A Model of the Greenhouse with a Storage-Type Heat Exchanger its verification. Shinichi TAKAMI * and Zenbei UCHIJIMA **

Transcription

1 A Model of the Greenhouse with a Storage-Type Heat Exchanger and its verification Shinichi TAKAMI * and Zenbei UCHIJIMA ** * College of Agriculture, Kyoto University, Kitashirakawa, Kyoto * * Div, of Meteorol., National Institute of Agricultural Sciences, Nishigahara, Tokyo Abstract A model describing the heat exchange in the plastic greenhouse with a storage-type heat exchanger was made in order to examine the feasibility of the storage-type heat exchanger for controlling the temperature and humidity in the plastic greenhouse. Relatively good agreement was obtained between measured and calculated environmental conditions in the plastic greenhouse with the storage-type heat exchanger. The magnitude of the heat storage ratio, defined as the ratio of the amount of heat accumulated in water as a heat accumulator to the amount of heat transferred from crop and soil surfaces into the house, was considerably influenced by factors such as short-wave irradiance, ventilation rate and difference in the operation of air circulation system. Sample calculations indicated clearly that under high irradiance the latent heat due to the condensation of water vapor on the inside surface of heat exchange pipes plays an important role for the accumulation of heat. 1. Introduction Recent awareness of the limited energy supply on the earth has stimulated various means to save energy in both industrial and agricultural production systems. The greenhouse system with a storage-type heat exchanger, now under the examination of its practical feasibility, is one of such efforts. In general, this system accumulates a part of the solar energy during daytime and rejects at night, thereby controlling the temperature in greenhouses without other energy imputs for cooling and warming. Yamamoto (1966) experimentally studied the efficiency of the soil-heat exchanger applied to the greenhouse. His heat exchanger consisted of soil as a heat accumulator and of vinyl pipes as a Presented at a Kinki Chapter meeting, 13 November Received 18 January 1977; revised 25 October heat transmitter. Theoretical considerations as to how the performance of the storage-type heat exchanger is determined in relation to the state of the greenhouse under various environmental conditions have not been given. This is partly because the exact calculating procedure for such a storagetype heat exchanger is extremely difficult and tedious. Jwakiri (1971), considering the heat balance of greenhouses with the storage-type heat exchanger, calculated the length of heat exchange pipe and the ventilation rate required to sustain the air temperature in the greenhouses at a necessary level. His model neglected the latent heat-conduction process for the sake of simplicity and was not examined through experiments. The air, as it passes through a greenhouse, is humidified with water vapor from plants and soil in the daytime, except in the case when no plants are grown and soil is completely dry. Accordingly, -155-

2 the air from a plastic greenhouse is likely to be exchange pipes. cooled below its condensation point as it enters into the heat exchange pipes within the storagetype heat exchanger. This means obviously that the latent heat conduction process in the heat exchange pipes may play an important role in the process of heat accumulation. The main objectives of this research were to develop a computer simulation model for the greenhouse with a storage-type heat exchanger, to evaluate the performance of this system and to examine it through an experiment. The process of latent heat exchange, along with other heat exchange processes, was taken into account. 2. Theoretical analysis Fig. 1 is the schematical representation of the plastic greenhouse with a storage-type heat exchanger used in this study. The system consists of two parts: one is the plastic greenhouse and other is the storage-type heat exchanger set up underground. Air is either circulated in the system (closed operation) or exhausted from the system after passing through the greenhouse and the heat exchanger (open operation). Sensible and latent heats in the air are transferred into the water as a heat accumulator through the wall of heat In this analysis the two parts described above are independently modeled, and then combined into the model for the whole system Greenhouse model This model is already reported in detail in Takami and Uchijima (1977). Here we shall give its brief description required to understand the whole model. The environmental factors as the inputs to the model are total short-wave irradiance (S0, W m-2), downward long-wave irradiance humidity (H00, g m-3), wind velocity (U0, m s-1) to be measured outside the greenhouse and soil water potential (WPOTS, bar) of the ground inside the greenhouse. The system parameters to be given are physical properties on the heat exchange of the greenhouse and the crop grown in it, physiological characteristics about the water exchange of the crop, the areas of the wall and ground surfaces, and the rate of air ventilation. Given these inputs, the model outputs the radiation and heat balances at the surface of crop layer, sensible heat fluxes at the wall surfaces, latent heat flux at the inside surface of the wall, and the heat exchange due to the air ventilation. The temperature of the wall, the air temperature in the greenhouse and all other system variables that determine environmental conditions in the greenhouse are also calculated. Additional outputs such as the canopy resistance to the water vapor transfer and the mean leaf water potential of the canopy can be computed as this model includes the feed-back regulation by the stomatal action on the heat and water vapor transfers. The input data should be the averages over a certain period of time, say an hour or half an hour, as the model deals with the steady state of the system. Consequently, the outputs are also Fig, 1. A schematic diagram of a greenhouse for which the model is developed. Top: operated by the closed circulation system. Bottom: operated by the open system. Arrows : directions of air flow. the averages over such a time interval. As already described in Takami and Uchijima (1977), important features of this model are; all environmental factors outside greenhouses are primary boundary conditions, the rate of transpiration from canopy is simultaneously evaluated -156-

3 S. TAKAMI, Z. UCHIJIMA: A Model of the Greenhouse with a Storage-Type Heat Exchanger and its Verification by the model, and the condition for either evaporation or condensation of water in the greenhouse is determined by comparing the air temperature and the dew point in the house Heat exchanger model Modeling The storage-type heat exchanger studied in this report is schematically illustrated in Fig. 2 (Okubo et al., 1977). The storage-type heat exchanger consists of a water tank as heat accumulator and heat exchange pipes submerged in the water tank. The water tank is insulated by a layer of stylofoam with thickness of 4 cm. The air, introduced from the one end of the pipes, flows out the other end of the pipes after exchanging heat with water through the wall of pipes. The amount of heat exchanged while the air passes the section of these pipes should be equal to the heat used to raise the water temperature in the heat accumulator from TWO to TW: (3) Fig. 2. A vinyl covered greenhouse with the storage-type heat exchanger used in the experiments. We shall consider the processes of heat and water vapor transfer at a section of the air flow in the pipes. The section is chosen in such a way that the change in temperature and humidity with time can be neglected. Then the heat and water mw = mass of water in the water tank, g. The heat exchanged in all sections of pipes is assumed to be used to change the water temperature in the entire heat accumulator. The heat loss from the heat accumulator to the surrounding is neglected, because it is insulated by stylofoam. and Pout in eq. (1) can be written as (4) (5) balance equations for the pipes in this section are: (1) (2) The sensible heat transfer at the pipe wall (Sh ; w.m2) -is calculated by use of the overall heat The overall heat transfer coefficient is expressed as

4 w = thickness of the pipe wall, m, hp = sensible heat transfer coefficient of air to the inner surface of the pipe, hw = heat transfer coefficient of water on the outer surface of the pipe, The air flow in the heat exchange pipes may be regarded as a turbulent flow for the house-heat exchanger system considered here. For example, the velocity of the air flow in the pipes is 2.2 m Esec-1 for the greenhouse-storage-type heat exchanger system that has 200 m3 of the house volume and 32 heat exchange pipes of 17 m long and 0.1 m in diameter, when operated at the ventilation rate of 10 hr-1. The corresponding Reynolds number is calculated to be about 14,000. The heat transfer coefficient hp between the air flow and the inner surfaces of the pipes may therefore be evaluated from a simplified formula (e.g., Uchida, 1936): where Re = dp V / V a, Reynolds number, Heat transfer between the outside surface of the pipes and the water in the heat accumulator may be due to the natural convection as the water in the tank is not moving. We may furthermore assume that the water flow around the pipes is laminar since the temperature difference between the pipe wall and the water is small (the Grashof number, Gr, for this heat exchange system is of the order of log). Thus the heat transfer coefficient hw is given by (Monteith, 1973) where Gr is defined as and a ' = coefficient of thermal expansion of g = acceleration of the gravity (= 9.8 m. sec-2 ), Because the resistance to the heat transfer from the outer surface of the pipes to the water and that of the pipe wall to the heat conduction are much less than the resistance between the air flow and the inner wall surface, the temperature difference between the outer surface of the pipes to that between the incoming air (Tin) and the water (Ti): Assuming that the latent heat exchange is solely by condensation of water vapor and that the heat released by the condensation is transferred according to the temperature gradient in the air flow-pipes-water system, we obtain the following relation in the case of Tin > T1: in which HS( Tln) is the saturation water vapor density at Tin. Hs( Tin) is a function of T;n and for this function we used an equation proposed by Murray (1966): Let us assume that the steady state exists (7) (g), that is, St = Ht = 0, while the air passes through the far obtained eight eqs. (1-8) for eight unknowns, which can be solved simultaneously Computational procedure To solve eqs, (1) through (8) simultaneously we shall rearrange them as follows. First step is to rewrite eq. (7) as -158-

5 S. TAKAMI, Z. UCHIJIMA: A Model of the Greenhouse with a Storage-Type Heat Exchanger and its Verification When Hind H(T), we impose that no evaporation takes place from the pipes, as expressed in the second equation above. With Ht = 0, eq. (2) is rewritten as (9) (10) As St = 0, eqs. (1), (4), and (5) can be solved for Tout From eq. (3), (11) (12) Geven Hin, Tin hence Hs(Tin) from eq. (8) as boundary conditions, E is determined from eq. (9). Hout is then calculated from eq. (10). With T i as another boundary condition and predetermined value of ht, eq. (6) determines 5h. Now Tout can be calculated from eq. (11), and T,~ from eq. (12). The above procedure is applied to the first section of the storage-type heat exchanger. The procedure is repeated successively for each section along the direction of the air flow by replacing Tin and Hin with Tout and Hout obtained for the preceding section. The heat transferred from the pipes in each section to the water is calculated from eq. (3), its sum over the whole pipe length being the heat stored in the water as a heat accumulator (Hstor, J) while the air passes through the heat exchange pipes. In our calculations the averaging time for depicting the distributions of each physical element in this system was taken as 1800 sec. of temperature and humidity of the air along the pipes are 30 minute averages and the water temperature is given after 30 minutes from the time when Ti is given. This modification was adopted, since preliminary calculations indicated that the being the number of iterations of the calculation while the air passes the heat exchange pipes Model for the greenhouse with a storagetype heat exchanger The two models so far described are now used as submodels: the model for the greenhouse as SUBROUTINE HOUSE and the model for the heat exchanger as SUBROUTINE EXCHAN. These models are written in FORTRAN (level 7000). We constructed a model for the total system by coupling these subroutines through common state variables. In the case of the open system of the house operation, the following relations are adopted at the first step in the calculation for respective averaging times. TO = TOO, HO = HOO. Then the SUBROUTINE HOUSE, with other environmental and system parameters as input humidity (HA, g. m-3) at the outlet of the greenhouse (2.1). By using these output data as the of the air flowing into the heat exchange pipes, that is, T;n= TA and Hln= HA, we can obtain the temperature (T2) and humidity (H2) as well as other necessary output data (2.2) at the outlet of the heat exchange pipes. When the greenhouse-heat exchanger system is operated as a closed circulation system, T2 and H2 thus obtained are respectively compared with TOO and H00. If T2 or H2 is close enough to TOO or H00 (T2 TOO, H2 ~H00), the computation is stopped. If not, we repeat the computation by setting TO equal to T2 and HO to H2, till change in both T2 and H2 with iteration of calculation becomes sufficiently small. 3. Test of model 3.1. Comparison of model with experimental results We used experimental results with a plastic greenhouse at Kochi Prefectural Technological -159-

6 Table 1. System parameters used in the experimental test of the model, as obtained for a vinyl house at Kochi Prefectural Institute of Agriculture and Forestry Technology in See Takami and Uchijima (1977) for the parameters not described in this paper

7 S. TAKAMI, Z. UCHIJIMA: A Model of the Greenhouse with a Storage-Type Heat Exchanger and its Verification Institute of Agriculture and Forestry in The greenhouse, single span plastic house, was 17 m long, 5.3 m wide, 2.6 m high to the ridge of the roof, and 1.4 m high to its eaves (Fig. 2). The plastic greenhouse with the storage-type heat exchanger was situated in the north-south direction and the air was circulated or ventilated in this direction by an electrically driven fan set up on the house wall. The storage-type heat exchanger was made up of a concreate water tank of 17 m long and of 1.0 m2 in the cross-sectional area. The depth of water in the water tank was 0.5 m. 32 galvanized iron pipes with the diameter of 0.1 m and the wall thickness of m were set as the heat exchanger in the water tank.-the water tank as a heat accumulator was insulated by stylofoam with 4 cm thickness. The storage-type heat exchanger as a whole was buried in the ground and the two ends of each heat exchange pipe set in the water tank were open to the greenhouse through the air ducts as can b e seen in Fig. 2. At the end of the outflowing duct there were two shutters to change the direction of air flow according to the difference of air circulation system (i.e., closed or open system). Table 1 summarizes the system parameters of this greenhouse. The ventilation rate of the greenhouse was measured to be 20.3 hr -1 for the closed circulation system and 19.9 hr-1 for the open system. Therefore, we used 20.0 hr--1 as this rate in our calculations. in this table were estimated so far obtained Some of the system parameters of the parameters. on the basis of values Table 2 shows the environmental conditions of May 22, 1975 under which the experiment was conducted. The sky was clear and the whole system was operated as the closed circulation system. Such environmental parameters as irradiance, air temperature and humidity were measured every hour. In the calculations, the values of these parameters estimated by interpolation at 30 minute interval starting at 0815 JST (Japan Standard Time) were used as listed in Table 2. The water temperature measured at 0800 JST was used as the initial water temperature (Tw1) in Table 2. Environmental conditions used in the experimental test of the model, (May 22, 1975). The sky was clear, and the system was operated by the closed method. the calculations. No measurements were made on the wind speed (U0, m sec-1), the downward long-wave irradiance (LO, W m-2) and the soil water potential (WPOTS, bar). UO was assumed to be a constant, 1.5 m sec-1, as the change in its value has little effect on the sensible heat transfer through the plastic film (Takakura and Okada, 1972). L 0 usually varies little in the daytime on clear days and was fixed at 300 W m-2. WPOTS was estimated to be -2.0 bar, representing slightly dry soil at the time of the experiment

8 3.2. Results and discussion Fig. 3 is the comparison between calculated and measured net radiant flux densities in the greenhouse. Net radiation was measured with a Funk type net radiometer above the top of the crop in the greenhouse. Calculation overestimated the measured net radiation by 20% in the maximum and by about 10% on the average till 1400 JST. But both agreed well after 1400 JST. From this result we believe that the accuracy of the model is sufficient to meet most practical purposes as the error in the net radiation measurements is usually more than 10%. For a more precise test one must measure LO and the parameters that were estimated in this study. Fig. 4 compares the calculated temperature and humidity in the greenhouse with the measured ones. Temperature and humidity were measured with a ventilated psychrometer at the center of the greenhouse. The agreement between measured and calculated values was good during the period from 0800 to 1400 JST in which the heat was being stored in the heat accumulator. Afterwards deviation of the calculated values from the observed values became large gradually. Part of the disagreement was presumably caused by evaporation of the water leaking into the heat exchange pipes, which was indicated by the higher humidity at the outflowing duct of the heat exchanger than at its inflowing duct. Other presumable cause for this disagreement seemed to be insufficiency of the consideration of the physical processes govern- Fig. 4. Changes of air temperature (TA) and water vapor pressure (HA) in the greenhouse, as calculated (-) and as measured (0), May 22, Fig. 3. Change of the net radiation over the crop surface in the greenhouse, May 22, Fig. 5. Time course of water temperature in the accumulator as calculated (-) and as measured (0)

9 S. TAKAMI, Z. UCHIJIMA: A Model of the Greenhouse with a Storage-Type Heat Exchanger and its Verification ing the release of heat from the accumulator and of the measurements of meteorological elements. Fig. 5 is the comparison of calculated and measured water temperatures in the heat accumulator. Satisfactory agreement was found for almost all of the daylight hours. The heat accumulated in the accumulator during the period from 0800 to 1830 JST was calculated to be 68,571 kcal, which was within 2% of the measured one, that is, 67,166 kcal. Table 3. Area ratio, short-wave irradiance and operational methods used in simulation experiments. 4. Simulation 4.1. Simulation method The proposed model was used to make clear characteristics of the heat transfer in the greenhouse - heat exchanger system. The effects of two greenhouse parameters, ventilation rate (R, hr-1) and area ratio (AR, the ratio of floor area to the wall area of the house), and of the environmental parameter, short-wave irradiance (SO, W. m-2), on the greenhouse environment and the performance of the storage-type heat exchanger were evaluated. These three parameters are well known to be most influential on the greenhouse environment. Simulation experiments were made for eight cases with the parameter combinations as presented in Table 3. For each case the ventilation rate was allowed to vary from 5 to 80 hr-1 in 10 hr-1 step. The cross-sectional area of the greenhouse was fixed at 10 m2, the wall area at 200 m2 and the greenhouse volume at 200 m3. The values for all other system parameters were identical as those given in Table 1. The values of meteorological parameters other than short-wave irradiance (SO) are listed in Table Results and discussions Fig. 6 shows the temperature between the outflowing and inflowing air ducts of the greenhouse) and the heat storage ratio of the storage-type heat exchanger, each as a function of the ventilation rate (R, hr-1), The heat storage defined as a ratio of the heat accumulated in the storage-type heat exchanger (Hstor, J) to the sum of sensible (AS) and latent (LES) heat fluxes released from the canopy surface into the air Table 4. Environmental conditions used in simulation experiments. rise in the green

10 inside the greenhouse: where Hgain = (A f(as + LES)) x 1800,J Af = floor area of the greenhouse, m2. At an irradiance of 700 W m-2, the air temperature always rose as the air passed through the greenhouse at a rate of 10 to 80 hr-1 (Fig. 6-a). The rise in air temperature was larger in the closed system for the air circulation than in the open system. But this difference was small, only 1.5 C at its maximum and rapidly decreased as R decreased below 20 hr-1. The influence of the area ratio (AR) on the temperature rise of the air in the greenhouse was more prominent as shown in between the greenhouses with AR = 0.5 and AR = increasing ventilation rate R. However, the area ratio gave relatively little was so because not only Hstor but also Hgain increased as AR increased. The heat storage efficiency increased with the increase of R (thus with increase in the heat transfer coefficient of the storage-type heat exchanger) in the closed system. This is due to the increase in Hstor with R, since the greenhouse-heat exchanger system exhausts no heat by the ventilation when operated as a closed system. was negative, i.e., the air temperature decreased as the air passed through the greenhouse, except when the air was circulated in the greenhouse with an area ratio of 0.8 (Fig. 6-c). Hence heat was released through the storage-type heat exchanger into the greenhouse, the heat exchange increasing proached to zero with increasing R owing to the heat loss from the storage-type heat exchanger. In the open system of air circulation, on the other in general, which depended on both outside temperature and humidity, since not only the heat loss from the storage-type heat exchanger but also the heat exhaust from the house was enhanced with the increase in R, that is, air ventilation. Tn contrast to the case of Sn = 701) W. m-2 the SO = 200 W. m-2 decreased monotonically even in the closed system when the greenhouse has the area ratio of 0.8. Also the difference in heat storage ratio between A = 0.8 and AR = 0.5 was large as the increase in Hgajn with increasing AR was accompanied with decrease in Hstor. The important role of the latent heat exchange in the process of heat accumulation by the storagetype heat exchanger is illustrated in Fig. 7. Contribution of the latent heat exchange to the heat accumulation was more than 50% at the high irradiance level (SO = 700 W. m-2). This was in good agreement with experimental results obtained by a plastic greenhouse equipped with the

11 S. TAKAMI, Z. UCHIJIMA: A Model of the Greenhouse with a Storage-Type Heat Exchanger and its Verification Fig. 7. Contributions of latent (HLE) and sensible (HSH) heat exchanges to the heat accumulation by the storage-type heat exchanger (Hstor) as functions of R for the greenhouse with AR = 0.80 under two radiant levels. storage-type heat exchanger (Okubo et al., 1977). It cannot be neglected, either under the lower irradiant conditions (SO = 200 W. m-2 ), though the effect of latent heat exchange rapidly declined as R increased. 5. Conclusions A semi-steady state model for the greenhouse with a storage-type heat exchanger was proposed and simulation results were compared with experimental results. The model calculates the air temperature and humidity in the greenhouse, radiations and heat balances on the house cover and in the house, and the heat flux exchanged between air flow and the heat accumulator, from the environmental and house parameters. Fairly good agreement between measured and calculated values was found for air temperature, humidity and net radiant density in the greenhouse with the storage-type heat exchanger. The calculated amount of heat stored in the heat accumulator agreed satisfactory with measured one. Simulation experiments, made on typical combinations of short-wave irradiance, area ratio and ventilation rate of the greenhouse, suggested that the proposed model could be useful to give design and operation criteria under various environmental conditions. Sample calculations also indicated an important role of the latent heat exchange in the processes of heat accumulation of the greenhouse-storage type heat exchanger system. References Iwakiri, S., 1971: Prediction and control of temperature environment inside the glasshouse. Report of the Natl. Research Center for Disaster Prevention, No. 6, pp 139. Monteith, J. L., 1973: Principles of environmental physics. Edward Arnold Ltd., London, pp 241. Murray, F. W., 1967: On the computation of saturation vapor pressure. J. Appl. Met., 6, Okubo, J., Ogata, K., Hashimoto, H., and Morita, Y., 1977: Experimental study of thermal efficiency of a vinyl-house with a storage-type heat exchanger (in press). Takakura, T., and Okada, M., 1972: Experimental determination of greenhouse heating load coefficient. J. Agri. Meteorol., Tokyo, 27, Takami, S., and Uchijima, Z., 1977: A model for the greenhouse environment as affected by the mass and energy exchange of a crop. J. Agr. Meteorol., 33, Uchida, S., 1936: Kogyo Dennetsu (Engineering heat transfer). Kyoritsu Shuppan Ltd., Tokyo, pp 173. Yamamoto, Y., 1966: An application of earth-air heat exchange. J. Agri. Meteorol., Tokyo, 22,

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