Abstract:
For passive Chinese solar greenhouses (CSGs), solar radiation serves as the primary internal energy source for winter production. 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, accurately predicting these shading effects is critical for optimizing the thermal environment and energy efficiency of CSGs. This study established a comprehensive dynamic analytical model for the shadow area of direct solar radiation in CSGs. The model incorporates structural parameters (span, ridge height, length, azimuth), geographical factors (latitude, longitude), temporal variables (solar altitude, solar azimuth), and crop canopy height to simulate the dynamic evolution of shadow areas. It quantitatively characterizes the synergistic shading effects between the gable wall geometry and the dynamically changing crop canopy on key heat storage surfaces, specifically the ground and north wall. A key innovation of this study is the derivation of physical analytical solutions for the shadow boundaries of curved gable surfaces, thereby revealing the precise mechanism of shadow superposition. To balance calculation accuracy with computational efficiency, the model employs geometric simplification strategies: the shadow of the gable wall on the ground is approximated as a triangle, while its shadow on the north wall is approximated as a trapezoid. Additionally, the crop population is modeled as a homogeneous rectangular prism based on average canopy height. The theoretical results were rigorously cross-validated against both field measured data and simulations from the commercial software SketchUp. The experimental CSG is 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 is 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 for 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. For crop shadows, the calculated values on the rear aisle matched the measured values perfectly, while the average relative error on the north wall was 1.6%. Comparisons between the theoretical calculations and SketchUp simulations showed that the maximum relative errors for gable wall shadows were 5.3% (ground) and 6.1% (north wall), with average relative errors of 2.3% and 5.2%, respectively. The theoretical calculations for crop shadows on the rear aisle were consistent with the software simulations. The study also outlines future research directions, including incorporating north roof shading, improving boundary precision via high-precision 3D scanning or image recognition, and employing numerical integration methods to balance computational efficiency with accuracy. In conclusion, this study overcomes the inherent limitations of discrete numerical simulations by providing a deterministic mathematical solution. The proposed model not only improves computational efficiency through valid geometric simplifications but also offers a robust theoretical tool for the precise quantification of solar energy acquisition. These findings provide critical reference data for the rational arrangement of solar energy utilization facilities and the optimization of greenhouse structural designs to maximize thermal performance.