Modifications of Heat Transfer and Induced Flow Rate of a Solar Chimney by an Obstacle in the Air Channel

Using renewable energy resources in buildings has been increasing for saving energy. Among widely used methods, solar chimneys absorb solar radiation and induce an airflow for ventilation, heating, or cooling buildings. The performance of a solar chimney depends on the heat transfer in its air channel, which can be modified by changing the shape of the heat exchange surface. In this study, we examine the effects of a rectangular obstacle placed on the heated surface of the air channel of a solar chimney. A numerical model was built with the Computational Fluid Dynamics (CFD) technique. By changing the geometries of the chimney and of the obstacle, and location of the obstacle, it was found that the obstacle had strong effects on the local flow and heat transfer properties close to the object, particularly the Nusselt number and the temperature field. However, average quantities of the whole air channel flow, such as the averaged Nusselt number and the induced flow rate, were modified insignificantly, except for the temperature rise through the chimney and the thermal efficiency. The change of the flow rate and the average Nusselt number was 5.0% while the temperature rises and the thermal efficiency was up to 13.0%. The height of the obstacle had more influence than the length. This study suggests more investigations to achieve the objective of enhancing the induced flow rate for ventilation of buildings with an obstacle in the air channel of a solar chimney. Keywords— Renewable energy; solar chimney; buildings; ventilation; nusselt number; CFD Manuscript received 26 Jul. 2020; revised 31 Jan. 2021; accepted 28 Feb. 2021. Date of publication 30 Apr. 2021. IJASEIT is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.


I. INTRODUCTION
Renewable energy resources have been employed in buildings with many methods [1], and among them, solar radiation has been harnessed for natural ventilation with solar chimneys [2]- [5]. A typical solar chimney consists of an air channel enclosed by a transparent cover and an absorber surface, such as a building wall [6]- [10]. Once exposed to solar radiation, the transparent cover allows the radiation to pass through and absorb the absorber surface. The air in the channel receives heat from the absorber surface and is warmed up. With thermal effects due to the air temperature rise and the elevation difference between the inlet and the air channel outlet, an airflow is induced and used for ventilating the building or cooling its facades [1], [2].
A solar chimney's exposed wall can also absorb solar radiation directly [2], [11]. The absorbed heat is conducted through the cover plate and transferred to the air in the channel. When integrated into a building, solar chimneys can have different forms, including Trombe wall [12], roof-top solar chimney [13], or combined wall and roof solar chimney [14]. Many factors influence the ventilation performance of a solar chimney [3], [15]- [17]. Major ones include geometries of the air channel and the wall, such as the height and the gap of the air channel; material of the walls of the air channel; and weather conditions, such as solar radiation [3], [15]- [17].
Modifications of the air channels' shapes have been tested to improve a solar chimney's performance [18]- [20]. Khanal and Lei [18] proposed a solar chimney with an inclined transparent cover for enhancing the induced flow rate by suppressing the flow reversal at the chimney's outlet. Al-Kayiem et al. [19] reported that the highest flow rate through a solar roof chimney was achieved when the glazing plate was longer than the absorber surface. A similar achievement was also obtained with a bell-shaped inlet of the air channel by Singh et al. [20].
Attempts have also been focused on enhancing the heat transfer between the absorber surface and the air in the chimney channel by changing the absorber surface's shape [13], [18]. Lei et al. [13] employed a perforated absorber plate for a roof solar chimney, while Pangavhane et al. [21] tested a corrugated one. Chorin et al. [22] measured heat transfer rate in a closed cavity heated on one wall and an obstacle on the heated wall. Their results show that the heat transfer rate increased around the obstacle. The velocity distribution of the flow around the obstacle was also significantly modified. However, because of the cavity in their experiment was closed, no induced flow rate through the cavity was reported. Therefore, the effects of a single obstacle on the heated wall of the air channel of a solar chimney are still questioned. In this study, we focused on the effects of an obstacle on a solar chimney's absorber surface whose cover surface absorbs solar radiation directly. A CFD model examined modifications of the heat transfer obstacle, induced flow rate, temperature rise, and thermal efficiency.

A. Descriptions of the Problem
The studied solar chimney, as sketched in Fig. 1a, was attached to a vertical wall of a building. It consisted of an absorber plate, such as a metal sheet, placed close to the wall. The air channel gap between the plate and the wall was denoted as G, while the chimney's height was H. It was assumed that the chimney's third dimension was much larger than G, and the chimney was considered in two dimensions as in Fig. 1a. Solar radiation was absorbed by the absorber plate and conducted through the plate thickness into its inner surface. Inside the air channel, the absorbed heat was then transferred to the air mostly through convection. Warmed air might rise in the air channel due to the stack (thermal) effects. The induced airflow can be used for ventilation on the building or cooling the building facades [23].
A rectangular obstacle (OB) was placed on the surface of the air channel's heated surface (Fig. 1a). Its length and height were denoted as L and h, respectively. y was the distance of the obstacle from the inlet of the air channel.

B. Numerical Method
A computational model based on the Computational Fluid Dynamics (CFD) technique was built to predict the airflow and heat transfer in the chimney's air channel. The governing equations described the continuity (mass), momentum, and energy conservation principles. They were described by the Reynolds Averaged Navier -Stokes (RANS) equations, with the following assumptions:  The airflow and heat transfer are steady and twodimensional.  The airflow is incompressible.  The fluid properties follow the Bossiness approximation.  Effects of radiation heat transfer between two surfaces of the air channel are negligible.  Heat loss through the thickness of the absorber plate is not modeled. A turbulence model is also required for simulation as the airflow in typical solar chimneys is turbulent [23]. The twodimensional forms of the governing equations in forms of tensor notation are as follows [23]- [25].
where u, p, and T denote the velocity, temperature, and pressure, respectively; ρ, ν, and Pr stand for the air density, kinematic viscosity, and the Prandtl number, respectively; β is the thermal expansion coefficient of the air; ' indicates the fluctuating component; presents a time-averaged quantity.
The reference temperature ref T was taken as the ambient one.
In this study, the RNG k-ε model [26] was employed for the turbulent stress ' ' j i u u and the turbulent heat flux It was selected as it offered the most stable and fastest convergence speed among the available turbulence models, such as the standard k-ε or the standard k-ω [23]- [25].
The governing equations were discretized with the Finite Volume Method on a structured rectangular grid, shown in Fig. 1b. The computational domain consisted of both the air channel and ambient air, as suggested by Gan [27]. The mesh was clustered near the solid surface, particularly near the heated and the obstacle surfaces.
For the flow boundary conditions, the building wall and the absorber plate's surfaces, and the obstacle were treated with no-slip conditions. Other open boundaries of the domain were set to atmospheric pressure. Uniform heat flux was applied on the heated surface. Other solid surfaces were considered as adiabatic walls.
The commercial CFD code ANSYS Fluent Academic Version 2019R3 was employed for the numerical setup, with the SIMPLE scheme for the coupling between the continuity and momentum equations. The mesh density was also checked carefully to achieve mesh -independence solutions. Details about the numerical setup can be found in [25,26].
For validation, the computational model was tested with the experiment by Burek and Habeb [12]. Their experiments were conducted with a vertical solar chimney with H=1.025 m. The gap changed from 20 mm to 110 mm, and the width of the chimney was 0.92 m. The induced flow rate through the air channel was measured at different heat fluxes. Fig. 2 shows the comparison of the measured and computed flow rate at two total heat inputs of 1000 W and 600 W. The computed data could match the measured ones well with the maximum discrepancy of less than 8.0%.

A. Flow and Temperature Fields
The flow and temperature fields of the solar chimney with and without the obstacle are presented in Fig. 3. The obstacle was placed at y/H=0.3 and 0.6. The thermal layer near the heated surface developed continuously from the air channel's inlet without the obstacle. With the obstacle, the thermal layer was disturbed around the object. The disturbed region was larger at y/H=0.6. However, at the outlet, the temperature distributions were slightly different from each other. Similar effects were also seen for the flow field. As passing the obstacle, where the flow area was contracted, the velocity increased. However, further downstream of the objects, the velocity distributions quickly recovered to the cases without the obstacle. Fig. 4 shows the distributions of the local Nusselt number on the cases' heated wall in Fig. 3. The Nusselt number is defined as in (4). It is seen in Fig. 4 that the Nusselt number was strongly modified around the obstacle. In both cases of y/H, close to OB, the Nusselt number dropped at both before and after OB. Further downstream, the Nu increased then went back to the base case (without the obstacle). The increase of Nu compared to that of the base case was higher for y/H=0.6. A similar increase of the Nu after the OB was also reported by Chorin et al. [22]. However, they did not report the decrease of Nu close to the OB. It is possible because their measurement points were not sufficiently close to the OB to capture that trend. According to (4), the local Nusselt number depends on both w q and w T . As w q and a T were fixed to 400 2 / m W on the whole surface of the heated wall and 293.15 K, respectively, the Nusselt number was proportional to w T / 1 .

 
As seen in Fig. 3, there were two separation zones right before and after OB. Inside these zones, the air temperatures were much higher than that of the base case's thermal layer at the same locations. This result may explain the reduction of the Nusselt number in those regions. Further downstream of the rear separation zone, the flow was re-attached with higher velocity, hence lower wall temperature and increase of the Nusselt number.

C. Averaged Nusselt number
The Nusselt number was averaged on the whole heated surface by (5).
The averaged Nusselt number is plotted in Fig. 5 for different values of G, h, L, and y. In general, the ratio of base av Nu Nu / increased with the distance y/H of OB. However, the change was minor and within 5%. The ratio was essentially less than 1.0. Therefore, the presence of OB reduced the averaged Nusselt number on the heated surface. In Fig. 5a, the data trends were similar for different L's but different for different h's. Similar trends can also be seen in Fig. 5b. Therefore, between the two dimensions of OB, it is expected that h had more influence on av Nu than L. It is also observed in Fig. 5 that increasing h shifted the data lines down; hence reduced the averaged Nusselt number compared to that of the base case.

D. Induced flow rate
The induced mass flow rate Q through the chimneys in Fig. 5 was plotted in Fig. 6 and normalized by the base case base Q . It is seen that the flow rate slightly increased compared to the base case when OB is on the lower half of the heated wall. As the location of OB moved up, the flow rate decreased. However, the change in the flow rate was only within % 0 . 4  . This number agrees with the observations in Fig. 3 and the data in Fig. 5, which indicate that OB had negligible effects on the averaged Nusselt number and the whole air channel's flow field.

E. Temperature rise
The temperature rise of the airflow through the channel is defined as the temperature difference between the outlet and the inlet by (6). is larger than 1.0. Therefore, the presence of OB increased the temperature rise through the air channel. The maximum increase was about 6.0% for G=0.1 m, but up to about 13.0% for G=0.2 m.
It is observed in Fig. 7 that base T T   / increased with both L and h. However, the effects of h are more significant than that of L. The increase of base T T   / due to L was less than 1.0% for both G values while that h was 4.0% for G=0.1 m and 8.0% for G=0.2 m.
As y/H increased, particularly when y/H > 0.6 in Fig. 7b, ΔT was strongly enhanced. This trend can be seen in Fig. 3. The thermal boundary layer was enlarged around OB. As OB was closer to the air channel outlet, the outlet's thermal boundary became thicker and yielded higher average air temperature To; hence higher ΔT.
Q is the mass flow rate; is the specific heat capacity of air, and is the air channel's heat input.
The thermal efficiency normalized by that of the base cases, base   / , is presented in Fig. 8. For G=0.1, the presence of OB reduced the thermal efficiency up to about 6.0%. In contrast, for G=0.2 m, the thermal efficiency was boosted up to 13.0%. For both cases of G, changing L had negligible effects on the trend of the data while increasing h shifted the curves up for both values of G. Therefore, increasing h boosted the thermal efficiency.
The trends of base   / versus the position of OB, y, are similar to those of ΔT. According to (7), the thermal efficiency change resulted from the change of both the flow rate and the temperature rise. As the change of the flow rate was minor (Fig. 6), the thermal efficiency changes mostly contributed to the change of the temperature rise.

IV. CONCLUSION
With the obstacle on the air channel's heated surface, the flow and temperature fields close to the object were strongly disturbed. The thermal boundary layer was enlarged around the obstacle. The enlarged region was enhanced as the obstacle approached the outlet of the air channel. This fact resulted in increasing the temperature rise, up to 13% compared to the base case.
The local Nusselt number significantly decreased before and after the obstacle where the flow and the temperature fields were strongly disturbed. Far upstream and downstream of the obstacle, the local Nusselt number was close to that of the base case. The averaged Nusselt number on the whole heated wall tended to decrease. However, the reduction was only less than 5.0% for the tested cases. Although the flow field was strongly disturbed around the obstacle, the air channel outlet's flow structure was similar to the case without an obstacle in the air channel. Change of the induced flow rate caused by the obstacle's presence was minor and less than 4.0% compared to that of the base case.
Change of the thermal efficiency due to the obstacle had similar trends to those of the temperature rise. For the cases with smaller gap, G=0.1 m, the thermal efficiency decreased.
For the cases with the larger gap, G=0.2 m, it increased up to 13.0%.
Among the two dimensions of the obstacle, the height h was seen to have more effects than the length L. Increasing h resulted in a decrease on the averaged Nusselt number and increase of the temperature rise and the thermal efficiency. The effects of changing L on the above parameters were insignificant. Although some effects of the obstacle have been observed in this study, the induced flow rate, which is the main parameter for ventilation application of solar chimneys, was not enhanced. Therefore, more investigations are suggested for this objective.