Modeling direct solar radiation shadows in Chinese solar greenhouses

Solar radiation can serve as the primary internal energy source for the winter production in the passive Chinese solar greenhouses (CSGs). The acquisition and storage of solar energy are significantly influenced by the complex, dynamic shadows cast by the greenhouse envelope (particularly the gable walls) and the growing crops inside. Therefore, it is often required to accurately predict these shadings for the thermal environment and energy efficiency of the CSGs. In this study, a dynamic analytical model was established for the shadow area of the direct solar radiation in CSGs. The dynamic evolution of the shadow areas was determined to incorporate the structural parameters (span, ridge height, length, and azimuth), geographical factors (latitude and longitude), temporal variables (solar altitude and solar azimuth), and crop canopy height. A systematic investigation was implemented to quantitatively characterize the synergistic shading between the gable wall geometry and the dynamically changing crop canopy on the key heat storage surfaces, specifically the ground and north wall. The physical analytical solutions were derived for the shadow boundaries of the curved gable surfaces, thereby revealing the precise mechanism of the shadow superposition. The geometric simplification was employed to balance the computational accuracy and efficiency. Among them, the shadow of the gable wall on the ground was approximated as a triangle, while its shadow on the north wall was approximated as a trapezoid. Additionally, the crop population was assumed to be a homogeneous rectangular prism, according to the average canopy height. Both field-measured data and simulations were selected to validate the theoretical derivation using the commercial software SketchUp. The experimental CSG was 60 m in length, 10.3 m in width, and 5 m in ridge height, with a north wall height of 3.2 m and an azimuth of 5° west of south. The south roof curve of the greenhouse was composed of two tangent arcs. Observation experiments on the gable wall and crop shadow were conducted on December 18, 2023, and December 11, 2024, from 09:00 to 12:00, respectively. Results indicated that in the gable wall shadow, the average relative errors between calculated and measured values were 0.3% on the ground and 6.8% on the north wall. In crop shadows, the calculation on the rear aisle perfectly matched the measurement. The average relative error on the north wall was 1.6%. A comparison was made between the theoretical derivation and SketchUp simulation. The maximum relative errors for the gable wall shadows were 5.3% (ground) and 6.1% (north wall), with the average relative errors of 2.3% and 5.2%, respectively. The theoretical derivation for the crop shadows on the rear aisle was consistent with the software simulations. The future research directions were also outlined, including the north roof shading incorporation, boundary precision via high-precision 3D scanning or image recognition, and numerical integration to balance the computational efficiency with the accuracy. In conclusion, the discrete numerical simulations provided the mathematical solution. The computational efficiency was improved after the geometric simplifications. A robust theoretical tool was offered for the precise quantification of solar energy acquisition. These findings can also provide the reference data for the solar energy utilization facilities and the greenhouse structural optimization for thermal performance.