Simulation-Based Natural Ventilation Performance Assessment of a Novel Phase-Change-Material-Equipped Trombe Wall Design: A Case Study

Abstract

To evaluate the potential of phase-change materials (PCMs) in improving the indoor thermal and airflow environment of Trombe walls under solar energy limitations, a computational fluid dynamics (CFDs) model was employed in this study to perform comparative simulations. Taking traditional Trombe walls (TWs) as the control group and PCM-Trombe walls (PCM-TWs) as the experimental group, the simulation analysis was carried out based on meteorological data from a typical spring day in Hangzhou in 2024. The results indicate that the application of PCM significantly reduced temperature fluctuations in the air channel, lowering the peak temperature by 8.3 °C. Meanwhile, it delayed the decline in ventilation rate, extending the effective ventilation time by approximately one hour. Moreover, by calculating the Grashof number and ventilation rate, it was observed that the buoyancy effect of PCM-TWs is weaker than that of TWs at the peak wind speed, resulting in a lower natural convection intensity. The ventilation rate variation trend of PCM-TWs was smoother, with its peak ventilation rate slightly lower than that of TWs by 0.008 kg/s.

1. Introduction

With the continuous advancement of urbanization in China and the mounting severity of energy-related challenges, energy consumption in the building sector has increased significantly. Public buildings account for approximately 22% of the total energy consumption of urban buildings [1,2]. This high level of energy use has made public buildings a critical focus of energy conservation and emission reduction efforts, thereby driving the rapid development of energy-saving technologies.

In terms of energy conservation and emission reduction, natural ventilation is regarded as an effective measure [3]. According to data from the International Energy Agency (IEA), natural ventilation in European countries could reduce building energy consumption by more than 50% [4]. Replacing or partially substituting traditional air conditioning systems with natural ventilation technology not only reduces energy consumption but also significantly improves indoor air quality, providing fresh air for occupants and thus having a positive impact on human health.

As an energy-saving technology capable of significantly enhancing indoor natural ventilation, solar chimneys have garnered widespread attention in recent years [5]. Extensive research has been conducted on solar chimneys by scholars both domestically and internationally, yielding numerous significant achievements in experimental testing, numerical simulation, and theoretical analysis. Solar ventilation structures primarily include three types: Trombe wall solar chimneys, vertical roof solar chimneys, and inclined roof solar chimneys. Roof solar chimneys feature a large heat collection area and high ventilation efficiency, but they occupy rooftop space, making them less adaptable in practical applications. In contrast, Trombe wall solar chimneys are better suited for retrofitting building walls.

In Trombe walls, components such as the glass cover and the heat-absorbing wall receive solar radiation, causing their temperature to rise. This process heats the air within the channel, causing the air to expand, reducing its density, and creating buoyancy-driven airflow as it rises. By configuring upper and lower ventilation openings, hot air enters the interior through the upper vent, while cooler air replenishes through the lower vent, achieving natural convective ventilation driven by temperature differences and thermal pressure effects. Current research primarily focuses on thermal pressure ventilation, and the factors influencing its effectiveness can be categorized into three main aspects: structural design, installation conditions, and material selection for Trombe walls.

Regarding structural design, the configuration of Trombe walls includes factors such as height, width, gap, and the area of inlet and outlet openings. Gan’s study showed that increasing the height of air channel openings by one-fourth can enhance heat transfer by three-fourths [6]. Numerical studies by Lee and Strand indicated that increasing the height from 3.5 m to 9.5 m led to a 73% increase in airflow [7]. Experimental results by Al-Kayiem demonstrated that raising the height from 5 m to 15 m increased the airspeed from 3.47 m/s to 4.5 m/s [8].

The cavity gap significantly impacts airflow. Most studies recommend a gap of 0.2–0.3 m to balance ventilation performance and material cost [9,10,11] and maximize the stack effect [12,13]. However, some research has found that when the gap increases from 0.15 m to 0.3 m, the rate of airflow velocity growth gradually decreases [14].

The areas of the inlet and outlet are also crucial. Spencer’s research found that increasing the inlet area can enhance the ventilation rate [15]. Bassiouny noted that tripling the inlet area results in an approximate 11% increase in air exchange [16]. Additionally, CFD simulations indicated that having equal inlet and outlet areas helps maintain optimal airflow, while unequal areas favor a larger outlet for better performance [17,18].

Although rationally designing the height, gap, and area configuration of solar chimneys is cost-effective and easier to implement, its overall effect on improving ventilation efficiency is not significant.

Regarding installation conditions, the installation parameters of Trombe walls include the arrangement of openings and the solar collector. The selection of opening positions significantly impacts performance. Experiments have shown that building windows can serve as one of the openings for a solar chimney [19]. Chantawong et al. [20] used 6 mm thick transparent glass to create windows in Thailand, validating their suitability for hot regions. By measuring the airflow velocity inside the chimney, they found an airflow rate ranging from 0.13 to 0.28 m³/s. Shi and Zhang [9,10] discovered through numerical simulations that the performance of skylight openings surpasses that of other doors and windows. Regarding solar collectors, a larger collector area [21] and a higher ratio of height to cavity gap [22] result in greater airflow. In terms of collector types, experiments by El-Sawi et al. [23] demonstrated that a herringbone pattern achieves 20% higher thermal efficiency than flat or V-shaped patterns. Mathur et al. [24] found that cylindrical chimneys with collector surfaces covered by transparent sheets can improve the ventilation rate of solar chimneys by 36.85%.

By adjusting installation conditions, the performance of Trombe walls can be flexibly improved, allowing the walls to be specifically optimized for different climatic conditions, solar angles, and building layouts to maximize the utilization of solar energy. However, their performance remains constrained by the instability of solar radiation, with effectiveness potentially diminishing under conditions of insufficient sunlight, such as during overcast or winter seasons.

Regarding material selection, the materials used in Trombe walls include transparent materials (such as glass), thermal storage materials, and insulating materials. The transmittance, reflectance, and absorbance of glass collectively affect the performance of stack ventilation, with transmittance having the most significant impact. Double-layer glass can significantly enhance performance [25,26,27].

For collector materials, absorptance plays a more crucial role in performance. Research by Lee and Strand [7] indicates that when the absorptance of thermal storage materials increases from 0.25 to 1.0, the airflow increases by 57%. Additionally, using black polished surfaces for absorber plates can raise the outlet temperature of the chimney, further improving performance [28,29].

Li et al. [30] experimentally studied the ventilation characteristics of Trombe walls incorporating phase-change materials for thermal storage. He found that using materials with a phase-change temperature of 60 °C resulted in a ventilation volume of 2800.8 m³ during an 8 h daytime period, indicating that such walls can effectively improve indoor thermal and humidity conditions in regions with high static wind rates. Zhou et al. [31] investigated the impact of phase-change energy storage walls adapted to hot summers and warm winters on indoor thermal environments. The results showed that phase-change materials could reduce wall temperatures by 2 °C, lower condensation risk, and achieve good ventilation between 8:00 and 18:00, with ventilation volumes ranging from 73.6 m³/h to 361.8 m³/h, meeting fresh air requirements.

Afonso et al. [32] found that hollow insulated walls can optimize the performance of Trombe walls, with the optimal insulation wall thickness being 5 cm. Beyond 10 cm, performance improvements become insignificant.

Selecting appropriate materials to enhance the performance of Trombe walls helps reduce heat loss and improve overall energy efficiency. However, these materials are often associated with higher costs, and the performance of certain materials may be constrained by specific climatic conditions, limiting their application effectiveness in different environments.

From the relevant studies mentioned above, it can be observed that the research on optimizing the ventilation performance of Trombe walls primarily focuses on improving the ventilation efficiency under the influence of solar radiation. Due to the heat-driven ventilation principle of the Trombe wall, such improvements are more effective when solar radiation is strong. Therefore, under conditions of weak solar radiation (such as cloudy, overcast days, or night-time), the ventilating effect of the Trombe wall is almost nonexistent [33]. To address this issue, we introduce phase-change materials (PCMs) as the heat-collecting plate material for the Trombe wall, aiming to mitigate the situation where the heat-driven ventilation of the Trombe wall is ineffective after sunset, and to explore the sustainability of the performance enhancement.

Phase-change materials (PCMs) rely on the transformation of the material’s phase to achieve latent heat storage and release. During the phase-change process, the material absorbs or releases heat, and the phase changes, while the temperature change is minimal. By absorbing and releasing energy, PCMs serve to moderate temperature fluctuations, primarily by reducing and delaying peak and valley temperatures under equivalent environmental conditions, thus ensuring smoother temperature variations [34,35]. When applied to the heat-collecting plates of a Trombe wall, the PCMs can store some of the heat induced by solar radiation and, in the absence of solar radiation after sunset, continue to release this stored heat slowly. This process enables the Trombe wall’s heat-driven ventilation effect to be extended beyond sunset.

There is significant room for further research on the integration of phase-change materials (PCMs) with night-time ventilation, especially when combined with Trombe wall technology. Existing studies primarily focus on numerical simulations that investigate the key factors influencing the heat storage effects of PCMs and the synergistic cooling effects of building sensible heat storage combined with night-time ventilation techniques. However, there is a lack of exploration into how the heat storage performance of PCMs can extend the night-time ventilation duration of Trombe walls. Additionally, current research on building PCM-based heat storage and ventilation technologies tends to focus on their application during hot seasons. There is relatively little research on the application of this technology in transitional seasons. Yet, during actual building operation, both transitional and hot seasons’ cooling demands must be considered. This is especially relevant for regions such as Hangzhou, where studies on natural ventilation through open windows and doors at night are more suited for research during the transitional season, when thermal comfort can be maintained without air conditioning [36].

This study constructs two Trombe wall models—the traditional Trombe wall (TW) and the phase-change material Trombe wall (PCM-TW)—and conducts comparative analyses by altering the materials used in the collector wall section. The aim is to investigate the variation in ventilation rates of Trombe walls over time under identical solar radiation conditions and to assess the impact of changes in collector wall materials on the performance of Trombe walls, particularly concerning limitations posed by solar radiation instability.

The improved models are validated for simulation accuracy using experimental data [37]. Based on this, the study further conducts a series of numerical analyses to examine the effects of solar radiation, ambient temperature, and Grashof number distribution on the performance of Trombe walls.

2. Materials and Methods

This study established physical models of the traditional Trombe wall (TW) and the phase-change material Trombe wall (PCM-TW), serving as the control group and the experimental group, respectively. Based on the availability and reliability of data, the study focuses on the transition season of spring in Hangzhou for the year 2024, defined from 9 March to 15 May [38]. A representative sunny spring day, 18 March was selected for environmental data input in the simulation, ensuring accurate and reliable environmental parameters for the analysis. Figure 1 below illustrates the main process of the study. Through simulation, a comparative analysis is conducted based on the temperature and wind speed distributions at different time points within a day for a TW and a PCM-TW. Based on these results, the Grashof number and ventilation flow rate are calculated and discussed, serving as reference indicators for analyzing the intensity of air convection and ventilation efficiency, respectively [39].

2.1. Construction of the Simulated Physical Model

The Trombe wall structure in this study mainly consists of a glass cover plate, an air cavity, and a heat-absorbing wall (Figure 2). An air vent (air vents 1) is set above the glass cover plate, and an air vent (air vents 2, 3) is set at the top and bottom of the heat-absorbing wall, respectively. The left side in the figure is the south-facing solar radiation surface, and the right side is the interior. The left side of the heat-absorbing wall is the heat-absorbing surface, and the right side is the insulated surface with insulation material. The difference between Figure 2a and Figure 2b lies in the material of the heat-absorbing surface, while other conditions remain the same.

Solar radiation heats the Trombe wall structure, causing the temperature of the glass cover plate, air cavity, and heat-absorbing surface to rise. This temperature difference changes the density and pressure of the air in the air cavity, generating buoyancy to drive the air movement.

The Trombe wall structure has two typical operating modes (Figure 2). In summer, air vents 1 and 3 are open, while air vent 2 is closed. Air flows from air vent 3 to air vent 1, driving natural indoor airflow and expelling hot air outdoors. In winter, air vents 2 and 3 are open, while air vent 1 is closed. Air flows from air vent 3 to air vent 2. The air in the air cavity is heated and returns indoors, promoting indoor air circulation. During the spring and autumn transitional seasons, the summer ventilation mode or winter insulation mode can be selected based on local climatic conditions [40]. This study focuses on the ventilation characteristics of the summer operation mode under spring climate conditions.

The physical properties of the main materials are shown in

Table 1. Physical properties of major materials.

Material	Density (kg/m3)	Thermal Conductivity (W/m·K)	Specific Heat Capacity (J/(kg·K))	Latent Heat of Phase-Change (kJ/kg)
Glass Cover	2500	0.75	837.4	-
Brick Layer	1400	0.58	1050	-
Phase-change Material	1475	0.43	2200	155
Insulation Material	100	0.047	1380	-

. The phase-change material used in this study is BocaPCM-V38, a product from Guangzhou Mayer Energy-saving Technology Co., Ltd. (Guangzhou, China), with an average phase-change temperature of 23 °C. The aforementioned material parameters will be input into the software as boundary conditions and wall conditions, and they will be associated with the corresponding material in the physical model, serving as the initial conditions for the numerical simulation. Figure 3 presents the 3D physical model structure used in the simulation, illustrating the components included in the model. These components can be roughly categorized into the air channels, heat-collecting walls, and interior spaces, with the relevant dimensions of each part indicated in the figure.

2.2. Mathematical Description of the Simulation

The equation presented in the image is the formula for calculating the Reynolds number (Re), which is used in fluid mechanics to predict the flow regime (whether it is laminar or turbulent). The formula is as follows:

$$Re={\displaystyle \frac{\rho vd}{\mathsf{\mu }}}$$

(1)

where ρ is the density of the fluid (kg/m³), v is the velocity of the fluid (m/s), d is the characteristic length or diameter (m), and μ is the dynamic viscosity of the fluid (N·s/m²).

In the given context, based on experimental results and related data, the Reynolds number is calculated to be Re = 1107.45, and so it can be determined that the airflow in the air cavity is in a turbulent state [41]. To simplify the calculation process and facilitate the study, the following assumptions are made:

• The entire airflow and heat transfer process is under steady-state conditions.
• The fluid is incompressible air, satisfying the Boussinesq assumption.
• Only natural ventilation driven by thermal buoyancy is considered.
• The enclosure structure is an adiabatic wall, and no air infiltration occurs.
• Heat storage of the absorber surface is not considered.

The Boussinesq assumption refers to neglecting density changes caused by pressure variations, only considering density changes caused by temperature variations.

Before performing numerical simulations, it is necessary to establish an appropriate mathematical model to ensure more accurate solutions. This simulation primarily considers the ventilation performance of the Trombe wall induced by thermal pressure. Accordingly, the following mathematical model is employed in the numerical calculations conducted in the study [42,43]. The flow problem investigated in this study relies on the fundamental laws of mass conservation, momentum conservation, and energy conservation. Before solving, corresponding governing equations need to be established.

The continuity equation is as follows:

$${\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial v}{\partial y}}=0$$

(2)

The momentum conservation equation is as follows:

$$\begin{array}{rr}{\displaystyle \frac{\partial \left(uu\right)}{\partial x}}+{\displaystyle \frac{\partial \left(uv\right)}{\partial y}}=& -{\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial p}{\partial x}}+{\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial }{\partial x}}\left[\left(\mathsf{\mu }+{\mathsf{\mu }}_t\right){\displaystyle \frac{\partial u}{\partial x}}\right]+\\ & {\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial }{\partial y}}\left[\left(\mathsf{\mu }+{\mathsf{\mu }}_t\right){\displaystyle \frac{\partial u}{\partial y}}\right]-{\displaystyle \frac{2}{3}}\cdot {\displaystyle \frac{\partial k}{\partial x}}\end{array}$$

(3)

$$\begin{array}{ll}{\displaystyle \frac{\partial \left(uv\right)}{\partial x}}+{\displaystyle \frac{\partial \left(vv\right)}{\partial y}}=& -{\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial p}{\partial x}}+{\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial }{\partial x}}\left[\left(\mathsf{\mu }+{\mathsf{\mu }}_t\right){\displaystyle \frac{\partial v}{\partial x}}\right]+\\ & {\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial }{\partial y}}\left[\left(\mathsf{\mu }+{\mathsf{\mu }}_t\right){\displaystyle \frac{\partial v}{\partial y}}\right]-{\displaystyle \frac{2}{3}}\cdot {\displaystyle \frac{\partial k}{\partial x}}+g\beta \left(T-T_0\right)\end{array}$$

(4)

The energy equation is as follows:

$$\begin{array}{rr}{\displaystyle \frac{\partial \left(uT\right)}{\partial x}}+{\displaystyle \frac{\partial \left(vT\right)}{\partial y}}=& {\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial }{\partial x}}\left[\left({\displaystyle \frac{\mathsf{\mu }}{Pr}}+{\displaystyle \frac{{\mathsf{\mu }}_t}{{\sigma }_t}}\right){\displaystyle \frac{\partial T}{\partial x}}\right]+\\ & {\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial }{\partial y}}\left[\left({\displaystyle \frac{\mathsf{\mu }}{Pr}}+{\displaystyle \frac{{\mathsf{\mu }}_t}{{\sigma }_t}}\right){\displaystyle \frac{\partial T}{\partial y}}\right]\end{array}$$

(5)

The turbulent kinetic energy $\kappa$ and its dissipation rate $ϵ$ satisfy the following two equations.

The turbulent kinetic energy equation is as follows:

$$\begin{array}{ll}{\displaystyle \frac{\partial \left(uk\right)}{\partial x}}+{\displaystyle \frac{\partial \left(vk\right)}{\partial y}}=& {\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial }{\partial x}}\left[\left(\mathsf{\mu }+{\displaystyle \frac{{\mathsf{\mu }}_t}{{\sigma }_k}}\right){\displaystyle \frac{\partial k}{\partial x}}\right]+\\ & {\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial }{\partial y}}\left[\left(\mathsf{\mu }+{\displaystyle \frac{{\mathsf{\mu }}_t}{{\sigma }_k}}\right){\displaystyle \frac{\partial k}{\partial y}}\right]+{\displaystyle \frac{1}{\rho }}\left(G_k+G_b\right)-\epsilon -{\displaystyle \frac{1}{\rho }}{Y}_M\end{array}$$

(6)

The turbulent dissipation rate equation is as follows:

$$\begin{array}{ll}{\displaystyle \frac{\partial \left(u\epsilon \right)}{\partial x}}+{\displaystyle \frac{\partial \left(v\epsilon \right)}{\partial y}}=& {\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial }{\partial x}}\left[\left(\mathsf{\mu }+{\displaystyle \frac{{\mathsf{\mu }}_t}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x}}\right]+\\ & {\displaystyle \frac{1}{\rho }}\cdot {\displaystyle \frac{\partial }{\partial y}}\left[\left(\mathsf{\mu }+{\displaystyle \frac{{\mathsf{\mu }}_t}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial y}}\right]+C_{1\epsilon }{\displaystyle \frac{\epsilon }{\rho k}}\left(G_k+C_{3\epsilon }{G}_b\right)-C_{2\epsilon }{\displaystyle \frac{{\epsilon }^2}{k}}\end{array}$$

(7)

where, in the equations above, G_k represents the generation of turbulent kinetic energy due to the mean velocity gradient, G_b accounts for the production of turbulent kinetic energy caused by buoyancy effects, and Y_M describes the contribution of compressibility-induced turbulence fluctuation expansion to the overall dissipation rate.

Based on the aforementioned equations, a numerical model of the physical structure was established. The model primarily consisted of the computational domain, mesh generation, discretization of the governing equations, and the application of appropriate boundary conditions. All configurations and simulations were carried out using the academic version of the CFD software ANSYS Fluent 2021R2 [44].

In Fluent, the constants C_1ϵ, C_2ϵ, and C_3ϵ are assigned values of 1.44, 1.92, and 0.09, respectively. The Prandtl numbers for turbulent kinetic energy ${\sigma }_{\kappa }$ and dissipation rate ${\sigma }_{ϵ}$ are 1.0 and 1.3, respectively.

2.3. Boundary Condition Settings for the Simulation

This study employs the realizable $\kappa -ϵ$ turbulence model combined with the enhanced wall function method, using the finite volume method to numerically solve the aforementioned governing equations. For velocity and pressure coupling, the SIMPLE algorithm is applied. The discretization of the convection term uses a second-order upwind scheme.

Regarding the radiation model, the DOs (discrete ordinates) radiation model [45] is adopted, with the incident angle of solar radiation determined using a solar calculator. The outdoor ambient temperature is set to 285 K, and the operating pressure is 101,325 Pa. The air inlet and outlet are defined as the pressure inlet and pressure outlet, respectively, with the inlet air temperature set to the average daily temperature in Hangzhou.

3. Validation

3.1. Mesh Validation for the Simulation

In CFD simulations, the accuracy of results and the computation time are closely related to the mesh division of the model. In this study, a structured mesh was used to model the fluid domain inside the Trombe wall using ANSYS-ICEM (Figure 4). The natural ventilation mode was selected, with wind speed and ventilation rate as the evaluation metrics. Three different mesh densities were tested for numerical validation (Figure 5).

The results indicate that as the number of mesh elements increases, the computation results converge, and the curves gradually stabilize. After calculation, the error for each result is within 10%. Therefore, the optimal mesh size for both the traditional Trombe wall and the phase-change Trombe wall is 357,440 elements. The minimum mesh size is 0.02 m × 0.015 m × 0.025 m, and the maximum size is 0.04 m × 0.015 m × 0.025 m. Over 95% of the mesh quality reached a value of one, indicating high-quality meshes suitable for subsequent simulation analysis [46].

3.2. Validation of the Simulation Method

This study selects the experimental results on natural ventilation of the Trombe wall from reference [37] to validate the proposed numerical simulation method and model. By constructing a model of the same dimensions as in the referenced study, the simulation results are compared and analyzed using the method described in this paper to assess the reliability and accuracy of the simulation approach.

Figure 6 presents a comparison between the numerical simulation results and experimental data. Due to the exclusion of wind pressure and other environmental factors in the simulation, a certain degree of relative error exists between the numerical and experimental results. However, the overall trend exhibited by the simulation closely matches that of the experimental data, with a relative error consistently below 7%. The numerical results indicate that the airflow rate in the solar chimney increases with rising solar heat flux, which aligns well with the trend observed in the experiments. The agreement between simulation and experimental results demonstrates the validity and reliability of the numerical model and methodology employed in this study, suggesting their suitability for use in future research [47].

4. Results

The ventilation performance of the Trombe wall is closely related to the temperature difference caused by solar radiation. In Hangzhou, on 18 March 2024, the sunrise time was 06:39:11, and the sunset time was 17:24:38, with an average outdoor temperature of 15 °C.

The study’s timeframe begins at 6:00. To facilitate the analysis of data differences between the traditional Trombe wall (TW) and the phase-change Trombe wall (PCM-TW) after sunset, as well as their impact on ventilation performance, the end time of the study was extended to four hours after sunset, i.e., 22:00. The selected research time period encompasses the complete variation process of solar radiation and temperature, from the lowest to the highest points, capturing the critical temperature change transitions [48].

4.1. Temperature Distribution Inside the Trombe Wall Structure

The temperatures of the absorber surface and air channel for PCM-TW (1) and TW (2) at different times are shown in

Table 2. Variation in Trombe wall surface temperature and air channel temperature over time.

Time (h)	Absorber Surface Temperature 1 (°C)	Channel Temperature 1 (°C)	Absorber Surface Temperature 2 (°C)	Channel Temperature 2 (°C)
6:00	15	13.3	15	15
7:00	16.2	14.5	17.5	16
8:00	17.1	14.8	20.8	18.2
9:00	19	15.7	25.4	21
10:00	22	17.3	30.6	25.5
11:00	25.9	19.6	38.2	30.2
12:00	31.8	22.4	45.1	35
13:00	36.9	25.2	50.1	38.5
14:00	42.1	30.3	54.2	40
15:00	45.9	32.1	49.5	38.2
16:00	43.8	31.7	43.1	34.5
17:00	41.5	31.6	35	28.5
18:00	37.2	27.5	23	22
19:00	32.1	23.2	20.5	19.5
20:00	25.2	19.4	18.5	18
21:00	21.3	17.1	17	17
22:00	17.2	15.2	16.5	16

and Figure 7.

After sunrise, influenced by solar radiation, the absorber surface temperature of the TW (2) rises rapidly and continues to increase at a relatively fast rate, reaching its peak of 54.2 °C at around 14:00. Subsequently, as solar radiation gradually diminishes, the temperature decreases symmetrically until sunset. After sunset, the temperature difference between the absorber surface and the air channel narrows, slowing the rate of temperature decline.

Since the specific heat capacity of air is greater than that of the brick wall in the absorber surface, the temperature rise rate of air channel 2 is slower than that of absorber surface 2. During the period from sunrise to sunset, the temperature of air channel 2 remains lower than that of absorber surface 2, with a temperature difference of 5–10 °C at corresponding times. Additionally, due to the lower thermal conductivity of air compared to brick walls, the temperature change rate in air channel 2 is relatively low, resulting in a smoother temperature curve.

For PCM-TW, the absorber surface temperature 1 is also influenced by its specific heat capacity and thermal conductivity, leading to a slower temperature rise rate compared to TWs absorber surface temperature 2. The overall change curve is more gradual. Compared to absorber surface temperature 2, the peak of absorber surface temperature 1 occurs nearly one hour later, with its peak temperature 8.3 °C lower. This phenomenon is mainly attributed to the unique thermal properties of the phase-change material (PCM) [49]. The BocaPCM-V38 phase-change material used in this study has a phase-change temperature range of 22–26 °C. During the phase-change process, the heat absorbed by the PCM is primarily used for phase transformation (e.g., from solid to liquid), keeping the temperature relatively constant. This results in most of the heat being used for the phase-change, thereby slowing the temperature rise rate of the absorber surface.

The properties of the PCM also influence the cooling process of the PCM-TW, making the cooling curve of absorber surface temperature 1 more gradual. When the temperature decreases to the phase-change temperature range, the PCM gradually solidifies from a liquid state, releasing latent heat and reducing the temperature drop rate [50]. Furthermore, the air channel temperature 1 of the PCM-TW remains lower than absorber surface temperature 1, maintaining a 5–10 °C temperature difference, but the overall trend is consistent. Due to the impact of the phase-change process, the peak temperature of air channel 1 can be maintained for approximately one hour.

In contrast, the absorber surface temperature 2 and air channel temperature 2 of the TW are more significantly affected by changes in solar radiation. After sunset, temperatures drop rapidly, with the air channel temperature differing from the outdoor temperature by only 2–3 °C and continuing to decrease. However, the PCM-TW cools more slowly after sunset, with absorber surface temperature 1 and air channel temperature 1 maintaining a higher temperature gradient. At sunset, the air channel temperature still shows a difference of 12.3 °C from the outdoor temperature, which gradually decreases thereafter.

Figure 8 illustrates the air temperature distribution in the ducts for the TW at 14:00 and PCM-TW at 15:00, which correspond to the highest duct air temperatures for each system throughout the day. From the figure, it can be observed that the air temperature on the left side of the duct is significantly higher than the indoor environment temperature on the right. This is primarily attributed to the main heat source in this simulation—solar radiation from the south side. Solar radiation passes through the glass cover to the absorber surface, heating the air inside the duct and causing the temperatures of the absorber surface, glass cover, and air to rise accordingly [51].

Through convection and radiation, the glass cover and absorber surface continuously transfer heat into the duct, maintaining the air temperature inside the duct higher than the indoor air temperature. Under the combined effects of the temperature gradient and buoyancy, the heated air in the duct rises and is expelled outdoors through air vent 1, driving the flow of indoor air.

As a result, the air temperature at the top of the duct is the highest, followed by the air temperatures along the sides of the duct in contact with the glass cover and absorber surface. In contrast, the air temperature in the center of the duct is relatively lower due to the higher frequency of air exchange (i.e., greater airflow velocity). Additionally, because of the unique thermophysical properties of the phase-change material (PCM), the duct air temperature in the PCM-TW is generally lower than in the TW. This is because the PCM can effectively absorb and release heat during the phase-change process, moderating air temperature fluctuations and slightly lowering the duct air temperature.

This difference in temperature distribution reflects the influence of solar radiation on different materials and structures, as well as the unique role of PCM in thermal management. Over longer time scales, the PCM-TW system effectively suppresses temperature fluctuations through the phase-change process, keeping the duct air temperature relatively stable. In contrast, the traditional TW system is unable to mitigate temperature fluctuations effectively, resulting in higher and more variable air temperatures in the duct.

4.2. Airflow Velocity Distribution Within the Trombe Wall Structure

Table 3. Velocity contours of traditional Trombe wall and PCM Trombe wall at different times under the climatic conditions of Hangzhou on 18 March.

Condition	Traditional Trombe Wall	PCM Trombe Wall
14:00
15:00
16:00
18:00
19:00

presents the wind speed distribution cloud diagrams for a typical Trombe wall (TW) and a phase-change material Trombe wall (PCM-TW) from 13:00 to 19:00. Data analysis reveals that the wind speed in the TW system exhibits a clear periodic fluctuation pattern. Between 13:00 and 14:00, the wind speed in the TW increases significantly, reaching its daily peak at 14:00, and then gradually decreases. By 19:00, the wind speed at the air inlet drops to 0.3 m/s, and the average indoor wind speed decreases to 0.1 m/s, close to the regular indoor wind speed range without the Trombe wall. This trend is highly consistent with the changes in the collector surface temperature and air channel temperature of the TW shown in Figure 8, indicating that higher air temperatures in the duct result in a larger temperature difference with the outside environment, which strengthens the natural convection driven by the temperature difference and promotes increased airflow speed.

In contrast, the PCM-TW system exhibits a different wind speed variation trend. From 13:00 to 16:00, the wind speed in the PCM-TW steadily increases, peaking at 15:00. According to the wind speed cloud diagram at 16:00, the maximum wind speed in the PCM-TW is slightly lower than that of the TW. This indicates that the thermophysical properties of the phase-change material result in smoother wind speed variations during high-temperature periods for the PCM-TW system. Subsequently, the wind speed gradually decreases, and by 19:00 the wind speed at the air inlet drops to 0.5 m/s, while the average indoor wind speed decreases to approximately 0.3 m/s. This remains higher than the regular wind speed range without a Trombe wall and also exceeds the indoor average wind speed of the TW system at the same time. The wind speed variation trend of the PCM-TW aligns closely with the changes in collector surface temperature and air channel temperature shown in Figure 8, further validating the unique advantages of phase-change materials in regulating system temperature and promoting airflow.

Notably, although the peak wind speed of the PCM-TW system is slightly lower than that of the TW, it maintains more stable and higher indoor ventilation over a longer period. Particularly at 19:00, the PCM-TW remains effectively operational, continuing to improve indoor ventilation, whereas the TW system has nearly ceased effective operation. This phenomenon is primarily attributed to the phase-change process of the material, which absorbs and releases heat to regulate air temperature, thereby delaying the wind speed decline and sustaining relatively stable airflow [52].

Compared to the traditional TW system, the PCM-TW more effectively extends the ventilation effect, especially after sunset, maintaining a relatively stable wind speed output even under conditions of significant temperature fluctuations.

5. Discussion

5.1. Comparison of Grashof Numbers in Air Ducts

The Grashof number (G_r) is a dimensionless parameter used to characterize the relative strength of buoyancy forces to viscous forces, serving as a critical indicator in the analysis of natural convection [53]. The formula for Grashof number is as follows:

$$G_r={\displaystyle \frac{g\beta ∆T{L}^3}{v^2}}$$

(8)

where $g$ is the gravitational acceleration, $\beta$ is the thermal expansion coefficient, $∆T$ is the temperature difference, $L$ is the characteristic length, and $v$ is the kinematic viscosity. The Grashof number reflects the competition between the density differences (buoyancy forces) caused by temperature variations and the internal viscous resistance of the fluid. The magnitude of the Grashof number affects not only the stability of the flow field but also determines boundary layer characteristics, such as velocity and temperature distributions.

The peak air duct temperature in the PCM-TW throughout the day is 32.1 °C, corresponding to a heat flux of 629.85 W/m². In contrast, the peak air duct temperature in the TW is 40 °C, corresponding to a heat flux of 867.26 W/m². Figure 9 illustrates the variation in the Grashof numbers along the height of the air duct for both the PCM-TW and TW under their respective peak heat flux conditions.

At heights of 1.0 m and 2.9 m in the air duct, corresponding to the airflow inlet and outlet, respectively (Figure 2), the temperature differences are relatively large, resulting in the strongest buoyancy forces and the highest intensity of natural convection. Consequently, the Grashof numbers (G_r) at these two heights are relatively high for both the PCM-TW and TW [54]. In these regions, natural convection is more likely to exhibit instability. However, since the Grashof numbers remain relatively small (<10⁹), the airflow maintains a stable turbulent state without fully transitioning to chaotic turbulence.

The Grashof number range for the PCM-TW is 21,384,765 to 57,849,213, while for the TW it ranges from 22,194,876 to 70,394,827, indicating that the convection intensity in the TW is significantly higher than in the PCM-TW. As the heat flux increases, the buoyancy forces generated by solar radiation within the solar chimney duct of the Trombe wall also strengthen, inducing upward airflow and enhancing the natural convection heat transfer intensity, thereby significantly increasing the heat transfer rate. However, throughout the day, the peak natural convection intensity in the PCM-TW is lower than in the TW, demonstrating that the buoyancy force produced by the TW is greater than that of the PCM-TW, leading to stronger airflow-driven effects.

5.2. Ventilation Rate Variation in the Air Duct

The ventilation rate is calculated using the following formula:

$$Q=\rho ·v·S$$

(9)

where $Q$ is the ventilation rate (kg/s); $v$ is the airflow velocity (m/s); $S$ is the vent opening area (m²); $\rho$ is the air density, taken as 1.158 kg/m³.

Figure 10 illustrates the variation in ventilation rates over time for the typical Trombe wall (TW) and the phase-change material Trombe wall (PCM-TW). The ventilation rate is calculated at the airflow outlet of the vent (air vents 1, see Figure 2). The TW system’s ventilation rate gradually increases from sunrise as solar radiation intensifies, peaking around 14:00 at approximately 0.06 kg/s. Subsequently, the ventilation rate decreases gradually, and by around 18:00, as sunset approaches, the variation stabilizes and eventually drops to the regular indoor ventilation rate level [55].

In contrast, the PCM-TW system shows a similar trend, with the ventilation rate increasing gradually from sunrise as solar radiation intensifies, but the rate of increase is slower compared to the TW system. The PCM-TW ventilation rate peaks around 15:00 at approximately 0.052 kg/s. Afterward, the ventilation rate decreases gradually but remains consistently higher than that of the TW system at the same time. It is evident that the ventilation rate of the PCM-TW system decreases more slowly due to the phase-change process, which slows the rate of temperature drop. Between 19:00 and 20:00, the ventilation rate stabilizes and drops to the regular indoor ventilation level. Compared to the TW system, the PCM-TW system extends the duration of increased ventilation rates by approximately one hour.

To further analyze the relationship between ventilation rate $Q$ and temperature $k$, Figure 11 illustrates the relationship between the ventilation rate of the PCM-TW and the air channel temperature at 1.5 m height. During the analysis, the least-squares method was used to derive the correlation between the two, as expressed in Equation (10):

$$Q=1.71\times {10}^7+194711.40k-220.69k^2-5.04\times 10-5k^4$$

(10)

As shown in Figure 11, when the relationship between the ventilation rate and the channel temperature is represented by a quartic polynomial, the correlation coefficient between the curve and the original data points is one. Each data point aligns closely with the fitted curve, indicating that Equation (10) effectively represents the relationship between ventilation rate and temperature in the PCM-TW system. The ventilation rate of the PCM-TW increases as the air channel temperature rises.

6. Conclusions

This study utilized the Fluent numerical simulation method to establish physical models for both the typical Trombe wall (TW) and the phase-change Trombe wall (PCM-TW). By inputting relevant meteorological data from Hangzhou on 18 March 2024, the simulation produced critical data on temperature variations, Grashof number distributions, wind speed cloud maps, and ventilation changes. A comparative analysis of the simulation results for the experimental group and the control group led to the following key conclusions:

(1)

Due to the phase-change process of the phase-change material, the PCM-TW effectively mitigates temperature fluctuations within the air channel. Compared to traditional TW systems, the PCM-TW reduces the impact of solar radiation on the enhanced ventilation effect of the Trombe wall, significantly lowering the peak air channel temperature by approximately 8.3 °C and delaying the temperature drop rate in the air channel by about one hour. This effect is primarily attributed to the phase-change material absorbing and releasing heat during the phase-change process, reducing the impact of temperature fluctuations on the system.

(2)

Under the combined influence of specific heat capacity and thermal conductivity, the heat flux density of the TW system is higher than that of the PCM-TW system. This indicates that the traditional TW system has higher heat flux density and stronger heat exchange capability during heat conduction. However, the natural convection intensity of the PCM-TW system is slightly weaker than that of the TW system. Consequently, under the same conditions, the TW system generates greater air buoyancy and forms stronger natural convection, leading to higher air velocity.

(3)

The peak ventilation rate of the PCM-TW system is approximately 0.052 kg/s, slightly lower than the 0.06 kg/s of the TW system. However, the PCM-TW system exhibits a slower rate of increase in ventilation, with its peak occurring around 15:00, later than the peak time for the TW system. Moreover, the PCM-TW system maintains higher ventilation rates for a longer duration compared to the TW system. Due to the phase-change process slowing the temperature decrease, the ventilation rate of the PCM-TW system declines at a slower pace, stabilizing between 19:00 and 20:00, about one hour later than the TW system. Further analysis reveals that the ventilation rate of the PCM-TW system is positively correlated with air channel temperature, where an increase in channel temperature directly promotes an increase in ventilation.

The PCM-TW system demonstrates significant advantages in temperature regulation, ventilation sustainability, and thermal management. The introduction of phase-change materials not only enhances the thermal stability of the system but also effectively delays the decline in ventilation performance. Particularly after sunset, the PCM-TW system provides sustained ventilation, improving indoor comfort. Compared to traditional TW systems, PCM-TWs offer potential application value in extending the effective ventilation time and improving indoor air quality, especially in climates with significant variations in solar radiation.

6.1. Research Limitations

This study utilized numerical simulations to analyze the thermal performance and ventilation characteristics of traditional Trombe walls and PCM-Trombe wall systems. Although the simulation method was validated with experimental data from the existing literature, confirming its feasibility and accuracy for similar problems, several limitations remain. First, the study lacked direct experimental validation of the simulation results, potentially leading to discrepancies with real-world conditions. Second, the simulation involved idealized assumptions regarding material properties, climate conditions, and boundary conditions, failing to account for complex factors in actual building environments, such as the heat transfer from walls to the interior. Additionally, the study focused on performance analysis under specific time, environmental, and structural conditions, and while control variables were addressed through experimental and control groups, the applicability of the conclusions in different environmental or structural settings requires further validation.

6.2. Future Research

Future research will place greater emphasis on the collection and analysis of experimental data. Conducting experiments that align with the simulation results will help validate the accuracy of numerical models and enhance the reliability of the conclusions. In addition, future studies will take into account more complex factors present in real-world environments, such as the thermal conductivity of different building materials, the interaction between indoor and outdoor airflow, and the influence of occupant behavior on system performance.

Moreover, ventilation airflow can partially compensate for thermal discomfort by improving indoor thermal conditions. Future research will explore how natural ventilation at various airflow rates can be utilized to optimize the indoor thermal environment and enhance occupant thermal comfort. Particular attention will be given to the influence of different climatic conditions, building structures, and airflow combinations on thermal comfort, with the aim of clarifying the relationship between ventilation and indoor temperature regulation. This will provide a theoretical basis for future building design and environmental control strategies.

Additionally, considering that climatic conditions and structural configurations may significantly impact system performance, future research will seek to extend validation across diverse climate zones and building designs to improve the generalizability and practical relevance of the findings.