enough perpendicularity to the window surface plane.

_{y}and vertical u

_{z}components, the energy is reduced throughout the entire frequency range. However, for the longitudinal component u

_{x}, the energy transported by the larger scales is maintained after passing through the mesh, whereas the energy transported by the smaller scales is highly dissipated or lost. The use of classic natural ventilation systems as windows with installed IPSs represents a very important barrier to the benefits of using turbulent airflows for ventilation. Providing details on the impact of screens on the turbulence properties of ventilation airflows is vital for commercial distribution. In addition, gaining more knowledge on the impact of the installation of IPSs is important in order to deliver and develop better and more suitable IPSs. Thus, future work involves finding the potential relations between the turbulent scales and the geometric parameters of the IPS since this can lead to the design of more efficient, low-cost, and sustainable natural ventilation systems. The performance of turbulence models in CFD simulations can be validated with the present experimental results. Once simulations are validated, many new designs can be tested computationally in order to find optimal IPS designs.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Agrafioti, P.; Faliagka, S.; Lampiri, E.; Orth, M.; Pätzel, M.; Katsoulas, N.; Athanassiou, C.G. Evaluation of silica-coated insect proof nets for the control of Aphis fabae, Sitophilus oryzae, and Tribolium confusum. Nanomaterials
**2020**, 10, 1658. [Google Scholar] [CrossRef] [PubMed] - Teitel, M. The effect of screened openings on greenhouse microclimate. Agric. For. Meteorol.
**2007**, 143, 159–175. [Google Scholar] [CrossRef] - Oliva, R.M.; Álvarez, A.J. Factors influencing the efficacy of insect-proof screens. Acta Hortic.
**2017**, 1170, 1027–1033. [Google Scholar] [CrossRef] - Berlinger, M.J.; Leblush-Mordechl, S.; Fridja, D.; Mor, N. The effect of types of greenhouse screens on the presence of western flower thrips: A preliminary study. OILB-SROP Bull.
**1992**, 16, 13–19. [Google Scholar] - Taylor, R.A.J.; Shalhevet, S.; Spharim, I.; Berlinger, M.J.; Lebiush-Mordechi, S. Economic evaluation of insect-proof screens for preventing tomato yellow leaf curl virus of tomatoes in Israel. Crop Prot.
**2001**, 20, 561–569. [Google Scholar] [CrossRef] - Bethke, J.A.; Paine, T.D. Screen hole size and barriers for exclusion on insect pest of glasshouse crops. J. Entomol. Sci.
**1991**, 26, 169–177. [Google Scholar] [CrossRef] - Verheye, P.; Verlodt, H. Comparison of different systems for static ventilation of hemispheric plastic greenhouses. Acta Hortic.
**1990**, 281, 183–197. [Google Scholar] [CrossRef] - Von Zabeltitz, C. L’efficacité énergétique dans la conception des serres méditerranéennes. Plasticulture
**1992**, 96, 6–16. [Google Scholar] - ANSI/ASAE. EP406.1: Heating, Ventilating, and Cooling Greenhouses; ASAE: St. Joseph, MI, USA, 1994. [Google Scholar]
- Kittas, C.; Boulard, T.; Papadakis, G. Natural ventilation of a greenhouse with ridge and side openings: Sensitivity to temperature and wind effects. Trans. ASAE
**1997**, 40, 415–425. [Google Scholar] [CrossRef] - Kittas, C.; Katsoulas, N.; Bartzanas, T.; Mermier, M.; Boulard, T. The impact of insect screens and ventilation openings on the greenhouse microclimate. Trans. ASABE
**2008**, 51, 2151–2165. [Google Scholar] [CrossRef] - Formisano, L.; El-Nakhel, C.; Corrado, G.; De Pascale, S.; Rouphael, Y. Biochemical, physiological, and productive response of greenhouse vegetables to suboptimal growth environment induced by insect nets. Biology
**2020**, 9, 432. [Google Scholar] [CrossRef] [PubMed] - López-Martínez, A.; Martínez, D.L.V.; Aiz, F.D.M.; Peña, A.; Membrive, P.M. Microclimate evaluation of a new design of insect-proof screens in a Mediterranean greenhouse. Span. J. Agric. Res.
**2014**, 2, 338–352. [Google Scholar] [CrossRef][Green Version] - Harmanto; Tantau, H.J.; Salokhe, V.M. Microclimate and air exchange rates in greenhouses covered with different nets in the humid tropics. Biosyst. Eng.
**2006**, 94, 239–253. [Google Scholar] [CrossRef] - Yang, G.; Guo, Z.; Ji, H.; Sheng, J.; Chen, L.; Zhao, Y. Application of insect-proof nets in pesticide-free rice creates an altered microclimate and differential agronomic performance. PeerJ
**2018**, 6, e6135. [Google Scholar] [CrossRef][Green Version] - Teitel, M.; Liang, H.; Vitoshkin, H.; Tanny, J.; Ozer, S. Airflow patterns and turbulence characteristics above the canopy of a tomato crop in a roof-ventilated insect-proof screenhouse. Biosyst. Eng.
**2020**, 190, 184–200. [Google Scholar] [CrossRef] - Bartzanas, T.; Boulard, T.; Kittas, C. Numerical simulation of the airflow and temperature distribution in a tunnel greenhouse equipped with insect-proof screen in the openings. Comput. Electron. Agric.
**2002**, 34, 207–221. [Google Scholar] [CrossRef] - Fatnassi, H.; Boulard, T.; Demrati, H.; Bouirden, L.; Sappe, G. Ventilation Performance of a Large Canarian-Type Greenhouse equipped with Insect-proof Nets. Biosyst. Eng.
**2002**, 82, 97–105. [Google Scholar] [CrossRef] - Fatnassi, H.; Boulard, T.; Bouirden, L. Simulation of climatic conditions in full-scale greenhouse fitted with insect-proof screens. Agric. For. Meteorol.
**2003**, 118, 97–111. [Google Scholar] [CrossRef] - Fatnassi, H.; Boulard, T.; Poncet, C.; Chave, M. Optimisation of greenhouse insect screening with computational fluid dynamics. Biosyst. Eng.
**2006**, 93, 301–312. [Google Scholar] [CrossRef] - Baeza, E.J.; Pérez-Parra, J.J.; Montero, J.I.; Bailey, B.J.; López, J.C.; Gázquez, J.C. Analysis of the role of sidewall vents on buoyancy-driven natural ventilation in parral-type greenhouses with and without insect screens using computational fluid dynamics. Biosyst. Eng.
**2009**, 104, 86–96. [Google Scholar] [CrossRef] - Teitel, M.; Barak, M.; Berlinger, M.J.; Lebiush-Mordechai, S. Insect-proof screens in greenhouses: Their effect on roof ventilation and insect penetration. Acta Hortic.
**1999**, 507, 25–34. [Google Scholar] [CrossRef] - López, A.; Martínez, D.L.V.; Aiz, F.D.M.; Peña, A. Sonic anemometry measurements to determine airflow patterns in multi-tunnel greenhouses. Span. J. Agric. Res.
**2012**, 3, 631–642. [Google Scholar] [CrossRef][Green Version] - López-Martínez, A.; Molina-Aiz, F.D.; Valera, D.L.; Peña, A. Wind tunnel analysis of the airflow through insect-proof screens and comparison of their effect when installed in a Mediterranean greenhouse. Sensors
**2016**, 16, 690. [Google Scholar] [CrossRef] [PubMed][Green Version] - López-Martínez, A.; Molina-Aiz, F.D.; Valera, D.L.; Espinoza-Ramos, K.E. Models for characterising the aerodynamics of insect-proof screens from their geometric parameters. Biosyst. Eng.
**2020**, 192, 42–55. [Google Scholar] [CrossRef] - Granados-Ortiz, F.-J.; Arrabal-Campos, F.M.; Lopez-Martinez, A.; Molina-Aiz, F.D.; Peña-Fernández, A.; Valera-Martínez, D.L. On the estimation of three-dimensional porosity of insect-proof screens. Comput. Electron. Agric.
**2022**. in Press. [Google Scholar] [CrossRef] - Teitel, M.; Tanny, T. Heat Fluxes and Airflow Patterns Through Roof Windows in a Naturally Ventilated Enclosure. Flow Turbul. Combust.
**2005**, 74, 21–47. [Google Scholar] [CrossRef] - Pope, S.B. Turbulent Flows; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Tanny, J.; Haslavsky, V.; Teitel, M. Airflow and heat flux through the vertical opening of buoyancy-induced naturally ventilated enclosures. Energ. Build.
**2008**, 40, 637–646. [Google Scholar] [CrossRef] - Valera, D.L.; Álvarez, A.J.; Molina-Aiz, F.D. Aerodynamic analysis of several insect-proof screens used in greenhouses. Span. J. Agric. Res.
**2006**, 4, 273–279. [Google Scholar] [CrossRef] - Shilo, E.; Teitel, M.; Mahrer, Y.; Boulard, T. Air-flow patterns and heat fluxes in roof-ventilated multi-span greenhouse with insect-proof screens. Agric. For. Meteorol.
**2004**, 122, 3–20. [Google Scholar] [CrossRef] - Von Karman, T. Some remarks on the statistical theory of turbulence. In Proceedings of the fifth International Congress for Applied Mechanics, Cambridge, MA, USA, 12–16 September 1938; p. 347. [Google Scholar]
- Hinze, J.O. Turbulence; McGraw-Hill: New York, NY, USA, 1975. [Google Scholar]
- Chapman, G.T.; MTobak, M. Observations, Theoretical Ideas, and Modeling of Turbulent Flows—Past, Present and Future. In Theoretical Approaches to Turbulence; Dwoyer, D.L., Hussaini, M.Y., Voigt, R.G., Eds.; Springer: New York, NY, USA, 1985; pp. 19–49. [Google Scholar]
- Gustavsson, H. Lecture notes: Introduction to turbulence. In Luleå: Division of Fluid Mechanics; Luleå University of Technology: Luleå, Sweden, 2006. [Google Scholar]
- Cebeci, T. Analysis of Turbulent Flows; Elsevier Science: Amsterdan, The Netherlands, 2004. [Google Scholar]
- Heber, A.J.; Boon, C.R.; Peugh, M.W. Air patterns and turbulence in an experimental livestock building. J. Agric. Eng. Res.
**1996**, 64, 209–226. [Google Scholar] [CrossRef][Green Version] - Maryami, R.; Showkat Ali, S.A.; Azarpeyvand, M.; Afshari, A. Turbulent flow interaction with a circular cylinder. Phys. Fluids
**2020**, 32, 015105. [Google Scholar] [CrossRef][Green Version] - Mora, D.O.; Obligado, M. Estimating the integral length scale on turbulent flows from the zero crossings of the longitudinal velocity fluctuation. Exp. Fluids
**2020**, 61, 199. [Google Scholar] [CrossRef] - O’Neill, P.L.; Nicolaides, D.; Honnery, D.; Soria, J. Autocorrelation functions and the determination of integral length with reference to experimental and numerical data. In Proceedings of the 15th Australasian Fluid Mechanics Conference, Sydney, NSW, Australia, 13–17 December 2004; Volume 1, pp. 1–4. [Google Scholar]
- Melikov, A.K.; Langkilde, G.; Derbiszewski, B. Airflow characteristic in the occupied zone of rooms with displacement ventilation. ASHRAE Trans.
**1990**, 96, 555–563. [Google Scholar] - Shen, Z.; Zhang, X. Random-eddy-superposition technique for leading edge noise predictions. In Proceedings of the 2018 AIAA/CEAS Aeroacoustics Conference, Atlanta, Georgia, 25–29 June 2018; p. 3597. [Google Scholar]
- Hamba, F. Turbulent energy density in scale space for inhomogeneous turbulence. J. Fluid Mech.
**2018**, 842, 532–553. [Google Scholar] [CrossRef] - Ouyang, Q.; Dai, W.; Li, H.; Zhu, Y. Study on dynamic characteristics of natural and mechanical wind in built environment using espectral analisis. Build. Environ.
**2006**, 41, 418–426. [Google Scholar] [CrossRef] - Stull, R.B. An Introduction to Boundary Layer Meteorology; Kluwer Academics Publishers: Dordrecht, The Netherlands, 1988. [Google Scholar]
- Laizet, S.; Nedić, J.; Vassilicos, J.C. The spatial origin of −5/3 spectra in grid-generated turbulence. Phys. Fluids
**2015**, 27, 065115. [Google Scholar] [CrossRef][Green Version] - Loomans, M.G.L.C. The Measurement and Simulation of Indoor Air Flow. Master’s Thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands, 1998. [Google Scholar]
- Ting, D. Basics of Engineering Turbulence; Academic Press: Cambridge, MA, USA; Elsevier: Amsterdam, The Netherlands, 2016. [Google Scholar]
- Abou-Hweij, W.; Azizi, F. CFD simulation of wall-bounded laminar flow through screens. Part I: Hydrodynamic characterization. Eur. J. Mech.-B/Fluids
**2020**, 84, 207–232. [Google Scholar] [CrossRef] - Muñoz, P.; Montero, J.I.; Antón, A.; Giuffrida, F. Effect of insect-proof screens and roof openings on greenhouse ventilation. J. Agric. Eng. Res.
**1999**, 73, 171–178. [Google Scholar] [CrossRef] - Teitel, M. The effect of insect-proof screens in roof openings on greenhouse microclimate. Agric. For. Meteorol.
**2001**, 110, 13–25. [Google Scholar] [CrossRef] - Molina-Aiz, F.D.; Valera, D.L.; Peña, A.A.; Gil, J.A.; López, A. A Study of Natural Ventilation in an Almería-Type Greenhouse with Insect Screens by Means of Tri-sonic Anemometry. Biosyst. Eng.
**2009**, 104, 224–242. [Google Scholar] [CrossRef] - Fang, F. A design method for contractions with square end sections. Trans. ASME
**1997**, 119, 454–458. [Google Scholar] [CrossRef] - Fang, F.; Chen, J.C.; Hong, Y.T. Experimental and analytical evaluation of flow in a square-to-square wind tunnel contraction. J. Wind Eng. Ind. Aerodyn.
**2001**, 89, 247–262. [Google Scholar] [CrossRef] - Melina, G.; Bruce, P.J.; Vassilicos, J.C. Vortex shedding effects in grid-generated turbulence. Phys. Rev. Fluids
**2016**, 1, 044402. [Google Scholar] [CrossRef][Green Version] - Boulard, T.; Wang, S.; Haxaire, R. Mean and turbulent air flows and microclimatic patterns in an empty greenhouse tunnel. Agric. For. Meteorol.
**2000**, 100, 169–181. [Google Scholar] [CrossRef]

**Figure 2.**Detail of the IPS under study: (

**a**) Microscope image of the insect-proof screen (IPS) under analysis (density: 13 × 30 threads·cm

^{−2}), and (

**b**) Computational reconstruction of the 3D shape using Poro3D software [26], where warp threads are shown in red color, and the weft threads in blue color.

**Figure 4.**Representation of the airflow on the outer and inner face of the north side window facing windward. Tests 1 (

**a**), 2 (

**b**), 3 (

**c**) and 4 (

**d**). Representation of the global mean vector for the XY plane and minute mean vectors for the XZ plane.

**Figure 5.**Three-dimensional sonic anemometry u

_{x}measurements from Test 1 at the side window windward oriented. Inner side of the IPS at the window (▬); outer side of the IPS at the window (▬). Total acquisition time: Five minutes.

**Figure 6.**Three-dimensional sonic anemometry measurements from Test 1 at the side window windward oriented. The measurements correspond to the transversal component u

_{y}(

**a**), and vertical component u

_{z}(

**b**). Inner side of the IPS at the window (▬); outer side of the IPS at the window (▬). Total acquisition time: Five minutes.

**Figure 7.**Energy density spectra at the north side window (Test 1). Outer window side (▬) and inner window side (▬).

**Figure 8.**Energy density spectra at outer window side at the north side window (Test 1). Spectra of u

_{x}(▬), u

_{y}(▬), and u

_{z}( ).

**Table 1.**Relevant geometric parameters of the insect-proof screen (IPS): Density of threads (D

_{th}, [threads cm

^{−2}]), porosity (φ, [%]), volumetric porosity (φ

_{3D}, [%]), separation of the warp threads (L

_{px}), separation of the weft threads (L

_{py}); average diameter of threads (D

_{h}), inner diameter of the mesh pore (D

_{i}), average surface of the pore (S

_{p}, [mm

^{2}]), thickness of the screen (e, [µm]). Lenghts are given in micrometers.

D_{th} | φ | φ_{3D} | L_{px} | L_{py} | D_{h} | D_{i} | S_{p} | e |
---|---|---|---|---|---|---|---|---|

13.1 × 30.5 | 39.0 | 75.1 | 164.6 | 593.3 | 165.5 | 167.4 | 0.098 | 391.7 |

**Table 2.**Climatic conditions from the experimental tests (inside and outside the greenhouse): Average wind speed u

_{o}[m s

^{−1}], wind direction θ [°], outside and inside temperature T

_{o}and T

_{i}[°C], respectively, outside and inside humidity HR

_{o}and HR

_{i}(%) and outside radiation R

_{g}[W m

^{−2}].

Test | Time | u_{o} | θ ^{a} | HR_{o} | HR_{i} | T_{o} | T_{i} | R_{g} |
---|---|---|---|---|---|---|---|---|

12 June 2009 | 10:25–10:55 | 10.28 ± 0.37 | 75 ± 3 | 19 ± 1 | 50 ± 1 | 29.7 ± 0.5 | 26.0 ± 0.4 | 539 ± 28 |

15 June 2009 | 11:00–11:30 | 3.20 ± 0.28 | 98 ± 14 | 32 ± 1 | 72 ± 2 | 32.0 ± 0.4 | 28.6 ± 0.6 | 578 ± 58 |

17 June 2009 | 10:58–11:28 | 5.77 ± 0.55 | 96 ± 7 | 62 ± 1 | 77 ± 1 | 26.6 ± 0.3 | 26.8 ± 0.3 | 486 ± 57 |

18 June2009 | 10:20–10:50 | 5.59 ± 0.56 | 76 ± 5 | 64 ± 1 | 78 ± 2 | 25.8 ± 0.1 | 25.4 ± 0.1 | 295 ± 10 |

^{a}Direction perpendicular to the windows is 28° for a Levante wind from northeast (NE).

**Table 3.**Mean values of air velocity u [m s

^{−1}], and the three components of the velocity vector field u

_{x}, u

_{y}and u

_{z}[m s

^{−1}]. Velocity data represents velocity before and after passing through the IPS of density 13 × 30 threads·cm

^{−2}. Subscript i and e stands for “inside” and “outside”, respectively.

Test | u | u_{i}/u_{e} | u_{x} | u_{x,i}/u_{x,e} | u_{y} | u_{y,i}/u_{y,e} | u_{z} | u_{z,i}/u_{z,e} | |
---|---|---|---|---|---|---|---|---|---|

1 | Inside | 2.09 ± 1.21 | 0.39 | 1.11 ± 0.79 | 0.97 | −1.56 ± 1.16 | 0.37 | −0.27 ± 0.33 | 0.13 |

Outside | 5.42 ± 2.53 | 1.15 ± 1.06 | −4.25 ± 2.82 | −2.12 ± 1.65 | |||||

2 | Inside | 0.22 ± 0.13 | 0.17 | 0.04 ± 0.18 | 0.39 | −0.11 ± 0.09 | 0.11 | 0.07 ± 0.04 | −0.27 |

Outside | 1.25 ± 0.87 | 0.10 ± 0.24 | −1.05 ± 0.91 | −0.27 ± 0.48 | |||||

3 | Inside | 0.62 ± 0.46 | 0.26 | 0.29 ± 0.45 | 1.19 | −0.39 ± 0.38 | 0.19 | 0.01 ± 0.12 | −0.02 |

Outside | 2.43 ± 1.52 | 0.24 ± 0.52 | −2.02 ± 1.58 | −0.72 ± 0.90 | |||||

4 | Inside | 1.23 ± 0.66 | 0.34 | 0.73 ± 0.41 | 1.18 | −0.93 ± 0.61 | 0.30 | −0.05 ± 0.12 | 0.05 |

Outside | 3.60 ± 1.66 | 0.62 ± 0.51 | −3.11 ± 1.83 | −1.12 ± 0.88 |

**Table 4.**Turbulence intensity i (longitudinal component, i

_{x}; transversal component, i

_{y}; vertical component, i

_{z}), turbulence kinetic energy, k [m

^{2}s

^{−2}], and turbulence dissipation rate ε [m

^{2}s

^{−3}].

Test | i | i_{x} | i_{y} | i_{z} | k | Ε | |
---|---|---|---|---|---|---|---|

1 | Inside | 0.58 | 0.71 | 0.74 | 1.22 | 1.04 | 1.35 |

Outside | 0.47 | 0.92 | 0.66 | 0.47 | 5.92 | 11.81 | |

2 | Inside | 0.61 | 4.69 | 0.82 | 0.58 | 0.02 | 0.04 |

Outside | 0.69 | 2.38 | 0.86 | 1.77 | 0.56 | 0.98 | |

3 | Inside | 0.74 | 1.56 | 0.97 | 8.29 | 0.18 | 0.31 |

Outside | 0.63 | 2.18 | 0.79 | 1.24 | 1.79 | 3.57 | |

4 | Inside | 0.53 | 0.56 | 0.66 | 2.37 | 0.28 | 0.20 |

Outside | 0.46 | 0.82 | 0.59 | 0.79 | 2.20 | 2.92 |

**Table 5.**Macroscale L

_{i}[m] and microscale λ [m] (longitudinal component, L

_{ix}; transversal component, L

_{iy}; vertical component, L

_{iz}).

Test | L_{i} | L_{ix} | L_{iy} | L_{iz} | λ | λ_{x} | λ_{y} | λ_{z} | |
---|---|---|---|---|---|---|---|---|---|

1 | Inside | 3.17 | 1.67 | 2.57 | 5.57 | 0.04 | 0.32 | 0.44 | 0.04 |

Outside | 9.61 | 0.92 | 6.07 | 8.85 | 0.36 | 0.13 | 0.99 | 0.36 | |

2 | Inside | 0.12 | 0.08 | 0.13 | 0.37 | 0.08 | 0.02 | 0.03 | 0.02 |

Outside | 3.36 | 0.10 | 2.48 | 2.32 | 0.43 | 0.01 | 0.34 | 0.06 | |

3 | Inside | 0.52 | 0.47 | 0.47 | 0.15 | 0.24 | 0.13 | 0.08 | 0.00 |

Outside | 2.94 | 0.23 | 2.23 | 2.54 | 0.67 | 0.03 | 0.53 | 0.14 | |

4 | Inside | 2.47 | 1.43 | 2.19 | 2.85 | 0.73 | 0.33 | 0.37 | 0.01 |

Outside | 9.62 | 0.65 | 6.93 | 10.71 | 1.12 | 0.08 | 1.01 | 0.21 |

**Table 6.**Spectral decay slope β (slope in the longitudinal component, β

_{x}; transversal component, β

_{y}; vertical component, β

_{z}).

Test | β | β_{x} | β_{y} | β_{z} | |
---|---|---|---|---|---|

1 | Inside | 1.58 | 1.45 | 1.55 | 1.08 |

Outside | 1.28 | 0.63 | 1.36 | 1.12 | |

2 | Inside | 1.40 | 2.13 | 1.83 | 1.85 |

Outside | 1.37 | 0.59 | 1.55 | 1.33 | |

3 | Inside | 1.53 | 1.82 | 1.59 | 1.31 |

Outside | 1.37 | 0.66 | 1.47 | 1.21 | |

4 | Inside | 1.76 | 1.69 | 1.67 | 1.21 |

Outside | 1.36 | 0.65 | 1.53 | 1.25 |

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## Share and Cite

**MDPI and ACS Style**

López-Martínez, A.; Granados-Ortiz, F.-J.; Molina-Aiz, F.D.; Lai, C.-H.; Moreno-Teruel, M.d.l.Á.; Valera-Martínez, D.L. Analysis of Turbulent Air Flow Characteristics Due to the Presence of a 13 × 30 Threads·cm^{−2} Insect Proof Screen on the Side Windows of a Mediterranean Greenhouse. *Agronomy* **2022**, *12*, 586.
https://doi.org/10.3390/agronomy12030586

**AMA Style**

López-Martínez A, Granados-Ortiz F-J, Molina-Aiz FD, Lai C-H, Moreno-Teruel MdlÁ, Valera-Martínez DL. Analysis of Turbulent Air Flow Characteristics Due to the Presence of a 13 × 30 Threads·cm^{−2} Insect Proof Screen on the Side Windows of a Mediterranean Greenhouse. *Agronomy*. 2022; 12(3):586.
https://doi.org/10.3390/agronomy12030586

**Chicago/Turabian Style**

López-Martínez, Alejandro, Francisco-Javier Granados-Ortiz, Francisco D. Molina-Aiz, Choi-Hong Lai, María de los Ángeles Moreno-Teruel, and Diego L. Valera-Martínez. 2022. "Analysis of Turbulent Air Flow Characteristics Due to the Presence of a 13 × 30 Threads·cm^{−2} Insect Proof Screen on the Side Windows of a Mediterranean Greenhouse" *Agronomy* 12, no. 3: 586.
https://doi.org/10.3390/agronomy12030586