Impact of the V CAP on induced turbulent air flow in a solar chimney a computational study

Abstract

Keywords: Solar Chimney; Natural Ventilation; CFD; Top Cap

Introduction

Solar chimney is a simple and efficient natural ventilation device without pumping power. Its absorber surface receives solar radiation and heats the air which moves upwards via the chimney effect. It is suitable for natural ventilation purposes in living spaces or farms in the areas where radiation intensity is high and stable. The different configurations of solar chimney have been studied experimentally, numerically or analytically to evaluate performance. Very

early, Ong [1] proposed a simple analytical model based on the flat plate collector theory. The model is the basis for next predictive models that have taken into account corrections to improve accuracy. Chen et al. [2] have experimentally investigated the vertical and inclined solar chimneys. They found that the 45° tilt angle provides the greatest air flow and is 45% higher than that of a vertical chimney. Bassiouny and Koura [3] investigated and analyzed a solar

*Corresponding author. *E-mail address: nguyenminhphu@iuh.edu.vn This paper was recommended for publication in revised form by Regional Editor Omid Mahian Published by Yıldız Technical University Press, İstanbul, Turkey Copyright 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

chimney coupled with a ventilated room. They reported that the effect of chimney width was more important than inlet size and suggested chamfering chimney inlet. Arce et al. [4] have experimentally surveyed a solar chimney to determine the discharge coefficient. The coefficient was defined as 0.52 which is useful for designing a solar chimney. Manca et al. [5] has simulated a vertical solar chimney with inclined glass. They confirmed that the air flow increased by 20% compared with the vertical glass cover. Khanal and Lei [6] determined the optimal angle of 4° to achieve maximum flow rate. In addition, they claimed that increasing inclination of solar chimney reduces turbulence kinetic energy and turbulence intensity. Exergetic analysis of a solar chimney was done by López et al. [7]. They demonstrated that the exergy performance of a solar chimney is very low and suggested improving this performance by changing the design. Jing et al. [8] experimentally evaluated the effect of solar chimney with large air gap on induced air flow. They conclude that the existing mathematical model exhibited a poor prediction, especially cases with a large chimney width. They modified the model by considering the reversed flow at the chimney outlet to improve accuracy. Recently, Duan [9] developed a new analytical model to predict air flow and air temperature difference across solar chimney. The prediction of this model has been compared with the experimental results with acceptable errors. More recently, Xamán et al. [10] evaluated a solar chimney in conjunction with a ventilated room. They showed that ventilation effectiveness was improved up to 45% and air change per hour up to 2.5. Kong et al. [11] simulated solar chimneys that were tilted 30 to 90° relative to the horizontal plane. They found that inclination angles from 45 to 60° achieved the greatest discharge depending on season and latitude. Nguyen and Wells [12] numerically investigated of horizontal solar chimneys. They concluded that outlet width had a notable effect on the thermal efficiency of a solar chimney. The efficiency dropped drastically from 90% to 30% when increasing outlet width beyond a specific dimension. The air outlet of a solar chimney is located outdoor. Therefore, it is obvious that a cap must be installed to protect against weather conditions such as rain, snow or bird waste. This cap results in a decrease in the natural ventilation air flow due to the effect of an obstruction at the exit. An evaluation of the effect of top retrofitted cap on induced air flow has not been found in open literature. Thus, this study investigates the effect of the position and size of the V-shaped cap on the air flow and temperature distribution of a vertical chimney by 2D numerical analysis using the commercial code ANSYS-Fluent.

Model Description And Validation

Figure 1 shows a solar chimney with the height of 521 mm and the air gap of 40 mm studied in this paper. The

right wall is glass cover and the left wall is the absorber plate. These dimensions were adopted from the previous study [11] to verify and compare. On the top of chimney there is a right-angle V cap with an offset (O) from chimney and a width (W). In this study, O varies between 40 and 60 mm, W in the range of 65 to 75 mm and the heat flux received from solar radiation of the absorber plate from 200 to 800 W/m2. To simulate the flow of air entering and leaving the chimney, the calculated domain is extended to a rectangle of 300 mm ´ 1000 mm. Figure 2 shows the meshing of the computational domain in which the absorber surface and the glass surface are refined for intensifying predictive accuracy. The problem of natural convection in open domain was numerically solved using the SST k-w turbulence model and the DO (Discrete Ordinates) radiative heat transfer model [11] in the ANSYS Fluent 18.2 simulation tool. The governing equations have been presented in the ANSYS Fluent manual so they are not presented here for simplicity [13-17]. The governing equations have been solved with the assignment of boundary conditions as shown in Table

Figure 2. Meshing of the domain with refinement for inner walls of the chimney.

1. Equations (1)-(6) summarize the governing equations in

No-slip conditions, emissivity = 0.95, heat flux = 200 to 800 W/m2

Energy equation:   ∇⋅ v (ρ E + P ) = ∇⋅ (keff )∇T + ∇⋅ (τ v )

Turbulence kinetic energy equation: ∂ ∂  ∂k  Γ k (rkui ) =  + Gk − Yk + Sk ∂xi ∂x j  ∂x j 

Dissipation rate equation: ∂ ∂  ∂ω  Γ ω ρωu j ) = (  + Gω − Yω + Sω + Dω ∂x j ∂x j  ∂x j  (5) ε2 + C3ε Gb − C2 ε ρ + Sε k Radiative transfer equation of DO model:    ∇⋅[ I (r , s ) s ] + (ac + σs ) I (r , s ) = ac n2

To deal with temperature-dependent density of air, ideal gas was assumed in the present study. The PRESTO! Scheme was employed to pressure term for catching up the buoyancy-driven problem [13, 18]. The errors for all governing equations are assigned as 10-4 for the convergence. Figure 3

shows the grid independence test for the case without a cap at heat flux of 800 W/m2. The tested number of meshes ranged from 14338 to 79859 elements. It can be seen clearly that when the mesh number is 36810 or more, the velocity profile at the chimney outlet does not change significantly. Therefore, the settings at this grid number are applied to all studied cases. Figure 4 shows the distribution of y+ value along the walls of the chimney. The average y+ of the glass wall and absorber plate reached 1.24 which was close to 1 as suggested by Kong et al. 2020 [11]. A further decrease in y+ increases the induced airflow negligibly. However, the computation time significantly increases. To confirm the results from the numerical methodology, the air flow at the chimney outlet in the absence of a cap is compared with published data with the same chimney height and chimney gap. Figure 5 shows the effect of the received heat of the absorber plate on the sucked air flow per 1 m of spanwise width. It can see a good agreement

Figure 4. Dimensionless wall distance (y+) along glazing and absorber plate.

Figure 5. Validation with experimental result [19], analytical result [8], and numerical simulation result [11].

between current simulation results with experimental, theoretical and simulated results in previous studies. The maximum errors of current research with analytical, simulated and experimental results are 5.4%, 9.2% and 15.8%, respectively. From this confirmation, simulation of the effect of V cap at top of the chimney was conducted to evaluate the flow rate and perform further analyzes in the next section.

Results And Discussion

The effects of the cap offset and heat flux on the intake air flow are shown in Figure 6 at fixed cap width of 70 mm. The airflow rate of the chimney without cap has also been plotted for the sake of comparison. It can be seen that due to the interference of the cap, the solar chimney with a cap has air flow rate about 20% lower than the no cap case. When

Figure 6. Effects of heat flux and V cap offset at W = 70 mm.

Figure 7. Temperature distribution with V cap offsets at q= 800 W/m2 and W=75 mm.

the offset increases, the air inside the chimney is easy to escape, so the induced flow increases. Figure 7 shows the air temperature distribution in the computational domain at the same heat flux and cap width. The air temperature at chimney core is close to the ambient temperature, the highest air temperature is near the absorber plate followed by the glass cover due to the transfer of radiant heat from the absorber plate to the glass cover. The air temperature around the cap with the smallest offset has the highest value. Due to the small offset, a low air flow results in a larger air temperature. The higher air, the lower is air temperature due to diffusion of the hot air with the cold air in the environment. Figure 8 shows the air velocity magnitude at a heat flux of 800 W/m2. The air flow rate in the chimney without cap is significantly larger than the actual chimney having a cap. The inlet velocity profile is quite similar between the

Figure 8. Velocity magnitude with V cap offsets at q = 800 W/m2 and W =75 mm.

Figure 10. Velocity magnitude variation with heat fluxes at O = 40 mm and W = 70 mm.

Figure 9. Turbulence kinetic energy and velocity vector around a V cap. Figure 11. Temperature distribution by varying heat flux at O = 40 mm and W=70 mm. presence and absence of a cap. However, in the last half of the chimney, the chimney core has almost no air moving because the V-shape of the cap causes the large static pressure field below the cap. This results in a reduction in the intake air flow. Figure 9 clarifies the flow mechanism around V cap via velocity vector and turbulence kinetic energy contour. A moving stream of air can be seen below the cap from the absorber plate to the glass cover. This is because the air near the plate absorbs thermal energy of the highest temperature surface resulting in maximum velocity. This high velocity flow is blocked and guided by the wall of the cap so it moves towards the glass cover. This can lead to the outflow from the left side higher than the right side as can be seen in Figure 6. This explains the fact that the air current above the cap tends to blow to the left. Above the cap, there is a vortex pair formed from two streams coming out of chimney. This causes the largest turbulence kinetic energy region like vortex shedding from a fluid moving past an obstruction. In

the absence of a cap, the largest turbulence kinetic energy is probably in the airflow leaving the chimney from the side of the absorber plate followed by the glass side. For a solar chimney without cap, Khanal and Lei [6] showed that the highest turbulence intensity occurred at the chimney exit close to the absorber plate. The current study coincides well with their observations. However, when a V-shaped cap is installed, the region with the highest turbulence intensity occurs at the downstream of the cap. Figures 10 and 11 show the velocity magnitudes and isotherms at different heat fluxes; meanwhile, the geometries of the cap are fixed. It can be seen clearly that increasing solar thermal energy to the absorber plate, the temperatures of air and surfaces inside the chimney raise monotonically. The increased temperature of absorber plate and glass cover leads to augment the buoyancy driven natural convection current.

12. It can be seen that when increasing cap width, it

reduces the cross-sectional area for escaping the induced air out of solar chimney. However, the effect of cap width

on the air flow is negligible compared to heat flux and offset. In order to facilitate the design and evaluation of the effects of the parameters on the ventilation air flow rate, the flow function according to the three variables examined above including heat flux, cap offset and cap width was developed upon linear regression. The development steps are illustrated in Figures 13a-c regarding to the sequential plot of the variables [20]. The results obtained the air flow correlation as equation (7). To confirm the accuracy of the predictive equation, Figure 13d shows the prediction result from equation 7 and input data. The results reveal that the equation has good predictability with errors less than 2.5%. From the exponents of the function, it can be seen that the effect of offset is equivalent to the absorption heat flux gained from solar radiation and the effect of cap width is less significant. V predicted = 0.00112172421q 0.25661058O 0.238275349W −0.0964393807 (7)

The equation (7) is applicable with the following parameters:

Figure 13. Correlation development of induced air flow with the examined variables.

• Solar chimney height of 521 mm • Solar chimney gap of 40 mm • Heat flux (q) from 200 to 800 W/m2 • Cap offset (O) from 40 to 60 mm • Cap width (W) from 65 to 75 mm Figure 3 shows a transparent enclosure includes a particulate (participating) media. This figure describes the radiative phenomena inside a particulate media. When radiative energy travels through participating media, the incident beams are attenuated by scattering and absorption, while others are transmitted through this media to the other side.

Conclusion

Effects of position and size of a V-shaped cap on the performance of a solar chimney are presented in this paper. A 2D numerical simulation used the SST k-w turbulence model and the DO radiation model to determine temperature distribution, air velocity, and induced air flow. The results show that the cap shield reduces air flow about 20%. The effect of cap offset on ventilation flow rate is more significant than that of cap width. There is a vortex below the cap in the direction from the absorber plate to the glass cover due to the higher temperature of the absorber plate resulting in a higher air velocity on the side of the glass cover. Two large vortices are observed at downstream of the cap that causes the energy loss of buoyancy-driven flow. A linear regression function of the induced air flow with independent variables of heat flux, cap offset and cap width was developed to quantify the influencing factors and facilitate the design and selection of cap shield for solar chimney. From the current research results, it is suggested that the design of natural ventilation using solar thermal energy should take into account the reduction in air flow caused by chimney cap. Also, the different configurations of solar chimney, i.e., inclined glazing, inclined absorber plate, horizontal chimney should be evaluated with respect to congested free convection current.

Nomenclature

Cap offset (mm) Pressure (Pa) Heat flux (W/m2) Temperature (°C) Volume flow rate (m3/s) Velocity vector (m/s) Cap width (mm) Horizontal coordinate Vertical coordinate Dimensionless wall distance

Acknowledgments

This research is funded by the Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number B2021-20-06.

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

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