Dynamic Simulation of Photothermal Environment in Solar Greenhouse Based on COMSOL Multiple Physical Fields

Abstract

Solar greenhouses are essential facilities for agricultural production in northern China, where uneven internal environments pose significant challenges. This study established a numerical model of photothermal conditions in solar greenhouses. Utilizing COMSOL Multiphysics^TM, we established a microclimate model that encompasses the greenhouse exterior and the soil directly below it, without considering the crops. This model coupled multiphysical fields with fluid flow and heat transfer processes. The boundary conditions and initial values of the external environment and soil were derived from meteorological data and an efficient interpolation function method, with the time step updated every 1h. The results demonstrate that the simulated values were in good agreement with the measured values. Our findings reveal the temporal dynamics of radiation and temperature changes, as well as spatial heterogeneity, within solar greenhouses under different winter weather conditions. Additionally, the potential of integrating with other real-time monitoring and control models was discussed. This study provides a theoretical foundation for developing microclimate models and predicting photothermal environments in greenhouses.

1. Introduction

A solar greenhouse is an agricultural facility that harnesses solar energy for passive heating [1,2]. It captures solar radiation as a heat source, raising the temperature inside by storing energy in the walls and soil during the day. This stored energy is then released slowly at night [3,4,5]. As a result, solar greenhouses enable agricultural production in winter without additional heating. They have become vital facilities in temperate regions, particularly in northern China [6,7,8].

Despite their advantages, solar greenhouses face several challenges in actual production. Firstly, in northern China, for solar greenhouses without any artificial heating and cooling measures, the internal lighting and temperature conditions in spring and autumn can meet the growth needs of crops widely cultivated in solar greenhouses, such as tomatoes, cucumbers, peppers, watermelons, etc. In summer, due to the high internal temperature, the greenhouse is usually closed for confinement and crops are not planted. During winter, the differences between sunny and cloudy days lead to significant variations in light intensity and temperature within the greenhouse. On cloudy days, crops often suffer from insufficient light and low temperatures, threatening their growth. Many northern greenhouses do not employ artificial heating to conserve energy and minimize operational costs, which exposes crops to low temperatures during the winter months. Although sunny days provide adequate light and warmth for crop growth, cloudy days cause a sharp decline in both light intensity and temperature [9,10]. Prolonged periods of cloudy weather, rain, or snow can severely hinder crop development. The resulting low temperatures may stunt growth, trigger frost, and cause significant frostbite in vegetables, posing serious risks to their survival and potentially leading to substantial economic losses [11,12,13]. Secondly, the single-sided transparent structure of a solar greenhouse can result in uneven distribution of environmental factors, impacting crop yield and quality [14]. The greenhouse’s design features an arched front roof covered with plastic film on the south side for optimal light capture, while a thermal blanket covers this area at night during colder months [15]. The east, west, and north sides consist of solid or composite thick walls [16]. This design enhances lighting efficiency and insulation, providing necessary conditions for crop growth even during extremely cold winters [17,18]. However, the three walls of the greenhouse block some incident light, creating shadows within the space [19]. This results in an uneven distribution of light, according to Li et al.’s research [20], and the distribution of incident photosynthetically active radiation (PAR) in a solar greenhouse showed significant imbalance throughout the day, with the central and south sections receiving significantly higher levels of PAR than the north section. This uneven distribution of light would lead to corresponding microclimate heterogeneity inside the greenhouse. And such heterogeneity negatively impacts crop physiology by hindering transpiration and photosynthesis. This variability is a key factor in differences in yield and quality [21,22].

To tackle the issue of crop growth caused by greenhouse heterogeneity, precise control of environmental factors is essential. However, greenhouse environmental control technology in China is still relatively underdeveloped, leading to limited capability to regulate the indoor environment [23]. A major challenge in environmental control is to fully understand the spatial distribution characteristics of the microclimate in greenhouses. The microclimate distribution in a greenhouse is affected by external climatic conditions, greenhouse structure, and the optical and thermal properties of materials used. This complex system involves multiple heat and mass transfer mechanisms, including convection, radiation, and conduction [24,25]. The formation of the greenhouse microclimate involves heat transfer processes in the walls and soil. Additionally, it includes convective heat exchange between indoor and outdoor air via the greenhouse cover, as well as radiative heat exchange among the interior solid surfaces [26,27]. By conducting in-depth studies on gas flow mechanisms and heat transfer processes within the greenhouse, we can develop an accurate microclimate prediction model. This model will enable precise control over the crop-growing environment, ensuring that crops grow well in a uniform environment [28]. Improved conditions will enhance crop yield and quality while also laying the groundwork for the mechanization and standardization of agricultural production.

The methods for analyzing and predicting the microclimate in greenhouses include analytical, experimental, and numerical simulation techniques [29]. Among these, numerical simulation methods are increasingly favored in modern engineering and scientific research due to their low computational costs. They do not require additional test materials or equipment, and computer software can simulate various working conditions, making them flexible and controllable. In numerical simulation studies of solar greenhouses, CFD (Computational Fluid Dynamics) methods are often used to simulate the internal airflow field and temperature distribution. Using a combination of CFD and experimental methods, Wu et al. explored the impact of north and south roofs on the thermal environment of a solar greenhouse. The model considered the distribution of solar energy, energy transfer, three-dimensional heat flux distribution, and thermal characteristics of the enclosure structure (including walls and soil). The P-1 radiation model was used to calculate the heat transfer inside the greenhouse [30]. Xu et al. used Autodesk Simulation CFD to simulate the temperature field inside the wall for 24 h on different dates to determine the thickness of the wall’s thermal storage layer. The simulation used a 2D span direction greenhouse cross-section as the computational domain, taking into account the solar radiation, indoor humid air, and thermal characteristics of the enclosure structure under typical sunny conditions [31]. Yu et al. simulated the thermal environment of two consecutive solar greenhouses without considering the presence of greenhouse crops and ventilation conditions. The simulation used a discrete coordinate radiation (DO) model to simulate the instantaneous changes in solar radiation and combined measured parameters to simulate the three-dimensional transient thermal environment within 24 h in winter [32]. In the above CFD simulation cases, the simulated values and the measured values showed good agreement.

However, despite significant progress in revealing the temperature and airflow distribution characteristics of solar greenhouses, there is still a lack of in-depth exploration of radiation changes inside the greenhouse. Radiation, as the cornerstone of regulating changes in the internal environment of greenhouses, has a profound impact on the formation of temperature gradients and the photosynthetic efficiency of crops, among other core processes. Given this, it is particularly urgent to conduct more accurate and detailed simulations and optimizations of the photothermal environment in solar greenhouses. In this study, detailed numerical simulations were conducted on the radiation and temperature distribution inside solar greenhouses over time for different winter weather scenarios, and the numerical simulations were validated through experimental data. This study aims to provide a solid theoretical basis and technical support for precise environmental regulation and efficient crop growth in solar greenhouses.

2. Materials and Methods

2.1. Greenhouse Parameters

The experimental solar greenhouse is located in Qingdao City, Shandong Province (36.38° N, 120.45° E), as shown in Figure 1. Its dimensions are 100.00 m in length, 10.15 m in width, a ridge height of 3.85 m, and a back wall height of 3.28 m. The north wall and the east/west gable walls each have a thickness of 0.50 m. There are no interior pillars. The front roof is covered with PO-type plastic film, while the top is insulated. The insulation blanket is rolled up at 7:30 a.m. and fully laid down at 4:30 p.m. during winter. Inside the greenhouse, cucumber plants of the ’Tianjiao No.1’ variety were cultivated, with a planting date of 19 January 2023.

2.2. Environmental Measurements

In order to investigate the uniformity of the distribution of different environmental factors inside the solar greenhouse, we arranged uniform measuring points in both the east–west and north–south directions of the greenhouse. And given that cucumbers maintain a canopy height of about 1.5 m during most growth stages, this study focused on this height to explore internal environmental distribution. Specifically, we evenly arranged five measurement points in the north–south direction and three measurement points in the east–west direction, for a total of fifteen measurement points (P1 to P15), as shown in Figure 2. The cultivation area refers to the effective planting space on the greenhouse floor, excluding the northern aisle, non-cultivated areas on the east and west sides, and the southern corner. The air temperature was measured using type K thermocouples(Anxindun, Changshu, China) at points P1 to P15. Data for air temperature were collected automatically by CR1000 data logger (Campbell Scientific Inc, Logan, UT, USA). Additionally, global radiation was measured and automatically recorded at points P1 to P15 using HOBO MX2202 (Onset, Bourne, MA, USA). All measurements were taken every 10 min.

During the test period, meteorological data outside the greenhouse were obtained from the US National Center for Atmospheric Research (NCAR). This included a continuous 24 h observation record from 5 February 2023 to 10 February 2023. The specific dataset covered air temperature, soil temperature from the surface to 2 m below ground, and global radiation values at the experimental greenhouse location in Qingdao, Shandong Province. For this study, 8 and 9 February 2023 were selected as a typical sunny day and a typical cloudy day in winter, respectively.

2.3. The Numerical Method

COMSOL Multiphysics™ served as the simulation tool for this study. Developed by COMSOL AB in Sweden, COMSOL is a numerical simulation software that provides a highly integrated environment. It offers a rich set of predefined interfaces for various physical fields and coupled simulations of multiphysics problems [33], including electrical, mechanical, fluid power, and chemical engineering. It is based on the finite element method and simulates real physical phenomena by solving partial differential equations (single field) or partial differential equation systems (multi field). Compared to the commonly used CFD software in greenhouse simulations, this software allows users to define physical models using mathematical equations, making it more flexible and powerful in handling complex simulations of multiple coupled physical fields and more intuitive and convenient in customizing equations and boundary conditions.

2.3.1. Geometry Model and Meshes

The greenhouse and its surroundings were modeled using COMSOL’s internal geometry function. To ensure accurate simulation results while conserving computational resources, we increased the modeling area of the soil and external air below the greenhouse. The soil domain’s depth was set to 2 m, and the air domain’s height was set to 6 m. Since the experiment focused on cucumber seedlings, which are relatively short and have minimal effect on the greenhouse’s thermal environment, crops were not included in the model. The geometric model was created in a Cartesian coordinate system, with the intersection of the east hill wall, north wall, and ground level inside the solar greenhouse as the origin (0,0,0). The orientation of the solar greenhouse was as follows: $+\mathrm{x}\equiv \mathrm{S}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{h},+\mathrm{y}\equiv \mathrm{W}\mathrm{e}\mathrm{s}\mathrm{t},+\mathrm{z}\equiv \mathrm{Z}\mathrm{e}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{h}$ (Figure 3a).

After setting up the physical field, the model was meshed. The shape and accuracy of the mesh significantly influence the solution time and results of the simulation model. The physical field control grid provided by COMSOL was used, with a “more refined” size selected to enhance areas with larger variable gradients. The results are depicted in Figure 3b. The constructed grid consisted of 153,436 cells, with a grid volume of 7.216 × 1012 mm³. The minimum cell mass was 0.001275, the average cell mass was 0.6801, and the overall cell quality was assessed as good [34].

2.3.2. Material Parameters

The computational model consists of five materials: air, film, insulation blanket, walls, and soil, with their respective material properties detailed in Table 1. For the insulation blanket, the thermal expansion coefficient was set at 2.8 × 10⁻⁴ (1/K), the surface emissivity was 0.8, and the relative dielectric constant was 4. It is noteworthy that, while the density of soil was fixed at 1400 kg·m⁻³, numerous material properties related to heat transfer and fluid dynamics for both air and soil exhibited a significant dependence on temperature. In this study, the parameters for soil (thermal conductivity, heat capacity, and thermal diffusivity) and air (kinetic viscosity, density, and thermal conductivity) were defined to vary with temperature.

2.3.3. Numerical Calculation

The physical field interfaces for solving the model include solid and fluid heat transfer, surface-to-surface radiation, and turbulence.

The calculation domain for solid and fluid heat transfer includes the air inside and outside the greenhouse, the greenhouse structure, and the soil. The energy conservation equation is expressed as follows:

(1)$\mathsf{\rho }{\mathrm{C}}_{\mathrm{P}}{\displaystyle \frac{\partial \mathrm{T}}{\partial \mathrm{t}}}+\mathsf{\rho }{\mathrm{C}}_{\mathrm{P}}\mathrm{u}\nabla \mathrm{T}+\nabla \mathrm{q}=\mathrm{Q}+{\mathrm{Q}}_{\mathrm{t}\mathrm{e}\mathrm{d}}$

where $\mathsf{\rho }{\mathrm{C}}_{\mathrm{P}}{\displaystyle \frac{\partial \mathrm{T}}{\partial \mathrm{t}}}$ represents the energy storage for temperature changes over time; $\mathsf{\rho }{\mathrm{C}}_{\mathrm{P}}\mathrm{u}\nabla \mathrm{T}$ represents the heat convection; $\nabla \mathrm{q}$ is heat conduction; Q represents volumetric heat source; ${\mathrm{Q}}_{\mathrm{t}\mathrm{e}\mathrm{d}}$ represents other heat source terms, here mainly for radiation heat input in W·m⁻². $\mathsf{\rho }$ is density in kg·m⁻³; ${\mathrm{C}}_{\mathrm{P}}$ is the constant pressure heat capacity in J·K⁻¹·kg⁻¹; T is the temperature; t is time; u is fluid velocity; since the test is conducted in winter, the greenhouse vents are closed, so only natural convection is considered for the air, and there is no forced convection; q is the heat flux, calculated as follows:

(2)$\mathrm{q}=-\mathrm{k}\nabla \mathrm{T}$

where k is the thermal conductivity in W·m⁻¹·K⁻¹.

The default soil-external air vertical interface is treated as a thermally insulating boundary. Due to the film’s minimal thickness, its geometry would consume excessive computational resources. Therefore, it is simplified to a thin layer in the COMSOL heat transfer interface, represented as a 2D plane. The thickness parameter is included in the actual solution calculations. In the heat transfer model, the thermal resistance of the sheeting is greater than that of the air on both sides, indicating that the sheeting does not contribute to tangential heat flux transfer. Consequently, the temperature gradient in the direction of the sheeting layer is neglected. The thermal thickness approximation—a lumped formula that assumes heat transfer primarily occurs in the normal direction of the thin structure—is used to streamline calculations by focusing solely on heat transfer in the layer direction [35] while ignoring transfer in other directions.

The surface-to-surface radiation interface computational domain includes all solid components, such as the greenhouse structure and the soil. The governing Equations are as follows:

(3)${\mathrm{J}}_{\mathrm{i}}={\mathsf{\epsilon }}_{\mathrm{j}}{\mathrm{e}}_{\mathrm{b}}\left(\mathrm{T}\right){\mathrm{F}\mathrm{E}\mathrm{P}}_{\mathrm{j}}\left(\mathrm{T}\right)+{\mathsf{\rho }}_{\mathrm{d},\mathrm{j}}{\mathrm{G}}_{\mathrm{j}}$

(4)${\mathrm{G}}_{\mathrm{j}}={\mathrm{G}}_{\mathrm{m},\mathrm{j}}+{\mathrm{G}}_{\mathrm{a}\mathrm{m}\mathrm{b},\mathrm{j}}+{\mathrm{G}}_{\mathrm{e}\mathrm{x}\mathrm{t},\mathrm{j}}$

(5)${\mathrm{G}}_{\mathrm{a}\mathrm{m}\mathrm{b},\mathrm{j}}={\mathrm{F}}_{\mathrm{a}\mathrm{m}\mathrm{b},\mathrm{j}}{\mathsf{\epsilon }}_{\mathrm{a}\mathrm{m}\mathrm{b}}{\mathrm{e}}_{\mathrm{b}}\left({\mathrm{T}}_{\mathrm{a}\mathrm{m}\mathrm{b}}\right){\mathrm{F}\mathrm{E}\mathrm{P}}_{\mathrm{j}}\left({\mathrm{T}}_{\mathrm{a}\mathrm{m}\mathrm{b}}\right)$

(6)${\mathrm{e}}_{\mathrm{b}}\left(\mathrm{T}\right)={\mathrm{n}}^2\mathsf{\sigma }{\mathrm{T}}^4$

(7)${\mathrm{F}\mathrm{E}\mathrm{P}}_{\mathrm{j}}(\mathrm{T})={\displaystyle \frac{15}{{\mathsf{\pi }}^4}}{\int }_{{\mathrm{C}}_2\left({\mathsf{\lambda }}_{\mathrm{j}-1}\mathrm{T}\right)}^{{\mathrm{C}}_2/\left({\mathsf{\lambda }}_{\mathrm{j}}\mathrm{T}\right)}{\displaystyle \frac{{\mathrm{x}}^3}{1-{\mathrm{e}}^{\mathrm{x}}}}\mathrm{d}\mathrm{x}$

where ${\mathrm{J}}_{\mathrm{i}}$ is the radiant energy density of the ${\mathrm{J}}_{\mathrm{t}\mathrm{h}}$ surface; ${\mathsf{\epsilon }}_{\mathrm{j}}$ is the emissivity of the ${\mathrm{J}}_{\mathrm{t}\mathrm{h}}$ surface; ${\mathrm{e}}_{\mathrm{b}}\left(\mathrm{T}\right)$ is the black body radiant energy density; ${\mathrm{F}\mathrm{E}\mathrm{P}}_{\mathrm{j}}\left(\mathrm{T}\right)$ is the shape factor and spectral radiance function; ${\mathsf{\rho }}_{\mathrm{d},\mathrm{j}}$ is the diffuse reflectivity of the ${\mathrm{J}}_{\mathrm{t}\mathrm{h}}$ surface; ${\mathrm{G}}_{\mathrm{j}}$ is the total radiant energy density incident on the surface; ${\mathrm{G}}_{\mathrm{m},\mathrm{j}}$, ${\mathrm{G}}_{\mathrm{a}\mathrm{m}\mathrm{b},\mathrm{j}}$, and ${\mathrm{G}}_{\mathrm{e}\mathrm{x}\mathrm{t},\mathrm{j}}$ are the contribution to the surface j from mutual, ambient, and external radiation, respectively; ${\mathrm{F}}_{\mathrm{a}\mathrm{m}\mathrm{b}}$ is the ambient viewing angle factor; n is the refractive index; $\mathsf{\sigma }$ is the Stefan–Boltzmann constant with the value $5.6\times {10}^{-8}$ in W·m⁻²·k⁻¹; and $\mathsf{\lambda }$ is the vacuum wavelength in m. The radiation direction of the diffusely reflecting surface is controlled by opacity in the full frequency band, and the surface emissivity is custom set in each band, where the solar spectral band [0, 2.5 µm] is 0.8, and the ambient spectral band [2.5 µm, +∞] is 0.2.

In the turbulence interface, the realizable k-εmodel was selected [36]. The Navier–Stokes equations for fluid dynamics were solved using Reynolds averaged Navier–Stokes (RANS) [37]. This study integrates solid and fluid heat transfer, surface-to-surface radiation, and turbulence physical fields. Turbulence and heat transfer coupling apply to non-isothermal flow, while heat transfer and surface-to-surface radiation coupling pertain to radiative heat transfer. The non-isothermal flow considers density changes in the fluid, which result from temperature variations in the flow field. Heat transfer turbulence calculations employ the Kays–Crawford model, which improves the conventional RANS model’s prediction accuracy by adjusting for the Prandtl number. Standard thermal wall functions address temperature fields in proximity to solid walls, where fluid velocity and temperature profiles are described using logarithmic-like laws per boundary layer theory. Utilizing thermal wall functions simplifies boundary layer temperature calculations, focusing on the near-wall temperature gradient and heat flux. Since the flow in this study consists solely of air, heating causes changes in density and pressure, resulting in flow within the greenhouse. Forced convection is not considered, and the control equations are simplified using the Boussinesq assumption [38].

2.3.4. Boundary Conditions and Initial Values

To accurately simulate the greenhouse environment, we must establish the external soil and environmental boundary conditions, along with their initial values. Soil boundary conditions and initial values were derived from temperature data provided by the NCAR at various subsurface depths (0.1 m, 0.4 m, 1.0 m, and 2.0 m). This approach accounts for the variance of soil temperatures with depth and time. An interpolation function was developed in COMSOL software to generate a soil temperature curve based on the temperature data collected from these depths (Figure 4). This curve was then accurately incorporated into the simulation model as the initial temperature condition.

The environmental boundary condition pertains to the air temperature surrounding the greenhouse. We defined an interpolation function within the global parameters to plot the ambient temperature based on 24 h daily air temperature values. The initial greenhouse temperature was set according to the meteorological data recorded at that time.

Solar heat sources were incorporated using the ’external radiation sources’ feature in COMSOL. This feature allowed for directional radiation source inclusion with a view factor calculation, ensuring that only the external view factor was recalculated when the source position changed. Historical weather data, along with statistical data for the solar greenhouse location, was inputted into the Environmental Conditions of the Shared Properties based on the 2023 ASHRAE Handbook Climate Zone Data and Typical Annual Weather files from the American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE). Latitude and longitude coordinates, time zones, and dates were specified in the External Radiation Sources node, which the solver updated automatically over time. The solar irradiance was determined using the solar radiation values for the day of the test. The full range of the radiation direction from the surface-to-surface interface was diffused and controlled based on opacity.

2.3.5. Solver Settings

The simulation software used in this study was COMSOL Multiphysics™ 6.2. All calculations were conducted on a system with 4 Intel(R) Xeon(R) CPU E5-2697A v4 processors (Intel Corporation, Santa Clara, CA, USA)running at 2.60 GHz and 32 cores in total (WIN-I7TFE9MKHUQ), with an available memory of 65.41 GB. The physical variables for the solution were categorized into radiance and combined variables (velocity field, pressure, temperature, external temperature) to address different time scales and properties. For radiance solutions, the PARDISO solver (a direct sparse matrix method) processed the sparse linear system derived from the radiative heat transfer equations, which included a complex radiation exchange matrix. This approach allows for more accurate and efficient predictions of thermal radiation effects. The non-isothermal flow was resolved using the Generalized Minimal Residual (GMRES) method. The transient study commenced at 0 h and concluded at 48 h, with a step size of 10 min and tolerance controlled by the physical field.

2.3.6. Validation Method

In order to verify the validity of the simulation, the root mean squared error (RMSE) was chosen for evaluation.

(8)$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}\times \sum _{\mathrm{i}=1}^{\mathrm{n}}{({\mathrm{y}}_{\mathrm{i}}-\widehat{{\mathrm{y}}_{\mathrm{i}}})}^2}$

where ${\mathrm{y}}_{\mathrm{i}}$, $\widehat{{\mathrm{y}}_{\mathrm{i}}}$ denote the measured data and the simulated data, respectively, and n is the number of samples.

3. Results and Discussion

3.1. Model Validation

For validation, a typical sunny day (8 February 2023) and a typical cloudy day (9 February 2023) during the cucumber cultivation period were selected to compare the measured and simulated radiation and temperature values across various time periods (P1-P15) in the solar greenhouse. According to Table 2, the radiation verification results indicated that the average RMSE for sunny conditions was 37.5 W·m⁻², while it was 28.9 W·m⁻² under cloudy conditions throughout the day. Notably, the highest error occurred near noon when the radiation intensity peaked. As for temperature, the RMSE values were 2.2 °C for the sunny day and 0.7 °C for the cloudy day. On the sunny day, the highest error of 4.4 °C appeared in the morning when the temperature inside the greenhouse rose rapidly. Conversely, errors remained relatively low throughout the day on the cloudy day.

3.2. Radiation Analysis

3.2.1. Time-Dependent Radiation

Figure 5 illustrates the simulation results of radiation on the sunny day (Figure 5a) and cloudy day (Figure 5b) within the solar greenhouse at a 1.5 m elevation. On the sunny day, radiation was first detected around 7:30 a.m., when the thermal blanket was retracted. It then increased steadily, peaking at 12:30 p.m. with a maximum value of 487.3 W∙m⁻², before declining until it reached zero at 5:30 p.m. In contrast, on the cloudy day, radiation levels inside were lower and exhibit significant fluctuations. From 10 a.m. to 1 p.m., solar radiation varied considerably due to weather conditions, peaking at 10 a.m. with a value of 157.9 W∙m⁻². By 12 p.m., this value dropped to 116.8 W∙m⁻², reaching a minimum of 93.7 W∙m⁻² after noon. Subsequently, radiation rose again, peaking at 170.2 W∙m⁻² at 1 p.m., before declining until the insulation was fully lowered.

We compared the radiation values inside the greenhouse with those outside. The radiation value inside the greenhouse was notably lower than that outside, and the variation trends inside and outside remained consistent, irrespective of weather conditions. On the sunny day, the maximum difference between the inside and outside was 65.2 W∙m⁻² near noon. On the cloudy day, the difference was significant in the morning and afternoon, hovering around 80.9 W∙m⁻², whereas during midday, the difference was relatively minor, within 45.6 W∙m⁻².

3.2.2. Radiation Distribution Inside Greenhouse

To examine radiation variability within the solar greenhouse, three side probes were installed at a 1.5 m ground level inside greenhouse model, oriented east–west. This setup enabled the analysis of radiation distribution across the plane. Figure 6 shows the radiation distribution at various times on the sunny day, with horizontal coordinates representing the distance from the west wall. On the sunny day, the radiation distribution consistently decreased from south to north throughout the day. The southern and central areas exhibit similar radiation values, while the northern area, affected by the rolled-up insulation, received significantly less radiation. To quantify this discrepancy, the “north–south difference” was defined as the maximum radiation difference between the southern and northern areas. The maximum-recorded difference of 56.8 W∙m⁻² occurred at 10 a.m. At 8 a.m., sunlight entered primarily from the east, with the east wall casting a shadow, leading to lower radiation values near the wall. By 4 p.m., sunlight approached the greenhouse diagonally from the west, with the west wall serving as a shield and further reducing radiation values in adjacent areas.

On cloudy days, solar radiation levels are generally lower and exhibit a higher proportion of scattered radiation compared to clear days [39]. Although planar radiation shows some variability during these cloudy periods, this variability is not as significant as that observed on a clear day. The radiation distribution on cloudy days resembles that on clear days, decreasing from south to north (as shown in Figure 7). Notably, the maximum difference in radiation in the north–south direction occurred at 2 p.m., with a difference of 6.2 W∙m⁻². By 4 p.m., specific areas in the southern part of the country were shaded by equipment inside the greenhouse, leading to relatively low radiation values. In contrast, unobstructed locations in the south showed higher radiation, resulting in an increased difference of 6.4 W∙m⁻² compared to the northern region.

To evaluate the uniformity of planar environmental factors, we calculated their variation coefficient at different time periods, which is defined as the ratio of standard deviation to mean. A large variation coefficient means a worse uniformity. As mentioned above, the difference in radiation in different areas was more significant on sunny days compared to cloudy days. However, from Table 3, we can see that the value of the variation coefficient is higher on the cloudy day. This phenomenon is related to the lower values of radiation throughout the cloudy day.

Solar radiation and temperature are critical for cucumber growth and development. In greenhouse production, optimal conditions vary for light-loving crops like tomatoes and cucumbers. There is no upper limit to optimal radiation intensity; stronger solar radiation leads to enhanced photosynthesis and increased yields [40,41]. In practice, on sunny days, it is advisable to supplement light in shaded areas during morning and evening hours, as well as in the central and northern parts of the greenhouse throughout the day, using artificial sources like high-pressure sodium lamps and LEDs. On cloudy days, it is essential to provide light based on the varying conditions throughout the day.

3.3. Temperature Analysis

3.3.1. Time-Dependent Temperature

Figure 8 illustrates the average temperature change inside the solar greenhouse throughout the day under varying weather conditions. On sunny days, the temperature gradually decreased from 14.1 °C at midnight to 12.0 °C by sunrise. After 7 a.m., temperatures began to rise due to increasing outdoor temperatures and solar radiation entering the greenhouse, reaching a peak of 30.4 °C at 2 p.m. After this peak, the temperature started to decline, with a slower cooling trend post-sunset around 5 p.m. Conversely, on cloudy days, the temperature dropped more rapidly after midnight and began to rise after sunrise. It increased steadily from 10 a.m. to 1 p.m., achieving a maximum of 18.0 °C, before falling to a minimum of 13.8 °C. The temperature then gradually recovered after covering the greenhouse with an insulation blanket.

In both weather conditions, the inside temperature consistently surpassed the outside temperature. During nighttime, irrespective of whether it was sunny or cloudy, the temperature differential between indoors and outdoors ranged from approximately 10.4 °C to 17.7 °C. During the daytime, however, the temperature disparity was more accentuated on sunny days, reaching a maximum of nearly 27 °C at noon. Conversely, on cloudy days, the largest temperature difference observed during the day was around 13.5 °C, occurring close to noon.

3.3.2. Temperature Distribution Inside Greenhouse

The temperature distribution in the greenhouse is primarily influenced by solar radiation patterns, thermal radiation from the ground and walls, and convective heat transfer between indoor and outdoor environments. To investigate temperature variability within the solar greenhouse, the area was divided into three regions: south, center, and north. The temperature distribution was measured using domain point probes inside the greenhouse model. Figure 9 illustrates the temperature distribution on a sunny day, characterized by notable differences in both east–west and north–south orientations. Throughout the day, temperature disparities between the east and west sides were more pronounced than those between the north and south. In the morning, at 8 a.m., low solar radiation led to significant heat loss through the front roof membrane on the south side. Meanwhile, the north wall, being relatively well insulated, allowed for accumulated heat to transfer indoors as thermal radiation and convection. Consequently, the temperature distribution from north to south exhibited a decline, with a maximum temperature difference of 0.6 °C. From 10 a.m. to 2 p.m., the intensity of solar radiation increased, further affecting temperatures. Areas receiving high radiation experienced higher temperatures, leading to a gradual rise in temperatures from north to south. In the east–west orientation, the east side recorded significantly higher temperatures than the west side due to morning sunlight primarily illuminating the eastern portion of the greenhouse. At 10 a.m., 12 p.m., and 2 p.m., the north–south temperature differences were 0.7 °C, 0.9 °C, and 0.8 °C, respectively. In contrast, the east–west temperature differences were notably larger, measuring 1.0 °C, 3.1 °C, and 8.2 °C, respectively. By 4 p.m., with the sun moving westward, temperatures on the west side of the greenhouse began to exceed those on the east side. The north–south temperature distribution in the east and west regions also showed distinct patterns: the west side peaked in the center, with lower temperatures to the north and the lowest to the south. Conversely, the east side exhibited a gradual decrease from south to north.

Figure 10 illustrates the temperature distribution inside the greenhouse at different time points under cloudy conditions. On cloudy days, the radiation intensity inside the greenhouse is lower and more uniformly distributed compared to sunny days, resulting in smaller temperature differences across the plane. The temperature distribution in the north–south direction exhibited a clear pattern of change over time, primarily influenced by several factors, including solar radiation, convective heat transfer from the front roof, and thermal radiation from the walls. At 8 a.m., the highest temperature was recorded in the northern region, followed by the central region, while the southern region had relatively low temperatures. By noon (12 p.m.), this pattern reversed, with the southern region recording the highest temperature, followed by the central region, and the northern region experiencing the lowest temperature. The temperature differences between the east–west and north–south directions peaked at 12 p.m., measuring 1.1 °C and 1.1 °C, respectively. By the evening (4 p.m.), the central region had the highest temperature again, followed by the northern region, while the southern region remained the coolest. Additionally, it is noteworthy that the dominant wind direction that day was easterly. This meteorological condition influenced the temperature distribution inside the greenhouse, as evidenced by the relatively low temperatures near the east mountain wall. The cold air brought by the easterly wind contributed to a more pronounced cooling effect in that area.

According to Table 4, the uniformity of temperature was the worst at the moment close to noon on sunny days, which coincides with the large differences in temperature values in different regions at this time of the day, as mentioned above. In addition, comparing the variation coefficient of all-day temperatures on sunny and cloudy days, we find that it is generally higher on sunny days, which represents a greater heterogeneity of temperature on sunny days.

The ideal temperature for cucumber varies during different growth stages. In this study, cucumbers are in the seedling stage. The three key temperature points for cucumber growth are as follows: the lower developmental temperature is 13 °C, the optimum lower temperature is 28 °C, the optimum upper temperature is 32 °C, and the upper temperature limit is 40 °C [42]. On sunny days, temperature within the greenhouse is generally suitable for cucumber growth, except during midday hours when it tends to be higher. Throughout the cloudy day, temperatures generally fall below the optimum lower limit for cucumber seedlings but remain above the lowest developmental threshold. Therefore, heating should be applied during daylight hours according to the temperature distribution. For local heating, methods such as hot air heating or localized hot water heating are recommended.

3.4. Model Feasibility Analysis and Future Application

3.4.1. Feasibility Analysis

The model developed in this study demonstrates high overall accuracy in simulating radiation and temperature, though further refinements are needed. The simulated radiation data were generally higher than the measured data throughout most of the day, with the largest discrepancies noted between noon and the afternoon. Specific conditions during this period warrant further investigation to enhance the model’s accuracy by refining parameters such as cloud cover, atmospheric conditions, and optical properties within the greenhouse. In temperature simulations, the trends in simulated and measured data were generally consistent. However, the simulated values were notably higher than the measured values at certain times, particularly during the peak temperature. This discrepancy may stem from the simulation algorithm’s sensitivity to certain environmental factors or biases in the simulation environment settings. Future simulations should consider factors such as the heat transfer properties of greenhouse covering materials, variations in external climatic conditions, and plant transpiration inside the greenhouse.

3.4.2. Future Application

The microclimate model employed in this study has significantly improved the accuracy of the model compared to previous simulation studies by using a transient simulation with a 1 h time step. In the future, we can learn from the virtual sensor modeling strategy established by Cheng et al.: this strategy constructed an external ambient temperature model through regression analysis, used real-time-generated UDF files of external environmental variables as input information to the controller, and dynamically adjusted these inputs with the closed-loop control system of ANSYS Fluent 19.0 to achieve efficient real-time monitoring of the environmental distribution of the greenhouse interior space [43]. In addition, the microclimate model has the potential to be integrated with the control system to automate the management of the greenhouse internal environment. As Chalill et al. demonstrated in their study: weather data were used as an external environmental data source, while monitoring points were arranged to collect environmental data inside the greenhouse. These data were monitored in real time and transmitted to a fully automated climate management system, and these data were then fed into ANSYS FLUENT for simulation and analysis. Based on the results of the simulation, the environmental distribution results were fed back to the air-conditioning system and other environmental control facilities [44].

In summary, in future studies, we will take more factors into account, such as crop species and greenhouse materials, and combine weather data with regression analysis to construct a more accurate model of external environmental factors, which will be input into the microclimate model in real time. By comparing the simulation results with the environmental conditions that different crop varieties and growth stages require, we will provide automatic feedback and utilize environmental control systems (such as cooling, supplemental light, and heating system) to carry out precise environmental control in order to optimize the growing environment of the crops.

4. Conclusions

In this study, a physical model was developed to analyze flow and heat transfer in a solar greenhouse located in Qingdao City, Shandong Province. COMSOL Multiphysics^TM was utilized to simulate changes in plane temperature and radiation over time, as well as their distribution during typical winter weather. The simulated values were compared to the measured data, revealing a maximum RMSE for radiation and temperature of 64.4 W·m⁻² and 4.4 °C, respectively. Overall, the simulated values closely matched the measured data, indicating a successful simulation. The simulation results show that, on sunny winter days, radiation intensity and temperature were maintained within the ideal range required for cucumber growth for most of the day. In contrast, throughout the cloudy day, the intensity of radiation was lower, while the temperature was also below the optimal lower temperature limit for cucumber growth. The spatial heterogeneity of the photothermal environment inside a solar greenhouse was strong. Regardless of weather conditions, radiation distribution was higher in the south, followed by the center, and lowest in the north. The difference was more pronounced on sunny days. Temperature differences within the greenhouse also varied significantly over time, with larger variations observed on sunny days compared to cloudy days, particularly in the east–west direction. In future research, it is completely feasible to achieve real-time monitoring of spatial environmental parameters and conduct feedback control of environmental control systems based on this.

Author Contributions

Conceptualization, X.L., Y.Y. and H.L.; methodology, H.L.; software, F.M.; validation, Z.Y. and Y.S.; data curation, H.L. and F.M.; writing—original draft preparation, F.M.; writing—review and editing, H.L.; supervision, X.L. and Y.Y.; funding acquisition, X.L. and S.T. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Data Availability Statement

The data presented in this study are available in the article.

Conflicts of Interest

Author Subo Tian was employed by the company Shandong Shouguang Vegetable Industry Group Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Photo of solar greenhouse in Qingdao City, Shandong Province.

Figure 2. Layout plan of the environmental measurement points.

Figure 3. Schematic of 3D model (a) and mesh (b) of solar greenhouse.

Figure 4. Soil temperature change with depth.

Figure 5. Radiation change in solar greenhouse plane in different weather: (a) sunny day; (b) cloudy day.

Figure 6. Radiation distribution in different periods on the sunny day.

Figure 7. Radiation distribution in different periods on the cloudy day.

Figure 8. Temperature change in solar greenhouse plane in different weathers: (a) sunny day; (b) cloudy day.

Figure 9. Temperature distribution in different periods on sunny days.

Figure 10. Temperature distribution in different periods on cloudy days.

Table 1

Material parameters.

Material Properties	Film	Insulation Blanket	Walls
Density (kg·m−3)	900	200	2000
Thermal conductivity (W·m−1·K−1)	1.38	0.26	0.5
Constant pressure heat capacity (J·kg−1·K−1)	703	1700	900

Table 2

RMSE value of radiation and temperature simulation in the solar greenhouse.

Forecast Time	Radiation (W·m−2)		Temperature (°C)
	Sunny Day	Cloudy Day	Sunny Day	Cloudy Day
6:00–8:00	10.9	27.2	1.2	0.3
8:00–10:00	33.3	30.6	4.4	0.4
10:00–12:00	64.3	32.7	0.8	1.0
12:00–14:00	51.9	47.3	2.0	0.8
14:00–16:00	27.0	6.6	2.7	0.8

Table 3

Variation coefficient of radiation at different time periods (%).

	8:00	10:00	12:00	14:00	16:00
Sunny day	11.79	8.59	9.68	8.88	10.49
Cloudy day	15.75	10.92	10.79	11.47	12.83

Table 4

Variation coefficient of temperature at different time periods (%).

	8:00	10:00	12:00	14:00	16:00
Sunny day	2.10	5.01	9.49	5.74	1.79
Cloudy day	1.95	1.27	1.23	1.26	1.42

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