Thermal Performance of Trombe Walls with Inclined Glazing and Guided Vanes

Abstract

The Trombe Wall (TW) has gained recognition for its simplicity, efficiency, and zero operational costs, making it a key contributor to Sustainable Development Goals (SDGs) 7 and 11 by enhancing energy access and providing sustainable heating solutions. This passive solar technology is particularly beneficial in rural areas, offering cost-effective thermal comfort while minimizing environmental impact. This study evaluates the performance of three TW configurations attached to a room, designed with inclined glazing relative to the vertical air layer and stone layers at the bottom acting as thermal mass, commonly used in rural installations in Peru. Using 2D Computational Fluid Dynamics, the analysis compares an inclined heated wall with guided vanes featuring three or five blades to a configuration without vanes. Results show that the three-blade guided flow configuration achieves the highest temperature rise of 4 °C, with a reference temperature of 20 °C, under an absorber heat flux of 200–400 W/m², albeit with a slightly lower flow rate of 0.17–0.23 kg/s compared to the configuration without guided flow. The maximum thermal efficiency of 57.90% was observed for the three-blade configuration, which is 2.26% higher than the efficiency of the configuration without guided flow, under an absorber heat flux of 400 W/m². The obtained path-lines reveals that the three-blade configuration minimizes flow detachment, nearly eliminates recirculation near the bottom corner of the glazing, and reduces the separation bubble at the top corner of the massive wall near the outlet. These findings highlight the potential of guided vanes to enhance the performance of Trombe Walls in rural settings.

1. Introduction

Due to increasing prices, limited availability of conventional energy sources, and the projected 37% rise in global energy demand by 2040 [1], finding new solutions to reduce conventional energy consumption has become a priority [2].

The construction sector accounts for approximately 40% of global energy consumption and 36% of carbon dioxide emissions [3]. Importantly, 33–55% of building energy usage is consumed by HVAC (Heating, Ventilation, and Air Conditioning) systems [4]. In response, legislation enforcing more stringent requirements for thermal resistance in building envelope elements and heat recovery systems has been proposed as a solution [5].

Special attention has been given to building envelope elements that can improve thermal comfort through the conversion of solar radiation energy [6]. A common design strategy for improving building envelope performance is to incorporate internally ventilated air layers. Various types of these ventilated systems include solar walls [7] or chimneys [8], double-skin façades [9], ventilated PV façades [10,11], and the TW [12]. The TW has gained increasing attention from researchers and engineers due to its simple construction, high efficiency, and zero operational costs [13]. A typical TW consists of a glass cover, an absorber plate or other heat-absorbing material attached to a massive wall, an air layer between these two components, and both upper and lower vents [14].

Computational Fluid Dynamics (CFD) has been used to design and evaluate TW operation, despite being time-consuming [15]. While 3D CFD simulations have been used [16,17,18], many researchers have opted for 2D CFD simulations due to computational cost constraints [19,20].

Regarding the simulation of solar radiation, several previous studies do not directly simulate incident solar radiation but instead use known values of radiation or heat fluxes [21,22,23]. These studies aimed to evaluate how different Trombe wall configurations affect buoyancy-induced flows in the air layer structure, as flow patterns and heat transfer conditions significantly influence building envelope performance.

A previous study evaluated the height and width of a vertical air layer under different heat flux inputs, finding that for the supply of warm air indoors, the width of the air layer should be less than 0.2 m [21]. Another study used 2D CFD simulations to evaluate three configurations of the vertical air layers in a TW, which included upper and lower vents with sharp edges, rounded edges, and a final configuration with guided vanes consisting of four blades at the exit of the lower vent [22]. In [23], isoflux and adiabatic heating conditions were applied to a TW geometry consisting of a heated wall inclined relative to the vertical air layer, which represents TW attached to a room. The study evaluated the influence of the heated wall’s slope angle. Another study modeled solar heating on the heated wall of an inclined passive solar chimney as isoflux heating to determine the optimal inclination angle [24].

To improve the structure of TWs, the addition of fins has been widely studied. In the arid climate of Yazd, Iran, vertical fins were added to the absorber plate of a TW [25]. Among the configurations analyzed, the three aluminum fins exhibited the lowest performance, while the two copper fins configuration achieved the highest performance, with increases in convective thermal efficiency and stored energy of 6% and 3%, respectively, compared to the TW without fins. Considering the cold climate of Xining, China, the authors [26] numerically investigated a TW with an absorber integrated with fins of different shapes. The study found that equilateral fins with equilateral triangular holes and an area ratio of 1:4 achieved the highest convective heat transfer efficiency and building energy savings, reaching 68.50% and 53.57%, respectively. Similarly, taking into account the climate conditions of Lanzhou, a TW with fins in the absorber was studied [27]. It was concluded that fins shaped as isosceles triangles with a top angle of 90°, arranged in-line, achieved 7.77% higher convective heat transfer efficiency and 8.25% greater energy savings compared to the finless TW.

To improve the thermal performance of TWs, previous studies have primarily focused on the vertical air layer formed between the heated wall—usually the glazing—and the absorber plate. Based on the reviewed studies, modifications to the TW structure include changes to the height and width of the air layer, the use of massive walls with rounded edges, the addition of guided vanes at the exit of the lower vent, and the integration of fins on the absorber plate. However, few studies have explored cases where the heated wall is inclined.

To the authors’ knowledge, no prior studies have evaluated a TW with an inclined heated wall that includes a stone layer at the exit of the lower vent. This configuration of TW, typically attached to a room, is commonly installed in existing houses located in rural areas of Peru [28]. To address this gap in the literature, the present work evaluates three TW configurations with an inclined heated wall and a stone layer using numerical simulations under different heat flux conditions. These configurations include a TW attached to a room without guided vanes, a TW with guided vanes consisting of three blades, and a TW with five blades.

First, the methodology is explained, including the assumptions and justification for the selected 2D approach. Second, the numerical model is detailed, covering the governing equations, solver settings, and meshing specifics. Finally, the results and discussion are presented.

2. Methodology

The simplified 2D model of an inclined heated wall relative to the vertical air layer is shown in Figure 1. The TW attached to a room includes an inclined glazing relative to a vertical air layer and a massive wall with lower and upper vents. On the exterior of the massive wall, a steel sheet, typically painted black, is used to promote solar heat absorption. Additionally, a stone layer, also usually painted black and located at the bottom, acts as thermal mass, storing excess heat for later use and enhancing the overall thermal performance of the TW.

Figure 1 also depicts the energy flows on the TW. When sunlight reaches the exterior glazing, most of the solar radiation passes through, while a small portion is reflected and absorbed by the glazing. Most of the transmitted solar radiation is absorbed by the absorber and the stone layer, with a small portion reflected back. As this reflected portion passes through the exterior glazing again, additional transmission, absorption, and reflection effects occur. Consequently, heat flux conditions can be imposed on the inclined glazing, massive wall, and stone layer.

The transport phenomena in the attached TW are described by the Reynolds-Averaged Navier–Stokes (RANS) equations [29] and are solved using the finite volume method. The continuity, momentum, energy equations, along with those corresponding to the turbulence model, are solved under steady-state conditions. A simplified 2D approach is justified because, in a cross-section including the lower and upper vents with buoyancy-driven flow, the buoyancy forces in the horizontal direction can be neglected. As mentioned earlier, a 2D approach is also less computationally expensive. Furthermore, the flow can be considered incompressible because, for natural convection, the expected velocity values are unlikely to exceed a Mach number of 0.1 [30].

With respect to the assumptions of the 2D model, the convective heat transfer loss from the inclined heated wall to the environment is ignored. Similarly, indoor heating, which is usually modeled as a heat flow boundary condition [27], is also neglected.

The numerical solution of the mass, momentum, and energy equations is obtained using CFD in ANSYS Fluent 2024 R1. The governing equations and solver settings are detailed in the next section. Figure 2 depicts the CFD simulation procedure for the TW attached to a room.

3. Numerical Model

To obtain the numerical solution of the governing equations, the pressure-based solver under steady-state conditions was used. The SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm was implemented for pressure–velocity coupling, ensuring robust convergence of the solution.

Spatial discretization schemes were carefully selected to achieve high accuracy while maintaining numerical stability. The gradient terms were computed using a least squares cell-based method. Second-order pressure discretization was employed to enhance the precision of pressure field calculations. Similarly, second-order upwind schemes were utilized for momentum, turbulent kinetic energy, specific dissipation rate, and energy equations, providing higher-order accuracy and reducing numerical diffusion compared to first-order schemes. This combination of numerical methods was chosen to minimize discretization errors while ensuring solution stability and convergence reliability.

When temperature differences are relatively small, the thermophysical properties of the fluid can be assumed constant, and the Boussinesq approximation [31] can be applied to the buoyancy term in the vertical component of the momentum equation [7]. This approximation has been widely used for simulating buoyancy forces [20,21,22,30]. Under this approximation, fluid properties are considered constant, with the buoyancy force varying linearly with temperature differences only, expressed as ${\mathsf{\rho }}_0\mathsf{\beta }\left(T-T_0\right)g$. Therefore, in this study, all physical parameters of air are assumed constant except for density, which follows the Boussinesq approximation.

Governing Equations

The governing equations for the 2D steady-state flow, incorporating the Boussinesq approximation for natural convection, are presented below. These equations describe the fluid flow and heat transfer phenomena in the TW.

Equation (1) represents the continuity equation for an incompressible fluid:

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

(1)

where $\mathrm{u}$ and $v$ are the velocity components in the $x$ and $y$ directions, respectively. Equations (2) and (3) are the momentum conservation equations in the $x$ and $y$ directions:

$${\rho }_{0}u{\displaystyle \frac{\partial u}{\partial x}}+{\rho }_{0}v{\displaystyle \frac{\partial u}{\partial y}}=-{\displaystyle \frac{\partial p}{\partial x}}+{\displaystyle \frac{\partial }{\partial x}}\left[\left(\mu +{\mu }_t\right){\displaystyle \frac{\partial u}{\partial x}}\right]+{\displaystyle \frac{\partial }{\partial y}}\left[\left(\mu +{\mu }_t\right){\displaystyle \frac{\partial u}{\partial y}}\right]$$

(2)

$${\rho }_{0}u{\displaystyle \frac{\partial v}{\partial x}}+{\rho }_{0}v{\displaystyle \frac{\partial v}{\partial y}}=-{\displaystyle \frac{\partial p}{\partial y}}+{\displaystyle \frac{\partial }{\partial x}}\left[\left(\mu +{\mu }_t\right){\displaystyle \frac{\partial v}{\partial x}}\right]+{\displaystyle \frac{\partial }{\partial y}}\left[\left(\mu +{\mu }_t\right){\displaystyle \frac{\partial v}{\partial y}}\right]-{\rho }_0\beta \left(T-T_0\right)g$$

(3)

Equation (4) represents the energy conservation equation:

$${\rho }_{0}u{\displaystyle \frac{\partial T}{\partial x}}+{\rho }_{0}v{\displaystyle \frac{\partial T}{\partial y}}={\displaystyle \frac{\partial }{\partial x}}\left[\left({\displaystyle \frac{\lambda }{c_p}}+{\displaystyle \frac{{\mu }_t}{P{r}_t}}\right){\displaystyle \frac{\partial T}{\partial x}}\right]+{\displaystyle \frac{\partial }{\partial y}}\left[\left({\displaystyle \frac{\lambda }{c_p}}+{\displaystyle \frac{{\mu }_t}{P{r}_t}}\right){\displaystyle \frac{\partial T}{\partial y}}\right]$$

(4)

$\lambda$ is thermal conductivity, $c_p$ is the specific heat capacity, and $P{r}_t$ represents the turbulent Prandtl number. The set of equations incorporates both molecular and turbulent transport phenomena through the effective viscosity (μ + μ_t) and effective thermal diffusivity (λ/c_p + μ_t/Pr_t) terms. This formulation allows for the accurate prediction of natural convection flows in the TW cavity, where buoyancy-driven circulation is the primary mechanism of heat transfer.

In the turbulent regimen, in contrast to the laminar regime, the turbulent viscosity ${\mu }_t$ is non-zero, and a turbulence model is necessary.

The low-Reynolds-number turbulence models allow the solution of the flow within a viscous sub-layer when the mesh becomes sufficiently fine and includes some nodes inside the viscous sub-layer. The $k-\omega$ SST is employed, as it combines the strengths of both the $k-\epsilon$ and $k-\omega$ models [32]. In addition, the $k-\omega$ SST model demonstrated superior performance compared to the RNG $k-\epsilon$, the RSM model, and the ${\nu }^2-f$ model approaches in modeling TW air layers [22].

The equations for $k$ and $\omega$ in a 2D steady-state case are as follows:

$${\mathsf{\rho }}_0\left(u{\displaystyle \frac{\partial k}{\partial x}}+v{\displaystyle \frac{\partial k}{\partial y}}\right)=P_k+P_b-{\mathsf{\beta }}_{\mathrm{\infty }}^{\ast }{\mathsf{\rho }}_{0}k\mathsf{\omega }+{\displaystyle \frac{\partial }{\partial x}}\left[\left(\mathsf{\mu }+{\mathsf{\sigma }}_k{\mathsf{\mu }}_t\right){\displaystyle \frac{\partial k}{\partial x}}\right]+{\displaystyle \frac{\partial }{\partial y}}\left[\left(\mathsf{\mu }+{\mathsf{\sigma }}_k{\mathsf{\mu }}_t\right){\displaystyle \frac{\partial k}{\partial y}}\right]$$

(5)

$$\begin{gathered} {\mathsf{\rho }}_0\left(u{\displaystyle \frac{\partial \mathsf{\omega }}{\partial x}}+v{\displaystyle \frac{\partial \mathsf{\omega }}{\partial y}}\right)={\mathsf{\alpha }}_{\mathrm{\infty }}{\displaystyle \frac{\mathsf{\omega }}{k}}{P}_k-{\mathsf{\beta }}_{\mathrm{\infty }}{\mathsf{\rho }}_0{\mathsf{\omega }}^2+{\displaystyle \frac{\partial }{\partial x}}\left[\left(\mathsf{\mu }+{\mathsf{\sigma }}_{\mathsf{\omega }}{\mathsf{\mu }}_t\right){\displaystyle \frac{\partial \mathsf{\omega }}{\partial x}}\right]+{\displaystyle \frac{\partial }{\partial y}}\left[\left(\mathsf{\mu }+{\mathsf{\sigma }}_{\mathsf{\omega }}{\mathsf{\mu }}_t\right){\displaystyle \frac{\partial \mathsf{\omega }}{\partial y}}\right] \\ +2\left(1-F_1\right){\displaystyle \frac{{\rho }_0{\sigma }_{{\omega }_2}}{\mathsf{\omega }}}\left({\displaystyle \frac{\partial k}{\partial x}}{\displaystyle \frac{\partial \mathsf{\omega }}{\partial x}}+{\displaystyle \frac{\partial k}{\partial y}}{\displaystyle \frac{\partial \mathsf{\omega }}{\partial y}}\right) \end{gathered}$$

(6)

Equation (5) for k represents the balance of turbulent kinetic energy, which is influenced by production, buoyancy, and dissipation. Meanwhile, Equation (6) for ω controls the rate at which turbulence is dissipated.

In Equation (5), ${\beta }_{\infty }^{\ast }$ represents an empirical constant, commonly set to 0.09 in the SST model; $P_k$ is the production of turbulent kinetic energy due to mean velocity gradients; and $P_b$ is the production of turbulent kinetic energy due to buoyancy [33]. The standard expression for $P_k$ in 2D is:

$$P_k={\mu }_t\left[2{\left({\displaystyle \frac{\partial u}{\partial x}}\right)}^2+{\left({\displaystyle \frac{\partial u}{\partial y}}+{\displaystyle \frac{\partial v}{\partial x}}\right)}^2+2{\left({\displaystyle \frac{\partial v}{\partial y}}\right)}^2\right]$$

(7)

The term $P_b$ becomes relevant with the Boussinesq approximation and depends on the temperature gradient. It is determined by:

$$P_b=-{\rho }_0\beta g{\displaystyle \frac{{\mu }_t}{P{r}_t}}{\displaystyle \frac{\partial T}{\partial y}}$$

(8)

where $\beta$ is the thermal expansion coefficient, which corresponds to a value of 0.0034 ${\mathrm{K}}^{-1}$, considering an ambient temperature of 20 °C. Additionally, $g$ is the acceleration due to gravity, 9.81 m/s; ${\displaystyle \frac{\partial T}{\partial y}}$ is the temperature gradient; and $P{r}_t$ is the turbulent Prandtl number, which has the value 0.85 for air flows.

Table 1. Simulation parameters.

Symbols	Parameter	Value	Unit
${\mathsf{\rho }}_0$	Reference Density	1.204	$\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$
$T_0$	Reference Temperature	20	°C
$c_p$	Specific Heat	1007	J/kg K
$\mathsf{\lambda }$	Thermal Conductivity	0.0242	W/m K
$\mu$	Dynamic Viscosity	$1.821\times {10}^{-5}$	Pa s
$\beta$	Thermal Expansion Coefficient	0.0034	${\mathrm{K}}^{-1}$
${{\alpha }_{\mathrm{\infty }}}^{\mathrm{*}}$	Model Constant (Outer Region)	1	-
${\alpha }_{\mathrm{\infty }}$	Model Constant (Outer Region)	0.52	-
${\beta }_{\mathrm{\infty }}^{\mathrm{*}}$	Model Constant (Outer Region)	0.09	-
$a_1$	Model Constant	0.31	-
${\beta }_i$ (Inner)	Model Constant (Inner Region)	0.075	-
${\beta }_i$ (Outer)	Model Constant (Outer Region)	0.0828	-
TKE Prandtl # (Inner)	Turbulent Kinetic Energy (Inner)	1.176	-
TKE Prandtl # (Outer)	Turbulent Kinetic Energy (Outer)	1	-
SDR Prandtl # (Inner)	Specific Dissipation Rate (Inner)	2	-
SDR Prandtl # (Outer)	Specific Dissipation Rate (Outer)	1.168	-
$P{r}_t$	Turbulent Prandtl Number	0.85	-

summarizes the CFD simulation parameters.

The three geometries studied are shown in Figure 3. The first, Figure 3a, represents a TW attached to a room without guided flow. The second geometry, Figure 3b, includes guided vanes at the bottom of the air cavity, consisting of three blades, while the last geometry, Figure 3c, also includes guided vanes but with five blades.

A grid independence test was performed using the first geometry with grids of 252,966; 161,790; 119,950; and 84,306 cells. The air mass flow rate at the outlet, specifically, the upper vent, differed by less than 1% between the grids with 252,966 and 161,790 cells. Therefore, the grid with 161,790 cells was selected. Furthermore,

Table 2. Outlet temperature values for different element numbers.

	Grid 1	Grid 2	Grid 3	Grid 4
Element number	83,402	119,950	161,790	252,966
Temperature	23.67 °C	23.86 °C	25.38 °C	25.3 °C

illustrates that the temperature variation at the outlet does not significantly change beyond the third grid with 161,790 cells.

The dimensionless distance $y^{+}$ for grid 4 is 1.6. The obtained $y^{+}$ is acceptable, as in a previous study of a TW attached to a room, using the k-$\omega$ model, it was found that with a $y^{+}<$ 2, the mass flow rate changed less than 1% when the mesh was refined [34]. Similarly, in [35], the authors reported no significant variation in the mass flow rate with a $y^{+}$ of less than 2.

4. Boundary Conditions

The width of the inlet and outlet vents, as well as the vertical air layer width, b, is set to 0.2 m (Figure 4). The slope angle of the heated wall is represented by $\mathsf{\gamma }$; it is worth noting that when $\mathsf{\gamma }=0$, the geometry corresponds to a typical TW with a vertical air layer. For a detailed explanation of the effect of different values of $\mathsf{\gamma }$ on the flow and heat transfer in a TW attached to a room, the reader is referred to [23].

The ratio of the heat flux of the glazing, ${\mathrm{q}}_1$, to the heat flux of the absorber, ${\mathrm{q}}_2$, is ${\mathrm{q}}_1/{\mathrm{q}}_2=0.077$. Similarly, the ratio between the heat flux of the glazing and the heat flux of the stone layer, ${\mathrm{q}}_3$, is ${\mathrm{q}}_1/{\mathrm{q}}_3=0.069$. A similar heat flux ratio is assumed, given that the stone layers are typically painted black, similar to the absorber. The heat flux ratio can be determined based on the transmission, reflection, and absorption coefficients of the glazing [21]. These coefficients are defined as ${\tau }_g$ = 0.8, r = 0.12, and ${\alpha }_g$ = 0.08, respectively. For the absorber, the absorption and transmission coefficients are ${\alpha }_p$= 0.95 and ${\tau }_p$= 0.05, respectively.

Equation (9) is used to calculate the solar radiation energy absorbed by the absorbing plate, expressed as the heat flux of the absorber in W/m². This calculation considers the transmittance of the glass cover; the absorptivity of the absorber; and the intensity of solar radiation, $I$, also measured in W/m² [27,36]:

$$q_2={\tau }_g{\alpha }_{p}I$$

(9)

Figure 4 illustrates the boundary conditions of the TW. In this research, different heat flux values are applied to the three TW configurations studied. The heat flux input values on the absorber are 200 W/m², 300 W/m², and 400 W/m². The top and bottom sides of the massive wall where the absorber is located have a heat transfer coefficient of 5 W/m²·K at 20 °C. Based on the heat flux ratios mentioned above, the corresponding heat flux values on the inclined glazing are 15.4 W/m², 23 W/m², and 30.8 W/m². For the stone layer, the applied heat flux values are 250 W/m², 350 W/m², and 450 W/m².

Even though a fixed heat flux represents an approximate solution, because of the transient nature of the solar radiation, it is easier to estimate the radiated heat flux rather than the wall film equilibrium temperature reached during the irradiation period, as done in [37]. In addition, it has been demonstrated that there is no significant difference between pure natural convection and radiation coupled with natural convection, for an inclined heated wall with respect to the vertical direction [23].

For the lower vent, a pressure inlet condition, $P_I=P+\rho (u^2+v^2)/2=0$, with an air temperature of 20 °C is applied, along with a turbulence intensity of 5%. For the upper vent, a pressure outlet condition is set with $P=0$, as the pressure is equal to the ambient pressure, and a room temperature of 20 °C is considered.

5. Validation of the Numerical Model

For a uniform heat flux value, $q$, at a wall, the Rayleigh number is designated as ${Ra}_H=\left({Gr}_H\right)\left(Pr\right)$, being the Prandtl number $Pr=0.71$ and the Grashof number, ${Gr}_H$, defined as

$$G{r}_H={\displaystyle \frac{g\mathsf{\beta }q{H}^4}{{\nu }^2\lambda }}$$

(10)

The flow becomes turbulent when the Rayleigh number is above ${10}^{10}$ [24]. Simulations are carried out for an input heat flux over the range of 200–450 W/m², which corresponds to the Rayleigh number range $9.29\times {10}^{13}\text{–}1.39\times {10}^{14}$.

To validate the numerical simulations, the average Nusselt number obtained in the present work is compared with the correlation proposed by Zamora and Kaiser, which is based on numerical simulations in a Trombe wall configuration similar to the present study but accounting for radiative effects [23].

$$\mathrm{N}{\mathrm{u}}_{\mathrm{H}}=0.141{\left(\mathrm{R}{\mathrm{a}}_{\mathrm{H}}\right)}^{0.244},\hspace{1em}{10}^6<\mathrm{R}{\mathrm{a}}_{\mathrm{H}}\le {10}^{16}$$

(11)

Figure 5 presents the average Nusselt number obtained across the range of Rayleigh numbers studied.

The dimensionless mass flow rate, as shown in Equation (12), where $m$ represents the mass flow rate per unit depth, in kg/s m, and ν is the kinematic viscosity [34], is obtained and compared with the correlation for the dimensionless mass flow rate provided in Equation (13).

$$M={\displaystyle \frac{m}{\rho \nu }}$$

(12)

$$M=0.0972{\left(\mathrm{R}{\mathrm{a}}_{\mathrm{H}}\right)}^{0.330},\hspace{1em}{10}^6<\mathrm{R}{\mathrm{a}}_{\mathrm{H}}\le {10}^{16}$$

(13)

Figure 6 presents the dimensionless mass flow rate obtained across the range of Rayleigh numbers studied, showing good agreement with the results.

6. Results

To study a TW attached to a room with guided vanes—specifically, in three-blade and five-blade configurations—and to compare it with a TW without guided vanes, a 2D numerical model was developed. Based on the results obtained, it is useful to first evaluate the path-lines of the three configurations, as shown in Figure 7.

For the TW without guided flow vanes (Figure 7a), the formation of three large vortices is evident. With the addition of a guided flow configuration with three blades (Figure 7b), the smaller vortex located at the lower end of the TW almost disappears, and the other two vortices become smaller. In the third configuration with guided flow using five blades (Figure 7c), the lower-end vortex does not disappear completely, but the other two vortices are further reduced in size. From the path-lines results, it is also evident that the TW configuration that produces the lower detachment of the flow is the guided flow with three blades.

Figure 8 shows the velocity field for the three configurations studied. It can be seen that the largest flow separation bubble, located at the top corner of the massive wall near the outlet, corresponds to the guided flow configuration with five blades, reducing the effective cross-sectional area of the upper vent. Meanwhile, the guided flow configuration with three blades is the one that most effectively reduces the separation bubble at the top corner of the massive wall near the outlet.

Although the inclusion of a TW configuration with guided flow can reduce flow detachment, it is observed that in the lower part of the massive wall near the lower vent, the blades induce local bubbles, which may explain the poorer performance of the guided flow configuration with five blades.

Figure 9 depicts the temperature contours for the three studied configurations. As a consequence of the separation bubble, evidenced by the largest vortices in the TW without a guided flow configuration, the heat transfer from the wall to the air is limited. For the guided flow configurations, the most evident difference is at the top corner of the massive wall near the outlet, where the guided flow configuration with five blades causes more effective heat transfer from the massive wall to the air.

Figure 10 shows the velocity curves in the near-wall regions for the three configurations studied at different heights, with a total height of 3 m. Here, $y$ = 0.7 m is near the lower vent, and $y$ = 2.8 m is near the upper vent. Figure 10a is the velocity curve for the TW without guided flow.

In the region adjacent to the glazing, velocity increases with height, reaching approximately 1.7 m/s as the maximum velocity observed among the three configurations, corresponding to the guided flow configuration with five blades (Figure 10c). Meanwhile, the guided flow configuration with three blades exhibits a similar velocity to the TW configuration without guided flow at y = 2.8 m.

Figure 11 depicts the temperature variation near the glazing and absorber regions. As the height increases, the width of the cavity decreases due to the geometry of the TW attached. The TW configuration without guided flow, shown in Figure 11a, exhibits the lowest temperature near the massive wall at $y$ = 0.7 m and $y$ = 1.4 m, reaching 25 °C. However, at $y$ = 2.8 m, the TW configuration with three blades, shown in Figure 11b, presents a lower temperature of 28 °C compared to 30 °C for the TW without guided flow, indicating more effective heat transfer from the absorber to the air. In contrast, the TW configuration with five blades, shown in Figure 11c, exhibits higher near-wall temperatures compared to the other two configurations, indicating poor heat transfer. At $y$ = 0.7 m and $y$ = 1.4 m, the temperature reaches approximately 38 °C.

From the discussion above, the guided flow configuration with three blades effectively enhances heat transfer from the absorber to the air compared to the other two configurations under heat flux conditions of 300 W/m² applied to the absorber.

Figure 12a shows the temperature variation at the outlet of the upper vent under different heat flux conditions, while Figure 12b presents the corresponding flow rate variation. Based on the previously described near-wall temperature and velocity, it can be observed that, for an input heat flux of 300 W/m², the guided flow configuration with three blades reaches the highest temperature at the outlet of the upper vent: 23 °C at a flow rate of 0.23 kg/s.

For an input heat flux condition of 200 W/m², the guided flow configuration with five blades shows a lower temperature, in contrast to the TW with three blades, which causes an outlet temperature in the upper vent of 22 °C at a flow rate of 0.17 kg/s.

At the condition of 400 W/m² as the input heat flux, the guided flow configuration with five blades features the highest outlet temperature at the upper vent, 24.45 °C; however, the mass flow rate is the lowest among the other two configurations, 0.19 kg/s.

Based on the observed trends in the temperature and flow rate, it is evident that the TW configuration without guided flow shows the highest flow rate, ranging from 0.22 to 0.27 kg/s. However, the configuration with three blades achieves the highest temperature range, 22–24 °C, albeit at a slightly lower flow rate of 0.17 kg/s to 0.23 kg/s. The configuration with five blades demonstrates lower performance in both temperature and flow rate.

The convective heat transfer per unit depth of the wall is calculated using Equation (14). Meanwhile, the thermal efficiency is calculated using Equation (15) [22,36]:

$$\dot{Q}=C_{p}m({\overline{T}}_{out}-{\overline{T}}_{in})$$

(14)

$$\eta ={\displaystyle \frac{C_{p}m\left({\overline{T}}_{out}-{\overline{T}}_{in}\right)}{I}}$$

(15)

At an input heat flux of 200 W/m² in the absorber ($q_2$), the convective heat transfer is 80.42 W/m, 112.55 W/m, and 65.47 W/m for the configurations without guided flow, with guided flow and three blades, and with guided flow and five blades, respectively. The configuration with three blades achieves the highest convective heat transfer, 112.55 W/m. Consequently, this configuration also exhibits the highest thermal efficiency at 200 W/m², reaching 42.77%. Similarly, at an input heat flux of 400 W/m² in the absorber, the guided flow configuration with three blades achieves the highest convective heat transfer and thermal efficiency, at 304.75 W/m and 57.90%, respectively. Figure 13 illustrates the thermal efficiency of the three studied configurations under varying absorber heat flux conditions.

7. Discussion

In the analyzed configurations, the base width is 0.8 m, decreasing to 0.4 m at the top due to the TW attached-to-room design. Under this geometric constraint, the temperature rise ranges from 21 °C to 24 °C, and the air flow rate increases from 0.18 kg/s to 0.27 kg/s with an input heat flux between 200 W/m² and 400 W/m². In contrast, in a vertical layer with glazing parallel to the absorber, another study reported a temperature rise of 0.66–14.70 °C and a flow rate increase of 0.042–0.255 kg/s across a layer width range of 0.1–0.8 m, with an input heat flux from 100 W/m² to 400 W/m² [21]. The broader range of the temperature rise in the vertical layer is likely due to the wider range of tested layer widths and different geometric constraints.

An analysis of the path-lines in the studied configurations reveals the formation of vortices, particularly in the TW configuration without guided flow. In the guided flow configuration with three blades, the recirculation zone near the bottom corner is almost eliminated. This path-line behavior aligns with previous research findings where a guided flow configuration in a vertical air layer reduced the recirculation zone, especially in narrow cavities [22].

Finally, it is worth mentioning that the Boussinesq approximation, used for simulating buoyancy forces by modifying the momentum equation, requires minimal temperature differences in the fluid’s thermophysical properties to treat these properties as constant. For air, this approximation introduces an error of about 1% if temperature differences are below 15 °C, or $T-T_0<15°\mathrm{C}$ [38]. For the studied configurations, with $T_0=20$ and a maximum obtained temperature of 24 °C, the temperature difference is 4 °C, which satisfies the condition mentioned above. In [21], considering the reported temperature rise range of 0.66–14.70 °C, the temperature difference condition $T-T_0<15°\mathrm{C}$ is also satisfied. In another study that employed the Boussinesq approximation [22], the temperature rise range is 20–30 °C, resulting in a temperature difference of 10 °C, so the approximation remains valid.

8. Conclusions

This research investigated three configurations of a TW attached to a room using 2D CFD simulations to evaluate the performance, in terms of heat transfer and flow characteristics. Based on the results, the following conclusions can be drawn:

(1)

Based on the path-line results and velocity contours, the TW configuration with three guided blades produces the least flow detachment, effectively reducing the separation bubble near the outlet at the top corner of the massive wall and almost eliminating the recirculation zone near the bottom corner.

(2)

The TW configuration with guided flow and three blades achieves the highest temperature rise, ranging from 22 to 24 °C, albeit at a slightly lower flow rate of 0.17–0.23 kg/s compared to the TW configuration without guided flow, under the applied heat flux conditions on the absorber, ranging from 200 to 400 W/m².

(3)

The three-blade configuration achieves the highest convective heat transfer, reaching 112.55 W/m, and the highest thermal efficiency, reaching 42.77% at 200 W/m². At 400 W/m², it also outperforms other configurations, with a convective heat transfer of 304.75 W/m and a thermal efficiency of 57.90%.

For practical implementation in building envelope elements, this study provides both a theoretical basis for assessing the thermal performance of Trombe walls and a decision-making framework for implementing guided vanes. The distinctive feature of our studied configuration, which includes a stone layer below the vanes, addresses a significant gap in the literature, as this type of Trombe wall, although widely used in rural areas, has not been extensively studied. This research therefore bridges the gap between theoretical understanding and practical applications, particularly benefiting rural construction, where stone-based Trombe walls are commonly implemented.