# Numerical Analysis on the Optimization of Evaporative Cooling Performance for Permeable Pavements

^{*}

## Abstract

**:**

## 1. Introduction

^{2}and 100 W/m

^{2}, respectively. Numerical simulations can simultaneously consider environmental factors, and examine the effects of changes in permeable structural parameters on cooling, such as water content and porosity, etc. However, the current simplified 1-D model is not accurate enough. The effects of water transport and temperature change on cooling in permeable pavements are still unclear and therefore cannot effectively guide design and production.

## 2. Materials and Methods

#### 2.1. Heat Transfer Theory

^{2}), heat convection H (W/m

^{2}), net long-wave radiation L (W/m

^{2}), and evaporation E (W/m

^{2}), as shown in Figure 1, and the heat balance equation is shown in Equation (1).

- The materials are assumed as homogeneous and isotropic, and thermal deformation is ignored.
- Heat loss by viscosity dissipation and pressure changes is ignored.
- Heat transfer in pores is neglected.
- The heat exchange satisfies local equilibrium.

^{−8}W·m

^{−2}K

^{−4}.

_{c}is the convection heat transfer coefficient, W/(m

^{2}·K), which can be estimated using Equation (8).

#### 2.2. Explanation of Modeling

#### 2.2.1. Geometrical and Physical Parameters

#### 2.2.2. Boundary Conditions

^{®}, Aurora, IL, USA). The perimeter and bottom surface were set as thermally insulated boundaries with an initial temperature setting of 20 °C. Ambient temperature, solar radiation, humidity, and wind speed were tested in Ref. [27] and imported into the model as the second type of thermal boundary conditions by interpolation functions, respectively (Figure 3).

#### 2.2.3. Validation Model

## 3. Results

#### 3.1. Effect of Thermal Material Parameters on Cooling

#### 3.1.1. Reflectivity

#### 3.1.2. Emissivity

#### 3.1.3. Specific Heat Capacity

#### 3.1.4. Thermal Conductivity

#### 3.2. Effect of Depth of Water Storage Layer on Cooling

#### 3.3. Pavement Spraying Scheme Selection

^{2}. With increasing water quantity, the cooling is not significantly improved, which indicates that its potential is played. Accordingly, 2.5 kg/m

^{2}of water quantity basically meets the maximum evaporation capacity of permeable pavements.

## 4. Discussion

## 5. Conclusions and Prospects

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

G | Thermal conduction (W/m^{2}) |

H | Thermal convection (W/m^{2}) |

L | Long wave radiation (W/m^{2}) |

E | Evaporation (W/m^{2}) |

I | Solar radiation (W/m^{2}) |

T_{s} | Solid-phase temperature (°C) |

T_{f} | Liquid phase temperature (°C) |

T | Porous substrate temperature (°C) |

T_{a} | Air temperature (°C) |

RH | Ambient relative humidity (%) |

ER | Surface evaporation rate (kg/(m^{2}·h)) |

q_{m} | Apparent internal heat source heat production rate |

q_{s} | Heat per unit volume of internal heat source of solids (W/m^{3}) |

q_{f} | Heat per unit volume of internal heat source of fluids (W/m^{3}) |

(ρc)_{m} | Apparent heat capacity (J/(kg·K)) |

c_{p} | Specific heat capacity of fluids (J/(kg·K)) |

c | Specific heat capacity of solids (J/(kg·K)) |

λ_{m} | Apparent thermal conductivity (W(m·K)) |

λ_{s} | Thermal conductivity of solids (W(m·K)) |

λ_{f} | Thermal conductivity of fluids (W(m·K)) |

ϕ | Porous media porosity |

ε | Emissivity |

T_{sky} | Sky temperature (°C) |

ε_{sky} | Sky emission rate (-) |

h_{c} | Convective heat transfer coefficient (W/(m^{2}·K)) |

v | Wind speed (m/s) |

ρ | Reflection |

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**Figure 4.**Simulated and measured values of the permeable surface temperature under dry and wet conditions. (

**a**) Dry condition, (

**b**) Wet condition.

**Figure 5.**Cooling results of permeable surfaces with different reflectivities. (

**a**) Diurnal surface temperature variation, (

**b**) Cooling amplitude.

**Figure 6.**Surface temperature variation and cooling amplitude of permeable surfaces with different emissivities. (

**a**) Diurnal surface temperature variation, (

**b**) Cooling amplitude.

**Figure 7.**Temperatures of permeable surfaces with different specific heat capacities. (

**a**) Diurnal surface temperature, (

**b**) Peak temperature.

**Figure 8.**Cooling results of permeable surfaces with different thermal conductivity. (

**a**) Diurnal surface temperature variation, (

**b**) Cooling amplitude.

**Figure 9.**Temperature fields of permeable pavements with different storage layer depths at different depths. (

**a**) 5 cm, (

**b**) 15 cm, (

**c**) 30 cm.

**Figure 11.**Variation of surface temperature during spraying at different times. (

**a**) 10:00, (

**b**) 12:00, (

**c**) 14:00.

Layer Name | Materials | Thickness (cm) | Density (kg/m^{3}) | Heat Capacity (J/(kg·K)) | Thermal Conductivity (W/m·K) | Porosity (%) |
---|---|---|---|---|---|---|

Permeable surface layer | Permeable concrete | 6 | 2000 | 880 | 0.68 | 20 |

Leveling layer | Cement mortar | 15 | 2100 | 800 | 0.9 | — |

Base layer | Gravel | 40 | 1400 | 900 | 0.55 | — |

Soil bedding | — | 80 | 1700 | 840 | 1.78 | — |

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**MDPI and ACS Style**

Xie, J.; Zhou, Z.
Numerical Analysis on the Optimization of Evaporative Cooling Performance for Permeable Pavements. *Sustainability* **2022**, *14*, 4915.
https://doi.org/10.3390/su14094915

**AMA Style**

Xie J, Zhou Z.
Numerical Analysis on the Optimization of Evaporative Cooling Performance for Permeable Pavements. *Sustainability*. 2022; 14(9):4915.
https://doi.org/10.3390/su14094915

**Chicago/Turabian Style**

Xie, Jinli, and Zuheng Zhou.
2022. "Numerical Analysis on the Optimization of Evaporative Cooling Performance for Permeable Pavements" *Sustainability* 14, no. 9: 4915.
https://doi.org/10.3390/su14094915