Simulation of an Earth-Air Heat Exchanger in a Commercial Greenhouse to Improve Energy Efficiency

Abstract

Purpose

Greenhouses in colder northern climates typically require significant supplemental heating for year-round operation, usually provided by natural gas combustion. One potential method of reducing greenhouse energy use is to incorporate an earth-air heat exchanger (EAHE) for seasonal heat storage; however, there is little guidance in the literature on the feasibility of this technology in cold-climate greenhouses.

Methods

This study uses simulations to examine the potential energy savings that could be achieved in cold-climate greenhouses by incorporating an EAHE system. A lumped parameter greenhouse energy model previously developed and tested against experimental data from several commercial and passive greenhouses was modified to simulate the addition of an EAHE in a commercial-scale lettuce greenhouse. The operation and energy use of this greenhouse was simulated at several locations across Canada. Crop evapotranspiration was included in the energy balance, and the greenhouse was assumed to deploy a thermal curtain at night.

Results

The EAHE sub-model was validated against experimental results available in the literature and was found to accurately predict the outlet air temperature of an EAHE. The predicted change in required supplemental heating with an operating EAHE varied from a 100% reduction in Victoria, BC, to a 13.3% reduction in Winnipeg, Manitoba.

Conclusions

EAHE use could reduce, or in a few locations with milder winters, even remove the need for supplemental heating at commercial-scale Canadian greenhouses.

Appendices

Appendix 1: Convergence Test

The number of discrete pipe segments required for accurate EAHE modelling was examined using a convergence test. For this test, pipe length was assumed to be 72 m, with a 15 cm diameter of 15 cm, a 2.7 m depth and a 4 m·s⁻¹ air speed. The inlet air temperature was assumed constant at 25 °C and the undisturbed soil temperature was set to 12 °C. Table 12 gives the soil and material properties. The simulation duration was set to 72 h, with a time step of dt = 10 s.

Table 12 Properties used in convergence test

The simulated outlet air temperature was used to evaluate the convergence, based on the absolute relative approximate error between successive segment lengths (Table 13). An absolute relative approximate error of less than 0.5% was used as the stopping criterion. The absolute RAE was found iteratively by comparing the predicted outlet temperatures between cases. For example, the absolute RAE between 1 and 2 discretized segments was found using the formula,

$$RAE\left(\%\right)=\left|\frac{Outlet\;temperature\;\left(1segment\right)-Outlet\;temperature\;(2\;segments)}{Outlet\;temperature\;(2\;segments)}\right|\bullet100\%=6.59\%$$

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As can be seen below, a minimum of 16 segments should be used when discretizing the EAHE model.

Table 13 Convergence test for EAHE with respect to outlet air temperature

Appendix 2: Equations for Temperature and Absolute Humidity Changes

In the equations below, dT_i represents the temperature change of layer i over time step dt, with c_i representing the layer-specific heat capacity (J·kg⁻¹·K⁻¹), ρ_i is the layer density (kg·m⁻³), and dx_i is layer vertical thickness (m). The heat transfer pathways between layers are a combination of convection (conv), conduction (cond), evapotranspiration (trans), and infrared radiation (IR), while the heat resulting from solar input (sol rad), EAHEs (EAHE), and ventilation (vent) are also included. Refer to Fig. 4 for the assignment of layer number subscripts (i.e., layer 1 is the glazing layer). The following equations are used when the energy curtain is not deployed. When the energy curtain is deployed, the equations are slightly modified to include an additional curtain layer. Details of this can be found in Nauta et al. (2022).

$${dT}_1=\frac{dt\;(Q_{solrad_1}+{Q_{solref}}_1-Q_{conv_{1\rightarrow amb}}-Q_{IR_{1\rightarrow sky}}+Q_{conv_{2\rightarrow1}}+Q_{IR_{5\rightarrow1}}+Q_{IR_{6\rightarrow1}})}{c_1\;\rho_1\;{dx}_1}$$

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$${dT}_2=\frac{dt\;(-Q_{conv_{2\rightarrow1}}+Q_{solrad_2}-{Q_{vent}}_2)}{c_2\;\rho_2{\;dx}_2}$$

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$${dT}_4=\frac{dt\;(Q_{solrad_4}+Q_{conv_{5\rightarrow4}}+Q_{{conv}_{6\rightarrow4}}-{0.5Q}_{t{rans}_{5\rightarrow4}}-Q_{{vent}_4}-Q_{EAHE\rightarrow air})}{c_4\;\rho_4{\;dx}_4}$$

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$${dT}_5=\frac{dt\;(Q_{solrad_5}+Q_{solra{d_{ref}}_5}-Q_{conv_{5\rightarrow4}}-Q_{IR_{5\rightarrow1}}-{0.5Q}_{tr{ans}_{5\rightarrow4}}-Q_{IR_{5\rightarrow sky}})}{c_5\;\rho_5{\;dx}_5}$$

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$${dT}_6=\frac{dt\;(Q_{solrad_6}-Q_{conv_{6\rightarrow4}}+Q_{{cond}_{7\rightarrow6}}-Q_{IR_{6\rightarrow1}}-Q_{IR_{6\rightarrow sky}})}{c_6\;\rho_6{\;dx}_6}$$

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*Note that Equation 12 is used for layers i = 7 through 12 with only the layer subscripts changing

$${dT}_i=\frac{dt\;(Q_{cond_{i+1\rightarrow i}}-Q_{cond_{i\rightarrow i-1}})}{c_{i\;}\rho_i{\;dx}_i}$$

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$${dT}_{13}=\frac{dt\;({-Q}_{cond_{13\rightarrow12}})}{c_{13\;}\rho_{13}\;{dx}_{13}}$$

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The change in absolute humidity of the greenhouse air over time step dt is dAH. The change is a result of crop transpiration (trans), latent heat transfer from ventilation (latent), and latent heat transfer from the EAHE. Here, λ is the latent heat of condensation for water (2250 J·kg⁻¹).

$$dAH\left(\frac{kg}{m^3}\right)=\frac{dt\;({\dot{Q}}_{trans}-{\dot{Q}}_{latent}-{\dot{L}}_{EAHE\rightarrow air})}{\lambda\;{dx}_{air\;layer}}$$

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