Mean and turbulent air flows and microclimatic patterns in an empty greenhouse tunnel

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1 Agricultural and Forest Meteorology 100 (2000) Mean and turbulent air flows and microclimatic patterns in an empty greenhouse tunnel T. Boulard, S. Wang, R. Haxaire I.N.R.A. Unité de Bioclimatologie Site Agroparc, Domaine Saint Paul, Avignon Cedex 9, France Received 17 March 1999; received in revised form 27 August 1999; accepted 20 September 1999 Abstract The turbulent air flow along with patterns of air temperature and humidity transport were studied in a classical Filclair tunnel, situated near Avignon in the south of France. Measurements with three-dimensional sonic anemometers and rapid-response hygrometers revealed a strong heterogeneity in the windward side of the tunnel. For winds perpendicular to the axis of the tunnel, the air flow exhibited a strong current crossing the tunnel between the windward and leeward openings and moderate air velocities in the vertical section situated between two consecutive series of openings. The temperature distribution showed a north south gradient due to the cold air penetration through the vent opening and a vertical gradient above the soil surface due to solar energy absorption at the soil level. Air water vapour patterns were quite different from air temperature patterns, with humid areas only concentrated along the soil surface close to the source of evaporating water. Analysis of the energy spectra showed that all the locations had similar spectral levels in the dissipation region Elsevier Science B.V. All rights reserved. Keywords: Greenhouse climate; Ventilation; 3-D Sonic anemometer; Turbulence intensity; Dissipation rate 1. Introduction Spatial variations in air velocity and microclimate inside greenhouses influence crop growth through their effects on transpiration and photosynthesis. This heterogeneity is particularly marked in the case of plastic tunnel houses, the most frequently used design in the Mediterranean basin. This variability leads growers to practise excess irrigation and fertilisation, as has been observed on lettuce crops in the south of France (de Tourdonnet, 1998). Variations in the wind flow are largely responsible for this heterogeneity; Corresponding author. Tel.: ; fax: address: boulard@avignon.inra.fr (T. Boulard). however, given the complexity of turbulent flows in general and the intricate boundary conditions that exist within greenhouses, it is not surprising that the details of the air flow remain elusive and seldom considered even in numerical simulations. To date, most experimental studies of ventilation in full-scale greenhouses have employed tracer techniques (de Jong, 1990; Fernandez and Bailey, 1992; Boulard and Draoui, 1995) that neither allow clear identification of the components of energy and mass transfer through the vent openings, nor a detailed information on the air-flow pattern within the structure. More recently, Mistriotis et al. (1997) have used computational fluid-dynamics techniques to simulate forced convective exchanges in a greenhouse subject to external winds. Experimental and numerical studies by Boulard et al. (1998) have /00/$ see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S (99)

2 170 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) investigated the detailed temperature and air-flow patterns under conditions of free convection in a greenhouse equipped with roof openings. All these numerical studies require further empirical validation particularly in the case of turbulent characteristics, which represent the most critical factors to take into account in simulations (Mohammadi and Pironneau, 1994). Further insight into the turbulent air flow and associated sensible heat exchange in a naturally ventilated bi-span greenhouse was provided by measurements with an ultrasonic anemometer operated in a horizontal plane at the level of continuous openings (Boulard et al., 1997). Similar data is lacking for tunnel-type greenhouses, a fact that provides the primary motivation for the current study. This paper deals with the characterisation of mean and turbulent air flows and patterns of air temperature and humidity inside a classical 8-m wide tunnel house. The tunnel under study was sheltered upwind by other tunnels and oriented perpendicularly to the dominant wind direction as is usual in this region. Natural ventilation was provided by means of discontinuous openings placed every 4 m on either side of the tunnel. Such conditions are common in southern France and in all other Mediterranean regions where the use of tunnel houses is widespread. The present study builds upon measurements of mean and fluctuating air speeds, and fluctuations in temperature and humidity to: 1. characterise patterns of air flow and the microclimatic heterogeneity in vertical cross sections of a tunnel; and 2. evaluate the mean and turbulence characteristics of air velocity components. 2. Theory For the convenience of the reader, we present a brief summary of the equations used in our analyses. For more details, the reader is referred to Kaimal and Finnigan (1994) for a general review of boundary-layer turbulence and to Heber and Boon (1993) and Heber et al. (1996) for discussion of the patterns of air flow and turbulence in barns Mean and turbulent air velocities Mean air velocity measured over a period t is: u = 1 t t 0 u dt (1) where u, the instantaneous air velocity, is represented using the Reynold s decomposition: u =ū + u (2) as the sum of time-mean value (ū) and a fluctuating component (u ) The discrete energy spectrum The structure of turbulence is commonly investigated by means of frequency domain analysis of the air velocity data. A large data record can be conveniently reduced to a spectrum of velocity fluctuations called the discrete energy spectrum E(f)(m 2 s 1 ). Its density, often plotted vs. frequency on a log log graph, provides (even for indoor conditions) a useful description of the air flux components (Lay and Bragg, 1988). The energy spectrum can be integrated over all frequencies f (Hz) for all variance spectra to yield the total variance: σ 2 = 0 E(f)df (3) If R(t) is a decaying oscillating function determined by the correlation between air velocities at a fixed position at two different instants, t and t + t R(t) = u (t )u (t + t) σu 2 (4) Pasquill and Smith (1983) defined the integral turbulence time scale as the integral of R(t) over time from zero to the first zero crossing, t int, such as R(t 0 ) = 0: t = t0 0 R(t) dt (5) and L int, the integral turbulence length scale as: L = ū t (6)

3 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) Turbulent kinetic energy (k) and dissipation rate (ε) The microscale of turbulence (λ) is a measure of the dimension of eddies mainly responsible for the dissipation of turbulent energy into heat. ū 2 σ λ = 2π 0 f 2 (7) E(f)df If k, the total turbulent kinetic energy, is calculated as k = 1 2 (σ 2 u + σ 2 v + σ 2 w ) (8) where σ u, σ v, σ w, respectively, are the standard deviations of the velocity fluctuations in the x, y, z directions, the turbulence energy dissipation rate is: ε = k 3/2 λ 1 (9) 3. Experimental setup 3.1. Site and tunnel description The measurements were carried out in Avignon (44 N latitude, 5 E longitude and 24 m altitude), in an empty 22 8m 2 tunnel equipped with discontinuous openings obtained by separating the plastic sheets every 4 m on either side of the tunnel with pieces of wood. Schematic views of the tunnel are shown in Fig. 1. Assuming a weak influence of the gable ends Fig. 1. Schematic plan of the experimental plastic tunnel. (u, v, w are three components of the air velocity measured by the sonic anemometer in the two sections). and symmetric air flows along the ydirection with respect to each opening, we have explored the tunnel s turbulent flow characteristics in two transverse sections: a middle section (I), situated 2 m westward from section (II) mid-way between two consecutive vent openings; and a vent section (II), situated in the middle of the vent openings, with a northern air inlet situated windward and a southern air outlet leeward. These parallel cross-sections were in the plane of the wind direction. In order to have a continuously evaporating soil surface, the tunnel was abundantly watered before, and during, experiments Instrumentation Rapid fluctuations in air velocity and temperature were measured by means of two three-dimensional (3-D) sonic anemometers (omnidirectional, R3, research ultrasonic anemometer, Gill R&D) and air humidity by means of two krypton hygrometers (Campbell, Utah). These four instruments were used to simultaneously sense air velocity, temperature and humidity fluctuations at two locations in each section. At each location, the measurement head of the krypton hygrometer was placed within 0.2 m of the sampling volume of the sonic anemometer in order to minimise the flow distortion. With only two sampling positions possible at any one time, a difficulty arises from how to deal with changing external conditions throughout the time needed to measure the 24 different measurement positions within each cross section (Fig. 2). This problem was overcome: 1. by selecting measurements for a fixed northerly external wind direction; and by using an external reference wind speed U 0 and the difference in air temperature (T i T o ) and humidity (X i X o ) between the centre of the greenhouse (subscript i ) and the external air stream (subscript o ) as scaling parameters. T i, X i, and T o, X o were measured 1.5 m above the soil surface inside, and outside, the tunnel while U o was measured at a height of 5 m, about 20 m from the centre of the tunnel. A detailed list of the normalisation

4 172 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) Fig. 2. Measurement positions in the central section of the tunnel. All dimensions are in metres. ( ), Air temperature, humidity and velocity measurements by 3-D sonic anemometers and krypton hygrometers (1 to 24); ( ), surface temperature measurements (T s1 -T s14 ); ( ), reference inside air temperature and humidity measurements (T i, X i ). formulae is given in Appendix A. Appendix B gives relations allowing the reader to derive actual physical values from the normalised figures using the average values of the scaling parameters (Ū o, T io, X io ) measured during the experiment. Three components of wind velocity, air temperature and humidity fluctuations were measured at 24 positions in each section together with the thermal boundary conditions at 14 positions along the inside soil surface and plastic cover surface (Fig. 2). Temperatures were measured by means of thin thermocouples stuck on the plastic cover or soil surface. The manufacturer s calibration was accepted for u, v, w, air temperature and humidity measurements. Sampling frequency was 5 Hz. The time duration of each measurement record (for characterisation of two locations) was about 10 min. The outside air temperature (T o ) and humidity (X o ), wind speed (U o ), and direction (θ), and the inside reference air temperature (T i ) and humidity (X i )atthe centre of the tunnel (Fig. 2) were measured each second and averaged over the length of each record. Analogue signals from the sonic anemometers and krypton hygrometers were processed on-line and stored in a portable computer with eddy correlation and rapid Fourier-transform programme options. Outside, and inside, mean climatic conditions and thermal boundary conditions were averaged on-line and results stored in a potable data logger (Campbell CR20: Campbell, Utah) Wind conditions The tunnel was located at Avignon in a region characterised by frequent northerly winds channelled by the Rhône Valley. This wind (the Mistral) provides remarkable conditions for wind research, because of its frequency, constancy of direction (north) and persistence (McAneney et al., 1988). Measurements were made one day (24/10/97) during a strong Mistral with an average wind speed of 3.8 m s 1. Table 1 summarises prevailing weather conditions during the experiment and illustrates the constancy of wind direction and uniformity of the main scaling parameters U o, (T i T o ), (X i X o ). Table 1 Climatic boundary conditions during the experimental period Parameters Mean Standard deviation T a o ( C) RH b o (%) T c i ( C) RH d i (%) U e o (m s 1 ) Dir f ( ) a Exterior air temperatures. b Relative humidities of the exterior air. c Interior air temperatures. d Relative humidities of the interior air. e External wind speed. f Direction.

5 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) Fig. 3. Polar graph of the experimental air velocity in section I. 4. Results 4.1. Tunnel flow field Polar plots Figs. 3 and 4 show frequency distributions of air flow directions in the vertical plane (u w) as polar plots at each position of sections I and II. The origin of each plot is the measurement position and the probability densities were calculated, accumulated and plotted at 10 intervals from 0 to 360. These values are plotted at the angle representing the interval mid-points and their extremities connected by a line to form the polar graph. In this way, the mean flow direction in the u, w planes together with the deviations in the flow can be easily represented. The air-flow pattern (Fig. 4) in the vent-opening section (section II) was characterised by a very strong air stream entering through the northern opening, crossing the tunnel and escaping through the southern opening. As shown in Fig. 3, air speed was much weaker in the mid-section (section I), centred between two consecutive openings. Here, we observed an airflow pattern characterised by two vortex, one rotating anticlockwise and centred on the southern side of the tunnel, and a second, rotating clockwise and centred on the northern side of the tunnel. Fig. 4. Polar graph of the experimental air velocity in section II Two-dimensional vectors The mean vector fields are presented in Fig. 5 for section II. This shows clearly that the air stream crosses the tunnel and escapes perpendicularly through the southern vent opening. If we only consider air circulation in section II, mass conservation did not hold with the inflow exceeding the outflow. As a consequence, and contrary to our initial expectations, lateral air circulations perpendicular to the mean flow (v component) were not symmetrical with respect to the middle of each vent opening. Vertical profiles of the reduced 3-D resultant air velocity in the middle of the tunnel (Fig. 6) were similar for both sections. Approximately the same values (13<U j *<18%) were observed between 0.25 and 2.7 m, with a peak value (Uj = 18%) at 0.9 m and decreasing to zero at soil and roof levels. As illustrated by the horizontal profile at 1 m height (Fig. 7), this similarity of profiles was only observed in the middle section of the greenhouse. Conversely, air velocity was maximum at the air inlet (Uj = 100%) and outlet (Uj = 30%) of section II and null at the same positions in section I Air-temperature patterns Patterns of reduced air temperature [T*(j) = {T(j,t) T o (t)}/{t i (t) T o (t)}] are shown in Figs. 8 and 9 for sections II and I, respectively. Physical values of air-temperature ( C) differences can be deduced by multiplying T with the average difference between inside and outside (2.2 C, see Appendix B). Lateral heterogeneity (perpendicular to the wind direction) was not very significant and the similar patterns of temperature, with comparable magnitudes, were observed in both the sections. On average, section I was only slightly warmer than section II, because less cold air penetrated into this section. Longitudinal heterogeneity (in the direction of the wind) was much more significant, particularly in section II where a strong north to south gradient, due to the cold air penetration, was observed. In the north opening, and along the north side of the tunnel cover in section I, the air-inflow temperature was close to the outside temperatures (0 < T* < 0.5). In contrast, the area situated along the south side of the tunnel and near the southern opening, was significantly warmer

6 174 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) Fig. 5. Normalised air velocity (expressed as a percentage of outside wind speed) distribution measured in section II. (1.5 < T* < 2.5). Solar absorption at soil surface also generated a vertical gradient (1.5 < T* < 2.5) in the first 20 cm above the soil, i.e. across the soil surface boundary layer Air humidity patterns Normalised air water vapour distributions X*(j) = [{X(j,t) X o (t)}/{x i (t) X o (t)}] are shown in Figs. 10 and 11 for sections I and II. respectively. Similar patterns were observed in both sections, with dry regions (X* < 1) situated windward in the northern and upper parts of the tunnel and the more humid regions (1.8 < X* < 3) near the soil surface, where water vapour was evaporated, and concentrated in the leeward part of the tunnel. This pattern is significantly different from that of the air temperature pattern presented above because, contrary to the heat diffusion from the cover to the inside air observed in Figs. 8 and 9, a gradient of water vapour can only be observed above the soil surface. Yet, water vapour transfer above the soil surface seemed to be more important than heat diffusion, as indicated by the larger extension of the areas with 1.8 < X* < 3 as compared to the area with 1.8 < T* < 3. However, one must consider cautiously the humidity measurements because air humidity gradients (kg kg 1 ) between inside and outside were rather weak (see Appendix B) Air turbulence characteristics Turbulent kinetic energy distribution Fig. 12 shows the map of the normalised and time averaged turbulent kinetic energy (k*(j) = (1/2) [{u 2 (j,t) + v 2 (j,t) + w 2 (j,t)}/uo 2 (t)] 100), obtained using least-squares methods for section II. Turbulence intensity was weak in the centre of the tunnel, and increased strongly toward the windward opening, Fig. 6. Normalised air speed (expressed as a percentage of outside wind speed) in the middle of the two sections of the tunnel. Fig. 7. Normalised air speed (expressed as a percentage of outside wind speed) in the two sections at 1-m height of tunnel.

7 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) Fig. 8. Normalised temperature distribution (T*(j) = [{T(j,t) T o (t)}/{t i (t) T o (t)}]) measured in section I. T(j,t), T o (t) and T i (t) are the mean temperatures ( C) measured at time t at positions j, outside the greenhouse and inside in the middle of the greenhouse, respectively. Fig. 9. Normalised temperature distribution (T*(j) = [{T(j,t) T o (t)}/{t i (t) T o (t)}]) measured in section II. T(j,t), T o (t) and T i (t) are the mean temperatures ( C) measured at the t time at positions j, outside the greenhouse and inside in the middle of the greenhouse, respectively. where k*(j) was ten times larger than at the centre. The value of k*(j) in the northern opening and in the areas situated just leeward reached 10%. It increased moderately in the leeward opening (k*(j) 4%), when compared to the values measured in the centre of the tunnel (k*(j) < 2%). However, even the stronger values measured in the opening were rather low when compared to external wind conditions (k* = 26%), measured outside at 1.8 m. Lateral (v-component) variations in turbulence intensity were also significant, k*(j) being much lower in section I (k*(j) < 2%) than in section II. Longitudinal heterogeneity in section I was also characterised by decreasing values of k* from the centre of the tunnel (where the mean wind speed was at a maximum) to the tunnel cover and soil surface. Fig. 10. Normalised water vapour distribution (X*(j) = [{X(j,t) X o (t)}/{x i (t) X o (t)}]) measured in section I. X(j,t), X o (t) and X i (t) are the mean air humidities (kg kg 1 ) measured at time t at positions j, outside the greenhouse and inside in the middle of the greenhouse, respectively.

8 176 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) Fig. 11. Normalised water vapour distribution (X*(j) = [{X(j,t) X o (t)}/{x i (t) X o (t)}]) measured in section II X(j,t), X o (t) and X i (t) are the mean humidities (kg kg 1 ) measured at time t at positions j, outside the greenhouse and inside in the middle of the greenhouse, respectively. Fig. 12. Normalised turbulent kinetic energy (k*(j) = (1/2)[{u 2 (j,t) + v 2 (j,t) + w 2 (j,t)}/uo 2 (t)] 100) distribution measured in section II. The values are expressed as percentages Turbulent energy dissipation rate distribution Turbulent energy dissipation rate, ε, was calculated both from spectral density analysis and from Eq. (3) and Eqs. (7) (9). The spatial distribution of ε obtained by least-squares analyses of sections II (Fig. 13) and I (not shown) followed the distribution of turbulent kinetic energy in both the sections. However, while the order of magnitude of varia- tions in ε was approximately the same in the two sections, the rate of turbulent kinetic energy was approximately five times greater in section II than in section I Integral length and time scales Integral length scales of turbulence (Table 2) show size of eddies in the flow field for cross-sections I and Fig. 13. Distribution of the energy dissipation rate ε (m 2 s 2 ) of velocity component u in section II.

9 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) Table 2 Integral length scale of the three velocity components outside (position 0) and inside (positions 1 to 24) the tunnel at sections I and II Positions Section I SectiomII integral length integral length scale (m) scale (m) L int,u L int,v L int,w L int,u L int,v L int,w Min Max Mean II. It should be noted that the mean integral length scales for the u, v and w directions were always higher than the path distance of the sonic anemometer, and was consequently only slightly modified by our measurement system. The integral length scale of the u velocity component decreases strongly from the jet inside the North vent opening, where it reaches 8.7 m - the same value as for outside. Towards the interior of the tunnel, the turbulence is characterised by smaller eddies, with integral length scales ranging, on average, between 1.8 and 0.38 m in section II and only between 0.87 and 0.3 m in section I. The distribution of the integral length scale in the u-direction in section II is shown in Fig. 14. The time required for an eddy to flow past a fixed position may be characterised by the integral time scale. Integral time scales of velocity for u, v, w directions were on average similar in both, sections I and II, with higher values confined close to the roof (measurement positions Nos. 14 and 18) and the soil surface (positions no. 15 and 19) in section II, and between the northern wall and the soil surface (point Nos. 22 and 23) in section I Microscale of turbulence The microscale of turbulence in the u-direction ranged between (point No. 9 in section I) near the roof mid-way between two openings to 1.12 (point No. 6 in section II) in the windward opening (Fig. 15). It is much larger in the jet situated in the windward opening and decreased as air flowed inside the tunnel. The distribution of average air velocity and microscale of turbulence were similar, as shown by the linear dependence of λ on ū (λ u = 0.334ū , R 2 = 0.97, Fig. 14. Integral length scale L int,u (m) distribution of velocity component u in section II.

10 178 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) Fig. 15. Microscale λ (m) distribution of velocity component u in section II. 48 points) in section II. An equivalent dependence was earlier signalled by Heber et al. (1996) in a barn Energy spectra Comparison of the energy spectra of the external wind (Fig. 16), in the vent opening at position No. 3 (Fig. 17) and that inside the tunnel at position No. 23 in section I (Fig. 18), show that the air current in the windward opening was the most turbulent, followed by the outside wind. The lowest values were found at position no. 23 between two openings. All locations had similar spectral levels at higher frequencies in the dissipation region. However, the behaviour at lower frequencies was quite divergent. In the vent opening, spectral densities at lower frequencies followed the dominance of outside conditions. Most positions with low average air speed showed very similar curves for u-, v- and w-components (see position No. 23, section I), with a spectral decay rate corresponding to the high frequency spectral energies equal to about 5/3, as it is normally the case for isotropic turbulence. 5. Discussion In experimental conditions marked by a strong external wind perpendicular to the tunnel axis and moderate inside outside temperature and humidity differences the wind driven ventilation flux prevails substantially over the buoyancy forces (de Jong, 1990; Boulard and Draoui, 1995). In these conditions, the measurements demonstrated an intense air current crossing the tunnel between the windward and leeward openings, while the air along the floor and in the vertical section between two consecutive series of opening remained still. The air temperature Fig. 16. Spectral energy distribution of the wind at a height of 1.65 m outside the greenhouse tunnel. Fig. 17. Spectral energy distribution of the internal airflow at position 3 in section II.

11 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) Fig. 18. Spectral energy distribution of the internal airflow at position 23 in section I. and water vapour distributions were considerably influenced by these fluxes, with a high north south gradient due to the cold and dry air penetration through the windward vent opening. The turbulence intensity notably increased from the centre of the tunnel toward the windward opening, where it was about ten times larger than in the centre of the tunnel. These experimental data can be compared with the experimental air-speed profiles measured at crop level with the same wind conditions (wind driven ventilation in Mistral conditions) in a multispan span greenhouse equipped with roof openings parallel to the wind direction (Wang et al., 1999 ; Haxaire et al., 1999). The average air speeds in the major volume of the tunnel were ranging between 20 and 80% of the outside wind velocity, against values between 10 and 20% only in the greenhouse equipped with roof openings. We can also observe that, contrary to the tunnel, the high air speed and turbulence intensities in the multispan greenhouse were not concerning the zones where the plants grow, but were confined near the roof openings in the upper volume of the greenhouse. 6. Concluding remarks With the current design of vent openings, the present results demonstrated that the mean and turbulent wind conditions within a large part of the greenhouse tunnel volume were similar to those outside, particularly near the soil surface where the crops would be growing. Plant growth would be enhanced by less heterogeneous and turbulent conditions, so there is a requirement for improved designs of vent opening, which would reduce the mean wind speed and the turbulence within the greenhouse tunnel. Computational fluid dynamics (CFD) simulations could be a valuable tool for analysing and designing better greenhouse ventilation. In this way, the size, position and shape of the vent openings can be designed so that the outdoor air mixes more smoothly at crop level with the indoor air, without forming regions with a direct penetration of outside air, or stagnant regions. As suggested by previous CFD simulations for greenhouses (Mistriotis et al., 1997; Boulard et al., 1998), experimental validation is needed for quantitatively analysing the predictive accuracy of CFD in detail, and particularly the fluctuating component of the flow. The results of the present study provide both, a high-resolution database with which to validate on-going efforts with computer simulations of the mean and turbulent characteristics of the greenhouse environment and a move towards a better understanding of the plant environment behaviour under such conditions. 7. Notation E spectral density (m 2 s 1 ) L turbulent length scale (m) R normalized autocorrelation function f frequency (s 1 ) k turbulent kinetic energy, (m 2 s 2 ) T air temperature ( C) t time (s) u horizontal air velocity, positive north to south (m s 1 ) v horizontal air velocity, positive west to east (m s 1 ) w vertical air velocity, positive upward (m s 1 ) U wind speed (m s 1 ) X air humidity content (kg kg 1 ) λ microscale (m) σ standard deviation θ wind direction ( ) ε turbulence energy dissipation rate (m 2 s 2 )

12 180 T. Boulard et al. / Agricultural and Forest Meteorology 100 (2000) Subscripts i inside int integral integral j position (1 to 24) o outside s surface 9. Superscripts fluctuating component of quantity in question * reduced quantity in question 10. Symbols above letters ˆ estimated value mean value Appendix A. Normalised parameters Air velocity (m s 1 ) Mean part u (j) = 100 Turbulent part u(j, t) U o (t) u (j) = 100 u (j, t) U o (t) ; 3-D resultant air speed (m s 1 ) U (j) = u 2 (j) + v 2 (j) + w 2 (j) Turbulent kinetic energy (m 2 s 2 ) k (j) = 1 u 2 (j, t) + v 2 (j, t) + w 2 (j, t) 2 Uo 2(t) 100 Temperature ( C) T (j) = T(j,t) T o(t) T i (t) T o (t) Humidity (kg kg 1 ) X (j) = X(j,t) X o(t) X i (t) X o (t) Appendix B. Physical values of the experimental parameters Physical values can be deduced from the normalised parameters knowing the average value of the three scaling parameters during the experiment: Ū o = 3.8ms 1, T io = 2.2 C, X io = kg kg 1. Air velocity (m s 1 ) Mean part ˆv(j) = Turbulent part v(j, t) U o (t) U o û (j) = u (j, t) U o (t) U o 3-D resultant air speed (m s 1 ) Û(j) = û 2 (j) +ˆv 2 (j) +ŵ 2 (j) Turbulent kinetic energy (m 2 s 2 ) ˆk(j) = 1 2 [û 2 (j) +ˆv 2 (j) +ŵ 2 (j)] Temperature ( C) ˆT(j)= T(j,t) T o(t) T i (t) T o (t) Humidity (kg kg 1 ) T io ˆX(j) = X(j,t) X o(t) X i (t) X o (t) X io References Boulard, T., Draoui, B., Natural ventilation of a greenhouse with continuous roof vents: measurements and analysis. J. Agric. Eng. Res. 61, Boulard, T., Papadakis, G., Kittas, C., Mermier, M., Air flow and associated sensible heat exchanges in a naturally-ventilated greenhouse. Agric. For. Meteorol. 88,

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