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Exergy analysis of Unglazed Transpired Solar Collectors (UTCs)
Available online at www.sciencedirect.com
ScienceDirect Solar Energy 107 (2014) 272–277 www.elsevier.com/locate/solener
Exergy analysis of Unglazed Transpired Solar Collectors (UTCs) A.A. Golneshan a, H. Nemati b,⇑ b
a School of Mechanical Engineering, Shiraz University, Shiraz, Iran Department of Mechanics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
Received 10 November 2012; received in revised form 21 January 2014; accepted 22 April 2014 Available online 28 June 2014 Communicated by: Associate Editor Hans-Martin Henning
Abstract The Unglazed Transpired Solar Collector (UTC) is a suitable device for preheating outside air directly. They are used mostly in preheating ventilation air as well as in heating air for crop drying. The thermal performance of UTC promises its popular usage in near future. A number of large scale installations have been used all over the world since 1990s. In this study, first, the exergy efficiency of UTC is derived. Based on this efficiency, optimization was performed on 200 different cases and finally, a simple but useful correlation was proposed to predict the optimum working temperature. After finding the optimum working temperature, an economic analysis may be performed to determine the most effective and least expensive geometry. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: UTC; Exergy; Optimum temperature; Effectiveness
1. Introduction Unglazed Transpired Solar Collectors are now in use all over the world, mostly for preheating the ventilation air, crop drying and desiccant cooling. The installation and well operating performance of over 70 large systems, each having collector areas between 500 and 10,000 m2, have been reported (Van Decker et al., 2001). These air heaters are composed of a perforated plate, typically with porosity less than 5%, mostly painted black (absorber). They are mounted on the south wall of buildings to heat up outside ambient air as it is sucked through the perforations via a plenum, formed in the space between the plate and the south wall (Fig. 1). The solar energy absorbed by the plate will maintain the plate temperature above the ambient air temperature. A fan on the top of
⇑ Corresponding author.
E-mail address: [email protected] (H. Nemati). http://dx.doi.org/10.1016/j.solener.2014.04.025 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
the plenum collects the sucked heated air and distributes it through the ducts into the space. Although, the preliminary installations had a transparent cover to prevent convection losses against wind, it was found that these losses are negligible and the air heater experiences high performance without any glazing (Van Decker, 1996; Golneshan and Hollands, 1998; Kutscher, 1992; Golneshan and Nemati, 2004). This leads to save up to 40% of the total expenses and the solar air heating to be less expensive and more attractive (Arulanandam, 1995). Ambient air is heated as it passes over the absorber, through perforations as well as passing over the back of the absorber plate in the plenum. The performance of this type of collectors is usually expressed by thermal effectiveness and the first law efficiency. The thermal effectiveness is defined as: e¼
T out T 1 Tc T1
ð1Þ
A.A. Golneshan, H. Nemati / Solar Energy 107 (2014) 272–277
273
Nomenclature Ac absorber area (m2) B dimensionless exergy destruction or loss Cp specific heat (kJ/kg K) D hole diameter (m) _ Ex exergy (kW) Is solar incident radiation (kW) air mass flow rate in collector (kg/s) m_ P hole pitch (m) Q_ conv;useful thermal energy transferred to air from collector (kW) absorbed solar energy (kW) Q_ in Q_ rad;loss radiation loss from the collector (kW) ReD ¼ qVlh D hole Reynolds number T temperature qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(K) ffi T max ¼ T 1 4 r ITs 4 þ 1 maximum accessible surface sb
t U1 V h ¼ Vrs Vs
1
collector temperature, when m_ ¼ 0 absorber plate thickness (m) wind velocity on front side of collector (m/s) suction velocity in hole (m/s) suction velocity on front side of collector (m/s)
Greek letters ac absorber plate absorptivity c dimensionless parameter defined by Eq. (3)
where Tout is the air outlet temperature, T c is the mean collector temperature and T1 is the superficial ambient air temperature (Fig. 2). This thermal effectiveness depends on numbers of geometrical, hydrodynamic and thermal characteristics of the collectors. Several experimental and numerical studies have been done to estimate the thermal effectiveness of UTCs for various types of perforations. Kutscher et al. (1991) proposed an analytical model and heat loss theory for UTCs experiencing continuous suction. He also performed some
e effectiveness defined by Eq. (1) ec absorber plate emissivity gI 1st law efficiency defined by Eq. (13) gII 2nd law efficiency h ¼ TT1 dimensionless temperature hmax ¼ TTmax maximum accessible dimensionless collector 1 temperature, when m_ ¼ 0 l air viscosity (kg/m s) q air density (kg/m3) r ¼ Ahole =Aplate collector porosity rsb Stefan–Boltzmann constant (5.67 1011 2 4 kW/m K ) volumetric flow rate (m3/s) /_ Subscript 1 ambient abs absorption c collector surface, absorber conv convection des destruction em emission out outlet ref reflection s sun, solar
experiments to investigate the performance of a UTC with 0.79 mm thick aluminum plates with circular holes on staggered layout (Kutscher et al., 1991; Kutscher, 1992, 1994). Golneshan (1994) and Golneshan and Hollands (1998) did an extensive experimental work on slot type collectors. Arulanandam (1995) was the first who modeled the effectiveness of UTCs in no-wind condition, with circular holes arranged on a square pitch (same as Fig. 2), using a commercial numerical code; TASKflow. Van Decker (1996) and Van Decker et al. (2001) worked experimentally on the performance of UTCs with circular holes, and presented an empirical correlation to predict the thermal effectiveness of such plates. Nemati (2004) and Golneshan and Nemati (2004) investigated the effect of wind direction on the performance of UTCs. They proposed a correlation to predict the thermal effectiveness of UTCs with circular holes on both staggered and aligned layout for various wind direction. For the aligned layout, Nemati (2004) proposed the following simple correlation with RMSE = 4.7%: rffiffiffiffi!0:161 D e ¼ 0:835 c t
Fig. 1. A section view of a typical UTC, air is sucked through the perforations and gets warm.
c¼
Vs U1
0:737
Re1:482 r D
ð2Þ
ð3Þ
274
A.A. Golneshan, H. Nemati / Solar Energy 107 (2014) 272–277
Fig. 2. A simplified view of absorber.
in which Vs is the superficial suction velocity on front side of the plate, U1 is wind velocity and r is the plate porosity and is defined as: r¼
Ahole pD2 =4 ¼ Aplate P2
ð4Þ
where P and D are the hole pitch and diameter, respectively. ReD is based on the air velocity in hole which is defined as: Vh ¼
Vs r
ð5Þ
He also showed that the correlations developed for aligned layout can be employed to predict the staggered layout cases if one multiplies hole pitch by 0.5. In addition to all above efforts in prediction of thermal effectiveness of UTC, based on Eq. (1), it is clear that the unity of effectiveness does not mean the optimum working condition. To determine the optimum working condition, exergy analysis should be performed. In the ensuing parts, the exergy balance is performed to determine exergy destruction and 2nd law efficiency of UTCs and then optimization is done over 200 different cases for a vast working condition to determine the best working temperature, based on effectiveness and some other dimensionless parameters. Knowing the best working temperature for the assumed effectiveness, it is only required to perform economic analysis to determine geometrical parameters such as hole diameter, hole pitch and so on, to meet the assumed effectiveness. 2. Energy analysis In this collector, the incident solar beam radiation is absorbed by a perforated plate while air is sucking in, through the perforations. Sucked air sweeps absorbed heat from the absorber plate and gets warm. It is an efficient collector, because the convective heat loss to the air in front of the plate is later recaptured when the boundary layer is sucked into the plenum (Gunnewiek et al., 1996). Owing
to this fact, radiation loss from the plate to the surroundings is the only important heat loss mechanism (Van Decker et al., 2001). So, under the steady state condition, energy balance is: Q_ in ¼ Q_ conv;useful þ Q_ rad;loss
ð6Þ
in which, Q_ in is the absorbed solar energy and defined as: Q_ in ¼ ac I s Ac
ð7Þ
where Is, ac and Ac are solar incident radiation, collector absorptivity and absorber area, respectively. Radiation loss from the collector can be expressed as: Q_ rad;loss ¼ ec rsb Ac T 4c T 41 ð8Þ in which ec is the absorber plate emissivity. As a reasonable approximation, one may assume that, ec = ac. Finally, the portion of energy absorbed by air is defined as: _ p ðT out T 1 Þ Q_ conv;useful ¼ mC
ð9Þ
In the absence of air flow ðQ_ conv;useful ¼ 0Þ, absorber plate reaches the maximum accessible temperature, Tmax, which can be derived as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 Is 4 4 ac I s Ac ¼ ec rsb Ac T max T 1 ! T max ¼ T 1 þ1 rsb T 41 ð10Þ The dimensionless form of temperature is defined by the ratio of temperature to ambient temperature, h ¼ TT1 . In this regard, maximum accessible absorber temperature may be defined as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Is 4 hmax ¼ þ1 ð11Þ rsb T 41 Combining Eq. (6) to Eq. (11), one has: _ pT 1 h4 h4 mC 4 max c ¼ ac I s Ac hmax 1 ðhout 1Þ
ð12Þ
A.A. Golneshan, H. Nemati / Solar Energy 107 (2014) 272–277
On the other hand, the collector 1st law efficiency may be defined as (Fleck et al., 2002): gI ¼
_ p ðT out T 1 Þ mC I s Ac
ð13Þ
So, using Eq. (12), the collector 1st law efficiency can be defined by dimensionless parameters as: 4 hmax h4c ac gI ¼ 4 ð14Þ hmax 1
ð15Þ
Considering that the effective sun temperature is 3=4 sun temperature as black body, Ts = 4500 K (Bejan et al., 1981). Useful exergy is the amount of increase in exergy level of air leaving collector. Assuming air as ideal gas with constant properties: T out _Exuseful ¼ mC _ p ðT out T 1 Þ mC _ p T 1 ln T1 ð17Þ
Ignoring the exergy losses due to fluid friction, exergy losses from the collector are due to collector reflection and collector emission, so:
Exergy loss due to reflection: _Exloss;ref ¼ I s Ac ð1 ac Þ 1 1 hs Exergy loss due to emission: _Exloss;em ¼ ec rsb Ac T 4 h4 1 hc 1 1 c hc
and finally, the 2nd law efficiency may be introduced as: gII ¼
_ useful mC _ p T 1 hout 1 lnðhout Þ Ex
¼ _ solar I s Ac Ex 1 1
ð24Þ
hs
Substituting from Eq. (13) or Eq. (14) in Eq. (24) yields: gII ¼
gI ac ½hout 1 lnðhout Þ
ðhout 1Þ 1 1 h4max
h4c
hs
ð25Þ
hs
Solar exergy may be introduced as (Dutta Gupta and Saha, 1990): _Exsolar ¼ I s Ac 1 T 1 ¼ I s Ac 1 1 ð16Þ hs Ts
_ loss ¼ Ex _ loss;ref þ Ex _ loss;em Ex
ð23Þ
ac ½hout 1 lnðhout Þ
¼ 4 hmax 1 ðhout 1Þ 1 1
The exergy balance for a UTC can be written as:
_ p T 1 ½hout 1 lnðhout Þ ¼ mC
hout 1 _ des;conv ¼ mC _ p T 1 lnðhout Þ Ex hc
3. Exergy analysis
_ solar Ex _ useful Ex _ loss Ex _ des ¼ 0 Ex
275
ð18Þ
ð19Þ
Introducing hc from Eq. (1): 4
h4max houte1 þ 1 ac ½ðh 1Þ lnðh Þ out
out gII ¼ 4 1 hmax 1 ðhout 1Þ 1
ð26Þ
hs
4. Collector optimization As a numerical example, it is assumed that T1 = 300 K, e = 0.7 and ac = 0.95. Figs. 3 and 4 show the variation of 1st law and 2nd law efficiency with respect to hout for various hmax. The optimum outlet temperature at which 2nd law efficiency is maximized also is shown on both figures. As it is clear from Fig. 4, there is a hout for which 2nd law efficiency reaches its maximum value. This maximum value can even reach 28%. Under this condition, the 1st law efficiency varies between 65% and 77%. Moreover, unlike 2nd law efficiency, no optimum outlet temperature may be expected based on 1st law efficiency, because the collector heat losses diminish only when the absorber temperature approaches to ambient temperature and, hc = hout = 1. Under this condition, the air outlet temperature is too cold to be usable. On the other hand, in the limiting case, the warmest temperature will be achieved when, hc = hmax in which, heat losses are maximized and collector efficiency approaches to zero.
ð20Þ
on the other hand, the exergy destruction may be divided into the followings: _ des ¼ Ex _ des;abs þ Ex _ des;conv Ex _ des;abs : Exergy destruction due to absorption, Ex _ des;abs ¼ I s Ac ac 1 1 Ex hc hs
ð21Þ
ð22Þ
Exergy destruction due to convection in finite tempera_ des;conv : ture, Ex
Fig. 3. The variation of 1st law efficiency with respect to hout for various hmax.
276
A.A. Golneshan, H. Nemati / Solar Energy 107 (2014) 272–277
Fig. 4. The variation of 2nd law efficiency with respect to hout for various hmax.
To explain the existence of an optimum temperature based on 2nd law efficiency, the dimensionless exergy losses and destructions are studied in detail. In this regard, dimensionless form of exergy losses and destructions may be presented as follows. Algebraic manipulations are omitted for brevity sake: _ loss;ref Ex
¼ ð1 ac Þ I s Ac 1 h1s _ loss;em ec h4c 1 ðhc 1Þ Ex
Bem ¼ ¼ I s Ac 1 h1s h4max 1 1 h1s hc 1 1 1 _ Babs ¼ Exdes;abs ¼ ac 1 hc hs hs Bref ¼
ð27Þ
exergy loss due to collector emission is low. While collector temperature increases, this exergy loss gets considerable. This behavior is in contrast with exergy destruction due to absorption, Babs. Temperature difference between incident radiation and collector is the reason of this exergy destruction and so, increasing the collector temperature decreases exergy destruction. The behavior of Bconv is basically different from the others. In low temperate condition in which, temperature difference between surface collector and air is low, Bconv is also low. Increasing the collector temperature amplifies the exergy destruction to a maximum value. However, as collector temperature approaches to its maximum value, hmax, the mass flow rate approaches to zero (based on Eq. (12)) and consequently, Bconv decreases again. Finally, the sum of all sources of exergy losses and destructions, Btotal, reaches a minimum value in that; the 2nd law efficiency is maximized. Although, there is a maximum value for 2nd law efficiency, no analytical solution may be found for optimum temperature. In this regard, the optimization was performed for 200 different cases over a wide range of hmax 6 4 and e 6 1. Based on the calculated results, the following simple but useful correlation was fitted with RMSE = 0.18%.
ð28Þ hout;Optimum ¼ 1 þ
0:575eðhmax 1Þ1:074 1 þ 0:0636eðhmax 1Þ
ð31Þ
ð29Þ
As an example, for a collector with e = 0.7, ac = 0.95 and hmax = 3, Eqs. (27)–(30) are shown in Fig. 5. It can be observed that Bref depends only on absorptivity and does not change with hc. In the case of high mass flow rate in which absorber temperature is relatively low, the
Contour plot of optimum outlet temperature based on hmax and e is shown in Fig. 6. It is a useful graph, since, it can be used to make a decision about the thermal effectiveness based on selected hmax and hout,Optimum where hmax depends only on the site condition. On the other hand, the required hout can be set as hout,Optimum and finally, by means of Fig. 6, one can select a proper effectiveness, e, in which collector efficiency is maximized. Based on economic consideration, geometrical parameters may be obtained. Proposed Eqs. (1)–(5) may be helpful in this regard. The important point about Eq. (32) is that it is based on dimensionless parameters such as hmax or e. Thermal effectiveness, in turn is a function of other dimensionless
Fig. 5. The variation of exergy losses and destructions with respect to hc.
Fig. 6. Contour plot of optimum dimensionless outlet temperature based on hmax and e.
Bconv
_ des;conv Ex
¼ I s Ac 1 h1s
ac h4max h4c ln½1 þ eðhc 1Þ eðhhc 1Þ c
¼ 4 1 hmax 1 eðhc 1Þ 1 hs
ð30Þ
A.A. Golneshan, H. Nemati / Solar Energy 107 (2014) 272–277
parameters. So, the proposed equation is a general rule regardless of site conditions or other parameters. 5. Numerical example As a numerical example, assume that ambient temperature is 283 K and it is required to have a UTC air heater with capacity of 7 m3/s at 310 K. Based on the geographical information it is found out that the amount of solar incident radiation is equal to 1000 W/m2 and the average wind velocity is U1 = 0.5 m/s. So, based on Eq. (11), hmax = 1.392. Now, the main question is that what the thermal effectiveness of collector should be. To answer to this question, one should consider the optimum outlet temperature hout,Optimum as required dimensionless outlet temperature, 310/283 = 1.095. Then, by means of Fig. 6 or Eq. (31), it is concluded that to have the maximum 2nd law efficiency, the collector thermal effectiveness should be equal to 0.457. The final step is to determine geometrical parameters based on economic considerations to have such effectiveness. For example, by means of Eq. (2), for Dt ¼ 1, c should be equal to 42.26 or for Dt ¼ 1:5, c should be equal to 34.5 and so on. The selection between different solutions returns to economic parameters. Suppose that based on economic parameters, manufacturing limitations or any other parameters, Dt ¼ 1:5 is preferable for which c = 34.5. To decrease the collector weight, the absorber thickness is usually less than 3 mm. Here, a 2 mm plate is selected as absorber. So, the hole diameter should be D = 1.5t = 3 mm. In the average temperature, 296.5 K, air thermo-physical properties are q = 1.19 kg/m3 and l = 1.8 105 Pa s. By means of Eqs. (4) and (5), Eq. (3) may be rearranged as: 0:737 1:482 2 Vs qV s 4P 2 pD c¼ ð32Þ U1 lpD 4P 2 Having 100 m2 available areas, the superficial suction veloc_ 7 ity is V s ¼ /A ¼ 100 m=s. So, the only unknown parameter in Eq. (32), P, is calculated to be 8.2 mm. As it can be observed during this example, the dimensionless form of parameters provides a valuable flexibility in collector design. 6. Conclusions In this paper, the exergy analysis was performed on UTC. Since UTC is effective equipment, it is very important
277
to know the optimal operating conditions. So, the optimum dimensionless outlet temperature was correlated based on two other important dimensionless parameters, hmax and e. Knowing hmax and hout, it remains just to justify about the geometrical parameters such as hole pitch or hole diameter based on economic parameters. Since all proposed parameters are dimensionless, the results are valid for all dimensional parameters and site conditions. References Arulanandam, S.J., 1995. A numerical investigation of unglazed transpired-plate solar collectors under zero-wind condition. M.Sc. Thesis, University of Waterloo, Canada. Bejan, A., Keary, D.W., Kreith, F., 1981. Second law analysis and synthesis of solar collector systems. J. Sol. Energy Eng. 103, 23–28. Dutta Gupta, K.K., Saha, S., 1990. Energy analysis of solar thermal collectors. Renew. Energy Environ. 103, 283–287. Fleck, B.A., Meier, R.M., Matovic´, M.D., 2002. A field study of the wind effects on the performance of an unglazed transpired solar collector. Sol. Energy 73 (3), 209–216. Golneshan, A.A., 1994. Forced convection heat transfer from a low porosity slotted transpired plate. Ph.D. Thesis, University of Waterloo, Canada. Golneshan, A.A., Hollands, K.G.T., 1998. Experiments on forced convection heat transfer from a slotted transpired plate. In: Proceeding of CMSE Forum 98, Toronto, Canada. Golneshan, A.A., Nemati, H., 2004. 3D numerical analysis of heat transfer from transpired perforated plates with circular holes arranged on square pitch. In: International Mechanical Engineering Conference, Kuwait, December 5–8, 2004. Gunnewiek, L.H., Brundrett, E., Hollands, K.G.T., 1996. Flow distribution in unglazed transpired solar air heaters of a large area. Sol. Energy 58, 227–237. Kutscher, C.F., 1992. An investigation of heat transfer for air flow through low porosity perforated plates. Ph.D. Thesis, University of Colorado, USA. Kutscher, C.F., 1994. Heat exchange effectiveness and pressure drop for air flow through perforated plate with and without crosswind. Trans. ASME J. Heat Transfer 116, 391–399. Kutscher, C.F., Christiansen, C.B., Barker, G.M., 1991. Unglazed transpired solar collectors: heat loss theory, solar engineering. In: Proc. 12th Annual ASME Int. Solar Energy Conf., Reno, Nevada, USA. Nemati, H., 2004. Numerical analysis of thermal performance of transpired plates, with circular holes, exposed to a parallel air flow with variable. Ph.D. Thesis, University of Shiraz, Iran. Van Decker, G.W.E., 1996. Asymptotic thermal effectiveness of unglazed transpired plate solar air heaters. Ph.D. Thesis, University of Waterloo, Canada. Van Decker, G.W.E., Hollands, K.G.T., Brunger, A.P., 2001. Heat exchange relation for unglazed transpired solar collectors with circular holes on a square or triangular pitch. Sol. Energy 71 (1), 33–45.
ScienceDirect Solar Energy 107 (2014) 272–277 www.elsevier.com/locate/solener
Exergy analysis of Unglazed Transpired Solar Collectors (UTCs) A.A. Golneshan a, H. Nemati b,⇑ b
a School of Mechanical Engineering, Shiraz University, Shiraz, Iran Department of Mechanics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
Received 10 November 2012; received in revised form 21 January 2014; accepted 22 April 2014 Available online 28 June 2014 Communicated by: Associate Editor Hans-Martin Henning
Abstract The Unglazed Transpired Solar Collector (UTC) is a suitable device for preheating outside air directly. They are used mostly in preheating ventilation air as well as in heating air for crop drying. The thermal performance of UTC promises its popular usage in near future. A number of large scale installations have been used all over the world since 1990s. In this study, first, the exergy efficiency of UTC is derived. Based on this efficiency, optimization was performed on 200 different cases and finally, a simple but useful correlation was proposed to predict the optimum working temperature. After finding the optimum working temperature, an economic analysis may be performed to determine the most effective and least expensive geometry. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: UTC; Exergy; Optimum temperature; Effectiveness
1. Introduction Unglazed Transpired Solar Collectors are now in use all over the world, mostly for preheating the ventilation air, crop drying and desiccant cooling. The installation and well operating performance of over 70 large systems, each having collector areas between 500 and 10,000 m2, have been reported (Van Decker et al., 2001). These air heaters are composed of a perforated plate, typically with porosity less than 5%, mostly painted black (absorber). They are mounted on the south wall of buildings to heat up outside ambient air as it is sucked through the perforations via a plenum, formed in the space between the plate and the south wall (Fig. 1). The solar energy absorbed by the plate will maintain the plate temperature above the ambient air temperature. A fan on the top of
⇑ Corresponding author.
E-mail address: [email protected] (H. Nemati). http://dx.doi.org/10.1016/j.solener.2014.04.025 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
the plenum collects the sucked heated air and distributes it through the ducts into the space. Although, the preliminary installations had a transparent cover to prevent convection losses against wind, it was found that these losses are negligible and the air heater experiences high performance without any glazing (Van Decker, 1996; Golneshan and Hollands, 1998; Kutscher, 1992; Golneshan and Nemati, 2004). This leads to save up to 40% of the total expenses and the solar air heating to be less expensive and more attractive (Arulanandam, 1995). Ambient air is heated as it passes over the absorber, through perforations as well as passing over the back of the absorber plate in the plenum. The performance of this type of collectors is usually expressed by thermal effectiveness and the first law efficiency. The thermal effectiveness is defined as: e¼
T out T 1 Tc T1
ð1Þ
A.A. Golneshan, H. Nemati / Solar Energy 107 (2014) 272–277
273
Nomenclature Ac absorber area (m2) B dimensionless exergy destruction or loss Cp specific heat (kJ/kg K) D hole diameter (m) _ Ex exergy (kW) Is solar incident radiation (kW) air mass flow rate in collector (kg/s) m_ P hole pitch (m) Q_ conv;useful thermal energy transferred to air from collector (kW) absorbed solar energy (kW) Q_ in Q_ rad;loss radiation loss from the collector (kW) ReD ¼ qVlh D hole Reynolds number T temperature qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(K) ffi T max ¼ T 1 4 r ITs 4 þ 1 maximum accessible surface sb
t U1 V h ¼ Vrs Vs
1
collector temperature, when m_ ¼ 0 absorber plate thickness (m) wind velocity on front side of collector (m/s) suction velocity in hole (m/s) suction velocity on front side of collector (m/s)
Greek letters ac absorber plate absorptivity c dimensionless parameter defined by Eq. (3)
where Tout is the air outlet temperature, T c is the mean collector temperature and T1 is the superficial ambient air temperature (Fig. 2). This thermal effectiveness depends on numbers of geometrical, hydrodynamic and thermal characteristics of the collectors. Several experimental and numerical studies have been done to estimate the thermal effectiveness of UTCs for various types of perforations. Kutscher et al. (1991) proposed an analytical model and heat loss theory for UTCs experiencing continuous suction. He also performed some
e effectiveness defined by Eq. (1) ec absorber plate emissivity gI 1st law efficiency defined by Eq. (13) gII 2nd law efficiency h ¼ TT1 dimensionless temperature hmax ¼ TTmax maximum accessible dimensionless collector 1 temperature, when m_ ¼ 0 l air viscosity (kg/m s) q air density (kg/m3) r ¼ Ahole =Aplate collector porosity rsb Stefan–Boltzmann constant (5.67 1011 2 4 kW/m K ) volumetric flow rate (m3/s) /_ Subscript 1 ambient abs absorption c collector surface, absorber conv convection des destruction em emission out outlet ref reflection s sun, solar
experiments to investigate the performance of a UTC with 0.79 mm thick aluminum plates with circular holes on staggered layout (Kutscher et al., 1991; Kutscher, 1992, 1994). Golneshan (1994) and Golneshan and Hollands (1998) did an extensive experimental work on slot type collectors. Arulanandam (1995) was the first who modeled the effectiveness of UTCs in no-wind condition, with circular holes arranged on a square pitch (same as Fig. 2), using a commercial numerical code; TASKflow. Van Decker (1996) and Van Decker et al. (2001) worked experimentally on the performance of UTCs with circular holes, and presented an empirical correlation to predict the thermal effectiveness of such plates. Nemati (2004) and Golneshan and Nemati (2004) investigated the effect of wind direction on the performance of UTCs. They proposed a correlation to predict the thermal effectiveness of UTCs with circular holes on both staggered and aligned layout for various wind direction. For the aligned layout, Nemati (2004) proposed the following simple correlation with RMSE = 4.7%: rffiffiffiffi!0:161 D e ¼ 0:835 c t
Fig. 1. A section view of a typical UTC, air is sucked through the perforations and gets warm.
c¼
Vs U1
0:737
Re1:482 r D
ð2Þ
ð3Þ
274
A.A. Golneshan, H. Nemati / Solar Energy 107 (2014) 272–277
Fig. 2. A simplified view of absorber.
in which Vs is the superficial suction velocity on front side of the plate, U1 is wind velocity and r is the plate porosity and is defined as: r¼
Ahole pD2 =4 ¼ Aplate P2
ð4Þ
where P and D are the hole pitch and diameter, respectively. ReD is based on the air velocity in hole which is defined as: Vh ¼
Vs r
ð5Þ
He also showed that the correlations developed for aligned layout can be employed to predict the staggered layout cases if one multiplies hole pitch by 0.5. In addition to all above efforts in prediction of thermal effectiveness of UTC, based on Eq. (1), it is clear that the unity of effectiveness does not mean the optimum working condition. To determine the optimum working condition, exergy analysis should be performed. In the ensuing parts, the exergy balance is performed to determine exergy destruction and 2nd law efficiency of UTCs and then optimization is done over 200 different cases for a vast working condition to determine the best working temperature, based on effectiveness and some other dimensionless parameters. Knowing the best working temperature for the assumed effectiveness, it is only required to perform economic analysis to determine geometrical parameters such as hole diameter, hole pitch and so on, to meet the assumed effectiveness. 2. Energy analysis In this collector, the incident solar beam radiation is absorbed by a perforated plate while air is sucking in, through the perforations. Sucked air sweeps absorbed heat from the absorber plate and gets warm. It is an efficient collector, because the convective heat loss to the air in front of the plate is later recaptured when the boundary layer is sucked into the plenum (Gunnewiek et al., 1996). Owing
to this fact, radiation loss from the plate to the surroundings is the only important heat loss mechanism (Van Decker et al., 2001). So, under the steady state condition, energy balance is: Q_ in ¼ Q_ conv;useful þ Q_ rad;loss
ð6Þ
in which, Q_ in is the absorbed solar energy and defined as: Q_ in ¼ ac I s Ac
ð7Þ
where Is, ac and Ac are solar incident radiation, collector absorptivity and absorber area, respectively. Radiation loss from the collector can be expressed as: Q_ rad;loss ¼ ec rsb Ac T 4c T 41 ð8Þ in which ec is the absorber plate emissivity. As a reasonable approximation, one may assume that, ec = ac. Finally, the portion of energy absorbed by air is defined as: _ p ðT out T 1 Þ Q_ conv;useful ¼ mC
ð9Þ
In the absence of air flow ðQ_ conv;useful ¼ 0Þ, absorber plate reaches the maximum accessible temperature, Tmax, which can be derived as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 Is 4 4 ac I s Ac ¼ ec rsb Ac T max T 1 ! T max ¼ T 1 þ1 rsb T 41 ð10Þ The dimensionless form of temperature is defined by the ratio of temperature to ambient temperature, h ¼ TT1 . In this regard, maximum accessible absorber temperature may be defined as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Is 4 hmax ¼ þ1 ð11Þ rsb T 41 Combining Eq. (6) to Eq. (11), one has: _ pT 1 h4 h4 mC 4 max c ¼ ac I s Ac hmax 1 ðhout 1Þ
ð12Þ
A.A. Golneshan, H. Nemati / Solar Energy 107 (2014) 272–277
On the other hand, the collector 1st law efficiency may be defined as (Fleck et al., 2002): gI ¼
_ p ðT out T 1 Þ mC I s Ac
ð13Þ
So, using Eq. (12), the collector 1st law efficiency can be defined by dimensionless parameters as: 4 hmax h4c ac gI ¼ 4 ð14Þ hmax 1
ð15Þ
Considering that the effective sun temperature is 3=4 sun temperature as black body, Ts = 4500 K (Bejan et al., 1981). Useful exergy is the amount of increase in exergy level of air leaving collector. Assuming air as ideal gas with constant properties: T out _Exuseful ¼ mC _ p ðT out T 1 Þ mC _ p T 1 ln T1 ð17Þ
Ignoring the exergy losses due to fluid friction, exergy losses from the collector are due to collector reflection and collector emission, so:
Exergy loss due to reflection: _Exloss;ref ¼ I s Ac ð1 ac Þ 1 1 hs Exergy loss due to emission: _Exloss;em ¼ ec rsb Ac T 4 h4 1 hc 1 1 c hc
and finally, the 2nd law efficiency may be introduced as: gII ¼
_ useful mC _ p T 1 hout 1 lnðhout Þ Ex
¼ _ solar I s Ac Ex 1 1
ð24Þ
hs
Substituting from Eq. (13) or Eq. (14) in Eq. (24) yields: gII ¼
gI ac ½hout 1 lnðhout Þ
ðhout 1Þ 1 1 h4max
h4c
hs
ð25Þ
hs
Solar exergy may be introduced as (Dutta Gupta and Saha, 1990): _Exsolar ¼ I s Ac 1 T 1 ¼ I s Ac 1 1 ð16Þ hs Ts
_ loss ¼ Ex _ loss;ref þ Ex _ loss;em Ex
ð23Þ
ac ½hout 1 lnðhout Þ
¼ 4 hmax 1 ðhout 1Þ 1 1
The exergy balance for a UTC can be written as:
_ p T 1 ½hout 1 lnðhout Þ ¼ mC
hout 1 _ des;conv ¼ mC _ p T 1 lnðhout Þ Ex hc
3. Exergy analysis
_ solar Ex _ useful Ex _ loss Ex _ des ¼ 0 Ex
275
ð18Þ
ð19Þ
Introducing hc from Eq. (1): 4
h4max houte1 þ 1 ac ½ðh 1Þ lnðh Þ out
out gII ¼ 4 1 hmax 1 ðhout 1Þ 1
ð26Þ
hs
4. Collector optimization As a numerical example, it is assumed that T1 = 300 K, e = 0.7 and ac = 0.95. Figs. 3 and 4 show the variation of 1st law and 2nd law efficiency with respect to hout for various hmax. The optimum outlet temperature at which 2nd law efficiency is maximized also is shown on both figures. As it is clear from Fig. 4, there is a hout for which 2nd law efficiency reaches its maximum value. This maximum value can even reach 28%. Under this condition, the 1st law efficiency varies between 65% and 77%. Moreover, unlike 2nd law efficiency, no optimum outlet temperature may be expected based on 1st law efficiency, because the collector heat losses diminish only when the absorber temperature approaches to ambient temperature and, hc = hout = 1. Under this condition, the air outlet temperature is too cold to be usable. On the other hand, in the limiting case, the warmest temperature will be achieved when, hc = hmax in which, heat losses are maximized and collector efficiency approaches to zero.
ð20Þ
on the other hand, the exergy destruction may be divided into the followings: _ des ¼ Ex _ des;abs þ Ex _ des;conv Ex _ des;abs : Exergy destruction due to absorption, Ex _ des;abs ¼ I s Ac ac 1 1 Ex hc hs
ð21Þ
ð22Þ
Exergy destruction due to convection in finite tempera_ des;conv : ture, Ex
Fig. 3. The variation of 1st law efficiency with respect to hout for various hmax.
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Fig. 4. The variation of 2nd law efficiency with respect to hout for various hmax.
To explain the existence of an optimum temperature based on 2nd law efficiency, the dimensionless exergy losses and destructions are studied in detail. In this regard, dimensionless form of exergy losses and destructions may be presented as follows. Algebraic manipulations are omitted for brevity sake: _ loss;ref Ex
¼ ð1 ac Þ I s Ac 1 h1s _ loss;em ec h4c 1 ðhc 1Þ Ex
Bem ¼ ¼ I s Ac 1 h1s h4max 1 1 h1s hc 1 1 1 _ Babs ¼ Exdes;abs ¼ ac 1 hc hs hs Bref ¼
ð27Þ
exergy loss due to collector emission is low. While collector temperature increases, this exergy loss gets considerable. This behavior is in contrast with exergy destruction due to absorption, Babs. Temperature difference between incident radiation and collector is the reason of this exergy destruction and so, increasing the collector temperature decreases exergy destruction. The behavior of Bconv is basically different from the others. In low temperate condition in which, temperature difference between surface collector and air is low, Bconv is also low. Increasing the collector temperature amplifies the exergy destruction to a maximum value. However, as collector temperature approaches to its maximum value, hmax, the mass flow rate approaches to zero (based on Eq. (12)) and consequently, Bconv decreases again. Finally, the sum of all sources of exergy losses and destructions, Btotal, reaches a minimum value in that; the 2nd law efficiency is maximized. Although, there is a maximum value for 2nd law efficiency, no analytical solution may be found for optimum temperature. In this regard, the optimization was performed for 200 different cases over a wide range of hmax 6 4 and e 6 1. Based on the calculated results, the following simple but useful correlation was fitted with RMSE = 0.18%.
ð28Þ hout;Optimum ¼ 1 þ
0:575eðhmax 1Þ1:074 1 þ 0:0636eðhmax 1Þ
ð31Þ
ð29Þ
As an example, for a collector with e = 0.7, ac = 0.95 and hmax = 3, Eqs. (27)–(30) are shown in Fig. 5. It can be observed that Bref depends only on absorptivity and does not change with hc. In the case of high mass flow rate in which absorber temperature is relatively low, the
Contour plot of optimum outlet temperature based on hmax and e is shown in Fig. 6. It is a useful graph, since, it can be used to make a decision about the thermal effectiveness based on selected hmax and hout,Optimum where hmax depends only on the site condition. On the other hand, the required hout can be set as hout,Optimum and finally, by means of Fig. 6, one can select a proper effectiveness, e, in which collector efficiency is maximized. Based on economic consideration, geometrical parameters may be obtained. Proposed Eqs. (1)–(5) may be helpful in this regard. The important point about Eq. (32) is that it is based on dimensionless parameters such as hmax or e. Thermal effectiveness, in turn is a function of other dimensionless
Fig. 5. The variation of exergy losses and destructions with respect to hc.
Fig. 6. Contour plot of optimum dimensionless outlet temperature based on hmax and e.
Bconv
_ des;conv Ex
¼ I s Ac 1 h1s
ac h4max h4c ln½1 þ eðhc 1Þ eðhhc 1Þ c
¼ 4 1 hmax 1 eðhc 1Þ 1 hs
ð30Þ
A.A. Golneshan, H. Nemati / Solar Energy 107 (2014) 272–277
parameters. So, the proposed equation is a general rule regardless of site conditions or other parameters. 5. Numerical example As a numerical example, assume that ambient temperature is 283 K and it is required to have a UTC air heater with capacity of 7 m3/s at 310 K. Based on the geographical information it is found out that the amount of solar incident radiation is equal to 1000 W/m2 and the average wind velocity is U1 = 0.5 m/s. So, based on Eq. (11), hmax = 1.392. Now, the main question is that what the thermal effectiveness of collector should be. To answer to this question, one should consider the optimum outlet temperature hout,Optimum as required dimensionless outlet temperature, 310/283 = 1.095. Then, by means of Fig. 6 or Eq. (31), it is concluded that to have the maximum 2nd law efficiency, the collector thermal effectiveness should be equal to 0.457. The final step is to determine geometrical parameters based on economic considerations to have such effectiveness. For example, by means of Eq. (2), for Dt ¼ 1, c should be equal to 42.26 or for Dt ¼ 1:5, c should be equal to 34.5 and so on. The selection between different solutions returns to economic parameters. Suppose that based on economic parameters, manufacturing limitations or any other parameters, Dt ¼ 1:5 is preferable for which c = 34.5. To decrease the collector weight, the absorber thickness is usually less than 3 mm. Here, a 2 mm plate is selected as absorber. So, the hole diameter should be D = 1.5t = 3 mm. In the average temperature, 296.5 K, air thermo-physical properties are q = 1.19 kg/m3 and l = 1.8 105 Pa s. By means of Eqs. (4) and (5), Eq. (3) may be rearranged as: 0:737 1:482 2 Vs qV s 4P 2 pD c¼ ð32Þ U1 lpD 4P 2 Having 100 m2 available areas, the superficial suction veloc_ 7 ity is V s ¼ /A ¼ 100 m=s. So, the only unknown parameter in Eq. (32), P, is calculated to be 8.2 mm. As it can be observed during this example, the dimensionless form of parameters provides a valuable flexibility in collector design. 6. Conclusions In this paper, the exergy analysis was performed on UTC. Since UTC is effective equipment, it is very important
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to know the optimal operating conditions. So, the optimum dimensionless outlet temperature was correlated based on two other important dimensionless parameters, hmax and e. Knowing hmax and hout, it remains just to justify about the geometrical parameters such as hole pitch or hole diameter based on economic parameters. Since all proposed parameters are dimensionless, the results are valid for all dimensional parameters and site conditions. References Arulanandam, S.J., 1995. A numerical investigation of unglazed transpired-plate solar collectors under zero-wind condition. M.Sc. Thesis, University of Waterloo, Canada. Bejan, A., Keary, D.W., Kreith, F., 1981. Second law analysis and synthesis of solar collector systems. J. Sol. Energy Eng. 103, 23–28. Dutta Gupta, K.K., Saha, S., 1990. Energy analysis of solar thermal collectors. Renew. Energy Environ. 103, 283–287. Fleck, B.A., Meier, R.M., Matovic´, M.D., 2002. A field study of the wind effects on the performance of an unglazed transpired solar collector. Sol. Energy 73 (3), 209–216. Golneshan, A.A., 1994. Forced convection heat transfer from a low porosity slotted transpired plate. Ph.D. Thesis, University of Waterloo, Canada. Golneshan, A.A., Hollands, K.G.T., 1998. Experiments on forced convection heat transfer from a slotted transpired plate. In: Proceeding of CMSE Forum 98, Toronto, Canada. Golneshan, A.A., Nemati, H., 2004. 3D numerical analysis of heat transfer from transpired perforated plates with circular holes arranged on square pitch. In: International Mechanical Engineering Conference, Kuwait, December 5–8, 2004. Gunnewiek, L.H., Brundrett, E., Hollands, K.G.T., 1996. Flow distribution in unglazed transpired solar air heaters of a large area. Sol. Energy 58, 227–237. Kutscher, C.F., 1992. An investigation of heat transfer for air flow through low porosity perforated plates. Ph.D. Thesis, University of Colorado, USA. Kutscher, C.F., 1994. Heat exchange effectiveness and pressure drop for air flow through perforated plate with and without crosswind. Trans. ASME J. Heat Transfer 116, 391–399. Kutscher, C.F., Christiansen, C.B., Barker, G.M., 1991. Unglazed transpired solar collectors: heat loss theory, solar engineering. In: Proc. 12th Annual ASME Int. Solar Energy Conf., Reno, Nevada, USA. Nemati, H., 2004. Numerical analysis of thermal performance of transpired plates, with circular holes, exposed to a parallel air flow with variable. Ph.D. Thesis, University of Shiraz, Iran. Van Decker, G.W.E., 1996. Asymptotic thermal effectiveness of unglazed transpired plate solar air heaters. Ph.D. Thesis, University of Waterloo, Canada. Van Decker, G.W.E., Hollands, K.G.T., Brunger, A.P., 2001. Heat exchange relation for unglazed transpired solar collectors with circular holes on a square or triangular pitch. Sol. Energy 71 (1), 33–45.