ANALYSIS OF EXERGY OF MOIST AIR AND ENERGY SAVING POTENTIAL IN HVAC BY EVAPORATIVE COOLING OR ENERGY RECOVERY

, Volume 2, Number 4, p.113-117, 2001 ANALYSIS OF EXERGY OF MOIST AIR AND ENERGY SAVING POTENTIAL IN HVAC BY EVAPORATIVE COOLING OR ENERGY RECOVERY C.Q. Ren, G.F. Tang, N.P. Li, G.F. Zhang and J. Yang College of Mechanical and Automotive Engineering Hunan University, Changsha, Hunan, People s Republic of China (Received 24 July 2001; Accepted 24 October 2001) ABSTRACT Of evaporative cooling or energy recovery potential in HVAC, the conventional thermodynamic analysis is based on the enthalpy of moist air. In fact, the available energy of moist air is its exergy and the available energy saving potential ought to be the exergy. Isoexergic lines on psychometric charts associated with different ambient states persuade us that exergy and enthalpy are completely independent of each other. Thus, the enthalpy analysis is at least imperfect. Selecting the saturated state of moist air at ambient temperature (T 0 ) and pressure (p 0 ) as the dead-state, this paper analyses the exergy of moist air. It is broken down into three components: thermal, mechanical and chemical, so that each of them may be represented with a special devised diagram applicable to various conditions and ambient states among HVAC applications. Two guidelines for such applications are extracted from the diagrams as these: lower dead-state temperature (T 0 ) with the same difference of the humidity ratio (ω - ω 0S ) is related with higher chemical exergy, and hence, the recovery of latent heat availability will probably be more valuable in winter than in summer; the exergy loss due to air flow resistance in a heat exchanger is usually small when compared with the potential of thermal and chemical exergy gaining. Further, the exergies of outdoor and exhaust room air are calculated and tabled for some Chinese cities and different types of air conditioning based on some statistic average parameters. Some general conclusions are drawn. For most districts on average room air parameters, the exhaust room air exergy is greater in winter than in summer. In winter, when exhaust room air temperature is low, the exergy of sensible heat is the main component of available energy saving potential. On contrast, the latent heat usually makes the prevailing contribution in summer, while at some dry locations, the exergy of outdoor air is even greater than that of exhaust room air. 1. INTRODUCTION Evaporative cooling and energy recovery may be utilized to reduce energy consumption in Heating Ventilating and Air Conditioning (HVAC). Many different types of equipment have been developed for such applications. For example, fixed plate heat exchangers [1,2], thermosiphon [3], energy wheel, run-around heat exchanger systems [4-6], desiccant assisted heat recovery [7], etc are among these equipments. Effectiveness defined on the basis of energy saving potential is used to evaluate the performances of different equipments. In reviewing the literature, the authors note that energy saving potential is usually defined on the basis of the first thermodynamic law analysis and even dependent on the type of equipments. Conventionally, two kinds of definition are used: sensible heat potential and enthalpy potential. Chen et al. [8] conducted the calculation of enthalpy potential by indirect evaporative cooling in detail for various U.S. and Chinese cities. However, the second law analysis tells us that the available energy of moist air that may be recovered or utilized is its exergy. Therefore, the available energy saving potential ought to be the exergy. This potential is independent of the equipment used and will be useful for comparison of performances of different equipments. Thus, the current analysis seems to be warranted. 2. ANALYSIS OF EXERGY OF MOIST AIR Moist air may be considered as a mixture of ideal gases, dry air, and water vapor. The exergy of moist air per unit mass dry air is represented by the following equation. Which appears in similar formats in many textbooks of thermodynamics [9,10]: ex = (C pa + ωc pv )[T T 0 T 0 ln(t/t 0 )] + (1 + 1.608ω)R a T 0 ln(p/p 0 ) + R a T 0 {(1 + 1.608 ω)ln[(1 + 1.608ω 0s )/ (1 + 1.608ω)] + 1.608ωln(ω/ω 0s )} (1) 113

where, T, p and ω denote temperature, pressure and humidity ratio respectively. Usually, the atmospheric condition (T 0, p 0, ω 0 ) is selected as the ambient or dead-state condition. In thermodynamic analysis, ambient is regarded as a heat and mass reservoir with infinite heat and mass capacity. Any system that is in unrestricted equilibrium with this environment will have no available energy. However, in air conditioning, the atmospheric air may also be used as the secondary air to cool incoming outdoor air by evaporative cooling [8] unless the secondary air is saturated. Thus, the authors suggest that the saturated state (T 0, p 0, ω 0s ) in thermal and mechanical equilibrium with the atmospheric condition is selected as the dead-state condition [11]. Where, ω 0s denotes the humidity ratio of saturated moist air at condition (T 0, p 0 ). Let p = p 0 = 1 atm, T 0 = 20 C and 30 C, two diagrams of isoexergic lines drawn on psychometric chart according to equation (1) are shown in Fig. 1. Where, isoexergic lines are represented with the dash curves. We can see from these diagrams that the enthalpy and exergy are completely independent of each other. Hence, enthalpy potential cannot be used instead of available energy potential. From these diagrams, we can also see that any adiabatic humidifying process, which is considered as no energy loss with respect to enthalpy change, will lead to the destruction of exergy. Hence, exergy analysis can help us to find out the opportunities of improving the system design in practice. For example, we can use regenerative evaporative cooling scheme to replace direct or indirect evaporative cooling scheme in evaporative cooling assisted air conditioning systems in order to obtain more energy savings [13]. Thus, exergy analysis is warranted. T Humidity ratio ω g/kg(a) 0 10 1 20 2 30 3 4042 3.8 3.04 60 2.28 0 1.2kJ/kg(a) 4 40 0.761 3 30 2 20 1 h=80kj/kg(a) 10 0 ex=0kj/kg(a) h=40kj/kg(a) - -10 T 0 =20 C p 0 =1atm -1 Exergy-Psychometric Chart Temperature T C The exergy of moist air expressed by equation (1) may be broken down into three components: thermal, mechanical and chemical. They are denoted as ex th, ex me and respectively and may be represented in the following equations: ex th = (c pa + ωc pv )(T T 0 T 0 ln(t/t 0 )) (2) ex me = (1 + 1.608 ω) R a T 0 ln(p/p 0 ) (3) ex Temperature T C ch Therefore, 60 0 4 40 3 30 2 20 1 10 0 - -10-1 1 + 1.608 ω0s = R at0[(1 + 1.608 ω) ln + 1 + 1.608 ω 1.608ωln(ω 0s /ω)] (4) ex = ex th + ex me + () Take p 0 = 1 atm, equations (2) to (4) may also be represented by three diagrams plotted against T, p = p p 0, ω respectively as shown in Figs. 2 to 4. Fig. 4b is given to get a distinct view of the bottom part in Fig. 4a. In air conditioning, thermal and chemical exergy is recovered with heat recovery systems at the expense of mechanical exergy lost due to flow friction. For this reason, the interests that concern us are whether the sum of retrieval gainings will be greater than the expense and which gaining will be more important. With the aid of these figures, a general comparison of the different exergies is conducted based on the common practices in air conditioning. Take a typical case (T = 24 C, T 0 = 36 C, p = 60 Pa, ϕ = 6%) for example, ex th 0.24, 1.71, ex me 0.03. We can see from these results that ex me << ex th + and > ex th. Similar relations may be obtained for other typical cases. Another interesting phenomenon may also be seen from Fig. 4 if the two extreme cases (1. ω 0s = 1.03 gkg -1 (a) Humidity ratio ω g/kg(a) 0 10 1 20 2 30 3 4042 2.2 h=40kj/kg(a) 1.12 kj/kg(a) ex=0kj/kg(a) h=80kj/kg(a) T 0 =30 C p 0 =1atm Exergy-Psychometric Chart (a) T 0 = 20 C (b) T 0 = 30 C Fig. 1: Diagrams of isoexergic lines on psychometric charts 114

Exergy ex th / (1+ϖ) () T 0 =4 C 3 1 C T 0 =-1 C - - 1 C Exergy ex me / (1+ϖ) () P 0 =1atm 1 2 3 4 1--T 0 =-4 C 2--T 0 =-1 C 3--T 0 =1 C 4--T 0 =4 C --T 0 =7 C 4 3 2 1 Temperature T ( C) Fig. 2: Thermal exergy of moist air Pressure difference p (kpa) Fig. 3: Mechanical exergy of moist air -1 C T 0 =4 Exergy () ω 0s =6.9 g/kg(a) T 0 =4 C 46.8 3 ω 0s =1.03 g/kg(a) 1.77 2.97 T 0 =-1 C 4.7 7.22 10.8 - - 1 C 1.9 23 32.9 Exergy () 3 - - T 0 = 1 C Humidity ratio ω (gkg -1 (a)) (a) Humidity ratio ω (gkg -1 (a)) (b) Fig. 4: Chemical exergy of moist air and ω = 6 gkg -1 (a), 2. ω 0s = 6 gkg -1 (a) and ω = 1.03 gkg -1 (a) ) are compared. The second case will possess much greater exergy than the first one though they hold the same humidity ratio difference. Thus, two guidelines may be extracted from the above analysis as these: the exergy loss due to air flow resistance in a heat exchanger is usually small when compared with the potential of thermal and chemical exergy gaining; chemical exergy will take much great importance in heat recovery, lower dead-state temperature (T 0 ) with the same difference of the humidity ratio (ω ω 0S ) is related with higher chemical exergy, and hence, the recovery of latent heat availability will probably be more valuable in winter than in summer. 3. APPLICATION OF EXERGY ANALYSIS IN ENERGY SAVING POTENTIAL To estimate the energy saving potential, exergies of exhaust room air or outdoor air is calculated and tabled for varies Chinese cities as shown in Table 1. The average outdoor-air conditions are obtained from handbooks of air conditioning [12]. The calculations are also based on the following room air conditions that are given in ranges of x ± σ, where x represents the average value of room air conditions recommended for different types of air conditioning and σ represents the corresponding mean square deviation. Winter: T = 17.6 ~ 24. C, ϕ = 4.2 ~ 6.9% Summer: T = 22.2 ~ 28.2 C, ϕ = 48 ~ 67% 11

In this table, the exergies are all given out in ranges between the lower and upper limits. In winter, the lower and upper limits correspond to the lower and upper limits of room air parameters in order. In summer, they are related in the reverse order. Because of the low temperature at winter condition, the humidity ratio difference (ω 0s ω 0 ) is very small and the exergy of outdoor air is negligible and not listed here. Table 1: Exergy of incoming outdoor air and exhaust room air for different locations cities winter outdoor exergy of exhaust room air outdoor T ( C) ϕ % ex th ex th + T T w ( C) ( C) exergy of outdoor air summer exergy of exhaust room air ex th ex th + Beijing -12 4 1.68~2.346 0.476~2.138 2.044~4.484 33.2 26.4 0.473 0.041~0.203 0.699~1.84 0.741~2.08 Taiyuan -1 1 1.909~2.78 0.618~2.49 2.27~.22 31.2 23.4 0.87 0.01~0.136 0.463~1.48 0.478~1.616 Shenyang -22 64 2.841~3.8 0.986~3.367 3.827~7.222 31.4 2.4 0.37 0.017~0.142 0.48~1.16 0.02~1.68 Dalian -14 8 1.791~2.617 0.69~2.372 2.36~4.989 28.4 2.0 0.111 0.0~0.06 0.219~1.039 0.219~1.104 Changchun -26 68 3.461~4.7 1.211~3.882 4.673~8.42 30. 24.2 0.384 0.009~0.116 0.389~1.3 0.398~1.471 Haerbin -29 74 3.969~.148 1.38~4.273.34~9.422 30.3 23.4 0.41 0.007~0.111 0.369~1.32 0.377~1.43 Shanghai -4 7 0.827~1.417 0.18~1.239 0.98~2.6 34.0 28.2 0.361 0.06~0.234 0.818~2.032 0.874~2.266 Nanjing -6 73 0.989~1.626 0.226~1.41 1.21~3.077 3.0 28.3 0.487 0.076~0.27 0.974~2.28 1.01~2.32 Hangzhou -4 77 0.827~1.417 0.18~1.239 0.98~2.6 3.7 28. 0.6 0.093~0.30 1.088~2.418 1.181~2.724 Hefei -7 7 1.076~1.737 0.262~1.6 1.339~3.296 3.0 28.2 0.01 0.076~0.27 0.974~2.28 1.01~2.32 Fuzhou 4 74 0.32~0.726 0.00~0.42 0.33~1.268 3.2 28.0 0.6 0.081~0.283 1.006~2.303 1.087~2.87 Xiamen 6 73 0.236~0.9 0.0~0.41 0.236~1 33.4 27.6 0.33 0.04~0.211 0.729~1.899 0.773~2.109 Nanchang -3 74 0.71~1.317 0.128~1.137 0.879~2.44 3.6 27.9 0.64 0.091~0.301 1.071~2.39 1.162~2.696 Jinan -10 4 1.36~2.091 0.38~1.9 1.744~3.99 34.8 26.7 0.69 0.072~0.266 0.942~2.212 1.014~2.478 Qingdao -9 64 1.261~1.969 0.342~1.78 1.604~3.74 29.0 26.0 0.087 0.001~0.078 0.262~1.123 0.263~1.202 Zhengzhou -7 60 1.076~1.737 0.262~1.6 1.339~3.296 3.6 27.4 0.722 0.091~0.301 1.071~2.39 1.162~2.696 Luoyang -7 7 1.076~1.737 0.262~1.6 1.339~3.296 3.9 27. 0.78 0.098~0.314 1.121~2.46 1.219~2.779 Wuhan - 76 0.906~1.2 0.191~1.347 1.098~2.867 3.2 28.2 0.31 0.081~0.283 1.006~2.303 1.087~2.87 Changsha -3 81 0.71~1.317 0.128~1.137 0.879~2.44 3.8 27.7 0.706 0.09~0.31 1.104~2.441 1.2~2.71 Guangzhou 70 0.278~0.66 0.001~0.47 0.279~1.131 33. 27.7 0.34 0.047~0.214 0.743~1.921 0.79~2.13 Haikou 10 8 0.1~0.361 0.03~0.193 0.136~0.4 34. 27.9 0.468 0.066~0.24 0.89~2.144 0.961~2.398 Nanning 7 0.278~0.66 0.001~0.47 0.279~1.131 34.2 27. 0.479 0.06~0.242 0.849~2.077 0.908~2.318 Guilin 0 71 0.46~1.042 0.04~0.84 0.6~1.887 33.9 27.0 0.04 0.04~0.23 0.803~2.01 0.87~2.239 Chengdu 1 80 0.48~0.97 0.037~0.76 0.23~1.722 31.6 26.7 0.246 0.019~0.149 0.07~1.2 0.26~1.701 Chongqing 2 82 0.428~0.877 0.024~0.687 0.42~1.64 36. 27.3 0.919 0.114~0.342 1.237~2.62 1.31~2.967 Guiyang -3 78 0.71~1.317 0.128~1.137 0.879~2.44 30.0 23.0 0.46 0.00~0.103 0.34~1.267 0.34~1.37 Lasa -8 28 1.167~1.81 0.302~1.673 1.469~3.24 22.8 13. 0.717 0..049~0.001 0.00~0.43 0.04~0.431 Xian -8 67 1.167~1.81 0.302~1.673 1.469~3.24 3.2 26.0 0.883 0.081~0.283 1.006~2.303 1.087~2.87 Lanzhou -13 8 1.677~2.479 0.24~2.261 2.202~4.74 30. 20.2 0.978 0.009~0.116 0.389~1.3 0.398~1.471 Yinchuan -18 8 1.862~3.204 0.398~2.862 2.29~6.066 30.6 22.0 0.692 0.01~0.119 0.4~1.373 0.409~1.492 Wulumuqi -27 80 3.627~4.78 1.269~4.012 4.896~8.771 34.1 18. 2.307 0.08~0.238 0.833~2.04 0.891~2.292 Taibei 9 82 0.129~0.413 0.02~0.241 0.149~0.64 33.6 27.3 0.418 0.048~0.218 0.78~1.943 0.806~2.161 Hong Kong 8 71 0.161~0.468 0.009~0.294 0.17~0.762 32.4 27.3 0.27 0.029~0.17 0.99~1.699 0.628~1.874 * T w denotes wet bulb temperature 116

From this table, some conclusions can be drawn as following: On average, the exergy of room air is greater in winter than in summer and so does the available energy saving potential; In winter, when exhaust room air temperature is low, the exergy of sensible heat is the main component of available energy saving potential. In contrast, the latent heat usually makes the prevailing contribution in summer, while at some dry locations, the exergy of outdoor air is even greater than that of exhaust room air. 4. SUMMARY Analysis of exergy of moist air has been carried out to explore the available energy saving potential for various conditions and locations. It is independent of the types and dimensions of the equipment used in practice. Thus it provides an objective criterion for evaluating the performance of evaporative cooling or heat recovery systems. Useful guidelines and conclusions are drawn in section 2 and 3. The special devised diagrams of thermal, mechanical and chemical exergies will provide convenience in calculations and qualitative analysis. Compared to the traditional study using enthalpy, exergy analysis can help us to locate the irrational design and the opportunities of improving system design and lead to larger energy saving. However, further work should be invested in evaluating the performance of different types of practical equipments and searching for the optimum design method. 6. P. Dhital, R.W. Besant and G.J. Schoenau, Integrating run-around heat exchanger systems into the design of a large office building, 979-991 (199). 7. M. Merkler, Desiccant outdoor air preconditioners maximize heat recovery ventilation potentials, 993-1000 (199). 8. P. Chen, H. Qin, Y.J. Huang, H. Wu and C. Blumstein, The energy-saving potential of precooling incoming outdoor air by indirect evaporative cooling, ASHRAE Transactions, Vol. 99, No. 1, pp. 322-331 (1993). 9. Kenneth Work, JR., Advanced thermodynamics for engineers, Chap. 6 and Chap. 11, McGraw-Hill, New York (199). 10. A. Bejan, Advanced engineering thermodynamics, Chap., Wiley, New York (1988). 11. C.Q. Ren, G.F. Tang, N.P. Li, G.F. Zhang and L. Ouyang, Discussion on principles of exergy analysis applied to HVAC systems, International Conference on Energy Conversion and Application (ICECA 2001), Wuhan (2001). 12. R.Y. Zhao, et al., Succinct handbook of air conditioning design, China Architecture and Building Press, Peking, China (1998) - In Chinese. 13. C.Q. Ren, Exergy analysis of evaporative cooling and numerical research on the heat transfer in a new plate heat exchanger, Ph.D. Thesis, Hunan University, China (2001). REFERENCES 1. D. Pescod, A heat exchanger for energy saving in an air-conditioning plant, ASHRAE Transactions, Vol. 8, No. 2, pp. 238-21 (1979). 2. P.T. Ninomura and R. Bhagava, Heat recovery ventilators in multifamily residences in the arctic, 961-966 (199). 3. L. Carnes, Air-to-air heat recovery systems for research laboratories, ASHRAE Transactions, Vol. 90, No. 2, pp. 327-340 (1984). 4. B.I. Forsyth and R.W. Besant, The design of a run-around heat recovery system, ASHRAE Transactions, Vol. 94, No. 2, pp. 11-31 (1988).. A.B. Johnson, R.W. Besant and G.J. Schoenau, Design of multi-coil run-around heat exchanger systems for ventilation air heating and cooling, 967-978 (199). 117