- Email: [email protected]
Comments on “available solar energy in an absorption cooling process”
Pergamon
PII: SOO3&092X(97) 00024-8
Solar Energy Vol. 61, No. 1, pp. 61-64, 1997 0 1997 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0038-092X/97 $17.00 + 0.00
LETTER TO THE EDITOR Comments on ‘Z4vailablesolar energy in an absorption cooling process” [M. Izquierdo Millan, F. Hernandez and E. Martin Solar Energy 56(6), 505-511( 1996)]
of these formulae is appropriate. Note that a discussion of the Petela-Press-Landsberg and Mallinson and Spanner formulae was made in the case of the conversion of both direct and diffuse solar radiation in Badescu (1989b). 4. Equation (5) from Izquierdo et al. (1996) proposed by Parrott (1978) is in need of correction (Parrott, 1979). When the correction is made this equation reduces to the present eqn (1). A main objective of any (solar) energy conversion theory is to estimate upper bounds for the effective performance of the converter. There are two ways of increasing the accuracy of the predicted performance: (i) to include in the model the most relevant processes involved and (ii) to take into account in an appropriate manner the irreversibilities of these processes. From this point of view the model developed by the authors took into consideration a number of effects meant to increase the accuracy of their estimated performance as compared to those obtained by using the three simple formulae above (which predict upper bounds around 94%, being of little help for actual practical applications). So, they included formally the effects of heat capacitance and convective losses and treated quantitatively the influence of other phenomena like the radiation absorption by the atmosphere or the fact that in practice solar radiation is a mixture of direct and diffuse radiation and it is not fully-concentrated (at the level of Earth orbit, fully-concentration means a concentration ratio around 46,200). Some (or all) of these effects were included and analyzed in models developed by other authors: (a) The effect of the heat capacitance was included formally in works such as Landsberg and Tonge (1980), Landsberg and Baruch (1989) and Badescu (1992) and treated quantitatively in Bejan (1988). (b) The effect of the convective losses was analyzed by Howell and Bannerot (1977) and Badescu (1991b) among others.
The authors presented a new model for the conversion of solar energy into work. There is now considerable literature on this subject and Izquierdo et al. (1996) used and/or referred to part of it. We think, however, that a number of comments and additions could be useful for readers of the quoted paper. 1. The authors attribute to Press (1976) the upper bound formula eqn (4) for the conversion of solar energy into available work (exergy). The history of this equation, which we remind for convenience:
(1) (T, - ambient temperature, T,,, - sun’s temperature) is more complicated. It was first derived by Petela (1964) and independently by Landsberg and Mallinson (1976) and Press (1976). As a consequence, it is sometimes called the Landsberg efficiency (De Vos et al., 1993), the Petela-Landsberg upper bound (Badescu, 1991a), or, more appropriately, the PetelaPress-Landsberg and Mallinson formula (Bejan, 1988, p. 496). 2. The Carnot factor (eqn (6) of Izquierdo et al. (1996)): rlcarnot= 1- +
(2) a was, indeed, applied by Jetter (1981). However, it was previously applied by using flux temperatures in Landsberg and Tonge (1980) (their eqn (3.5)). 3. Apart from the two efficiencies quoted in Izquierdo et al. (1996) (present eqn (1) and eqn (2)) another upper bound formula, first derived by Spanner (1964), is (3) A detailed criticism of these three formulae was already made by Landsberg and Tonge (1980), Bejan (1987) and Bejan (1988). Also, the model from Badescu (1992) allows to decide when each 61
Letter to the Editor
62
(c) The combined effect of solar direct and diffuse radiation was taken into account by many authors including Howell and Bannerot (1977) and Badescu (1991b). (d) Previous studies (see e.g. Badescu, 1989a, Badescu, 1991~) proved that when low concentration or unconcentrated radiation is considered the maximum conversion efficiency is as small as that obtained by Izquierdo et al. (1996). As an example, the best performance predicted by the last authors is a maximum hourly value of solar exergy efficiency of 4.75% (obtained on 29 July 1993 at 12 a.m. for an ambient temperature 311.1 K and a mean incident flux of global solar radiation 3.62 MJ/m’/h = 1005 W/m’; see their Tables 1 and 2). If one assumes a solar constant 1367 W/m2 one obtains an atmospheric transmittance r = 1005.5/1367 = 0.736. Solar global radiation is a mixture of diffuse and direct radiation. The maximum efficiency for the conversion of diffuse radiation was found to be 5.3% (eqn (22) of Badescu (1991~)) for an atmospheric transmittance z= 1 and is surely smaller in the case we studied here. On the other hand, from Fig. l(a) of Badescu (1989a) one obtains for r = 0.736 a maximum efficiency for the conversion of direct radiation around 7%.
REFERENCES Badescu V. (1989a) The theoretical maximum efficiency of Energy solar converters with and without concentration. 14(4), 237-239. Badescu V. (1989b) On the theoretical maximum efficiency of solar-radiation utilization. Energy 14(9), 571-573. Badescu V. (1991a) Maximum conversion efficiency for the utilization of multiply scattered solar radiation. J. Phys. D 24, 1882-1885. Badescu V. (1991b) Note concerning the maximal efficiency and the optimal operating temperature of solar convertRenewable Energy ers with or without concentration. l(l), 131-135. Badescu V. (1991~) Maximum conversion efficiency for the utilization of diffuse radiation. Energy 16(4), 783-786. Badescu V. (1992) Thermodynamics of the conversion of partially-polarized black-body radiation. J. Phys. III France 2, 1925-1941. Bejan A. (1987) Unification of three different theories concerning the ideal conversion of enclosed radiation. J. Solar Energy Eng. 109,46-51. Bejan A. (1988) Advanced Engineering Thermodynamics. Wiley, New York, Chap. 9. Howell J. R. and Bannerot R. B. (1977) Optimum solar collector operation for maximizing cycle work output. Solar Energy 19, 149-153. Izquierdo M., Hernandez F. and Martin E. (1996) Available solar energy in an absorption cooling process. Solar Energy 56(6), 505-511. Jetter 3. (1981) Maximum conversion efficiency for the utilization of direct solar radiation. Solar Energy 26,231-236.
Landsberg P. T. and Mallinson J. R. (1976) Thermodynamic Constraints. Effective Temperatures and Solar Cells. CNES, Toulouse, pp. 27-46. Landsberg P. T. and Tonge G. (1980) Thermodynamic energy conversion efficiencies. J. Appl. Phys. 51(7), Rl-R20. Landsberg P. T. and Baruch P. (1989) The thermodynamics of the conversion of radiation energy for photovoltaics. J. Phys. A 22, 1911-1926. Parrott J. E. (1978) Theoretical upper limit to the conversion efficiencv of solar energy. Solar Enerav 21, 227-229. Parrott J. E. (1979) Lette;-to the Editor: Solar Energy 22, 572-573. Petela R. (1964) Energy of heat radiation. J. Heat Transfer 86, 187-192. Press W. H. (1976) Theoretical maximum for energy from direct and diffuse sunlight. Nature 264, 734-735. Spanner D. C. (1964) Introduction to Thermodynamics. Academic Press, London, p. 218.
VIOREL BADESCU ISES Member Candida Oancea institute of Solar Energy Faculty of Mechanical Engineering Polytechnic University of Bucharest Spl Independentai 313, Bucharest, Romania Email: [email protected]
Author’s reply.. . Thank you for your letter dated 11/l l/96 which contained comments on our paper Available solar exergy in an absorption cooling process by M. Izquierdo Millan, F. Hernandez and E. Martin (Solar Energy 56 (6) 505-511 (1996)). We would like to express our appreciation to Dr Badescu for the interest shown in our work. We were pleased with the tone of his letter as well as the discussion topics which he mentioned. Concerning the extensive bibliographic references provided by Dr Badescu, we would like to point out the fact that some of the foregoing were not taken into account in our work. Nevertheless, let it be known that we have made an effort to synthesize throughout the paper, especially in the introduction. Despite the high scientific value of the references provided by Dr Badescu, some of them have escaped our attention and we would like to express our apologies to him and to the readers for this. Nevertheless, some of his references are indeed included in our work. Further to the comments in the aforementioned letter, we would like to point out the following: COMMENT No 1. We agree with Dr Badescu. Our paper included all references except for Petela (1964) and Badescu (1991a). For exam-
PII: SOO3&092X(97) 00024-8
Solar Energy Vol. 61, No. 1, pp. 61-64, 1997 0 1997 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0038-092X/97 $17.00 + 0.00
LETTER TO THE EDITOR Comments on ‘Z4vailablesolar energy in an absorption cooling process” [M. Izquierdo Millan, F. Hernandez and E. Martin Solar Energy 56(6), 505-511( 1996)]
of these formulae is appropriate. Note that a discussion of the Petela-Press-Landsberg and Mallinson and Spanner formulae was made in the case of the conversion of both direct and diffuse solar radiation in Badescu (1989b). 4. Equation (5) from Izquierdo et al. (1996) proposed by Parrott (1978) is in need of correction (Parrott, 1979). When the correction is made this equation reduces to the present eqn (1). A main objective of any (solar) energy conversion theory is to estimate upper bounds for the effective performance of the converter. There are two ways of increasing the accuracy of the predicted performance: (i) to include in the model the most relevant processes involved and (ii) to take into account in an appropriate manner the irreversibilities of these processes. From this point of view the model developed by the authors took into consideration a number of effects meant to increase the accuracy of their estimated performance as compared to those obtained by using the three simple formulae above (which predict upper bounds around 94%, being of little help for actual practical applications). So, they included formally the effects of heat capacitance and convective losses and treated quantitatively the influence of other phenomena like the radiation absorption by the atmosphere or the fact that in practice solar radiation is a mixture of direct and diffuse radiation and it is not fully-concentrated (at the level of Earth orbit, fully-concentration means a concentration ratio around 46,200). Some (or all) of these effects were included and analyzed in models developed by other authors: (a) The effect of the heat capacitance was included formally in works such as Landsberg and Tonge (1980), Landsberg and Baruch (1989) and Badescu (1992) and treated quantitatively in Bejan (1988). (b) The effect of the convective losses was analyzed by Howell and Bannerot (1977) and Badescu (1991b) among others.
The authors presented a new model for the conversion of solar energy into work. There is now considerable literature on this subject and Izquierdo et al. (1996) used and/or referred to part of it. We think, however, that a number of comments and additions could be useful for readers of the quoted paper. 1. The authors attribute to Press (1976) the upper bound formula eqn (4) for the conversion of solar energy into available work (exergy). The history of this equation, which we remind for convenience:
(1) (T, - ambient temperature, T,,, - sun’s temperature) is more complicated. It was first derived by Petela (1964) and independently by Landsberg and Mallinson (1976) and Press (1976). As a consequence, it is sometimes called the Landsberg efficiency (De Vos et al., 1993), the Petela-Landsberg upper bound (Badescu, 1991a), or, more appropriately, the PetelaPress-Landsberg and Mallinson formula (Bejan, 1988, p. 496). 2. The Carnot factor (eqn (6) of Izquierdo et al. (1996)): rlcarnot= 1- +
(2) a was, indeed, applied by Jetter (1981). However, it was previously applied by using flux temperatures in Landsberg and Tonge (1980) (their eqn (3.5)). 3. Apart from the two efficiencies quoted in Izquierdo et al. (1996) (present eqn (1) and eqn (2)) another upper bound formula, first derived by Spanner (1964), is (3) A detailed criticism of these three formulae was already made by Landsberg and Tonge (1980), Bejan (1987) and Bejan (1988). Also, the model from Badescu (1992) allows to decide when each 61
Letter to the Editor
62
(c) The combined effect of solar direct and diffuse radiation was taken into account by many authors including Howell and Bannerot (1977) and Badescu (1991b). (d) Previous studies (see e.g. Badescu, 1989a, Badescu, 1991~) proved that when low concentration or unconcentrated radiation is considered the maximum conversion efficiency is as small as that obtained by Izquierdo et al. (1996). As an example, the best performance predicted by the last authors is a maximum hourly value of solar exergy efficiency of 4.75% (obtained on 29 July 1993 at 12 a.m. for an ambient temperature 311.1 K and a mean incident flux of global solar radiation 3.62 MJ/m’/h = 1005 W/m’; see their Tables 1 and 2). If one assumes a solar constant 1367 W/m2 one obtains an atmospheric transmittance r = 1005.5/1367 = 0.736. Solar global radiation is a mixture of diffuse and direct radiation. The maximum efficiency for the conversion of diffuse radiation was found to be 5.3% (eqn (22) of Badescu (1991~)) for an atmospheric transmittance z= 1 and is surely smaller in the case we studied here. On the other hand, from Fig. l(a) of Badescu (1989a) one obtains for r = 0.736 a maximum efficiency for the conversion of direct radiation around 7%.
REFERENCES Badescu V. (1989a) The theoretical maximum efficiency of Energy solar converters with and without concentration. 14(4), 237-239. Badescu V. (1989b) On the theoretical maximum efficiency of solar-radiation utilization. Energy 14(9), 571-573. Badescu V. (1991a) Maximum conversion efficiency for the utilization of multiply scattered solar radiation. J. Phys. D 24, 1882-1885. Badescu V. (1991b) Note concerning the maximal efficiency and the optimal operating temperature of solar convertRenewable Energy ers with or without concentration. l(l), 131-135. Badescu V. (1991~) Maximum conversion efficiency for the utilization of diffuse radiation. Energy 16(4), 783-786. Badescu V. (1992) Thermodynamics of the conversion of partially-polarized black-body radiation. J. Phys. III France 2, 1925-1941. Bejan A. (1987) Unification of three different theories concerning the ideal conversion of enclosed radiation. J. Solar Energy Eng. 109,46-51. Bejan A. (1988) Advanced Engineering Thermodynamics. Wiley, New York, Chap. 9. Howell J. R. and Bannerot R. B. (1977) Optimum solar collector operation for maximizing cycle work output. Solar Energy 19, 149-153. Izquierdo M., Hernandez F. and Martin E. (1996) Available solar energy in an absorption cooling process. Solar Energy 56(6), 505-511. Jetter 3. (1981) Maximum conversion efficiency for the utilization of direct solar radiation. Solar Energy 26,231-236.
Landsberg P. T. and Mallinson J. R. (1976) Thermodynamic Constraints. Effective Temperatures and Solar Cells. CNES, Toulouse, pp. 27-46. Landsberg P. T. and Tonge G. (1980) Thermodynamic energy conversion efficiencies. J. Appl. Phys. 51(7), Rl-R20. Landsberg P. T. and Baruch P. (1989) The thermodynamics of the conversion of radiation energy for photovoltaics. J. Phys. A 22, 1911-1926. Parrott J. E. (1978) Theoretical upper limit to the conversion efficiencv of solar energy. Solar Enerav 21, 227-229. Parrott J. E. (1979) Lette;-to the Editor: Solar Energy 22, 572-573. Petela R. (1964) Energy of heat radiation. J. Heat Transfer 86, 187-192. Press W. H. (1976) Theoretical maximum for energy from direct and diffuse sunlight. Nature 264, 734-735. Spanner D. C. (1964) Introduction to Thermodynamics. Academic Press, London, p. 218.
VIOREL BADESCU ISES Member Candida Oancea institute of Solar Energy Faculty of Mechanical Engineering Polytechnic University of Bucharest Spl Independentai 313, Bucharest, Romania Email: [email protected]
Author’s reply.. . Thank you for your letter dated 11/l l/96 which contained comments on our paper Available solar exergy in an absorption cooling process by M. Izquierdo Millan, F. Hernandez and E. Martin (Solar Energy 56 (6) 505-511 (1996)). We would like to express our appreciation to Dr Badescu for the interest shown in our work. We were pleased with the tone of his letter as well as the discussion topics which he mentioned. Concerning the extensive bibliographic references provided by Dr Badescu, we would like to point out the fact that some of the foregoing were not taken into account in our work. Nevertheless, let it be known that we have made an effort to synthesize throughout the paper, especially in the introduction. Despite the high scientific value of the references provided by Dr Badescu, some of them have escaped our attention and we would like to express our apologies to him and to the readers for this. Nevertheless, some of his references are indeed included in our work. Further to the comments in the aforementioned letter, we would like to point out the following: COMMENT No 1. We agree with Dr Badescu. Our paper included all references except for Petela (1964) and Badescu (1991a). For exam-