- Email: [email protected]
The thermal performances of a solar wall
Energy 39 (2012) 11e16
Contents lists available at SciVerse ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
The thermal performances of a solar wall K. Hami a, c, *, B. Draoui b, c, O. Hami b, c a
Faculty of Mechanical Engineering, University of Sciences and Technology of Oran (USTO), Algeria Faculty of Sciences and Technology, Bechar University, Algeria c Laboratoire d’Energétique En Zones Arides (ENRGARID), Bechar University, Algeria b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 February 2011 Received in revised form 30 September 2011 Accepted 12 October 2011 Available online 22 November 2011
In this paper, the computational fluid dynamics technique (CFD) was used for air flow simulation in the solar chimney. The flow is assumed laminar, unsteady and incompressible. The air flow model consisted of a system of governing equations continuity, momentum, energy are solved for 2D Cartesian system uses the SIMPLE algorithm and the PowereLaw differencing scheme. The influence of the variation depth of the solar chimney on the thermal efficiency of the system was studies. The principle of functioning of the system is visualized. The temperatures obtained on the level of the zone of occupation are adaptable to the interval of thermal comfort. The results of simulation are congruent with those of the literature. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Heating passive Natural convection Solar energy Trombe wall Numerical modeling
1. Introduction Taking into account the exhaustion and the cost of energies used currently, such as fossil energies, and of the report established by the experts concerning the ecological requirements, it is necessary to find new sources of clean and free energies i.e. renewable energies, in order to preserve the planetary resources for the future generations. In the current context, solar energy is the most interesting alternative and most advantageous. Our objective is to use it in the housing. Our work consists with the use of a storage wall (wall Trombe) which remains one of the most effective systems for the passive heating of the buildings. In any solar energy system for space heating there are three functions performed: collection of solar energy, storage, and distribution of that energy (heat) from storage to living space. The two basic categories of solar systems for space heating - active and passive - perform these three functions, but in different ways. Additional fans or pumps are required to bring stored heat to areas where it is needed [1]. Passive solar heating systems, on the other hand, require no electrical or petroleum based energy to operate; they utilize natural
* Corresponding author. Faculty of Sciences and Technology, Bechar University, P.O Box: 417, 08000 Bechar, Algeria. Tel./fax: þ213 49 81 52 44. E-mail address: [email protected] (K. Hami). 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.10.017
methods of heat transfer -thermal conduction, natural convection, and thermal radiation. Passive systems perform the three functions of collection, storage, and distribution of solar energy in the following way. Sunlight enters the clear or translucent section of a wall. This section (known as glazing) should be on the south side of a building (in the Northern Hemisphere) to collect the maximum amount of solar radiation available. Solar radiation is then absorbed by the storage medium behind the glazing. This stored heat is distributed into the living space by means of the three transfer mechanisms mentioned above. There are five basic designs for passive solar space heating: direct gain, solar greenhouse, convective air loop, roof pond, and thermal storage walls. Thermal storage walls fall into three general categories: those utilizing a massive wall to store heat - these are known as Trombe walls; those utilizing a water wall to store heat; and the more experimental type in which heat is stored in eutectic salts or salt hydrates. Because Trombe walls are the most used type of thermal storage wall, much of our discussion will focus on them [2]. Five elements of a thermal storage wall can be identified: glazing, air space between glazing and wall, the mass or storage wall, vents (in some thermal storage walls), and roof overhang (especially in warm climates). It is important here only to introduce how these elements enable a thermal storage wall to function in heating a building. Several numerical and experimental studies were carried out on the heat transfer by natural convection and thermal radiation in
12
K. Hami et al. / Energy 39 (2012) 11e16
partitioned rectangular cavities. This interest is due to the various industrial applications that these geometries reflect in several problems of engineering. Among this work, one quotes in particular that of Mezrhab A., Bouali H and Abid C [3] analyzed the effect of the thermal radiation on the heat transfer and the air flow within an enclosure containing a solid block generating heat. They found that the thermal radiation reduces the maximum temperature in the enclosure, because of radiative fluxes lost by the side bordering solid block. An experimental and numerical study concerning the effect of a partition placed at the medium of a rectangular enclosure was carried out by Nakamura and Asko [4]. They concluded that emissivities of the walls opposite influence considerably the heat transfer by convection. Among technologies, search and studies carried out in simple enclosure of geometry, several works was interested in the study of the thermal behavior of the solar systems of the type wall Trombe and its alternatives. Ong K.S. [5] studied numerically the coupled heat transfer by conduction, natural convection and radiation in a vertical rectangular enclosure delimited by a glass and a massive wall absorbing a solar flux. They noted that for DT ¼ 10 K, there is a critique value (Rac) of Ra about 1.7 108 for which the flow change direction. They have also shown that more than 75% of the total heat transfer in the enclosure is through radiation. Torcellini P and Pless S [6] presented a numerical solution to the problem of natural convection in the case of heating buildings by a passive solar system, which is a variant of the system Trombe-Michel. Gan [7] studied the Trombe walls for use in the cooling of buildings in summer conditions. He pointed to a study which showed that the computer code developed by CFD (Computational Fluid Dynamics) can be used for predicting the movement of the air flow and buoyant in the fences with the geometry of Trombe wall. Awbi H.B and Gan G [8] studied numerically turbulent convective flow free in a Trombe wall. They then developed correlations to estimate the performance of Trombe walls. Smolec W and Thomas A [9] proposed a simple mathematical model of a solar chimney; the physical model is similar to the Trombe wall. Hami K, Draoui B and Hami O [10] used a CFD programs to simulate air flow and heat transfer in a solar chimney. In this paper, the computational fluid dynamics technique (CFD) was used for air flow simulation in the solar chimney. The flow is assumed laminar, unsteady and incompressible. The air flow model consisted of a system of governing equations continuity, momentum, energy are solved for 2D Cartesian system uses the SIMPLE algorithm and the PowereLaw differencing scheme. 2. Positioning of the problem
Fig. 1. The monthly distribution of the: (a) Temperatures; (b) Relative humidity, [weather station of the town of Bechar, average of 10 years (1998e2008) [10].
3. Principle of functioning The hot air which is in the chimney solar (glazing and wall ¼ b) penetrates in the room through openings located in top of the wall and that inside colder, is aspired naturally by the openings located
In this work we study a room located in the town of Bechar, (south-west of Algeria) whose geographical situation is as follows: Latitude 31370 N, Longitude 2140 W, Altitude 813 m. 2.1. Climatic zoning of the town of Bechar (south-west of Algeria) The city belongs to the climatic zone (Fig. 1) of summer and the winter (E3, H3a) with two main seasons (summer and winter). With strong sunshine, exceeding the 3500 h per year, and intense solar radiation that can reach 1100 (W/m2) on a horizontal plane, the climate of Bechar has a very mixed thermal regime. In summer the temperature easily exceeds 45 C in the shade, and the relative humidity remains low at around 35%. Moreover, in winter the outside temperature can drop to 5 C at night with scarce and irregular rainfall [10].
Fig. 2. Geometry model.
K. Hami et al. / Energy 39 (2012) 11e16
Fig. 3. Physical model.
Fig. 5. Change of the temperature on the level of surface external of the Trombe wall and on the level of the zone of occupation to 1 h and 8 h hours of functioning.
in bottom, this course is called "thermocirculation". The heating of the room is obtained mainly by convection on the internal face of the wall which restores the heat stored with a certain dephasing, whereas an instantaneous heating is possible. Valves are placed in front of the openings of bottom to avoid a reverses circulation the night (Fig. 2), with: b ¼ 0.30 m; d ¼ 0.20 m; H ¼ 3 m; L ¼ 5 m; c ¼ 2.60 m; e ¼ 0.40 m. 4. Mathematical formulation and numerical procedure The room is unoccupied or only heated by direct sunlight at, 8:00 h to 18:00 h, 4(t): Solar flow (W/m2), 36000 (s): time of sunshine, this corresponds to the length of day in winter. 4max ¼ 550 (W/m2), the (max) solar flow at 13:00 h. By adopting the assumptions below: The flow and the heat transfer are two-dimensional (2D) and the mode is transitory. The flow is laminar taking into account the weak variations in temperature is generally met in thermal of the buildings, the air is incompressible and Newtonian, the thermo-physical properties of the air are constant and the approximation of Bousinesq is used:
Fig. 4. Evolution of the temperature at the outer surface of the Trombe wall.
13
Fig. 6. Heat exchange of the system: (a) 1 h, (b) 8 h and (c) 24 h of functioning.
14
K. Hami et al. / Energy 39 (2012) 11e16
r ¼ r0 ½1 bðT T0 Þ
(1)
The equations controlling the flow and the heat transfer of our system are:
vui ¼ 0 vxi
(2)
"
vu vu r i þ uj i vt vxj
rCP
#
vP v vu m i ¼ þ vxj vxi vxj
! þ Fi
vT vT v vT l ¼ þ rCP uj vt vxj vxi vxi
(3)
(4)
4.1. Initial end boundary conduction On the internal walls of the room (condition of no slip):
Fig. 8. Wall solar heat gain during the 24 h of functioning.
U ¼ V ¼ 0; 4.2. Numerical resolution
Tðx; y; 0Þ ¼ 10 C TðL; H; tÞ ¼ Tf Tð0; H; tÞ ¼ Tf In the level of the left surface of the wall Trombe one applies a heat flow of the solar radiation (Fig. 3): x ¼ b; d < y < c, Trombe wall surface
4x¼b ¼ 550 sin
p 36000
t
with: 0 < t < 36000
The computational fluid dynamics technique (CFD) was used for air flow simulation in the solar chimney. The flow is assumed to be laminar, unsteady and incompressible. The air flow model consisted of a system of governing equations representing continuity, momentum, energy are solved for 2D Cartesian system using the SIMPLE algorithm and the PowereLaw differencing scheme. 5. Results and discussions
(5)
The results obtained are presented in the form of figures for various values of the depth of the solar chimney in order to see its influence on the thermal efficiency of the system. 5.1. Heating effect of the system Fig. 4 represents the improvement of the thermal transfer by thermal conduction in the course of time to the level thickness of the wall Trombe (strong inertia preferably). It is clear that the wall Trombe starts collecting heat which comes from the sunning during the day, and then it restores this energy during the night time.
Fig. 7. (a) Streams lines; (b) isotherms at 8 h of functioning.
Fig. 9. Change of the temperature on the level of the solar chimney with 1 h, 3 h, 6 h and 8 h.
K. Hami et al. / Energy 39 (2012) 11e16
Fig. 10. Mass flow rate in the solar chimney during the 10 h of functioning.
The results represented in Fig. 5 show the importance of the passive heating in the course of time on the level of the zone of occupation, the temperature of the zone of occupation increases by effect of the thermocirculation. The effect of thermal inertia plays the role of storage to heat the room after the hours of the sunning. Fig. 6 represent the distribution of the temperature during the 24 operating hours of the system, the room is heated by the principle thermocirculation during the day and by inertia of the wall the evening. The results obtained show that in full winter, the temperatures on the level of the zone of occupation are suitable with the interval of the thermal comfort which is between (18 Ce24 C). Fig. 7 presents the streams and the isotherms of current obtained in the course of time. The air circulates in a clockwise direction and is monocellulaire because of the position of the isothermal walls hot and cold. Indeed, the fluid goes up along the hot wall and goes down along the cold wall. With the medium of the room, one attends a thermal stratification of the temperature under the effect of the voluminal forces. Also, the isotherms are dense in the vicinity of the hot wall, like those of the cold wall of the right face of the room. The results represented in Fig. 8 and Fig. 9 show that the thermal efficiency of the system is a function of the contribution of heat and does not depend on the depth of the solar chimney.
15
Fig. 12. Profile of velocity U at 8 h of functioning on the level of vertical surface in the medium of the room.
The system efficiency, h, as the ratio of maximum wall solar heat gain to the maximum possible solar irradiance (Fig. 8):
h¼
Maximum Wall solar Heat Gain Maximum solar irradiance
h¼
ð371:13 104:19Þ ; h ¼ 48:54% ð550 0Þ
(6)
5.2. Dynamic effect of the system The mass flow rate and the air flow rate in the solar chimney in the course of time Fig. 10 And Fig. 11 is a function at the same time of the contribution of heat and depth of the solar chimney. The mathematical expressions required to estimating the mass flow rate and the air flow rate used in [11]:
_ ¼ 0:0197 DT 0:4015 ðkg=s:mÞ m
(7)
Q ¼ 4:5725 q0:4015 ðl=s:mÞ
(8)
Fig. 12 represents the Profile of velocity (U) following the height to the medium of the room, one notices that there are three areas, the first is located in top (zone of hot puff blowing), the second in bottom (extraction zone of the cold air is located) and the third is a thermal zone of stratification under the effect of the voluminal forces where we note that the speeds are very low. 6. Conclusions
Fig. 11. The air flow rate in the solar chimney during the 10 h of functioning.
The simulations studied in this work enable us to draw the following conclusions: The temperature on the level of the openings the top (hot air) depends closely on solar flow. The results of simulation obtained give a temperature of the air rather high to the exit, favorable to ensure a good thermal comfort. The use of solar energy consists in profiting from the direct contribution of the solar radiation, one must take account of solar energy at the time of the architectural design (double frontages, orientation toward the south, surfaces glazed, etc.). The mass wall is the most crucial component of a Trombe wall type thermal storage wall. In it the solar heat will be stored and transmitted to the inside of the building. The material used for a mass wall, therefore, very important.
16
K. Hami et al. / Energy 39 (2012) 11e16
With vented thermal storage walls, the vents can provide an important control mechanism both in heating and cooling the building. They can facilitate heat transfer into the building during a winter day. The use of vents through the glazing while upper vents through the mass wall are closed reduces heat gain by the mass wall. A roof overhang can also reduce heat gain during the warm months when the sun is high by shading the thermal storage wall. And, as will be shown, there are many other ways to adapt thermal storage walls to increase or decrease solar gain and reduce heat loss. The results obtained for the area of Bechar seem interesting, which makes it possible to do much energy saving.
Q _ m
Air flow rate [l/s.m] Mass flow rate [kg/s.m]
Greek letters Dimension of the opening of circulation of air [m] Coefficient of cubic dilatation [1/K] Kinematics viscosity of the fluid [m2/s] Density of the fluid [kg/m3] Thermal conductivity [W/m K] Solar flow [W/m2]
d b n r l 4
References Nomenclature
a b c e H L P Cp To Tob Toh Tin ui q
h
Thermal diffusivity [m2/s] Outdistance depth of walked on solar [m] Height of the Trombe wall [m] Thickness of the Trombe wall [m] Height of the local one [m] Length of the local one [m] Pressure [Pa] Specific heat [J/kg K] Temperature of reference [K] Temperature on the level of low opening [K] Temperature on the level of high opening [K] Temperature on the level of the zone of occupation [K] Air velocity according to x, y [m/s] Wall solar heat gain [W/m2] System efficiency (%)
[1] Chel A, Nayak JK, Kaushik G. Energy conservation in honey storage building using Trombe wall. Energy and Buildings 2008;40:1643e50. Elsevier. [2] Burek SAM, Habeb A. Flow and thermal efficiency characteristics in solar chimneys and Trombe Walls. Energy and Buildings 2007;39:128e35. Elsevier. [3] Mezrhab A, Bouali H, Abid C. Modelling of combined radiation and convection heat transfer in an enclosure with a heat generating conducting body. International Journal of Computational Methods 2005;2(3):431e50. [4] Nakamura H, Asko Y. Combined free convection and radiation heat transfer in rectangular cavities with a partition wall. Heat Transfer Japanese Research; 1986:60e81. [5] Ong KS. A mathematical model of a solar chimney. Renewable Energy 2003; 28:1047e60. [6] Torcellini P, Pless S. Trombe walls in low-energy buildings: practical experiences. Congress VIII and Expo Denver, Colorado; 2004. NREL/CP-550e36277. [7] Gan G. A parametric study of Trombe walls for passive cooling of buildings. Energy and Buildings 1998;27(1):37e43. [8] Awbi HB, Gan G. Simulation of solar-induced ventilation. Renewable Energy Technology and the Environment 1992;4:2016e30. [9] Smolec W, Thomas A. Problems encountered in heat transfer studies of a Trombe wall. Energy Conversion and Management 1994;35:483e91. [10] Hami K, Draoui et B, Hami O. Modélisation d’un système de chauffage passif dans la région de Béchar. Revue des Energies Renouvelables 2010;13(2):355e68. [11] Gan Guohui. A parametric of Trombe Walls for passive cooling of building. Energy and Buildings 1998;27:37e43. Elsevier.
Contents lists available at SciVerse ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
The thermal performances of a solar wall K. Hami a, c, *, B. Draoui b, c, O. Hami b, c a
Faculty of Mechanical Engineering, University of Sciences and Technology of Oran (USTO), Algeria Faculty of Sciences and Technology, Bechar University, Algeria c Laboratoire d’Energétique En Zones Arides (ENRGARID), Bechar University, Algeria b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 February 2011 Received in revised form 30 September 2011 Accepted 12 October 2011 Available online 22 November 2011
In this paper, the computational fluid dynamics technique (CFD) was used for air flow simulation in the solar chimney. The flow is assumed laminar, unsteady and incompressible. The air flow model consisted of a system of governing equations continuity, momentum, energy are solved for 2D Cartesian system uses the SIMPLE algorithm and the PowereLaw differencing scheme. The influence of the variation depth of the solar chimney on the thermal efficiency of the system was studies. The principle of functioning of the system is visualized. The temperatures obtained on the level of the zone of occupation are adaptable to the interval of thermal comfort. The results of simulation are congruent with those of the literature. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Heating passive Natural convection Solar energy Trombe wall Numerical modeling
1. Introduction Taking into account the exhaustion and the cost of energies used currently, such as fossil energies, and of the report established by the experts concerning the ecological requirements, it is necessary to find new sources of clean and free energies i.e. renewable energies, in order to preserve the planetary resources for the future generations. In the current context, solar energy is the most interesting alternative and most advantageous. Our objective is to use it in the housing. Our work consists with the use of a storage wall (wall Trombe) which remains one of the most effective systems for the passive heating of the buildings. In any solar energy system for space heating there are three functions performed: collection of solar energy, storage, and distribution of that energy (heat) from storage to living space. The two basic categories of solar systems for space heating - active and passive - perform these three functions, but in different ways. Additional fans or pumps are required to bring stored heat to areas where it is needed [1]. Passive solar heating systems, on the other hand, require no electrical or petroleum based energy to operate; they utilize natural
* Corresponding author. Faculty of Sciences and Technology, Bechar University, P.O Box: 417, 08000 Bechar, Algeria. Tel./fax: þ213 49 81 52 44. E-mail address: [email protected] (K. Hami). 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.10.017
methods of heat transfer -thermal conduction, natural convection, and thermal radiation. Passive systems perform the three functions of collection, storage, and distribution of solar energy in the following way. Sunlight enters the clear or translucent section of a wall. This section (known as glazing) should be on the south side of a building (in the Northern Hemisphere) to collect the maximum amount of solar radiation available. Solar radiation is then absorbed by the storage medium behind the glazing. This stored heat is distributed into the living space by means of the three transfer mechanisms mentioned above. There are five basic designs for passive solar space heating: direct gain, solar greenhouse, convective air loop, roof pond, and thermal storage walls. Thermal storage walls fall into three general categories: those utilizing a massive wall to store heat - these are known as Trombe walls; those utilizing a water wall to store heat; and the more experimental type in which heat is stored in eutectic salts or salt hydrates. Because Trombe walls are the most used type of thermal storage wall, much of our discussion will focus on them [2]. Five elements of a thermal storage wall can be identified: glazing, air space between glazing and wall, the mass or storage wall, vents (in some thermal storage walls), and roof overhang (especially in warm climates). It is important here only to introduce how these elements enable a thermal storage wall to function in heating a building. Several numerical and experimental studies were carried out on the heat transfer by natural convection and thermal radiation in
12
K. Hami et al. / Energy 39 (2012) 11e16
partitioned rectangular cavities. This interest is due to the various industrial applications that these geometries reflect in several problems of engineering. Among this work, one quotes in particular that of Mezrhab A., Bouali H and Abid C [3] analyzed the effect of the thermal radiation on the heat transfer and the air flow within an enclosure containing a solid block generating heat. They found that the thermal radiation reduces the maximum temperature in the enclosure, because of radiative fluxes lost by the side bordering solid block. An experimental and numerical study concerning the effect of a partition placed at the medium of a rectangular enclosure was carried out by Nakamura and Asko [4]. They concluded that emissivities of the walls opposite influence considerably the heat transfer by convection. Among technologies, search and studies carried out in simple enclosure of geometry, several works was interested in the study of the thermal behavior of the solar systems of the type wall Trombe and its alternatives. Ong K.S. [5] studied numerically the coupled heat transfer by conduction, natural convection and radiation in a vertical rectangular enclosure delimited by a glass and a massive wall absorbing a solar flux. They noted that for DT ¼ 10 K, there is a critique value (Rac) of Ra about 1.7 108 for which the flow change direction. They have also shown that more than 75% of the total heat transfer in the enclosure is through radiation. Torcellini P and Pless S [6] presented a numerical solution to the problem of natural convection in the case of heating buildings by a passive solar system, which is a variant of the system Trombe-Michel. Gan [7] studied the Trombe walls for use in the cooling of buildings in summer conditions. He pointed to a study which showed that the computer code developed by CFD (Computational Fluid Dynamics) can be used for predicting the movement of the air flow and buoyant in the fences with the geometry of Trombe wall. Awbi H.B and Gan G [8] studied numerically turbulent convective flow free in a Trombe wall. They then developed correlations to estimate the performance of Trombe walls. Smolec W and Thomas A [9] proposed a simple mathematical model of a solar chimney; the physical model is similar to the Trombe wall. Hami K, Draoui B and Hami O [10] used a CFD programs to simulate air flow and heat transfer in a solar chimney. In this paper, the computational fluid dynamics technique (CFD) was used for air flow simulation in the solar chimney. The flow is assumed laminar, unsteady and incompressible. The air flow model consisted of a system of governing equations continuity, momentum, energy are solved for 2D Cartesian system uses the SIMPLE algorithm and the PowereLaw differencing scheme. 2. Positioning of the problem
Fig. 1. The monthly distribution of the: (a) Temperatures; (b) Relative humidity, [weather station of the town of Bechar, average of 10 years (1998e2008) [10].
3. Principle of functioning The hot air which is in the chimney solar (glazing and wall ¼ b) penetrates in the room through openings located in top of the wall and that inside colder, is aspired naturally by the openings located
In this work we study a room located in the town of Bechar, (south-west of Algeria) whose geographical situation is as follows: Latitude 31370 N, Longitude 2140 W, Altitude 813 m. 2.1. Climatic zoning of the town of Bechar (south-west of Algeria) The city belongs to the climatic zone (Fig. 1) of summer and the winter (E3, H3a) with two main seasons (summer and winter). With strong sunshine, exceeding the 3500 h per year, and intense solar radiation that can reach 1100 (W/m2) on a horizontal plane, the climate of Bechar has a very mixed thermal regime. In summer the temperature easily exceeds 45 C in the shade, and the relative humidity remains low at around 35%. Moreover, in winter the outside temperature can drop to 5 C at night with scarce and irregular rainfall [10].
Fig. 2. Geometry model.
K. Hami et al. / Energy 39 (2012) 11e16
Fig. 3. Physical model.
Fig. 5. Change of the temperature on the level of surface external of the Trombe wall and on the level of the zone of occupation to 1 h and 8 h hours of functioning.
in bottom, this course is called "thermocirculation". The heating of the room is obtained mainly by convection on the internal face of the wall which restores the heat stored with a certain dephasing, whereas an instantaneous heating is possible. Valves are placed in front of the openings of bottom to avoid a reverses circulation the night (Fig. 2), with: b ¼ 0.30 m; d ¼ 0.20 m; H ¼ 3 m; L ¼ 5 m; c ¼ 2.60 m; e ¼ 0.40 m. 4. Mathematical formulation and numerical procedure The room is unoccupied or only heated by direct sunlight at, 8:00 h to 18:00 h, 4(t): Solar flow (W/m2), 36000 (s): time of sunshine, this corresponds to the length of day in winter. 4max ¼ 550 (W/m2), the (max) solar flow at 13:00 h. By adopting the assumptions below: The flow and the heat transfer are two-dimensional (2D) and the mode is transitory. The flow is laminar taking into account the weak variations in temperature is generally met in thermal of the buildings, the air is incompressible and Newtonian, the thermo-physical properties of the air are constant and the approximation of Bousinesq is used:
Fig. 4. Evolution of the temperature at the outer surface of the Trombe wall.
13
Fig. 6. Heat exchange of the system: (a) 1 h, (b) 8 h and (c) 24 h of functioning.
14
K. Hami et al. / Energy 39 (2012) 11e16
r ¼ r0 ½1 bðT T0 Þ
(1)
The equations controlling the flow and the heat transfer of our system are:
vui ¼ 0 vxi
(2)
"
vu vu r i þ uj i vt vxj
rCP
#
vP v vu m i ¼ þ vxj vxi vxj
! þ Fi
vT vT v vT l ¼ þ rCP uj vt vxj vxi vxi
(3)
(4)
4.1. Initial end boundary conduction On the internal walls of the room (condition of no slip):
Fig. 8. Wall solar heat gain during the 24 h of functioning.
U ¼ V ¼ 0; 4.2. Numerical resolution
Tðx; y; 0Þ ¼ 10 C TðL; H; tÞ ¼ Tf Tð0; H; tÞ ¼ Tf In the level of the left surface of the wall Trombe one applies a heat flow of the solar radiation (Fig. 3): x ¼ b; d < y < c, Trombe wall surface
4x¼b ¼ 550 sin
p 36000
t
with: 0 < t < 36000
The computational fluid dynamics technique (CFD) was used for air flow simulation in the solar chimney. The flow is assumed to be laminar, unsteady and incompressible. The air flow model consisted of a system of governing equations representing continuity, momentum, energy are solved for 2D Cartesian system using the SIMPLE algorithm and the PowereLaw differencing scheme. 5. Results and discussions
(5)
The results obtained are presented in the form of figures for various values of the depth of the solar chimney in order to see its influence on the thermal efficiency of the system. 5.1. Heating effect of the system Fig. 4 represents the improvement of the thermal transfer by thermal conduction in the course of time to the level thickness of the wall Trombe (strong inertia preferably). It is clear that the wall Trombe starts collecting heat which comes from the sunning during the day, and then it restores this energy during the night time.
Fig. 7. (a) Streams lines; (b) isotherms at 8 h of functioning.
Fig. 9. Change of the temperature on the level of the solar chimney with 1 h, 3 h, 6 h and 8 h.
K. Hami et al. / Energy 39 (2012) 11e16
Fig. 10. Mass flow rate in the solar chimney during the 10 h of functioning.
The results represented in Fig. 5 show the importance of the passive heating in the course of time on the level of the zone of occupation, the temperature of the zone of occupation increases by effect of the thermocirculation. The effect of thermal inertia plays the role of storage to heat the room after the hours of the sunning. Fig. 6 represent the distribution of the temperature during the 24 operating hours of the system, the room is heated by the principle thermocirculation during the day and by inertia of the wall the evening. The results obtained show that in full winter, the temperatures on the level of the zone of occupation are suitable with the interval of the thermal comfort which is between (18 Ce24 C). Fig. 7 presents the streams and the isotherms of current obtained in the course of time. The air circulates in a clockwise direction and is monocellulaire because of the position of the isothermal walls hot and cold. Indeed, the fluid goes up along the hot wall and goes down along the cold wall. With the medium of the room, one attends a thermal stratification of the temperature under the effect of the voluminal forces. Also, the isotherms are dense in the vicinity of the hot wall, like those of the cold wall of the right face of the room. The results represented in Fig. 8 and Fig. 9 show that the thermal efficiency of the system is a function of the contribution of heat and does not depend on the depth of the solar chimney.
15
Fig. 12. Profile of velocity U at 8 h of functioning on the level of vertical surface in the medium of the room.
The system efficiency, h, as the ratio of maximum wall solar heat gain to the maximum possible solar irradiance (Fig. 8):
h¼
Maximum Wall solar Heat Gain Maximum solar irradiance
h¼
ð371:13 104:19Þ ; h ¼ 48:54% ð550 0Þ
(6)
5.2. Dynamic effect of the system The mass flow rate and the air flow rate in the solar chimney in the course of time Fig. 10 And Fig. 11 is a function at the same time of the contribution of heat and depth of the solar chimney. The mathematical expressions required to estimating the mass flow rate and the air flow rate used in [11]:
_ ¼ 0:0197 DT 0:4015 ðkg=s:mÞ m
(7)
Q ¼ 4:5725 q0:4015 ðl=s:mÞ
(8)
Fig. 12 represents the Profile of velocity (U) following the height to the medium of the room, one notices that there are three areas, the first is located in top (zone of hot puff blowing), the second in bottom (extraction zone of the cold air is located) and the third is a thermal zone of stratification under the effect of the voluminal forces where we note that the speeds are very low. 6. Conclusions
Fig. 11. The air flow rate in the solar chimney during the 10 h of functioning.
The simulations studied in this work enable us to draw the following conclusions: The temperature on the level of the openings the top (hot air) depends closely on solar flow. The results of simulation obtained give a temperature of the air rather high to the exit, favorable to ensure a good thermal comfort. The use of solar energy consists in profiting from the direct contribution of the solar radiation, one must take account of solar energy at the time of the architectural design (double frontages, orientation toward the south, surfaces glazed, etc.). The mass wall is the most crucial component of a Trombe wall type thermal storage wall. In it the solar heat will be stored and transmitted to the inside of the building. The material used for a mass wall, therefore, very important.
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With vented thermal storage walls, the vents can provide an important control mechanism both in heating and cooling the building. They can facilitate heat transfer into the building during a winter day. The use of vents through the glazing while upper vents through the mass wall are closed reduces heat gain by the mass wall. A roof overhang can also reduce heat gain during the warm months when the sun is high by shading the thermal storage wall. And, as will be shown, there are many other ways to adapt thermal storage walls to increase or decrease solar gain and reduce heat loss. The results obtained for the area of Bechar seem interesting, which makes it possible to do much energy saving.
Q _ m
Air flow rate [l/s.m] Mass flow rate [kg/s.m]
Greek letters Dimension of the opening of circulation of air [m] Coefficient of cubic dilatation [1/K] Kinematics viscosity of the fluid [m2/s] Density of the fluid [kg/m3] Thermal conductivity [W/m K] Solar flow [W/m2]
d b n r l 4
References Nomenclature
a b c e H L P Cp To Tob Toh Tin ui q
h
Thermal diffusivity [m2/s] Outdistance depth of walked on solar [m] Height of the Trombe wall [m] Thickness of the Trombe wall [m] Height of the local one [m] Length of the local one [m] Pressure [Pa] Specific heat [J/kg K] Temperature of reference [K] Temperature on the level of low opening [K] Temperature on the level of high opening [K] Temperature on the level of the zone of occupation [K] Air velocity according to x, y [m/s] Wall solar heat gain [W/m2] System efficiency (%)
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