A Numerical Method for Solving Global Irradiance on the Facades of Building Stocks
Abstract
:1. Introduction
2. Radiation Scheme
2.1. Analysis of the Radiant Energy Balance on the Building Surface
2.2. Solar Direct Irradiance on the Facades of Building Stocks
2.2.1. Calculation of the Solar Orientation
2.2.2. Judgment of Occlusion
2.3. Sky Diffuse Irradiance on the Facades of Building Stocks
2.3.1. Determination of the Discrete Precision of the Sky Vault
2.3.2. Determination of the Sky Diffuse Radiation Distribution Algorithm
2.4. Reflected Irradiance on the Facades of Building Stocks
3. Numerical Solution of the Radiation Scheme
3.1. Surface Discretization
3.2. Matrix of Each Component of the Global Irradiance
3.3. Numerical Equation for the Global Irradiance Value of the Building Facades
4. Results and Discussion
4.1. Comparison between the New Sky Diffuse Irradiance Algorithm and the Existing Algorithm
4.2. Comparison between the New Reflection Irradiance Algorithm and the Existing Algorithm
5. Conclusions
- (1)
- A model for irradiance on the facade of building stocks (IFBS Model) was constructed, based on the characteristics of the uneven surface radiation, narrow surface sky view, and the multiple reflected radiation processes of the building groups. The equation of the global irradiance value matrix is obtained. The model is based on the analysis of the radiation energy balance of the building surface after discretization, and the numerical expression of the influence of the building complex on the radiation transfer process is perfected.
- (2)
- In calculating the sky diffuse irradiance in a narrow surface sky view, the traditional solution of the sky diffuse irradiance can be improved by ascending the sky lattice discretization precision and applying a more accurate sky diffuse radiation model. It is suggested to replace the traditional Perez model with the Igawa model for the radiation intensity distribution rendering.
- (3)
- Compared with the infinite reflection algorithm, the existing mainstream one-time reflection algorithm has a significant error, especially on the surface where the radiation can reach only after multiple reflections. Such an error increases with the increase of the floor area ratio and the reflectivity of the building complex. It is recommended to use the infinite reflection algorithm, based on the net radiation analysis method in simulating the reflection irradiance of building facades. When the calculation resources are limited, the maximum error can be maintained within 5% by applying the four-time reflection algorithm.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Numerical Solution of the Reflection Irradiance Matrix
References
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Model or Software * | Reflection Irradiance | Sky Diffuse Irradiance |
---|---|---|
Urban Canyon Model [11] | 1 time reflection | isotropic |
ENVI-met * | 1 time reflection | isotropic |
Town Energy Balance (TEB) [12] | Infinite reflection | isotropic |
Temperature of Urban Facets in 3D (TUF-3D) [8] | Simplified multiple reflection | isotropic |
Model for Urban Surface Temperature (MUST) [13] | Simplified multiple reflection | isotropic |
DeST * | 1 time reflection | isotropic |
Fluent * + Solene * | 1 time reflection | Perez model |
TEB + EnergyPlus * | Infinite reflection | isotropic |
Citysim * | 1 time reflection | Perez model |
INSEL * + ISO model | 1 time reflection | Direct dispersion separation model |
UMI * | Simplified multiple reflection | Perez model |
Urban Energy Performance Calculator [14] | 1 time reflection | isotropic |
1 Time of Reflection | 2 X 1 | 3 X 1 | 4 X 1 | 5 X 1 | 6 X 1 | 7 X 1 | 8 X 1 | 9 X 1 | 10 X 1 | Infinite Reflections |
---|---|---|---|---|---|---|---|---|---|---|
16.4 | 28.4 | 44.0 | 64.5 | 73.8 | 91.7 | 110.9 | 128.4 | 154.9 | 167.1 | 54.2 |
Number of Reflections | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
average error (%) | −27.63 | −3.47 | −1.00 | −0.25 | −0.07 | −0.02 | −0.01 | 0.00 | 0.00 | 0.00 |
standard deviation (%) | 16.91 | 3.09 | 1.07 | 0.32 | 0.10 | 0.03 | 0.01 | 0.00 | 0.00 | 0.00 |
maximum error (%) | −60.21 | −23.47 | −8.52 | −2.82 | −0.90 | −0.28 | −0.08 | −0.03 | −0.01 | 0.00 |
25% quantile | −42.11 | −4.06 | −1.37 | −0.29 | −0.09 | −0.02 | −0.01 | 0.00 | 0.00 | 0.00 |
50% quantile | −23.40 | −2.36 | −0.62 | −0.14 | −0.04 | −0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
75% quantile | −13.54 | −1.68 | −0.33 | −0.08 | −0.02 | −0.01 | 0.00 | 0.00 | 0.00 | 0.00 |
Plot Ratio | 1 X 1 | 2 X 1 | 3 X 1 | 4 X 1 | 5 X 1 | 6 X 1 | 7 X 1 | 8 X 1 | 9 X 1 | 10 X 1 |
---|---|---|---|---|---|---|---|---|---|---|
0.25 | −16.74 | −1.52 | −0.25 | −0.04 | −0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
0.75 | −20.49 | −1.95 | −0.41 | −0.07 | −0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
1.25 | −22.30 | −1.98 | −0.44 | −0.08 | −0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
1.75 | −23.33 | −1.94 | −0.44 | −0.08 | −0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
2.25 | −24.00 | −1.89 | −0.43 | −0.08 | −0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
2.75 | −24.28 | −1.88 | −0.43 | −0.08 | −0.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
Plot Ratio | 1 X 1 | 2 X 1 | 3 X 1 | 4 X 1 | 5 X 1 | 6 X 1 | 7 X 1 | 8 X 1 | 9 X 1 | 10 X 1 |
---|---|---|---|---|---|---|---|---|---|---|
0.25 | −46.39 | −5.05 | −1.01 | −0.16 | −0.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
0.75 | −50.00 | −11.00 | −3.03 | −0.64 | −0.15 | −0.03 | −0.01 | 0.00 | 0.00 | 0.00 |
1.25 | −52.36 | −14.72 | −4.05 | −1.01 | −0.24 | −0.06 | −0.01 | 0.00 | 0.00 | 0.00 |
1.75 | −55.41 | −16.48 | −4.62 | −1.20 | −0.30 | −0.07 | −0.02 | 0.00 | 0.00 | 0.00 |
2.25 | −57.58 | −17.25 | −4.88 | −1.29 | −0.32 | −0.08 | −0.02 | 0.00 | 0.00 | 0.00 |
2.75 | −58.48 | −17.81 | −5.02 | −1.34 | −0.33 | −0.08 | −0.02 | 0.00 | 0.00 | 0.00 |
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Xing, H.; Yang, Y.; Chen, S. A Numerical Method for Solving Global Irradiance on the Facades of Building Stocks. Buildings 2022, 12, 1914. https://doi.org/10.3390/buildings12111914
Xing H, Yang Y, Chen S. A Numerical Method for Solving Global Irradiance on the Facades of Building Stocks. Buildings. 2022; 12(11):1914. https://doi.org/10.3390/buildings12111914
Chicago/Turabian StyleXing, Haowei, Yi Yang, and Shuqin Chen. 2022. "A Numerical Method for Solving Global Irradiance on the Facades of Building Stocks" Buildings 12, no. 11: 1914. https://doi.org/10.3390/buildings12111914