# Numerical Study of Micro-Thermal Environment in Block Based on Porous Media Model

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Models and Methods

#### 2.1. Macroscopic Turbulence Model

#### 2.2. Parameterization of Buildings as Porous Media

#### 2.3. Physical Model

#### 2.4. Boundary Conditions and Simulation Settings

_{zef}is the average wind speed of incoming flow at the height of Z

_{ref}; u

_{in}is the average wind speed at Z

_{in}at any height, α is the ground roughness coefficient, which is taken as 0.22 in the urban center according to China’s specifications.

^{−5}. The convection term and the diffusion term were simulated by the second-order upwind style, which had higher accuracy and slower convergence speed. After several attempts, the under-relaxation factor for speed and pressure was set to 0.5 and the other factor below 0.5.

## 3. Actual Measurement Verification

#### 3.1. Measured Plan

#### 3.2. Comparison of Measured and Simulated Results

## 4. Discussion

#### 4.1. Comparison between Porous Media Modeling Method and Standard Modeling Method

#### 4.1.1. Comparative Analysis of Calculation Results

#### 4.1.2. Comparative Analysis of Computational Cost

#### 4.2. Effect of Porous Media Parameters on Micro-Thermal Environment

#### 4.3. Influence of Anthropogenic Heat on Micro-Thermal Environment

^{2}were selected in this study to investigate the effects of anthropogenic heat intensity on the microthermal environment of the block. They represent non-anthropogenic heat emission, anthropogenic heat intensity in other cities, anthropogenic heat intensity in the study area, and anthropogenic heat intensity in the central city of Nanjing, respectively. Figure 14 shows the effect of anthropogenic heat on the block at different heights.

## 5. Conclusions

- (1)
- The actual measurement shows that both the porous media method and the standard model method can accurately characterize the overall regional ventilation capacity of the building complex. The wind speed and temperature of each area in the block with different simulation methods have a similar distribution. Porous media also improves the efficiency of modeling and calculation. The porous media model method reduces the number of meshes by about 15.3% compared with the traditional method, and the calculation rate is about 70.8% faster than the traditional method.
- (2)
- As an essential parameter of porous media, porosity, reflects the density of the building layout in the block. From the building ground to the average height of the block, the wind speed is positively correlated with the porosity change, and the temperature is negatively correlated with the porosity change. Above the block height, say 50 m, the wind speed is still affected by the porosity due to airflow disturbances over the block edge, but the temperature is hardly affected by the porosity at this height.
- (3)
- The anthropogenic heat emission is one of the critical factors leading to increased temperature in the block. The intensity of anthropogenic heat has little effect on the wind speed of the block, but the regional temperature at the same height increases linearly with the intensity of anthropogenic heat. The change gradient is about 0.025 K/W.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${u}_{i}^{f}$ | intrinsic averages of time-averaged velocity components (m·s^{−1}) |

${x}_{i}$ | Cartesian coordinates |

$T$ | temperature (°C) |

${p}^{f}$ | intrinsic averages of time-averaged pressure (Pa) |

${k}^{f}$ | intrinsic averages of time-averaged turbulent kinetic energy (m^{2}·s^{−2}) |

${J}_{1}$ | viscosity ratio |

k | von Karman’s constant, 0.4 |

${Q}^{f}$ | intrinsic averages of time-averaged velocity (m·s^{−1}) |

${C}_{\mu}$ | constant value: 0.09 |

K | permeability (m^{2}) |

${C}_{F}$ | Forchheimer coefficient |

${d}_{p}$ | characteristic size of the solid particles (m) |

$U$ | volume of the porous media (m^{3}) |

$V$ | volume of the block (m^{3}) |

${h}_{i}$ | height of each building (m) |

${S}_{i}$ | floor area of each building (m^{2}) |

$S$ | area of the block (m^{2}) |

$H$ | height of the block (m) |

u | average wind speed (m/s) |

z | height (m) |

${R}^{2}$ | coefficient of determination |

${y}_{i}$ | measured value |

$\overline{y}$ | mean measured value |

$\widehat{{y}_{i}}$ | simulation value |

Greek symbols | |

$\varphi $ | porosity |

$\rho $ | density (kg·m^{−3}) |

$\beta $ | thermal expansion coefficient (K^{−1}) |

${\mu}_{l}$ | dynamic viscosities (kg·m^{−1}·s^{−2}) |

${\mu}_{t}$ | turbulent viscosities (kg·m^{−1}·s^{−2}) |

${\delta}_{ij}$ | Kronecker delta operator |

${\epsilon}^{f}$ | intrinsic averages of time-averaged dissipation (m^{2}·s^{−3}) |

α | ground roughness coefficient |

$\u0138$ | turbulent kinetic energy (m^{2}·s^{−2}) |

$\epsilon $ | $\mathrm{dissipation}\mathrm{of}\u0138$ (m^{2}·s^{−3}) |

$\varphi $ | porosity |

Subscripts | |

in | inlet |

ref | reference |

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**Figure 9.**Comparison of measured and simulated (

**a**) wind velocity and (

**b**) temperature at different points.

**Figure 10.**Diagram of wind velocity distribution modeled by the (

**a**) standard CFD method and (

**b**) porous media method.

**Figure 11.**Diagram of temperature distribution modeled by the (

**a**) standard CFD method and (

**b**) porous media method.

**Figure 14.**Temperature of the area corresponding to the heights of 2 m (

**a**), 10 m (

**b**), and 50 m (

**c**) under different intensities of anthropogenic heat.

Surfaces | Standard CFD Model | Porous Media Model |
---|---|---|

Inlet | Velocity inlet | Velocity inlet |

Outlet | Outflow | Outflow |

Top and sides | Symmetry | Symmetry |

Underlying surface | Non-slipping wall | Non-slipping wall |

Building wall | Non-slipping wall | — |

Porous zone | — | Interior |

Name | Measuring Parameters | Range | Resolution | Precision |
---|---|---|---|---|

GM1361 split type of thermometer | Temperature | −10–50 °C | 0.1 °C | ±1.0 °C |

Anemometer | Velocity | 0~45 m/s | 0.1 m/s | ±0.3 m/s |

Parameters | Velocity (m/s) | Temperature (K) | Standard Deviation of Temperature |
---|---|---|---|

1 | 0.284 | 310.1 | 0.116 |

2 | 0.345 | 309.4 | 0.136 |

3 | 0.39 | 309.2 | 0.196 |

4 | 0.317 | 308.7 | 0.129 |

5 | 0.26 | 308.1 | 0.143 |

6 | 0.22 | 309.6 | 0.123 |

7 | 0.396 | 309.1 | 0.219 |

8 | 0.54 | 308.8 | 0.224 |

Simulation Method | Velocity | Temperature |
---|---|---|

Porous media method | 0.86 | 0.67 |

Standard CFD simulation method | 0.94 | 0.83 |

Standard CFD Modeling Method | Porous Media Model Method | |
---|---|---|

Number of grids | 3,268,935 | 2,767,710 |

Time per iteration/s | 14~20 | 6~12 |

Number of iterations | 1516 | 854 |

Simulation time/min | 480 | 140 |

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**MDPI and ACS Style**

Lei, J.; Wang, D.; Chen, Z.
Numerical Study of Micro-Thermal Environment in Block Based on Porous Media Model. *Buildings* **2022**, *12*, 595.
https://doi.org/10.3390/buildings12050595

**AMA Style**

Lei J, Wang D, Chen Z.
Numerical Study of Micro-Thermal Environment in Block Based on Porous Media Model. *Buildings*. 2022; 12(5):595.
https://doi.org/10.3390/buildings12050595

**Chicago/Turabian Style**

Lei, Jie, Dengyun Wang, and Zhenqian Chen.
2022. "Numerical Study of Micro-Thermal Environment in Block Based on Porous Media Model" *Buildings* 12, no. 5: 595.
https://doi.org/10.3390/buildings12050595