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Comparison of heating and natural ventilation in a solar house induced by two roof solar collectors
Applied Thermal Engineering 25 (2005) 741–757 www.elsevier.com/locate/apthermeng
Comparison of heating and natural ventilation in a solar house induced by two roof solar collectors X.Q. Zhai, Y.J. Dai, R.Z. Wang
*
Institute of Refrigeration and Cryogenics, School of Mechanical Engineering, Shanghai Jiao Tong University, 1954 Huanshan Road, Shanghai 200030, China Received 18 March 2004; accepted 4 August 2004 Available online 22 September 2004
Abstract In this paper, two kinds of roof solar collectors (RSCs), namely, the single pass RSC, and the double pass RSC are analyzed and compared. The double pass roof solar collector, which is configured by integrating a double pass solar air collector with the building roof, can be operated more efficiently for space heating in winter, and for natural ventilation in other seasons. To evaluate the effects of two RSCs for both space heating and natural ventilation, a single traditional Chinese style house, on which the two RSCs will be mounted respectively, is developed. Through comparison, it is found that the instantaneous efficiency of solar heat collecting for the double pass RSC is higher than that of the single pass one by 10% on average, and natural ventilation air mass flow rate contributed by natural ventilation for the double pass RSC can be improved to a great extent for most cases, indicating that double pass RSC is superior to the single pass one from the points of view of both space heating and natural ventilation. The double pass RSC is therefore more potential for improving indoor thermal environment and energy saving of buildings. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Roof solar collector; Space heating; Natural ventilation
*
Corresponding author. Tel.: +86 21 6293 3838/3250; fax: +86 21 6293 3250. E-mail address: [email protected] (R.Z. Wang).
1359-4311/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.08.001
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Nomenclature A Cp D f g h hb hc hr I k L m M q Q r t T Vw Greek a b e m n s q g r Dp2
area (m2) specific heat of air (J kg1 K1) hydraulic diameter of the air channels (m) friction factor for the channel wall gravitational constant (m s2) global heat transfer coefficient (W m2 K1) global heat transfer coefficient from insulation plate to the attic (W m2 K1) convection heat transfer coefficient (W m2 K1) radiation heat transfer coefficient (W m2 K1) solar insolation rate (W m2) thermal conductivity (W m1 K1) length of RSC (m) air mass flow rate per unit area of RSC (kg m2 s1) air mass flow rate of RSC (kg h1) heat gains of air (W) heat transferred from the studied house to the ambient air (W) air change rate of the house (ACH) temperature (°C) temperature (K) wind velocity of the ambient air (m s1) symbols absorptivity inclination angle of RSC (degree) emissivity kinematic viscosity of air (m2 s1) local loss coefficient transmissivity density of air (kg m3) instantaneous efficiency of solar heat collecting Stefan–Boltzmann constant (W m2 K4) Thickness of insulation plate (m)
Subscripts 1 air channel 1 2 air channel 2 a ambient air attic attic of the studied house ceiling ceiling of the studied house d double pass RSC door door of the studied house
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757
e f floor g in o p1 p2 r s sky su w wi wind
743
exhaust air air in channels floor of the studied house glass cover inlet of RSC outlet of RSC absorber plate insulation plate indoor air single pass RSC sky supply air wall of the studied house window of the studied house wind
Dimensionless terms Gr Grashof number Nu Nusselts number Pr Prandtl number Ra Rayleigh number Re Reynolds number
1. Introduction A solar house promotes a comfortable indoor environment utilizing solar radiation, which is one of the most important sources of heat gain in a building and through its surroundings. It is also considered as an appropriate architecture for developing countries to provide heating, cooling and ventilation and improve indoor air quality depending on season [1,2]. The traditional Chinese house, mainly in rural areas, with a gable roof, can be well designed for integration with a solar air collector to form the roof solar collector (RSC). In summer, it is feasible to use the roof structure to induce natural air circulation, which is a part of the houseÕs thermal comfort. In winter, it can be employed for space heating by mechanical ventilation. In the past decade, RSC has attracted so much attention in various investigations. Most of them were concerned with natural ventilation. Khedari et al. [3] conducted an experimental study of a RSC made by using CPAC (Concrete Product and Aggregate Company Ltd.) Monier concrete tiles on the outer side and gypsum board on the inner side, and gave the optimum dimensions of the RSC. Khedari et al. [4] carried out another field measurements for the same kind of roof solar collector, and the experimental results showed that large air gap and equal size of openings would induce the highest rate of air flow rate. Jongjit et al. [5] proposed four different configurations of the roof solar collector to maximize natural ventilation through numerical modeling. Another kind of RSC is solar chimney which is similar to those mentioned above except
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that the outer side of the RSC is replaced by glazing. Bouchair et al. [6] and Bouchair [7] carried out some experiments to testify the applicability of solar chimneys to improve indoor thermal environment by promoting natural ventilation in summer. Chen et al. [8] investigated experimentally solar chimneys with a uniform heat flux on a single wall for different chimney gaps, heat flux input and different chimney inclinations. Results showed that a maximum airflow rate was achieved at an inclination angle around 45° for a 200 mm gap and 1.5 m high chimney. Afonso and Oliveira [9] compared the behavior of a solar chimney with a conventional one. Their results showed that there was a significant increase in ventilation rate with the solar chimney. Theoretical and experimental studies on natural ventilation of buildings were also carried out by Awbi and Gan [10], Gan [11], Li [12], Rodrigues et al. [13], and Ong [14]. In addition, Bansal [15] depicted a RSC used in high mountain regions in the North and North-Eastern Himalayas for space heating during the winter periods. The former investigations were almost all based on single pass solar air collectors integrated with building roofs. Moreover, the majority of them were concerned with natural ventilation. However, space heating in winter is as necessary as ventilation in summer for most regions of China. So the practical RSC in China should be made to implement passive cooling by natural ventilation as well as space heating by mechanical ventilation. According to Forson et al. [16], the principal types of solar air collectors are: the single pass with front duct, rear duct, double duct and double pass. It has been observed that the double pass solar air collector performs better than the single pass one. In this paper, a double pass solar air collector integrated with the building roof is designed and analyzed, and the effect of natural ventilation and space heating in a given house is studied. In order to identify the superiority of the double pass RSC to the single pass one, numerical analysis for the two RSCs regarding the air change rate, as well as the instantaneous efficiency of solar heat collecting are also made.
2. Description of structure and operating principle 2.1. Single pass RSC The configuration of single pass RSC, which is formed by integrating single pass solar air collector with southern roof of the building, is shown in Fig. 1. By switching damper 1 and 2, the RSC can be used to implement two operating modes, namely, space heating in winter and natural ventilation in other seasons. In winter, space heating is needed. The indoor air can be circulated between the inner house and the roof solar collector by closing damper 1 and opening damper 2. In this case, a fan is used to move the air. Natural ventilation, which is necessary for other seasons, can be effected by closing damper 2 and opening damper 1. Thus the indoor air can enter the air channel through tuyere 7 under the chimney effect caused by solar radiation. The air is then exhausted to the ambient. 2.2. Double pass RSC The double pass RSC studied in this paper, which is configured by integrating a double pass solar air collector with the southern roof of the building, is presented in Fig. 2. Some changes
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757 2(Open) 1(Close)
2(Close)
3 5
745
1(Open)
3
4 5
6
4
6
Attic 8
7
Attic
9
10
Ceiling
8
7
9
10
Ceiling
House
House
(a)
(b)
Fig. 1. Structure of single pass roof solar collector. (a) Space heating mode. (b) Natural ventilation mode. 1—damper, 2—damper, 3—glass cover, 4—absorber plate, 5—insulation plate, 6—-air channel, 7—tuyere, 8—air duct, 9—fan, 10—tuyere.
7(Open) 8 12 9
6
3(Open) 2(Close) 1(Close) 4 13 5 Attic 14 Ceiling
10
11
7(Close) 8 12 9
6
3(Close) 2(Open) 1(Open) 4 13 5 Attic 14
10
11
Ceiling
House
House
(a)
(b)
Fig. 2. Structure of double pass roof solar collector. (a) Space heating mode. (b) Natural ventilation mode. 1—damper, 2—damper, 3—damper, 4—glass cover, 5—absorber plate, 6—insulation plate, 7—damper, 8—tuyere, 9—tuyere, 10— fan, 11-tuyere, 12—air channel 1, 13—air channel 2, 14—air duct.
are made to rebuild the double pass solar air collector, as is shown in Fig. 2, four additional dampers 1, 2, 3, and 7 are installed to switch operating modes between space heating by warm air in winter and natural ventilation in other seasons. Space heating is operated with the following procedures: (1) Closing dampers 1 and 2, (2) opening dampers 3 and 7, (3) closing tuyere 8. In this way, the indoor air can enter air channel 1 through tuyere 9 and get heat from solar radiation. Then the air flows into air channel 2, where the absorber plate secondly heats the air; thereafter it flows into air duct, and is supplied into the house by the fan through tuyere 11. Natural ventilation mode is accomplished by closing dampers 3 and 7, and opening dampers 1 and 2. Thus the indoor air can enter both air channel 1 and 2 through tuyeres 8
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and 9, respectively. In the air channels, the air is heated by solar radiation and the natural ventilation can thus be produced in the end due to the chimney effect.
3. Formulation of the mathematical model The equations governing the performance of the RSCs are formulated by coupling the energy balance equations of components of the RSCs with those for the useful heat extracted in the channels, making the following assumptions: (1) The RSCs operate under steady state conditions. (2) Thermal inertia of RSCs components is negligible. (3) Operating temperatures of RSCs components and mean air temperatures in air channels are all assumed to be uniform. (4) Temperature of the air varies only in the direction of the flow. (5) Heat flow through the glass cover, absorber plate and the insulation plate is one-dimensional and in the direction vertical to air flow. (6) All air channels are assumed to be no leakage. (7) The temperature in the attic equals to that of the ambient air. (8) Neglecting thermal inertia of the enclosures and indoor waste heat, the heat transferred through the house enclosures to the ambient is assumed to be proportional to the temperature difference between indoor air and ambient air.
3.1. Single pass RSC For the single pass RSC, the energy balance equations for various components in both space heating and natural ventilation modes are given below: For glass cover ag I ¼ hga ðT g T a Þ þ hcgf ðT g T f Þ þ hrp1g ðT g T p1 Þ
ð1Þ
For air channel C p mf ðT o T r Þ ¼ hcgf ðT g T f Þ þ hcp1f ðT p1 T f Þ
ð2Þ
For absorber plate sg ap1 I ¼ hcp1f ðT p1 T f Þ þ hrp1g ðT p1 T g Þ þ hb ðT p1 T a Þ
ð3Þ
Air heat gains in space heating mode is defined as qs ¼ C p mf Ap1 ðT o T r Þ
ð4Þ
and then, instantaneous efficiency of solar heat collecting in either space heating or natural ventilation mode is given as gs ¼ C p mf ðT o T r Þ=I
ð5Þ
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3.2. Double pass RSC For the double pass RSC, attention should be paid to the difference of the mathematical model for different operating modes. From Fig. 2, it can be seen that, in space heating mode, the double pass RSC acts as a double pass solar air collector, however, in natural ventilation mode, it serves as a single pass double duct solar air collector. The energy balance equations for various components of the double pass RSC when it is used for space heating are expressed as For glass cover ag I ¼ hga ðT g T a Þ þ hcgf1 ðT g T f1 Þ þ hrp1g ðT g T p1 Þ
ð6Þ
For air channel 1 C p mf1 ðT 1o T r Þ ¼ hcgf1 ðT g T f1 Þ þ hcp1f1 ðT p1 T f1 Þ
ð7Þ
For absorber plate sg ap1 I ¼ hcp1f1 ðT p1 T f1 Þ þ hcp1f2 ðT p1 T f2 Þ þ hrp1p2 ðT p1 T p2 Þ þ hrp1g ðT p1 T g Þ
ð8Þ
For air channel 2 C p mf2 ðT 2o T 1o Þ ¼ hcp1f2 ðT p1 T f2 Þ þ hcp2f2 ðT p2 T f2 Þ
ð9Þ
For insulation plate hrp1p2 ðT p1 T p2 Þ ¼ hcp2f2 ðT p2 T f2 Þ þ hb ðT p2 T a Þ
ð10Þ
Air heat gains in space heating mode is given as qd ¼ C p mf2 Ap1 ðT 2o T r Þ
ð11Þ
and then, instantaneous efficiency of solar heat collecting in space heating mode is expressed as gd ¼ qd =ðIAp1 Þ
ð12Þ
For the double pass RSC under natural ventilation mode, the above equations can still be used except that Eq. (9) for air channel 2 should be modified as follows: C p mf2 ðT 2o T r Þ ¼ hcp1f2 ðT p1 T f2 Þ þ hcp2f2 ðT p2 T f2 Þ
ð13Þ
Meanwhile, instantaneous efficiency of solar heat collecting in natural ventilation mode is changed as gd ¼ ½C p mf1 ðT 1o T r Þ þ C p mf2 ðT 2o T r Þ=I
ð14Þ
3.3. Determination of mean air temperature For the RSCs under space heating mode, mean air temperatures in air channels are calculated using the method of Choudhury et al. [17] For air channel of single pass RSC T f ¼ ðT o þ T r Þ=2
ð15Þ
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For air channel 1 of double pass RSC T f1 ¼ ðT 1o þ T r Þ=2
ð16Þ
For air channel 2 of double pass RSC T f2 ¼ ðT 2o þ T 1o Þ=2
ð17Þ
In natural ventilation mode, however, mean air temperatures in each channel are calculated according to Hirunlabh et al. [21] T fi ¼ 0:75T io þ 0:25T r
ð18Þ
where the subscript, i, represents different air channels for double pass RSC. In addition, the above equation corresponds to single pass RSC when the subscript, i, is not included. 3.4. Modeling of air mass flow rate The space heating modes in winter for both RSCs are all accomplished by mechanical ventilation. For comparison, the space heating modes for both RSCs use the fans with the same specification. Therefore, air mass flow rate mf, mf1 and mf2 in the above equations are also the same in the simulation. Air mass flow rate in natural ventilation mode is mainly determined by two aspects, which are stack pressure built up in the air channels and the pressure losses at the inlet, outlet and along the RSC channels. The energy conservation equation can be expressed as qðAp1 mfi =qAin Þ2 qðAp1 mfi =qAo Þ2 L qðAp1 mfi =qAi Þ2 þ no þf ð19Þ D 2 2 2 where, the left hand of Eq. (19) stands for stack pressure, and the right side represents pressure losses, according to Chen et al. [8], nin = 1.5, no = 1.0, f = 0.056, respectively. The subscript, i, denotes different air channels for double pass RSC, but will vanish when the single pass RSC is considered. Moreover, it is assumed here that the open areas of the air channel at the inlet and outlet, the cross section area of the air channels, are equal to each other. Consequently, in terms of Eq. (19), natural ventilation air mass flow rate per unit RSC area in each air channel can be calculated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ain 2gL sin bðT io T r Þ ð20Þ mfi ¼ q Ap1 T r nin þ no þ f DL qgL sin bðT io T r Þ=T r ¼ nin
3.5. Estimation of heat transfer coefficients Global heat transfer coefficient between glass cover and the ambient is given as hga ¼ hcwind þ hrgsky
ð21Þ
Convection heat transfer coefficient from glazing due to wind is recommended by McAdams [18] hcwind ¼ 5:7 þ 3:8V w
ð22Þ
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757
749
Radiation heat transfer coefficient from glass cover to sky referred to the ambient air temperature may be obtained from hrgsky ¼ reg ðT g þ T sky ÞðT 2g þ T 2sky Þ
ðT g T sky Þ ðT g T a Þ
ð23Þ
Sky temperature is predicted using the formulation given by Swinbank [19] T sky ¼ 0:0552T 1:5 a
ð24Þ
The radiation heat transfer coefficient between glass cover and absorber plate may be predicted by hrp1g ¼
rðT 2p1 þ T 2g ÞðT p1 þ T g Þ 1 ep1
þ e1g 1
ð25Þ
The radiation heat transfer coefficient between absorber plate and insulation plate may be calculated by hrp1p2 ¼
rðT 2p1 þ T 2p2 ÞðT p1 þ T p2 Þ 1 ep1
þ e1p2 1
ð26Þ
Global heat transfer coefficient from insulation plate to the attic is written below hb ¼ 1=ð1=hcp2attic þ Dp2 =k p2 Þ
ð27Þ
In the analysis, the fully developed flow condition is assumed for calculating forced convection heat transfer coefficients between plates and air in space heating mode. According to Kays and Crawford [20], the following correlation can be adopted Nu ¼ 0:019Re0:8 Pr1:3
ð28Þ
It is realized that the above correlation is valid for fully developed turbulent flow between two flat plates, one of which is heated. However, this assumption may not alter the comparison results between two different RSCs. For the air channel of single pass RSC and the air channel 1 of double pass RSC, the average natural convection heat transfer coefficient between plates and air is calculated according to Hollands et al. [22] " # #þ þ " 1=3 1708ðsin 1:8bÞ1:6 1708 Ra cos b 1 þ 1 ð29Þ Nu ¼ 1 þ 1:44 1 Ra cos b 5830 Ra cos b where the meaning of the + exponent is that only positive values of the terms in the square brackets are to be used (i.e., use zero if the term is negative). It should be noted that the correlations given by Eq. (29) does not cover the range of tilt angles from 75° to 90°, however, it is recommended that the 75° correlation be used to represent the vertical case adequately. For the air channel 2 of double pass RSC, it is determined according to Arnold et al. [23] Nu ¼ 1 þ ½Nuð90 Þ 1 sin b where Nu(90°) approximates the 75° tilt value of Eq. (29).
ð30Þ
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X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757
Table 1 Detailed characters of the studied house Aceiling
Adoor
Afloor
Aw
Awi
hceiling
hdoor
hfloor
hw
hwi
20
2.0
20
49.75
2.25
1.24
4.65
0.47
2.08
5.82
3.6. Energy balance equation of the house For comparison, an identical house is chosen to install different RSCs respectively. The studied house integrated with two different RSCs is shown in Figs. 1 and 2. The dimensional sizes for this house are: width: 4 m, length: 5 m, height: 3 m. All walls are made of the same material, brick, with a thickness of 240 mm, except for a wooden window and a wooden door in the walls. The ceiling is made of gypsum planks, with a thickness of 30 mm. The floor is not insulated. Detailed characters of the studied house are listed in Table 1, in which the global heat transfer coefficients are suggested by Lu et al. [24]. Heat transferred through the house enclosures to the ambient, Q, is assumed to be proportional to the temperature difference between Tr and Ta. Here, Q is calculated by Q ¼ hw Aw ðT r T a Þ þ hwi Awi ðT r T a Þ þ hdoor Adoor ðT r T a Þ þ hceiling Aceiling ðT r T a Þ þ hfloor Afloor ðT r T a Þ
ð31Þ
In simulation, the house is considered to be in instantaneous thermal equilibrium, i.e., in space heating mode, air heat gains by RSCs are all used to counteract heat transferred from the house to the ambient, analogously, in natural ventilation mode, heat transferred from the ambient to the house is all exhausted by natural ventilation. 4. Results and discussion Based on the above detailed analysis of the mathematical model, a FORTRAN computer program was written and developed to estimate both space heating and natural ventilation effects. The physical properties of air are assumed to vary linearly with temperature. Some basic parameters for calculation are listed in Table 2. For certain operating conditions, the temperatures of glass cover, absorber plate, insulation plate, indoor air and air of each channel are initially guessed, and various heat transfer coefficients are estimated with these temperatures, and then the heat balance equations are solved to obtain new temperatures which are compared with old ones. The iteration process is continued with the most updated variables until all the temperature values converge. Hence, air heat gains and instantaneous efficiency of solar heat collecting for space heating mode can be determined, in addition, natural ventilation air mass flow rate and instantaneous efficiency of solar heat collecting can be calculated when the program is used for natural ventilation mode. Then, comparisons of space heating and natural ventilation effects between two RSCs are discussed as follows. 4.1. Space heating Four indices, namely, supply air temperature (air temperature at the exit of RSC), indoor air temperature, air heat gains and instantaneous efficiency of solar heat collecting are used to eval-
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751
Table 2 Some basic parameters for calculation hcp2attic
kp2
ag
ap1
eg
ep1
ep2
sg
Dp2
10
0.0275
0.06
0.95
0.90
0.94
0.94
0.84
0.05
uate space heating effect of two RSCs. For single pass RSC, supply air temperature is To in terms of Eq. (2), while it is represented by T2o according to Eq. (9) for double pass one. In calculation, Some constant parameters used in the analysis are listed below: the width of RSCs is 4.0 m, the gap of air channels is 0.2 m, the inclination angle is 45°, the ambient air temperature is 0°C and the ambient air velocity is taken to be 1.5 m s1. The impact of solar insolation rate on the space heating effect for the two RSCs is shown in Fig. 3. Here, the length of the RSCs is 3 m, and the air mass flow rate is 2000 kg h1. It can be found from Fig. 3 that, as the dominant factor, solar radiation actively promotes space heating effect. The supply air temperature and air heat gains for both RSCs increase linearly with solar insolation rate, which leads to the corresponding improvement of space heating determined by indoor air temperature. Also can be seen is that the supply air temperature, indoor air temperature and air heat gains increase more rapidly for double pass RSC than those for single pass one. The reason is that instantaneous efficiency of solar heat collecting of double pass RSC is higher than that of single pass one by about 10% (see Fig. 3(a)). Moreover, when solar insolation rate is about 500 W m2, instantaneous efficiencies of solar heat collecting of both RSCs reach their peak values about 26.5% for single pass one and 39.5% for double pass one, respectively, and then they all tend to be smooth. Such a trend is encouraging, since double pass RSC can run at a high efficiency in most hours during a dayÕs operation, which is very favorable for space heating.
5000
35
0.40
-1
mfi=2000kg h ηd
0.38
30
4000
0.34 0.32
qs
2000
0.30 0.28
Air temperature (° C)
3000
25 Instantaneousefficiency
Air heat gains (W)
0.36
qd
L=3m ta=0°C
tsud trd
20
tsus 15 10
trs
1000 0.26
5
0.24 0 200 400 600 800 1000 Solar insolation rate(W m-2)
0
ηs
0 (a)
(b)
0 200 400 600 800 1000 Solar insolation rate(W m-2)
Fig. 3. Space heating effect with solar insolation rate. (a) Instantaneous efficiency of solar heat collecting and air heat gains versus solar insolation rate. (b) Supply air temperature and indoor air temperature versus solar insolation rate.
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X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757 25
0.55
3000
-1
mfi=2000kg.h -2
0.45 2000 0.40
qs
1500
0.35 1000
ηs
0.30
500
tsud
trd
15
tsus 10
trs 5
0.25
0
0
0.20 0
(a)
I=500W.m ta=0°C
20 Air temperature (° C)
Air heat gains (W)
0.50
qd
Instantaneous efficiency
ηd
2500
1
2
3
4
RSC length (m)
0
5 (b)
1
2
3
4
5
RSC length (m)
Fig. 4. Space heating effect with length of RSC. (a) Instantaneous efficiency of solar heat collecting and air heat gains versus RSC length. (b) Supply air temperature and indoor air temperature versus RSC length.
Fig. 4 presents the influence of air channel length on the space heating effect with respect to these two RSCs, under the condition that the air mass flow rate is about 2000 kg h1 and solar insolation rate is 500 W m2. It is found that the increase in length for RSCs is helpful for improvement of space heating. As expected, with a higher instantaneous efficiency of solar heat collecting, the supply air temperature, indoor air temperature and air heat gains increase more rapidly for double pass RSC than those for single pass one, which again proves the superiority of the double pass RSC. However, sharp decrease of instantaneous efficiency of solar heat collecting can be seen for both RSCs with the increase of the channel length, which means that, the amount of heat gains supplied by one longer RSC would be lower than that supplied by two units of the RSC, with a total length equal to that of the longer unit. Comparison of space heating effect with air mass flow rate when the length of air channel for the RSCs is 3 m and the solar radiation is 500 W m2 is shown in Fig. 5. As can be seen, initially, the supply air temperature of single pass RSC descends gradually with the increase of air mass flow rate, and then reaches a relatively constant value when the air mass flow rate exceeds 2000 kg h1. In contrast, the supply air temperature for double pass RSC sharply falls down, and approaches to the value of the single pass one. It means that the double pass RSC tends to lose its superiority when the air mass flow rate is high. Meanwhile, in the beginning, air heat gains, indoor air temperature and instantaneous efficiency of solar heat collecting for both RSCs all move up with the increment of air mass flow rate, and then tend to be smooth, indicating that excessive air mass flow rate makes no contribution to space heating effect. For the studied double pass RSC, the upper limit of air mass flow rate is considered to be about 5000 kg h1. Also found is that the space heating effect of two RSCs behaves similarly with the increase of air mass flow
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757 0.50
3200
0.45
Air heat gains (W)
2400 2000
ηs
qs
20 0.40 0.35 0.30
1600 0.25 1200
0.20
Airtemperature(°C)
qd
Instantaneous efficiency
2800
ηd
25
15
753
L=3m -2 I=500W m ta=0°C
tsud trd
tsus 10
trs
5 800
0.15
400
0.10 0 2000 4000 6000 800010000 Air mass flow rate(kg h-1)
(a)
0
(b)
0 2000 4000 6000 800010000 Air mass flow rate (kg h-1)
Fig. 5. Space heating effect with air mass flow rate of fan. (a) Instantaneous efficiency of solar heat collecting and air heat gains versus air mass flow rate. (b) Supply air temperature and indoor air temperature versus air mass flow rate.
rate. Fig. 5 denotes that it is necessary to choose suitable fans in practical applications, on condition that supply air temperature and indoor air temperature could be satisfied, low air mass flow rate fans are recommended, which is important in making full use of solar energy as well as reducing initial investment and operating cost. 4.2. Natural ventilation For natural ventilation, exhaust air temperature (air temperature at the exit of air channels), te which equals to To for single pass RSC and T1o for double pass one, is used to evaluate stack pressure. The other three indices considered for comparison of natural ventilation effect include air mass flow rate by natural ventilation, air change rate per hour (ACH) and instantaneous efficiency of solar heat collecting are calculated to compare natural ventilation effect. For the single pass RSC, air mass flow rate Ms is calculated by: Apmf according to the corresponding mathematical model; for the double pass RSC, natural ventilation air mass flow rate Md is given by: Ap(mf1 + mf2) in contrast. Additionally, air change rate per hour (ACH) represents the volume ratio of induced air flow rate to the house volume per hour. In calculation, the dimensional sizes of the RSCs take the same values as those in space heating mode. The influence of solar insolation rate on the natural ventilation effect for the two RSCs is plotted in Fig. 6. Here, the channel length of the RSCs is 3 m, the inclination angle is 45°, and the ambient air temperature is 30 °C. It can be seen that exhaust air temperature goes up with solar insolation rate rapidly, indicating the increment of stack pressure, which in turn is helpful to induce natural ventilation. Consequently, air mass flow rate rapidly increases with solar insolation rate for the two RSCs, resulting in higher air change rate, which is important to improve indoor thermal environment. Although the exhaust air temperature for single pass RSC is always higher than that for double pass RSC. However, the latter one has a higher instantaneous efficiency of
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757 0.46 ηd
0.42
tes
0.40 0.38
36
ηs
34
0.36 0.34
32
rd
25
2000
Md
20
rs
1500
15
Ms
1000
10
0.32
30 0
(a)
ted
30
-1
40 38
L=3m β =45° ta=30°C
0.44
Air mass flow rate (kg h )
Exhaust air temperature (°C)
42
2500
Air change rate (ACH)
44
Instantaneous efficiency
754
0.30 200 400 600 800 1000
Solar insolation rate(W. m-2)
500 0
(b)
5 200 400 600 800 1000
Solar insolation rate(W. m-2)
Fig. 6. Natural ventilation effect with solar insolation rate. (a) Instantaneous efficiency of solar heat collecting and exhaust air temperature versus solar insolation rate. (b) Natural ventilation air mass flow rate and air change rate versus solar insolation rate.
solar heat collecting and has two air channels used for natural ventilation, which leads to a larger natural ventilation air mass flow rate. Under the aforementioned conditions, if the solar insolation rate is 400 W/m2, the air mass flow rate induced by the double pass RSC is about 1584 kg h1, which means the air change rate for the house is about 20.8 times per hour (20.8 ACH). In contrast, the natural ventilation rate induced by the single pass RSC is only 1008 kg h1, indicating an air change rate about 12.9 ACH. According to Khedari et al. [4], a high air change rate (>20) is required for houses without any mechanical cooling device (depending on season). Thus, if 20 ACH is taken to be the criterion for thermal comfort under natural ventilation, the double pass RSC can create a thermal comfort environment when the solar insolation rate exceeds 400 W m2. Variations of natural ventilation effect with the length of air channel for the two RSCs are shown in Fig. 7. In this case, their inclination angle is 45°, the ambient air temperature is 30 °C and the solar insolation rate is 500 W m2. Under otherwise identical conditions, increasing RSCs length will augment stack pressure according to Eq. (16), moreover, as expected from Fig. 7, the longer the RSC, the higher the exhaust air temperature, which leads to the enhancement of natural ventilation air mass flow rate, and therefore increases air change rate. Also found is that higher air mass flow rate can be induced by double pass RSC as a result of higher instantaneous efficiency of solar heat collecting. According to the figure, air change rate in the studied house reaches 20 ACH for double pass RSC when the length is 2.0 m, whereas, it is only 12 ACH for the single pass one under identical conditions, which again proves the superiority of double pass RSC. In addition, similar to the space heating mode discussed above, it is also seen that the instantaneous efficiency of solar heat collecting tends to decrease with the increase of length for both RSCs. As a result, the amount of air mass flow rate induced by one longer RSC would be lower than that induced by two units of the RSC, with a total length equal to that of the longer unit.
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757 0.60
40
0.40
ted
0.35
34
ηs
0.25
(a)
2
Md
rs
1500
15
1000
10
Ms
0.30
32 1
20
-1
Air mass flow rate (kg h )
0.45 36
2000 Instantaneous efficiency
0.50
tes
Air change rate (ACH)
I=500W m ta=30°C
0.55
38
0
25
rd
β =45°
-2
ηd Exhaust air temperature(°C)
2500
755
3
4
500
5
5 0
2
3
4
5
RSC length (m)
(b)
RSC length (m)
1
Fig. 7. Natural ventilation effect with length of RSC. (a) Instantaneous efficiency of solar heat collecting and exhaust air temperature versus RSC length. (b) Natural ventilation air mass flow rate and air change rate versus RSC length.
0.46
0.40 0.38
38
0.36
ted
0.34 36
ηs
30
60
-1
rs
1500
16
12
Ms
1000
8
0.30 0
20
Md
0.32
34
(a)
Air mass flow rate (kg h )
tes
24
2000 Instantaneous efficiency
Exhaust air temperature (°C)
0.42 40
28
-2
I=500W.m L=3m rd ta=30°C
0.44
ηd
42
2500
500
90
RSC inclination angle (degree)
Air change rate (ACH)
44
4 0
(b)
30
60
90
RSC inclination angle (degree)
Fig. 8. Natural ventilation effect with inclination angle of RSC. (a) Instantaneous efficiency of solar heat collecting and exhaust air temperature versus inclination angle. (b) Natural ventilation air mass flow rate and air change rate versus inclination angle.
The impact of inclination angle on natural ventilation effect for the two RSCs are demonstrated in Fig. 8, where, length of air channel is 3 m, ambient air temperature is 30 °C and solar radiation is 500 W m2. It is seen that exhaust air temperature for the two RSCs decreases, while the instantaneous efficiency of solar heat collecting is improved with increase of the inclination angle. When the inclination angle reaches 45°, exhaust air temperature and instantaneous efficiency of solar heat
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collecting curves tend to be smooth, and natural ventilation air mass flow rate and air change rate increase slowly. This can be understood by considering that the stack height is increased for large inclination angles, but it is counteracted by reduction of the exhaust air temperature. Moreover, double pass RSC can induce air change rate of 20 ACH when the inclination angle is about 30°, however, it is impossible for the single pass one even at an inclination angle of 75°. It is therefore reasonable to recommend an inclination angle about 30° for double pass RSC in practical applications.
5. Conclusions A double pass RSC, which can be integrated with various building roofs compactly, is studied. The space heating and natural ventilation effects are investigated and compared with the single pass RSC. As a brief summary, it is wished to emphasize the novel points of this work in the following. (1) The instantaneous efficiency of solar heat collecting for double pass RSC is generally 10% higher than that of single pass RSC, which leads to the superiority of double pass RSC either in space heating or in natural ventilation. (2) For a double pass RSC in space heating mode, a reasonable balance should be made between the supply air temperature and a suitable mechanical air mass flow rate. It is necessary to choose suitable fans in practical applications, on condition that supply air temperature and indoor air temperature could be satisfied, low air mass flow rate fans are recommended, which is important in making full use of solar energy as well as reducing initial investment and operating cost. (3) Increasing RSC length leads to the severe reduction of instantaneous efficiency of solar heat collecting although it still contributes to the improvement of space heating and natural ventilation. As a result, both space heating and natural ventilation effects caused by one longer RSC would be weaker than those caused by two units of the RSC, with a total length equal to that of the longer unit. In practical applications, two or more shorter RSCs in parallel are recommended instead of one longer RSC. (4) The double pass RSC can induce more air change rate to satisfy occupant comfort for most cases, and is of great potential to create passive cooling by natural ventilation. In the studied cases, double pass RSC can induce air change rate of 20 ACH when the inclination angle is about 30°, however, it is impossible for the single pass one even at an inclination angle of 75°. It is therefore reasonable to recommend an inclination angle about 30° for double pass RSC in practical applications.
Acknowledgments This work is supported by the state Key Fundamental Research Program under the contract no. G2000026309 P.R.C., and the Shanghai Commission of Science and Technology under the contract no. 03DZ12012.
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References [1] Y.J. Dai, K. Sumathy, R.Z. Wang, Y.G. Li, Enhancement of natural ventilation in a solar house with a solar chimney and a solid adsorption cooling cavity, Solar Energy 74 (2003) 65–75. [2] S. Kumar, S. Siaha, N. Kumar, Experimental investigation of solar chimney assisted bioclimatic architecture, Energy Conversion and Management 39 (1998) 441–444. [3] J. Khedari, J. Hirunlabh, T. Bonnag, Experimental study of a roof solar collector towards the natural ventilation of new houses, Energy and Buildings 26 (1997) 159–164. [4] J. Khedari, W. Mansirisub, S. Chaima, N. Pratinsong, J. Hirunlabh, Field measurements of performance of roof solar collector, Energy and Buildings 31 (2000) 171–178. [5] J. Hirunlabh, S. Wachirapuwadon, N. Pratinthong, J. Khedari, New configurations of a roof solar collector maximizing natural ventilation, Building and Environment 36 (2001) 383–391. [6] A. Bouchair, D. Fitzgerald, J.A. Tinker, Moving air using stored solar energy, in: Proceedings of the 13th National Passive Conference, Cambridge, MA, ASES, 1988. [7] A. Bouchair, Solar chimney for promoting cooling ventilation in southern Algeria, Building Service Engineering Research and Technology 15 (1994) 81–93. [8] Z.D. Chen, P. Bandopadhayay, J. Halldorsson, C. Byrjalsen, P. Heiselberg, Y. Li, An experimental investigation of a solar chimney model with uniform wall heat flux, Building and Environment 38 (2003) 893–906. [9] C. Afonso, A. Oliveira, Solar chimneys: simulation and experiment, Energy and Buildings 32 (2000) 71–79. [10] H.B. Awbi, G. Gan, Simulation of solar induced ventilation, Renewable Energy Technology Environment 4 (1992) 2016–2030. [11] G. Gan, A parametric study of Trombe walls for passive cooling of buildings, Energy and Buildings 27 (1998) 37– 43. [12] Y. Li, Buoyancy-driven natural ventilation in a thermally stratified one-dimensional zone building, Building and Environment 35 (2000) 207–214. [13] A.M. Rodrigues, A. Canha, A. Lahellec, J.Y. Grandpeix, Modeling natural convection in a heated vertical channel for room ventilation, Building and Environment 35 (2000) 455–469. [14] K.S. Ong, A mathematical model of a solar chimney, Renewable Energy 28 (2003) 1047–1060. [15] N.K. Bansal, Solar air heater applications in India, Renewable Energy 16 (1999) 618–623. [16] F.K. Forson, M.A.A. Nazha, H. Rajakaruna, Experimental and simulation studies on a single pass, double duct solar air heater, Energy Conversion and Management 44 (2003) 1209–1227. [17] C. Choudhury, P.M. Chauhan, H.P. Garg, Performance and cost analysis of two-pass solar air heaters, Heat Recovery System & CHP 15 (1995) 755–773. [18] W.H. McAdams, Heat Transmission, third ed., McGraw-Hill, New York, 1954. [19] W.C. Swinbank, Long-wave radiation from clear skies, QJR Meteorological Society 89 (1963) 339. [20] W.M. Kays, M.E. Crawford, Convective heat and mass transfer, third ed., McGraw-Hill, New York, 1993. [21] J. Hirunlabh, W. Kongduang, P. Namprakai, J. Khedari, Study of natural ventilation of houses by a metallic solar wall under tropical climate, Renewable Energy 18 (1999) 109–119. [22] K.G.T. Hollands, T.E. Unny, G.D. Raithby, L.J. Konicek, Free convection heat transfer across inclined air layers, Transaction ASME, Journal of Heat transfer 98 (1976) 189–193. [23] J.N. Arnold, P.N. Bonaparte, I. Catton, D.K. Edwards, in: Proceedings of the 1974 Heat Transfer and Fluid Mechanics Institute, Stanford University Press, Stanford, CA, 1974. [24] Y.Q. Lu, Heating and Air Conditioning Design Handbook , China Architecture & Building Press, Beijing, 1993 (in Chinese).
Comparison of heating and natural ventilation in a solar house induced by two roof solar collectors X.Q. Zhai, Y.J. Dai, R.Z. Wang
*
Institute of Refrigeration and Cryogenics, School of Mechanical Engineering, Shanghai Jiao Tong University, 1954 Huanshan Road, Shanghai 200030, China Received 18 March 2004; accepted 4 August 2004 Available online 22 September 2004
Abstract In this paper, two kinds of roof solar collectors (RSCs), namely, the single pass RSC, and the double pass RSC are analyzed and compared. The double pass roof solar collector, which is configured by integrating a double pass solar air collector with the building roof, can be operated more efficiently for space heating in winter, and for natural ventilation in other seasons. To evaluate the effects of two RSCs for both space heating and natural ventilation, a single traditional Chinese style house, on which the two RSCs will be mounted respectively, is developed. Through comparison, it is found that the instantaneous efficiency of solar heat collecting for the double pass RSC is higher than that of the single pass one by 10% on average, and natural ventilation air mass flow rate contributed by natural ventilation for the double pass RSC can be improved to a great extent for most cases, indicating that double pass RSC is superior to the single pass one from the points of view of both space heating and natural ventilation. The double pass RSC is therefore more potential for improving indoor thermal environment and energy saving of buildings. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Roof solar collector; Space heating; Natural ventilation
*
Corresponding author. Tel.: +86 21 6293 3838/3250; fax: +86 21 6293 3250. E-mail address: [email protected] (R.Z. Wang).
1359-4311/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.08.001
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Nomenclature A Cp D f g h hb hc hr I k L m M q Q r t T Vw Greek a b e m n s q g r Dp2
area (m2) specific heat of air (J kg1 K1) hydraulic diameter of the air channels (m) friction factor for the channel wall gravitational constant (m s2) global heat transfer coefficient (W m2 K1) global heat transfer coefficient from insulation plate to the attic (W m2 K1) convection heat transfer coefficient (W m2 K1) radiation heat transfer coefficient (W m2 K1) solar insolation rate (W m2) thermal conductivity (W m1 K1) length of RSC (m) air mass flow rate per unit area of RSC (kg m2 s1) air mass flow rate of RSC (kg h1) heat gains of air (W) heat transferred from the studied house to the ambient air (W) air change rate of the house (ACH) temperature (°C) temperature (K) wind velocity of the ambient air (m s1) symbols absorptivity inclination angle of RSC (degree) emissivity kinematic viscosity of air (m2 s1) local loss coefficient transmissivity density of air (kg m3) instantaneous efficiency of solar heat collecting Stefan–Boltzmann constant (W m2 K4) Thickness of insulation plate (m)
Subscripts 1 air channel 1 2 air channel 2 a ambient air attic attic of the studied house ceiling ceiling of the studied house d double pass RSC door door of the studied house
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e f floor g in o p1 p2 r s sky su w wi wind
743
exhaust air air in channels floor of the studied house glass cover inlet of RSC outlet of RSC absorber plate insulation plate indoor air single pass RSC sky supply air wall of the studied house window of the studied house wind
Dimensionless terms Gr Grashof number Nu Nusselts number Pr Prandtl number Ra Rayleigh number Re Reynolds number
1. Introduction A solar house promotes a comfortable indoor environment utilizing solar radiation, which is one of the most important sources of heat gain in a building and through its surroundings. It is also considered as an appropriate architecture for developing countries to provide heating, cooling and ventilation and improve indoor air quality depending on season [1,2]. The traditional Chinese house, mainly in rural areas, with a gable roof, can be well designed for integration with a solar air collector to form the roof solar collector (RSC). In summer, it is feasible to use the roof structure to induce natural air circulation, which is a part of the houseÕs thermal comfort. In winter, it can be employed for space heating by mechanical ventilation. In the past decade, RSC has attracted so much attention in various investigations. Most of them were concerned with natural ventilation. Khedari et al. [3] conducted an experimental study of a RSC made by using CPAC (Concrete Product and Aggregate Company Ltd.) Monier concrete tiles on the outer side and gypsum board on the inner side, and gave the optimum dimensions of the RSC. Khedari et al. [4] carried out another field measurements for the same kind of roof solar collector, and the experimental results showed that large air gap and equal size of openings would induce the highest rate of air flow rate. Jongjit et al. [5] proposed four different configurations of the roof solar collector to maximize natural ventilation through numerical modeling. Another kind of RSC is solar chimney which is similar to those mentioned above except
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that the outer side of the RSC is replaced by glazing. Bouchair et al. [6] and Bouchair [7] carried out some experiments to testify the applicability of solar chimneys to improve indoor thermal environment by promoting natural ventilation in summer. Chen et al. [8] investigated experimentally solar chimneys with a uniform heat flux on a single wall for different chimney gaps, heat flux input and different chimney inclinations. Results showed that a maximum airflow rate was achieved at an inclination angle around 45° for a 200 mm gap and 1.5 m high chimney. Afonso and Oliveira [9] compared the behavior of a solar chimney with a conventional one. Their results showed that there was a significant increase in ventilation rate with the solar chimney. Theoretical and experimental studies on natural ventilation of buildings were also carried out by Awbi and Gan [10], Gan [11], Li [12], Rodrigues et al. [13], and Ong [14]. In addition, Bansal [15] depicted a RSC used in high mountain regions in the North and North-Eastern Himalayas for space heating during the winter periods. The former investigations were almost all based on single pass solar air collectors integrated with building roofs. Moreover, the majority of them were concerned with natural ventilation. However, space heating in winter is as necessary as ventilation in summer for most regions of China. So the practical RSC in China should be made to implement passive cooling by natural ventilation as well as space heating by mechanical ventilation. According to Forson et al. [16], the principal types of solar air collectors are: the single pass with front duct, rear duct, double duct and double pass. It has been observed that the double pass solar air collector performs better than the single pass one. In this paper, a double pass solar air collector integrated with the building roof is designed and analyzed, and the effect of natural ventilation and space heating in a given house is studied. In order to identify the superiority of the double pass RSC to the single pass one, numerical analysis for the two RSCs regarding the air change rate, as well as the instantaneous efficiency of solar heat collecting are also made.
2. Description of structure and operating principle 2.1. Single pass RSC The configuration of single pass RSC, which is formed by integrating single pass solar air collector with southern roof of the building, is shown in Fig. 1. By switching damper 1 and 2, the RSC can be used to implement two operating modes, namely, space heating in winter and natural ventilation in other seasons. In winter, space heating is needed. The indoor air can be circulated between the inner house and the roof solar collector by closing damper 1 and opening damper 2. In this case, a fan is used to move the air. Natural ventilation, which is necessary for other seasons, can be effected by closing damper 2 and opening damper 1. Thus the indoor air can enter the air channel through tuyere 7 under the chimney effect caused by solar radiation. The air is then exhausted to the ambient. 2.2. Double pass RSC The double pass RSC studied in this paper, which is configured by integrating a double pass solar air collector with the southern roof of the building, is presented in Fig. 2. Some changes
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757 2(Open) 1(Close)
2(Close)
3 5
745
1(Open)
3
4 5
6
4
6
Attic 8
7
Attic
9
10
Ceiling
8
7
9
10
Ceiling
House
House
(a)
(b)
Fig. 1. Structure of single pass roof solar collector. (a) Space heating mode. (b) Natural ventilation mode. 1—damper, 2—damper, 3—glass cover, 4—absorber plate, 5—insulation plate, 6—-air channel, 7—tuyere, 8—air duct, 9—fan, 10—tuyere.
7(Open) 8 12 9
6
3(Open) 2(Close) 1(Close) 4 13 5 Attic 14 Ceiling
10
11
7(Close) 8 12 9
6
3(Close) 2(Open) 1(Open) 4 13 5 Attic 14
10
11
Ceiling
House
House
(a)
(b)
Fig. 2. Structure of double pass roof solar collector. (a) Space heating mode. (b) Natural ventilation mode. 1—damper, 2—damper, 3—damper, 4—glass cover, 5—absorber plate, 6—insulation plate, 7—damper, 8—tuyere, 9—tuyere, 10— fan, 11-tuyere, 12—air channel 1, 13—air channel 2, 14—air duct.
are made to rebuild the double pass solar air collector, as is shown in Fig. 2, four additional dampers 1, 2, 3, and 7 are installed to switch operating modes between space heating by warm air in winter and natural ventilation in other seasons. Space heating is operated with the following procedures: (1) Closing dampers 1 and 2, (2) opening dampers 3 and 7, (3) closing tuyere 8. In this way, the indoor air can enter air channel 1 through tuyere 9 and get heat from solar radiation. Then the air flows into air channel 2, where the absorber plate secondly heats the air; thereafter it flows into air duct, and is supplied into the house by the fan through tuyere 11. Natural ventilation mode is accomplished by closing dampers 3 and 7, and opening dampers 1 and 2. Thus the indoor air can enter both air channel 1 and 2 through tuyeres 8
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and 9, respectively. In the air channels, the air is heated by solar radiation and the natural ventilation can thus be produced in the end due to the chimney effect.
3. Formulation of the mathematical model The equations governing the performance of the RSCs are formulated by coupling the energy balance equations of components of the RSCs with those for the useful heat extracted in the channels, making the following assumptions: (1) The RSCs operate under steady state conditions. (2) Thermal inertia of RSCs components is negligible. (3) Operating temperatures of RSCs components and mean air temperatures in air channels are all assumed to be uniform. (4) Temperature of the air varies only in the direction of the flow. (5) Heat flow through the glass cover, absorber plate and the insulation plate is one-dimensional and in the direction vertical to air flow. (6) All air channels are assumed to be no leakage. (7) The temperature in the attic equals to that of the ambient air. (8) Neglecting thermal inertia of the enclosures and indoor waste heat, the heat transferred through the house enclosures to the ambient is assumed to be proportional to the temperature difference between indoor air and ambient air.
3.1. Single pass RSC For the single pass RSC, the energy balance equations for various components in both space heating and natural ventilation modes are given below: For glass cover ag I ¼ hga ðT g T a Þ þ hcgf ðT g T f Þ þ hrp1g ðT g T p1 Þ
ð1Þ
For air channel C p mf ðT o T r Þ ¼ hcgf ðT g T f Þ þ hcp1f ðT p1 T f Þ
ð2Þ
For absorber plate sg ap1 I ¼ hcp1f ðT p1 T f Þ þ hrp1g ðT p1 T g Þ þ hb ðT p1 T a Þ
ð3Þ
Air heat gains in space heating mode is defined as qs ¼ C p mf Ap1 ðT o T r Þ
ð4Þ
and then, instantaneous efficiency of solar heat collecting in either space heating or natural ventilation mode is given as gs ¼ C p mf ðT o T r Þ=I
ð5Þ
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3.2. Double pass RSC For the double pass RSC, attention should be paid to the difference of the mathematical model for different operating modes. From Fig. 2, it can be seen that, in space heating mode, the double pass RSC acts as a double pass solar air collector, however, in natural ventilation mode, it serves as a single pass double duct solar air collector. The energy balance equations for various components of the double pass RSC when it is used for space heating are expressed as For glass cover ag I ¼ hga ðT g T a Þ þ hcgf1 ðT g T f1 Þ þ hrp1g ðT g T p1 Þ
ð6Þ
For air channel 1 C p mf1 ðT 1o T r Þ ¼ hcgf1 ðT g T f1 Þ þ hcp1f1 ðT p1 T f1 Þ
ð7Þ
For absorber plate sg ap1 I ¼ hcp1f1 ðT p1 T f1 Þ þ hcp1f2 ðT p1 T f2 Þ þ hrp1p2 ðT p1 T p2 Þ þ hrp1g ðT p1 T g Þ
ð8Þ
For air channel 2 C p mf2 ðT 2o T 1o Þ ¼ hcp1f2 ðT p1 T f2 Þ þ hcp2f2 ðT p2 T f2 Þ
ð9Þ
For insulation plate hrp1p2 ðT p1 T p2 Þ ¼ hcp2f2 ðT p2 T f2 Þ þ hb ðT p2 T a Þ
ð10Þ
Air heat gains in space heating mode is given as qd ¼ C p mf2 Ap1 ðT 2o T r Þ
ð11Þ
and then, instantaneous efficiency of solar heat collecting in space heating mode is expressed as gd ¼ qd =ðIAp1 Þ
ð12Þ
For the double pass RSC under natural ventilation mode, the above equations can still be used except that Eq. (9) for air channel 2 should be modified as follows: C p mf2 ðT 2o T r Þ ¼ hcp1f2 ðT p1 T f2 Þ þ hcp2f2 ðT p2 T f2 Þ
ð13Þ
Meanwhile, instantaneous efficiency of solar heat collecting in natural ventilation mode is changed as gd ¼ ½C p mf1 ðT 1o T r Þ þ C p mf2 ðT 2o T r Þ=I
ð14Þ
3.3. Determination of mean air temperature For the RSCs under space heating mode, mean air temperatures in air channels are calculated using the method of Choudhury et al. [17] For air channel of single pass RSC T f ¼ ðT o þ T r Þ=2
ð15Þ
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For air channel 1 of double pass RSC T f1 ¼ ðT 1o þ T r Þ=2
ð16Þ
For air channel 2 of double pass RSC T f2 ¼ ðT 2o þ T 1o Þ=2
ð17Þ
In natural ventilation mode, however, mean air temperatures in each channel are calculated according to Hirunlabh et al. [21] T fi ¼ 0:75T io þ 0:25T r
ð18Þ
where the subscript, i, represents different air channels for double pass RSC. In addition, the above equation corresponds to single pass RSC when the subscript, i, is not included. 3.4. Modeling of air mass flow rate The space heating modes in winter for both RSCs are all accomplished by mechanical ventilation. For comparison, the space heating modes for both RSCs use the fans with the same specification. Therefore, air mass flow rate mf, mf1 and mf2 in the above equations are also the same in the simulation. Air mass flow rate in natural ventilation mode is mainly determined by two aspects, which are stack pressure built up in the air channels and the pressure losses at the inlet, outlet and along the RSC channels. The energy conservation equation can be expressed as qðAp1 mfi =qAin Þ2 qðAp1 mfi =qAo Þ2 L qðAp1 mfi =qAi Þ2 þ no þf ð19Þ D 2 2 2 where, the left hand of Eq. (19) stands for stack pressure, and the right side represents pressure losses, according to Chen et al. [8], nin = 1.5, no = 1.0, f = 0.056, respectively. The subscript, i, denotes different air channels for double pass RSC, but will vanish when the single pass RSC is considered. Moreover, it is assumed here that the open areas of the air channel at the inlet and outlet, the cross section area of the air channels, are equal to each other. Consequently, in terms of Eq. (19), natural ventilation air mass flow rate per unit RSC area in each air channel can be calculated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ain 2gL sin bðT io T r Þ ð20Þ mfi ¼ q Ap1 T r nin þ no þ f DL qgL sin bðT io T r Þ=T r ¼ nin
3.5. Estimation of heat transfer coefficients Global heat transfer coefficient between glass cover and the ambient is given as hga ¼ hcwind þ hrgsky
ð21Þ
Convection heat transfer coefficient from glazing due to wind is recommended by McAdams [18] hcwind ¼ 5:7 þ 3:8V w
ð22Þ
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749
Radiation heat transfer coefficient from glass cover to sky referred to the ambient air temperature may be obtained from hrgsky ¼ reg ðT g þ T sky ÞðT 2g þ T 2sky Þ
ðT g T sky Þ ðT g T a Þ
ð23Þ
Sky temperature is predicted using the formulation given by Swinbank [19] T sky ¼ 0:0552T 1:5 a
ð24Þ
The radiation heat transfer coefficient between glass cover and absorber plate may be predicted by hrp1g ¼
rðT 2p1 þ T 2g ÞðT p1 þ T g Þ 1 ep1
þ e1g 1
ð25Þ
The radiation heat transfer coefficient between absorber plate and insulation plate may be calculated by hrp1p2 ¼
rðT 2p1 þ T 2p2 ÞðT p1 þ T p2 Þ 1 ep1
þ e1p2 1
ð26Þ
Global heat transfer coefficient from insulation plate to the attic is written below hb ¼ 1=ð1=hcp2attic þ Dp2 =k p2 Þ
ð27Þ
In the analysis, the fully developed flow condition is assumed for calculating forced convection heat transfer coefficients between plates and air in space heating mode. According to Kays and Crawford [20], the following correlation can be adopted Nu ¼ 0:019Re0:8 Pr1:3
ð28Þ
It is realized that the above correlation is valid for fully developed turbulent flow between two flat plates, one of which is heated. However, this assumption may not alter the comparison results between two different RSCs. For the air channel of single pass RSC and the air channel 1 of double pass RSC, the average natural convection heat transfer coefficient between plates and air is calculated according to Hollands et al. [22] " # #þ þ " 1=3 1708ðsin 1:8bÞ1:6 1708 Ra cos b 1 þ 1 ð29Þ Nu ¼ 1 þ 1:44 1 Ra cos b 5830 Ra cos b where the meaning of the + exponent is that only positive values of the terms in the square brackets are to be used (i.e., use zero if the term is negative). It should be noted that the correlations given by Eq. (29) does not cover the range of tilt angles from 75° to 90°, however, it is recommended that the 75° correlation be used to represent the vertical case adequately. For the air channel 2 of double pass RSC, it is determined according to Arnold et al. [23] Nu ¼ 1 þ ½Nuð90 Þ 1 sin b where Nu(90°) approximates the 75° tilt value of Eq. (29).
ð30Þ
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X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757
Table 1 Detailed characters of the studied house Aceiling
Adoor
Afloor
Aw
Awi
hceiling
hdoor
hfloor
hw
hwi
20
2.0
20
49.75
2.25
1.24
4.65
0.47
2.08
5.82
3.6. Energy balance equation of the house For comparison, an identical house is chosen to install different RSCs respectively. The studied house integrated with two different RSCs is shown in Figs. 1 and 2. The dimensional sizes for this house are: width: 4 m, length: 5 m, height: 3 m. All walls are made of the same material, brick, with a thickness of 240 mm, except for a wooden window and a wooden door in the walls. The ceiling is made of gypsum planks, with a thickness of 30 mm. The floor is not insulated. Detailed characters of the studied house are listed in Table 1, in which the global heat transfer coefficients are suggested by Lu et al. [24]. Heat transferred through the house enclosures to the ambient, Q, is assumed to be proportional to the temperature difference between Tr and Ta. Here, Q is calculated by Q ¼ hw Aw ðT r T a Þ þ hwi Awi ðT r T a Þ þ hdoor Adoor ðT r T a Þ þ hceiling Aceiling ðT r T a Þ þ hfloor Afloor ðT r T a Þ
ð31Þ
In simulation, the house is considered to be in instantaneous thermal equilibrium, i.e., in space heating mode, air heat gains by RSCs are all used to counteract heat transferred from the house to the ambient, analogously, in natural ventilation mode, heat transferred from the ambient to the house is all exhausted by natural ventilation. 4. Results and discussion Based on the above detailed analysis of the mathematical model, a FORTRAN computer program was written and developed to estimate both space heating and natural ventilation effects. The physical properties of air are assumed to vary linearly with temperature. Some basic parameters for calculation are listed in Table 2. For certain operating conditions, the temperatures of glass cover, absorber plate, insulation plate, indoor air and air of each channel are initially guessed, and various heat transfer coefficients are estimated with these temperatures, and then the heat balance equations are solved to obtain new temperatures which are compared with old ones. The iteration process is continued with the most updated variables until all the temperature values converge. Hence, air heat gains and instantaneous efficiency of solar heat collecting for space heating mode can be determined, in addition, natural ventilation air mass flow rate and instantaneous efficiency of solar heat collecting can be calculated when the program is used for natural ventilation mode. Then, comparisons of space heating and natural ventilation effects between two RSCs are discussed as follows. 4.1. Space heating Four indices, namely, supply air temperature (air temperature at the exit of RSC), indoor air temperature, air heat gains and instantaneous efficiency of solar heat collecting are used to eval-
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757
751
Table 2 Some basic parameters for calculation hcp2attic
kp2
ag
ap1
eg
ep1
ep2
sg
Dp2
10
0.0275
0.06
0.95
0.90
0.94
0.94
0.84
0.05
uate space heating effect of two RSCs. For single pass RSC, supply air temperature is To in terms of Eq. (2), while it is represented by T2o according to Eq. (9) for double pass one. In calculation, Some constant parameters used in the analysis are listed below: the width of RSCs is 4.0 m, the gap of air channels is 0.2 m, the inclination angle is 45°, the ambient air temperature is 0°C and the ambient air velocity is taken to be 1.5 m s1. The impact of solar insolation rate on the space heating effect for the two RSCs is shown in Fig. 3. Here, the length of the RSCs is 3 m, and the air mass flow rate is 2000 kg h1. It can be found from Fig. 3 that, as the dominant factor, solar radiation actively promotes space heating effect. The supply air temperature and air heat gains for both RSCs increase linearly with solar insolation rate, which leads to the corresponding improvement of space heating determined by indoor air temperature. Also can be seen is that the supply air temperature, indoor air temperature and air heat gains increase more rapidly for double pass RSC than those for single pass one. The reason is that instantaneous efficiency of solar heat collecting of double pass RSC is higher than that of single pass one by about 10% (see Fig. 3(a)). Moreover, when solar insolation rate is about 500 W m2, instantaneous efficiencies of solar heat collecting of both RSCs reach their peak values about 26.5% for single pass one and 39.5% for double pass one, respectively, and then they all tend to be smooth. Such a trend is encouraging, since double pass RSC can run at a high efficiency in most hours during a dayÕs operation, which is very favorable for space heating.
5000
35
0.40
-1
mfi=2000kg h ηd
0.38
30
4000
0.34 0.32
qs
2000
0.30 0.28
Air temperature (° C)
3000
25 Instantaneousefficiency
Air heat gains (W)
0.36
qd
L=3m ta=0°C
tsud trd
20
tsus 15 10
trs
1000 0.26
5
0.24 0 200 400 600 800 1000 Solar insolation rate(W m-2)
0
ηs
0 (a)
(b)
0 200 400 600 800 1000 Solar insolation rate(W m-2)
Fig. 3. Space heating effect with solar insolation rate. (a) Instantaneous efficiency of solar heat collecting and air heat gains versus solar insolation rate. (b) Supply air temperature and indoor air temperature versus solar insolation rate.
752
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757 25
0.55
3000
-1
mfi=2000kg.h -2
0.45 2000 0.40
qs
1500
0.35 1000
ηs
0.30
500
tsud
trd
15
tsus 10
trs 5
0.25
0
0
0.20 0
(a)
I=500W.m ta=0°C
20 Air temperature (° C)
Air heat gains (W)
0.50
qd
Instantaneous efficiency
ηd
2500
1
2
3
4
RSC length (m)
0
5 (b)
1
2
3
4
5
RSC length (m)
Fig. 4. Space heating effect with length of RSC. (a) Instantaneous efficiency of solar heat collecting and air heat gains versus RSC length. (b) Supply air temperature and indoor air temperature versus RSC length.
Fig. 4 presents the influence of air channel length on the space heating effect with respect to these two RSCs, under the condition that the air mass flow rate is about 2000 kg h1 and solar insolation rate is 500 W m2. It is found that the increase in length for RSCs is helpful for improvement of space heating. As expected, with a higher instantaneous efficiency of solar heat collecting, the supply air temperature, indoor air temperature and air heat gains increase more rapidly for double pass RSC than those for single pass one, which again proves the superiority of the double pass RSC. However, sharp decrease of instantaneous efficiency of solar heat collecting can be seen for both RSCs with the increase of the channel length, which means that, the amount of heat gains supplied by one longer RSC would be lower than that supplied by two units of the RSC, with a total length equal to that of the longer unit. Comparison of space heating effect with air mass flow rate when the length of air channel for the RSCs is 3 m and the solar radiation is 500 W m2 is shown in Fig. 5. As can be seen, initially, the supply air temperature of single pass RSC descends gradually with the increase of air mass flow rate, and then reaches a relatively constant value when the air mass flow rate exceeds 2000 kg h1. In contrast, the supply air temperature for double pass RSC sharply falls down, and approaches to the value of the single pass one. It means that the double pass RSC tends to lose its superiority when the air mass flow rate is high. Meanwhile, in the beginning, air heat gains, indoor air temperature and instantaneous efficiency of solar heat collecting for both RSCs all move up with the increment of air mass flow rate, and then tend to be smooth, indicating that excessive air mass flow rate makes no contribution to space heating effect. For the studied double pass RSC, the upper limit of air mass flow rate is considered to be about 5000 kg h1. Also found is that the space heating effect of two RSCs behaves similarly with the increase of air mass flow
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757 0.50
3200
0.45
Air heat gains (W)
2400 2000
ηs
qs
20 0.40 0.35 0.30
1600 0.25 1200
0.20
Airtemperature(°C)
qd
Instantaneous efficiency
2800
ηd
25
15
753
L=3m -2 I=500W m ta=0°C
tsud trd
tsus 10
trs
5 800
0.15
400
0.10 0 2000 4000 6000 800010000 Air mass flow rate(kg h-1)
(a)
0
(b)
0 2000 4000 6000 800010000 Air mass flow rate (kg h-1)
Fig. 5. Space heating effect with air mass flow rate of fan. (a) Instantaneous efficiency of solar heat collecting and air heat gains versus air mass flow rate. (b) Supply air temperature and indoor air temperature versus air mass flow rate.
rate. Fig. 5 denotes that it is necessary to choose suitable fans in practical applications, on condition that supply air temperature and indoor air temperature could be satisfied, low air mass flow rate fans are recommended, which is important in making full use of solar energy as well as reducing initial investment and operating cost. 4.2. Natural ventilation For natural ventilation, exhaust air temperature (air temperature at the exit of air channels), te which equals to To for single pass RSC and T1o for double pass one, is used to evaluate stack pressure. The other three indices considered for comparison of natural ventilation effect include air mass flow rate by natural ventilation, air change rate per hour (ACH) and instantaneous efficiency of solar heat collecting are calculated to compare natural ventilation effect. For the single pass RSC, air mass flow rate Ms is calculated by: Apmf according to the corresponding mathematical model; for the double pass RSC, natural ventilation air mass flow rate Md is given by: Ap(mf1 + mf2) in contrast. Additionally, air change rate per hour (ACH) represents the volume ratio of induced air flow rate to the house volume per hour. In calculation, the dimensional sizes of the RSCs take the same values as those in space heating mode. The influence of solar insolation rate on the natural ventilation effect for the two RSCs is plotted in Fig. 6. Here, the channel length of the RSCs is 3 m, the inclination angle is 45°, and the ambient air temperature is 30 °C. It can be seen that exhaust air temperature goes up with solar insolation rate rapidly, indicating the increment of stack pressure, which in turn is helpful to induce natural ventilation. Consequently, air mass flow rate rapidly increases with solar insolation rate for the two RSCs, resulting in higher air change rate, which is important to improve indoor thermal environment. Although the exhaust air temperature for single pass RSC is always higher than that for double pass RSC. However, the latter one has a higher instantaneous efficiency of
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757 0.46 ηd
0.42
tes
0.40 0.38
36
ηs
34
0.36 0.34
32
rd
25
2000
Md
20
rs
1500
15
Ms
1000
10
0.32
30 0
(a)
ted
30
-1
40 38
L=3m β =45° ta=30°C
0.44
Air mass flow rate (kg h )
Exhaust air temperature (°C)
42
2500
Air change rate (ACH)
44
Instantaneous efficiency
754
0.30 200 400 600 800 1000
Solar insolation rate(W. m-2)
500 0
(b)
5 200 400 600 800 1000
Solar insolation rate(W. m-2)
Fig. 6. Natural ventilation effect with solar insolation rate. (a) Instantaneous efficiency of solar heat collecting and exhaust air temperature versus solar insolation rate. (b) Natural ventilation air mass flow rate and air change rate versus solar insolation rate.
solar heat collecting and has two air channels used for natural ventilation, which leads to a larger natural ventilation air mass flow rate. Under the aforementioned conditions, if the solar insolation rate is 400 W/m2, the air mass flow rate induced by the double pass RSC is about 1584 kg h1, which means the air change rate for the house is about 20.8 times per hour (20.8 ACH). In contrast, the natural ventilation rate induced by the single pass RSC is only 1008 kg h1, indicating an air change rate about 12.9 ACH. According to Khedari et al. [4], a high air change rate (>20) is required for houses without any mechanical cooling device (depending on season). Thus, if 20 ACH is taken to be the criterion for thermal comfort under natural ventilation, the double pass RSC can create a thermal comfort environment when the solar insolation rate exceeds 400 W m2. Variations of natural ventilation effect with the length of air channel for the two RSCs are shown in Fig. 7. In this case, their inclination angle is 45°, the ambient air temperature is 30 °C and the solar insolation rate is 500 W m2. Under otherwise identical conditions, increasing RSCs length will augment stack pressure according to Eq. (16), moreover, as expected from Fig. 7, the longer the RSC, the higher the exhaust air temperature, which leads to the enhancement of natural ventilation air mass flow rate, and therefore increases air change rate. Also found is that higher air mass flow rate can be induced by double pass RSC as a result of higher instantaneous efficiency of solar heat collecting. According to the figure, air change rate in the studied house reaches 20 ACH for double pass RSC when the length is 2.0 m, whereas, it is only 12 ACH for the single pass one under identical conditions, which again proves the superiority of double pass RSC. In addition, similar to the space heating mode discussed above, it is also seen that the instantaneous efficiency of solar heat collecting tends to decrease with the increase of length for both RSCs. As a result, the amount of air mass flow rate induced by one longer RSC would be lower than that induced by two units of the RSC, with a total length equal to that of the longer unit.
X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757 0.60
40
0.40
ted
0.35
34
ηs
0.25
(a)
2
Md
rs
1500
15
1000
10
Ms
0.30
32 1
20
-1
Air mass flow rate (kg h )
0.45 36
2000 Instantaneous efficiency
0.50
tes
Air change rate (ACH)
I=500W m ta=30°C
0.55
38
0
25
rd
β =45°
-2
ηd Exhaust air temperature(°C)
2500
755
3
4
500
5
5 0
2
3
4
5
RSC length (m)
(b)
RSC length (m)
1
Fig. 7. Natural ventilation effect with length of RSC. (a) Instantaneous efficiency of solar heat collecting and exhaust air temperature versus RSC length. (b) Natural ventilation air mass flow rate and air change rate versus RSC length.
0.46
0.40 0.38
38
0.36
ted
0.34 36
ηs
30
60
-1
rs
1500
16
12
Ms
1000
8
0.30 0
20
Md
0.32
34
(a)
Air mass flow rate (kg h )
tes
24
2000 Instantaneous efficiency
Exhaust air temperature (°C)
0.42 40
28
-2
I=500W.m L=3m rd ta=30°C
0.44
ηd
42
2500
500
90
RSC inclination angle (degree)
Air change rate (ACH)
44
4 0
(b)
30
60
90
RSC inclination angle (degree)
Fig. 8. Natural ventilation effect with inclination angle of RSC. (a) Instantaneous efficiency of solar heat collecting and exhaust air temperature versus inclination angle. (b) Natural ventilation air mass flow rate and air change rate versus inclination angle.
The impact of inclination angle on natural ventilation effect for the two RSCs are demonstrated in Fig. 8, where, length of air channel is 3 m, ambient air temperature is 30 °C and solar radiation is 500 W m2. It is seen that exhaust air temperature for the two RSCs decreases, while the instantaneous efficiency of solar heat collecting is improved with increase of the inclination angle. When the inclination angle reaches 45°, exhaust air temperature and instantaneous efficiency of solar heat
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X.Q. Zhai et al. / Applied Thermal Engineering 25 (2005) 741–757
collecting curves tend to be smooth, and natural ventilation air mass flow rate and air change rate increase slowly. This can be understood by considering that the stack height is increased for large inclination angles, but it is counteracted by reduction of the exhaust air temperature. Moreover, double pass RSC can induce air change rate of 20 ACH when the inclination angle is about 30°, however, it is impossible for the single pass one even at an inclination angle of 75°. It is therefore reasonable to recommend an inclination angle about 30° for double pass RSC in practical applications.
5. Conclusions A double pass RSC, which can be integrated with various building roofs compactly, is studied. The space heating and natural ventilation effects are investigated and compared with the single pass RSC. As a brief summary, it is wished to emphasize the novel points of this work in the following. (1) The instantaneous efficiency of solar heat collecting for double pass RSC is generally 10% higher than that of single pass RSC, which leads to the superiority of double pass RSC either in space heating or in natural ventilation. (2) For a double pass RSC in space heating mode, a reasonable balance should be made between the supply air temperature and a suitable mechanical air mass flow rate. It is necessary to choose suitable fans in practical applications, on condition that supply air temperature and indoor air temperature could be satisfied, low air mass flow rate fans are recommended, which is important in making full use of solar energy as well as reducing initial investment and operating cost. (3) Increasing RSC length leads to the severe reduction of instantaneous efficiency of solar heat collecting although it still contributes to the improvement of space heating and natural ventilation. As a result, both space heating and natural ventilation effects caused by one longer RSC would be weaker than those caused by two units of the RSC, with a total length equal to that of the longer unit. In practical applications, two or more shorter RSCs in parallel are recommended instead of one longer RSC. (4) The double pass RSC can induce more air change rate to satisfy occupant comfort for most cases, and is of great potential to create passive cooling by natural ventilation. In the studied cases, double pass RSC can induce air change rate of 20 ACH when the inclination angle is about 30°, however, it is impossible for the single pass one even at an inclination angle of 75°. It is therefore reasonable to recommend an inclination angle about 30° for double pass RSC in practical applications.
Acknowledgments This work is supported by the state Key Fundamental Research Program under the contract no. G2000026309 P.R.C., and the Shanghai Commission of Science and Technology under the contract no. 03DZ12012.
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