- Email: [email protected]
Experimental and theoretical study of solar chimneys in buildings with uniform wall heat flux
Solar Energy 193 (2019) 244–252
Contents lists available at ScienceDirect
Solar Energy journal homepage: www.elsevier.com/locate/solener
Experimental and theoretical study of solar chimneys in buildings with uniform wall heat flux Yicun Hou, Huang Li, Angui Li
T
⁎
School of Building Services Science and Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Experiments Solar chimney Temperature measurement Velocity measurement Prediction method
Solar chimneys are often used in buildings to enhance natural ventilation; thus, accurate assessment of the ventilation effect is essential for their design. However, the prediction method available in the literature usually overpredicts the airflow rate. In the present study, a solar chimney with a variable gap-to-height ratio between 0.1 and 0.5 is used as the research object to develop an improved prediction method. Experiments and theoretical analyses were conducted to investigate the induced airflow characteristics, such as air temperature distribution, air velocity distribution, and the reverse flow phenomenon. The results show that the distribution of induced air temperature and velocity were highly nonuniform and that the optimum chimney gap-to-height ratio was estimated to be 0.4. The reverse flow phenomenon appeared at the outlet when the chimney gap was 400 mm, and the reverse flow continued to penetrate downward into the chimney as the chimney gap increased. The proposed method considers the variation in the pressure loss coefficient for various flow conditions at the chimney outlet. By comparing the predicted value and the experimental data, the proposed method was demonstrated to be valid for predicting the induced airflow rate with or without reverse flow. Moreover, the current study motivates further research on prediction method for airflow rates in solar chimneys.
1. Introduction The building industry accounts for between 35% and 45% of global energy consumption (Monghasemi and Vadiee, 2018). In recent years, interest in solar chimneys has been stimulated by an increasing awareness of energy savings and the need for effective ventilation in buildings (Khanal and Lei, 2012; Harris and Helwig, 2007; Chantawong and Khedari, 2018; Liu et al., 2019). Solar chimneys convert solar energy into the kinetic energy of the air inside the chimney: The opaque elements of solar chimneys absorb solar radiation and heat the air inside the chimney. The density of the heated air decreases, which causes an updraft inside the chimney owing to thermal buoyancy (Dordelly et al., 2019). The main tasks in solar chimney studies are generally assessment and enhancement of the ventilation effect provided by the solar chimney (Ahmed and Hussein, 2018; Abdeen et al., 2019). Ong (2003) proposed a steady mathematical model for predicting the induced airflow rate. Their analytical results were consistent with those of experiments in which the chimney height was more than 10 times the gap. Based on Ong’s work, Martı and Heras-Celemin (2007) achieved good results when using a dynamic model to analyze the thermal performance of a solar chimney. The experimental results obtained by Afonso ⁎
and Oliveira (2000) showed that the chimney width had a greater effect than the chimney height on the ventilation rate. Reverse flow in a solar chimney affects the negatively induced airflow rate. Boucher (1994) found that reverse flow appeared when the chimney gap was 0.5 m for a vertical solar chimney (Gap/H = 0.25). Chen et al. (2003) conducted experimental visualizations and reported that reverse flow began to appear at the outlet when the chimney gap was equal to 300 mm. As the chimney gap increased, the reverse flow increased and continued to penetrate downward into the chimney. Khanal and Lei (2012) developed and quantitatively examined an inclined passive wall solar chimney (IPWSC). The proposed IPWSC significantly suppressed the reverse flow when the passive wall was inclined at a 5° angle from the vertical wall (Khanal and Lei, 2014). The optimum chimney gap is highly debatable. Some researchers have demonstrated the existence of an optimum chimney gap that induces the maximum ventilation rate in a chimney. Jing et al. (2015) performed experiments and reported that the optimum ratio between the gap and height is approximately 0.5. Gan (2006) investigated the effect of the chimney width on the induced airflow rate by numerical simulation. Their results showed an optimum gap in the range of 0.55–0.6 m. Boucher (1994) conducted experiments and demonstrated that the maximum ventilation rate occurred when the ratio between the gap and
Corresponding author. E-mail address: [email protected] (A. Li).
https://doi.org/10.1016/j.solener.2019.09.061 Received 11 July 2019; Received in revised form 8 September 2019; Accepted 17 September 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
Nomenclature
w q Q ρ cp Taverage Tamb ΔPs ΔPL ΔP H A Ain Aout
f cin cout CD \* Dh u u1 Gr ∗ Pr
chimney width (mm) heat flux (W/m2) induced airflow rate (m3/s) air density (kg/ m3) specific heat capacity J/(kg · °C) average air temperature (°C) ambient temperature (°C) stack pressure (Pa) pressure loss along the chimney (Pa) cross-vent pressure difference (Pa) chimney height (m) chimney channel cross-sectional area (m2) inlet area (m2) outlet area (m2)
Greek letters boundary layer thickness (m) air expansion coefficient kinetic viscosity of air (m2/s)
δ β v
the heat flux, Q is the induced airflow rate, ρ represents the air density, cp is the specific heat capacity, Taverage is the average air temperature at h, and Tamb is the ambient temperature. The stack pressure, ΔPs , can be determined by using Eq. (2):
height was approximately 0.1. However, neither Chen et al. (2003) nor Shi et al. (2018) found optimum gaps in their studies. Spencer et al. (2000) reported that the optimal gap is related to the chimney inlet design. Thus, the optimum chimney gap problem needs further research. The methods commonly used for predicting the airflow rate have generally been proposed based on the assumption that the air temperature is uniformly distributed at the same height. Such a method was successfully used by Awbi and Gan (1992) to predict the induced airflow rate. Sandberg and Moshfegh (2002) performed experiments with a rectangular solar panel and reported that the predicted induced airflow rate was close to the experimental results. Similar results were reported by Aboulnaga (1998); Ong (2003); Bansal et al. (1994); Mathur et al. (2006). It is noted that the aforementioned method for predicting the airflow rate is only suitable for narrow chimneys. With regard to wide chimneys, Chen et al. (2003); Arce et al. (2009) found that the values predicted by using the existing method available in the literature were usually larger than the actual induced airflow rate. The resulting overprediction may be caused by the following factors. First, the actual temperature distributions in the experiments were uneven. Second, the adopted pressure loss coefficients did not necessarily apply to buoyancy-driven natural ventilation because these coefficients were obtained in normal forced flows. Third, the occurrence of reverse flow may exert a negative influence on the accuracy of the predicted value. Therefore, further studies are necessary to guarantee adequate prediction of the induced airflow rates in chimneys. In the present study, the induced airflow inside a solar chimney is investigated by experiments and theoretical analyses, and the reverse flow phenomenon is qualitatively investigated by experimental visualization. The air temperature and airflow rates are measured under different conditions to lay the foundation for further analysis. This study presents a novel method for predicting the airflow rate and verifies the results with experimental data. The proposed method is valid for predicting the induced airflow rate with or without reverse flow. Moreover, the current study motivates further research on solar chimneys.
ΔPs =
∫0
H
(Taverage − Tamb) ρg Tamb
dh =
where B is the buoyancy flux, B =
ρBH , 2Q gqwH , ρcp Tamb
(2) and H represents the chimney
height. The pressure loss, ΔPL , can be calculated by using Eq. (3):
ΔPL = cin
ρ (Q/ Ain )2 ρ (Q/ Aout )2 H ρ (Q/ A)2 + cout +f , 2 2 2 Dh
(3)
where A is the chimney channel cross-sectional area; Ain and Aout are the inlet and outlet areas, respectively; f is the friction factor for the channel wall; cin and cout are the inlet and outlet pressure loss coefficients, respectively; and Dh is the hydraulic diameter of the chimney channel. The airflow rate, Q, can be determined by using Eqs. (4) and (5): 1/3
B Q = A ⎜⎛ ⎟⎞ ⎝ 2ψ ⎠
,
(4)
where 2
ψ=
2
A⎡ H 1 A ⎞ A ⎞ ⎤⎤ f cin ⎛ + ⎡ + cout ⎛ ⎥ ⎥. H ⎢ 2Dh 2⎢ A A in ⎠ ⎝ out ⎠ ⎦ ⎦ ⎣ ⎝ ⎣ ⎜
⎟
⎜
⎟
(5)
The values of cin and cout are determined generally by analyzing the available data for normal forced flow. This finding indicates that the airflow rate is affected mainly by the stack pressure and the pressure losses. Therefore, it is vital to evaluate the air temperature distribution and the pressure coefficients when predicting the induced airflow. 3. Experiments As shown in Fig. 1, the height and width of the experimental solar chimney were 2.0 and 1.0 m, respectively, and the gap of investigated chimney varied from 0.2 to 1.0 m at intervals of 0.2 m. The experimental chimney resembled a rectangular channel composed of three walls with uniform heat flux and a movable glass plate to observe the induced airflow pattern. The heated walls were covered with a 1.2 mm thick electrothermal film to provide a variable heat flux. All of the walls were insulated with 50 mm mineral fiber to reduce heat loss. The base of the investigated chimney was 0.5 m from the ground. Fig. 2 displays the layout of the measuring points. As shown in Fig. 2(a), each heated surface was equipped with 15 T-type thermocouples for measuring the wall temperature. The induced air
2. Analysis of prediction methods The available methods for predicting the airflow rate under a given solar radiation intensity are based on the assumption of uniform air temperature (Awbi, 1994; Bassiouny and Koura, 2008; Ong, 2003; Martı and Heras-Celemin, 2007). The energy balance can be expressed by Eq. (1):
qhw = QρCp (Taverage − Tamb),
friction factor for the channel wall inlet pressure loss coefficient outlet pressure loss coefficient MERGEFORMAT vent discharge coefficient hydraulic diameter of the chimney channel (m) local air velocity (m/s) characteristic air velocity in the boundary layer (m/s) modified Grashof number Prandtl number
(1)
where h is the height along the chimney, w is the chimney width, q is 245
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
Fig. 1. (a) Experimental model of solar chimney, (b) A real image showing the experimental test rig.
A Digitrend PF66B data logger was used to record the temperature, and the sampling interval was set to 10 s to ensure accurate average temperatures. A TSI8455 air anemometer was used to measure the induced air velocity with a calibrated accuracy of ± 5% at full range. The anemometer has a measurement range from 0.05 m/s to 3.0 m/s, and the uncertainty of the velocity measurements was of the order of 0.02 m/s. The random error was about ± 0.02 m/s owing to the stability of the
temperature was measured by seven T-type thermocouples mounted on a movable test lever inside the chimney channel, as shown in Fig. 2(b). A thermocouple was also required to measure the ambient air temperature. The thermocouples have a measurement range of −200 °C to +300 °C and were calibrated to within ± 0.2 °C in a thermostatic water bath before use. The total uncertainty of the temperature measurements was estimated to be less than 0.04 °C. The difference in temperature for the same measuring point with repeated experiments was less than 1 °C. 246
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
Fig. 2. Locations of measuring points (Unit: mm): (a) on the surface, (b) on a test lever.
1000 mm × 1000 mm × 800 mm in length, height, and width, respectively. The static pressure tank has two functions: to reduce the dynamic pressure and minimize the disturbance of the generated smoke and to ensure that the smoke temperature identifies with the ambient air temperature. The stored smoke is drawn naturally into the solar chimney through a passage via buoyancy-driven natural convection. The entire process of air movement in the chimney channel was recorded by a charge-coupled device (CCD) camera. A section of black fabric was used to cover the chimney wall to facilitate the visualization process. In the measurement process, the fabric cover was removed to avoid its influence on the induced airflow. 3.2. Experimental procedure Experiments were conducted with various heat input values ranging from 100 to 600 W/m2 at intervals of 100 W/m2; for each heat flux, the chimney gaps varied from 0.2 to 1.0 m at 0.2 m intervals. Each experimental condition was repeated three times to ensure the accuracy of the experimental data, and the average values were used for the following analysis. The temperatures and induced airflow rates were recorded until the solar chimney system achieved a steady state, which typically took 3–5 h
Fig. 3. Temperature distribution under various chimney gap values with 300 W/m2 at 1000 mm above the chimney inlet.
experiments. Thus, the total uncertainty was estimated to be less than or equal to 0.04 m/s for velocity measurements. To ensure the accuracy of the experimental data, it is important to determine the position of the probe. If the probe is incorrectly positioned, the measurement error will increase owing to air disturbance. According to the results of experimental visualization, the probe was placed 0.8 m above the inlet, where the reverse flow is limited and the airflow is parallel to the chimney walls. Chen et al. (2003) performed experiments using a chimney model with a height and width of 1.5 and 0.62 m, respectively, in which the probe was set 1.1 m above the inlet. Similarly, Jing et al. (2015) placed the probe 1.0 m above the inlet to reduce the measurement error. The sampling frequency for the airflow velocity was set to 2 Hz in the present study to ensure accurate time-averaged values (Kovanen et al., 1989). To determine the induced airflow rate, the probe was arranged at 30 points at the cross-section 0.8 m above the chimney inlet
4. Results and discussion 4.1. Temperature distribution Fig. 3 displays the typical temperature distributions along the chimney gap direction at a height of 1000 mm on the symmetrical plane. The induced air temperature distribution was highly nonuniform. The air temperature was the highest near the back wall, and the maximum temperature difference reached 30 °C. The induced air temperature gradually decreased with distance from the back wall. Interestingly, a slight increase in air temperature occurred near the moveable glass plate owing to radiation from the heated wall. As shown in Fig. 4, the air temperature distribution was such that the side air temperature was highest; otherwise, the air temperature was relatively low. In addition, the air temperatures were reasonably uniform across the main part of the width. Fig. 5 describes the distribution of the average air temperature in the height direction and shows that the average air temperature
3.1. Experimental visualization Smoke was pregenerated by using a Rosco 1700 fog generator and was collected in a cardboard static pressure tank 247
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
According to analysis by Cooper (1995); Eckert and Jackson (1950), the dimensionless velocity distributions are dependent mainly on the thermal boundary layer thickness, and Eqs. (8)–(11) can be obtained as
y1/7 y 4 u ⎛1 − ⎞ , = u1 δ ⎝ δ⎠ δ=
0.505Gr ∗− 1/14Pr −1/2 (1
(8)
+
0.445Pr 2/3)1/14h,
v u1 = 4.35 Gr ∗5/14Pr −1/16 (1 + 0.445Pr 2/3)−5/14 , h
(9) (10)
where δ is the boundary layer thickness, u is the local air velocity, u1 is the characteristic air velocity in the boundary layer, Gr ∗ is the modified Grashof number, β is the air expansion coefficient, v is the kinetic viscosity of air, and Pr is the Prandtl number. Fig. 7 reveals the velocity distributions under a heat flux of 200 W/ m2. The induced air velocity decreased as the distance from the back heated wall increased. The dimensionless air velocity decreased to a small value in the range of 0.3 ⩽ y / gap ⩽ 1, which indicates that those regions contributed little to the airflow rate. Compared with the induced air velocity, the calculated air velocity based on the boundary theory was larger, although it decreased rapidly to zero when the y/gap was approximately 0.15.
Fig. 4. Temperature distribution with 500 W/m2 at 1000 mm above the chimney inlet.
4.3. Airflow rates and improved prediction method A comparison of the experimental and predicted airflow rates (shown in Fig. 8) revealed that the induced airflow rate increased with an increase in heat flux. This phenomenon occurred because the increase in heat flux increased the temperature of the induced air temperature, which produced higher stack pressure to drive the airflow. Furthermore, the values predicted by Eq. (4) are approximately 45% greater than the measured results. Therefore, an improved method is needed to predict the induced airflow rate. Fig. 9 compares the experimental and predicted airflow rates with respect to the chimney gap. The induced airflow rate increased as the chimney gap increased, and the maximum induced airflow rate occurred when the chimney gap was approximately 0.8 m. Therefore, the optimal ratio between the gap and height was estimated to be 0.4. In addition, the difference between the experimental and predicted airflow rates increased as the chimney gap increased. The flow visualization experiments revealed that reverse flow began to appear when the chimney gap was 400 mm, although it was limited only to the outlet. As the chimney gap increased, the reverse flow continued to penetrate downward into the chimney channel. Fig. 9 also shows that the predicted airflow was quite acceptable at a chimney gap of 200 mm. However, as the chimney gap increased, the difference
Fig. 5. Average air temperature distribution under various conditions.
increases as the height increases. The average air temperature is calculated by Eq. (6):
Tave =
∫A (T − Tamb ) ds A
+ Tamb,
(6)
where Tave is average air temperature. It should be noted that Tave is different from Taverage , which is shown in Eq. (7) as
Taverage =
∫ (T − Tamb ) uds qhw + Tamb = A + Tamb, QρCp Q
(7)
where u is the induced air velocity. The formula above clearly shows that the value of Tave is equal to Taverage when the air velocity or temperature is uniform. Therefore, the heat balance analysis method might not be suitable for predicting the stack pressure in the case of nonuniform temperature distribution. 4.2. Velocity distribution Fig. 6 presents the velocity distributions in the gap direction. The air velocity profiles were highly nonuniform, and the induced air velocity decreased gradually as the distance from the back wall increased. The maximum air velocity was approximately three times the minimum velocity. Furthermore, the velocity increased as the heat flux increased at the same distance from the back heated wall.
Fig. 6. Velocity distribution under various heat input values. 248
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
can be applied only to narrow chimneys; this method resulted in overprediction of the airflow rates in wider chimneys. The available method, Eq. (4), can be used to calculate the airflow rate with the following conditions. (1) The air temperature or air velocity in the chimney is uniformly distributed. (2) The air velocity distributions at the chimney inlet and the outlet resemble normal forced flows. The above requirements can be met for narrow chimneys, and the predicted values calculated by Eq. (4) are quite acceptable, as reported by Sandberg and Moshfegh (2002); Chen et al. (2003). However, other chimneys do not necessarily satisfy the above conditions. As shown in Figs. 3 and 6, the distributions of air temperature and velocity inside chimneys are highly nonuniform. In an undesirable situation, the reverse flow phenomenon appears, which further exacerbates the nonuniformity of these distributions. In such situations, the above demands cannot be satisfied; thus, the available method, Eq. (4), cannot be used to calculate the airflow rate. It should be noted that no clear criteria are available for distinguishing wide and narrow chimneys; such a distinction is dependent on the boundary layer thickness of the heated wall (Jing et al., 2015). For example, the boundary layer thickness for a 2 m high vertical plate with 400 W/m2 is approximately 13 cm according to Eq. (9). In this case, a chimney is considered to be narrow when the chimney gap is less than 13 cm; otherwise, the chimney is considered to be wide. The above analysis demonstrates the importance of developing a relatively adequate prediction method for the induced airflow rate. Cooper (1995) investigated the flow through a horizontal vent in which the vent-connected spaces were filled with fluids of various densities in an unstable configuration. With zero-to-moderate cross-vent pressure difference, ΔP , the flow through the vent is bidirectional, and reverse flow can occur. The air distribution through the vent is highly nonuniform. For relatively large ΔP , the flow is unidirectional, and no reverse flow is present. Cooper (1995) also reported that the discharge coefficient through the vent, CD, varies with the value of the Froude Number (Fr). CD can be calculated by Eq. (11):
Fig. 7. Dimensionless velocity distributions under 200 W/m2.
Fig. 8. Distribution of airflow rate though chimneys with 400 mm gaps and various heat input values.
CD =
0.6Fr / Frrev , [(Fr / Frrev − 1 + σ22 )2 + σ12 − σ24 ]0.5
(11)
where Frrev is the Froude number when reverse flow occurs, σ1 = 3.37 \* MERGEFORMAT, and σ2 = 1.045\* MERGEFORMAT. For the investigated chimney, the induced air ascended through the cold surrounding ambient air at the chimney outlet, which is similar to a horizontal vent problem. Therefore, based on the results of Cooper (1995); Epstein (1988), Eq. (12) was developed in the present study, which considers the variation in the pressure coefficient both with and without reverse flow: −2
Fr ⎞ ⎞ ⎞ ′ = 1 + ⎜⎛0.61*⎜⎛0.1 + 0.19*⎛ Cout , ⎟⎟ Fr rev ⎠ ⎠ ⎠ ⎝ ⎝ ⎝ ⎜
where
⎟
(12)
Q Fr = \* MERGEFORMAT; D is the characteristic span A* 2*g*D∗ε Δρ ΔT opening; ε = ρ ≈ T \* MERGEFORMAT, and Δρ \* MERGEFamb
of the ORMAT and ΔT \* MERGEFORMAT are the density and temperature differences of the two layers, respectively. Eq. (4) is then transformed into Eqs. (13) and (14). 1/3
Fig. 9. Distribution of airflow rate though chimneys with 400 W/m2 and different chimney gap values.
B ⎞ Q = A ⎜⎛ ⎟ ⎝ 2ψ′ ⎠
between the experimental results and the predictions increased, and the maximum difference was approximately 107% larger than the measured result. This finding suggests that the existing prediction method
ψ′ =
(13) 2
2
A⎡ H 1 A ⎞ A ⎞ ⎤⎤ ′ ⎛ + ⎡ + cout f cin ⎛ ⎥⎥ H ⎢ 2Dh 2⎢ A A in ⎠ ⎝ out ⎠ ⎦ ⎦ ⎣ ⎝ ⎣ ⎜
⎟
⎜
⎟
(14)
The application of proposed prediction method needs further 249
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
verification with experimental data. It is critical to determine when the reverse flow occurs to verify Eq. (13). Fig. 10(b) shows a region of reverse flow. The experimental visualization showed that the reverse flow began to appear when the chimney gap was 400 mm, but it was limited to only the outlet. As the chimney gap increased, the reverse flow continued to penetrate downward into the chimney channel. In these situations, the induced flow was bidirectional, and the velocity and temperature distributions were highly nonuniform. Fig. 11 compares the experimental and predicted results under a chimney gap of 200 mm. In this situation, no reverse flow occurred in the experiment, and the induced airflow was unidirectional. In addition, the predictions made by Eq. (13) were closer to the actual induced airflow rates than those made by Eq. (4): The difference between the predicted values and experimental data were in the range of 16–25% for Eq. (4) and 9–15% for Eq. (13). The comparison result indicates that the predictions made by Eqs. (4) and (13) are both in an acceptable range. Thus, the proposed method was proved valid for predicting the induced airflow rate without reverse flow. Fig. 12 compares the predicted and experimental results under different chimney gap values. For the investigated chimney with these gaps, reverse flow occurred, and the intensity increased with an increase in the chimney gap. In these situations, the induced flow was bidirectional, and the velocity and temperature distributions were highly nonuniform. The results show that the predictions calculated by using original method using Eq. (4) are significantly larger than the experimental airflow rate because reverse flow occurred under these conditions and the induced flow was bidirectional. The difference between the predicted values made by original method using Eq. (4) and the experimental data increased as the chimney gap increased, with a difference of 45–125%. However, the predictions made by the proposed method using Eq. (13) remained in a reasonable range under these conditions, and the difference between the predicted and experimental airflow rates was −9% to +23%. The prediction by the novel method is acceptable; therefore, the proposed method using Eq. (13) can be used to predict the induced airflow rate with reverse flow. To verify the accuracy of the proposed prediction method further, the experimental results reported by Sandberg and Moshfegh (2002) were selected for comparison with the predictions made by Eqs. (13) and (4), as shown in Fig. 13. The gap-to-height ratio was 0.035; thus,
Fig. 11. Comparisons of the predicted values and the experimental results under a chimney gap of 200 mm.
the investigated chimney is considered a narrow chimney. Fig. 13 shows that both predicted values were close to the experimental airflow rates, with differences of −6% to +12% for Eq. (4) and −3% to +10% for Eq. (13). The correlation coefficients (R) between the measured results and the values predicted by Eqs. (13) and (4) were 0.98 and 0.97, respectively. Therefore, the established predicted methods are both valid for predicting the induced airflow rate for a narrow chimney. Fig. 14 shows a comparison of the predicted and experimental results under a heat flux of 400 W/m2. The results show that both the experimental and predicted airflow rates increased as the chimney gap increased. In addition, Eq. (13) appeared to provide a more accurate prediction than Eq. (4), particularly when the chimney gap was greater than 400 mm. This finding indicates that the proposed Eq. (13) has an advantage over Eq. (4) in predicting the induced airflow rate for wide chimneys. Fig. 15 shows a comparison of the predicted values and the experimental data reported by Chen et al. (2003). The predictions calculated by Eqs. (13) and (4) were both acceptable in the case of a small
Fig. 10. Experimental visualizations with smoke: (a) visual image with 200 mm gap and 400 W/m2 heat input; (b) visual image with 400 mm gap and 400 W/m2 heat input. 250
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
Fig. 12. Comparisons of the predicted and experimental airflow rates through a chimney with gaps of (a) 400 mm, (b) 600 mm, (c) 800 mm, and (d) 1000 mm.
Fig. 13. Comparison of the predicted values and the experimental results obtained by Sandberg and Moshfegh (2002).
Fig. 14. A comparison of the predicted and experimental airflow rates through a chimney with a heat flux of 400 W/m2.
chimney gap. However, as the chimney gap increased, Eq. (4) appeared to overpredict the airflow rate by approximately 20–190%, whereas the predictions made by Eq. (13) were still in good agreement with the experimental results.
4.4. Uncertainty analysis The uncertainty of the velocity measurements using the anemometer was of the order of 0.02 m/s, and the random error was 251
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
Acknowledgment This paper was supported by the National Natural Science Foundation of China (51478377). References Abdeen, A., Serageldin, A.A., Ibrahim, M.G., El-Zafarany, A., Ookawara, S., Murata, R., 2019. Solar chimney optimization for enhancing thermal comfort in Egypt: an experimental and numerical study. Sol. Energy 180, 524–536. Aboulnaga, M.M., 1998. A roof solar chimney assisted by cooling cavity for natural ventilation in buildings in hot arid climates: an energy conservation approach in AlAin city. Renew. Energy 14 (1–4), 357–363. Afonso, C., Oliveira, A., 2000. Solar chimneys: simulation and experiment. Energy Build. 32 (1), 71–79. Ahmed, O.K., Hussein, A.S., 2018. New design of solar chimney (case study). Case Stud. Thermal Eng. 11, 105–112. Arce, J., Jiménez, M.J., Guzmán, J.D., Heras, M.R., Alvarez, G., Xamán, J., 2009. Experimental study for natural ventilation on a solar chimney. Renew. Energy 34 (12), 2928–2934. Awbi, H.B., 1994. Design considerations for naturally ventilated buildings. Renew. Energy 5 (5–8), 1081–1090. Awbi, H.B., Gan, G., 1992. Simulation of solar-induced ventilation. Renew. Energy Technol. Environ. 4, 2016–2030. Bansal, N.K., Mathur, R., Bhandari, M.S., 1994. A study of solar chimney assisted wind tower system for natural ventilation in buildings. Build. Environ. 29 (4), 495–500. Bassiouny, R., Koura, N.S., 2008. An analytical and numerical study of solar chimney use for room natural ventilation. Energy Build. 40 (5), 865–873. Boucher, A., 1994. Solar chimney for promoting cooling ventilation in southern Algeria. Build. Serv. Eng. Res. Technol. 15 (2), 81–93. Chantawong, P., Khedari, J., 2018. Natural ventilation by using PV blinds glazed solar chimney wall under the tropical climate conditions of Thailand. Mater. Today:. Proc. 5 (7), 14874–14879. Chen, Z.D., Bandopadhayay, P., Halldorsson, J., Byrjalsen, C., Heiselberg, P., Li, Y., 2003. An experimental investigation of a solar chimney model with uniform wall heat flux. Build. Environ. 38 (7), 893–906. Cooper, L.Y., 1995. Combined buoyancy and pressure-driven flow through a shallow, horizontal, circular vent. J. Heat Transf. 117 (3), 659–667. Dordelly, J.C.F., El Mankibi, M., Roccamena, L., Remion, G., Landa, J.A., 2019. Experimental analysis of a PCM integrated solar chimney under laboratory conditions. Sol. Energy 188, 1332–1348. Eckert, E.R., Jackson, T.W., 1950. Analysis of turbulent free-convection boundary layer on flat plate (No. NACA-TN-2207). National Aeronautics and Space Administration, Washington DC. Epstein, M., 1988. Buoyancy-driven exchange flow through small openings in horizontal partitions. J. Heat Transf. 110 (4a), 885–893. Gan, G., 2006. Simulation of buoyancy-induced flow in open cavities for natural ventilation. Energy Build. 38 (5), 410–420. Harris, D.J., Helwig, N., 2007. Solar chimney and building ventilation. Appl. Energy 84 (2), 135–146. Jing, H., Chen, Z., Li, A., 2015. Experimental study of the prediction of the ventilation flow rate through solar chimney with large gap-to-height ratios. Build. Environ. 89, 150–159. Khanal, R., Lei, C., 2012. Flow reversal effects on buoyancy induced air flow in a solar chimney. Sol. Energy 86 (9), 2783–2794. Khanal, R., Lei, C., 2014. An experimental investigation of an inclined passive wall solar chimney for natural ventilation. Sol. Energy 107, 461–474. Kovanen, K., Seppänen, O., Sirèn, K., Majanen, A., 1989. Turbulent air flow measurements in ventilated spaces. Environ. Int. 15 (1), 621–626. Liu, Z., Wu, D., He, B.J., Wang, Q., Yu, H., Ma, W., Jin, G., 2019. Evaluating potentials of passive solar heating renovation for the energy poverty alleviation of plateau areas in developing countries: a case study in rural Qinghai-Tibet Plateau, China. Sol. Energy 187, 95–107. Martı, J., Heras-Celemin, M.R., 2007. Dynamic physical model for a solar chimney. Sol. Energy 81 (5), 614–622. Mathur, J., Bansal, N.K., Mathur, S., Jain, M., 2006. Experimental investigations on solar chimney for room ventilation. Sol. Energy 80 (8), 927–935. Monghasemi, N., Vadiee, A., 2018. A review of solar chimney integrated systems for space heating and cooling application. Renew. Sustain. Energy Rev. 81, 2714–2730. Ong, K.S., 2003. A mathematical model of a solar chimney. Renew. Energy 28 (7), 1047–1060. Sandberg, M., Moshfegh, B., 2002. Buoyancy-induced air flow in photovoltaic facades: Effect of geometry of the air gap and location of solar cell modules. Build. Environ. 37 (3), 211–218. Shi, L., Zhang, G., Yang, W., Huang, D., Cheng, X., Setunge, S., 2018. Determining the influencing factors on the performance of solar chimney in buildings. Renew. Sustain. Energy Rev. 88, 223–238. Spencer, S., Chen, Z.D., Li, Y., Haghighat, F., 2000. Experimental investigation of a solar chimney natural ventilation system. Air Distrib. Rooms 813–818.
Fig. 15. Comparison between the predicted values and the experimental results reported by Chen et al. (2003).
about ± 0.02 m/s owing to the stability of experiments. Thus, the total uncertainty was estimated to be less than or equal to 0.04 m/s for velocity measurements. The total uncertainty of the temperature measurements was estimated to be less than 0.04 °C, and the difference in temperature for the same measuring point with repeated experiments was less than 1 °C. 5. Conclusions Accurate prediction of airflow rates is critical for the effective design of solar chimneys. In the present study, a solar chimney with a variable gap-to-height ratio between 0.1 and 0.5 was used as the research object to explore an improved prediction method. Based on the above analysis, the following conclusions were drawn. The distribution of induced air temperature and velocity were highly nonuniform in the chimney gap direction. In the height direction, the average air temperature increased as the distance from the chimney inlet increased. Furthermore, as the chimney gap increased, the maximum induced airflow rate was found at a chimney gap of approximately 0.8 m; thus, the optimum chimney gap-toheight ratio was estimated to be 0.4. The flow visualization experiments showed that the reverse flow phenomenon appeared at the outlet when the chimney gap was 400 mm; as the chimney gap increased, the reverse flow continued to penetrate downward into the chimney. In these situations, the induced flow was bidirectional and exerted a negative influence on the accuracy of the predicted value. The experimental results showed that the prevalent prediction method can substantially overpredict the airflow rate. A novel method for predicting the airflow rate was proposed and verified based on the experimental results obtained in the present experiment and those available in the literature. The proposed method considers the variation in the pressure loss coefficient for various flow conditions at the chimney outlet. Moreover, the proposed prediction method was applicable to the investigated chimney and was in better agreement with the experimental results with or without reverse flow. Additional studies are needed to develop methods for more accurate predictions of airflow rates in solar chimneys. Although the proposed method for such prediction is not perfect, the results of the present study, to some extent, can provide a foundation for further improvement.
252
Contents lists available at ScienceDirect
Solar Energy journal homepage: www.elsevier.com/locate/solener
Experimental and theoretical study of solar chimneys in buildings with uniform wall heat flux Yicun Hou, Huang Li, Angui Li
T
⁎
School of Building Services Science and Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Experiments Solar chimney Temperature measurement Velocity measurement Prediction method
Solar chimneys are often used in buildings to enhance natural ventilation; thus, accurate assessment of the ventilation effect is essential for their design. However, the prediction method available in the literature usually overpredicts the airflow rate. In the present study, a solar chimney with a variable gap-to-height ratio between 0.1 and 0.5 is used as the research object to develop an improved prediction method. Experiments and theoretical analyses were conducted to investigate the induced airflow characteristics, such as air temperature distribution, air velocity distribution, and the reverse flow phenomenon. The results show that the distribution of induced air temperature and velocity were highly nonuniform and that the optimum chimney gap-to-height ratio was estimated to be 0.4. The reverse flow phenomenon appeared at the outlet when the chimney gap was 400 mm, and the reverse flow continued to penetrate downward into the chimney as the chimney gap increased. The proposed method considers the variation in the pressure loss coefficient for various flow conditions at the chimney outlet. By comparing the predicted value and the experimental data, the proposed method was demonstrated to be valid for predicting the induced airflow rate with or without reverse flow. Moreover, the current study motivates further research on prediction method for airflow rates in solar chimneys.
1. Introduction The building industry accounts for between 35% and 45% of global energy consumption (Monghasemi and Vadiee, 2018). In recent years, interest in solar chimneys has been stimulated by an increasing awareness of energy savings and the need for effective ventilation in buildings (Khanal and Lei, 2012; Harris and Helwig, 2007; Chantawong and Khedari, 2018; Liu et al., 2019). Solar chimneys convert solar energy into the kinetic energy of the air inside the chimney: The opaque elements of solar chimneys absorb solar radiation and heat the air inside the chimney. The density of the heated air decreases, which causes an updraft inside the chimney owing to thermal buoyancy (Dordelly et al., 2019). The main tasks in solar chimney studies are generally assessment and enhancement of the ventilation effect provided by the solar chimney (Ahmed and Hussein, 2018; Abdeen et al., 2019). Ong (2003) proposed a steady mathematical model for predicting the induced airflow rate. Their analytical results were consistent with those of experiments in which the chimney height was more than 10 times the gap. Based on Ong’s work, Martı and Heras-Celemin (2007) achieved good results when using a dynamic model to analyze the thermal performance of a solar chimney. The experimental results obtained by Afonso ⁎
and Oliveira (2000) showed that the chimney width had a greater effect than the chimney height on the ventilation rate. Reverse flow in a solar chimney affects the negatively induced airflow rate. Boucher (1994) found that reverse flow appeared when the chimney gap was 0.5 m for a vertical solar chimney (Gap/H = 0.25). Chen et al. (2003) conducted experimental visualizations and reported that reverse flow began to appear at the outlet when the chimney gap was equal to 300 mm. As the chimney gap increased, the reverse flow increased and continued to penetrate downward into the chimney. Khanal and Lei (2012) developed and quantitatively examined an inclined passive wall solar chimney (IPWSC). The proposed IPWSC significantly suppressed the reverse flow when the passive wall was inclined at a 5° angle from the vertical wall (Khanal and Lei, 2014). The optimum chimney gap is highly debatable. Some researchers have demonstrated the existence of an optimum chimney gap that induces the maximum ventilation rate in a chimney. Jing et al. (2015) performed experiments and reported that the optimum ratio between the gap and height is approximately 0.5. Gan (2006) investigated the effect of the chimney width on the induced airflow rate by numerical simulation. Their results showed an optimum gap in the range of 0.55–0.6 m. Boucher (1994) conducted experiments and demonstrated that the maximum ventilation rate occurred when the ratio between the gap and
Corresponding author. E-mail address: [email protected] (A. Li).
https://doi.org/10.1016/j.solener.2019.09.061 Received 11 July 2019; Received in revised form 8 September 2019; Accepted 17 September 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
Nomenclature
w q Q ρ cp Taverage Tamb ΔPs ΔPL ΔP H A Ain Aout
f cin cout CD \* Dh u u1 Gr ∗ Pr
chimney width (mm) heat flux (W/m2) induced airflow rate (m3/s) air density (kg/ m3) specific heat capacity J/(kg · °C) average air temperature (°C) ambient temperature (°C) stack pressure (Pa) pressure loss along the chimney (Pa) cross-vent pressure difference (Pa) chimney height (m) chimney channel cross-sectional area (m2) inlet area (m2) outlet area (m2)
Greek letters boundary layer thickness (m) air expansion coefficient kinetic viscosity of air (m2/s)
δ β v
the heat flux, Q is the induced airflow rate, ρ represents the air density, cp is the specific heat capacity, Taverage is the average air temperature at h, and Tamb is the ambient temperature. The stack pressure, ΔPs , can be determined by using Eq. (2):
height was approximately 0.1. However, neither Chen et al. (2003) nor Shi et al. (2018) found optimum gaps in their studies. Spencer et al. (2000) reported that the optimal gap is related to the chimney inlet design. Thus, the optimum chimney gap problem needs further research. The methods commonly used for predicting the airflow rate have generally been proposed based on the assumption that the air temperature is uniformly distributed at the same height. Such a method was successfully used by Awbi and Gan (1992) to predict the induced airflow rate. Sandberg and Moshfegh (2002) performed experiments with a rectangular solar panel and reported that the predicted induced airflow rate was close to the experimental results. Similar results were reported by Aboulnaga (1998); Ong (2003); Bansal et al. (1994); Mathur et al. (2006). It is noted that the aforementioned method for predicting the airflow rate is only suitable for narrow chimneys. With regard to wide chimneys, Chen et al. (2003); Arce et al. (2009) found that the values predicted by using the existing method available in the literature were usually larger than the actual induced airflow rate. The resulting overprediction may be caused by the following factors. First, the actual temperature distributions in the experiments were uneven. Second, the adopted pressure loss coefficients did not necessarily apply to buoyancy-driven natural ventilation because these coefficients were obtained in normal forced flows. Third, the occurrence of reverse flow may exert a negative influence on the accuracy of the predicted value. Therefore, further studies are necessary to guarantee adequate prediction of the induced airflow rates in chimneys. In the present study, the induced airflow inside a solar chimney is investigated by experiments and theoretical analyses, and the reverse flow phenomenon is qualitatively investigated by experimental visualization. The air temperature and airflow rates are measured under different conditions to lay the foundation for further analysis. This study presents a novel method for predicting the airflow rate and verifies the results with experimental data. The proposed method is valid for predicting the induced airflow rate with or without reverse flow. Moreover, the current study motivates further research on solar chimneys.
ΔPs =
∫0
H
(Taverage − Tamb) ρg Tamb
dh =
where B is the buoyancy flux, B =
ρBH , 2Q gqwH , ρcp Tamb
(2) and H represents the chimney
height. The pressure loss, ΔPL , can be calculated by using Eq. (3):
ΔPL = cin
ρ (Q/ Ain )2 ρ (Q/ Aout )2 H ρ (Q/ A)2 + cout +f , 2 2 2 Dh
(3)
where A is the chimney channel cross-sectional area; Ain and Aout are the inlet and outlet areas, respectively; f is the friction factor for the channel wall; cin and cout are the inlet and outlet pressure loss coefficients, respectively; and Dh is the hydraulic diameter of the chimney channel. The airflow rate, Q, can be determined by using Eqs. (4) and (5): 1/3
B Q = A ⎜⎛ ⎟⎞ ⎝ 2ψ ⎠
,
(4)
where 2
ψ=
2
A⎡ H 1 A ⎞ A ⎞ ⎤⎤ f cin ⎛ + ⎡ + cout ⎛ ⎥ ⎥. H ⎢ 2Dh 2⎢ A A in ⎠ ⎝ out ⎠ ⎦ ⎦ ⎣ ⎝ ⎣ ⎜
⎟
⎜
⎟
(5)
The values of cin and cout are determined generally by analyzing the available data for normal forced flow. This finding indicates that the airflow rate is affected mainly by the stack pressure and the pressure losses. Therefore, it is vital to evaluate the air temperature distribution and the pressure coefficients when predicting the induced airflow. 3. Experiments As shown in Fig. 1, the height and width of the experimental solar chimney were 2.0 and 1.0 m, respectively, and the gap of investigated chimney varied from 0.2 to 1.0 m at intervals of 0.2 m. The experimental chimney resembled a rectangular channel composed of three walls with uniform heat flux and a movable glass plate to observe the induced airflow pattern. The heated walls were covered with a 1.2 mm thick electrothermal film to provide a variable heat flux. All of the walls were insulated with 50 mm mineral fiber to reduce heat loss. The base of the investigated chimney was 0.5 m from the ground. Fig. 2 displays the layout of the measuring points. As shown in Fig. 2(a), each heated surface was equipped with 15 T-type thermocouples for measuring the wall temperature. The induced air
2. Analysis of prediction methods The available methods for predicting the airflow rate under a given solar radiation intensity are based on the assumption of uniform air temperature (Awbi, 1994; Bassiouny and Koura, 2008; Ong, 2003; Martı and Heras-Celemin, 2007). The energy balance can be expressed by Eq. (1):
qhw = QρCp (Taverage − Tamb),
friction factor for the channel wall inlet pressure loss coefficient outlet pressure loss coefficient MERGEFORMAT vent discharge coefficient hydraulic diameter of the chimney channel (m) local air velocity (m/s) characteristic air velocity in the boundary layer (m/s) modified Grashof number Prandtl number
(1)
where h is the height along the chimney, w is the chimney width, q is 245
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
Fig. 1. (a) Experimental model of solar chimney, (b) A real image showing the experimental test rig.
A Digitrend PF66B data logger was used to record the temperature, and the sampling interval was set to 10 s to ensure accurate average temperatures. A TSI8455 air anemometer was used to measure the induced air velocity with a calibrated accuracy of ± 5% at full range. The anemometer has a measurement range from 0.05 m/s to 3.0 m/s, and the uncertainty of the velocity measurements was of the order of 0.02 m/s. The random error was about ± 0.02 m/s owing to the stability of the
temperature was measured by seven T-type thermocouples mounted on a movable test lever inside the chimney channel, as shown in Fig. 2(b). A thermocouple was also required to measure the ambient air temperature. The thermocouples have a measurement range of −200 °C to +300 °C and were calibrated to within ± 0.2 °C in a thermostatic water bath before use. The total uncertainty of the temperature measurements was estimated to be less than 0.04 °C. The difference in temperature for the same measuring point with repeated experiments was less than 1 °C. 246
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
Fig. 2. Locations of measuring points (Unit: mm): (a) on the surface, (b) on a test lever.
1000 mm × 1000 mm × 800 mm in length, height, and width, respectively. The static pressure tank has two functions: to reduce the dynamic pressure and minimize the disturbance of the generated smoke and to ensure that the smoke temperature identifies with the ambient air temperature. The stored smoke is drawn naturally into the solar chimney through a passage via buoyancy-driven natural convection. The entire process of air movement in the chimney channel was recorded by a charge-coupled device (CCD) camera. A section of black fabric was used to cover the chimney wall to facilitate the visualization process. In the measurement process, the fabric cover was removed to avoid its influence on the induced airflow. 3.2. Experimental procedure Experiments were conducted with various heat input values ranging from 100 to 600 W/m2 at intervals of 100 W/m2; for each heat flux, the chimney gaps varied from 0.2 to 1.0 m at 0.2 m intervals. Each experimental condition was repeated three times to ensure the accuracy of the experimental data, and the average values were used for the following analysis. The temperatures and induced airflow rates were recorded until the solar chimney system achieved a steady state, which typically took 3–5 h
Fig. 3. Temperature distribution under various chimney gap values with 300 W/m2 at 1000 mm above the chimney inlet.
experiments. Thus, the total uncertainty was estimated to be less than or equal to 0.04 m/s for velocity measurements. To ensure the accuracy of the experimental data, it is important to determine the position of the probe. If the probe is incorrectly positioned, the measurement error will increase owing to air disturbance. According to the results of experimental visualization, the probe was placed 0.8 m above the inlet, where the reverse flow is limited and the airflow is parallel to the chimney walls. Chen et al. (2003) performed experiments using a chimney model with a height and width of 1.5 and 0.62 m, respectively, in which the probe was set 1.1 m above the inlet. Similarly, Jing et al. (2015) placed the probe 1.0 m above the inlet to reduce the measurement error. The sampling frequency for the airflow velocity was set to 2 Hz in the present study to ensure accurate time-averaged values (Kovanen et al., 1989). To determine the induced airflow rate, the probe was arranged at 30 points at the cross-section 0.8 m above the chimney inlet
4. Results and discussion 4.1. Temperature distribution Fig. 3 displays the typical temperature distributions along the chimney gap direction at a height of 1000 mm on the symmetrical plane. The induced air temperature distribution was highly nonuniform. The air temperature was the highest near the back wall, and the maximum temperature difference reached 30 °C. The induced air temperature gradually decreased with distance from the back wall. Interestingly, a slight increase in air temperature occurred near the moveable glass plate owing to radiation from the heated wall. As shown in Fig. 4, the air temperature distribution was such that the side air temperature was highest; otherwise, the air temperature was relatively low. In addition, the air temperatures were reasonably uniform across the main part of the width. Fig. 5 describes the distribution of the average air temperature in the height direction and shows that the average air temperature
3.1. Experimental visualization Smoke was pregenerated by using a Rosco 1700 fog generator and was collected in a cardboard static pressure tank 247
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
According to analysis by Cooper (1995); Eckert and Jackson (1950), the dimensionless velocity distributions are dependent mainly on the thermal boundary layer thickness, and Eqs. (8)–(11) can be obtained as
y1/7 y 4 u ⎛1 − ⎞ , = u1 δ ⎝ δ⎠ δ=
0.505Gr ∗− 1/14Pr −1/2 (1
(8)
+
0.445Pr 2/3)1/14h,
v u1 = 4.35 Gr ∗5/14Pr −1/16 (1 + 0.445Pr 2/3)−5/14 , h
(9) (10)
where δ is the boundary layer thickness, u is the local air velocity, u1 is the characteristic air velocity in the boundary layer, Gr ∗ is the modified Grashof number, β is the air expansion coefficient, v is the kinetic viscosity of air, and Pr is the Prandtl number. Fig. 7 reveals the velocity distributions under a heat flux of 200 W/ m2. The induced air velocity decreased as the distance from the back heated wall increased. The dimensionless air velocity decreased to a small value in the range of 0.3 ⩽ y / gap ⩽ 1, which indicates that those regions contributed little to the airflow rate. Compared with the induced air velocity, the calculated air velocity based on the boundary theory was larger, although it decreased rapidly to zero when the y/gap was approximately 0.15.
Fig. 4. Temperature distribution with 500 W/m2 at 1000 mm above the chimney inlet.
4.3. Airflow rates and improved prediction method A comparison of the experimental and predicted airflow rates (shown in Fig. 8) revealed that the induced airflow rate increased with an increase in heat flux. This phenomenon occurred because the increase in heat flux increased the temperature of the induced air temperature, which produced higher stack pressure to drive the airflow. Furthermore, the values predicted by Eq. (4) are approximately 45% greater than the measured results. Therefore, an improved method is needed to predict the induced airflow rate. Fig. 9 compares the experimental and predicted airflow rates with respect to the chimney gap. The induced airflow rate increased as the chimney gap increased, and the maximum induced airflow rate occurred when the chimney gap was approximately 0.8 m. Therefore, the optimal ratio between the gap and height was estimated to be 0.4. In addition, the difference between the experimental and predicted airflow rates increased as the chimney gap increased. The flow visualization experiments revealed that reverse flow began to appear when the chimney gap was 400 mm, although it was limited only to the outlet. As the chimney gap increased, the reverse flow continued to penetrate downward into the chimney channel. Fig. 9 also shows that the predicted airflow was quite acceptable at a chimney gap of 200 mm. However, as the chimney gap increased, the difference
Fig. 5. Average air temperature distribution under various conditions.
increases as the height increases. The average air temperature is calculated by Eq. (6):
Tave =
∫A (T − Tamb ) ds A
+ Tamb,
(6)
where Tave is average air temperature. It should be noted that Tave is different from Taverage , which is shown in Eq. (7) as
Taverage =
∫ (T − Tamb ) uds qhw + Tamb = A + Tamb, QρCp Q
(7)
where u is the induced air velocity. The formula above clearly shows that the value of Tave is equal to Taverage when the air velocity or temperature is uniform. Therefore, the heat balance analysis method might not be suitable for predicting the stack pressure in the case of nonuniform temperature distribution. 4.2. Velocity distribution Fig. 6 presents the velocity distributions in the gap direction. The air velocity profiles were highly nonuniform, and the induced air velocity decreased gradually as the distance from the back wall increased. The maximum air velocity was approximately three times the minimum velocity. Furthermore, the velocity increased as the heat flux increased at the same distance from the back heated wall.
Fig. 6. Velocity distribution under various heat input values. 248
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
can be applied only to narrow chimneys; this method resulted in overprediction of the airflow rates in wider chimneys. The available method, Eq. (4), can be used to calculate the airflow rate with the following conditions. (1) The air temperature or air velocity in the chimney is uniformly distributed. (2) The air velocity distributions at the chimney inlet and the outlet resemble normal forced flows. The above requirements can be met for narrow chimneys, and the predicted values calculated by Eq. (4) are quite acceptable, as reported by Sandberg and Moshfegh (2002); Chen et al. (2003). However, other chimneys do not necessarily satisfy the above conditions. As shown in Figs. 3 and 6, the distributions of air temperature and velocity inside chimneys are highly nonuniform. In an undesirable situation, the reverse flow phenomenon appears, which further exacerbates the nonuniformity of these distributions. In such situations, the above demands cannot be satisfied; thus, the available method, Eq. (4), cannot be used to calculate the airflow rate. It should be noted that no clear criteria are available for distinguishing wide and narrow chimneys; such a distinction is dependent on the boundary layer thickness of the heated wall (Jing et al., 2015). For example, the boundary layer thickness for a 2 m high vertical plate with 400 W/m2 is approximately 13 cm according to Eq. (9). In this case, a chimney is considered to be narrow when the chimney gap is less than 13 cm; otherwise, the chimney is considered to be wide. The above analysis demonstrates the importance of developing a relatively adequate prediction method for the induced airflow rate. Cooper (1995) investigated the flow through a horizontal vent in which the vent-connected spaces were filled with fluids of various densities in an unstable configuration. With zero-to-moderate cross-vent pressure difference, ΔP , the flow through the vent is bidirectional, and reverse flow can occur. The air distribution through the vent is highly nonuniform. For relatively large ΔP , the flow is unidirectional, and no reverse flow is present. Cooper (1995) also reported that the discharge coefficient through the vent, CD, varies with the value of the Froude Number (Fr). CD can be calculated by Eq. (11):
Fig. 7. Dimensionless velocity distributions under 200 W/m2.
Fig. 8. Distribution of airflow rate though chimneys with 400 mm gaps and various heat input values.
CD =
0.6Fr / Frrev , [(Fr / Frrev − 1 + σ22 )2 + σ12 − σ24 ]0.5
(11)
where Frrev is the Froude number when reverse flow occurs, σ1 = 3.37 \* MERGEFORMAT, and σ2 = 1.045\* MERGEFORMAT. For the investigated chimney, the induced air ascended through the cold surrounding ambient air at the chimney outlet, which is similar to a horizontal vent problem. Therefore, based on the results of Cooper (1995); Epstein (1988), Eq. (12) was developed in the present study, which considers the variation in the pressure coefficient both with and without reverse flow: −2
Fr ⎞ ⎞ ⎞ ′ = 1 + ⎜⎛0.61*⎜⎛0.1 + 0.19*⎛ Cout , ⎟⎟ Fr rev ⎠ ⎠ ⎠ ⎝ ⎝ ⎝ ⎜
where
⎟
(12)
Q Fr = \* MERGEFORMAT; D is the characteristic span A* 2*g*D∗ε Δρ ΔT opening; ε = ρ ≈ T \* MERGEFORMAT, and Δρ \* MERGEFamb
of the ORMAT and ΔT \* MERGEFORMAT are the density and temperature differences of the two layers, respectively. Eq. (4) is then transformed into Eqs. (13) and (14). 1/3
Fig. 9. Distribution of airflow rate though chimneys with 400 W/m2 and different chimney gap values.
B ⎞ Q = A ⎜⎛ ⎟ ⎝ 2ψ′ ⎠
between the experimental results and the predictions increased, and the maximum difference was approximately 107% larger than the measured result. This finding suggests that the existing prediction method
ψ′ =
(13) 2
2
A⎡ H 1 A ⎞ A ⎞ ⎤⎤ ′ ⎛ + ⎡ + cout f cin ⎛ ⎥⎥ H ⎢ 2Dh 2⎢ A A in ⎠ ⎝ out ⎠ ⎦ ⎦ ⎣ ⎝ ⎣ ⎜
⎟
⎜
⎟
(14)
The application of proposed prediction method needs further 249
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
verification with experimental data. It is critical to determine when the reverse flow occurs to verify Eq. (13). Fig. 10(b) shows a region of reverse flow. The experimental visualization showed that the reverse flow began to appear when the chimney gap was 400 mm, but it was limited to only the outlet. As the chimney gap increased, the reverse flow continued to penetrate downward into the chimney channel. In these situations, the induced flow was bidirectional, and the velocity and temperature distributions were highly nonuniform. Fig. 11 compares the experimental and predicted results under a chimney gap of 200 mm. In this situation, no reverse flow occurred in the experiment, and the induced airflow was unidirectional. In addition, the predictions made by Eq. (13) were closer to the actual induced airflow rates than those made by Eq. (4): The difference between the predicted values and experimental data were in the range of 16–25% for Eq. (4) and 9–15% for Eq. (13). The comparison result indicates that the predictions made by Eqs. (4) and (13) are both in an acceptable range. Thus, the proposed method was proved valid for predicting the induced airflow rate without reverse flow. Fig. 12 compares the predicted and experimental results under different chimney gap values. For the investigated chimney with these gaps, reverse flow occurred, and the intensity increased with an increase in the chimney gap. In these situations, the induced flow was bidirectional, and the velocity and temperature distributions were highly nonuniform. The results show that the predictions calculated by using original method using Eq. (4) are significantly larger than the experimental airflow rate because reverse flow occurred under these conditions and the induced flow was bidirectional. The difference between the predicted values made by original method using Eq. (4) and the experimental data increased as the chimney gap increased, with a difference of 45–125%. However, the predictions made by the proposed method using Eq. (13) remained in a reasonable range under these conditions, and the difference between the predicted and experimental airflow rates was −9% to +23%. The prediction by the novel method is acceptable; therefore, the proposed method using Eq. (13) can be used to predict the induced airflow rate with reverse flow. To verify the accuracy of the proposed prediction method further, the experimental results reported by Sandberg and Moshfegh (2002) were selected for comparison with the predictions made by Eqs. (13) and (4), as shown in Fig. 13. The gap-to-height ratio was 0.035; thus,
Fig. 11. Comparisons of the predicted values and the experimental results under a chimney gap of 200 mm.
the investigated chimney is considered a narrow chimney. Fig. 13 shows that both predicted values were close to the experimental airflow rates, with differences of −6% to +12% for Eq. (4) and −3% to +10% for Eq. (13). The correlation coefficients (R) between the measured results and the values predicted by Eqs. (13) and (4) were 0.98 and 0.97, respectively. Therefore, the established predicted methods are both valid for predicting the induced airflow rate for a narrow chimney. Fig. 14 shows a comparison of the predicted and experimental results under a heat flux of 400 W/m2. The results show that both the experimental and predicted airflow rates increased as the chimney gap increased. In addition, Eq. (13) appeared to provide a more accurate prediction than Eq. (4), particularly when the chimney gap was greater than 400 mm. This finding indicates that the proposed Eq. (13) has an advantage over Eq. (4) in predicting the induced airflow rate for wide chimneys. Fig. 15 shows a comparison of the predicted values and the experimental data reported by Chen et al. (2003). The predictions calculated by Eqs. (13) and (4) were both acceptable in the case of a small
Fig. 10. Experimental visualizations with smoke: (a) visual image with 200 mm gap and 400 W/m2 heat input; (b) visual image with 400 mm gap and 400 W/m2 heat input. 250
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
Fig. 12. Comparisons of the predicted and experimental airflow rates through a chimney with gaps of (a) 400 mm, (b) 600 mm, (c) 800 mm, and (d) 1000 mm.
Fig. 13. Comparison of the predicted values and the experimental results obtained by Sandberg and Moshfegh (2002).
Fig. 14. A comparison of the predicted and experimental airflow rates through a chimney with a heat flux of 400 W/m2.
chimney gap. However, as the chimney gap increased, Eq. (4) appeared to overpredict the airflow rate by approximately 20–190%, whereas the predictions made by Eq. (13) were still in good agreement with the experimental results.
4.4. Uncertainty analysis The uncertainty of the velocity measurements using the anemometer was of the order of 0.02 m/s, and the random error was 251
Solar Energy 193 (2019) 244–252
Y. Hou, et al.
Acknowledgment This paper was supported by the National Natural Science Foundation of China (51478377). References Abdeen, A., Serageldin, A.A., Ibrahim, M.G., El-Zafarany, A., Ookawara, S., Murata, R., 2019. Solar chimney optimization for enhancing thermal comfort in Egypt: an experimental and numerical study. Sol. Energy 180, 524–536. Aboulnaga, M.M., 1998. A roof solar chimney assisted by cooling cavity for natural ventilation in buildings in hot arid climates: an energy conservation approach in AlAin city. Renew. Energy 14 (1–4), 357–363. Afonso, C., Oliveira, A., 2000. Solar chimneys: simulation and experiment. Energy Build. 32 (1), 71–79. Ahmed, O.K., Hussein, A.S., 2018. New design of solar chimney (case study). Case Stud. Thermal Eng. 11, 105–112. Arce, J., Jiménez, M.J., Guzmán, J.D., Heras, M.R., Alvarez, G., Xamán, J., 2009. Experimental study for natural ventilation on a solar chimney. Renew. Energy 34 (12), 2928–2934. Awbi, H.B., 1994. Design considerations for naturally ventilated buildings. Renew. Energy 5 (5–8), 1081–1090. Awbi, H.B., Gan, G., 1992. Simulation of solar-induced ventilation. Renew. Energy Technol. Environ. 4, 2016–2030. Bansal, N.K., Mathur, R., Bhandari, M.S., 1994. A study of solar chimney assisted wind tower system for natural ventilation in buildings. Build. Environ. 29 (4), 495–500. Bassiouny, R., Koura, N.S., 2008. An analytical and numerical study of solar chimney use for room natural ventilation. Energy Build. 40 (5), 865–873. Boucher, A., 1994. Solar chimney for promoting cooling ventilation in southern Algeria. Build. Serv. Eng. Res. Technol. 15 (2), 81–93. Chantawong, P., Khedari, J., 2018. Natural ventilation by using PV blinds glazed solar chimney wall under the tropical climate conditions of Thailand. Mater. Today:. Proc. 5 (7), 14874–14879. Chen, Z.D., Bandopadhayay, P., Halldorsson, J., Byrjalsen, C., Heiselberg, P., Li, Y., 2003. An experimental investigation of a solar chimney model with uniform wall heat flux. Build. Environ. 38 (7), 893–906. Cooper, L.Y., 1995. Combined buoyancy and pressure-driven flow through a shallow, horizontal, circular vent. J. Heat Transf. 117 (3), 659–667. Dordelly, J.C.F., El Mankibi, M., Roccamena, L., Remion, G., Landa, J.A., 2019. Experimental analysis of a PCM integrated solar chimney under laboratory conditions. Sol. Energy 188, 1332–1348. Eckert, E.R., Jackson, T.W., 1950. Analysis of turbulent free-convection boundary layer on flat plate (No. NACA-TN-2207). National Aeronautics and Space Administration, Washington DC. Epstein, M., 1988. Buoyancy-driven exchange flow through small openings in horizontal partitions. J. Heat Transf. 110 (4a), 885–893. Gan, G., 2006. Simulation of buoyancy-induced flow in open cavities for natural ventilation. Energy Build. 38 (5), 410–420. Harris, D.J., Helwig, N., 2007. Solar chimney and building ventilation. Appl. Energy 84 (2), 135–146. Jing, H., Chen, Z., Li, A., 2015. Experimental study of the prediction of the ventilation flow rate through solar chimney with large gap-to-height ratios. Build. Environ. 89, 150–159. Khanal, R., Lei, C., 2012. Flow reversal effects on buoyancy induced air flow in a solar chimney. Sol. Energy 86 (9), 2783–2794. Khanal, R., Lei, C., 2014. An experimental investigation of an inclined passive wall solar chimney for natural ventilation. Sol. Energy 107, 461–474. Kovanen, K., Seppänen, O., Sirèn, K., Majanen, A., 1989. Turbulent air flow measurements in ventilated spaces. Environ. Int. 15 (1), 621–626. Liu, Z., Wu, D., He, B.J., Wang, Q., Yu, H., Ma, W., Jin, G., 2019. Evaluating potentials of passive solar heating renovation for the energy poverty alleviation of plateau areas in developing countries: a case study in rural Qinghai-Tibet Plateau, China. Sol. Energy 187, 95–107. Martı, J., Heras-Celemin, M.R., 2007. Dynamic physical model for a solar chimney. Sol. Energy 81 (5), 614–622. Mathur, J., Bansal, N.K., Mathur, S., Jain, M., 2006. Experimental investigations on solar chimney for room ventilation. Sol. Energy 80 (8), 927–935. Monghasemi, N., Vadiee, A., 2018. A review of solar chimney integrated systems for space heating and cooling application. Renew. Sustain. Energy Rev. 81, 2714–2730. Ong, K.S., 2003. A mathematical model of a solar chimney. Renew. Energy 28 (7), 1047–1060. Sandberg, M., Moshfegh, B., 2002. Buoyancy-induced air flow in photovoltaic facades: Effect of geometry of the air gap and location of solar cell modules. Build. Environ. 37 (3), 211–218. Shi, L., Zhang, G., Yang, W., Huang, D., Cheng, X., Setunge, S., 2018. Determining the influencing factors on the performance of solar chimney in buildings. Renew. Sustain. Energy Rev. 88, 223–238. Spencer, S., Chen, Z.D., Li, Y., Haghighat, F., 2000. Experimental investigation of a solar chimney natural ventilation system. Air Distrib. Rooms 813–818.
Fig. 15. Comparison between the predicted values and the experimental results reported by Chen et al. (2003).
about ± 0.02 m/s owing to the stability of experiments. Thus, the total uncertainty was estimated to be less than or equal to 0.04 m/s for velocity measurements. The total uncertainty of the temperature measurements was estimated to be less than 0.04 °C, and the difference in temperature for the same measuring point with repeated experiments was less than 1 °C. 5. Conclusions Accurate prediction of airflow rates is critical for the effective design of solar chimneys. In the present study, a solar chimney with a variable gap-to-height ratio between 0.1 and 0.5 was used as the research object to explore an improved prediction method. Based on the above analysis, the following conclusions were drawn. The distribution of induced air temperature and velocity were highly nonuniform in the chimney gap direction. In the height direction, the average air temperature increased as the distance from the chimney inlet increased. Furthermore, as the chimney gap increased, the maximum induced airflow rate was found at a chimney gap of approximately 0.8 m; thus, the optimum chimney gap-toheight ratio was estimated to be 0.4. The flow visualization experiments showed that the reverse flow phenomenon appeared at the outlet when the chimney gap was 400 mm; as the chimney gap increased, the reverse flow continued to penetrate downward into the chimney. In these situations, the induced flow was bidirectional and exerted a negative influence on the accuracy of the predicted value. The experimental results showed that the prevalent prediction method can substantially overpredict the airflow rate. A novel method for predicting the airflow rate was proposed and verified based on the experimental results obtained in the present experiment and those available in the literature. The proposed method considers the variation in the pressure loss coefficient for various flow conditions at the chimney outlet. Moreover, the proposed prediction method was applicable to the investigated chimney and was in better agreement with the experimental results with or without reverse flow. Additional studies are needed to develop methods for more accurate predictions of airflow rates in solar chimneys. Although the proposed method for such prediction is not perfect, the results of the present study, to some extent, can provide a foundation for further improvement.
252