Wind-driven natural ventilation of greenhouses with vegetation

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Research Paper

Wind-driven natural ventilation of greenhouses with vegetation Chia-Ren Chu a,*, Ting-Wei Lan a, Ren-Kai Tasi a, Tso-Ren Wu b, Chih-Kai Yang c a

Department of Civil Engineering, National Central University, Taiwan Graduate Institute of Hydrological and Oceanic Sciences, National Central University, Taiwan c Taiwan Agricultural Research Institute, Council of Agriculture, Taiwan b

article info

A large eddy simulation (LES) model was used to examine the wind-driven cross ventilation

Article history:

of gable-roof greenhouses containing vegetation. The obstruction of air flow by vegetation

Received 29 July 2017

was described by a porous drag model in the numerical model, and the simulation results

Received in revised form

were validated using wind tunnel experiments. The numerical model was then utilised to

12 October 2017

inspect the influences of vegetation and greenhouse length (in the wind direction) on the

Accepted 25 October 2017

ventilation rate. The results revealed that the diminishing effects of the vegetation, insect

Published online 21 November 2017

screen and internal friction on the ventilation rate can all be quantified by a physical-based resistance model. The driving force (the difference between windward and leeward pres-

Keywords:

sures) of long, multi-span greenhouses was found to be less than that of a short, single-

Greenhouse

span greenhouse leading to a lower ventilation rate. The resistance factor of the vegeta-

Wind-driven ventilation

tion and the insect screen depends on their porosity, while the resistance factor of the

Vegetation

internal friction increased as the greenhouse length increased. In addition, the internal

Large Eddy Simulation

friction of multi-span greenhouses should be considered when the length of the green-

Porous drag model

house was greater than six times the greenhouse height. © 2017 IAgrE. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

Natural ventilation is an effective way to maintain an agreeable micro-climate in greenhouses, as well as a means to reduce the energy consumption required for mechanical ventilation (Kumar, Tiwari, & Jha, 2009; Von Zabeltitz, 2011). Natural ventilation can be separated into wind-driven and buoyancy-driven ventilation (Boulard, Haxaire, Lamrani, Roy, & Jaffrin, 1999; Santamouris & Allard, 1998). However, both types of ventilation are dependent on the external wind speed, direction, temperature, and the configuration of the

* Corresponding author. E-mail address: [email protected] (C.-R. Chu). https://doi.org/10.1016/j.biosystemseng.2017.10.008 1537-5110/© 2017 IAgrE. Published by Elsevier Ltd. All rights reserved.

greenhouse and the size of the openings (Burnett and Boulard, 2010; Etheridge, 2011). Greenhouse designers need to evaluate the cooling effects of natural ventilation before using mechanical ventilation. In recent years, computational fluid dynamics (CFD) models have successfully simulated the micro-climate of greenhouses. Reichrath and Davies (2002) and Norton, Sun, Grant, Fallon, and Dodd (2007) provided comprehensive reviews of past studies on the application of CFD models to simulate the micro-climates in greenhouses. A good numerical model could simulate all the flow parameters (wind speed,

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Nomenclature A cross-section area of the opening void area (porous area) of the vegetation AV total cross-sectional area of the vegetation AT effective opening area A* discharge coefficient of the opening Cd drag coefficient CD momentum loss coefficient CF Cp ¼ (P  Po)/0.5rU2 pressure coefficient Smagorinsky parameter Cs d average size of the leaves g gravitational acceleration H height of the greenhouse roof height of the greenhouse eave He height of the vegetation hv Iu ¼ su/U(z) turbulence intensity L length of the greenhouse LAI leaf area index of the canopy n porosity of the vegetation Q ventilation rate dimensionless ventilation rate Q* Re ¼ UHH/n Reynolds number rate of strain Sij wind speed at the height of greenhouse roof UH shear velocity u*

temperature, and humidity) of different greenhouse configurations under various climatic conditions. Mistriotis, Arcidiacono, Picuno, Bot, and ScarasciaMugnozza (1997) used the k-ε turbulence model to investigate the natural ventilation of a two-span greenhouse under no wind and low wind speed conditions. They also analysed the effects of different ventilators and showed that CFD can be a powerful tool for improving the ventilation efficiency of greenhouses. Campen (2005) applied numerical simulation to investigate the micro-climate of four different greenhouse designs and showed that a greenhouse without a top opening has the highest ventilation rate, and the lowest maximum temperature when there is external wind. In the case of no wind, the climate in the greenhouse without a top opening was shown to be slightly worse than that of other designs, and insect screens can reduce ventilation rate by more than 50%. Teitel, Ziskind, Liran, Dubovsky, and Letan (2008) studied the wind-driven natural ventilation and temperature distribution of multi-span greenhouse using a CFD model, wind-tunnel tests, and measurements in a full-scale greenhouse. They showed that the flow patterns inside the greenhouse and at the roof openings were considerably affected by the external wind direction. The ventilation rate and the crop temperature distribution were dependent on the wind direction. Majdoubi, Boulard, Fatnassi, and Bouirden (2009) used field observation and the standard keε model to inspect the airflow pattern in a 1-ha Canary type greenhouse. They found that the insect screen significantly reduced indoor wind speed and increased the temperature and humidity inside the greenhouse. Their simulation results also showed that the wind speed above the canopy is greater than that within the canopy.

W width of the greenhouse Wv width of the vegetation z height from the ground a permeability coefficient b inertia factor d boundary layer thickness DCp ¼ Cpw  CpL difference between windward and leeward pressure coefficient l thickness of the vegetation k von Karman constant q wind direction r air density standard deviation of stream wise velocity su t ¼ tUH/H dimensionless time n kinematic viscosity of the air m dynamic viscosity of the air effective viscosity meff viscosity of sub-grid scale turbulence mSGS z resistance factor Subscripts i internal L leeward v vegetation w windward

Bournet and Boulard (2010) employed turbulent models (standard keε model and realisable keε model) to simulate the climatic environment in greenhouses, and found that the ventilation rate of a naturally ventilated greenhouse was directly proportional to the size of the side wall opening and to the wind velocity when the wind force prevailed. They also confirmed that the insect screens and dense rows of crops perpendicular to the airflow can substantially hinder the wind-driven ventilation of greenhouses. In view of the above studies on greenhouse ventilation, there is a need for a simple and accurate model to estimate the ventilation rate and the cooling effect of natural ventilation, especially when there are internal vegetation and insect screen on the greenhouse openings. This study used wind tunnel experiments and a large eddy simulation (LES) model to investigate the wind-driven ventilation through greenhouses containing vegetation. The LES model was used because the numerical model is an in-house computer code, and it did not have the option of different turbulence models. Moreover, the accuracy of LES model is better than that of standard k-ε models (Tominaga et al., 2008). The simulation results were validated by the wind tunnel experiments, and then utilised to develop a physical-based resistance model for wind-driven natural ventilation of greenhouses.

2.

Materials and methods

2.1.

Physical model

Wind-driven natural ventilation through buildings can be assessed by physical-based ventilation models (Etheridge,

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2011). For buildings with two openings, one on the windward wall and another on the leeward wall, the ventilation rate, Q, through the openings can be determined by using the continuity equation, Qw ¼ QL, and the orifice equation (Baptista, Bailey, Randall, & Meneses, 1999; Chu, Chiu, Chen, Wang, & Chou, 2009; Karava, Stathopoulos, & Athienitis, 2011):
1=2 Qmodel ¼ UH A* Cpw  CpL

(1)

where UH is the wind velocity at the greenhouse roof; A is the opening area; and Cp is the dimensionless pressure coefficient, with subscripts w and L represents the windward and leeward openings, respectively. The pressure coefficient is defined as the difference between the pressure on the external wall and that of free stream flow: Cp ¼

P  Po 0:5rU2H

(2)

where Po is the undisturbed pressure in front of the building; r is the density of the air. The ventilation rate can be normalised by the external wind speed and opening area: Q Q ¼ UH A* *

Aw AL CwL CdL A* ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C2dw A2w þ C2dL A2L

(4)

where A is the cross-sectional area of the opening; Cd is the discharge coefficient. Typical discharge coefficients given in the literature are in the range of 0.60e0.67 for sharp-edged, no screen openings (Awbi, 2003; Etheridge, 2011). However, Eq. (1) does not consider the flow resistance caused by the insect screen or the vegetation in the greenhouses (Wang, Boulard, & Haxaire, 1999). Therefore, Eq. (1) may over-estimate the ventilation rate of greenhouse with vegetation and insect screen. Chu, Chiu, and Wang (2010) used wind tunnel experiments to investigate the wind-driven cross ventilation of partitioned buildings. They found that, due to the extra resistance caused by the internal partition, the ventilation rate of a partitioned building is always lower than that of a single-zone building. Chu and Wang (2010) and Chu and Chiang (2013) used the energy equation to derive a resistance model to predict the dimensionless ventilation rate Q* when there are obstacles in the buildings: 

1 Cpw  CpL A* zw þ zi þ zL

1=2 (5)

where zi is the resistance factor of the internal obstacle; zw and zL are the resistance factors of the windward and leeward openings, respectively. The resistance factors of the external openings can be calculated as follows: zw ¼

resistance factor, z, the smaller the ventilation rate, Q. This model can be used for buildings without internal obstacles, and the resistance factor zi ¼ 0. The extra resistance caused by the vegetation inside the greenhouses can be expressed in terms of internal resistance factor zi; while the resistance caused by the insect screen on the openings can be considered in terms of the discharge coefficient Cd. The value of Cd with an insect screen is dependent on the porosity of the screen, but should be smaller than that without the screen, such as Cd ¼ 0.66.

2.2.

Numerical model

This study used a Large Eddy Simulation (LES) model to investigate the wind-driven ventilation of greenhouses with internal vegetation (crops). The governing equations are: vui ¼0 vxi

(7)

" !# vrui vrui uj vP v vui vuj þ ¼  þ rgdi3 þ þ meff þ rfdi vxi vxj vt vxj vxj vxi

(8)

(3)

The effective opening area A* is defined as:

* Qresist ¼

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1 C2dw A2w

zL ¼

1 C2dL A2L

(6)

The unit of the resistance factor is [m4], and Eq. (5) is consistent in dimension. The pressure difference between the windward and leeward openings is the driving force to overcome the resistances of cross ventilation. The larger the

where the subscripts i, j ¼ 1, 2, 3 represent the x, y and z direction, respectively; t is time; uand P are the filtered velocity and pressure; r is the density of air; dij is the Kronecker delta; g is the gravitational acceleration; fd is the drag of the porous vegetation. If there is no vegetation in the flow field, the term fd equals zero. The effective dynamic viscosity, meff, is defined as: meff ¼ m þ mSGS

(9)

where m is the dynamic viscosity of the air; mSGS is the viscosity of sub-grid scale turbulence. Its definition is: mSGS ¼ rðCs Ds Þ2

qffiffiffiffiffiffiffiffiffiffiffiffiffi 2Sij Sij

(10)

where Cs is the Smagorinsky parameter; and Sij is the rate of strain: Sij ¼

  1 vui vuj þ 2 vxj vxi

(11)

where Ds is the characteristic length of the spatial filter, and it can be calculated as: Ds ¼ ðDxDyDzÞ1=3

(12)

In this study, the value of the Smagorinsky parameter was set to Cs ¼ 0.15 after a comparison with the experimental results. The projection method (DeLong, 1997) was used to solve the Poisson pressure equation (PPE) and to decouple the velocity and pressure in the NaviereStokes equations. The wall function was used to calculate the velocity near the solid wall. Cabot and Moin (2000) suggested the following wall function:

2 mSGS zþ w =A ¼ kzþ w 1e m zþ w ¼

zu* n

(13)

(14)

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where z is the distance from the grid centre to the wall; n is the kinematic viscosity of the air; u* is the shear velocity; k (¼0.41) is the von Karman constant; and the coefficient A ¼ 19. Furthermore, the present LES model integrated a porous drag model to account for the drag caused by the vegetation. Kozeny (1927) suggested that the pressure loss due to the porous obstacles is linearly proportional to the fluid velocity (Darcy law): 1 an ð1  nÞ2 u  VP ¼ 2 , r d n3

(15)

where n is the porosity of the porous media; n is the kinematic viscosity of the fluid; u is the fluid velocity; d is the characteristic length scale representing the porous material; and a is a permeability coefficient to be determined empirically. Forchheimer (1901) suggested that the inertia effect on flows through porous media should be considered for high Reynolds number flows and proposed the following equation to calculate the drag of porous obstacles: fd ¼ au þ bujuj

(16)

where a and b are both dimensional coefficients. The first term can be considered as the Darcy's law, while the second term represents the inertia effect. Raupach and Thom (1981) suggested that the form drag of the canopy can be modelled as: 1 . V P ¼ CD ,LAI,u2 r

(17)

where CD is the drag coefficient, LAI is the leaf area index of the canopy. Miguel, van de Braak, Silva, and Bot (1998) computed the drag forces induced by the insect screens using the DarcyeForchheimer equation: .

"

VP¼

m CF u þ r pffiffiffiffiffiffiu2 Kp Kp

# (18)

where m is the dynamic viscosity of the air; Kp is the permeability coefficient; and CF is the momentum loss coefficient. The value of the permeability coefficient, Kp, is related to the porosity of the screen. Verboven, Flick, Nicolai, and Alvarez (2006) suggested an additional viscous term for the DarcyeForchheimer equation: .

"

VP¼

# m CF u þ r pffiffiffiffiffiffiu2 þ meff V2 u Kp Kp

(19)

where meff is the effective dynamic viscosity in the boundary layer at the porous-media interface. In their study, the value of Kp ¼ 1.89  107, and CF ¼ 1.25  102. Van Gent (1995) performed experiments in an oscillating water flume to determine the drag force of porous media, and proposed a porous drag model for wave/current flows: an ð1  n Þ2 b ð1  n Þ vu u 2 , ujuj  CA fd ¼  2 , n3 vt n3 d50 d50

(20)

where a is the permeability constant; b is the inertia factor; d50 is the equivalent mean diameter of the porous materials.

In this study, because the unsteady term is small, the drag of the porous vegetation, fd, is calculated by the following model: " rfdi ¼ r  a

n ð1  nÞ2 b ð1  nÞ 〈ui 〉  〈ui 〉2 d2 d n3 n3

# (21)

where a, b are the dimensionless coefficients; n is the porosity; and d is a characteristic length scale representing the average size of the pores in the vegetation. The permeability coefficient and inertia factor in each direction can be treated independently.

3.

Model validation

Tominaga et al. (2008) and Ramponi and Blocken (2012) discussed the application of CFD models to simulate the wind environment inside and around buildings. They concluded that the numerical setup, such as the computational domain, mesh size, boundary conditions and convergence criterion, could influence the simulation results. Therefore, numerical models should be compared with the results of laboratory experiments and/or field observation to validate simulation results. In this study, the simulation results were compared with the measured velocity and pressure of wind tunnel experiments to demonstrate the accuracy of the present numerical model. The wind tunnel experiments were carried out in an open, suction-type wind tunnel. The total length of the wind tunnel is 30 m, and the test section was 18.5 m long, 3.0 m wide and 2.1 m high. A scaled down gable-roof greenhouse model was placed at the centreline of the test section (see Fig. 1). The model was made from centre smooth acrylic plate, and the scale ratio of the model to the prototype greenhouse was 1:20. The width of the prototype greenhouse was W ¼ 20 m, length L ¼ 8.0 m, the height of roof was H ¼ 4.0 m, the height of the eaves He ¼ 3.0 m, and the slope of the roof f ¼ 14 . The centre of the windward and leeward wall each has one opening, with the opening area Aw ¼ AL ¼ 12 m (width)  1.60 m (height), and the opening ratio of the windward wall area AF was Aw/ AF ¼ 32%. The maximum ventilation rate usually occurs when the wind direction is normal to the side vents of the greenhouse (Chu, Chiu, Tsai, & Wu, 2015). Therefore, this study only investigate the wind-driven ventilation when the wind direction is normal to the ridge of the roof (wind direction q ¼ 0 ). There were pressure taps on the roof, windward and leeward sides of the greenhouse model. All of the pressure taps were flush to the external walls and connected to a multichannel high-speed pressure scanner (ZOC33/64PX, Scanivalve Inc., Liberty Lake, Washington, U.S.) by short pneumatic tubing. The measuring range of the pressure sensor was ±2758 Pa, with a resolution of ±2.2 Pa. The sampling frequency was 100 Hz, and the sampling duration was 163.84 s. The velocities of the approaching flow and inside the greenhouse were measured by a four-hole Cobra probe (Turbulent Flow Instrument, Victoria, Australia).

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225

Fig. 2 e Profiles of time-averaged velocity U(z) and stream wise turbulence intensity Iu(z) of the approaching flow.

Fig. 1 e Schematic diagram and photograph of the gableroof greenhouse model.

The approaching flow is a turbulent boundary layer flow and the stream wise velocity U(z) follows the power law velocity profile: UðzÞ z h ¼ Uo d

(22)

where z is the height from the ground; d is the thickness of the boundary layer; h is the exponent of the velocity profile; Uo is the wind speed outside the boundary layer. The vertical profile of time-averaged velocity U(z) and turbulence intensity Iu(z) (¼su(z)/U(z)) are shown in Fig. 2. The value of ¼ 0.9 m and h ¼ 0.251 were used in this study. The wind speed at the greenhouse roof is UH ¼ 10 m s1, and the Reynolds number Re ¼ UHH/n ¼ 1.33  105. This wind speed was shown to increase the accuracy of pressure and velocity measurements. For example, the resolution of the pressure scanner used in this study was 2.2 Pa. When the external wind speed UH ¼ 10 m s1, the pressure P on the windward wall is around 40 Pa. Therefore, the uncertainty of the pressure measurement was 5%. When the wind speed decreased, the uncertainty of pressure measurement will increase. Figure 3 shows the schematic diagram of the computational domain (height 1.2 m, width 3.4 m and length 3.4 m). The blockage ratio of the frontal area of the greenhouse to the cross-sectional area of the computational domain was 4.90%. The greenhouse walls and the bottom boundary were specified as the no-slip and no-penetration boundary conditions,

and the top and two lateral boundaries were set as the freeslip boundary condition. The stream wise velocity U(z) at the inlet boundary follows Eq. (22), and the outlet boundary is specified as the zero gradient condition for the velocity. The computational domain was divided into eight different zones (see Fig. 4). The greenhouse was located in Zone V, where it was discretized by a mixed non-structured grid, with the smallest grid size. The other seven zones adopted nonuniform grids with the stretching ratio 1.04. The dimensionless time step was Dt ¼ DtUH/H ¼ 0.021 (normalised by the velocity UH and the height H). The simulation results after the dimensionless time t ¼ tUH/H ¼ 250 were used for the analysis to avoid the initial transient results (t ¼ 0e250) of the numerical model. The time-averaged velocity and pressure were calculated from the simulation results between t ¼ 250e500. Figure 5 compares the predicted and measured timeaveraged stream wise velocity profiles at four different locations (x/L ¼ 0.075, 0.225, 0.45, 0.775) inside the single-span greenhouse. The velocities were measured along the centreline of the greenhouse openings. There was no insect screen or vegetation in the greenhouse. The good agreement between the predicted and measured velocities demonstrated that the LES model was capable of simulating the air flow inside greenhouses. Figure 6 compares the measured pressure coefficients on the centrelines of the single-span greenhouse model (Re ¼ 1.33  105) and the predicted wall pressure of the fullscale greenhouse (Re ¼ 2.66  106). The pressure coefficient Cp was calculated by Eq. (3) using the velocity UH ¼ 10.0 m s1 at height z ¼ H. The present LES model was used to simulate two different cases: (1) greenhouse without openings; (2) greenhouse with inlet and outlet openings. For the wind tunnel experiment, surface pressures were measured using the greenhouse model without openings. The simulated windward pressure coefficients with and without the openings were very close, except near the edge of the inlet opening.

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Fig. 3 e Side view of the computational domain.

Fig. 4 e Computational domain and mesh layout of the grid 108 £ 78 £ 88. (a) 3D view; (b) Side view of Zone V.

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Fig. 5 e Comparison of predicted and measured time-averaged stream wise velocities inside the single-span greenhouse. (a) x/L ¼ 0.075; (b) x/L ¼ 0.225; (c) x/L ¼ 0.45; (d) x/L ¼ 0.775.

This is due to the local acceleration as the air flow entered the inlet opening. The good agreement between the predicted Cp of full-scale greenhouse and measured Cp of scale-down model confirmed that the pressure coefficients of blunt bodies were independent of the Reynolds number in high Reynolds number (Re > 104) flows (Hoerner, 1965; Holmes, 2001). Grid sensitivity was checked by comparing the simulation results of three different computational grids (see Table 1). The ventilation rates Q through the greenhouse openings were computed by two different methods. The first method is to integrate the simulated time-averaged velocities at the inlet and outlet openings. The ventilation rates computed by the integration method at the windward and leeward openings are represented by Qw and QL, respectively. The average * * ¼ ðQw þ QL* Þ=2. For Grid 2, the ventilation rate is defined as Qavg relative difference between the computed ventilation rates of the inlet and outlet openings Qw ¼ 0.235 m3 s1 and * ¼ 0.694 and QL* ¼ 0.665) was 4.2%. This QL ¼ 0.226 m3 s1 (Qw indicates the error of not satisfying the mass conservation law at the inlet and outlet openings being less than 5%. The second method to compute the dimensionless venti* is using Eqs. (1) and (3). The simulated lation rate Qmodel windward and leeward pressure coefficients Cpw ¼ 0.695 and CpL ¼ 0.220 from the LES model (with Grid 2) were used. The * ¼ 0.642 was computed by predicted ventilation rate Qmodel substituting the discharge coefficient Cdw ¼ CdL ¼ 0.66 into Eqs. (1) and (4). The relative difference between the ventilation

rates computed by the integration method and by ventilation model, Eq. (1), is calculated as: DQ ¼

  Qavg  Qmodel  Qmodel

(23)

As can be seen in Table 1, the differences of Grids 1, 2 and 3 were 25.9%, 5.9%, 4.8%, respectively. Nevertheless, the computational time of Grid 3 was 456 h. Therefore, Grid 2 was used for the rest of the simulations to reduce computational time.

4.

Results and discussion

4.1.

Single-span greenhouse with vegetation

In order to study the obstruction effect of vegetation (crops) in the greenhouse, plastic models of vegetation were placed inside the greenhouse model (see Fig. 7). The average height of the vegetation model was hv ¼ 72 mm, the width Wv ¼ 600 mm (normal to the wind direction), and the average size of the leaves d ¼ 8.6 mm. The vegetation model was parallel to the windward and leeward walls of the greenhouse, and normal to the external wind direction. The porosity of the vegetation is defined as: n¼

AV AT

(24)

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Fig. 6 e Comparison of measured time-averaged pressure coefficients of the scale-down model (Re ¼ 1.33 £ 105) and full-scale greenhouse (Re ¼ 2.66 £ 106). (a) windward wall; (b) leeward wall.

Table 1 e Comparison of simulation results of different computational grids.

Smallest grid size

time step Dt (sec) Total grid number * Q* Qw QL* * Qavg Cpw CpL * Qmodel DQ CPU time

Grid 1

Grid 2

Grid 3

Dx/H ¼ 0.10 Dy/H ¼ 0.10 Dz/H ¼ 0.10 8.4  104 457,312 0.864 0.836 0.850 0.684 0.234 0.675 25.9% 37 h

Dx/H ¼ 0.05 Dy/H ¼ 0.05 Dz/H ¼ 0.04 4.2  104 1,216,372 0.694 0.665 0.680 0.695 0.220 0.642 5.9% 245 h

Dx/H ¼ 0.04 Dy/H ¼ 0.04 Dz/H ¼ 0.025 3.4  104 3,163,880 0.686 0.666 0.676 0.705 0.215 0.645 4.8% 456 h

* Qw , QL* are the dimensionless ventilation rates at the inlet and * outlet openings calculated by the integration method, Qmodel is the ventilation rate calculated by Eq. (1).

Fig. 7 e Photograph of the vegetation model. (a) Side view of the greenhouse; (b) Frontal view of the vegetation; (c) Processed photograph of the vegetation (blue area represents the void area, white areas are leaves and branch). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

where AV is the void area (porous area) of the vegetation and AT is the total cross-sectional area of the vegetation. In this study, the void area of the vegetation was measured by an image processing method. Figure 7(b) and (c) show the original and the processed photograph of the vegetation model. When the grey level was higher than a threshold value, the pixels represent the void area that the air can pass through; otherwise, the pixels were occupied by the leaves and/or branch that the air cannot pass through. After several trials, the porosity remained constant when the threshold of the grey level was set at 140. This method is similar to the measurement concept of the leaf area index (LAI) meter. Nevertheless, the LAI meter measures the porosity of the vegetation in the vertical direction (because illumination is from the sky); the present method measures the vegetation porosity in the horizontal direction (which is the mean wind

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Fig. 8 e Comparison of predicted and measured timeaveraged stream wise velocities inside the greenhouse with one row of vegetation by different a and b. (a) x/L ¼ 0.225; (b) x/L ¼ 0.65; (c) x/L ¼ 0.775. direction). This method for the porosity measurement can be used for any kind of real vegetation. By using this method on several photographs of the vegetation model, the average value of the porosity for the single-row of vegetation was determined n ¼ 0.37; n ¼ 0.187 for two rows; and n ¼ 0.126 for three rows of vegetation. The vegetation was parallel to the windward and leeward walls. The total height of the vegetation was hv ¼ 1.44 m (in

229

full-scale), and the width was b ¼ 12 m (b/W ¼ 0.6) placed inside the greenhouse at location x/L ¼ 0.5. Figure 8 compares the predicted and measured time-averaged stream wise velocities at locations x/L ¼ 0.225, 0.65 and 0.775 inside the greenhouse. The location x/L ¼ 0.225 was in front of the vegetation; while x/L ¼ 0.65 and 0.775 were behind the vegetation. This comparison disclosed that the simulation results were sensitive to the inertia factor b, rather than the permeability coefficient a. The predicted velocities by the permeability coefficient a ¼ 50 and the inertia factor b ¼ 0.02 were closest to the measured velocities. The characteristic length d ¼ 8.6 mm was used in Eq. (21), based on the average size of the leaves on the vegetation model. The coefficient of determination for the measured and predicted velocities behind the vegetation was 0.897, and the Root Mean Square Error (RMSE) was 0.165. Therefore, the permeability coefficient a ¼ 50 and the inertia factor b ¼ 0.02 were used for the rest of the simulation. The equivalent values for the coefficients in Eq. (18) are: the permeability coefficient Kp ¼ 1.88  107, and the momentum loss coefficient CF ¼ 0.0126. A parametric study showed that the inertial effect became larger than viscous effect and dominated the total drag when the velocity larger than 3.0 m s1. Figure 9 displays the simulated time-averaged velocity vectors on the mid-plane of the greenhouse with single and two rows of vegetation. The thickness of the vegetation was l ¼ 0.40 m, 1.40 m and 2.40 m for single, two and three rows of vegetation, respectively. As can be seen, the vegetation inside the greenhouse led to a reduction in the air velocity behind the vegetation, and the air flow was deflected upwards above the vegetation. Figure 10 compares the stream wise velocity along the centreline of the openings at height z/H ¼ 0.2. The stream wise velocities were normalised by the wind speed at the roof height UH. For empty greenhouse (without vegetation), the internal velocity was the highest due to the low resistance for air flow to pass through the greenhouse. When there were vegetation inside the greenhouse, although the external wind speed was 10 m s1, the velocity behind the vegetation dropped to 1e3 m s1 and gradually increased to 4e5 m s1 as it approached the leeward opening due to the leeward suction pressure. Figure 11(a) compares the ventilation rate Q (computed by the integration method) with and without vegetation in a single-span greenhouse. It illustrates that the ventilation rate decreased as the row number of vegetation increased (or as the porosity decreased). The ventilation rate of three rows of vegetation was 62% of that the greenhouse without vegetation. The resistance factor zv of the vegetation can be calculated from Eq. (5) using the ventilation rate Q and the pressure difference DCp ¼ Cpw  CpL (see Table 2). The resistance factors of the external openings, zw ¼ zL ¼ 0.00623 m4, were computed from Eq. (6) with the discharge coefficient Cdw ¼ CdL ¼ 0.66, and the opening area Aw ¼ AL ¼ 19.2 m2 (effective opening area A* ¼ 8.96 m2). Figure 11(b) shows the relationship between the normalised resistance factor zv/zw and the porosity n of the vegetation. As expected, the resistance factor increased as the porosity of the vegetation decreased (or as the row number of vegetation increased). Figure 12 shows the measured stream wise velocity profiles at location x/L ¼ 0.30 behind the insect screens of different

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(a)

(b)

Fig. 9 e Time-averaged velocity vectors on mid-plane of the greenhouse with vegetation. (a) single row; (b) two rows of vegetation.

Fig. 11 e Effect of vegetation porosity n on the ventilation rate. (a) dimensionless ventilation rate Q*. (b) resistance factor zv/zw.

inch. As expected, the measured velocity decreased as the mesh number increased. The velocity behind the mesh 48 is less than 50% of the velocity without a screen.

4.2.

Fig. 10 e Simulated stream wise velocity along the centreline of the openings at height z/H ¼ 0.2 for the greenhouses with vegetation.

meshes. The polyethylene screens were installed on the windward and leeward openings (opening height z/H ¼ 0.40), and there is no vegetation inside the greenhouse. The mesh number 16, 24, 32 and 48 represent the number of threads per

Multi-span greenhouse without vegetation

This section examines the influence of the greenhouse length on the cross ventilation. The windward and leeward wall each has one opening (height 1.6 m and width 12 m) at the centre of the walls. The openings area Aw ¼ AL ¼ 19.2 m2. There is no insect screen on the openings, no vegetation or obstacle inside the greenhouse. Figure 13 shows the time-averaged velocity vectors on the mid-plane of single-, two-, and three-span greenhouses without internal walls. The velocity near the floor (z/H < 0.3) of the greenhouse is larger than the velocity above the opening height (z/H > 0.4). The simulated stream wise velocities along the centreline of the openings at height z/H ¼ 0.2 in the multi-span greenhouses are compared with the measured velocities of the single-span greenhouse in Figure 14. As can be seen, the velocity inside the single-span

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Table 2 e Simulation results of the single-span greenhouse with vegetation. Case No vegetation Single row Two rows Three rows

Porosity n

Thickness l (m)

DCp

* Qavg

* Qavg =Qo*

zv (m4)

zv/zw

1.0 0.370 0.187 0.126

0 0.40 1.40 2.40

0.947 0.951 0.950 0.944

0.680 0.644 0.504 0.461

100% 95% 74% 62%

0 1:5  103 9:2  103 1:3  102

0 0.23 1.47 2.08

Qo* : dimensionless ventilation rate of single-span greenhouse without vegetation or insect screen.

Fig. 12 e Measured stream wise velocities behind the insect screens of different meshes.

greenhouse was larger than that of multi-span greenhouses. This implies that the ventilation rate of the single-span greenhouse is larger than that of multi-span greenhouses. Figure 15 depicts the distribution of pressure coefficients on the mid-plane of the greenhouses. The positive pressures on the windward walls were similar for single-span and multispan greenhouses, while the maximum negative pressure coefficient, Cp ¼ 0.914, occurred at the first ridge of the greenhouse roof. The suction pressures of the second and third ridges were very close. These pressure coefficients can be used for the structure design of the greenhouses. Figure 16 compares the simulated and measured pressure coefficients on the centrelines of the windward and leeward walls of greenhouses of different lengths. The pressure coefficients above the windward opening was around Cpw ¼ 0.70, regardless of the greenhouse length. The pressure coefficient Cpw decreased as it approached the opening, due to the local acceleration when the air flow entered the opening. However, the suction pressure on the leeward wall, CpL, of the singlespan greenhouse was larger than those of two- and threespan greenhouses. Table 3 summarises the ventilation rate, Qavg, computed by the integration method, and the pressure difference, DCp ¼ Cpw  CpL, between the windward and leeward walls (the driving force for cross ventilation). The pressure difference the single-span greenhouse, DCp ¼ 0.947, was larger than those of two- and three-span greenhouses (DCp ¼ 0.811 and 0.806,

Fig. 13 e Simulated velocity vectors on the mid-plane of the greenhouses. (a) single-span; (b) two-span; (c) three-span greenhouse.

respectively). This indicates that the ventilation rate of the single-span greenhouse should be larger than that of multispan greenhouses. Figure 17(a) demonstrates that the ventilation rate decreased as the length of greenhouse, L/H, increased. The ventilation rates were normalised by the ventilation rate of

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Fig. 14 e Stream wise velocity along the centrelines of the openings at height z/H ¼ 0.2 inside the greenhouses.

Fig. 16 e Comparison of predicted and measured pressure coefficients on the centrelines of the external walls of single-, two- and three-span greenhouses. (a) windward wall; (b) leeward wall.

Table 3 e Simulation results of multi-span greenhouse without internal wall and vegetation. Case Single Two-span Three-span Five-span

L/H

DCp

* Qavg

* Qavg =Qo*

zL (m4)

zL/zw

2 4 6 10

0.947 0.811 0.806 0.811

0.680 0.631 0.612 0.526

100% 93% 90% 70%

0 0 5:6  104 4:78  103

0 0 0.09 0.77

Without insect screen.

Fig. 15 e Distribution of the pressure coefficients on the mid-plane of the greenhouses. (a) single-span; (b) twospan; (c) three-span greenhouse.

the single-span greenhouse without vegetation or insect * , prescreen Qo* ¼ 0.680. Note that the ventilation rates, Qmodel dicted by Eq. (1) for single- and two-span greenhouses were * , computed by the integration method. very close to Qavg * * were larger than Qavg for fiveHowever, the predicted Qmodel span greenhouse (greenhouse length L/H ¼ 10), suggesting that the diminishing effect of the internal friction on the air

b i o s y s t e m s e n g i n e e r i n g 1 6 4 ( 2 0 1 7 ) 2 2 1 e2 3 4

(a)

233

screen and internal vegetation, the ventilation rate can be predicted by the resistance model: * Qresist ¼

 1=2 Cpw  CpL 1 A* zw þ zi þ zv þ zL

(25)

where zi and zv are the resistance factors of the internal friction and vegetation, respectively; The obstruction effect of insect screen can be expressed in terms of the resistance factors of the external openings, zw and zL. The values of the resistance factors of the insect screen and vegetation are dependent on their porosity, can be determined by experiments.

5.

(b)

Fig. 17 e Predicted ventilation rates and the resistance factors of multi-span greenhouses with length L/H. (a) Dimensionless ventilation rate Q*; (b) Normalised resistance factor zi/zw.

flow can be neglected when L/H  4, but should be considered when the greenhouse length L/H > 6. This is similar to the rule of thumb for effective cross ventilation that the building length should be less than five times the ceiling height (CIBSE, 1997; Chu & Chiang, 2014). The extra resistance caused by the internal friction of an empty greenhouse can be expressed in terms of the resistance factor zi in Eq. (5). The value of zi was computed by substituting the predicted external pressure coefficients and ventilation * , by the integration method into Eq. (5). Figure 17(b) rates, Qavg displays the normalised resistance factor zi/zw as a function of greenhouse length L/H. The internal resistance was negligible when L/H  4, but increased non-linearly as the greenhouse length increased. Also note that, the internal resistance zv/zw of an empty five-span greenhouse (length L/H ¼ 10) is smaller than that of the resistance zi/zw of two rows of vegetation (see Fig. 11(b)). In other words, the obstruction effect of vegetation is larger than that of greenhouse length. In this study, the obstruction effects of the insect screen, internal vegetation and greenhouse length were examined separately. Therefore, their resistance factors can be quantified independently. For multi-span greenhouses with insect

Conclusions

This study used a large eddy simulation (LES) model and wind tunnel experiments to investigate the wind-driven cross ventilation of gable-roof greenhouses. The effects of internal vegetation, insect screen and length of the greenhouse on the ventilation rate were simulated and analysed. A resistance model, based on the mass conservation and energy concept, is used to calculate the mean ventilation rates of greenhouses with vegetation and insect screen. The results of this study are summarised in the following: 1. The numerical results indicated that the present LES model can accurately simulate the velocity and surface pressure of multi-span greenhouses, and the porous drag model was able to predict the velocity distribution behind porous vegetation. 2. The windward pressure was independent of the greenhouse length or the vegetation inside the greenhouse, while the suction pressure on the leeward side of the single-span greenhouse was larger than that of the multispan greenhouse. In other words, the pressure difference (driving force for wind-driven ventilation) of a single-span greenhouse is larger than that of the multi-span greenhouse, and leads to the larger ventilation rate. 3. The diminishing effects of the vegetation, insect screen and the length of greenhouse on the wind-driven ventilation rate can all be quantified by the resistance model. The resistance factor of the vegetation increased as the porosity of the vegetation decreased. The diminishing effect of the insect screen on the ventilation rate can be expressed in terms of the resistance factors of external openings. 4. The internal resistance of the greenhouse increased as the greenhouse length increased. When the length (in the wind direction) of the greenhouse is larger than six times the greenhouse height, the diminishing effect of the internal friction should be taken into account in the resistance model.

Acknowledgements The authors are grateful to the Taiwan Agricultural Research Institute, Council of Agriculture (grant no. 106AS-12.4.1-STa3), and the Ministry of Science and Technology (grant no. MOST 105-2221-E-008-012) of Taiwan, R.O.C.

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