An ASABE Meeting Presentation DOI: https://doi.org/10.13031/aim.201800084 Paper Number: 1800084
Proposal of a CFD index applied to thermal greenhouse characterization
Jorge Flores-Velázquez1, Cruz Aguilar-Rodríguez1, Fernando Rojano Aguilar2 Waldo Ojeda Bustamante1 1 Instituto Mexicano de Tecnología del Agua. Paseo Cuauhnahuac 8532, Col. Progreso. 62550. Jiutepec, Morelos. Mexico. (+52) 777 329 36 58.
[email protected] 2 Instituto de Ecologia. Carretera antigua a Coatepec 351, El Haya, Xalapa 91070, Veracruz, México. Tel.(228) 842 18 00 Written for presentation at the 2018 ASABE Annual International Meeting Sponsored by ASABE Detroit, Michigan July 29-August 1, 2018 ABSTRACT. In agriculture matters quality and quantity of the produce. In this work is proposed an index for climate characterization of a greenhouse. Such index is derived from the error complementary function, where the weight to a weather variable is assigned depending on the defined optimal range for crop development. The index is calculated using normal meteorological data from a local weather station and also with climate data obtained from CFD predictions of a specific greenhouse. Then, the proposed index can be applied to regions, during the cycle of a crop or a specific day, depending on availability of meteorological data. For instance, if the greenhouse does not have a climate control system, there will be periods in the season where the greenhouse may generate adverse condition for crop. Then, the index will aid to point out that, in some specific hours during the day or night, a greenhouse is not an advantage when compared to crop production in open-field. Another scenario with application of this index may be for the same greenhouse during sun rise, and solar rays penetrate to the greenhouse; then, the internal temperature increases, sometimes more than 10 °C with respect to external temperature. And finally other crucial scenario where this index can be applied is the period of cold months, where the same greenhouse may require heating. So, this proposed tool as an overall index can become a viable alternative for quantitatively estimate the needs to achieve desirable climate conditions for successful greenhouse crop production. Keywords. CFD, Greenhouse, indicator, meteorological, the error complementary function.
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INTRODUCTION It is expected that in the coming years there will be an increase in temperature, which would lead to an increase in evaporation and evapotranspiration, as well as a reduction in precipitation, that consequently leads to a redistribution of the water resources. The distribution of ecosystems and farming zones will be affected by changes in water distribution and temperature (Sánchez & Martínez, 2006, Moreno et al., 2011). At the same time, there will be increase in demand for food by a growing population, meaning also an increase in agricultural activity. Modern techniques have succeeded for increasing production, although this fact has an impact on the environment. The efficiency of agricultural production derives from the search to satisfy demands with less agricultural land and water, but also such farming zones with reduced costs. Modern agricultural activity has also generated increments in production and consequently environmental impacts. The increase in food needs an increase in satisfying increased demands with less agricultural land and water (ArmendárizErives, 2007). In a study of a crop's productive potential, two basic processes are necessary, the definition of the crop's agro-ecological requirements and their contrast with the environmental conditions of the region where it is intended to produce. Producing a crop in a place where agro-ecological requirements are covered ensures better yield with higher profits and lower environmental impact. For instance, success in tomato production depends on the accomplishment of the temperature requirement. A study of Jones et al., (1999) found that the optimal average temperature is 23 °C similar to findings of Atherton y Rudich, 1986. However, during a day, another research (Heuvelink, 1989; De Koning, 1990; Korner y Challa, 2003) affirmed that, in the tomato crop develop, the effect of temperature at daily integration is better than daily temperature oscillation. Then, the approach of thermal integration can be applied to greenhouses and it can be a representative index of the efficiency. Even though the temperature in the greenhouse, depend on the quantity of radiation in each specific region. The determination of potential production has been of special interest for outdoor and seasonal crops. In the studies of potential production that have been carried out, climatic, topographical and soil factors are mainly considered. In addition, the potential production of several crops is analyzed in studies with regional impact. Those studies can be adapted to protected agriculture, since in this way there is a partial or total control of various of the limiting conditions of a crop's development. In the case of high-tech greenhouses, external environmental conditions produce fewer effects than in medium- and low-tech greenhouses. Therefore, this study is focused in agro-production mainly for medium and low technology installations, in which it is possible to take advantage of the regional climatic factors in order to increase production per area. Climatic information becomes fundamental in the decision making related to agriculture, and being essential the study of climatic variables and their distribution in the various farming zones. Also a way to study the effect of climatic variables on protected crops such as greenhouses is through the development of models with numerical solution. With these models, it is possible to evaluate diverse phenomena such as perspiration, hydraulic properties of the soil, plant growth and the nutrient content of the soil. In addition to the models, which can be dynamics and be resolved by means of Computational Fluid Dynamics (CFD), it is possible to understand the heat and mass transfer of the greenhouse environment by comprehensive analysis of air movement and gaseous exchanges, also allowing to determine the needs of crops under different temperature and humidity conditions. The aim of this work, is to show an index to characterize qualitatively thermal conditions of a typical 3-span greenhouse in central Mexico. Temperature was set as the main climate factor to get an optimal microclimate for favoring crop productivity. The climate index shows the suitability of a region to succeed with low-tech greenhouse crop production, and the advantage of the internal climate dynamics predicted by a CFD model.
MATERIALS AND METHODS Thermal index Climate index is derived from climatic data. A first approximation is considering climate data of meteorological stations. In this case, temperature is the parameter chosen. On the second phase, CFD model of a 3-span greenhouse was simulated for climate conditions nearby the meteorological station. Similar analysis is carry on, in order to infer the influence of temperature. Outside analysis used meteorological data and inside of the greenhouse, CFD simulations depended on data corresponding to exterior temperature and wind velocity as boundary conditions. ASABE 2018 Annual International Meeting
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Thermal effectiveness in a greenhouse was established based on the ambient temperature that could fall within a temperature range. The estimation of temperature effectiveness is done by using an equation that defines a weight function: (𝑻𝒊 − 𝑻𝒆 )𝟐 𝝎𝒊 = 𝒆𝒓𝒇𝒄 { } 𝑨𝟐
(1)
Where A represents the amplitude of the variable, in this case temperature, Ti (such variable is exchangeable for humidity, DPV or other climate variable of interest) is the observed value, and Te is the optimal value of the variable. The Te and A values are defined according to the optimum values reported by the bibliography for the crops to be analyzed. The climatic variable recorded in the greenhouse may approach to the optimal average, considering the maximum effectiveness when it tends to the unit (Figure 1). For example, tomatoes have an optimal average daily mean temperature (Te) of 23°C and an amplitude A=10 °C (Hannan, 1997). Figure 1 shows the distribution of wi for this case.
1 0.8
wi
0.6 0.4 0.2 0 5
10
15
20
25
30
35
40
Temperatura (oC)
Figure 1 Change of wi as a function of Temperature (Ti) The erfc (x) function represents the complementary error function. The function is a rational approximation of the erfc (x) function, for z 0 , represented by Abramowitz and Stegun (1972) is given by: −𝟒
𝟒
(2)
𝒌
𝒆𝒓𝒇𝒄(𝒙) = ⌊𝟏 + ∑ 𝒂𝒌 𝒛 ⌋ 𝒌=𝟏
Where z is a wi and k are the values of 1-4. Assuming similar behavior between tomato and maize. Ojeda et al., (2005) found the values of constants a1, a2, a3 and aa, which were 0.278393, 0.230389, 0.000972 and 0.078108, respectively. The quantity of the Thermal Effectiveness Degrees (TED) for a daily temperature (Ti) can be estimated with the following equation: 𝑻𝑬𝑫 = 𝝎𝒊 𝑻𝒊
(3)
If the daily ambient temperature Tj is close to the optimal value Te, the wj value is close to one, and consecutively, the Thermal Effectiveness Grades (TEG) are close to Te. Accumulated TED quantitatively defined the effectiveness of a greenhouse in maintaining potential conditions to a crop development. The cumulative values (DA) of TED were estimated according to the following equation:
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𝑵
𝑵
∑ 𝑻𝑬𝑫 = ∑ 𝝎𝒊 𝑻𝒊 = ∑ 𝑫𝑨 𝒊=𝟏
𝒊=𝟏
(4)
where N is the number of days under study. For this study, the first part was focused in analyzing weather for a region. TED´s were estimated for each of five weather stations located in Central Mexico (Figure 2), considering the average daily temperature Ti (364 days) during more than 24 years.
Figure 2 Localization of meteorological stations in Central Mexico
The TED based on the weight function was evaluated using temperature data (Ti) of five stations in the State of Mexico. Besides, efficiency ranges from 20% to 100% were considered. The spring, summer and autumn winter cycles were also considered to see the distribution of thermal efficiency over time, which according to SAGARPA (2017) Mexican agricultural production is divided into two seasons: spring-summer and autumn-winter. The first one runs from March to September, and the second one from October to February. The second part of this study was focused on the analysis of temperature inside a 3-span greenhouse. A CFD model was built and simulated using the same climate data derived from the analysis aforementioned and becoming boundary conditions. The computational model is fully described in a previous study by Flores et al., 2015. The series of simulations were conducted on five local meteorological stations (Figure 3) in order to get the simulated temperatures inside the greenhouse.
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20
Wind direction
T (average °C)
16 12 8 4 0 J
F M A M J
J
A S O N D
Figure 3. Distribution of the thermal efficiency of the greenhouse during the spring-summer cycle in the five analyzed stations of the State of Mexico. Average month temperatures were used to calculate Thermal Efficiency degree (TED) and Accumulate Degree (DA) to estimate the efficiency of the greenhouse to cultivate tomato in this specific area.
RESULTS AND DISCUSSION Index of external climate only using climate station data
16
4500
14
4000
12
3500 3000
10
2500 8 2000 6
DA
TED Daily
Figure 4 shows the calculus of values for Thermal Effectiveness Degrees (TED), an accumulate value in one year (DA) for the Central Mexico. Under this temperature data, along the year 2798 units Degree were collected, being in May with the higher temperatures occurring, and therefore when the more quantity of hours of temperature can be accumulated in the greenhouse.
1500
4
1000
2
500
0
0 J
F
M
A
M
J
J
A
S
O
N
D
Figure 4. Distribution of the thermal efficiency of the greenhouse along year using normal data of Chalco, State of Mexico meteorological station. TED ----- DA - - - The quantity of Degree units than can be accumulated, depend on geographic location; if it is analyzed for many agroclimatic stations and it is spread in a spatial map, is possible to illustrate the distributed TED. Kriging Interpolation method was used to determinate TED spatial representation. Figure 5 shows the cumulative TEDs for the Central Mexico. It is observed that in the north-central region of the state the TEDs are prevailing low (< 2000), which indicates that there was not enough time to complete the cycle of tomato cultivation. However, other crops that demand temperature in ASABE 2018 Annual International Meeting
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the ranges found with prevailing shorter cycle may be produced in these regions.
Figure 5. Spatial representation of Cumulative Thermal Effectiveness Degree (TED) for the State of Mexico. Figure 6 shows that the greatest number of days with thermal efficiency greater than 60% (i.e. Chalco station), Central Mexico, occurs during the spring-summer cycle. However, during the autumn-winter cycle, in the same season, most of days have thermal efficiency between 20 and 40. The spring-summer is the more suitable period, while in the autumnwinter period it is not advisable to cultivate tomatoes. 240
160 120 80
160 120 80
40
40
0
0 0-20
b)
200
Number of days
Number of days
200
240
a)
20-40
40-60 TED (%)
60-80
80-100
0-20
20-40
40-60
60-80
80-100
TED (%)
Figure 6. Days with thermal efficiency in the station Chalco, State of Mexico in the cycles a) spring-summer, b) autumn-winter.
Table 1 Days inside range of effectivity
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Station
TED (%)
spring-summer
0-20 20-40 40-60 60-80 80-100
Chalco
Tonatico
78 49 37
29 147 38
0-20 20-40 40-60 60-80 80-100 0-20 20-40 40-60 60-80
Tecamac
autumn-winter
1 75 35 28 10
14 32 168
7
80-100
214
144
0-20 Metepec
99
20-40
24
33
40-60
111
40
60-80
79
80-100 0-20 20-40 Tejupilco
40-60 60-80 80-100
214
151
Figure 7 shows a comparison of the five stations analyzed. The Tonatico and Tejupilco stations had the highest thermal efficiencies throughout the year because they were located in areas with average temperatures between 20.0 °C, the warmest in Central Mexico. The Tecámac station was located in an area with moderate average temperatures, so that the thermal efficiency throughout the year did not fall below 40%, maintaining the highest efficiencies in the spring summer cycle. The season with the lowest efficiencies during the year was Metepec, since it was located in the area surrounding high mountains nearby Toluca, where the average daily temperatures are low (13.2 °C)). 1.0 0.8
Wi
0.6 0.4 0.2 Chalco 0.0 01-ene
02-mar
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Tecamac 01-may
Tonatico 30-jun day-month
Metepec 29-ago
Tejupilco 28-oct
27-dic
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Figure 7. Distribution of the thermal efficiency of the greenhouse throughout the year in the five analyzed stations of the State of Mexico. In the spring-summer cycle for the five stations analyzed, efficiencies of more than 40% were achieved. In mid-March, the thermal efficiency started to increase in the cold season and stayed above 60% until mid-August. In the case of the hot season, the thermal efficiency decreased in May due to the incidence of high temperatures in that month. Higher temperatures also reduced thermal efficiency as they were far from the optimal temperature, and the weight function began to decrease but keeping higher values than the optimal setpoint. The results of this work showed that in Tonatico and Tejupilco there was a greater distribution of thermal efficiency throughout the year for the cultivation of tomatoes, however for Chalco, Tecamac and Metepec the greatest thermal efficiency was during spring summer, however during winter it was impossible to complete the cycle of tomatoes, for this reason it was advisable to take advantage of the climatic conditions and grow some other crops.
Index determined by inside climate of a greenhouse predicted by a CFD model. The results of CFD simulations were conducted by taking input data of the monthly-average temperature, in order to predict the internal climate conditions inside the greenhouse at the level of the crop zone. In this case were simulated the greenhouse each month, and then, it was calculated the total number of hours out of the range of minimal and maxima basal temperatures. Figure 8 shows a top view of temperature distribution at 0.9 m height in the extreme conditions, a) May and b) January
a)
b)
Figure 8. Top view of temperature distribution at 0.9 m height in a) May and b) January
The efficiency of the greenhouse to create a best temperature range for cultivating tomato is showed in Figure 9. Outside the greenhouse, the maximums quantity of temperature accumulated (DA) per year in this region (Chalco, Edo. De Mex.) was around 2700 (Figure 9a). Inside the greenhouse, DA increase until 5800 hours. TED could be used to plan the growing season. Additionally, this index can be useful to determine the growing dates, that can rule the expected date of the harvest with the best window to the market.
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600
5000 4000
400 3000 300 2000
200
1000
100 0
0 J
F
M
A
M
J
J
A
S
O
N
6000
600
5000
500
TED Month
TED Month
500
b)
700
4000
400 3000 300 2000
200
1000
100 0
D
DA Year
6000
DA Year
a)
700
0 J
F
M
A
M
J
J
A
S
O
N
D
Figure 9. Average month Temperature (°C) (a) and Computational Model (b).
CONCLUSION In this work it was possible to analyze the distribution of the greenhouse's thermal efficiency, considering five weather stations in Central Mexico. The supplementary error function was applied as an index to assign a weight to the meteorological variable considering an optimal temperature range for the development of a crop (which was applied to tomato). Nonetheless, the index proposed in this paper can also be used to estimate the thermal efficiency of a low-tech greenhouse at any region. Furthermore, this index is helpful in the defining periods and regions with suitable climatic conditions for any crop either cultivated in open field or greenhouses.
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De Koning, A. N. M. 1989. The effect of temperature on fruit growth and fruit load of tomato. Acta Horticulturae. 248:229-336. De Koning, A. N. M. 1990. Long term temperature integration of tomato. Growth and development under alternating temperature regimes. Scientia Horticulturae. 45:117-127. Hannan J. Joe. 1997. Greenhouses, Advanced technology for protected horticulture. CRC Press. 708 pages. Boca Raton, USA. Heuvelink, E. 1989. Influence of day and night temperature on the growth of young tomato plants. Scientia Horticulturae. 38:11-22. Jones, J. W., A. Kenig, y C. E. Vallejos. 1999. Reduced state–variable tomato growth model. 42: 255-265. ASABE 2018 Annual International Meeting
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Körner, O. y H. Challa. 2003. Design for an improved temperature integration concept in greenhouse cultivation. Computer and Electronics in Agr. 39:39-59. INIFAP. (2008). Uso de estaciones meteorológicas en la agricultura. Folleto informativo No. 50. Moreno Reséndez, A., Aguilar Durón, J., & Luévano González, A. (2011). Características de la agricultura protegida y su entorno en México. Revista Mexicana de Agronegocios, 15(29). Ojeda B., Waldo, Sifuentes I. E., Unland W. H. 2006. Programación integral del riego en maíz en el norte de Sinaloa, México. Agrociencia, vol. 40, núm. 1, enero-febrero, 2006, pp. 13-25. Colegio de Postgraduados. Texcoco, México. Prenger, J. J. Y P. P. Ling. 2001. Greenhouse Condensation Control: Understanding and Using Vapor Pressure Deficit (VPD). Fact Sheet AEX-804-01. Ohio State University Extension, Columbus, OH. USA. Sánchez-Salazar, M. T., & Martínez-Galicia, M. (2006). La vulnerabilidad de la industria y los sistemas energéticos Ante el cambio climático global. Instituto de Geografía. UNAM. Sato, S., Peet, M. M., Thomas, J. F. 2000. Physiological factors limit fruit set tomate (Lycopersicon esculentum Mill.) under chronic, mild heat stress. Plant cell and environment. 23:719-726. Spanomitsios, K. G. 2001. Temperature control and energy conservation in a plastic greenhouse. J. agricultural engineering research. 80:251-259. SIAP-SAGARPA. (2017). Boletín mensual de la producción. Tomate rojo (Jitomate). SIAP. (2017a). Anuario Estadístico de la Producción http://infosiap.siap.gob.mx/aagricola_siap_gb/icultivo/index.jsp.
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