Achieving standard natural ventilation rate of dwellings in a hot-arid climate using solar chimney

Accepted Manuscript Title: Achieving standard natural ventilation rate of dwellings in a hot-arid climate using solar chimney Author: Ahmed Abdeen Saleem Mahmoud Bady Shinichi Ookawara Ali K. Abdel-Rahman PII: DOI: Reference:

S0378-7788(16)31062-3 http://dx.doi.org/doi:10.1016/j.enbuild.2016.10.001 ENB 7060

To appear in:

ENB

Received date: Revised date: Accepted date:

29-5-2016 29-9-2016 3-10-2016

Please cite this article as: Ahmed Abdeen Saleem, Mahmoud Bady, Shinichi Ookawara, Ali K.Abdel-Rahman, Achieving standard natural ventilation rate of dwellings in a hot-arid climate using solar chimney, Energy and Buildings http://dx.doi.org/10.1016/j.enbuild.2016.10.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Achieving standard natural ventilation rate of dwellings in a hot-arid climate using solar chimney Ahmed Abdeen Saleem a *, Mahmoud Bady a, Shinichi Ookawara b, Ali K. Abdel-Rahman a a

Energy Resources Engineering Department, Egypt-Japan University of Science and Technology, Alexandria, Egypt b Department of Chemical Engineering, Graduate School of Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan *

Corresponding author: +2-010-16611600; [email protected]

Graphical abstract

Literature Review

Identifying the research gab

Analytical study

Validation study Comparisons against published experimental and analytical data

Validated mathematical model to scrutinize different1536 solar chimney design under real weather data

Determine which design achieve the standard ventilation rate under operation conditions as long as possible

This 3D model was compared against the validated developed model

Rresearch Aim

Develop a mathematical model using MATLAB program to evaluate thermal performance of solar chimney

Employing CFD study using DesignBuilder software to predict the space flow pattern

    

Highlights: A steady-state mathematical model of the solar chimney has been developed. Comparisons against published experimental work outline the validity of the model. The acceptability ratio of air flow rate ranges from of 0.019 to 0.033 m3/s. Standard air flow rate was achieved by 88.2% using the proposed solar chimney. Computational Fluid Dynamics (CFD) was applied to predict space flow pattern.

Abstract Increasingly, passive ventilation solutions are receiving considerable attention for inducing natural ventilation in dwellings regarding operation costs, energy demands, and carbon dioxide emissions. Solar chimney, in particular, is a promising alternative to enhance thermal and ventilation performance for the indoor environment by using convection of air heated by passive solar energy. The present study focuses on achieving optimum natural ventilation rate by incorporating solar chimney into a single room in a hot climatic context. Specifically, a mathematical model is developed through an overall energy balance on the solar chimney. This model examines a wide range of geometry parameters under real weather data to determine the optimum design solutions for the solar chimney. Furthermore, the model predicts the temperatures of the glazing and the black painted absorber as well as air velocity exiting from the chimney. The analytical results showed that an optimum air flow rate of 0.019 to 0.033 m3/s was achieved by 88.2% during the daytime when the dimensions of a proposed solar chimney are 45 inclination angle, 1.4 m length, 0.6 m width and 0.20 m air gab. Moreover, Computational Fluid Dynamics (CFD) was applied to predict space flow pattern using CFD module in DesignBuilder software, which is based on Energy-Plus dynamic simulation engine. The renormalization group (RNG) k-ε turbulence model was applied to solving the mass and energy equations within the solar chimney. Comparisons of the model predictions with CFD calculations and bibliographic experimental work outline the validity of the model.

Keywords – Natural ventilation; Dwellings; solar chimney; CFD simulation

Nomenclature A ACH Cd cf

area cross section [m2] air change per hour coefficient of discharge of air channel = [0.6] specific heat of air [J kg-1 K-1]

Subscripts g-a glass to air channel i inlet o outlet

d g h

abs-a abs-g g-sky

absorber wall to air channel absorber wall to glass cover glass to sky

f

flow

hr hwind I k L m· q r Sabs

distance between wall and glass [m] gravitational constant = 9.81 [ms-2] convective heat transfer coefficient [W m-2 K-1] convective heat transfer coefficient between vertical wall and room [2.8 W m-2 K-1] radiative heat transfer coefficient [W m-2 K-1] convective wind heat loss coefficient [W m-2 K-1] incident solar radiation on vertical surface [Wm-2] thermal conductivity [W m-1 K-1] length of wall [m] mass flow rate [kg s -1] heat transfer [W m -2] correlation coefficient Solar radiation flux absorbed by absorber [W m -2]

s abs g amb r conv cond f,in f,out

sky absorber wall glass surface ambient room convection conduction flow inlet flow outlet

Sg

Solar radiation flux absorbed by glass cover [W m -2]

T

Ambient temperature [K]

hi

Dimensionless terms Nu Nusselts number

Ub Ut V V˙ W Δwins

overall convective heat transfer coefficient from the inclined wall to the room [W m-2 K-1] overall convective heat transfer coefficient from top of glass cover [W m-2 K-1] Wind velocity [m s -1] Volumetric air flow rate [m3 s -1] Width of air channel [m] absorber wall thickness [m]

Pr Ra

Prandtl number Rayleigh number

Greek symbols αg absorptivity of glass e error absorptivity of wall αabs ε emissivity μ dynamic viscosity of air [kg m-1 s-1] υ kinematic viscosity of air [m2 s-1] ρ density of air [kg m-3] ɳ instantaneous efficiency of solar chimney [%] σ Stefan-Boltzmann constant [5.67*10-8 W m-2 K-4] ω constant in mean temperature approximation

1. Introduction Concerns about climate change caused by anthropogenic greenhouse gas emissions have globally emerged. Indeed, buildings represent the largest energy-consuming sector, with 42% of the total annual world energy consumption [1]. As a result, they are also responsible for 33% of global carbon emissions [2]. It is documented that the employed criteria for Heating, Ventilating, and Air-Conditioning (HVAC) systems are estimated to nearly 60% of the global energy consumption in the buildings sector [3]. Thus, passive design approaches are considered as an essential contributor to the future of energy supply portfolio, as they contribute to mitigating the dependency on fossil energy resources and providing opportunities for diminishing greenhouse gas emissions. Furthermore, they are an effective means for providing indoor air quality with proper thermal comfort conditions. In this context, solar chimney is a feasible and economically viable option for passive design solutions to create a healthy indoor environment within residential buildings through renewable energy of sun. This, in turn, would simultaneously reduce the environmental impact resulting from energy utilization. The solar chimney is a thermo-syphoning air channel that generates a driving force through thermal buoyancy, which is created by the absorbed solar energy into a surface, then releasing this energy to an adjunct column of air by natural convection raising its temperature as well as a density drop in the air. Accordingly, the warm air flows upward allowing a fresh outdoor air to enter the building from the fenestrations to create an air breeze inside the space. The solar chimney as a natural draft system has gained momentum lately due to its potential advantages over mechanical ventilation systems in terms of energy requirement, economic and environmental benefits. 2. Literature review Various theoretical, experimental and numerical studies were conducted to enhance the performance of the solar chimney. A pioneer work on a mathematical modelling of the solar chimney was carried out by Ong [4]. In this study, a one-dimensional mathematical model was developed to predict the thermal performance of solar chimney. Furthermore, Ong and Chow

[5] validated the Ong's mathematical model of solar chimney against experimental results. Experiments were employed on a 2 m height 0.45 m wide physical model with air gaps of 0.1, 0.2 and 0.3 m. Air velocities between 0.25 m/s and 0.39 m/s for radiation intensity up to 650 W/m2 were obtained. Marti-Herrero and Heras-Celemin [6] proposed a transient mathematical model to evaluate the energy performance of a solar chimney with thermal inertia in Mediterranean climates. The maximum air mass flow rate induced was 0.011 kg/s for a 2 m height of 24 cm of concrete wall and 14.5 cm of air channel gab at 450 W/m2 solar radiation. In a study on the performance of vertical solar chimney, Hirunlabh et al. [7] examined the performance of the vertical solar chimney experimentally and analytically for natural ventilation of a room in Thailand. The findings revealed that optimum natural ventilation was achieved with 2 m height and 14.5 cm gap. Burek and Habed [8] carried out an experimental set-up to correlate the air mass flow rate and thermal efficiency by varying the heat input and channel depth in a test rig resembling a vertical solar chimney. Recently, Imran et al. [9] investigated experimentally and numerically the performance of solar chimney under different geometrical dimensions in Iraq. In these experiments, the solar chimney of 2 m height, 2 m width, and three gap thickness (50, 100 and 150 mm) was incorporated to the roof of a single room with a volume of 12 m3. The numerical experiments revealed that the optimum chimney inclination angle was 60 in order to obtain the maximum rate of ventilation. Bassiouny and Korah [10] studied numerically and analytically the effect of the vertical chimney width on space ventilation. They concluded that increasing the width of the chimney from 0.1 m to 0.3 m enhances the volume airflow rate by almost 25%, keeping the chimney inlet size fixed. As it relates to the performance of an inclined solar chimney, Bassiouny and Korah [11] extended their studies by investigating the effect of different chimney inclination angle on the air change per hour and the space flow pattern for latitude 28.4º. They highlighted that an optimum flow rate was achieved at an inclination angle ranges from 45º to 70º. Moreover, Mathur et al. [12] examined the air flow rate at different inclination angle varies from 40º to 60º. They reported that the air flow rate was 10% higher at an angle of 45º compared to 30º and 60º. In continuance of that, Mathur et al. [13] carried out experimental investigations with nine different combinations of absorber height and air gab. Their findings were consistent with results from the steady-state mathematical model. Hamdy and Fikry [14] investigated mathematically the optimum tilt angle for a south oriented solar chimney located in Alexandria, Egypt during summer season. Their finding showed that a tilt angle of 60 stands for the ultimate performance in the study zone. Additionally, they argued that air flow rate through roof solar chimney increases if the height between inlet and outlet is increased. Similarly, Jianliu and Weihua [15] computationally investigated the performance of the solar chimney, which is integrated into a one-story building in Nanjing, using Energy-Plus program for the simulation to determine the energy impact of the thermal chimney. They reported that inclination angle of 45 was the optimum for the maximum rate of ventilation. Reddy et al. [16] carried out experimental set-up of a solar chimney at different inclination

angles for various gabs between glass and absorber plate. The maximum ventilation rate was found to be 0.32 m3 with 50º inclination angle and 10 cm air gab. On the other hand, Roof Top Solar Chimney (RTSC) has attracted many scholars. Al-Kayiem et al. [17] mathematically investigated the RTSC performance under different heights and collector area under Malaysian climate conditions. Their results showed that the average velocity, average mass flow rate and system performance increased gradually by increasing the area of the collector. For an area of 600 m2, the average velocity from 8:00 am to 5:00 pm is 4.65 m/s, and the average mass flow rate is 0.084 kg/s. While for the 150 m2 area, the average velocity is 3.29 m/s, and the mass flow rate is 0.05 kg/s. Aboulnaga and Abdrabboh [18] theoretically predicted the induced air flow rate of a combined wall-roof solar chimney in hotarid climate under the different height of the solar chimney. The maximum air flow rate of 2.3 m3/s occurs at 3.45 m wall height. Besides, numerical modelling of solar chimney using computational fluid dynamics (CFD) technique has attracted increasing attention. Harris and Helwig [19] carried out CFD analysis to investigate the performance of solar chimney with different inclination angles in Edinburg, Scotland conditions. The results showed that the optimum angle for a maximum air flow rate was 67.58 from the horizontal, giving an average benefit of 11% increase in flow rate in comparison with that for a vertical chimney. Tan and Wong [20] carried out parameterization analysis of the four input parameters (solar chimney’s stack height, depth, and inlet position) using FLUENT as the computational software. In this study, 300 cases were examined, and among the four parameters, the results showed that the solar chimney’s width is the most significant factor influencing output air speed. The above review indicates that improving solar chimney performance depends significantly on the combination of height, width, inclination angle and spacing of the channel. Although previous studies have provided several contributions to that, most of those attempts investigated chimney parameters independently to determine the optimum design solutions. It could be argued that the cumulative impact of all parameters might produce different optimal solar chimney design. Accordingly, this study develops a mathematical model to derive the optimum design of solar chimney parameters that achieves the optimal air flow rate according to the international standards [21]. The model integrates all parameters such as depth, width, air gab and inclination angle of the solar chimney under actual weather data. Following that, the thermal buoyancy of the selected solar chimney design is investigated using Computational Fluid Dynamics (CFD) simulations to predict the space flow pattern in detailed depiction within both the room and solar chimney. This approach is one of the first attempts that scrutinizes all parameters of solar chimney jointly under real weather data to determine the optimum design solutions corresponds to natural ventilation rate. 3. Mathematical model 3.1. Physical configuration and assumptions

The physical domain configuration considered in the present study, illustrated in Fig. 1, is located in Alexandria (a Northeast city in Egypt), with longitude and latitude of 31.2º N 29.91º E respectively. The average temperatures in summer are ranging from a maximum of 37º C and a minimum of 33º C, the average wind speed is 3–8 m/s, and the mean global radiation varies from 800 to 900 W/m2 [2]. This domain is a square area 4 m2 with a height of 2 m. The fenestration will face north with an area of 0.64 m2 (0.8 m height by 0.8 m width, gives a window to wall ratio of 16%). Whilst, the solar chimney glass-wall is oriented towards the south direction, and an absorber wall that works as a capturing surface, which warms up the trapped air in the channel. The absorber wall, due to its thermal inertia, produces natural convection even when solar radiation is not impinging it. Additionally, this chimney is supposed to be isolated to reduce losses. The mathematical model was established from the energy balance principles over the different parts of the solar chimney. Due to the complicated phenomena that occur in the thermal chimney, several simplifying assumptions are proposed while solving the governing equations for modelling as follow:  Steady-state conditions in the entire system,  One-dimensional heat transfer for all energy transfer processes through the glass cover and also between the absorber and air channel,  The glass cover is considered to be opaque for infrared radiation,  The air in the gab is a non-radiation absorbing fluid,  Temperatures at different points on the absorber and glass are considered to be equal along the width,  The temperature of the air at the inlet of the flow channel is assumed to be equal to room temperature,  Only buoyancy force is considered, the wind induces natural ventilation is approximately neglected,  Frictional losses are neglected due to the low order of flow velocity. 3.2.Governing equations The analogical diagram for the thermal heat transfer in an element of the modelled solar chimney is shown in Fig. 2. An overall energy balance on the chimney is considered. This balance includes the glass cover wall, the black absorber wall, and the air in between as suggested by Ong [4]. 3.2.1. Energy balance over the glass cover Applying the energy balance concept on the glass cover under the aforementioned assumptions could be expressed mathematically as:

Sg Ag  hrabs g Aabs Tabs  Tg   hg a Ag Tfsc  Tg   q1

(1)

The last term on the right-hand side represents the losses from the glass cover to the surroundings by convection, radiation, and conduction. It could be expressed as: (2)  q1  U t Ag Tg  Ta





Where, Ut counts for the two heat-transfer coefficients as:

U t  hwind  hrg  sky

(3)

3.2.2. Energy balance over the flowing air Similarly, the energy balance on the air flowing through the solar chimney channel could be expressed mathematically as: hg  a Ag Tg  T f  habs  a Aabs Tabs  T f  m C p T f , out  T f ,in (4)













While, the average air temperature is calculated as: T fsc  T f , out  1   T f ,in





(5)

where, ω (mean temperature weighting factor) is assumed as 0.74 following the recommendations of Ong [4]. Furthermore, as assumed earlier, Tfsc,in is identified to be equal to the room temperature Tr. Therefore, the useful heat transferred to the moving air stream can be translated in terms of mean and inlet air temperatures as follows: q  



m C f T f  Tr



  M T

f

 T f , in



(6)

Where; M represents the heat transfer to fluid that leaves the chimney as; M 

m c f

(7)

 WL

and m is the air volume that crosses the chimney, that has the following expression as identified by Bansal et al. [22]: m  Cd



 f A

2 gL T f  Tamb

1  Ao Ai

Tamb



(8)

Where Cd is the coefficient of discharge according to Flourentzou et al. [23]

is 0.60.

Rearranging Eq. (4) moreover, substituting the value of q" gives the following:  m C  f hg  a Ag Tg  T f  habs  a Aabs Tabs  T fsc      









   Tr  

(9)

In natural ventilation, it is much significant to know air exchange rate, the ratio of the air volume flow rate to the room volume. This expression is known as the Air Change per Hour (ACH). This index is defined by ASHRAE [21] as: ACH 

V  3600

(10)

room total volume

3.2.3. Energy balance over the absorber wall The absorber wall with its black surface is the main element in the chimney. The conservation of energy for this wall is represented as follows: S abs  hrabsg Aabs  Tabs  Tg   habsa Aabs  Tabs  T fsc   U b Aabs  Tabs  Tr  (11)

where Ub is the overall heat transfer coefficient from the rear of the inclined wall to the room and it is calculated as: 1 Ub  1 hi  wins Kins  (12) 3.3 Heat transfer coefficients 3.3.1. Radiative heat transfer coefficients The radiative heat transfer coefficient between the absorber wall and the glass cover hrabs-g is: hrabs  g  

T



2 Tg  Tabs   Tabs 1  g  1  abs  1

2 g

(13)

The radiative heat transfer coefficient from the outer glass surface to the sky refereed to the ambient temperature hrsky is obtained from:

hrsky 

 g Tg  Ts  Tg2  Ts2  Tg  Ts 

T

g

 Ta



(14)

where Ts is the sky temperature given by Swinbank [24] as; T s  0 . 0552 T

1 .5 amb

(15)

3.3.2. Convective heat transfer coefficients The convective heat transfer coefficient due to the wind hwind, which affects the glass and the later surface of the wall, is estimated as reported by Ong [4]. hwind  5.7  3.8V (16) Air flowing in the chimney carries thermal energies from the glass and absorber walls by convection. So, the convective heat-transfer coefficients between air and both walls are: Nu.k f @Tg hg a  (17) Lg

hwa 

Nu.k f @Tw Lw

(18)

The Nusselt number (Nu) calculation was carried out through empirical correlations given by Incropera and Dewitt [25], where Nu depends on the Rayleigh number (Ra) and the Prandtl number (Pr). The Rayleigh number depends on the temperature difference between the surface and the fluid where;

Ra 





g Tabs  Tf L3



2

and (β) is the volumetric coefficient of expansion;   1 Tf 9

If Ra < 10 the flow is laminar flow and the expression to calculate Nu has the form:

(19)

(20)



Nu  0 . 68  0 . 67 Ra 1 4

 1  0 .429

Pr 

9 16



4 9

(21)

9

If Ra > 10 the flow is turbulent flow and the Nu has the form:

 0.387 Ra1 6 Nu   0.825  9 16 1   0.492 Pr  



3.4.



  8 27 

2

(22)

Physical properties of air

The following empirical correlations are used to update the air properties that vary linearly with air temperature. Such correlations were reported by Ong [4] as: (23)  f   1 .846  0 .00472 T f  300    10 5  f  1 . 1614  0 . 00353

T

f

 300



k f  0 .0263  0 .000074 T f  300 





c f  1.007  0.00004 T f  300   10 3

(24) (25) (26)

The instantaneous efficiency of heat collection by the solar chimney is calculated from Ong and Chow [5]: 



m c f T f ,out  T f ,in

  100%

(27)

WLI

4. Analysis

To calculate the induced air flow rates through the cavity of the solar chimney, a computer program using MATLAB was developed for solving the set of equations that were obtained through an overall energy balance on the solar chimney as illustrated in section 3-2. The governing equations have to be solved iteratively using the Gauss-Seidel method until convergence of the results is achieved. Fig. 3 illustrates a graphical representation of the solution procedure. The solution initiates with an initial guess for the unknown temperatures Tg, Tf and Tabs. Then, the matrix is solved to obtain the converged temperatures. This theoretical model is capable of predicting mass flow rate through the solar chimney for different combinations of its geometric features over a wide range of variables under real weather data. In order to evaluate the model proposed, it is necessary to define the physical dimensions of various ingredients of the system (see Fig. 4) and the physical characteristics of a solar chimney with thermal inertia (see Table 1). The analysis was applied to 1536 combinations of parameters as shown in Table 2. Additionally, a series of real hourly weather data was utilized that corresponds to the selected week from 1st to 7th August; which represents the typical summer design week and the most crucial time of the year regarding building's maximum cooling energy consumption in Alexandria, Egypt. The model simulates and analyses the behaviour of the solar chimney computationally during daytime (from 8:00 AM to 5:00 PM).

5. Numerical analysis

A three-dimensional DesignBuilder model for the case study was firstly developed (see Fig. 5) for simulation. In such simulation, ambient wind speed in the used weather data file was

modified to 0.01 m/s using Element software to investigate the buoyancy effect of the solar chimney only. All external facades are exposed to the outside environment without overlapping with any other buildings that prevent over shading. In this study, CFD model is developed in order to investigate the transport phenomena developed inside the room equipped with the solar chimney. The numerical method employed by DesignBuilder’s CFD module is known as a primitive variable method, which involves the solution of a set of equations that describe the conservation of heat, mass and momentum. The equation set includes the three velocity component momentum equations (known as the Navier-Stokes equations), the temperature equation where the k-з turbulence model is used, equations for turbulence kinetic energy and the dissipation rate of turbulence kinetic energy [26]. The equations comprise a set of coupled non-linear secondorder partial differential equations having the following general form, in which φ represents the dependent variables [27]:  t

 ρΦ   div  ρυΦ   div  Γ grad Φ   S



(28)

where the δ ̸ δt (ρΦ) term represents the rate of change, the div  ρυΦ  term is convection, the





div Γ gradΦ term is diffusion and S  is a source term.

In this study, the renormalization group (RNG) k-ε turbulence model was applied for the prediction of buoyant air flow and flow rate in enclosures with solar chimney geometry. The second order upwind scheme was adopted for the momentum equations, which are discretized by the finite volume method. Moreover, the boundary conditions for DesignBuilder's CFD simulations are established from previously calculated values using the thermal modelling software Energy-Plus. The computational procedures for such three-dimensional turbulent airflow is based on solving the governing equations for the dependent variables (velocity components in x, y and zdirection, and the pressure) using finite volume grid. To ensure the numerical stability, the discretized equations are iterated with the under-relaxation factor. In the DesignBuilder CFD, a grid is automatically generated for the required model domain by identifying all contained model object vertices and then generating key coordinates from these vertices along the major grid axes. However, the accuracy of the representation of non-orthogonal surfaces can be improved by using smaller default grid spacing. In this study, the grid independence test is performed by calculating the inlet air velocity to chimney at different numbers of grids as shown in Fig. 6. It could be clearly seen that the inlet air velocity stabilizes at 0.512 m/sec at a number of grids 400,000. Therefore, the present simulation is performed using 406,640 grids (68 grids in the x-direction, 65 grids in y-direction and 92 grids in the z-direction) to get results that are independent of the grid size, and to reduce the computational time. Generally, DesignBuilder applied a domain-decoupled technique that separating the simulation of external airflows fields and internal airflows fields [28]. Thus, in the technical option setting, “calculated” module is preferred over “scheduled” module where the natural ventilation and infiltration are calculated based on the total window openings and natural ventilation criteria. 6. Experimental validation

To validate the mathematical model, the calculations were carried out for the solar chimney under the same conditions of experimental studies of Mathur et al. [13] and Imran et al. [9]. In Imran et al. work, the experimental setup, was a room of 2 m × 3 m × 2 m built using sandwich panels of 5 cm thick. The solar chimney was installed on the roof of this room to draw air from outside environment. Fresh air enters the room from a bottom suction opening through the room toward the solar chimney inlet. The chimney consists of a collector wall of 1 mm thickness aluminium sheet, glued and painted with a matt black paint. While, the opposite side for the solar radiation was covered by a 4 mm thick glass panel to be opaque for infrared radiation. The dimensions of the solar chimney are 2 m long, 2 m wide provided by three air gap thicknesses (50 mm, 100 mm and 150 mm) with variable chimney tilt angles ranging between 15º and 60º. The air velocity exits from the channel was recorded using an anemometer. A comparison between the obtained results and the theoretical and experimental results of Imran et al. [9] is shown in Fig. 7 with an average error (e) and correlation coefficient (r) around 6.67 % and 97.42 %, respectively. Whilst, in Mathur et al. [13], a cubical wooden chamber having a size, 1 m × 1 m × 1 m with a solar chimney inclined at an angle of 45º fitted on the top was constructed. The chimney consists of a 1 mm thickness of aluminium sheet acting as a solar radiation absorber. The aluminium sheet was painted with ordinary black paint. The absorber sheet was covered with glass cover of 4 mm thickness, keeping an air gab of 0.35 m. Inlet to the chimney was also kept as 0.35 m × 1.0 m covering the entire width of the base chamber. The outlet of the chimney was kept equal to the inlet, exhaling out the warm air in the atmosphere. All the exposed sides of the base chamber included the absorber was insulated. The temperatures of absorber surface, glass cover, flow channel, and the exit flow velocity were recorded during the experimental set-up. A summary of those results for different configurations and solar intensities are listed in Table 3. The quantitative comparison showed a reasonable agreement between the results obtained from the developed model and the published results under the operation condition they considered, and it could be clearly seen that the difference between the published experimental data and predicted theoretical values ranges from 1.27 % to 3.36%, which achieved better accuracy compared to published analytical counterpart calculations. 7. Results and discussion

A MATLAB computer program is adopted to solve the governing equations for 1536 combinations of different geometrical dimensions of solar chimney under real operation conditions (from 1st to 7th August), as illustrated in section 4. To determine the optimum geometry, it is possible to quantify the combination which achieves the standard ventilation rates of 0.019 to 0.033 m3/s according to ASHRAE Standard 62 [21] as long as possible. Accordingly, throughout the solar chimney configurations simulation tests, the optimum design was found to be 45 for inclination angle, 1.4 m for length, 0.6 m width and 0.20 m air gab. As the standard ventilation rate was achieved by 88.2% during the daytime of the selected operation conditions. Variation in volume airflow rate, and solar radiation intensity with respect to selected operation conditions for the optimum geometry design of the solar chimney have been shown in Fig. 8. It could be clearly seen that the mathematically simulated results of volume airflow rate increases as the solar intensity increased with the time of the day. Since the solar intensity is the main motive force for the chimney performance, the maximum airflow rate of 0.0422 m3/s was

noticeable at solar intensity 640 W/m2 (at 12:00 pm). Whilst, the volume airflow rate is lower the standard flow rate (0.019 m3/s), whereas the solar intensity is less than 250 W/m2.

Significant temperature difference through the chimney was resulted due to solar energy transmission over its component. Using the verified mathematical model to a series of real weather data, the temperatures of glass cover wall, the black absorber wall, the air in between and instantaneous efficiency were obtained, as shown in Fig. 9-10, respectively. Moreover, in these figures, the theoretical results from the validated mathematical model were compared with the numerical results. It could be seen that the graph pattern fluctuated in the same trend in predicting the performance of the solar chimney components. Specifically, the average deviation between the numerical and validated model results was calculated and found to be 8.97% which indicates a fair agreement. Such deviation is due to neglecting heat losses from the solar chimney and the wind speed effect. The figures manifest the significant temperature difference corresponding to solar intensity. Furthermore, as intensity increases, there is a linear increase in all temperatures as well as instantaneous efficiency. As depicted in Fig. 9, the glass surface temperature is approximately equal to ambient air temperature at the radiation level lower than 250 W/m2. However, it reaches to a maximum of 42 ºC at the solar intensity of 500 W/m2. Whilst, air flow temperature within the chimney cavity is always higher than the glass surface temperature due to exposure to convection from both sides with a very high temperature for the black absorber wall that reaches to 62 ºC at the solar intensity of 650 W/m2. It has been observed that the black absorber possesses a high-temperature value compared to chimney air temperature; this increase due to more captured radiation and storage of high thermal energy. This absorbed energy for the black absorber wall accelerates the flow of air through the chimney during the daytime. As a result, this exit air flow will help more fresh air to enter the space from the side-opening. Regarding the numerical results, the numerical flow prediction could be effectively used as an alternative procedure for flow visualization. Therefore, a further detailed CFD simulation study of air flow and temperature fields for two work-case scenarios were investigated: first where the outside temperature is equal or higher than the indoor temperature, and the second where the outside temperature is lower than the indoor temperature (see Fig. 11). As can be noticed in Fig. 11, there is a noticeable effect of the solar radiation intensity on the space flow pattern. Generally, the flow starts to penetrate more through the window into space, filling a significant portion of the space. The figure shows that the flow covers most of the area including the occupied zone (1.8 m above the floor). Noticeable recirculation of the airflow is observed in the regions close to the entering points. The inlet flow to the chimney is definitely affected by the discharge coefficient which is, in turn, dependent on the contracted area due to the sudden contraction in geometry to the main inlet area shape. As shown, the sudden contraction increases the air velocity and decrease the relative pressure in this region, the vena-contracta effect, creating a capable draught. Temperature fields in the room and the solar chimney are exhibited in Fig. 12. It could be clearly seen that the air temperature varies vertically from the floor to the ceiling. It is related to

the existence of vortex which, in turn, forms air circulation. Additionally, the air temperature at these areas is influenced by ambient air, and air flow enters the solar chimney. It is known that the vertical temperature gradient is a source of thermal discomfort. ASHRAE Standard 55 determines a maximum air temperature gradient vertically of 3 ºC between 1.7 m and 1.0 m above the floor [29]. The findings of numerical study reveal that vertical temperatures difference has not exceeded 2 C. According to the solar chimney, Fig. 12 shows that the maximum temperature at the absorber wall is due to the progressive heating absorbed from solar radiation. Consequently, the temperatures of trapped air in the channel rise due to natural convection. 8. Conclusion

In this study, a steady-state mathematical model has been developed to derive the optimal design of the solar chimney, which achieves optimum air flow rate according to the international standards. The developed model is cable of predicting air flow rates for a wide range of variables. Moreover, a numerical simulation using CFD module in DesignBuilder software was employed to predict the flow pattern in detailed depiction within the room and a solar chimney. The main achievements of this study could be drawn as follows:  An average deviation of 8.97% was found between the numerical experiments and validated model results which indicates a fair agreement,  The acceptability ratio of air flow rate ranges from of 0.019 to 0.033 m3/s as reported by ASHRAE Standard 62 [21]. The findings show that the proposed solar chimney (45º inclination angle, 1.4 m length, 0.60 m width, and 0.20 m air gab) is capable of providing such standard by 88.2% during daytime,  The numerical visualization of space flow pattern in a single room incorporated with the proposed solar chimney emphasized that the air flow penetrates large area of the space through the opening window. Also, the vertical temperatures difference has not exceeded 2 C. Clearly, it is found that the proposed solar chimney may be applied successfully in a hot-arid climate to fulfil the optimum air flow in residential buildings. Further experimental work is in progress to refine the model. Acknowledgment

The first author would like to thank the Egyptian Ministry of Higher Education for the financial support (Ph.D. scholarship), as well as the Egypt-Japan University of Science and Technology (E-JUST) for offering the facilities and tools needed to conduct this work. Thanks are extended to Mr. Awny El-Mohendes, a research assistant at Mansoura University, Egypt for his assistance regards to MATLAB software.

Reference

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[20] A. Tan, N. Wong, Parameterization Studies of Solar Chimneys in the Tropics, Energies. 6 (2013) 145–163. doi:10.3390/en6010145. [21] ASHRAE, Ventilation for Acceptable Indoor Air Quality, American Society of Heating, Refrigerating and Air-Conditioning Engineers, 2016. [22] N.K. Bansal, R. Mathur, M.S. Bhandari, Solar chimney for enhanced stack ventilation, (1993). http://eprint.iitd.ac.in/handle/2074/2258 (accessed December 11, 2015). [23] F. Flourentzou, J. Van der Maas, C.-A. Roulet, Natural ventilation for passive cooling: measurement of discharge coefficients, Energy Build. 27 (1998) 283–292. doi:10.1016/S0378-7788(97)00043-1. [24] W.C. Swinbank, Long-wave radiation from clear skies, Q. J. R. Meteorol. Soc. 89 (1963) 339–348. doi:10.1002/qj.49708938105. [25] T.L. Bergman, F.P. Incropera, Introduction to Heat Transfer, John Wiley & Sons, 2011. [26] DesignBuilder - Building design, simulation and visualisation - Building Simulation... Made Easy, (n.d.). http://www.designbuilder.co.uk/ (accessed June 3, 2014). [27] H.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Education Limited, 2007. [28] T.E. Jiru, G.T. Bitsuamlak, Application of CFD in Modelling Wind-Induced Natural Ventilation of Buildings - A Review, Int. J. Vent. 9 (2010) 131–147. doi:10.5555/ijov.2010.9.2.131. [29] ASHRAE, Thermal Environmental Conditions for Human Occupancy, American Society of Heating, Refrigerating and Air-Conditioning Engineers, 2010.

(L) Le ng th

Fig. 1 Schematic view of the physical domain.

Sun

Sabs hwind Sg hg

habs

1/hg 1/hw

Tsky

Angle (θ )

Fig. 2 Schematic of the heat transfer process within the solar chimney.

Start Input data; chimney dimensions and properties

Guess the initial values of Tg, Tf and Tabs

Do I =1, comb. index= N

Compute the system equations to obtain Tg, Tf and Tabs Tg,new= Tg,prev Tf,new= Tf,prev Tabs,new = Tabs,prev

Comb. Index = N+1

Update air properties based on the new values of Tg, Tf and Tabs

No

If error ≤ tolerence Yes Output; Calculate volume flow rate and ACH

Select the optimum design which achieve the standard ventilation rate long as possible during studied period

End

Fig. 3 Flow chart of the iterative procedures to solve the governing equations. 0

0

0.6 .

0.4 .

6 0 0.8 . 6 0 1.0 . 6 0 1.2 . 6 0 1.4 . 6 0 1.6 . 6 0 1.8 . 6 2 2.0 . 0 Length of solar chimney

6 0 0.6 . 6 0 0.8 . 6 0 1.0 . 6 0 1.2 . 6 0 1.4 . 6 0 1.6 . 6 1 1.8 . 8 width of solar chimney

0 0.10 .

6 0 0.15 . 6 0 0.20 . 6 0 0.25 . 6 0 0.30 . 0 6 . 0.35 3 5

0 30 .

6 0 45 . 6 0 60 . 6 0 75 . 6

Inclination angle Air gap of solar chimney solar chimney

Fig. 4 Physical dimensions of various ingredients of the system.

Inlet air velocity to the chimeny, (m/s)

Fig. 5 Reference case model in DesignBuilder. 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 0

200000

400000

600000

800000

1000000 1200000 1400000

Number of grids

Fig. 6 Inlet air velocity to the chimney versus number of grids

0.6

(a)

Exit air velocity, (m / sec)

0.5

0.4

0.3

Experimental results of Imran et al. [8] Theoretical results of Imran et al. [8] Theoretical results of present study

0.2

0.1

200

400

600

800

2

Solar radiation intensity, (W/m )

0.7

(b)

Exit air velocity, (m / sec)

0.6 0.5 0.4 0.3 Experimental results of Imrn et al, [8] Theoretical results of Imran et al, [8] theoretical results of present study

0.2 0.1 100

200

300

400

500

600

700

800

2

Solar radiation intensity, (W/m )

(c)

0.6

Exit air velocity, (m / sec)

0.5

0.4

0.3 Experimental results of Imran et al, [8] Theoretical results of Imran et al, [8] Theoretical results of present study

0.2 100

200

300

400

500

600 2

Solar radiation intensity, (W/m )

700

800

Exit air velocity, (m / sec)

(f)

0.6

0.5

0.4

0.3

0.2 100

Experimental results of Imran et al, [8] Theoretical results of Imran et al, [8] Theoretical results of present study

200

300

400

500

600

700

800

2

Solar radiation intensity, (W/m )

0.045

20

0.040 0.035 0.030 0.025 0.020

700

Air change per hour Solar radiation intensity

600

2

18 16

500

14 400 12 10

300

8 200

0.015

6

0.010

4

Solar radiation intensity, (W/m )

22

Air change per hour, (ACH)

0.050

3

Volume flow rate, (m /s)

Fig. 7 Comparison between the developed mathematical model against experimental and theoretical results of Imran et al. [9] as regards the exit air velocity. (a) at 0.05 cm air gab and 15º inclination angle, (b) at 0.1 cm air gab and 30º inclination angle, (c) at 0.15 cm air gab and 45º inclination angle and (f) at 0.15 cm air gab and 60º inclination angle.

Optimum volume flow rate (0.019 to 0.033 m3/s) 0

20

100 40

Time, (hrs)

60

Fig. 8 Volume airflow rate variations of the selected design of solar chimney.

Glass cover temperature evolution 340

700

(a)

600 2

Solar radiation intensity, (W/m )

330 Temperature, (K)

500 320

400 300

310

200 300

Theo. glass cover temp. Simul. Glass cover temp. Solar radiation intensity

100

290

0 0

20

40 Time, (hrs)

60

Air flow temperature evolution

(b)

340

700

2

500 Temperature, (K)

Solar radiation intensity, (W/m )

600 330

320

400 300

310

200 300

Theo. air flow temp. Simul.air flow temp. Solar radiation intensity

100

290

0 0

20

Time, (hrs)

40

60

Absorber wall temperature evolution 340

700

(c) 2

500 Tempertaure, (K)

Solar radiation intensity, (W/m )

600 330

320

400 300

310

200 300

Theo. absorber temp. Simul. Absorber Surface temp Solar radiation intensity

100

290

0 0

20

Time, (hrs)

40

60

Fig. 9 Temperatures hourly variations of; (a) glass cover, (b) air flow and (c) absorber wall

Instantene ous Efficiency Solar radiation intensity

700 600 2

0.5

Solar radiation intensity, (W/m )

Instanteneous Efficiency x 100, (%)

0.6

500 0.4

400 300

0.3

200 0.2 100 0.1

0 0

20

40

60

Time, (hrs)

Fig. 10 Instantaneous efficiency versus incident solar radiation

(a)

(b)

Fig. 11 Flow pattern in the room and solar chimney: (a) at solar heat flux 640 W/m2 and outdoor temperature was lower than room temperature and (b) at solar heat flux 400 W/m2 and outdoor temperature was higher than room temperature.

Fig. 12 Temperature fields in the room and solar chimney

Table 1 Thermal properties of solar chimney materials. Material Glass cover Absorber cover Insulation layer

Density ()

Thermal conductivity ()

Specific heat (Cp)

kg/m3

W/m2.K

J/kg

184 2700 104

5.91 237 0.037

23 900 1.2

Table 2 Parametric analysis ranges of four input parameters Input parameter

Parametric analysis ranges Lower bound

Upper bound

Increment

No. of values

Stack height (L)

0.6 m

2.0 m

0.2 m

8

Air gap (d)

0.10 m

0.3 m

0.05 m

6

Width (w)

0.4 m

2.0 m

0.2 m

8

Inclination angle (Ѳ)

30

75

15

4

Total no. of combinations

1536

Table 3 Comparison of experimental and theoretical results for the solar chimney performance

Theo. of Muthar el al. [13]

Present study

Exp. of Muthar el al. [13]

Theo. of Muthar el al. [13]

Present study

Exp. of Muthar el al. [13]

Theo. of Muthar el al. [13]

Present study

Exp. of Muthar el al. [13]

Theo. of Muthar el al. [13]

Present study

Exit air velocity (m/sec)

Exp. of Muthar el al. [13]

Absorber temp. (K)

Out. Temp. (K)

Air flow temp. (K)

Solar Rad. (W/m2)

Glass cover temp. (K)

500

299.2

314.3

310.70

313.40

306.93

300.96

304.34

329.04

344.46

324.859

0.174

0.1517

0.1764

550

302.6

317.3

315.45

317.82

308.95

304.13

308.17

340.65

351.01

330.35

0.184

0.1563

0.1842

600

306

326.02

321.30

321.64

312.22

308.30

312.11

346.28

358.27

336.82

0.1948

0.1613

0.1907

650

310.3

330.18

327.15

327.6

316.82

312.48

316.64

354.66

365.40

342.749

0.1979

0.1639

0.1968

700

312.2

333.51

330.83

329.02

319.07

314.64

318.89

358.49

370.70

346.82

0.2132

0.1724

0.2025

750

313

337.29

333.40

330.64

320.75

315.79

320.02

361.38

375.05

349.80

0.2201

0.1761

0.2079