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Experimental heat flux analysis of a solar wall design in Tunisia
Author’s Accepted Manuscript Experimental heat flux analysis of a solar wall design in Tunisia Narjes Dimassi, Leila Dehmani
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PII: DOI: Reference:
S2352-7102(16)30211-X http://dx.doi.org/10.1016/j.jobe.2016.10.001 JOBE180
To appear in: Journal of Building Engineering Received date: 23 June 2016 Revised date: 28 September 2016 Accepted date: 2 October 2016 Cite this article as: Narjes Dimassi and Leila Dehmani, Experimental heat flux analysis of a solar wall design in Tunisia, Journal of Building Engineering, http://dx.doi.org/10.1016/j.jobe.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 galley proof before it is published in its final citable 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.
Experimental heat flux analysis of a solar wall design in Tunisia
Narjes Dimassi1*, Leila Dehmani1
1
Laboratory of Wind Energy Management and Waste Energy Recovery (LMEEVED), Research and Technology Center of Energy, B.P. 95 Hammam-Lif, 2050, Tunisia
*
Author to whom correspondence should be addressed: [email protected]
Abstract The present paper contributes to the strengthening of efforts to encourage the integration of a solar passive system inside buildings, which can provide further heating in winter. This study is based on experimental results to establish a heat analysis of a Trombe wall. For this purpose, experiments were conducted in Borj Cedria Tunisia on a test cell under real time circumstances to measure the different parameters influencing the Trombe wall operation. We carried out a detailed study leading to the estimation of heat exchanges for the essential Trombe wall features. Experimental results with predictions based on heat analysis, allow the evaluation of different coefficients of heat exchange in function of climatic data and geometrical dimensions of the wall. The results revealed that the radiation exchange is higher than the convective exchange in the air gap and inside the test room too. The
thermocirculation in the gap was also estimated by using four different correlations and compared to the thermal flux calculated directly with the air flow through the upper vent. It turned out that Fischenden-Saunders and Alamdari-Hammond correlations have correctly interpreted the case study.
Keys words Trombe wall, Solar wall, Solar heating, Heat transfer, Heat exchange coefficients.
NOMENCLATURE a
Thermal diffusivity (m2/s)
Cp
Specific heat (J/kg°C)
F
A parameter to be measured
g
Acceleration of gravity (m/s2)
gr
Grashof number
hc
Convection coefficient (W/m2K)
hr
Radiation coefficient (W/m2K)
H
Height (m)
I
Global solar radiation flux density (W/m2)
m
Air mass flow rate (kg/s)
Nu
Nusselt number
Pr
Prandtl number
Ra
Rayleigh number
S
Surface (m2)
T
Temperature (°C)
U
Uncertainty measurement
v
Fluid velocity (m/s)
x
Independent variable of equations
Greek letters a
Solar absorptivity
b
Thermal expansion coefficient (K-1)
e
emissivity
l
Thermal conductivity (W/m2°C)
m
Dynamic viscosity (kg/ms)
r
Density (kg/m3)
s
Stefan Boltzmann constant (5.67 ´ 10-8W/m2K4)
t
Transmissivity
u
Cinematic viscosity (m2/s)
f
Heat flux (W)
Subscripts amb
ambiance
c
convection
conv
convection
e
exterior
f
fluid
g
glazing
in
interior
lv
Lower vent
lam
laminar
r
radiation
s
solar
tur
turbulent
uv
Upper vent
w
Wall
1
INTRODUCTION
Nowadays, energy requirements of Tunisian buildings, for winter heating and summer cooling, have extremely increased. This has drawn the awareness of many architects and engineers toward renewable energy applications, with adopting suitable building design. In recent years, passive solar systems have enjoyed an increase in popularity, since they embody a diversity of strategies and technologies by using free solar energy. One of the most attractive technology of building heating is the Trombe wall. It is a south-facing wall blackened and covered on the exterior by a glazing situated at a small distance from the wall. The vents of the massive wall at high and low positions allow connection of air in the gap with the room. The wall absorbs solar radiation and transmits a part of it into the dwelling by both conduction and natural convection through the vents.
Trombe wall has been the subject of numerous experiments and studies all over the world and it has received considerable attention for space heating as an effective mean of solar energy exploitation. Various investigations of this system concerned basic science, which refers to the study of the fundamental heat transfer phenomena that affect Trombe wall efficiency. Many of these phenomena are not unique to the Trombe wall, such as, conduction through a wall, heat loss and transmitted solar radiation through a glazing, longwave radiation exchange ([1], [2], [3]). The nature of convection in the air gap has also been well studied by researchers and it is referred as natural convection in a cavity (also enclosure or channel) of high aspect ratio ([4], [5], [6], [7]). Several researches reported on Trombe wall, show to be an effective technology for reducing heating energy and improving the interior comfort for many climates. The evaluation of this system is generally based on computer simulation programs such as Energy plus and Trnsys, which allow the variation of many physical parameters in order to optimize its design [8], [9], [10], [11], [12]. Other researchers have focused their work on enhancing the efficiency of this system with many aspects such as glazing design ([13], [14], [15]) management [16], [17], [18], operation... To check the Trombe wall working, scientists have attempted to devise performancemeasuring models using real buildings or test cells under outdoor conditions [19] [20] [21].
In reality, heat exchanges in a Trombe wall are coupled phenomena of heat and mass transfer and the natural convection occurring in the air gap is complex and tricky. Not only that, but also, the operating system is very sensitive to the surrounding climate data, for example, the wall temperature and air velocity are strongly related to solar radiation, which has a very fluctuating aspect. Whilst the importance and the scientific value of earlier studies, these deductions have led many researchers to recommend the exploration and the strengthening of experimental studies under real weather conditions, in order to target the most influential parameters especially heat transfer coefficients to optimize the Trombe wall efficiency. In this context, we present, through an experimental study, a comprehensive energy study of a Trombe wall, where we quantified all heat flux for different wall components from the outside to the inside and heat transfer coefficients using many empirical correlations, in order to assess the system performance and to predict the convection patterns occurring in the air gap. 2 2.1
Theoretical study Study and characterization of thermal exchanges
In Trombe walls, the heat transfer and the fluid flow are closely linked phenomena. To analyze the heat transfer for different parts of the wall, it is suitable to look at a thermal network analogy drawn in Figure 1, which involves the different temperatures.
Figure. 1. Thermal network analogy of Trombe wall
Because of the low temperature range encountered, the physical properties of air are assumed to vary linearly with air temperature. We used the following empirical relationships, based on tabulated data from handbooks for air properties between 300– 350 K [22]: The dynamic viscosity is:
m f = éë1.846 + 0.00472 (Tf - 300)ùû ´10-5
(1)
r f = 1.1614 - 0.00353(Tf - 300)
(2)
l f = 0.0263 + 0.000074(Tf - 300)
(3)
The density is:
The thermal conductivity is:
The specific heat is:
Cp f = éë1.007 + 0.00004(T f - 300) ùû ´103
(4)
The volumetric coefficient of expansion is:
bf =
2.2
1 Tf
(5)
Heat flux analysis of Trombe wall components
2.2.1 Outer surface of the glazing Solar radiation, reaching the outer surface of the glazing, is reflected, transmitted and absorbed in varied proportions, depending on the glazing nature. For this part of the wall, heat exchanges occur in two ways: the convective exchange between the outer glazing surface and the external environment and the radiation exchange between the glazing and the outside; the flux expression is given by: [23] Fout = hce (Tam - Tg ) + hre (Tsky - Tg ) + Fsg
(6)
With The sky temperature is given by Swinbank [24] as: 1.5 Tsky = 0.0552 Tamb
(7)
hce : the convection coefficient with the outside is given by [25]: hce = 5.7 + 3.8Vwind
(8)
The radiation coefficient on the outside surface of the glazing is given by [26]: 2 hre = se g (Tsky + Tg2 )(Tsky + Tg )
(9)
The solar flux absorbed by the glazing is given by [26]: F sg = a g I
(10)
2.2.2 Inner surface of glazing The inner glazing surface is directly in contact with the air gap of the Trombe wall, so the occurred thermal exchanges are essentially a convective exchange between the glazing and the air gap and a radiative exchange between the massive wall and the glazing. The thermal flux on the inner glazing surface is written as follows [23]: F g = hg , f (Tg - Tf ) + hrw1g (Tw1 - Tg )
where hg,f and hrwlg are the radiation coefficients between the outside surface of the massive wall and the glazing; they are given by the following equations:
(11)
hg , f =
Nul f H
hrw1g = s Fegw (Tg2 + Tw21 )(Tg + Tw1 )
Fegw = (
1
eg
+
1 1
ew
(12)
(13)
is the emission factor between the glazing and the outside surface of - 1)
the wall. 2.2.3 Outer surface of the massive wall The heat flux at the outer surface of the massive wall is given by [23]: Fswall = hw1, f (Tw1 - Tf ) + hrw1g (Tw1 - Tg ) + Fsw
(14)
Where Φsw is the solar heat flux absorbed by the massive wall: F sw = t ga w I
(15)
hw1, f is the convective heat transfer coefficient between the outer surface of the wall and
the air in the gap, and it is determined by [26]:
hw1, f =
Pr =
n n = m a= l a
r
r Cp
l NuH H
(16)
RaH =
g b (Tw1 - T f ) H 3 an
RaH = Pr GrH
GrH =
g b (Tw1 - T f ) H 3
n2
(17)
(18)
(19)
2.2.4 Convection in the air gap The heat is transferred into the test room from the upper vent and through the air gap. It can be defined by using the air flow rate or by thermal heat exchanges. By thermal heat exchanges The energy transferred to the inside through the air gap can be written [23]: Fconv = hw1, f (Tw1 - Tf ) + hg , f (Tg - Tf )
hw1, f = hg , f =
Nul f H
The Nusselt number is defined according to the correlations encountered in the literature and proposed by various authors [27]. They are mainly based on a number of Graschoff ranging between 108 and 1012 to evaluate the thermal resistance of the air in the gap. The Graschoff number is given by:
(20)
(21)
GrH =
b f g r 2f H 3 (Tuv - Tlv ) mf 2
(22)
Sometimes, the correlations involve the Rayleigh number: ·
Alamdari and Hammond Correlation [28] Nu = [ (0.55Gr1/4 )6 + (0.095Gr1/3 )6 ]1/6
·
·
·
(23)
Fischenden-Saunders Correlation [29] Nu = 0.107 Gr1/3
(24)
Nu = 0.13 Ra H1/3
(25)
Mc Adams Correlation [25]
Curchill and Chu Correlation [30]
If RaH > 109 the flow is turbulent and Nu is given by: é ù 1/6 0.387 ( RaH ) ê ú Nu = ê0.825 + 9/16 8/ 27 ú é1 + 0.492 / Pr ) ù ú êë ë ( û û
2
(26)
If RaH < 109 the flow is laminar and Nu is given by: 0.67 ( RaH )
1/4
Nu = 0.68 +
é1 + ( 0.492 / Pr )9/16 ù ë û
4/9
(27)
By air flow rate The air circulates via the wall vents under the effect of gravitational forces. It is assumed that the air enters the gap at Tlv temperature and exits at the temperature Tuv [31]. The average temperature of the air in the gap is given by:
Tf =
Tuv + Tlv 2
(28)
The air flow rate is given by ·
m = r f vS
(29)
Where :v is the velocity of the air at the upper vent in m / s S is the section of the upper vent in m² ρ is the density of air which varies with the temperature in Kg / m3 And the energy carried on the inside of the test room via the upper vent is given by [32]: ·
F conv =
mCP f (Tuv - Tlv ) Sw
(30)
2.2.5 Inner surface of the wall Within the test room, convective and radiative exchanges occur between the inner wall surface and the interior. The flux is given by [26]: Fin = hin (Tw2 - Tin )
(31)
hin = hr in + hc in
(32)
where: hrin is the radiation coefficient on the inside surface of the wall: hr in = se w (Tw22 + Tin2 )(Tw2 + Tin )
(33)
hcin is the convection coefficient of the inside surface of the wall and H is the wall height:
hc in =
Nul f in H
(34)
To quantify this coefficient, we use the correlations of vertical plates in order to identify the Nusselt number [33]: · If 108 < GrH < 1012
NuH = 0.117 Ra1/3 H
(35)
· If 104 < GrH < 108
NuH = 0.516 Ra1/4 H
(36)
The literature provides another correlation permitting the direct evaluation of the convective heat transfer coefficient inside the building under normal atmospheric conditions. It corresponds to an average of the laminar exchange coefficient hlam and the turbulent exchange coefficient htur. This expression is given by Mc Adams [25]:
hc in =
hlam + htur 2
(37)
with: Tsin - Tin 1/4 ) H
(38)
htur = 1.13(Tsin - Tin )1/3
(39)
hlam = 1.22(
3 3.1
Experimental methodology Test cell description
A small test cell was designed to evaluate the thermal exchanges of different Trombe wall components. The experimentation was performed in the Research and Technology Center of Energy of Borj Cedria (CRTEn) in Tunisia, which exemplifies a typical Mediterranean climate. The test cell is a single room measuring 1.86 m×1.52 m×1.52 m (Figure 2). It was made of wood whose thickness is 0.02 m and was insulated by a panel
of 0.04 m thick polystyrene. The storage wall is 0.10 m thick and is built up of solid concrete brick. Its south surface was painted black matt and an insulating panel was placed on the sides of the storage wall to reduce lateral heat losses. For convective heat transfer, two vents measuring 0.25 m/0.15 m were located at the upper and the lower positions of the wall. The air gap between the wall and the glazing is 0.12 m. The north façade of the test room has an entry with the dimensions of 0.50 m/0.20 m. Chromel alumel thermocouples were used to assess the temperature at different positions in the test cell. Wall surfaces temperatures were measured at different heights and at different horizontal positions. The uncertainty of the temperature measurements is estimated to be less than ±0.1°C.
A small meteorological station measures the total solar radiation incident on the wall and the wind speed with a KIPP-ZONEN CM-21 Pyranometer and an anemometer LITTOCLIME (13N-219-S34), respectively. The accuracies of the pyranometer and the anemometer are ±10 W/m2 and ±0.5 m/s, respectively. The temperature and the humidity transmitters (HD 9008 TR) measure the ambient temperature and the relative humidity. Their precisions are ±0.15°C and ±2% HR, respectively. The air velocities at the vents were measured utilizing a hot-film anemometer (T.S.I model 8455 Air Velocity transducer) whose precision is ±0.02 m/s. To get a mean velocity and to avoid edge effects, the anemometer was located in the middle of each vent.
The recorded data was saved in the Agilent (HP34970A) data acquisition system, every 10 minutes, then; it was stored in the computer with a data-logger device. Figure. 2. External view of the test cell
3.2
Error and uncertainty analysis
Since this experimental heat flux analysis incorporates many measured parameters and equations, a measurement uncertainty analysis was established using the uncertainty propagation theory [34]. It is a derived statistical calculation designed to combine uncertainties from multiple variables to provide an accurate measurement. If we consider a parameter (F) depending on n measured variables (x1, x2, . . ., xn). The relative uncertainty of this parameter depends on the uncertainties of the measured variables xi, which are also depending on the measuring instruments uncertainties. The relative uncertainty of the parameter (F) is given by Equation (40)
U (F ) =± F
[U ( F )] x1 F
2
[U ( F )] x2 + F
2
+
[U ( F )] xn +
2
F
Where U(F) is the uncertainty measurement of the parameter F [U(F)]xi/F are the relative uncertainties of the parameters xi which are calculated by:
(40)
[U ( F )]xi ¶F Uxi = F ¶xi F Where: Uxi is the measurement uncertainty of the parameter xi. ∂F/∂xi is the coefficient of sensibility associated to xi. It informs about the influence of the variation of the variables xi on the parameter F. In this study, the most calculated factors depend on different quantities, which are wind speed, humidity, temperature, solar radiation, ambient temperature, velocity. These quantities were measured by calibrated instruments at accredited calibration laboratory. Their uncertainties combine both sensor and data acquisition system errors. The heat flux calculation for the Trombe wall involves the estimation of radiation coefficients whose relative uncertainties goes from 0.2 up to 0.217% for the radiation coefficient with exterior and it varies between 0.388 and 0.42% for both the radiation coefficient between the glazing and the exterior surface of the wall and the radiation coefficient inside the test room. The most influential parameter on the thermocirculation are convection coefficients whose relative measured uncertainty remained between 0.15 and 0.22% for the thermocirculation coefficient and for the convection coefficient on the wall surface and it goes from 0.037 to 0.045 % for the convection coefficient inside the test room.
(41)
Moreover, the used calculation method for the Trombe wall involves the estimation of different heat fluxes. For instance, the relative measurement uncertainties of thermal heat fluxes observed in the tests were between 2.4 and 4.8%.
4 4.1
Results and discussion Climatic data
To discuss results, it is preferable to extract a typical period of the recorded data. Figure 3 shows the variation of solar radiation and outside temperature for a sequence of 3 days. The incident solar radiation on the south face of the Trombe wall reaches a value exceeding 800 W/m² at noon, which tolerates a good efficiency of the Trombe wall. The outside temperature is characterized by lower values of temperatures, especially at nighttime (from 10 to 17 ° C). Figure 4 shows the variation of wind speed and humidity for this period. Relative humidity is high with an average of 60% because of the location of the test room near the sea. The wind speed values are important and often fluctuate around an average value of 2 m/s.
Figure. 3. Variation of solar radiation and outside temperature
Figure. 4. Variation of wind speed and humidity
4.2
Heat flux at the outer surface of the glazing
To quantify the heat flux at the outer surface of the glazing, we evaluated experimentally the thermal exchange coefficients by convection and radiation on the glazing shown in Figure 5 and Figure 6. The convection coefficient between the glazing and the outside (Figure 5) can exceed 25 W/m²K since it is directly proportional to the wind speed, while the radiation coefficient fluctuates around a value of 5 W/m²K (Figure 6). The experimental values indicate the strong effect of the convection exchange between the outside and the glazing, which contributes with a large degree in the cooling of the outer surface of the glazing by forced convection. A portion of the incident solar radiation is lost as an energy absorbed by the glazing as shown in Figure 7. The maximum is associated with a value of 80 W/m² for bright sunny periods. Once various thermal exchanges on the glazing are estimated, we can get the amount of energy lost to the outside through the glazing given by Figure 8, it is clear that the variation of heat losses and solar radiation are proportional.
Figure. 5. The coefficient of convection heat transfer between glazing and outdoor
Figure. 6. The coefficient of radiation heat transfer between glazing and outdoor
Figure. 7. Solar flux absorbed by the glazing
Figure. 8. Solar flux lost via glazing
4.3
Heat flux at the outer surface of the wall
For this part of the wall, we evaluated the radiative and convective exchanges. Figure 9 gives the variation of the experimental heat exchange coefficient of radiation on the outer wall surface. The evolution of this coefficient is periodic and its experimental value varies between 4.2 W/m²K and 5.6 W/m²K, which is in good agreement with the results found in the literature, including the work of Nayak et al [35] who cited a coefficient in the order of 4.9 W/m²K.
Figure. 9. Variation of experimental heat exchange coefficient by radiation of the outer wall surface The convective heat transfer occurs between the outer surface of the wall and the air gap, thus, to identify the corresponding coefficient hm1,f, it is necessary to quantify the
Nusselt number. The heat transfer in the air gap is seen as a natural convection between two parallel vertical plates (wall and glazing). The channel between the two plates may be considered as an extended channel and consequently, we can neglect the air circulation along a plate relative to the other. Therefore, the natural convection in the channel is supposed as a problem of a single vertical plate [26]. For a further interpretation and according to the experimental results, Figure 10 shows that the average outer surface temperature of the wall and the air gap temperature are constantly higher than the glazing temperature. Therefore, the natural convection on the wall side dominates the convection on the glazing side.
Figure. 10. Evolution of the temperature of the outer wall surface, glazing and air gap At the vertical air gap, the air moves upward and its density decreases. Moreover, a closed loop is produced and warm air enters the room from the upper vent while cold air leaks from the lower vent. In order to identify the adequate correlation, Figure 11 gives the experimental Rayleigh number RaH values, which are always greater than 109. For this reason, we have adopted two empirical correlations in the case of a vertical and isothermal plate to estimate the Nusselt number, which are:
·
The correlation of Mc Adams given by the expression (25)
·
The correlations of Churchill and Chu given by the expressions (26) and (27)
The experimental Nusselt number calculated with two different correlations leads to close values as shown in Figure 12. Once the Nusselt number is determined, we can deduce the coefficient of heat exchange by natural convection between the outer wall surface and the air gap given in Figure 13. Since the heat exchange by convection is induced by solar radiation absorbed by the wall, we remark that the evolution of hm1,f is periodic and repetitive. For each day, the maximum-recorded value is about 2.5 W/m²K. As a verification in the literature, Damien [36] quoted values varying between 2-3 W/m²K for a temperature difference of 5°C between the wall and the air, which approximates many our experimental results. Figure. 11. Evolution of experimental Rayleigh number
Figure. 12. Experimental Nusselt number evaluated by Adams and Churchil and Chu correlations
Figure. 13. Evolution of the heat exchange coefficient by natural convection between the outer wall surface and the air gap
4.4
Heat flux at the inner surface of the glazing
The heat exchanges occur by convection between the glazing and the air gap and by radiation to the outside wall surface and the heat flux is calculated using equation (11). We give on Figure 14 both the thermal flux evolution of the inner surface of the glazing and the outer wall surface. It is clear that the flux on the glazing side (Figure 14) is negligible compared to the thermal flux at the outer wall surface. Figure. 14. Flux density at the inner surface of the glazing and at the outer wall surface 4.5
Calculation of the energy gain by convection in the air gap
The objective here is to estimate the energy gain by convection in the test room using both: experimental heat transfer coefficients given by the expression (20) and experimental air flow given by the expression (30). The thermocirculation is produced when the average temperature in the gap is higher than the indoor temperature. Indeed, in the gap, the air temperature is lower than the temperature of the wall and the glazing. Therefore, the buoyancy forces produce a free movement in which the heated air moves upward, carrying the fluid in the steady area. Warm air enters the test room from the upper vent while cold air comes in from the lower vent. The Grashoff number is often used when assessing the performance of buoyancy driven convection. Consequently, we proceed by evaluating the Grashoff number (Figure 15). During the studied period, it is observable from the curve that
experimental Grashoff values are higher than 108 [27] indicating the turbulent aspect of fluid flow. As a result, many correlations proposed by different authors lead to the estimation of the Nusselt number for a vertical plate and for a number of Graschoff ranging between 108 and 1012 [27]. • Correlation of Alamdari-Hammond and given by the expression (23) • Correlation of Fischenden-Saunders and given by the expression (24) • Correlation of Mc Adams and given by the expression (25) • Correlations of Churchill and Chu and given by the expressions (26) and (27)
We clustered on the same graph (Figure 16) the variation of the Nusselt number for the four previous correlations. Figure 16 shows a good concordance between different results and the Nusselt number values are quite close. Nusselt numbers increased slightly as the mass transfer gaps in the Trombe wall were increased. Once the Nusselt number is identified, we can deduce the thermocirculation coefficient given by four correlations (Figure 17). The comparison of the obtained values shows that the Churchill and Chu correlations and Adams correlations give very similar values of heat transfer coefficient. While, we observe a 20% difference between these correlations and those of Fischenden-Saunders and Alamdari and Hammond.
Figure. 15. Evolution of experimental Grashoff number
Figure. 16. Nusselt number with four different correlations
Figure. 17. Evolution of experimental coefficient of thermocirculation The flow in the air gap occurs naturally by the thermosiphon effect and depends on the air flow rate through the vents. As the air moves upward in the gap, the fluid is expanded and its density decreases. Free circulation occurs when a volumetric force resulting from the gravitational field acts upon the air with density slope. The immediate effect is the development of a buoyancy force, which induces free circulation. This buoyancy is caused by the simultaneous existence of air density difference and the volumetric force proportionate to fluid density. The flux entering the room through the upper vent contributes to the test room heating by thermocirculation. The estimation of this flux requires the flow rate in the air gap, temperatures at the two vents and the recordings of air velocity profiles. From the expression (30), the flux exchanged by convection in the air gap was evaluated with experimental measurements (Figure 18).
Since the convective heat transfer coefficient was calculated by four different correlations, the selection of the appropriate correlation involves a comparison between the convective flux calculated from the flow rate and the calculated flux by the thermal convection coefficients in the air gap. The final calculation proves that the correlations of Alamdari and Hammond or Fischenden-Saunders approximate our case study (Figure 18). Indeed, the difference between the calculated fluxes by both methods is 24%, confirming the choice of the adopted correlations.
Figure. 18. Thermal flux reaching test room via thermocirculation 4.6
Heat flow within the test room
For the heat exchange between the inner surface of the Trombe wall and the room inside, it is essential to estimate the convective and radiative heat transfer coefficients. The convective heat transfer coefficient between the inner surface of the Trombe wall and the room inside hcint, was determined simultaneously by the correlations proposed by ASHRAE [33] and given by equations (35) and (36), as well as by using the Adams formula [25] given by equation (37). The comparison of results (Figure 19) evidences a good agreement between correlations with a maximum deviation of 15%. The values of the radiative heat transfer coefficient between the inner surface of the Trombe wall and inside the room hrint, vary between 4.4 and 5.8 W/m²K as shown in Figure 20. It is clear
that the radiative exchange is greater than the convective exchange discussed previously. Eventually, the heat flux exchanged between the inner wall surface and inside of the room has been evaluated by the expression (31) (Figure 21). This flux represents the energy reaching the interior of the test cell, when the solar radiation is maximal the energy reaches its maximum with a value of 78 W/m². The temperature profile inside the experimental test cell is also depicted in Figure 21. It reveals that the indoor temperature was recorded lowest in the early morning hours from 2:00 AM to 7:00 AM, until the break of daylight when the heating effect through the Trombe wall starts. Indeed, when the incident solar radiation is absorbed by the black wall, the radiation and the natural convection contribute gradually to the increase of indoor temperature, which reaches a peak of 27.06°C at 14:23 on 11 January. The heat is also released inside the test room after a lag time between heat absorption and emission. This characteristic configures specifically the system heat storage and it depends on the wall size and structure.
Figure. 19. Indoor convective exchange coefficient
Figure. 20. Indoor radiative exchange coefficient
Figure. 21. Evolution of flux density and temperature in the test room
5
Conclusion
A comprehensive energy study and an estimation of the Trombe wall heat exchanges were performed on its different components. This study shows the interest of this passive device under real time circumstances. A prediction of the important parameters influencing the complex convection pattern occurring in the air gap is accomplished based on heat analysis. A particular attention is paid to the variation of Grashoff and Nusselt numbers against time. Adequate data correlation for the experimental results has been used to assess the different coefficients of convective heat exchange in function of temperature and the geometrical dimensions of the wall. The results show that the radiation exchange dominates the convective exchange in the air gap and inside the test room too. The thermocirculation in the gap was also estimated using four different correlations. The comparison between the thermal fluxes calculated with thermal exchange coefficients and directly calculated with the air flow through the upper vent leads to the adoption of Fischenden-Saunders and Alamdari-Hammond correlations which represent correctly the case study. This study allowed us to furnish a further understanding of the Trombe wall performance to quantify the convective and radiative exchanges for different elements
of the wall and to evaluate the energy transferred to the test room. It helps, as a contribution, to determinate suitable circumstances of the Trombe wall installation in a larger scale construction under the appropriate climate for the best exploitation. Consequently, we can guarantee a heating autonomy at a very low cost and provide a suitable opportunity for conserving a significant amount of energy.
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[27] L. Zalewski, M. Chantant, S. Lassue, B. Duthoit, Experimental thermal study of a solar wall of composite type, Energy Build. 25 (1) (1997) 7-18. [28] F. Alamdari, G. Hammond, Improved data correlations for buoyancy-driven convection in rooms, Build. Serv. Eng. Res. Technol. 4 (3) (1983) 106-112. [29] S.Ø. Jensen, The PASSYS project phase 1, Subgroup model validation and development, Final report 1986–1989, EUR 13034 EN, Commission of the European Communities, Directorate General XII for Science, Research and Development, Brussels, Belgium, 1990 [30] S.W. Churchill, H.H. Chu, Correlation Equations for Laminar and Turbulent Free Convection from a Vertical Plate, Int. J. Heat Mass Transf. 18 (11) (1975) 1323-1329. [31] N.K. Bansal, R.C. Gaur, Application of U and g values for sizing passive heating concepts, Sol. Energy 57 (5) (1996) 361-373. [32] J.A. Duffie, W.A. Beckman, Solar Engineering of thermal processes, second edition, Wiley-Inter science Publication, New York, 1991. [33] ASHRAE Handbook, Fundamentals, SI Edition, American Society of Heating, Refrigerating and Air Conditioning Engineers, Atlanta, 2001. [34]
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Highlights · · · ·
An experimental thermal analysis of a Trombe Wall was established. Heat analysis allows the evaluation of heat exchange coefficients and fluxes. The variation of Grashoff and Nusselt numbers against time was discussed. Adequate correlation allows the prediction of thermocirculation in the air gap.
Figure 1: Thermal network analogy of Trombe wall
Figure 2: External view of the test cell
Figure 3: Variation of solar radiation and outside temperature
Figure 4: Variation of wind speed and humidity
Figure 5: The coefficient of convection heat transfer between gl
Figure 6: The coefficient of radiation heat transfer between gla
Figure 7: Solar flux absorbed by the glazing
Figure 8: Solar flux lost via glazing
Figure 9: Variation of experimental heat exchange coefficient by
Figure 10: Evolution of the temperature of the outer wall surfac
Figure 11: Evolution of experimental Rayleigh number
Figure 12: Experimental Nusselt number evaluated by Adams and Ch
Figure 13: Evolution of the heat exchange coefficient by natural
Figure 14: Flux density at the inner surface of the glazing and
Figure 15: Evolution of experimental Grashoff number
Figure 16: Nusselt number with four different correlations
Figure 17: Evolution of experimental coefficient of thermocircul
Figure 18: Thermal flux reaching test room via thermocirculation
Figure 19: Indoor convective exchange coefficient
Figure 20: Indoor radiative exchange coefficient
Figure 21: Evolution of flux density and temperature in the test
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PII: DOI: Reference:
S2352-7102(16)30211-X http://dx.doi.org/10.1016/j.jobe.2016.10.001 JOBE180
To appear in: Journal of Building Engineering Received date: 23 June 2016 Revised date: 28 September 2016 Accepted date: 2 October 2016 Cite this article as: Narjes Dimassi and Leila Dehmani, Experimental heat flux analysis of a solar wall design in Tunisia, Journal of Building Engineering, http://dx.doi.org/10.1016/j.jobe.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 galley proof before it is published in its final citable 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.
Experimental heat flux analysis of a solar wall design in Tunisia
Narjes Dimassi1*, Leila Dehmani1
1
Laboratory of Wind Energy Management and Waste Energy Recovery (LMEEVED), Research and Technology Center of Energy, B.P. 95 Hammam-Lif, 2050, Tunisia
*
Author to whom correspondence should be addressed: [email protected]
Abstract The present paper contributes to the strengthening of efforts to encourage the integration of a solar passive system inside buildings, which can provide further heating in winter. This study is based on experimental results to establish a heat analysis of a Trombe wall. For this purpose, experiments were conducted in Borj Cedria Tunisia on a test cell under real time circumstances to measure the different parameters influencing the Trombe wall operation. We carried out a detailed study leading to the estimation of heat exchanges for the essential Trombe wall features. Experimental results with predictions based on heat analysis, allow the evaluation of different coefficients of heat exchange in function of climatic data and geometrical dimensions of the wall. The results revealed that the radiation exchange is higher than the convective exchange in the air gap and inside the test room too. The
thermocirculation in the gap was also estimated by using four different correlations and compared to the thermal flux calculated directly with the air flow through the upper vent. It turned out that Fischenden-Saunders and Alamdari-Hammond correlations have correctly interpreted the case study.
Keys words Trombe wall, Solar wall, Solar heating, Heat transfer, Heat exchange coefficients.
NOMENCLATURE a
Thermal diffusivity (m2/s)
Cp
Specific heat (J/kg°C)
F
A parameter to be measured
g
Acceleration of gravity (m/s2)
gr
Grashof number
hc
Convection coefficient (W/m2K)
hr
Radiation coefficient (W/m2K)
H
Height (m)
I
Global solar radiation flux density (W/m2)
m
Air mass flow rate (kg/s)
Nu
Nusselt number
Pr
Prandtl number
Ra
Rayleigh number
S
Surface (m2)
T
Temperature (°C)
U
Uncertainty measurement
v
Fluid velocity (m/s)
x
Independent variable of equations
Greek letters a
Solar absorptivity
b
Thermal expansion coefficient (K-1)
e
emissivity
l
Thermal conductivity (W/m2°C)
m
Dynamic viscosity (kg/ms)
r
Density (kg/m3)
s
Stefan Boltzmann constant (5.67 ´ 10-8W/m2K4)
t
Transmissivity
u
Cinematic viscosity (m2/s)
f
Heat flux (W)
Subscripts amb
ambiance
c
convection
conv
convection
e
exterior
f
fluid
g
glazing
in
interior
lv
Lower vent
lam
laminar
r
radiation
s
solar
tur
turbulent
uv
Upper vent
w
Wall
1
INTRODUCTION
Nowadays, energy requirements of Tunisian buildings, for winter heating and summer cooling, have extremely increased. This has drawn the awareness of many architects and engineers toward renewable energy applications, with adopting suitable building design. In recent years, passive solar systems have enjoyed an increase in popularity, since they embody a diversity of strategies and technologies by using free solar energy. One of the most attractive technology of building heating is the Trombe wall. It is a south-facing wall blackened and covered on the exterior by a glazing situated at a small distance from the wall. The vents of the massive wall at high and low positions allow connection of air in the gap with the room. The wall absorbs solar radiation and transmits a part of it into the dwelling by both conduction and natural convection through the vents.
Trombe wall has been the subject of numerous experiments and studies all over the world and it has received considerable attention for space heating as an effective mean of solar energy exploitation. Various investigations of this system concerned basic science, which refers to the study of the fundamental heat transfer phenomena that affect Trombe wall efficiency. Many of these phenomena are not unique to the Trombe wall, such as, conduction through a wall, heat loss and transmitted solar radiation through a glazing, longwave radiation exchange ([1], [2], [3]). The nature of convection in the air gap has also been well studied by researchers and it is referred as natural convection in a cavity (also enclosure or channel) of high aspect ratio ([4], [5], [6], [7]). Several researches reported on Trombe wall, show to be an effective technology for reducing heating energy and improving the interior comfort for many climates. The evaluation of this system is generally based on computer simulation programs such as Energy plus and Trnsys, which allow the variation of many physical parameters in order to optimize its design [8], [9], [10], [11], [12]. Other researchers have focused their work on enhancing the efficiency of this system with many aspects such as glazing design ([13], [14], [15]) management [16], [17], [18], operation... To check the Trombe wall working, scientists have attempted to devise performancemeasuring models using real buildings or test cells under outdoor conditions [19] [20] [21].
In reality, heat exchanges in a Trombe wall are coupled phenomena of heat and mass transfer and the natural convection occurring in the air gap is complex and tricky. Not only that, but also, the operating system is very sensitive to the surrounding climate data, for example, the wall temperature and air velocity are strongly related to solar radiation, which has a very fluctuating aspect. Whilst the importance and the scientific value of earlier studies, these deductions have led many researchers to recommend the exploration and the strengthening of experimental studies under real weather conditions, in order to target the most influential parameters especially heat transfer coefficients to optimize the Trombe wall efficiency. In this context, we present, through an experimental study, a comprehensive energy study of a Trombe wall, where we quantified all heat flux for different wall components from the outside to the inside and heat transfer coefficients using many empirical correlations, in order to assess the system performance and to predict the convection patterns occurring in the air gap. 2 2.1
Theoretical study Study and characterization of thermal exchanges
In Trombe walls, the heat transfer and the fluid flow are closely linked phenomena. To analyze the heat transfer for different parts of the wall, it is suitable to look at a thermal network analogy drawn in Figure 1, which involves the different temperatures.
Figure. 1. Thermal network analogy of Trombe wall
Because of the low temperature range encountered, the physical properties of air are assumed to vary linearly with air temperature. We used the following empirical relationships, based on tabulated data from handbooks for air properties between 300– 350 K [22]: The dynamic viscosity is:
m f = éë1.846 + 0.00472 (Tf - 300)ùû ´10-5
(1)
r f = 1.1614 - 0.00353(Tf - 300)
(2)
l f = 0.0263 + 0.000074(Tf - 300)
(3)
The density is:
The thermal conductivity is:
The specific heat is:
Cp f = éë1.007 + 0.00004(T f - 300) ùû ´103
(4)
The volumetric coefficient of expansion is:
bf =
2.2
1 Tf
(5)
Heat flux analysis of Trombe wall components
2.2.1 Outer surface of the glazing Solar radiation, reaching the outer surface of the glazing, is reflected, transmitted and absorbed in varied proportions, depending on the glazing nature. For this part of the wall, heat exchanges occur in two ways: the convective exchange between the outer glazing surface and the external environment and the radiation exchange between the glazing and the outside; the flux expression is given by: [23] Fout = hce (Tam - Tg ) + hre (Tsky - Tg ) + Fsg
(6)
With The sky temperature is given by Swinbank [24] as: 1.5 Tsky = 0.0552 Tamb
(7)
hce : the convection coefficient with the outside is given by [25]: hce = 5.7 + 3.8Vwind
(8)
The radiation coefficient on the outside surface of the glazing is given by [26]: 2 hre = se g (Tsky + Tg2 )(Tsky + Tg )
(9)
The solar flux absorbed by the glazing is given by [26]: F sg = a g I
(10)
2.2.2 Inner surface of glazing The inner glazing surface is directly in contact with the air gap of the Trombe wall, so the occurred thermal exchanges are essentially a convective exchange between the glazing and the air gap and a radiative exchange between the massive wall and the glazing. The thermal flux on the inner glazing surface is written as follows [23]: F g = hg , f (Tg - Tf ) + hrw1g (Tw1 - Tg )
where hg,f and hrwlg are the radiation coefficients between the outside surface of the massive wall and the glazing; they are given by the following equations:
(11)
hg , f =
Nul f H
hrw1g = s Fegw (Tg2 + Tw21 )(Tg + Tw1 )
Fegw = (
1
eg
+
1 1
ew
(12)
(13)
is the emission factor between the glazing and the outside surface of - 1)
the wall. 2.2.3 Outer surface of the massive wall The heat flux at the outer surface of the massive wall is given by [23]: Fswall = hw1, f (Tw1 - Tf ) + hrw1g (Tw1 - Tg ) + Fsw
(14)
Where Φsw is the solar heat flux absorbed by the massive wall: F sw = t ga w I
(15)
hw1, f is the convective heat transfer coefficient between the outer surface of the wall and
the air in the gap, and it is determined by [26]:
hw1, f =
Pr =
n n = m a= l a
r
r Cp
l NuH H
(16)
RaH =
g b (Tw1 - T f ) H 3 an
RaH = Pr GrH
GrH =
g b (Tw1 - T f ) H 3
n2
(17)
(18)
(19)
2.2.4 Convection in the air gap The heat is transferred into the test room from the upper vent and through the air gap. It can be defined by using the air flow rate or by thermal heat exchanges. By thermal heat exchanges The energy transferred to the inside through the air gap can be written [23]: Fconv = hw1, f (Tw1 - Tf ) + hg , f (Tg - Tf )
hw1, f = hg , f =
Nul f H
The Nusselt number is defined according to the correlations encountered in the literature and proposed by various authors [27]. They are mainly based on a number of Graschoff ranging between 108 and 1012 to evaluate the thermal resistance of the air in the gap. The Graschoff number is given by:
(20)
(21)
GrH =
b f g r 2f H 3 (Tuv - Tlv ) mf 2
(22)
Sometimes, the correlations involve the Rayleigh number: ·
Alamdari and Hammond Correlation [28] Nu = [ (0.55Gr1/4 )6 + (0.095Gr1/3 )6 ]1/6
·
·
·
(23)
Fischenden-Saunders Correlation [29] Nu = 0.107 Gr1/3
(24)
Nu = 0.13 Ra H1/3
(25)
Mc Adams Correlation [25]
Curchill and Chu Correlation [30]
If RaH > 109 the flow is turbulent and Nu is given by: é ù 1/6 0.387 ( RaH ) ê ú Nu = ê0.825 + 9/16 8/ 27 ú é1 + 0.492 / Pr ) ù ú êë ë ( û û
2
(26)
If RaH < 109 the flow is laminar and Nu is given by: 0.67 ( RaH )
1/4
Nu = 0.68 +
é1 + ( 0.492 / Pr )9/16 ù ë û
4/9
(27)
By air flow rate The air circulates via the wall vents under the effect of gravitational forces. It is assumed that the air enters the gap at Tlv temperature and exits at the temperature Tuv [31]. The average temperature of the air in the gap is given by:
Tf =
Tuv + Tlv 2
(28)
The air flow rate is given by ·
m = r f vS
(29)
Where :v is the velocity of the air at the upper vent in m / s S is the section of the upper vent in m² ρ is the density of air which varies with the temperature in Kg / m3 And the energy carried on the inside of the test room via the upper vent is given by [32]: ·
F conv =
mCP f (Tuv - Tlv ) Sw
(30)
2.2.5 Inner surface of the wall Within the test room, convective and radiative exchanges occur between the inner wall surface and the interior. The flux is given by [26]: Fin = hin (Tw2 - Tin )
(31)
hin = hr in + hc in
(32)
where: hrin is the radiation coefficient on the inside surface of the wall: hr in = se w (Tw22 + Tin2 )(Tw2 + Tin )
(33)
hcin is the convection coefficient of the inside surface of the wall and H is the wall height:
hc in =
Nul f in H
(34)
To quantify this coefficient, we use the correlations of vertical plates in order to identify the Nusselt number [33]: · If 108 < GrH < 1012
NuH = 0.117 Ra1/3 H
(35)
· If 104 < GrH < 108
NuH = 0.516 Ra1/4 H
(36)
The literature provides another correlation permitting the direct evaluation of the convective heat transfer coefficient inside the building under normal atmospheric conditions. It corresponds to an average of the laminar exchange coefficient hlam and the turbulent exchange coefficient htur. This expression is given by Mc Adams [25]:
hc in =
hlam + htur 2
(37)
with: Tsin - Tin 1/4 ) H
(38)
htur = 1.13(Tsin - Tin )1/3
(39)
hlam = 1.22(
3 3.1
Experimental methodology Test cell description
A small test cell was designed to evaluate the thermal exchanges of different Trombe wall components. The experimentation was performed in the Research and Technology Center of Energy of Borj Cedria (CRTEn) in Tunisia, which exemplifies a typical Mediterranean climate. The test cell is a single room measuring 1.86 m×1.52 m×1.52 m (Figure 2). It was made of wood whose thickness is 0.02 m and was insulated by a panel
of 0.04 m thick polystyrene. The storage wall is 0.10 m thick and is built up of solid concrete brick. Its south surface was painted black matt and an insulating panel was placed on the sides of the storage wall to reduce lateral heat losses. For convective heat transfer, two vents measuring 0.25 m/0.15 m were located at the upper and the lower positions of the wall. The air gap between the wall and the glazing is 0.12 m. The north façade of the test room has an entry with the dimensions of 0.50 m/0.20 m. Chromel alumel thermocouples were used to assess the temperature at different positions in the test cell. Wall surfaces temperatures were measured at different heights and at different horizontal positions. The uncertainty of the temperature measurements is estimated to be less than ±0.1°C.
A small meteorological station measures the total solar radiation incident on the wall and the wind speed with a KIPP-ZONEN CM-21 Pyranometer and an anemometer LITTOCLIME (13N-219-S34), respectively. The accuracies of the pyranometer and the anemometer are ±10 W/m2 and ±0.5 m/s, respectively. The temperature and the humidity transmitters (HD 9008 TR) measure the ambient temperature and the relative humidity. Their precisions are ±0.15°C and ±2% HR, respectively. The air velocities at the vents were measured utilizing a hot-film anemometer (T.S.I model 8455 Air Velocity transducer) whose precision is ±0.02 m/s. To get a mean velocity and to avoid edge effects, the anemometer was located in the middle of each vent.
The recorded data was saved in the Agilent (HP34970A) data acquisition system, every 10 minutes, then; it was stored in the computer with a data-logger device. Figure. 2. External view of the test cell
3.2
Error and uncertainty analysis
Since this experimental heat flux analysis incorporates many measured parameters and equations, a measurement uncertainty analysis was established using the uncertainty propagation theory [34]. It is a derived statistical calculation designed to combine uncertainties from multiple variables to provide an accurate measurement. If we consider a parameter (F) depending on n measured variables (x1, x2, . . ., xn). The relative uncertainty of this parameter depends on the uncertainties of the measured variables xi, which are also depending on the measuring instruments uncertainties. The relative uncertainty of the parameter (F) is given by Equation (40)
U (F ) =± F
[U ( F )] x1 F
2
[U ( F )] x2 + F
2
+
[U ( F )] xn +
2
F
Where U(F) is the uncertainty measurement of the parameter F [U(F)]xi/F are the relative uncertainties of the parameters xi which are calculated by:
(40)
[U ( F )]xi ¶F Uxi = F ¶xi F Where: Uxi is the measurement uncertainty of the parameter xi. ∂F/∂xi is the coefficient of sensibility associated to xi. It informs about the influence of the variation of the variables xi on the parameter F. In this study, the most calculated factors depend on different quantities, which are wind speed, humidity, temperature, solar radiation, ambient temperature, velocity. These quantities were measured by calibrated instruments at accredited calibration laboratory. Their uncertainties combine both sensor and data acquisition system errors. The heat flux calculation for the Trombe wall involves the estimation of radiation coefficients whose relative uncertainties goes from 0.2 up to 0.217% for the radiation coefficient with exterior and it varies between 0.388 and 0.42% for both the radiation coefficient between the glazing and the exterior surface of the wall and the radiation coefficient inside the test room. The most influential parameter on the thermocirculation are convection coefficients whose relative measured uncertainty remained between 0.15 and 0.22% for the thermocirculation coefficient and for the convection coefficient on the wall surface and it goes from 0.037 to 0.045 % for the convection coefficient inside the test room.
(41)
Moreover, the used calculation method for the Trombe wall involves the estimation of different heat fluxes. For instance, the relative measurement uncertainties of thermal heat fluxes observed in the tests were between 2.4 and 4.8%.
4 4.1
Results and discussion Climatic data
To discuss results, it is preferable to extract a typical period of the recorded data. Figure 3 shows the variation of solar radiation and outside temperature for a sequence of 3 days. The incident solar radiation on the south face of the Trombe wall reaches a value exceeding 800 W/m² at noon, which tolerates a good efficiency of the Trombe wall. The outside temperature is characterized by lower values of temperatures, especially at nighttime (from 10 to 17 ° C). Figure 4 shows the variation of wind speed and humidity for this period. Relative humidity is high with an average of 60% because of the location of the test room near the sea. The wind speed values are important and often fluctuate around an average value of 2 m/s.
Figure. 3. Variation of solar radiation and outside temperature
Figure. 4. Variation of wind speed and humidity
4.2
Heat flux at the outer surface of the glazing
To quantify the heat flux at the outer surface of the glazing, we evaluated experimentally the thermal exchange coefficients by convection and radiation on the glazing shown in Figure 5 and Figure 6. The convection coefficient between the glazing and the outside (Figure 5) can exceed 25 W/m²K since it is directly proportional to the wind speed, while the radiation coefficient fluctuates around a value of 5 W/m²K (Figure 6). The experimental values indicate the strong effect of the convection exchange between the outside and the glazing, which contributes with a large degree in the cooling of the outer surface of the glazing by forced convection. A portion of the incident solar radiation is lost as an energy absorbed by the glazing as shown in Figure 7. The maximum is associated with a value of 80 W/m² for bright sunny periods. Once various thermal exchanges on the glazing are estimated, we can get the amount of energy lost to the outside through the glazing given by Figure 8, it is clear that the variation of heat losses and solar radiation are proportional.
Figure. 5. The coefficient of convection heat transfer between glazing and outdoor
Figure. 6. The coefficient of radiation heat transfer between glazing and outdoor
Figure. 7. Solar flux absorbed by the glazing
Figure. 8. Solar flux lost via glazing
4.3
Heat flux at the outer surface of the wall
For this part of the wall, we evaluated the radiative and convective exchanges. Figure 9 gives the variation of the experimental heat exchange coefficient of radiation on the outer wall surface. The evolution of this coefficient is periodic and its experimental value varies between 4.2 W/m²K and 5.6 W/m²K, which is in good agreement with the results found in the literature, including the work of Nayak et al [35] who cited a coefficient in the order of 4.9 W/m²K.
Figure. 9. Variation of experimental heat exchange coefficient by radiation of the outer wall surface The convective heat transfer occurs between the outer surface of the wall and the air gap, thus, to identify the corresponding coefficient hm1,f, it is necessary to quantify the
Nusselt number. The heat transfer in the air gap is seen as a natural convection between two parallel vertical plates (wall and glazing). The channel between the two plates may be considered as an extended channel and consequently, we can neglect the air circulation along a plate relative to the other. Therefore, the natural convection in the channel is supposed as a problem of a single vertical plate [26]. For a further interpretation and according to the experimental results, Figure 10 shows that the average outer surface temperature of the wall and the air gap temperature are constantly higher than the glazing temperature. Therefore, the natural convection on the wall side dominates the convection on the glazing side.
Figure. 10. Evolution of the temperature of the outer wall surface, glazing and air gap At the vertical air gap, the air moves upward and its density decreases. Moreover, a closed loop is produced and warm air enters the room from the upper vent while cold air leaks from the lower vent. In order to identify the adequate correlation, Figure 11 gives the experimental Rayleigh number RaH values, which are always greater than 109. For this reason, we have adopted two empirical correlations in the case of a vertical and isothermal plate to estimate the Nusselt number, which are:
·
The correlation of Mc Adams given by the expression (25)
·
The correlations of Churchill and Chu given by the expressions (26) and (27)
The experimental Nusselt number calculated with two different correlations leads to close values as shown in Figure 12. Once the Nusselt number is determined, we can deduce the coefficient of heat exchange by natural convection between the outer wall surface and the air gap given in Figure 13. Since the heat exchange by convection is induced by solar radiation absorbed by the wall, we remark that the evolution of hm1,f is periodic and repetitive. For each day, the maximum-recorded value is about 2.5 W/m²K. As a verification in the literature, Damien [36] quoted values varying between 2-3 W/m²K for a temperature difference of 5°C between the wall and the air, which approximates many our experimental results. Figure. 11. Evolution of experimental Rayleigh number
Figure. 12. Experimental Nusselt number evaluated by Adams and Churchil and Chu correlations
Figure. 13. Evolution of the heat exchange coefficient by natural convection between the outer wall surface and the air gap
4.4
Heat flux at the inner surface of the glazing
The heat exchanges occur by convection between the glazing and the air gap and by radiation to the outside wall surface and the heat flux is calculated using equation (11). We give on Figure 14 both the thermal flux evolution of the inner surface of the glazing and the outer wall surface. It is clear that the flux on the glazing side (Figure 14) is negligible compared to the thermal flux at the outer wall surface. Figure. 14. Flux density at the inner surface of the glazing and at the outer wall surface 4.5
Calculation of the energy gain by convection in the air gap
The objective here is to estimate the energy gain by convection in the test room using both: experimental heat transfer coefficients given by the expression (20) and experimental air flow given by the expression (30). The thermocirculation is produced when the average temperature in the gap is higher than the indoor temperature. Indeed, in the gap, the air temperature is lower than the temperature of the wall and the glazing. Therefore, the buoyancy forces produce a free movement in which the heated air moves upward, carrying the fluid in the steady area. Warm air enters the test room from the upper vent while cold air comes in from the lower vent. The Grashoff number is often used when assessing the performance of buoyancy driven convection. Consequently, we proceed by evaluating the Grashoff number (Figure 15). During the studied period, it is observable from the curve that
experimental Grashoff values are higher than 108 [27] indicating the turbulent aspect of fluid flow. As a result, many correlations proposed by different authors lead to the estimation of the Nusselt number for a vertical plate and for a number of Graschoff ranging between 108 and 1012 [27]. • Correlation of Alamdari-Hammond and given by the expression (23) • Correlation of Fischenden-Saunders and given by the expression (24) • Correlation of Mc Adams and given by the expression (25) • Correlations of Churchill and Chu and given by the expressions (26) and (27)
We clustered on the same graph (Figure 16) the variation of the Nusselt number for the four previous correlations. Figure 16 shows a good concordance between different results and the Nusselt number values are quite close. Nusselt numbers increased slightly as the mass transfer gaps in the Trombe wall were increased. Once the Nusselt number is identified, we can deduce the thermocirculation coefficient given by four correlations (Figure 17). The comparison of the obtained values shows that the Churchill and Chu correlations and Adams correlations give very similar values of heat transfer coefficient. While, we observe a 20% difference between these correlations and those of Fischenden-Saunders and Alamdari and Hammond.
Figure. 15. Evolution of experimental Grashoff number
Figure. 16. Nusselt number with four different correlations
Figure. 17. Evolution of experimental coefficient of thermocirculation The flow in the air gap occurs naturally by the thermosiphon effect and depends on the air flow rate through the vents. As the air moves upward in the gap, the fluid is expanded and its density decreases. Free circulation occurs when a volumetric force resulting from the gravitational field acts upon the air with density slope. The immediate effect is the development of a buoyancy force, which induces free circulation. This buoyancy is caused by the simultaneous existence of air density difference and the volumetric force proportionate to fluid density. The flux entering the room through the upper vent contributes to the test room heating by thermocirculation. The estimation of this flux requires the flow rate in the air gap, temperatures at the two vents and the recordings of air velocity profiles. From the expression (30), the flux exchanged by convection in the air gap was evaluated with experimental measurements (Figure 18).
Since the convective heat transfer coefficient was calculated by four different correlations, the selection of the appropriate correlation involves a comparison between the convective flux calculated from the flow rate and the calculated flux by the thermal convection coefficients in the air gap. The final calculation proves that the correlations of Alamdari and Hammond or Fischenden-Saunders approximate our case study (Figure 18). Indeed, the difference between the calculated fluxes by both methods is 24%, confirming the choice of the adopted correlations.
Figure. 18. Thermal flux reaching test room via thermocirculation 4.6
Heat flow within the test room
For the heat exchange between the inner surface of the Trombe wall and the room inside, it is essential to estimate the convective and radiative heat transfer coefficients. The convective heat transfer coefficient between the inner surface of the Trombe wall and the room inside hcint, was determined simultaneously by the correlations proposed by ASHRAE [33] and given by equations (35) and (36), as well as by using the Adams formula [25] given by equation (37). The comparison of results (Figure 19) evidences a good agreement between correlations with a maximum deviation of 15%. The values of the radiative heat transfer coefficient between the inner surface of the Trombe wall and inside the room hrint, vary between 4.4 and 5.8 W/m²K as shown in Figure 20. It is clear
that the radiative exchange is greater than the convective exchange discussed previously. Eventually, the heat flux exchanged between the inner wall surface and inside of the room has been evaluated by the expression (31) (Figure 21). This flux represents the energy reaching the interior of the test cell, when the solar radiation is maximal the energy reaches its maximum with a value of 78 W/m². The temperature profile inside the experimental test cell is also depicted in Figure 21. It reveals that the indoor temperature was recorded lowest in the early morning hours from 2:00 AM to 7:00 AM, until the break of daylight when the heating effect through the Trombe wall starts. Indeed, when the incident solar radiation is absorbed by the black wall, the radiation and the natural convection contribute gradually to the increase of indoor temperature, which reaches a peak of 27.06°C at 14:23 on 11 January. The heat is also released inside the test room after a lag time between heat absorption and emission. This characteristic configures specifically the system heat storage and it depends on the wall size and structure.
Figure. 19. Indoor convective exchange coefficient
Figure. 20. Indoor radiative exchange coefficient
Figure. 21. Evolution of flux density and temperature in the test room
5
Conclusion
A comprehensive energy study and an estimation of the Trombe wall heat exchanges were performed on its different components. This study shows the interest of this passive device under real time circumstances. A prediction of the important parameters influencing the complex convection pattern occurring in the air gap is accomplished based on heat analysis. A particular attention is paid to the variation of Grashoff and Nusselt numbers against time. Adequate data correlation for the experimental results has been used to assess the different coefficients of convective heat exchange in function of temperature and the geometrical dimensions of the wall. The results show that the radiation exchange dominates the convective exchange in the air gap and inside the test room too. The thermocirculation in the gap was also estimated using four different correlations. The comparison between the thermal fluxes calculated with thermal exchange coefficients and directly calculated with the air flow through the upper vent leads to the adoption of Fischenden-Saunders and Alamdari-Hammond correlations which represent correctly the case study. This study allowed us to furnish a further understanding of the Trombe wall performance to quantify the convective and radiative exchanges for different elements
of the wall and to evaluate the energy transferred to the test room. It helps, as a contribution, to determinate suitable circumstances of the Trombe wall installation in a larger scale construction under the appropriate climate for the best exploitation. Consequently, we can guarantee a heating autonomy at a very low cost and provide a suitable opportunity for conserving a significant amount of energy.
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Highlights · · · ·
An experimental thermal analysis of a Trombe Wall was established. Heat analysis allows the evaluation of heat exchange coefficients and fluxes. The variation of Grashoff and Nusselt numbers against time was discussed. Adequate correlation allows the prediction of thermocirculation in the air gap.
Figure 1: Thermal network analogy of Trombe wall
Figure 2: External view of the test cell
Figure 3: Variation of solar radiation and outside temperature
Figure 4: Variation of wind speed and humidity
Figure 5: The coefficient of convection heat transfer between gl
Figure 6: The coefficient of radiation heat transfer between gla
Figure 7: Solar flux absorbed by the glazing
Figure 8: Solar flux lost via glazing
Figure 9: Variation of experimental heat exchange coefficient by
Figure 10: Evolution of the temperature of the outer wall surfac
Figure 11: Evolution of experimental Rayleigh number
Figure 12: Experimental Nusselt number evaluated by Adams and Ch
Figure 13: Evolution of the heat exchange coefficient by natural
Figure 14: Flux density at the inner surface of the glazing and
Figure 15: Evolution of experimental Grashoff number
Figure 16: Nusselt number with four different correlations
Figure 17: Evolution of experimental coefficient of thermocircul
Figure 18: Thermal flux reaching test room via thermocirculation
Figure 19: Indoor convective exchange coefficient
Figure 20: Indoor radiative exchange coefficient
Figure 21: Evolution of flux density and temperature in the test