Establishment and Solution of a Finite Element Gas Exchange Model in Greenhouse-Grown Tomatoes for Two-Dimensional Porous Media with Light Quantity and Light Direction

Abstract

An accurate gas utilization model is essential for precisely detecting plant photosynthetic capacity. Existing equipment for measuring the plant photosynthetic rate typically considers the key parameters of mesophyll cell conductance and a photosynthetic model based on the carbon reaction process under direct light conditions. However, the light environment signals received by the plant canopy not only vary significantly in incidence angles, but the effective light intensity also differs greatly from the measured values under vertical incidence conditions. To reduce the deviation between existing photosynthetic models and the actual photosynthetic efficiency of leaves, this study employs the gas diffusion method from engineering, using the finite element approach. Based on elastic mechanics and seepage mechanics, the internal stress field control equation of tomato leaves and the two-phase flow equation under a CO2 porous medium were derived. A mathematical model of porous gas–liquid two-phase fluid-solid coupling was established, solved, and analyzed. Preliminary verification was conducted through tests. The results show that in the initial stage of CO2 entering the leaf, the gas flow velocity is higher because of the larger pressure gradient between the pore and the leaf. In this stage, the gas diffusion rate is higher. As the intake time increases, the pressure gradient gradually decreases, and the inlet velocity slows down. Consequently, the diffusion rate gradually reduces. Because of the coupling of light quantity and light direction, the gas diffusion rate significantly increases compared with the uncoupled model. Additionally, a diffusion model that does not consider fluid–solid coupling will overestimate the gas flow rate as the depth of gas entry increases. Therefore, the internal gas diffusion model must account for the effect of coupling on the diffusion rate.