Numerical modelling of temperature variations in a Chinese solar greenhouse

Numerical modelling of temperature variations in a Chinese solar greenhouse

Computers and Electronics in Agriculture 68 (2009) 129–139 Contents lists available at ScienceDirect Computers and Electronics in Agriculture journa...

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Computers and Electronics in Agriculture 68 (2009) 129–139

Contents lists available at ScienceDirect

Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag

Numerical modelling of temperature variations in a Chinese solar greenhouse G. Tong a,∗ , D.M. Christopher b , B. Li c a

College of Water Conservancy, Shenyang Agricultural University, Dongling Road 120, Shenyang 110161, China Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China c Key Lab of Bioenvironmental Engineering, Ministry of Agriculture, China Agricultural University, Beijing 100083, China b

a r t i c l e

i n f o

Article history: Received 11 February 2008 Received in revised form 5 May 2009 Accepted 15 May 2009 Keywords: Solar greenhouse Temperatures Modelling Energy conservation

a b s t r a c t The time-dependent temperature distributions inside a Chinese solar greenhouse are numerically predicted from external climatic conditions using a computational fluid dynamics (CFD) analysis. The boundary conditions are based on hourly measured data for the solar insolation and the sky, soil (1 m below the soil surface) and outside air temperatures, plus other parameters describing the external convection and radiation. The numerical model takes into account all of the heat transfer mechanisms including the variable solar insolation, the air infiltration, the heat capacities of the thick walls and the ground and the natural convection inside the greenhouse. The temperatures were measured experimentally in an enclosed solar greenhouse with a 12 m span and 5.5 m ridge height during the winter in northern China with the south roof covered with a thin plastic film during the daytime and with a thermal blanket added at night to reduce heat losses. The large temperature variations in the greenhouse were measured and predicted for the climatic conditions in northern China during three clear days followed by a cloudy day during the winter. The simulated air and soil temperatures have the same profile as the measured temperatures with the average temperature differences between the simulated and measured air temperatures during the nighttime less than 1.0 ◦ C on the clear days and no more than 1.5 ◦ C during the entire cloudy day. © 2009 Elsevier B.V. All rights reserved.

1. Introduction During the day, northern China experiences sunshine more than 50% of the time but the temperatures are very low during the winter with monthly daily average temperatures in the colder three months falling below −10 ◦ C in northeast China. Greenhouses enable the extension of the crop growing season in the cold climatic conditions of northern China, so flowers and vegetables can be produced year round. However, in large glass-covered heated greenhouses, the heating accounts for 30–50% of the total production cost (Wang et al., 1999). The fuel consumption then becomes an important economic factor for the greenhouse production, with the utilisation of renewable energy as the main measure for resolving the problem. The greenhouse industry is one field that can effectively use renewable solar energy. The average ratio of the solar energy input to the total energy (solar energy input plus the fuel energy input) inside a large greenhouse with a double polyethylene film covering the top from November to March in Iraq was about 0.41 (Hasson, 1991). Chinese solar greenhouses are relatively

∗ Corresponding author. Tel.: +86 24 88487134; fax: +86 24 88417416. E-mail addresses: [email protected] (G. Tong), [email protected] (D.M. Christopher), [email protected] (B. Li). 0168-1699/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.compag.2009.05.004

small, simple, energy-saving greenhouses that have a plastic film (usually about 0.0001 m thick) covering the slanted front roof during the day with a thermal blanket added at night to maintain the heat inside. A typical greenhouse structure is shown in Fig. 1. Chinese solar greenhouses are widely used in northern China and can produce vegetables and fruits in severe cold areas from 32 to 41◦ N latitude, and even beyond 43◦ N latitude with little or no auxiliary heating. Statistics for the year 2000 showed that more than 2600 million m2 of solar greenhouses were in use (Pan et al., 2005). These greenhouses produce 90% of the vegetables eaten in northern China in the winter (Li, 2004). However, the greenhouses experience large air temperature and humidity variations inside the greenhouse with the microclimate inside largely dependent on the external climatic conditions when no auxiliary heating is supplied inside the greenhouse. Therefore, accurate models are needed to predict the temperature fluctuations inside the greenhouses as functions of the external conditions to improve the structural design and climate control. In China, considerable attention has been given to the solar energy efficiency in solar greenhouses. Solar radiation absorption in solar greenhouses has been numerically simulated in various studies (Sun et al., 1993; Du et al., 2001; Li and Chen, 2004). The air temperatures inside solar greenhouses with various types of walls, spans and heights have been measured and analysed

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Nomenclature A Cp D d E h k L l N q R RH T t V

v ˛ ˇ ε  ω   b d 

area (m2 ) specific heat (J kg−1 K−1 ) total layer thickness (m) individual layer thicknesses (m) canopy transpiration (kg m−2 s−1 ) heat transfer coefficient (W m−2 K−1 ) thermal conductivity (W m−1 K−1 ) latent heat of vaporization (J kg−1 ) length (m) air change rate (s−1 ) heat flux (W m−2 ) ratio relative humidity temperature (K) temperature (◦ C) volume (m3 ) wind speed (m s−1 ) reflection of the ground angle between the south roof plane and the horizontal plane (◦ ) emissivity density (kg m−3 ) humidity ratio incidence angle (◦ ) time (s) cover transmittance for beam radiation cover transmittance for diffuse radiation view factor

oped to predict the temperatures inside solar greenhouses (Li et al., 1994, 1997), but these models all assume uniform temperatures in each part of the system. However, the temperature variations in each part of the greenhouse system are actually very dynamic processes both in time and in space that are not accurately modelled by these lumped capacitance models. Computational fluids dynamics (CFD) techniques provide powerful methods for simulating the time- and space-dependent microclimatic conditions within the greenhouses, and have been increasingly used in analysing greenhouse structures. Bartzanas et al. (2002), Fath and Abdelrahman (2004), Boulard and Wang (2002), and Molina-Aiz et al. (2004) numerically predicted air temperatures, air flows and/or humidity distributions inside greenhouses. However, these simulations were conducted for large plastic or glass greenhouses with the simulations using steady or quasi steady-state CFD models. Chinese solar greenhouses are relatively small with a large thermal masses in the walls and in the ground which have important influences on the thermal conditions; therefore, the rapidly varying solar input and environmental conditions are much better simulated using fully time-dependent simulations. The model used in this research accounts for the solar energy absorbed by and stored in the walls and the soil including the temperature variations within these structures with the calculations based on actual measured hourly variations of the climatic conditions and of the soil temperatures 1.0 m below the soil surface. The time-dependent temperature distributions in a greenhouse are predicted using CFD simulations of the entire system during three successive clear days followed by a cloudy day. 2. Materials and methods

Subscripts a air ao air outside ab, bc, cd, bd, ac, ad lines b beam solar radiation c cover cond condensation d diffuse solar radiation dp dew point g ground eff effective encl enclosure i number of each layer inf infiltration l latent heat o outside r north roof re reflection s sensible heat sf south roof sky sky solar solar insolation w north wall z horizontal

(Chen et al., 1990; Kang et al., 1993; Tao et al., 2002; Tong et al., 2003). However, these repeated measurements are too expensive in terms of both material and labour, and the results are only useful for the specified experimental conditions and the specified designs. Hence, a theoretical model is needed to accurately predict temperatures inside various types of solar greenhouse designs for various climatic conditions. Various theoretical models have been devel-

2.1. Simulated solar greenhouse The simulations were performed for a Chinese solar greenhouse aligned lengthwise in the east–west direction in Shenyang, China (latitude: 41.8◦ N, longitude: 123.4◦ E, altitude: 42 m). The crosssection of the greenhouse structure shown in Fig. 1 includes a thick wall on the north side, a partial roof on the north side and the cover over the southern part of the top. The greenhouse was 60 m long and 12.6 m wide. The north wall was a layered structure 0.6 m thick constructed of brick, Styrofoam insulation and an air layer. The 0.2 m thick north roof was made of layers of wood, Styrofoam and other structural materials. The cover on the south roof was made of a 0.00012 m thick polyvinyl chloride (PVC) film during the daytime with a 0.02 m thick cotton blanket laid over the roof each night. Therefore, during the daytime the south roof of the greenhouse was covered with only a thin plastic film to allow sunlight in but was covered with the thick cover at night to insulate the greenhouse. Lettuce was planted on October 20, 2003 in the eastern part of the greenhouse with the soil under the plants covered by a plastic film. The soil and potted plants in the western section of the greenhouse were covered with plastic. 2.2. Experimental setup The measurements were taken in the centre cross-section of the greenhouse. During the experiments, the data acquisition system recorded the solar insolation on horizontal surfaces inside and outside the greenhouse and temperatures and humidities inside and outside the greenhouse. The measurement positions inside the central section of the solar greenhouse are shown in Fig. 2. Sensors numbered from 00 to 39 and from RH3 to RH7 were installed on November 25, 2003 while the sensors numbered from 40 to 51 were installed on February 11, 2004.

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Fig. 1. Cross-sectional view of a solar greenhouse with dimensions in m.

(1) Air temperatures at various locations inside and outside the greenhouse, soil temperatures at various depths in the soil, and the inner surface temperatures of the north wall, north roof and the cover on the south roof were measured by 0.00032 m diameter copper-constantan thermocouples. The thermocouples used to measure the air temperatures were shielded; however, a heat transfer analysis of the shields and the thermocouples indicated that the thermocouples still experienced somewhat higher temperatures due to the solar insolation absorbed by the shields and then transferred to the thermocouples (Incropera and DeWitt, 1985). The analysis balanced the solar insolation absorbed by the shields with the natural convection and thermal radiation to the surroundings to predict the shield temperature. Then, the equilibrium thermocouple bead temperature was calculated by balancing the conduction heat transfer from the shield through the thermocouple wires to the thermocouple bead and the thermal radiation from the shield to the bead with the natural convection and the thermal radiation from the bead to the surroundings. The thermocouple bead temperature correction for Tair = 290 K can be correlated by: T = 0.00762qsolar

(1)

where qsolar is the solar insolation flux with the unit of W m−2 and T is the correction temperature in K. The film surface temperatures were also corrected for errors according to Abdel-Ghany et al. (2006), which is

suitable for thermocouples with diameters in the range of 0.0001–0.0003 m. T = −0.22 + 5.11(1 − e−0.0024qsolar )

(2)

(2) The outside global solar radiation (located at point 37) was measured by an EKO MS-601 pyranometer (Japan) while the inside solar radiation (located at point 38) was measured by an EKO-020VS pyranometer (Japan). (3) The relative humidities, absolute humidities, dew point temperatures and humidity ratios measured by sensors RH3 to RH7 were recorded by an EKO data logger (model HN-CH, Japan). The measurement range for the relative humidity was 0–100% with an accuracy of ±2% relative humidity (RH) (0–90% RH at 25 ◦ C) or ±3% RH for 90–95% RH at 25 ◦ C. Measurements were automatically recorded every 600 s. During the daytime, the measured RH was used to calculate the latent heat leakage and the crop transpiration as shown in Section 2.5. However, the resulting equivalent heat fluxes are much less than the heat fluxes due to the solar insolation on the various surfaces. Therefore, the accuracies of the RH measurements will not significantly affect the simulation results and the measured RH were not corrected for this study. The temperature and solar radiation measurements were sampled every 1 s and averaged every 600 s by the data logger (EKO, CADAC21, Japan).

Fig. 2. Measurement positions inside the central section of the solar greenhouse with vertical dimensions in m and horizontal dimensions in mm. Point 37 is for the external solar radiation measurement, 39 is for the outside air temperature measurement and RH6 is for the outside humidity measurement.

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Fig. 3. External climatic conditions during the three clear days (February 18–20, 2004) and the cloudy day (February 21, 2004): (a) air temperature outside; (b) total solar radiation outside on a horizontal surface; (c) air relative humidity outside; (d) soil temperature half way across the greenhouse at 1.0 m deep, () stands for 1.0 m from front; (+)stands for 3.0 m from front; (䊉)stands for 6.0 m from front; () stands for 9.0 m from front; and () stands for 11.0 m from front.

The external climatic conditions measured during three clear days, February 18–20, and a cloudy day, February 21, 2004 are shown in Fig. 3. The distances in Fig. 3d are from the front point shown in Fig. 1. The data shown in Fig. 3 are hourly averages of the data recorded every 600 s. 2.3. Governing equations The system was simulated by discretising space and time using the finite-volume method and by solving the unsteady, twodimensional laminar conservation equations for the velocity and temperature fields on an unstructured grid. The general conservation equation given by Versteeg and Malalasekera (1995) is: ∂(ϕ) + div(ϕv) = div( ϕ gradϕ) + Sϕ ∂

(3)

where ϕ represents the dependent variable in the conservation of mass, momentum, and energy equations,  is the fluid density in kg m−3 , v is the velocity vector in m s−1 , ϕ is the diffusion coefficient in m2 s−1 and Sϕ are the source terms. 2.4. Hypothesis and numerical method The analysis was based on the following assumptions: (1) Each surface is grey (the thermal radiation properties are independent of wavelength and the emissivity equals the absorptivity). (2) The air does not participate in the thermal radiation exchange.

(3) The greenhouse length is assumed to be very large compared to its width. Therefore, the end effects can be neglected and the temperature variations in the cross-section shown in Fig. 1 in the middle of the long greenhouse can be assumed to be two-dimensional for the simulations. (4) Inside the greenhouse, natural convection occurs due to the temperature differences within the enclosure. The air infiltration is assumed to not affect the flow field inside the greenhouse. (5) The physical properties of the materials are constant. The governing equations were solved numerically using the finite-volume based program Fluent 6.1. The two-dimensional simulation area included the greenhouse, the soil to 1.0 m deep under the greenhouse, the north wall, the north roof and the combination of the plastic film and the blanket on the south roof. The actual physical properties for the layered structures on the south roof, north roof and north wall were approximated by effective properties averaged over the layers as described below and listed in Table 1. The analysis also included the thermal radiation heat transfer between the surfaces due to the temperature differences including radiation heat transfer between the outside surfaces of the wall, north roof and south roof of the solar greenhouse enclosure and the sky and between the inner surfaces of the wall, north roof, south roof and soil of the solar greenhouse due to nonuniform heat gains from the sunlight and heat losses to the outside. The surface thermal emissivities are listed in Table 1. The radiation heat transfer between surfaces assumed that the air was transparent. The ther-

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Table 1 Natural and effective properties of the layered surfaces used in the numerical analyses. Location

Layer(s) thickness (mm)

Density,  (kg m−3 )

Specific heat, Cp (J kg−1 K−1 )

Thermal conductivity, K (W m−1 K−1 )

Emissivity, ε

South roof daytime South roof nighttime North wall inside layer North wall middle layer North wall outside layer North roof Soil Air

0.12 20a 360 120 120 200 1000

1400 107.8a 1800 6.9a 1800 555.8a 2050 1.3

1045 819a 1050 1329a 1050 1091a 1010 1006.4

0.17 0.03a 0.81 0.03a 0.81 0.06a 0.6 0.02

0.9 0.9 0.93

a

0.93 0.91 0.96

Effective properties for the layered surfaces.

mal radiation heat transfer between surfaces inside the greenhouse was calculated using the Surface-to-Surface model in Fluent which included calculation of the view factors between surfaces. The convection heat transfer on the outside surfaces of the greenhouse was calculated in the model based on the heat transfer coefficient equation listed in Table 2 assuming an outside wind speed of 3 m s−1 , which is the average wind speed given by the meteorological bureau for the area in February and is similar to the average measured wind speed during the experiments. The effective density used in the calculations was calculated as the average over all the layers: eff =

D



1

(4)

d layers i i

where D is the total layer thickness in m, d is the individual layer thicknesses in m,  is the material density in kg m−3 and i is the layer number. The effective specific heat was calculated as the weighted average of the individual material specific heats: Cp,eff =



(eff D)

1

layers

(5)

Cp,i di

The effective thermal conductivity, Keff , was calculated so that the equivalent thermal resistance would be the same as for the series of individual layers:

 di D = Keff layers ki

(6)

The south roof was covered by a thin plastic film 0.00012 m thick during the day with the 0.02 m thick blanket added during

the night (and during the day when cloudy). The effective physical properties given by Eqs. (4)–(6) for the south roof at night listed in Table 1 were then a function of the daytime plastic film properties and the nighttime blanket properties. The 0.2 m thick north roof was made of a pine wood panel approximately 0.02 m thick and a 0.12 m thick Styrofoam panel covered by an average thickness of 0.08 m of slag and cement mortar and a waterproofing layer with the effective physical properties listed in Table 1. The north wall was also a layered structure 0.6 m thick with brick walls on the inside and outside walls and two 0.05 m thick Styrofoam panels next to the brick walls with an air layer in the middle. The Styrofoam panels and the air layer were also simplified to the effective material properties listed in Table 1 assuming negligible natural convection in the air layer. Calculations were carried out with three different unstructured meshes having 26,000, 62,000 and 106,000 elements with the mesh having 62,000 cells then used for the analyses. This mesh resulted in a temperature difference of less than 0.6 ◦ C for the air temperature at 13:00 h on February 18 compared with the denser mesh but a difference of more than 2.5 ◦ C compared with the smaller mesh. The iterations were terminated in each time step after 20 iterations when the residuals (the sum of the residuals for all the elements for each equation) were no longer decreasing. Calculations with 60 iterations per time step changed the air temperature at 13:00 h by less than 0.2 ◦ C. Simulations using the standard k–ε turbulence model, the renormalization-group k–ε turbulence model and the realizable k–ε turbulence model yielded nearly the same air temperatures at 13:00 h as the laminar model with differences of less than 0.5 ◦ C. Therefore, the laminar model was used to reduce the rather long calculation time for the transient analysis.

Table 2 Boundary conditions. Time

Items

Boundary conditions

Nighttime

Enclosure outside surface

Tout Tsky h qinf qcond

Measured Eq. (7) 2.8 + 3.0 v (Watmuff et al., 1977) Eqs. (19) and (20) Eq. (16)

T q

Measured Assumed to be negligible

Tout Tsky h qsf,o qinf qr qw

Measured Eq. (7) 2.8 + 3.0 v (Watmuff et al., 1977) Eq. (12) Eqs. (19) and (20) Eqs. (9) and (11) Eqs. (9) and (11)

qg T q LE

Eqs. (9) and (11) Measured Assumed to be negligible Calculated based on Luo et al. (2004)

Enclosure inside surface Soil Bottom Sides Daytime

Enclosure outside surface

South roof outside Enclosure inside North roof inside North wall inside Soil Inside Bottom Sides Crop

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2.5. Boundary conditions The influence of the external climatic conditions on the microclimate inside the greenhouse is a function of various complex heat and mass transfer mechanisms. The external climatic conditions including the solar insolation, the sky temperature and the air temperature outside the enclosure all affect the convection, radiation and conduction heat transfer into and out of the greenhouse. Simultaneously, radiation exchange between the surfaces inside the greenhouse and convection between the air and the inside surfaces also strongly affect the temperature distribution inside the greenhouse. Furthermore, condensation on the cover and air infiltration also result in heat exchange to the microclimate. 2.5.1. Sky temperature In this study, the sky temperature, Tsky (K), was calculated as (Berdahl and Fromberg, 1982) (tao + 273) Tsky = ε0.25 sky

(7)

εsky = 0.74 + 0.006Tdp

(8)

where εsky is the sky emissivity and the dew point temperature, Tdp , is a function of the relative humidity and the air temperature outside the greenhouse. The sky temperature from Eq. (7) was then calculated using the measured air temperatures and relative humidity outside the greenhouse shown in Fig. 3(a) and (c). 2.5.2. Solar insolation The measured solar insolation fluxes on the horizontal surfaces inside and outside the solar greenhouse were used as the solar input into the model. The transmission of solar radiation into the greenhouse was a function of the radiative properties of the cover material and the structural shape. The transmissivity was calculated from the measured solar fluxes inside and outside the greenhouse and the solar radiation distribution on the inner surfaces was predicted based on the solar angle and the greenhouse geometry (Tong and Li, 2006). The beam solar radiation fluxes on the inner surfaces were given by qb,g = qb b qb,w = qb,r

cos w qb,g cos z

(9)

cos r = qb,g cos z

where qb,g , qb,w , and qb,r are the beam radiation fluxes on the inner surfaces of the soil, north wall and north roof in W m−2 , qb is the solar beam radiation flux on a horizontal surface outside in W m−2 ,  b is the cover film transmittance for beam radiation, and z , w and  r are the angles of incidence on the horizontal (soil), north wall and north roof surfaces. The view factors for calculating the diffuse solar radiation on the inner surfaces were given by ab,bc =

lab + lbc − lac 2lab

ab,ad =

lab + lad − lbd 2lab

ab,cd =

(10)

lbd + lac − lbc − lad 2lab

where ab,bc , ab,ad and ab,cd are the view factors from the south roof surface to the soil, north roof, and north wall surfaces. lab , lbc , lcd , lad , lbd and lac stand for the lengths of lines, ab, bc, cd, ad, db and ac shown in Fig. 4 with the corresponding dimensions shown in

Fig. 4. Sketch illustrating the greenhouse surface view factors where line segment ab represents the length of the film surface, lab , bc represents the soil surface, lbc , cd represents the inner surface of the north wall, lcd , and da represents the inner surface of the north roof, lda .

Fig. 1. Then, the diffuse solar radiation fluxes to the inner surfaces were qd,g = qd,sf d ab,bc qd,w = qd,sf d ab,cd

(11)

qd,r = qd,sf d ab,ad where qd,g , qd,w and qd,r are the diffuse radiation fluxes to the soil surface, north wall and north roof in W m−2 , qd,sf is the diffuse radiation flux to the tilted surface (south roof surface) outside in W m−2 , which is given by the radiation shape factor for a tilted surface multiplied by the diffuse radiation flux falling on a horizontal surface, and  d is the film transmittance for diffuse radiation. The diffuse radiation flux on a horizontal surface was assumed to be 20% of the total solar radiation during clear days as indicated by Tong and Li (2006). Thus, the solar radiation fluxes to the inner surfaces are given by the beam solar radiation (Eq. (9)) plus the diffuse solar radiation (Eq. (11)) to the same surface. During the clear days in February, 2004, the blanket that was put over the south roof at night was rolled half way up the south roof from 08:00 h to 15:00 h so direct sunlight only came into the greenhouse through half of the south roof during the day. The blanket was only rolled half way up because the farmer’s experience has shown that this procedure is most effective. The blanket on the south roof was all one piece, so when rolled more than half way up in the morning, it was difficult to unroll in the afternoon because the surface is flatter near the top and the blanket became stiff in the cold weather. The solar insolation reaching the inside surfaces during the daytime was calculated based on only the actual open area of the south roof. On the cloudy day, the blanket was rolled half way up only from 08:00 h to 13:00 h. After that the blanket was unrolled on the south roof to reduce the heat losses from inside the greenhouse. The solar fluxes and the exposed surface fractions were calculated using an hourly average of the data recorded every 600 s during the experiment. Heat source on the soil surface. The solar radiation reaching the soil surface was partially absorbed by the soil, partially reflected by the soil (Papadakis et al., 1989), and partially absorbed by the canopy as canopy transpiration and converted into sensible heat in the greenhouse. Generally, a large part of the solar energy incident on a fully transpiring plant canopy in a greenhouse is absorbed by evaporation with only about one-third of the incident energy transformed into sensible heat in the air (Boulard et al., 1998). In the current simulation, the latent heat exchange due to the canopy transpiration was estimated according to the model given by Luo et al. (2004) who calculated the transpiration of cucumbers inside a closed Venlo-type greenhouse in winter. Heat source on the inner north wall surface. During the clear days, the solar thermal source on the inner north wall surface was obtained by multiplying the predicted solar radiation on the wall

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Fig. 5. Air relative humidity half way across the greenhouse 1.0 m above the soil surface during the three clear days (February 18–20, 2004) and the cloudy day (February 21, 2004), () stands for 1.0 m from the front point (measured at sensor RH7); (+) stands for 3.0 m from the front point (measured at sensor RH5); (䊉) stands for 6.0 m from the front point (measured at sensor RH4); and () stands for 9.0 m from the front point (measured at sensor RH3).

surface from 08:00 h to 15:00 h by 0.75 (the wall surface reflectivity was approximately 0.25). However, the solar thermal source on the inner north wall surface was assumed to be zero on the cloudy day since the blanket was put over the south roof at 13:00 h and the solar insolation to the north roof was blocked by the rolled blanket from 10:00 h to 13:00 h. Heat source on the south roof. The solar radiation incident on the south roof includes beam solar radiation, diffuse solar radiation and solar radiation reflected from the ground and the surroundings as indicated by Tiwari (2002).

oped as shown in Fig. 5 with only the humidity near the south roof reaching 100% during the night and on the cloudy day. Therefore, no condensation occurred on the wall, north roof and soil surfaces during the three clear days and on the cloudy day since the surface temperatures were higher than the dew point temperature of the greenhouse air. However, condensation occurred on the inside south roof surface during the three clear days before the blanket was rolled up and after it was unrolled and the whole cloudy day. The latent heat flux due to condensation given by Garzoli (1985) is

qsf,o = Rb qb + Rd qd + Rre (qb + qd )

qcond =

(12)

where qsf,o is the total solar radiation flux outside the south roof in W m−2 , qb and qd are the beam and diffuse radiation fluxes on a horizontal outside surface in W m−2 , and Rb is the ratio of the beam radiation incident flux on the south roof to that on the horizontal surface given by Rb =

cos sf

(13)

cos z

where  sf and  z are the angles of incidence relative to the south roof and the horizontal surface, respectively. Rd is the ratio of the diffuse radiation incident flux on the south roof to that on the horizontal surface given by 1 + cos ˇ Rd = 2

(14)

where ˇ is the angle between the south roof plane and the horizontal plane. Rre is the reflected component calculated as



Rre = ˛

1 − cos ˇ 2



(15)

where ˛ is the reflection coefficient of the ground. The solar energy reaching the cover on the south roof is more complicated than for the other enclosure surfaces because the cover is a thin plastic film during the day but with the film covered by the thick blanket at night. On February 18, 2004 in Shenyang, sunrise was at 06:50 h with sunrise occurring about 60 s earlier each day and sunset was at 17:13 h with sunset occurring about 60 s later each day. Hence, the sunlight was reaching the south roof nearly an hour before the blanket was rolled up and 2 h after the blanket was unrolled during clear days and for 4 h after the blanket was unrolled early on the cloudy day. All the absorbed solar energy before the blanket was rolled up and after the blanket was unrolled was included in the heat source of south surface in the simulation. 2.5.3. Condensation With the large thermal mass in the walls and in the ground, a large air relative humidity gradient across the greenhouse devel-

hc L(ωa − ωc ) Cp

(16)

where qcond is the latent heat flux due to condensation in W m−2 , hc is the inside surface heat transfer coefficient, 7.2 W m−2 K−1 (Garzoli and Blackwell, 1981), Cp is the specific heat of air in J kg−1 K−1 , L is the latent heat of vaporization in J kg−1 , ωa is the humidity ratio in the greenhouse air and ωc is the humidity ratio of air saturated at the cover temperature with ωa =

RH (0.004055 + 0.0001152ta + 0.00002167ta2 ) 100

ωc = 0.004055 + 0.0001152tc + 0.00002167tc2

(17) (18)

where RH is the relative humidity of the greenhouse air, ta is the greenhouse air temperature in ◦ C and tc is the cover temperature in ◦ C. The latent heat calculated from Eq. (16) using the experimentally measured air and cover temperatures was then applied to the south roof energy equation as an equivalent heat source term during the three clear days before the blanket was rolled up and after it was unrolled and on the entire cloudy day. 2.5.4. Air infiltration The total leakage heat losses due to air infiltration are the sum of the sensible and latent leakage losses. The effect of the air infiltration was modelled using the model given by Baille et al. (2006): qinf,s =

NVCp T Aencl

(19)

qinf,l =

NVLω Aencl

(20)

where V is the volume in m3 ,  is the air density in kg m−3 , Cp is the heat capacity of air in J kg−1 K−1 , L is the latent heat of vaporization in J kg−1 , and T is the air temperature difference between the inside and the outside of the greenhouse which was assumed to be constant at 10 K. During the clear days, the hourly air temperature difference between the inside and the outside varied from 7 K to 16 K; while during the cloudy day the difference varied from 7 K to 11 K, so the average difference was approximately 10 K. ω is the

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Fig. 6. Simulated (top) and measured (bottom) temperature distributions (K) on a clear day, February 20, 2004 at: (a) 13:00 h and (b) 22:00 h.

air humidity ratio difference between the inside and the outside of the greenhouse, Aencl is the total surface area of the wall, the north roof and the south roof of the greenhouse in m2 , and N is the air change rate per hour estimated by the energy balance method (Harmanto et al., 2006). The influence of the air change rate per hour on the inner temperatures was investigated by Tong et al. (2007) for exchange rates of from 0.5 to 1.25 air exchanges per hour, who showed that the inner temperature changes due to the different air change rates were insignificant because of the large amount of solar radiation absorbed by and stored in the walls and the large thermal masses in the walls and in the ground. The average total heat loss due to the sensible and latent heat losses in Eqs. (19) and (20) was then applied as a constant heat loss per square meter during the three clear days and the cloudy day to the energy equations for the north and south roof areas and the wall area. 2.5.5. Soil boundary conditions The measured soil temperatures at a depth of 1 m under the greenhouse measured over the entire 12.6 m width of the greenhouse from the front to the back shown in Fig. 3(d) were used as the boundary conditions. The vertical front and back soil surfaces were assumed to be thermally insulated. In reality, the measured temperature distributions indicated some heat losses through the vertical front and back soil surfaces, but these losses were assumed to be small. All the boundary conditions are summarized in Table 2. 2.6. Initial conditions The average measured temperature at 23:00 h on February 17 was used as the initial temperature for the calculation with all the velocities initialized as zero. 3. Results and discussion 3.1. Temperature distributions on a clear day The greenhouse temperature distributions on February 20, 2004 are presented as representative of the distributions during the three clear days. Fig. 6 compares the simulated and measured tempera-

ture distributions during the daytime at 13:00 h and at night at 22:00 h. In the soil, the soil temperatures in the upper soil layers are higher than lower down in the soil during the day due to the solar radiation heating the surface, with the soil temperatures in the middle of the greenhouse higher than near the front and back of the greenhouse because of heat transfer to the soil outside the greenhouse. The temperatures on the inner north roof, north wall and soil surfaces are higher during the day than at night due to the absorbed solar radiation. Since the thermal capacity of the plastic film is relatively small, the film temperatures increase quickly after the roof is uncovered. As the plastic film temperature increases, the air temperatures increase due to convection along the inner surface of the south roof. The calculations then indicate that during the day, energy is transferred from the plastic film to the air and from the air to the north roof, the north wall and the soil in addition to the radiative heating of the soil and the north wall. The relatively large temperature differences across the insulated north wall illustrate the effectiveness and importance of the insulation in the wall. Fig. 6 also shows that at 22:00 h, the air temperatures in the greenhouse are quite uniform both in the simulations and in the experiments with the simulated air temperatures agreeing quite well with the measured air temperatures. The predicted surface temperatures on the inside of the north roof and the north wall and the predicted soil temperatures also all agree well with the measurements. The surface temperatures on the inside north wall surface and in the soil at night are higher than the air temperatures indicating that the surfaces are now transferring energy back into the air in the greenhouse. The temperatures inside the wall and the soil are also higher than the air temperatures which shows that the walls and soil store a large amount of energy that can be returned to the air during the night. Similar effects were found during experiments with layered wall solar greenhouses with a width of 6.0 m and ridge height of 2.7 m (Chen et al., 1990) and a width of 7.5 m and ridge height of 3.5 m (Tong et al., 2003). The temperatures along the inner surface of the south roof at night are lower than the air temperatures even with the insulating blanket indicating that heat losses will occur through these surfaces that are more exposed to the atmosphere. This finding is in agreement with the experiments by Chen et al. (1990) for solar greenhouses.

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Fig. 7. Simulated (top) and measured (bottom) temperature distributions (K) on a cloudy day, February 21, 2004 at: (a) 10:00 h and (b) 22:00 h.

3.2. Temperature distributions on a cloudy day The south roof of the greenhouse was covered with the blanket at 13:00 h on the cloudy day, February 21, 2004 due to the small amount of solar radiation coming into the greenhouse to reduce the energy losses to the outside. Both the simulated and measured temperature distributions at 10:00 h and at 22:00 h shown in Fig. 7 show that the temperature distribution in the evening was very similar to that in the morning. Fig. 7 shows that at 10:00 h and 22:00 h, the predicted and measured air temperatures in the greenhouse were quite uniform with the surface temperatures on the inside soil, north wall and north roof surfaces all higher than the interior air temperature. In the soil, the temperatures at depths from 0.2 m to 0.5 m were higher than at the soil surface due to heat losses from the soil surface to the air and were also higher than the essentially constant temperature soil at the lowest measured depth of 1 m due to relatively slow heat transfer in the soil which enabled the middle layers of the soil to retain their heat. Therefore, the soil would continue to act as an energy reservoir supplying energy to the air in the greenhouse during the cloudy day and also during the night due to the large thermal mass in the soil. The soil temperatures between 3.0 m and 6.0 m from

the front were still higher than near the front and back at the same depth due to heat losses to the soil outside the greenhouse. The results also show that the north roof, north wall and soil contribute heat to the interior air throughout the day, with most of the heat coming from the north wall and the soil due to their large temperature differences relative to the interior air. The inner part of the north wall is still warmer than the air at night after the cloudy day so it will continue to help maintain the temperature inside the greenhouse at night. 3.3. Comparison of temperatures variations on the clear and cloudy days The simulated and measured air temperatures half way across the greenhouse at a height of 1 m shown in Fig. 8 for all four days show that during the clear days (February 18–20, 2004), the simulated and measured air temperatures compare well during the night (before 08:00 h and after 19:00 h) with the average temperature differences being about 1.0 ◦ C. However, the simulations somewhat under predict the air temperatures during the day when the sun is heating the greenhouse indicating that the greenhouse may be absorbing somewhat more heat than given in the model while the

Fig. 8. Comparisons of simulated (lines) and measured (symbols) air temperature variations in the middle of the greenhouse at a height of 1.0 m during the three clear days (February 18–20, 2004) and the cloudy day (February 21, 2004).

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simulations slightly over predict the temperatures for 4 h after the blanket was rolled out over the south roof probably because the blanket was actually a little colder than in the model. During the first three sunny days, the air temperature is seen to rise rapidly with the maximum at about 14:00 h each day. The temperature variations on each of these three days were all quite similar with the temperatures in the afternoon on the third day being slightly higher due to the higher outside air temperature on that day as shown in Fig. 3(a) and the slightly higher solar insolation as shown in Fig. 3(b). During the cloudy day (February 21, 2004), the simulated and measured air temperatures again compare well, with the average temperature differences being within 1.5 ◦ C throughout the day and into the night. The measured and calculated results both show that the temperature dropped during the time when the blanket was rolled half way up the south roof on the cloudy day indicating that more heat was being lost to the outside than was being received from the limited solar insolation during the cloudy day. Comparison of the air temperatures in the greenhouse on the clear day to those on the cloudy day shows how the air temperatures continued to drop on the cloudy day but the decrease is quite slow and the air temperatures actually increased slightly when the blanket was again rolled out over the south roof at 13:00 h on the fourth day as the warmer soil and north wall surfaces actually heated the air. The air temperature stayed reasonably constant then for the rest of the fourth day. The predicted air temperatures during the clear days in this study have similar trends with those of Li et al. (1994) but with more detail in the air space, wall, soil and north roof area. Accurate predictions of the air temperatures in these unheated solar greenhouses during the night and during cloudy days are very important for optimizing the geometry and structural materials of the greenhouse to maintain reasonable inside temperatures. The results of this study indicate that use of measured hourly external conditions in this model gives reasonable predictions during the clear days and the cloudy day. The model can be easily generalized using hourly weather data to predict the temperatures in various solar greenhouse designs in different regions with different climatic conditions. Future work will focus on the crop–aerial transfer interactions which have been studied in detail in plastic/glass covered greenhouses with controlled microclimates. However, there are not yet any known studies on the mechanisms of these interactions in Chinese solar greenhouses with no auxiliary heating in the winter. The average temperature differences between the day and night inside Chinese solar greenhouses can vary by more than 10 ◦ C with the temperature differences between the inside and the outside exceeding 10 ◦ C. In addition, the greenhouses are closed and unventilated during the winter which is very different from the greenhouses in known studies dealing with crop transpiration such as Pollet et al. (2000), Boulard and Wang (2000, 2002), and Luo et al. (2004). The crop–aerial energy and mass transport are very important; therefore, our future work will investigate the crop–aerial transfer mechanisms in Chinese solar greenhouses to develop improved simulation models. 4. Conclusions The temperatures in a solar greenhouse were measured during three clear days and on a cloudy day in February in northern China. The measurements were compared to predictions of the transient temperatures in the greenhouse based on solutions of the two-dimensional Navier-Stokes and energy equations. The model boundary conditions included the solar insolation to each surface, the sky temperature, the air temperatures and velocities outside the greenhouse, and the soil temperatures 1 m below the greenhouse. The model also took into account the variations of the transient

temperature distributions along the walls, the effect of the soil and the effect of the plastic cover. The calculated results, which agree well with the measured data, show how the temperatures inside the greenhouse vary during the day due to the solar heating, the air infiltration and other heat losses. The calculated and measured results during the clear day also indicate that only the surface temperatures on the north wall and the soil are higher than the interior air temperatures during the night, so only these surfaces contribute heat to the interior air to maintain the air temperatures during the night. The results on the cloudy day, however, show that the north wall, the north roof and the soil all contribute heat to the interior air throughout the day since the interior air is not heated significantly by the substantially reduced solar insulation on the cloudy day. The results also show that the temperatures inside the greenhouse can be maintained at reasonable temperatures even though the outside temperature is below freezing. In future work, the model will be used to predict the greenhouse conditions on successive cloudy days to evaluate the effects of the structural design and climatic conditions on the greenhouse microclimate so as to optimize the greenhouse design. Acknowledgements The authors thank Dr Tomoharu Yamaguchi of the Institute of Agricultural and Forest Engineering, University of Tsukuba, Japan, for his help in the experimental work. This work was supported by the Ph.D. Programs Foundation of Liaoning Province, China (20061040), the Co-Construction Project Construction Program from the Beijing Educational Committee under contract numbers XK 100190553, and the National Natural Science Foundation of China under contract numbers 50876050. References Abdel-Ghany, A.M., Ishigami, Y., Goto, E., Kozai, T., 2006. A method for measuring greenhouse cover temperatures using a thermocouple. Biosyst. Eng. 95 (1), 99–109. Baille, A., López, J.C., Bonachela, S., González-Real, M.M., Montero, J.I., 2006. Night energy balance in a heated low-cost plastic greenhouse. Agric. Forest Meteorol. 137, 107–118. Bartzanas, T., Boulard, T., Kittas, C., 2002. Numerical simulation of the airflow and temperature distribution in a tunnel greenhouse equipped with insect-proof screen in the opening. Comput. Electron. Agric. 34, 207–221. Berdahl, P., Fromberg, R., 1982. Thermal radiance of clear skies. Solar Energy 29 (4), 299–314. Boulard, T., Lamrani, M.A., Roy, J.C., 1998. Natural ventilation by thermal effect in a one-half scale model mono-span greenhouse. Trans. ASAE 41 (3), 773–781. Boulard, T., Wang, S., 2002. Experimental and numerical studies on the heterogeneity of crop transpiration in a plastic tunnel. Comput. Electron. Agric. 34, 173–190. Boulard, T., Wang, S., 2000. Greenhouse crop transpiration simulation from external climate conditions. Agric. Forest Meteorol. 100, 25–34. Chen, D., Zheng, H., Liu, B., 1990. Comprehensive study on the meteorological environment of the sunlight greenhouse. 1. Preliminary study on the thermal effect of the wall body and covering materials. Trans. CSAE 6 (2), 77–81 (in Chinese with English abstract). Du, J., Wang, H., Yang, L., 2001. Distribution and calculation of net solar radiation in greenhouse. Acta Energiae Solaris Sin. 22 (1), 115–118 (in Chinese with English abstract). Fath, E.S.H., Abdelrahman, K., 2004. Micro-climatic environmental conditions inside a greenhouse with a built-in solar distillation system. Desalination 171 (3), 267–287. Garzoli, K.V., 1985. A simple greenhouse climate model. Acta Hortic. 174, 393–400. Garzoli, K.V., Blackwell, I., 1981. An analysis of the nocturnal heat loss from a single skin plastic greenhouse. J. Agric. Eng. Res. 26, 204–214. Harmanto, Tantau, H.J., Salokhe, V.M., 2006. Microclimate and air exchange rates in greenhouses covered with different nets in the humid tropics. Biosyst. Eng. 94 (2), 239–253. Hasson, A.M., 1991. A study of solar energy and its components under a plastic greenhouse. Energy Convers. Manage. 31 (1), 1–5. Incropera, F.P., DeWitt, D.P., 1985. Fundamentals of Heat and Mass Transfer. Wiley, New York. Kang, S., Dai, Y., Fang, S., Wei, K., 1993. Study on shape of south roof, height and span of solar greenhouses. China Vegetables 1, 6–9 (in Chinese). Li, T., 2004. Present situation and development trend of protected horticulture in China. In: Proc. Annu. Conf. Chinese Hortic. Soc. 1–4, Wuhan, China (in Chinese).

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