Simulation of a Novel Cooling System for a Closed Greenhouse

Abstract

A simulation of a cooling system for a closed greenhouse is described. The cooling system relies upon cool ambient temperatures during the night and morning to discharge heat accumulated within the greenhouse during the day. Radiative heat into the greenhouse is transferred to a large reservoir of water inside the greenhouse using an unpressurized droplet system. During the night and morning the accumulated reservoir heat is discharged to ambient air using the same droplet system to transfer reservoir heat into a restricted volume of air above the reservoir, while simultaneously circulating the heated air through an air-to-air heat exchanger comprised of thin-walled plastic tubes.

1. Introduction

Climate change is creating a crisis for food security. Grain yields are threatened by elevated temperatures and drought stress that shorten the grain filling period and impair starch biosynthesis [1]. Increasing irrigation to counter high temperatures and drought is a progressively less likely option because climate change impacts other aspects of the hydrological cycle in addition to precipitation, including glaciers, river flows, and aquifer replenishment, increasing competition to agriculture for freshwater resources required for wild ecosystems, consumption and sanitation, industry, and cooling [2]. Climate change also reduces arable land by desertification of drylands [3], soil erosion from extreme precipitation events [4], and saltwater intrusion into river deltas [5].

Mitigating climate change will require removing gigatonnes of CO₂ annually from the atmosphere [6]. It is generally assumed that captured CO₂ will be liquified under pressure and geologically sequestered. For schemes where CO₂ is not mineralized underground and where no fluid is produced from the well, it has been argued that the increase in well pressure precludes underground sequestration of CO₂ at scales required to mitigate climate change [7]. Storage in saline formations would be possible by simultaneously producing brine to relieve the pressure, but this would require desalinating the produced brine and pumping the highly concentrated waste brine back into the formation for disposal [8]. Storage of CO₂ in oil wells during enhanced oil recovery (EOR) is possible because oil is produced to relieve the pressure. The CO₂ sequestered by EOR could be managed to exceed the CO₂ emitted by combusting the produced oil [9].

Use of captured CO₂ to enhance greenhouse yields provides a potentially profitable route of sequestration into biomass such as biochar, woody products, or humus, and CO₂ could be provided at ambient pressure from the output stream of the CO₂ capture facility. The greenhouses must be closed or unventilated so that the CO₂ is confined until it is consumed by the plants. Water is also conserved and recycled because it is confined within the greenhouse with the CO₂. Closed greenhouses can enhance yields of C₃ crops by maintaining a high concentration of CO₂ during the afternoon period of maximum photosynthesis, when other greenhouses are normally ventilated for cooling. High CO₂ concentrations might increase the temperature for optimal photosynthesis [10, 11, 12, 13, 14], increasing the yield while reducing the cooling load for the greenhouse.

Cooling a closed greenhouse generally requires much more energy than evaporatively cooling a ventilated greenhouse. However, renewable energy and energy storage costs are falling while freshwater resources are diminishing, and CO₂ will need to be sequestered at scale. Therefore an important engineering challenge for addressing food security and CO₂ sequestration in a changing climate is the problem of economically cooling a closed greenhouse.

Different solutions to the closed greenhouse cooling problem have been prototyped and commercialized in the past. Closed greenhouses sited in northern climates have used borehole heat exchangers to access cold ground temperatures that are recharged to low temperatures during the winter [15]. Closed greenhouses have been sited over aquifers to access seasonal storage of cold water temperatures [16]. The closed greenhouse cooling system for the Watergy prototype operated on a diurnal cycle using a water-to-air heat exchanger that accessed a reservoir of water outside the greenhouse that was cooled by low ambient nighttime temperatures [17, 18]. The Novarbo Oy Company commercialized a closed greenhouse that cools and dehumidifies the greenhouse air using water droplets, returning the water to an outside reservoir that is cooled with a heat pump [19, 20].

The closed greenhouse design described in this report relies upon cool ambient nighttime and morning temperatures to discharge heat removed from the greenhouse air during the day and stored in a reservoir of water inside the greenhouse [21]. During the day heat entering the greenhouse from solar radiation is transferred to a reservoir of water by an unpressurized droplet system. The novelty of the proposed design is the method of discharging the accumulated reservoir heat to the ambient air. During the night and morning heat in the reservoir is discharged to ambient air by using the same droplet system to transfer reservoir heat into a restricted volume of air above the reservoir, while simultaneously circulating the heated air through an air-to-air heat exchanger composed of thin-walled plastic tubes. This design avoids the cost and maintenance of a chiller as well as the supported weight and risk of leaks using a water-to-air heat exchanger. The design requires a climate with a low minimum ambient temperature during the morning, preferably 13°C or less. Because the greenhouse is convectively cooled, it could be sited equally well in deserts and in high humidity climates.

The greenhouse cooling simulation described here uses a “well-stirred” energy balance model where the temperature and humidity are assumed to be uniform throughout the greenhouse volume. Heat and mass transfers are modeled with correlation formulas developed for forced convection applications that are based upon dimensionless Nusselt numbers. These formulas have an accuracy of about 20% [22].

Experiments were performed on small components of the cooling system: a single plastic heat exchanger tube and droplet dispensers [21]. These experiments confirmed the air-to-air heat transfer properties of the plastic tube, and informed the simulation on the effective droplet surface temperature for simulating the heat and mass transfer to a falling droplet. The droplet surface temperature is modeled using a linear combination of the bulk temperature in the droplet and the surrounding air temperature [21].

The simulation advances in time steps of $\mathrm{\Delta }t=90$ seconds for a 24-hour period. More refined time steps are required to model the reservoir and heat exchanger system during the heat discharge period. The 24-hour simulation is repeated iteratively until the total heat within the greenhouse at the end of the 24-hour cycle is within 10 kJ of the total heat at the beginning of the cycle.

2. Components and operation of the cooling system

Figure 1 shows a schematic of four greenhouse modules taken from an array of closed greenhouses, where the cover is not shown for one of the modules in the drawing. The green cultivated regions in this example have an area of 20 m by 50 m or 0.1 ha. Adjacent to each cultivated region is a reservoir of water with a depth $d_r$ of 1 m and an area $A_r$ of 10 m by 50 m. Above each reservoir is a restricted volume of air or “tunnel” that is optionally open to a bank of plastic tubes located above the tunnel that serves as an air-to-air heat exchanger. The individual heat exchanger tubes are not shown.

Figure 1.

Four modules from a greenhouse array that share a common volume of air. One of the modules has the cover removed from the drawing. White outlined arrows show the direction of airflow during the day, when warm greenhouse air is circulated through cool reservoir droplets to transfer heat and water vapor from the air into the reservoirs. Blue arrows show the direction of airflow during the night through the heat exchanger tube bank, when cool tunnel air is circulated through warm reservoir droplets to transfer reservoir heat into the air-to-air heat exchanger.

During the day the reservoir water is cool, the sides of the tunnels are open to the cultivated regions in the greenhouses on either side, and the ends of the tunnels are closed off from the C-shaped ducts that lead to the outside heat exchanger. 1.6 m above the reservoir surface, below the roof of the tunnel, there are trays with a pattern of short tubes that comprise the droplet dispensers.

Cool reservoir water pumped into the trays returns to the reservoir as 1.5 mm diameter droplets that exchange heat and water vapor with the air above the reservoir. Warm greenhouse air is circulated by fans across the width of the tunnel and through the falling droplets in the direction of the white outlined arrows, shown for one the modules, transferring both heat and water vapor to the reservoir to cool and dehumidify the air. A complete greenhouse array would be configured to return the airflow through a similar string of greenhouses in the opposite direction so that the airflow is cycled through all the greenhouse modules.

During the night the reservoir water is warm, the sides of the tunnel are closed, and the ends of the tunnel are opened to the ducts that lead to the heat exchanger tube bank. The same droplet system is activated and fans move saturated air down the length of the tunnel through the falling droplets, and then through the heat exchanger tube bank in the opposite direction, shown by blue arrows in Figure 1, where the forced convection of greenhouse air transfers both sensible and latent heat to the ambient air. Outside fans also pull a crossflow of cool ambient air through the tube bank.

The tube bank is comprised of 900 PETG tubes that are 30 m in length and in contact with the ambient air. Each tube has an outer diameter $D_1$ of 10 cm and a wall thickness of 0.5 mm. The tubes are arranged in a staggered configuration of 30 rows with 30 tubes per row, with a pitch of $a=$2 within a row and a pitch of $b=$1.25 in the vertical direction. The tubes may be slightly angled to allow condensed water to drain back into the reservoir. Figure 2 is a closer view of one end of the cooling system showing the surface of the reservoir, the top of the tunnel where the droplet dispensers are located, the duct leading to the heat exchanger, and the region occupied by the heat exchanger tube bank.

Figure 2.

View of one end of the cooling system schematic from Figure 1, where the cover was removed from the drawing. Adjacent to the cultivated region is the primary heat exchanger system comprising a reservoir of water, a tunnel with droplet dispensers to transfer heat to or from the reservoir, and a C-shaped duct that leads to a bank of 900 thin-walled plastic tubes.

Figure 3 shows the solar radiation into the 1000 m² greenhouse in the simulation. The integral of this curve is the heat load that must be transferred during the day to the reservoir or to the soil and plants, or conducted to the ambient air through the cover. If the integrated outside radiation is 9.5 kWh m⁻² day⁻¹, then the transmission of the greenhouse cover must reduce the incoming insolation by 50% to achieve the radiation heat load shown in Figure 3. During the day the reservoir water temperature is roughly 15°C cooler than the greenhouse air. The reservoir droplet dispensers are activated to flow 100 L s⁻¹ of droplets to transfer both latent and sensible heat into the reservoir. During the night the reservoir droplet dispensers flow 450 L s⁻¹ to transfer heat from the reservoir to the air.

Figure 3.

Model of the daily radiative heat load into the 1000 m² greenhouse.

Figure 4 is a plot of temperature versus distance through 50 m in the tunnel, shown to the left of the vertical dashed line, and through 30 m of the heat exchanger tubes, shown to the right of the dashed line. It is assumed that the air temperature does not change within the ducts; the distance through the ducts is not shown in Figure 4. As cooled air moves through the warm reservoir droplets down the length of the tunnel the temperature increases and the humidity remains saturated. When the air moves through the heat exchanger the temperature falls as reservoir heat is transferred to the ambient air. Water condenses inside the tubes and eventually drains back into the reservoir.

Figure 4.

Air temperature versus distance in the heat exchanger system. During the first 50 m the temperature rises in the tunnel as reservoir heat is transferred by warm reservoir droplets to the air. During the last 30 m the air cools as it passes through the heat exchanger and transfers heat originally stored in the reservoir into the cool ambient air.

During the night heat is conducted through the walls and roof of the cultivated regions and the air temperature falls, increasing the relative humidity. A second air-to-air heat exchanger, denoted as the condenser, is positioned on the apex of each greenhouse roof as shown in Figure 2 to reduce the relative humidity at night. The condenser has the same tube arrangement as the primary heat exchanger over the tunnel, but the PETG tubes are smaller, with an outside diameter of 2.5 cm and a wall thickness of 0.3 mm. Indoor fans pull air through the condenser tubes, while outside fans pull a crossflow of cool ambient air through the condenser tube bank.

Water is completely recycled within the closed greenhouse. All the water that evaporates into the air, including water transpired by the plants, eventually condenses on the falling reservoir droplets or on the inner surfaces of the heat exchanger tubes and returns to the reservoir.

3. Simulation

3.1 Daytime cooling

During the day radiative heat must be transferred to the reservoir by the droplet system at approximately the same rate that it enters the greenhouse. The plants also transpire and the additional water vapor must be removed by the droplet system to maintain an acceptable vapor pressure deficit (VPD) for the plants. Figure 5 shows the model for plant transpiration over a 24-hour cycle, assuming a transpiration rate of 3 L m⁻² day⁻¹ in the cultivated region. The simulated transpiration rate at any given time depends upon the insolation and VPD. Because the VPD depends upon the solution for the greenhouse temperature and humidity, the time dependence of the transpiration is iterated together with the simulated temperature and humidity to provide a self-consistent result after the simulation converges [21].

Figure 5.

Transpiration rate from plants cultivated in the greenhouse.

During a time step $\mathrm{\Delta }t$ the reservoir droplets absorb the heat $\mathrm{\Delta }{Q}_r$ and the water vapor mass $\mathrm{\Delta }{M}_r$ from the greenhouse air. These are signed quantities: $\mathrm{\Delta }{Q}_r$ and $\mathrm{\Delta }{M}_r$ are positive when heat and water vapor are transferred from the greenhouse air to the reservoir droplets, and negative when heat and water vapor are transferred from the reservoir droplets to the greenhouse air. During $\mathrm{\Delta }t$ the reservoir temperature increases by:

$$\mathrm{\Delta }{T}_r=\frac{\mathrm{\Delta }{Q}_r}{A_r{d}_r{\rho }_w{C}_{\mathit{pw}}}$$E1

where ${\rho }_w$ and $C_{\mathit{pw}}$ are the density and specific heat capacity of water. The mixing ratio $X_a$ (grams of water per grams of dry air) for the total greenhouse air volume $V_a$ changes by:

$$\mathrm{\Delta }{X}_a=\frac{\mathrm{\Delta }{M}_{\mathit{Tr}}-\mathrm{\Delta }{M}_r}{V_a{\rho }_a}$$E2

where $\mathrm{\Delta }{M}_{\mathit{Tr}}$ is the mass of water vapor transpired by the plants during $\mathrm{\Delta }t$. During $\mathrm{\Delta }t$ the radiative heat $\mathrm{\Delta }{Q}_S$ enters the greenhouse, and conductive heat $\mathrm{\Delta }{Q}_C$> 0 (< 0) also enters (leaves) the greenhouse through the cover over the cultivated region. The greenhouse air temperature $T_a$ changes by:

$$\mathrm{\Delta }{T}_a=\frac{\mathrm{\Delta }{Q}_S+\mathrm{\Delta }{Q}_C-H_v\mathrm{\Delta }{M}_{\mathit{Tr}}-\left(\mathrm{\Delta }{Q}_r-H_v\mathrm{\Delta }{M}_r\right)}{V_a{\rho }_a{C}_{\mathit{pa}}+m_s{C}_{\mathit{ps}}}$$E3

where $H_v$ is the enthalpy of vaporization for water, $C_{\mathit{pa}}$ is the specific heat capacity of air, $m_s$ is the mass of the soil in the cultivated region (g), and $C_{\mathit{ps}}$is the specific heat capacity of the soil (0.92 J °C⁻¹ g⁻¹). The simulation assumes that heat transfers instantly to the soil mass and neglects any heat transfer to the plants or other objects in the greenhouse.

3.2 Discharging reservoir heat to the ambient air

Ninety percent of the energy required to operate the greenhouse is used to discharge the accumulated reservoir heat to the ambient air during the night and morning. The simulation discharges reservoir heat between 19:00 in the evening and 9:00 in the morning. During this period the sides of the tunnel are closed to the remainder of the greenhouse volume and the ports to the heat exchanger on either end of the tunnel are open. The tunnel and heat exchanger form an isolated system that is simulated independently from the remainder of the greenhouse. Figure 6 shows the model of ambient temperature $T_o$ used by the simulation. The most critical feature for discharging heat is the minimum diurnal temperature, assumed to be 11.8°C in this example, at 7:00.

Figure 6.

Model of the ambient temperature for the simulation over 24 hours. The temperature reaches a minimum of 11.8°C at 7:00.

If the ambient temperature is at least 2°C less than the reservoir temperature, pumps are activated to circulate 450 L s⁻¹ into the droplet dispensers and fans are activated to pull air through the heat exchanger tubes and to push the cool, saturated air through the falling droplets down the length of the tunnel. The fan power is adjusted so that the airspeed in the heat exchanger tubes $v_x$ is linearly proportional to the difference between the reservoir water temperature $T_r$ and the ambient air temperature $T_o$, reaching a maximum of 5 m s⁻¹ during the morning. The airspeed $v_T$ in the tunnel is a factor 2.20 less than $v_x$ and determined by the ratio of cross-sectional areas of the tunnel and heat exchanger tubes.

The air circulating through the tunnel and heat exchanger is always saturated. As cool air moves down the tunnel the warm reservoir droplets transfer both heat and water vapor to the air at the surface of the droplet, but as the water vapor diffuses away from the warm surface of the droplet it is assumed to recondense as fog, so that both the sensible and latent heat contributed from the droplet raise the temperature of the tunnel air. When the warmed air at the end of the tunnel enters the heat exchanger, it loses heat to the ambient air through the wall of the heat exchanger tube, and water condenses within the tube as the temperature and saturation vapor pressure fall. The simulation follows a Lagrangian air parcel through the tunnel to calculate the heat transfer from the reservoir water to the air, and a second Lagrangian parcel through a heat exchanger tube to calculate the transfer of heat from the air in the heat exchanger tube to the outside.

The tunnel Lagrangian parcel is a lamina of tunnel cross section with volume $\mathrm{\Delta }{V}_T=h\mathrm{\Delta }W\mathrm{\Delta }Z$, where $h$ = 1.54 m is the height between the reservoir water surface and the bottom of the droplet dispenser trays, $\mathrm{\Delta }Z$ = 10 m is the width of the tunnel, and $\mathrm{\Delta }W$ = 5 cm is the thickness of the lamina along the direction of tunnel airflow. During the small time step $\mathit{dt}=\mathrm{\Delta }W/v_T<<\mathrm{\Delta }t$, the heat ${\mathit{dQ}}_{T,\mathrm{Cnv}}$ that is transferred convectively from the falling droplets to the tunnel air is calculated within the parcel volume $\mathrm{\Delta }{V}_T$. The time step $\mathit{dt}$ that is used to update the Lagrangian parcel is much smaller than the simulation time step $\mathrm{\Delta }t$ that is used to update Eqs. (1)–(3). The reservoir droplets also release the water vapor mass $-{\mathit{dM}}_r$ into the parcel air. The temperature increase ${\mathit{dT}}_{T,a}$ of the parcel air due to both sensible and latent heat is then:

$${\mathit{dT}}_{T,a}=\left({\mathit{dQ}}_{T,\mathrm{Cnv}}-H_v{\mathit{dM}}_r\right)/\left(\mathrm{\Delta }{V}_T{\rho }_a{C}_{\mathit{pa}}\right)$$E4

After the parcel has traversed the entire length of the tunnel it has accumulated the heat $\delta Q_T$ so that heat is removed from the reservoir at the rate $\delta Q_T/\mathit{dt}$. Therefore, during the simulation time step $\mathrm{\Delta }t$ the reservoir temperature changes by:

$$\mathrm{\Delta }{T}_r=-\left(\frac{\mathrm{\Delta }t}{\mathit{dt}}\right)\frac{\delta Q_T}{A_r{d}_r{\rho }_w{C}_{\mathit{pw}}}$$E5

Within the heat exchanger tube the simulation follows a cylindrical Lagrangian parcel with volume $\mathrm{\Delta }{V}_x=\pi {D_0}^2\mathrm{\Delta }L/4$ where $\mathrm{\Delta }L=3$ cm is the length of the parcel and $D_0$ is the inner diameter of the tube. The time step for the heat exchanger tube simulation is $\mathit{dt}=\mathrm{\Delta }L/v_x<<\mathrm{\Delta }t$.

The heat exchanger tube enables the forced convection of heat to the ambient air through the total heat transfer coefficient $h_c$. There are three contributions to $h_c$ that each represent a resistance to heat transfer out of the tube [22]:

$$\frac{1}{D_0{h}_c}=\frac{1}{D_0{h}_0}+\frac{log\left(D_1/D_0\right)}{2k_{01}}+\frac{1}{D_1{h}_1}$$E6

The first term on the right hand side with heat transfer coefficient $h_0$ computes the convection across the boundary layer of air flowing within the tube. The third term with heat transfer coefficient $h_1$ computes the convection across the boundary layer of the outside crossflow air stream flowing through the heat exchanger tube bank. Outside fans pull air across the tube bank at the same speed $v_1=v_T$ as the airspeed through the tunnel.

The second term with thermal conductivity coefficient $k_{01}$ computes the heat conduction through the wall of the tube. For PETG tubing, $k_{01}=0.0029$W cm⁻¹ K⁻¹. Although the thermal conductivity of plastic tubing is very low, metal tubing for the heat exchanger was rejected as impractical because of cost. Because the 0.5 mm tube wall is very thin, the thermal conductivity through the wall contributes only about 3% of the total resistance to heat transfer in Eq. (6).

The heat transfer coefficients are calculated from dimensionless Nusselt numbers: $h_0={\mathrm{Nu}}_0{k}_a/D_0$ and $h_1={\mathrm{Nu}}_1{k}_a/D_1$, where $k_a$ is the thermal conductivity for air. For turbulent air flow [23, 24]:

$$\begin{array}{l}{\mathrm{Nu}}_0=0.023{Re}_0^{0.8}{Pr}^{0.33}\\ {\mathrm{Nu}}_1=0.33{Re}_1^{0.6}{Pr}^{1/3}\end{array}$$E7

${Re}_0=D_0{v}_x{\rho }_a/{\mu }_a$ is the Reynolds number for air flow inside the tube, where ${\mu }_a$ is the viscosity of air, and ${Re}_1=D_1{v}_1{\rho }_a/{\mu }_a$ is the Reynolds number for the outside cross flow of air within the tube bank. The Prandtl number is given by $Pr=C_{\mathit{pa}}{\mu }_a/k_a$. Note that the temperature loss down the tube is only a weak function of the airspeed $v_x$: although the residence time for a parcel of air within a tube section of length $\mathrm{\Delta }L$ is $\mathit{dt}=\mathrm{\Delta }L/v_x$, the heat transfer coefficient is proportional to $v_x^{0.8}$. Hence the total rate of heat transfer roughly scales with $v_x$ so that high speed turbulent flow through the heat exchanger tubes is preferred.

The temperature drop $\mathrm{\Delta }T$ within a tube parcel during a time step $\mathit{dt}$ depends upon the heat ${\mathit{dQ}}_w$ transferred from the air through the wall of the tube and on the heat of fusion ${\mathit{dQ}}_m$ released into the volume of the parcel as water vapor in the saturated air condenses due to the drop in temperature:

$${\rho }_a{C}_{\mathit{pa}}\mathrm{\Delta }{V}_x\mathrm{\Delta }T={\mathit{dQ}}_w-{\mathit{dQ}}_m$$E8

In Eq. (8), the temperature drop $\mathrm{\Delta }T$, ${\mathit{dQ}}_w$, and ${\mathit{dQ}}_m$ are all unsigned positive quantities. ${\mathit{dQ}}_w$ and ${\mathit{dQ}}_m$ are given by:

$$\begin{array}{l}{\mathit{dQ}}_w=h_c\left(\pi D_0\mathrm{\Delta }L\right)\left(T-T_o\right)\mathit{dt}\\ {\mathit{dQ}}_m=\left(\pi D_0^2\mathrm{\Delta }L/4\right){\rho }_a{H}_v\mathrm{\Delta }T\frac{\mathit{dX}}{\mathit{dT}}\end{array}$$E9

where $X$ and $T$ are the mixing ratio and temperature of the tube parcel air. Eqs. (8) and (9) may be combined to solve for the temperature drop $\mathrm{\Delta }T$ during the time interval $\mathit{dt}$:

$$\mathrm{\Delta }T=\frac{4h_c\left(T-T_o\right)\mathit{dt}}{{\rho }_a{D}_0\left(C_{\mathit{pa}}+H_v\frac{\mathit{dX}}{\mathit{dT}}\right)}$$E10

The derivative $\mathit{dX}/\mathit{dT}$ is obtained by differentiating the expression for the mixing ratio in terms of the saturation vapor pressure $P_s\left(T\right)$:

$$X\left(T\right)=\frac{M_w{P}_s\left(T\right)}{M_a\left(P_{\mathrm{atm}}-P_s\left(T\right)\right)}$$E11

where $M_a$ and $M_w$ are the gram molecular weights of air and water and $P_{\mathrm{atm}}$ is one atmosphere of pressure [21].

3.3 Greenhouse temperature, humidity, and VPD over a 24 hour cycle

Figure 7 shows the temperature of the greenhouse air and reservoir over a 24-hour cycle. The sun sets at 19:00 and the reservoir water is warm from the previous day. The sides of the tunnel are closed off from the remainder of the greenhouse volume and the tunnel is opened at each end to the ducts that lead to the heat exchanger tube bank in preparation for discharging the accumulated reservoir heat. The ambient temperature decreases (Figure 6) and the temperature of the greenhouse air also decreases as heat is conducted through the greenhouse cover. At 22:47 the ambient air temperature has fallen to 2°C less than the reservoir temperature and the fans and dispensers are activated in the tunnel to discharge the reservoir heat. The temperature in the reservoir continues to drop until 9:00 when the heat discharge period ends. During this time the sides of the tunnel are opened to the remainder of the greenhouse volume and the ports to the heat exchanger at the ends of the tunnel are closed. Droplets are dispensed to cool the greenhouse air and the reservoir temperature begins to rise.

Figure 7.

Greenhouse air and reservoir water temperatures over a 24-hour cycle.

The sun rises and begins to heat the greenhouse at 7:00. The temperature begins to climb rapidly until the daytime droplet activation period begins at 9:00. After 9:00 the temperature continues to climb more slowly as the insolation increases and the reservoir temperature increases, reducing the efficacy of the droplet system. At 15:30 the air temperature begins to gradually subside as the solar insolation drops. At 17:00 the droplet flow is reduced by 60% from 100 L s⁻¹ to 40 L s⁻¹ and there is a cusp in the air temperature curve when the temperature starts to rise. At 18:00 the droplets are turned off entirely creating a second cusp in the curve.

Figure 8 is a plot of the relative humidity (RH) of the greenhouse air. During the night the RH gradually drops because the drop in air temperature is more than compensated with the removal of water vapor by the condensing tubes on the roof of the greenhouse. At 7:00 light begins to enter the greenhouse and the plants transpire, overwhelming the condensing tubes and causing the RH to rise rapidly. The humidity drops sharply at 9:00 when the droplet dispensers are activated for daytime cooling. The rising greenhouse temperature and falling efficacy of the droplet cooling compensate one another to keep the RH roughly constant until 15:00, when the RH begins to rise. At 17:00 the droplet flow is reduced by 60%, causing a small jump in RH that is quickly counteracted by the rise in temperature. At 18:00 when the droplets are shut off the RH rises rapidly, but this is counteracted by the steep drop in plant transpiration as the sunlight disappears, so that the condensing tubes begin reducing the humidity after 20:00.

Figure 8.

Greenhouse relative humidity over a 24-hour cycle.

The greenhouse temperature and relative humidity may be combined to compute VPD. The VPD controls the transpiration of the plants, and it has been argued that the VPD is the parameter most relevant to the comfort of the plants [25, 26]. Figure 9 is a plot of the greenhouse VPD for several values of the daytime droplet flow, demonstrating that the VPD may be tuned for this greenhouse design by adjusting the daytime droplet flow. VPD values in the range of 0.4–1.3 kPa are optimal for greenhouse cultivation [25].

Figure 9.

Sensitivity of the vapor pressure deficit to the daytime droplet flow in the greenhouse over a 24-hour cycle. The previous plots were created for a daytime droplet flow of 100 L s⁻¹.

4. Discussion and conclusions

The simulation predicts that 191.5 kWh are required to operate the fans and pumps during a 24-hour cycle to cool a 1000 m² greenhouse, assuming the conditions specified in Figures 3 and 6 for the incoming solar radiation and the ambient temperature. 62.4% of this energy is used to operate the pumps. Once the reservoir is cold, the greenhouse air may be cooled during the day with a smaller expenditure of energy. 90.3% of the energy required to operate the greenhouse is used to discharge the accumulated reservoir heat using the air-to-air heat exchanger, or 173 kWh. The strategy to leverage the ambient temperature difference between the morning and afternoon significantly reduces the energy cost compared to using an air-cooled chiller, which requires 6.9 times the energy for a coefficient of performance of 4 [21]. The maintenance of the proposed cooling system would be simpler than the maintenance of a chiller, requiring the occasional replacement of pumps, fans, heat exchanger tubes, and tiles for the dispensers.

The energy cost per cultivated area for the closed greenhouse is far greater than using a conventional ventilated greenhouse cooled by a fan-pad system. Cooling a 1000 m² greenhouse evaporatively with a fan-pad system for 8 h during the day would require 14.8 kWh for the fans, assuming an airflow of 60 m³ s⁻¹ [21], a factor 13 less than the closed greenhouse design proposed here. Furthermore the conventional greenhouse does not require the costs for constructing the closed greenhouse cooling system including pumps, extra fans, reservoirs, dispensers, and heat exchanger tubes. The significant additional costs of constructing and operating a closed greenhouse enable conserving fresh water, maintaining an arbitrarily high concentration of CO₂ during the afternoon period of peak photosynthesis, and sequestering captured CO₂ into biomass.

Civilization is entering an era of abundant renewable energy but diminishing freshwater resources. Photovoltaics and battery storage have enormous potential for future innovation, and renewable energy costs will continue to fall from economy of scale as solar and wind replace fossil fuels. However freshwater resources are increasingly precious. The conventional fan-pad greenhouse used in the comparison above consumes 7.9 m³ d⁻¹ of water for evaporative cooling assuming an ambient temperature of 33°C and ambient relative humidity of 37% [21]. For a limited number of greenhouses this amount of water may not be a concern, but for many square kilometers under greenhouse cultivation in the desert a water loss this high becomes impractical.

It may be possible to reduce the cost of cooling system components by using recycled plastic. The reservoirs, heat exchanger tubes, and dispensers are made from thermoplastics that may be melted and reformed repeatedly. Recycling used plastic products into new products is the most desired means of disposal [27], so that extensive closed greenhouse construction might become a useful output stream for plastic waste.

The enhancement of photosynthesis at higher temperatures in the presence of elevated levels of CO₂ is fortuitous for closed greenhouses because of the energy demand by the cooling system to reduce the temperature and dehumidify the air. If the greenhouse temperature is allowed to increase, then the greenhouse relative humidity must also increase to maintain the same VPD for plant transpiration.

The photosynthesis enhancement at elevated temperature and CO₂ has been investigated for tomatoes [11, 12] and other plants [10, 13, 14]. The biochemical mechanism for this enhancement, and the mechanism for inducing damage to photosynthesis under significant heat stress when elevated levels of CO₂ are not present, remain active areas of investigation [12]. At the beginning of the Calvin cycle in photosynthesis, CO₂ attaches to the sugar substrate RuBP (ribulose bisphosphate), catalyzed by the enzyme rubisco (ribulose bisphosphate carboxylase). As the temperature increases a competing reaction becomes more favorable, where oxygen attaches to RuBP instead of CO₂, leading to photorespiration rather than photosynthesis. By increasing the concentration of CO₂ the photorespiration reaction may be suppressed so that photosynthesis can take advantage of the increased activity of rubisco at higher temperature. This mechanism holds at all light intensities, although the effect is enhanced with increasing light intensity [11].

If the temperature increases too much it may damage plant photosynthesis if the CO₂ concentration is not also increased. One hypothesis [12] argues that increased heat stress reduces the stomatal conductance, reducing the CO₂ available to the Calvin cycle and effectively reducing or interrupting electron transport to rubisco and RuBP, reducing both the activity of rubisco and the regeneration of RuBP. Thylakoid electron transport away from the PSII reaction center (PSII RC) is effectively blocked or reduced, causing excessive reduction of the acceptor which damages the PSII RC. Elevating ambient CO₂ restores the flow of electrons from the PSII RC to the Calvin cycle, restoring the redox balance along the electron transport path so that damage to the PSII RC is prevented.

Closed greenhouses could extend agriculture in higher elevation deserts into regions far beyond what might be currently irrigated near a river or lake. In addition to enhancing yields for standard greenhouse crops such as tomatoes and peppers, closed greenhouses could cultivate woody plants to sequester CO₂ into lumber and biochar. Bamboo for example is fast-growing and very responsive to enhanced concentrations of CO₂ [28]. A large-scale program of CO₂ sequestration into biomass might best be implemented in selected climates that are extremely favorable for deployment of the cooling system, such as the Altiplano plateau in Bolivia, Peru, and Chile.

The cooling system functions equally well in high humidity climates where evaporative cooling may be impractical. Coffee may be a suitable closed greenhouse crop because it prefers high humidity and shade, and a greenhouse would help protect the plants from unfavorable climate change induced conditions such as droughts, heat waves, and pests. Enhanced CO₂ concentrations also allow coffee plants and bean quality to endure supra-optimal temperatures during the day and night [13]. The coffee plant shows both reduced photorespiration in the presence of elevated CO2 and increased thylakoid electron transport [14].

Future research will include building and testing a full prototype and further simulations to explore variations and improvements to the design. One variation under consideration is an aquaponic system, where cold water fish are raised in tall cisterns that serve as reservoirs, and nutrient rich reservoir water is circulated between the reservoirs and hydroponically grown vegetables or a deep water culture of lettuce or rice. Another variation is a closed greenhouse for northern climates, where the heat exchanger tubes are optionally enclosed within the greenhouse volume during the winter. Heat captured by the reservoir during the day is released by the heat exchanger into the cold greenhouse air at night to prevent the plants from freezing.

In summary, the simulation has demonstrated that it is possible to cool a closed greenhouse with a large reservoir of water and an air-to-air heat exchanger comprised of thin-walled plastic tubes. The reservoir volume used in the design is A/2 m³, where A is the area of the cultivated region in m². The closed greenhouse requires about an order of magnitude more energy to cool than a conventional greenhouse cooled evaporatively using a fan-pad system. Hence the cooling system relies upon a high expenditure of electric power to conserve water and to maintain high concentrations of CO₂ during the day to enhance yields. The summer insolation and minimum daily temperature are the most important parameters that decide the size and cost of the cooling system, so that regions where the greenhouse design may be deployed are restricted to climates with cool morning temperatures. The VPD within the greenhouse may be tuned by adjusting the droplet flow that cools the greenhouse during the day. Deployment of closed greenhouses in regions with very low minimum diurnal temperatures (< 8°C) during summer potentially allow profitably sequestering CO₂ into biomass.

Acknowledgments

The author gratefully acknowledges the advice and encouragement of Professor J. Heiner Lieth at the University of California, Davis, and his consent to conduct heat and mass transfer experiments using a greenhouse on the Davis campus.

Conflict of interest

The author declares no conflict of interest.