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liquid desiccant solution
Energy 187 (2019) 115976
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Theoretical analysis of exergy destruction and exergy flow in direct contact process between humid air and water/liquid desiccant solution Lun Zhang*, Xia Song, Xiaosong Zhang School of Energy and Environment, Southeast University, Nanjing, 210096, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 April 2019 Received in revised form 15 August 2019 Accepted 18 August 2019 Available online 21 August 2019
Direct contact between humid air and water/liquid desiccant (LD) solution is common in air-conditioning systems, where transfer (heat/mass) and conversion (evaporation/condensation) processes occur. This work analyzes these processes using exergy theory and a two-film model. The exergy flow and exergy destruction of heat transfer and mass transfer can be expressed using a unified exergetic expression and depicted by a psychrometric chart. Results show that the equivalent air film of the water/solution is a medium for exergy flow and is thus used to determine the exergy change of the water/solution. Direct evaporative cooling and condensation dehumidification are two representative cases between humid air and water. In the former, the thermal exergy and humid exergy both flow from the humid air to water, where exergy destruction and conversion of the humid exergy into thermal exergy are inevitable. In the latter, thermal and humid exergy flows are all reversed. Dehumidification and regeneration are two crucial and reversed processes between the humid air and solution. The concentration exergy of the solution is involved in the thermal and humid exergy flows. The solution exports its concentration exergy to complete the exergy flows during dehumidification, and it obtains the concentration exergy from exergy flows during regeneration. © 2019 Published by Elsevier Ltd.
Keywords: Exergy Air-conditioning Liquid desiccant Heat and mass transfer
1. Introduction Water evaporation into humid air or vapor condensation into water/liquid desiccant (LD) solution is an integral process in many devices such as open or closed cooling towers [1,2], water spray cooling [3], dehumidifiers and humidifiers [4], which are common components of air-conditioning systems. In such a process, heat transfer and mass transfer coexist, directly affecting one another [4]. The mathematical models for heat and mass transfer processes between humid air and water have been presented in Refs. [2,5,6]. The models usually include four equations (the continuity equation, momentum equation, energy conservation equation, and the mass conservation equation) and the developed heat and mass transfer equations. Furthermore, Hawlader et al. [2] and Klimanek et al. [6] numerically predicted the distributions of velocity, density, temperature, and humidity ratio of humid air and water. The transfer
* Corresponding author. E-mail address: [email protected] (L. Zhang). https://doi.org/10.1016/j.energy.2019.115976 0360-5442/© 2019 Published by Elsevier Ltd.
characteristics and influencing factors (inlet parameters, flow rates, flow patterns) have also attracted much attention. Correlations for the mass and heat transfer coefficients in a closed wet cooling tower have been proposed [1]. Enayatollahi et al. [7] identified four distinct flow regimes in the interaction between humid air and water, where the transfer processes were characterized by empirical correlations. Likewise, Chuck et al. [8] measured the thermal conditions of humid air passing over the surface of water and determined its mass transfer coefficient. Furthermore, mass transfer plays an important role in the heat and mass transfer characteristics between the water surface and airstream [9]. The surface vapor pressure of LD solution is lower than that of pure water, so it is very effective in dehumidifying humid air [10]. The thermal properties of often-used solutions, such as lithium bromide and lithium chlorides, were studied in Refs. [11,12]. Mathematical models for the coupled heat and mass transfer processes between humid air and LD solution have been developed [4,13,14], which were solved numerically or analytically and were verified by experimental results. Performance indexes used to evaluate these processes include the outlet air state, the moisture removal rate, and the enthalpy or moisture effectiveness. Based on
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Fig. 1. Air-treatment processes in air-conditioning systems.
these indexes, various studies have researched and optimized the coupled heat and mass transfer processes regarding their influencing factors, such as solution type [15], flow path [4] (mainly counter-flow, cross-flow, or parallel-flow), flow rate [16,17], and inlet states of the humid air and solution [17e19]. Besides focusing on the performances of a single dehumidifier and regenerator, researchers have proposed and analyzed various LD dehumidification systems, such as the heat pump driven LD system [20], the LD system regenerated by solar energy [21], the two-stage LD system by the cascade utilization of low-temperature heat [22], and the optimum area distribution between the dehumidifier and regenerator in the LD system [23]. The studies discussed above are mainly based on the first law of thermodynamics and the heat and mass transfer equations. Research from the perspective of the second law of thermodynamics, especially in the context of exergy, remains limited. Wepfer et al. [24] demonstrated the application of the second law to airconditioning systems. Exergy or availability is an accurate metric related to the quality of energy [25]. It can be used to evaluate the efficiency of energy systems and energy conversion processes. Qureshi et al. [26] presented a parametric work of air-conditioning processes by applying exergy analysis for measuring irreversible losses (or entropy generation). Akpinar et al. [27] and Hepbasli et al. [28] performed energy and exergy analyses for ground-source heat pump systems and gave exergy efficiency values for the systems. They concluded that the exergetic evaluation method may be a
Fig. 2. Two-film model as part of a differential transfer process between humid air and the equivalent air film of water/solution [37].
Fig. 3. Temperature difference and moisture difference between two air states.
useful tool, as ignored problems in energy systems can be found and new techniques can be proposed to further improve the systems’ performances. For example, an exergy model for the airconditioning system of a building was presented by Razmara et al. [29], and a model predictive control technique using the exergy model was developed to reduce exergy destruction. Bejan et al. [25] defined the total exergy of humid air, which is the sum of the thermomechanical exergy and chemical exergy, enabling exergy analysis to be applied to air-water contact systems. Muangnoi et al. [30] proposed the exergy distributions for water and humid air and the exergy destruction of a cooling tower. Moreover, second law efficiency based on the exergy changes of humid air and water in the tower was defined [31] to illustrate its performance under various inlet parameters. Wang et al. [32] investigated schematically the exergy transfer process in a tower and discussed the relationship between the exergy efficiency and thermal efficiency. The unmatched characteristic in the coupled heat and mass transfer processes between humid air and water was presented using exergy analysis [33] and it was found that reducing the unmatched coefficient could result in the decrease of exergy destruction. Exergy analysis has also been conducted on LD dehumidification systems. Ahmed et al. [34] investigated the exergy of a hybrid system, incorporating a dehumidifier based on LD, then calculated the irreversible losses of the system and attempted to optimize the desiccant flow rate. An exergy analysis model, incorporating a desiccant solution, was proposed by Xiong et al. [35] to facilitate the performance evaluation of a two-stage LD dehumidification system. Likewise, Su et al. [36] presented the exergy distribution in a two-stage LD system driven by low-temperature heat and power. Exergy of humid air, water and liquid desiccant were defined carefully by Peng et al. [37] to obtain exergy evaluation indexes of an LD evaporative cooling system. Most work has focused on either the direct contact between humid air and water or that between the humid air and solution, but little work has deployed a useful exergetic strategy to associate them. This work thus builds a unified model of the direct contact between humid air and water/solution, analyzing the heat transfer and mass transfer using exergetic theory. Then, the exergy destruction and exergy flow in several typical cases are clearly presented.
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Fig. 4. Definition of work and exergy.
Fig. 5. Thermal exergy destruction in heat transfer.
Fig. 6. Thermal exergy flow during heat transfer.
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Pv ¼ Pe
(2)
where subscripts e, w, v, and S denote the equivalent air film, water, vapor, and solution, respectively, and Pe is the equivalent vapor pressure of the state in equilibrium with the water/solution. The equivalent humidity ratio of the water/solution is defined as:
ue ¼ 0:622
Fig. 7. Mass transfer between two air states.
2. Model and basic definition 2.1. Transfer and conversion processes between humid air and water/LD solution In air-conditioning systems, many air-treatment processes involve direct contact between humid air and water or LD solution. Evaporative cooling in cooling towers, condensation dehumidification, dehumidification, and regeneration in LD dehumidification systems are the four main processes, as illustrated in Fig. 1. When humid air flows over the water/LD solution surface, a stagnant air film forms, which adheres to the surface [38]. A twofilm model theory can be used here [39], as shown in Fig. 2. The following assumptions are made: (a) The resistance of mass transfer is mainly located at the air side; (b) The properties of the water/solution side are uniformly distributed; (c) The properties of the air film are determined by the water/ solution side. The air film remains in equilibrium with the water/solution and is, therefore, regarded as the equivalent state of the water/solution. Accordingly, the temperature and vapor pressure of the film are given by Eqs. (1) and (2), respectively:
Te ¼ Tw orTe ¼ TS
(1)
Pe B Pe
(3)
where B is the standard atmospheric pressure. Owing to the temperature difference between the humid air and water/solution, heat transfer occurs between them. The air film is not capable of storing thermal energy. If Pv of the humid air is higher than Pe, vapor in the humid air will be transferred to the air film. Excessive vapor in the air film condenses into the water/solution. Conversely, vapor in the air film will be transferred to the humid air. Water evaporates into the air film, supplementing the transferred vapor. Thus, mass transfer occurs between the humid air and air film, and conversion (condensation or evaporation) occurs between the air film and water/solution, as demonstrated in Fig. 2. Fig. 2 shows a differential transfer process, after which, the states of both the humid air and air film fluctuate infinitesimally around the initial states. Any complete process consists of a series of consecutive differential processes, and thus, the following analysis mainly concerns about a differential process. The heat transfer and mass transfer between the two air states (the humid air and equivalent air film) are expressed in Eqs. (4) and (5). The driving forces (difference in temperature and moisture) are shown in the psychrometric chart in Fig. 3.
cp:a ma dTa ¼ aðTe Ta ÞdA
(4)
ma dua ¼ am ðua ue ÞdA
(5)
2.2. Exergy definition Exergy is defined as the available energy when any system develops reversibly into the state that is in equilibrium with a given reference state [40]. There are two key terms here: one is “reversibly”, representing an ideal, optimal process; the other is “reference state”, whose exergy is zero. Fig. 4(a) shows an object with temperature, T, and a reference object at temperature, T0. The infinitesimal sensible heat, dQ, is defined as positive when sensible heat is released from the considered object to the reference object and negative when heat
Table 1 Unified expression of heat transfer and mass transfer.
Driving forces Differential equations Transfer equations Derivation of exergy destruction Exergy destruction Deduction Unified exergetic expression
Heat transfer
Mass transfer
DT dQ ¼ mcp ,dT Q ¼ aA,DT dExd;h dExðT1 Þ dExðT2 Þ ¼ dQ dQ dQ
Du dD ¼ m,du D ¼ am A,Du dExd;m dExðu1 Þ dExðu2 Þ ¼ dD dD dD
dExd;h ¼ T0
dExd;m ¼ 1:608Ra T0 ln
-
dExd;h ¼ T0
1 1 dQ T2 T1
1 1 dQ T2 T1
Appendix A
dExd;m ¼ T0
u1
1 þ 1:608u1
! 1 1 ,rdD T2;dp T1;dp
ln
u2
1 þ 1:608u2
,dD
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Fig. 8. Humid exergy flow during mass transfer.
flow is the other way round. When T is higher than T0, the maximum produced work, can be expressed by Eq. (6). The object supplies exergy. When T is lower than T0, the minimum absorbed work can also be expressed by Eq. (6). The object obtains exergy. Exergy is a positive value. For an object, the direction of exergy flow is distinguished by supplied exergy and obtained exergy.
dW ¼ T0
1 1 ,dQ T0 T
(6)
Accordingly, Fig. 4(b) shows the four possible situations concerning exergy flow for an object. The two background colors in Fig. 4(b) correspond, respectively, to those in Fig. 4(a). The exergy of an object is directly related to the reference state, which is the horizontal axis in Fig. 4(b). The exergy of humid air itself, which consists of 1 kg of dry air and u kg of vapor, at standard atmospheric pressure, is the sum of thermal exergy and humid exergy [33], which is:
where Ra denotes the gas constant of air, u0 is the reference humidity ratio, and cp.m is defined as:
cp:m ¼ cp:a þ u,cp:v
(8)
cp.a is the specific heat of dry air and cp.v is the specific heat of vapor. The reference temperature of thermal exergy, T0, is chosen as the ambient temperature, and the reference humidity ratio of humid exergy, u0, is chosen as the saturated humidity ratio of T0 [41]. Since the equivalent state of the water/solution is shown to be, in the psychrometric chart, similar to that of the humid air, their exergy can also be expressed by the above equation using the temperature (Te) and the equivalent humidity ratio (ue) of the equivalent air film.
3. Exergy destruction during heat and mass transfer 3.1. Exergy destruction during heat transfer
ExðT; uÞ ¼ m,exðT; uÞ T T 1 þ 1:608u0 u ¼ cp:m mT0 þ mRa T0 ð1 þ 1:608uÞln 1 ln þ 1:608u ln u0 T0 T0 1 þ 1:608u
(7)
Fig. 5(a) shows that dQ is transferred between object 1, with temperature T1, and object 2 with temperature T2, a transferal which is an irreversible process with exergy destruction. This transferal assumes a possible corresponding reversible process with a Carnot cycle and a reverse Carnot cycle, as illustrated in Fig. 5(b). The reversible process can produce extra work (dW1þdW2) compared with the irreversible process, which is exactly the exergy destruction during heat transfer, as depicted in Eq. (9):
dExd;h ¼ dW1 þ dW2 ¼ T0
1 1 dQ T2 T1
(9)
In the process, as seen in Fig. 5(a), according to the exergy definition, object 1 releases dQ, so it exports exergy. Object 2 absorbs dQ, so it obtains exergy. The exergy destruction is the difference between the supplied exergy and the obtained exergy as shown by Eq. (10):
dExd;h ¼ dExðT1 Þ dExðT2 Þ ¼ T0 Fig. 9. Thermal and humid exergy destruction.
1 1 dQ T2 T1
(10)
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Fig. 11. Exergetic analysis of the transfer and conversion processes of condensation dehumidification.
Fig. 10. Exergetic analysis of the transfer and conversion processes of evaporative cooling.
Object 1 offers the exergy, part of which is absorbed by object 2, and the rest is destroyed, as demonstrated in Fig. 6(a). Accordingly, the exergy balance is demonstrated in Fig. 6(b). dEx(T1) is divided into two parts, dExd,h and dEx(T2), expressed as a dotted line. dEx(T2) should have been at the second quadrant, so it is moved to the right with a solid line. According to Eqs. (7) and (8), the exergy destruction during heat transfer (thermal exergy destruction) between two air states, with temperatures T1 and T2, respectively, can be calculated as in Eq. (11). The result is the same as that shown in Eq. (10):
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Table 2 A case study of the condensation dehumidification process.
Water Equivalent air film
Parameter
Value
dExh
dExm
dExd,h
dExd,m
T
15 C
-
e
-
T or Tdp
15 C 10.65 g/kg 32 C 20 g/kg 24.91 C
1.333$(dQþrdD) (Supplied) 1.333$dQ (Medium)
(Conversion) 1.333$rdD (Medium) 0.405$rdD (Obtained)
1.240$dQ (Destroyed)
0.928$rdD (Destroyed)
u
Humid air
T
u Tdp
0.093$dQ (Obtained)
Table 3 A case study of the regeneration process. Parameter Value Humid air
20 C 8 g/kg 10.89 C 33 C 20 g/kg 24.91 C 33 C 34.84%
T
u Tdp Equivalent air film T
u
Tdp T X
Solution
dExh
dExm
0.750$dQ (Supplied)
2.214$rdD (Supplied) e
0.061$dQ (Medium)
0.405$rdD (Medium)
(Conversion) e 0.061$dQþ0.061$rdD (Obtained)
dExd;h dExðT1 Þ dExðT2 Þ 1 vexðT1 Þ vexðT2 Þ ¼ ¼ cp:m vT vT dQ dQ dQ
¼ T0
1 1 T2 T1
(11)
3.2. Exergy destruction during mass transfer The mass transfer between two air states with different moisture contents is shown in Fig. 7. dD is transferred from the state 1 to state 2. The exergy destruction during mass transfer (humid exergy destruction) can be calculated by Eq. (12):
dExd;m dExðu1 Þ dExðu2 Þ vexðu1 Þ vexðu2 Þ ¼ ¼ vu vu dD dD dD
(12)
Substituting the exergy equation of humid air, Eq. (12) is rewritten as [33]:
dExd;m u1 u2 ¼ 1:608Ra T0 ln ln dD 1 þ 1:608u1 1 þ 1:608u2
dExC
dExd,h
dExd,m
0.689$dQ (Destroyed) 1.809$rdD (Destroyed)
e
0.344$rdD (Obtained) e
e
the expression for humid exergy destruction consists of dew point temperatures (T1,dp and T2,dp) and latent heat, rdD. Accordingly, when a state with humidity ratio, u, transfers dD with reference state, u0, its humid exergy can also be defined as expressed in Eq. (15), using its dew point temperature, Tdp, and latent heat, rdD, similar to the thermal exergy shown in Fig. 4 and Eq. (6). In Fig. 7, state 1 transfers dD to state 2, so humid exergy destruction during this process can be calculated using the same method as that in Fig. 5. State 1 releases rdD, but its dew point temperature is lower than T0, so it obtains exergy. State 2 absorbs rdD, so it exports exergy. The exergy destruction is given by Eq. (16). Fig. 8 shows humid exergy flow and exergy balance. Part of the exergy supplied by state 2 flows to state 1 and the rest is destroyed.
dEx Tdp ¼ T0
! 1 1 r dD T0 Tdp
dExd;m ¼ dEx T2;dp dEx T1;dp ¼ T0
(15)
1 T2;dp
1 T1;dp
! ,r dD
(13)
(16) In summary, thermal exergy destruction and humid exergy destruction can be expressed in a unified way, as shown in Fig. 9.
3.3. Unified expression of thermal exergy destruction and humid exergy destruction Since thermal exergy is expressed using temperature but humid exergy using the humidity ratio, it is difficult to compare the two. In order to further illuminate the relationship between thermal and humid exergy, humid exergy can be expressed in a unified way as thermal exergy (the derivation process is in Appendix A). As shown in Fig. 7, humid exergy destruction is thus written as:
dExd;m ¼ T0
1 T2;dp
1 T1;dp
! ,rdD
(14)
Table 1 clearly demonstrates the unified expression of heat and mass transfer. The expression for thermal exergy destruction consists of temperatures (T1 and T2) and transferred heat, dQ. However,
4. Exergy analysis for direct contact processes between humid air and water/solution 4.1. Transfer and conversion processes between humid air and water The equivalent water state is located on the saturation curve, as shown in Fig. 1. Given a specific water temperature, Tw, the corresponding equivalent humidity ratio, ue, is exactly that of the saturated air with temperature Tw. This paper considers the two cases between humid air and water, evaporative cooling and condensation dehumidification. 4.1.1. Evaporative cooling process Direct evaporative cooling is common in air-conditioning
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dExh;a þ dExm;a dExh;w;1 þ dExh;w;2 ¼ dExd;h þ dExd;m
(17)
Fig. 12. Heat, mass and exergy flowing through the equivalent air film.
systems, where humid air is usually used to cool water, such as occurs in a cooling tower. Owing to the temperature difference and moisture difference, water releases heat and evaporates into humid air. For an infinitesimal process, dQ is thus transferred from water to humid air through the equivalent air film. Meanwhile, liquid dD first evaporates into the air film and is then transferred to humid air, with latent heat rdD. The thermal and humid exergy of the humid air and water are presented in Fig. 10(a). The equivalent water state is the saturated humid air, consisting of both thermal exergy, dExh,e, and humid exergy, dExm,e. However, water is completely liquid with thermal exergy only [33]. Thermal exergy destruction and humid exergy destruction, during the transfer process, are illustrated in Fig. 10(b). Fig. 10(c) shows exergy flow in this process. During heat transfer, humid air provides its thermal exergy, dExh,a, part of which is absorbed by the equivalent air film and then flows to the water (dExh,w,1). The rest is destroyed through thermal exergy destruction. In mass transfer, humid air supplies its humid exergy, dExm,a, part of which is destroyed through humid exergy destruction. The rest flows to the equivalent air film and then is converted to thermal exergy of the water (dExh,w,2). The air film is not capable of storing exergy and is merely a medium for exergy flow. Fig. 10(d) and Eq. (17) present the exergy balance during this process. The two terms on the left in Eq. (17) are the total supplied exergy and the total obtained exergy, respectively. The term on the right is the total exergy destruction.
4.1.2. Condensation dehumidification process During the condensation dehumidification process, humid air is cooled and dehumidified. dQ is thus transferred from the humid air to the equivalent air film, and finally to chilled water. Meanwhile, gaseous dD in humid air is first transferred into the air film and then condenses into chilled water, with latent heat rdD. Fig. 11(a) presents the thermal and humid exergy destruction in this process, and Fig. 11(b) displays its exergy flow. The water offers two portions of thermal exergy, dExh,w,1 and dExh,w,2. dExh,w,1 flows directly through the equivalent air film and part of it is absorbed by the humid air, with the rest being destroyed. dExh,w,2 is first converted into the humid exergy of the air film, then part of it flows to the humid air, with the rest being destroyed. Again, the air film is merely a medium for exergy flow. Fig. 11(c) and Eq. (18) demonstrate the exergy balance in this process. The three terms in Eq. (18) are the total exergy supplied by water, the total exergy absorbed by humid air, and the total exergy destruction.
dExh;w;1 þ dExh;w;2 dExh;a þ dExm;a ¼ dExd;h þ dExd;m
(18)
4.1.3. Case study The condensation dehumidification process at standard atmospheric pressure is taken as an example. Table 2 gives detailed values of relevant parameters. The exergy destruction occurs between the humid air and equivalent air film. Humid exergy of the air film derives from the conversion process between water and its air film. 4.2. Transfer and conversion processes between humid air and liquid desiccant solution 4.2.1. Definition of exergy concentration of solution As discussed above, the equivalent air film of water is only a medium for heat transfer, mass transfer, and exergy flow, as shown in Fig. 12, so the supplied exergy or the obtained exergy of the water
Fig. 13. Concentration exergy definition of the LD solution.
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dExw ¼ dExh;w;1 þ dExh;w;2 ¼ dExh;e;w þ dExm;e;w
vex ue;w vexðTw Þ vexðT0 Þ vexðu0 Þ þ cp:m vT vT vu vu 1 1 ,ðdQ þ rdDÞ ¼ T0 T0 Tw
¼
1
(19)
Likewise, the change in exergy of the solution can also be expressed using the exergy flowing through its equivalent air film, as shown in Eq. (20).
dExS ¼ dExh;e;S þ dExm;e;S
vex ue;S vexðTS Þ vexðT0 Þ vexðu0 Þ þ cp:m vT vT vu vu ! 1 1 1 1 ,dQ þ T0 ¼ T0 ,rdD T0 TS T0 TS;dp ¼
1
(20)
The equivalent air film of pure water with temperature, Tw, is located on the saturation curve, as shown in Fig. 13. The equivalent air film of solution (TS ¼ Tw, concentration X) is also shown in Fig. 13. The thermal exergies of the water and solution are identical. The humid exergy difference between them results from concentration, X. The excess part is thus the concentration exergy of the LD solution, expressed by Eq. (21):
vex ue;S vex ue;w dExC;S ¼ dExS dExw ¼ vu vu ! 1 1 ¼ T0 ,rdD TS TS;dp
(21)
The higher the concentration, the greater the concentration exergy of the solution. Unlike pure water, the LD solution includes not only the thermal exergy but also the concentration exergy.
Fig. 14. Exergetic analysis of the transfer and conversion processes of dehumidification process.
(the exergy change of the water) can be expressed by the exergy flowing through the air film. As shown in Figs. 10(c) and Fig. 11(b), the exergy change of the water can be written as:
4.2.2. Dehumidification process This work considers the two possibilities between humid air and solution, dehumidification and regeneration, as shown in Fig. 1. The LD solution with a lower temperature and humidity ratio is used to cool and dehumidify humid air. dQ is transferred from humid air to the solution through the equivalent air film. Meanwhile, gaseous dD in humid air is first transferred into the air film and then condenses into solution, with latent heat rdD. The solution concentration, X, thus decreases, and so too does the concentration exergy of the solution. Fig. 14(a) shows the thermal, humid, and concentration exergy of the solution and humid air. Transfer loss between the humid air and equivalent state is demonstrated in Fig. 14(b). The solution offers two parts of thermal exergy, dExh,S,1, with sensible heat, dQ, and dExh,S,2 with latent heat, rdD, as demonstrated in Fig. 14(a) and (c). dExh,S,1 flows through the equivalent air film and then part of it is lost through thermal exergy destruction. The rest is obtained by humid air. dExh,S,2 is first converted to the humid exergy of the air film together with the concentration exergy, dExC,S, supplied by the solution, as shown by Fig. 14(c) and 14(d) and Eq. (22). Part of dExm,e flows to the humid air and the rest is destroyed. The equivalent air film is also a medium for exergy flow. Fig. 14(d) and Eq. (23) demonstrate the exergy balance in this process. The two terms on the left in Eq. (23) are the total supplied exergy and total obtained exergy, respectively, while the term on the right is the total exergy destruction.
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between humid air and the equivalent air film is demonstrated in Fig. 15(a). The humid air offers its thermal exergy, dExh,a, and humid exergy, dExm,a. Part of dExh,a is destroyed through thermal exergy destruction, the remainder flowing to the solution through the equivalent air film. Part of dExm,a is destroyed and the rest flows to the equivalent air film. Then, dExm,e is divided into two parts: one part becomes the concentration exergy of the solution and the other part is converted into the thermal exergy of the solution, as demonstrated in Fig. 15(b) and Eq. (24). Fig. 15(c) and Eq. (25) demonstrate the exergy balance in this process. The three terms in Eq. (25) are the total supplied exergy, the total obtained exergy, and the total exergy destruction, respectively.
dExm;e ¼ dExC;S þ dExh;S;2
dExh;a þ dExm;a dExh;S;1 þ dExh;S;2 þ dExC;S
¼ dExd;h þ dExd;m
(24) (25)
4.2.4. Case study The regeneration process at standard atmospheric pressure is taken as an example. Table 3 gives detailed values, which exactly satisfy Eq. (24) and Eq. (25).
5. Conclusions This work theoretically analyzes the direct contact process between humid air and water/LD solution using exergy theory. The following is a summary of the conclusions:
Fig. 15. Exergetic analysis of the transfer and conversion processes of regeneration process.
dExC;S þ dExh;S;2 ¼ dExm;e
(22)
dExh;S;1 þ dExh;S;2 þ dExC;S dExh;a þ dExm;a ¼ dExd;h þ dExd;m
(23)
4.2.3. Regeneration process Humid air with a lower temperature and lower humidity ratio is used to cool and concentrate the solution during the regeneration process. dQ is thus transferred from the solution to humid air. Meanwhile, liquid dD first evaporates into the equivalent state and then is transferred to humid air, with latent heat, rdD. The solution concentration, X, thus increases, and so too does the concentration exergy of solution. The transfer loss, in other words, the exergy destruction,
(1) Exergy flow and exergy destruction of heat transfer and mass transfer between two air states can be expressed in a unified expression (as in Eqs. (10) and (16)), in which the heat transfer and mass transfer are expressed by dry-bulb temperatures and dew point temperatures, respectively. (2) The equivalent air film of water or a solution is a medium not only for the transfer of heat and mass but also for exergy and is thus used to determine the supplied exergy or obtained exergy of the water/solution. Accordingly, the concentration exergy of the solution can be defined as the exergy difference between the two equivalent air films. (3) During direct evaporative cooling between humid air and water, humid air provides its thermal exergy and humid exergy, which flow through the equivalent air film, except for the exergy destruction part. Then, the rest all become the thermal exergy of the water. In condensation dehumidification, the preceding processes are reversed. (4) In dehumidification between humid air and solution, the solution supplies its thermal exergy and concentration exergy to complete the exergy flow from solution to water. In the regeneration process, the humid exergy supplied by humid air, except for the exergy destruction part, is divided into two parts: one becomes the concentration exergy of the solution and the other is converted into the thermal exergy of the solution.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 51708104) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20160669).
L. Zhang et al. / Energy 187 (2019) 115976
11
Nomenclature a nv 1:608,u Mv ,u B¼ ,B ¼ ,B n 1 þ 1:608,u 1 þ Ma , u
M
A cp D Ex ex Exh Exm Exd,h Exd,m LD m M n P B Q r R Rv Ra T T0 V W X
u u0 a am
4
DT Du Subscripts a dp e S s v w
Pv ¼
Heat and mass transfer area (m2) Specific heat (kJ/(kgK)) Mass flux (kg/s) Exergy (kW) Exergy per mass flow rate (kJ/kg) Thermal exergy (kW) Humid exergy (kW) Thermal exergy destruction (kW) Humid exergy destruction (kW) Liquid desiccant Mass flow rate (kg/s) Molar mass (kg/mole) Number of moles (mole) Pressure (Pa) Atmospheric pressure (Pa) Heat (kW) Latent heat of vaporization (kJ/kg) General gas constant (kJ/(kgK)) Gas constant of vapor (kJ/(kgK)) Gas constant of dry air (kJ/(kgK)) Temperature (ºC) Reference temperature (ºC) Volume (m3) Work (kW) Concentration (%) Humidity ratio (g/kg) Reference humidity ratio (g/kg) Heat transfer coefficient (W/m2K) Mass transfer coefficient (kg/m2s) Relative humidity (%) Temperature difference (ºC) Moisture difference (g/kg)
(A4)
Mv
Humid exergy destruction during the mass transfer between two air states, as shown in Fig. A1, can be expressed in Eq. (A5):
dExd;m u1 u2 ¼ 1:608Ra T0 ln ln dD 1 þ 1:608u1 1 þ 1:608u2
(A5)
u1 and u2 are the humidity ratios of the two air states; TB and TA are the corresponding temperatures of u1 and u2, respectively, along the relative humidity line, 4; and TC and TD are the corresponding dew point temperatures of u1 and u2, respectively. According to Eq. (A4), Eq. (A5) can be rewritten as:
dExd;m P ¼ 1:608Ra T0 ln 1 dD P2
(A6)
The Clapeyron equation shows the relationship between any temperature and its saturated vapor pressure, as expressed in Eq. (A7):
lnPs ¼
r þ A0 Rv T
(A7)
where A0 and Rv are a constant and gas constant of vapor, respectively, r denotes the latent heat of vaporization, and Ps is the saturated vapor pressure. P1 and P2 can be thus expressed using the dew point temperature, TC, and TD separately. The following equation can then be obtained:
ln
P1 r 1 1 ¼ P2 Rv TD TC
(A8)
For any iso-relative humidity, 4, according to Eq. (A9), Eq. (A7) can be rewritten as Eq. (A10):
Air Dew point Equivalent air film Solution Saturation state Vapor Water
P ¼ fPs ln P ¼
(A9) r þ A0 ln f Rv T
(A10)
The temperatures at the same iso-relative humidity line, TB and TA, can thus be used to express P1 and P2, respectively:
Appendix A
ln Both the dry air and vapor in the humid air can be regarded as an ideal gas, so Eq. (A1) and (A2) can be obtained:
Pv V ¼ nv RT
(A1)
BV ¼ nRT
(A2)
P1 r 1 1 ¼ P2 Rv TA TB
(A11)
Eq. (A6) is rewritten as:
dExd;m r 1 1 r 1 1 ¼ 1:608Ra T0 ¼ 1:608Ra T0 Rv TD TC Rv TA TB dD
(A12)
where V denotes the volume, R is the general gas constant, B is the atmospheric pressure, and n is the total number of moles of dry air and vapor. Eq. (A1) is divided by Eq. (A2), shown as Eq. (A3):
where Rv/Ra ¼ 1.608, according to the molar masses of dry air and vapor, and the ideal gas thermodynamics state equation; thus Eq. (A12) can be rewritten as:
Pv nv ¼ B n
dExd;m 1 1 1 1 ¼ T0 ,r ¼ T0 ,r TD TC TA TB dD
(A3)
1 kg of dry air and u kg of vapor constitute the humid air, so 1 kmol of dry air corresponds to Ma/Mv$u kmol of vapor. Eq. (A3) can thus be rewritten as Eq. (A4):
(A13)
The humid exergy destruction is expressed by dew point temperatures or temperatures when they are exactly located at the same iso-relative humidity line.
12
L. Zhang et al. / Energy 187 (2019) 115976
Conflict of interest statement No conflicts of interest exist in the submission of this manuscript, and it has neither been published before nor been submitted to another journal for consideration. All authors listed have approved the enclosed manuscript for publication. I hereby declare that the work described in this manuscript was original research.
Fig. A.1 Mass transfer between two air states.
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[15] Chung TW. Predictions of moisture removal efficiencies for packed-bed dehumidification systems. Gas Sep Purif 1994;8:265e8. [16] Sanjeev J, Sagun T, Rajat SD. Experimental performance of a liquid desiccant dehumidification system under tropical climates. Energy Convers Manag 2011;52:2461e6. [17] Liu XH, Zhang Y, Qu KY, Jiang Y. Experimental study on mass transfer performances of cross flow dehumidifier using liquid desiccant. Energy Convers Manag 2006;47:2682e92. [18] Abdul-Wahab SA, Zurigat YH, Abu-Arabi MK. Predictions of moisture removal rate and dehumidification effectiveness for structured liquid desiccant air dehumidifier. Energy 2004;29:19e34. [19] Ullah MR, Kettleborough CF, Gandhidasan P. Effectiveness of moisture removal for an adiabatic counter flow packed tower absorber operating with CaCl2-air contact system. J Sol Energy-T ASME 1988;110:98e101. [20] Xie Y, Zhang T, Liu XH. Performance investigation of a counter-flow heat pump driven liquid desiccant dehumidification system. Energy 2016;115: 446e57. [21] Gomez-Castro FM, Schneider D, Paßler T, Eicker U. Review of indirect and direct solar thermal regeneration for liquid desiccant systems. Renew Sustain Energy Rev 2018;82:545e75. [22] Su Bosheng, Han Wei, Sui Jun, Jin Hongguang. A two-stage liquid desiccant dehumidification system by the cascade utilization of low-temperature heat for industrial applications. Appl Energy 2017;207:643e53. [23] Song Xia, Zhang Lun, Zhang Xiaosong. NTUm-based optimization of heat or heat pump driven liquid desiccant dehumidification systems regenerated by fresh air or return air. Energy 2018;158:269e80. [24] Wepfer WJ, Gaggioli RA, Obert EF. Proper evaluation of available energy for HVAC. ASHRAE Transact 1979;85:214e30. [25] Bejan A. Advanced engineering thermodynamics. second ed. New York: John Wiley & Sons; 1997. p. 217e35. [26] Qureshi BA, Zubair SM. Application of exergy analysis to various psychrometric processes. Int J Energy Res 2003;27:1079e94. [27] Akpinar EK, Hepbasli A. Comparative study on exergetic assessment of two ground-source (geothermal) heat pump systems for residential applications. Build Environ 2007;42. 2004e13. [28] Hepbasli A, Akdemir O. Energy and exergy analysis of a ground source (geothermal) heat pump system. Energy Convers Manag 2004;45:737e53. [29] Razmara M, Maasoumy M, Shahbakhti M, RobinettIII RD. Optimal exergy control of building HVAC system. Appl Energy 2015;156:555e65. [30] Muangnoi T, Asvapoositkul W, Wongwises S. An exergy analysis on the performance of a counterflow wet cooling tower. Appl Therm Eng 2007;27: 910e7. [31] Muangnoi T, Asvapoositkul W, Wongwises S. Effects of inlet relative humidity and inlet temperature on the performance of counterflow wet cooling tower based on exergy analysis. Energy Convers Manag 2008;49:2795e800. [32] Wang L, Li N. Exergy transfer and parametric study of counter flow wet cooling towers. Appl Therm Eng 2011;31:954e60. [33] Zhang L, Liu X, Jiang Y. Exergy analysis of parameter unmatched characteristic in coupled heat and mass transfer between humid air and water. Int J Heat Mass Transf 2015;84:327e38. [34] Ahmed CSK, Gandhidasan P, Zubair SM, Al-Farayedhi AA. Exergy analysis of a liquid-desiccant-based, hybrid air-conditioning system. Energy 1998;23: 51e9. [35] Xiong ZQ, Dai YJ, Wang RZ. Development of a novel two-stage liquid desiccant dehumidification system assisted by CaCl2 solution using exergy analysis method. Appl Energy 2010;87:1495e504. [36] Su Bosheng, Han Wei, Sui Jun, Jin Hongguang. Feasibility of a two-stage liquid desiccant dehumidification system driven by low-temperature heat and power. Appl Therm Eng 2018;128:795e804. [37] Peng D, Zhou J, Luo D. Exergy analysis of a liquid desiccant evaporative cooling system. Int J Refrig 2017;82:495e508. [38] Incropera FP, DeWitt DP, Bergman TL, Lavine AS. Fundamentals of heat and mass transfer. sixth ed. New York: John Wiley & Sons; 2005. [39] Kays WM, Crawford ME. Convective heat and mass transfer. second ed. New York: McGraw-Hill; 1980. [40] Bejan A. Advanced engineering thermodynamics. fourth ed. Newark: Wiley; 2016. p. 95e103. [41] Ren CQ, Li NP, T bang GF. Principles of exergy analysis in HVAC and evaluation of evaporative cooling schemes. Build Environ 2002;37:1045e55.
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Theoretical analysis of exergy destruction and exergy flow in direct contact process between humid air and water/liquid desiccant solution Lun Zhang*, Xia Song, Xiaosong Zhang School of Energy and Environment, Southeast University, Nanjing, 210096, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 April 2019 Received in revised form 15 August 2019 Accepted 18 August 2019 Available online 21 August 2019
Direct contact between humid air and water/liquid desiccant (LD) solution is common in air-conditioning systems, where transfer (heat/mass) and conversion (evaporation/condensation) processes occur. This work analyzes these processes using exergy theory and a two-film model. The exergy flow and exergy destruction of heat transfer and mass transfer can be expressed using a unified exergetic expression and depicted by a psychrometric chart. Results show that the equivalent air film of the water/solution is a medium for exergy flow and is thus used to determine the exergy change of the water/solution. Direct evaporative cooling and condensation dehumidification are two representative cases between humid air and water. In the former, the thermal exergy and humid exergy both flow from the humid air to water, where exergy destruction and conversion of the humid exergy into thermal exergy are inevitable. In the latter, thermal and humid exergy flows are all reversed. Dehumidification and regeneration are two crucial and reversed processes between the humid air and solution. The concentration exergy of the solution is involved in the thermal and humid exergy flows. The solution exports its concentration exergy to complete the exergy flows during dehumidification, and it obtains the concentration exergy from exergy flows during regeneration. © 2019 Published by Elsevier Ltd.
Keywords: Exergy Air-conditioning Liquid desiccant Heat and mass transfer
1. Introduction Water evaporation into humid air or vapor condensation into water/liquid desiccant (LD) solution is an integral process in many devices such as open or closed cooling towers [1,2], water spray cooling [3], dehumidifiers and humidifiers [4], which are common components of air-conditioning systems. In such a process, heat transfer and mass transfer coexist, directly affecting one another [4]. The mathematical models for heat and mass transfer processes between humid air and water have been presented in Refs. [2,5,6]. The models usually include four equations (the continuity equation, momentum equation, energy conservation equation, and the mass conservation equation) and the developed heat and mass transfer equations. Furthermore, Hawlader et al. [2] and Klimanek et al. [6] numerically predicted the distributions of velocity, density, temperature, and humidity ratio of humid air and water. The transfer
* Corresponding author. E-mail address: [email protected] (L. Zhang). https://doi.org/10.1016/j.energy.2019.115976 0360-5442/© 2019 Published by Elsevier Ltd.
characteristics and influencing factors (inlet parameters, flow rates, flow patterns) have also attracted much attention. Correlations for the mass and heat transfer coefficients in a closed wet cooling tower have been proposed [1]. Enayatollahi et al. [7] identified four distinct flow regimes in the interaction between humid air and water, where the transfer processes were characterized by empirical correlations. Likewise, Chuck et al. [8] measured the thermal conditions of humid air passing over the surface of water and determined its mass transfer coefficient. Furthermore, mass transfer plays an important role in the heat and mass transfer characteristics between the water surface and airstream [9]. The surface vapor pressure of LD solution is lower than that of pure water, so it is very effective in dehumidifying humid air [10]. The thermal properties of often-used solutions, such as lithium bromide and lithium chlorides, were studied in Refs. [11,12]. Mathematical models for the coupled heat and mass transfer processes between humid air and LD solution have been developed [4,13,14], which were solved numerically or analytically and were verified by experimental results. Performance indexes used to evaluate these processes include the outlet air state, the moisture removal rate, and the enthalpy or moisture effectiveness. Based on
2
L. Zhang et al. / Energy 187 (2019) 115976
Fig. 1. Air-treatment processes in air-conditioning systems.
these indexes, various studies have researched and optimized the coupled heat and mass transfer processes regarding their influencing factors, such as solution type [15], flow path [4] (mainly counter-flow, cross-flow, or parallel-flow), flow rate [16,17], and inlet states of the humid air and solution [17e19]. Besides focusing on the performances of a single dehumidifier and regenerator, researchers have proposed and analyzed various LD dehumidification systems, such as the heat pump driven LD system [20], the LD system regenerated by solar energy [21], the two-stage LD system by the cascade utilization of low-temperature heat [22], and the optimum area distribution between the dehumidifier and regenerator in the LD system [23]. The studies discussed above are mainly based on the first law of thermodynamics and the heat and mass transfer equations. Research from the perspective of the second law of thermodynamics, especially in the context of exergy, remains limited. Wepfer et al. [24] demonstrated the application of the second law to airconditioning systems. Exergy or availability is an accurate metric related to the quality of energy [25]. It can be used to evaluate the efficiency of energy systems and energy conversion processes. Qureshi et al. [26] presented a parametric work of air-conditioning processes by applying exergy analysis for measuring irreversible losses (or entropy generation). Akpinar et al. [27] and Hepbasli et al. [28] performed energy and exergy analyses for ground-source heat pump systems and gave exergy efficiency values for the systems. They concluded that the exergetic evaluation method may be a
Fig. 2. Two-film model as part of a differential transfer process between humid air and the equivalent air film of water/solution [37].
Fig. 3. Temperature difference and moisture difference between two air states.
useful tool, as ignored problems in energy systems can be found and new techniques can be proposed to further improve the systems’ performances. For example, an exergy model for the airconditioning system of a building was presented by Razmara et al. [29], and a model predictive control technique using the exergy model was developed to reduce exergy destruction. Bejan et al. [25] defined the total exergy of humid air, which is the sum of the thermomechanical exergy and chemical exergy, enabling exergy analysis to be applied to air-water contact systems. Muangnoi et al. [30] proposed the exergy distributions for water and humid air and the exergy destruction of a cooling tower. Moreover, second law efficiency based on the exergy changes of humid air and water in the tower was defined [31] to illustrate its performance under various inlet parameters. Wang et al. [32] investigated schematically the exergy transfer process in a tower and discussed the relationship between the exergy efficiency and thermal efficiency. The unmatched characteristic in the coupled heat and mass transfer processes between humid air and water was presented using exergy analysis [33] and it was found that reducing the unmatched coefficient could result in the decrease of exergy destruction. Exergy analysis has also been conducted on LD dehumidification systems. Ahmed et al. [34] investigated the exergy of a hybrid system, incorporating a dehumidifier based on LD, then calculated the irreversible losses of the system and attempted to optimize the desiccant flow rate. An exergy analysis model, incorporating a desiccant solution, was proposed by Xiong et al. [35] to facilitate the performance evaluation of a two-stage LD dehumidification system. Likewise, Su et al. [36] presented the exergy distribution in a two-stage LD system driven by low-temperature heat and power. Exergy of humid air, water and liquid desiccant were defined carefully by Peng et al. [37] to obtain exergy evaluation indexes of an LD evaporative cooling system. Most work has focused on either the direct contact between humid air and water or that between the humid air and solution, but little work has deployed a useful exergetic strategy to associate them. This work thus builds a unified model of the direct contact between humid air and water/solution, analyzing the heat transfer and mass transfer using exergetic theory. Then, the exergy destruction and exergy flow in several typical cases are clearly presented.
L. Zhang et al. / Energy 187 (2019) 115976
Fig. 4. Definition of work and exergy.
Fig. 5. Thermal exergy destruction in heat transfer.
Fig. 6. Thermal exergy flow during heat transfer.
3
4
L. Zhang et al. / Energy 187 (2019) 115976
Pv ¼ Pe
(2)
where subscripts e, w, v, and S denote the equivalent air film, water, vapor, and solution, respectively, and Pe is the equivalent vapor pressure of the state in equilibrium with the water/solution. The equivalent humidity ratio of the water/solution is defined as:
ue ¼ 0:622
Fig. 7. Mass transfer between two air states.
2. Model and basic definition 2.1. Transfer and conversion processes between humid air and water/LD solution In air-conditioning systems, many air-treatment processes involve direct contact between humid air and water or LD solution. Evaporative cooling in cooling towers, condensation dehumidification, dehumidification, and regeneration in LD dehumidification systems are the four main processes, as illustrated in Fig. 1. When humid air flows over the water/LD solution surface, a stagnant air film forms, which adheres to the surface [38]. A twofilm model theory can be used here [39], as shown in Fig. 2. The following assumptions are made: (a) The resistance of mass transfer is mainly located at the air side; (b) The properties of the water/solution side are uniformly distributed; (c) The properties of the air film are determined by the water/ solution side. The air film remains in equilibrium with the water/solution and is, therefore, regarded as the equivalent state of the water/solution. Accordingly, the temperature and vapor pressure of the film are given by Eqs. (1) and (2), respectively:
Te ¼ Tw orTe ¼ TS
(1)
Pe B Pe
(3)
where B is the standard atmospheric pressure. Owing to the temperature difference between the humid air and water/solution, heat transfer occurs between them. The air film is not capable of storing thermal energy. If Pv of the humid air is higher than Pe, vapor in the humid air will be transferred to the air film. Excessive vapor in the air film condenses into the water/solution. Conversely, vapor in the air film will be transferred to the humid air. Water evaporates into the air film, supplementing the transferred vapor. Thus, mass transfer occurs between the humid air and air film, and conversion (condensation or evaporation) occurs between the air film and water/solution, as demonstrated in Fig. 2. Fig. 2 shows a differential transfer process, after which, the states of both the humid air and air film fluctuate infinitesimally around the initial states. Any complete process consists of a series of consecutive differential processes, and thus, the following analysis mainly concerns about a differential process. The heat transfer and mass transfer between the two air states (the humid air and equivalent air film) are expressed in Eqs. (4) and (5). The driving forces (difference in temperature and moisture) are shown in the psychrometric chart in Fig. 3.
cp:a ma dTa ¼ aðTe Ta ÞdA
(4)
ma dua ¼ am ðua ue ÞdA
(5)
2.2. Exergy definition Exergy is defined as the available energy when any system develops reversibly into the state that is in equilibrium with a given reference state [40]. There are two key terms here: one is “reversibly”, representing an ideal, optimal process; the other is “reference state”, whose exergy is zero. Fig. 4(a) shows an object with temperature, T, and a reference object at temperature, T0. The infinitesimal sensible heat, dQ, is defined as positive when sensible heat is released from the considered object to the reference object and negative when heat
Table 1 Unified expression of heat transfer and mass transfer.
Driving forces Differential equations Transfer equations Derivation of exergy destruction Exergy destruction Deduction Unified exergetic expression
Heat transfer
Mass transfer
DT dQ ¼ mcp ,dT Q ¼ aA,DT dExd;h dExðT1 Þ dExðT2 Þ ¼ dQ dQ dQ
Du dD ¼ m,du D ¼ am A,Du dExd;m dExðu1 Þ dExðu2 Þ ¼ dD dD dD
dExd;h ¼ T0
dExd;m ¼ 1:608Ra T0 ln
-
dExd;h ¼ T0
1 1 dQ T2 T1
1 1 dQ T2 T1
Appendix A
dExd;m ¼ T0
u1
1 þ 1:608u1
! 1 1 ,rdD T2;dp T1;dp
ln
u2
1 þ 1:608u2
,dD
L. Zhang et al. / Energy 187 (2019) 115976
5
Fig. 8. Humid exergy flow during mass transfer.
flow is the other way round. When T is higher than T0, the maximum produced work, can be expressed by Eq. (6). The object supplies exergy. When T is lower than T0, the minimum absorbed work can also be expressed by Eq. (6). The object obtains exergy. Exergy is a positive value. For an object, the direction of exergy flow is distinguished by supplied exergy and obtained exergy.
dW ¼ T0
1 1 ,dQ T0 T
(6)
Accordingly, Fig. 4(b) shows the four possible situations concerning exergy flow for an object. The two background colors in Fig. 4(b) correspond, respectively, to those in Fig. 4(a). The exergy of an object is directly related to the reference state, which is the horizontal axis in Fig. 4(b). The exergy of humid air itself, which consists of 1 kg of dry air and u kg of vapor, at standard atmospheric pressure, is the sum of thermal exergy and humid exergy [33], which is:
where Ra denotes the gas constant of air, u0 is the reference humidity ratio, and cp.m is defined as:
cp:m ¼ cp:a þ u,cp:v
(8)
cp.a is the specific heat of dry air and cp.v is the specific heat of vapor. The reference temperature of thermal exergy, T0, is chosen as the ambient temperature, and the reference humidity ratio of humid exergy, u0, is chosen as the saturated humidity ratio of T0 [41]. Since the equivalent state of the water/solution is shown to be, in the psychrometric chart, similar to that of the humid air, their exergy can also be expressed by the above equation using the temperature (Te) and the equivalent humidity ratio (ue) of the equivalent air film.
3. Exergy destruction during heat and mass transfer 3.1. Exergy destruction during heat transfer
ExðT; uÞ ¼ m,exðT; uÞ T T 1 þ 1:608u0 u ¼ cp:m mT0 þ mRa T0 ð1 þ 1:608uÞln 1 ln þ 1:608u ln u0 T0 T0 1 þ 1:608u
(7)
Fig. 5(a) shows that dQ is transferred between object 1, with temperature T1, and object 2 with temperature T2, a transferal which is an irreversible process with exergy destruction. This transferal assumes a possible corresponding reversible process with a Carnot cycle and a reverse Carnot cycle, as illustrated in Fig. 5(b). The reversible process can produce extra work (dW1þdW2) compared with the irreversible process, which is exactly the exergy destruction during heat transfer, as depicted in Eq. (9):
dExd;h ¼ dW1 þ dW2 ¼ T0
1 1 dQ T2 T1
(9)
In the process, as seen in Fig. 5(a), according to the exergy definition, object 1 releases dQ, so it exports exergy. Object 2 absorbs dQ, so it obtains exergy. The exergy destruction is the difference between the supplied exergy and the obtained exergy as shown by Eq. (10):
dExd;h ¼ dExðT1 Þ dExðT2 Þ ¼ T0 Fig. 9. Thermal and humid exergy destruction.
1 1 dQ T2 T1
(10)
6
L. Zhang et al. / Energy 187 (2019) 115976
Fig. 11. Exergetic analysis of the transfer and conversion processes of condensation dehumidification.
Fig. 10. Exergetic analysis of the transfer and conversion processes of evaporative cooling.
Object 1 offers the exergy, part of which is absorbed by object 2, and the rest is destroyed, as demonstrated in Fig. 6(a). Accordingly, the exergy balance is demonstrated in Fig. 6(b). dEx(T1) is divided into two parts, dExd,h and dEx(T2), expressed as a dotted line. dEx(T2) should have been at the second quadrant, so it is moved to the right with a solid line. According to Eqs. (7) and (8), the exergy destruction during heat transfer (thermal exergy destruction) between two air states, with temperatures T1 and T2, respectively, can be calculated as in Eq. (11). The result is the same as that shown in Eq. (10):
L. Zhang et al. / Energy 187 (2019) 115976
7
Table 2 A case study of the condensation dehumidification process.
Water Equivalent air film
Parameter
Value
dExh
dExm
dExd,h
dExd,m
T
15 C
-
e
-
T or Tdp
15 C 10.65 g/kg 32 C 20 g/kg 24.91 C
1.333$(dQþrdD) (Supplied) 1.333$dQ (Medium)
(Conversion) 1.333$rdD (Medium) 0.405$rdD (Obtained)
1.240$dQ (Destroyed)
0.928$rdD (Destroyed)
u
Humid air
T
u Tdp
0.093$dQ (Obtained)
Table 3 A case study of the regeneration process. Parameter Value Humid air
20 C 8 g/kg 10.89 C 33 C 20 g/kg 24.91 C 33 C 34.84%
T
u Tdp Equivalent air film T
u
Tdp T X
Solution
dExh
dExm
0.750$dQ (Supplied)
2.214$rdD (Supplied) e
0.061$dQ (Medium)
0.405$rdD (Medium)
(Conversion) e 0.061$dQþ0.061$rdD (Obtained)
dExd;h dExðT1 Þ dExðT2 Þ 1 vexðT1 Þ vexðT2 Þ ¼ ¼ cp:m vT vT dQ dQ dQ
¼ T0
1 1 T2 T1
(11)
3.2. Exergy destruction during mass transfer The mass transfer between two air states with different moisture contents is shown in Fig. 7. dD is transferred from the state 1 to state 2. The exergy destruction during mass transfer (humid exergy destruction) can be calculated by Eq. (12):
dExd;m dExðu1 Þ dExðu2 Þ vexðu1 Þ vexðu2 Þ ¼ ¼ vu vu dD dD dD
(12)
Substituting the exergy equation of humid air, Eq. (12) is rewritten as [33]:
dExd;m u1 u2 ¼ 1:608Ra T0 ln ln dD 1 þ 1:608u1 1 þ 1:608u2
dExC
dExd,h
dExd,m
0.689$dQ (Destroyed) 1.809$rdD (Destroyed)
e
0.344$rdD (Obtained) e
e
the expression for humid exergy destruction consists of dew point temperatures (T1,dp and T2,dp) and latent heat, rdD. Accordingly, when a state with humidity ratio, u, transfers dD with reference state, u0, its humid exergy can also be defined as expressed in Eq. (15), using its dew point temperature, Tdp, and latent heat, rdD, similar to the thermal exergy shown in Fig. 4 and Eq. (6). In Fig. 7, state 1 transfers dD to state 2, so humid exergy destruction during this process can be calculated using the same method as that in Fig. 5. State 1 releases rdD, but its dew point temperature is lower than T0, so it obtains exergy. State 2 absorbs rdD, so it exports exergy. The exergy destruction is given by Eq. (16). Fig. 8 shows humid exergy flow and exergy balance. Part of the exergy supplied by state 2 flows to state 1 and the rest is destroyed.
dEx Tdp ¼ T0
! 1 1 r dD T0 Tdp
dExd;m ¼ dEx T2;dp dEx T1;dp ¼ T0
(15)
1 T2;dp
1 T1;dp
! ,r dD
(13)
(16) In summary, thermal exergy destruction and humid exergy destruction can be expressed in a unified way, as shown in Fig. 9.
3.3. Unified expression of thermal exergy destruction and humid exergy destruction Since thermal exergy is expressed using temperature but humid exergy using the humidity ratio, it is difficult to compare the two. In order to further illuminate the relationship between thermal and humid exergy, humid exergy can be expressed in a unified way as thermal exergy (the derivation process is in Appendix A). As shown in Fig. 7, humid exergy destruction is thus written as:
dExd;m ¼ T0
1 T2;dp
1 T1;dp
! ,rdD
(14)
Table 1 clearly demonstrates the unified expression of heat and mass transfer. The expression for thermal exergy destruction consists of temperatures (T1 and T2) and transferred heat, dQ. However,
4. Exergy analysis for direct contact processes between humid air and water/solution 4.1. Transfer and conversion processes between humid air and water The equivalent water state is located on the saturation curve, as shown in Fig. 1. Given a specific water temperature, Tw, the corresponding equivalent humidity ratio, ue, is exactly that of the saturated air with temperature Tw. This paper considers the two cases between humid air and water, evaporative cooling and condensation dehumidification. 4.1.1. Evaporative cooling process Direct evaporative cooling is common in air-conditioning
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dExh;a þ dExm;a dExh;w;1 þ dExh;w;2 ¼ dExd;h þ dExd;m
(17)
Fig. 12. Heat, mass and exergy flowing through the equivalent air film.
systems, where humid air is usually used to cool water, such as occurs in a cooling tower. Owing to the temperature difference and moisture difference, water releases heat and evaporates into humid air. For an infinitesimal process, dQ is thus transferred from water to humid air through the equivalent air film. Meanwhile, liquid dD first evaporates into the air film and is then transferred to humid air, with latent heat rdD. The thermal and humid exergy of the humid air and water are presented in Fig. 10(a). The equivalent water state is the saturated humid air, consisting of both thermal exergy, dExh,e, and humid exergy, dExm,e. However, water is completely liquid with thermal exergy only [33]. Thermal exergy destruction and humid exergy destruction, during the transfer process, are illustrated in Fig. 10(b). Fig. 10(c) shows exergy flow in this process. During heat transfer, humid air provides its thermal exergy, dExh,a, part of which is absorbed by the equivalent air film and then flows to the water (dExh,w,1). The rest is destroyed through thermal exergy destruction. In mass transfer, humid air supplies its humid exergy, dExm,a, part of which is destroyed through humid exergy destruction. The rest flows to the equivalent air film and then is converted to thermal exergy of the water (dExh,w,2). The air film is not capable of storing exergy and is merely a medium for exergy flow. Fig. 10(d) and Eq. (17) present the exergy balance during this process. The two terms on the left in Eq. (17) are the total supplied exergy and the total obtained exergy, respectively. The term on the right is the total exergy destruction.
4.1.2. Condensation dehumidification process During the condensation dehumidification process, humid air is cooled and dehumidified. dQ is thus transferred from the humid air to the equivalent air film, and finally to chilled water. Meanwhile, gaseous dD in humid air is first transferred into the air film and then condenses into chilled water, with latent heat rdD. Fig. 11(a) presents the thermal and humid exergy destruction in this process, and Fig. 11(b) displays its exergy flow. The water offers two portions of thermal exergy, dExh,w,1 and dExh,w,2. dExh,w,1 flows directly through the equivalent air film and part of it is absorbed by the humid air, with the rest being destroyed. dExh,w,2 is first converted into the humid exergy of the air film, then part of it flows to the humid air, with the rest being destroyed. Again, the air film is merely a medium for exergy flow. Fig. 11(c) and Eq. (18) demonstrate the exergy balance in this process. The three terms in Eq. (18) are the total exergy supplied by water, the total exergy absorbed by humid air, and the total exergy destruction.
dExh;w;1 þ dExh;w;2 dExh;a þ dExm;a ¼ dExd;h þ dExd;m
(18)
4.1.3. Case study The condensation dehumidification process at standard atmospheric pressure is taken as an example. Table 2 gives detailed values of relevant parameters. The exergy destruction occurs between the humid air and equivalent air film. Humid exergy of the air film derives from the conversion process between water and its air film. 4.2. Transfer and conversion processes between humid air and liquid desiccant solution 4.2.1. Definition of exergy concentration of solution As discussed above, the equivalent air film of water is only a medium for heat transfer, mass transfer, and exergy flow, as shown in Fig. 12, so the supplied exergy or the obtained exergy of the water
Fig. 13. Concentration exergy definition of the LD solution.
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9
dExw ¼ dExh;w;1 þ dExh;w;2 ¼ dExh;e;w þ dExm;e;w
vex ue;w vexðTw Þ vexðT0 Þ vexðu0 Þ þ cp:m vT vT vu vu 1 1 ,ðdQ þ rdDÞ ¼ T0 T0 Tw
¼
1
(19)
Likewise, the change in exergy of the solution can also be expressed using the exergy flowing through its equivalent air film, as shown in Eq. (20).
dExS ¼ dExh;e;S þ dExm;e;S
vex ue;S vexðTS Þ vexðT0 Þ vexðu0 Þ þ cp:m vT vT vu vu ! 1 1 1 1 ,dQ þ T0 ¼ T0 ,rdD T0 TS T0 TS;dp ¼
1
(20)
The equivalent air film of pure water with temperature, Tw, is located on the saturation curve, as shown in Fig. 13. The equivalent air film of solution (TS ¼ Tw, concentration X) is also shown in Fig. 13. The thermal exergies of the water and solution are identical. The humid exergy difference between them results from concentration, X. The excess part is thus the concentration exergy of the LD solution, expressed by Eq. (21):
vex ue;S vex ue;w dExC;S ¼ dExS dExw ¼ vu vu ! 1 1 ¼ T0 ,rdD TS TS;dp
(21)
The higher the concentration, the greater the concentration exergy of the solution. Unlike pure water, the LD solution includes not only the thermal exergy but also the concentration exergy.
Fig. 14. Exergetic analysis of the transfer and conversion processes of dehumidification process.
(the exergy change of the water) can be expressed by the exergy flowing through the air film. As shown in Figs. 10(c) and Fig. 11(b), the exergy change of the water can be written as:
4.2.2. Dehumidification process This work considers the two possibilities between humid air and solution, dehumidification and regeneration, as shown in Fig. 1. The LD solution with a lower temperature and humidity ratio is used to cool and dehumidify humid air. dQ is transferred from humid air to the solution through the equivalent air film. Meanwhile, gaseous dD in humid air is first transferred into the air film and then condenses into solution, with latent heat rdD. The solution concentration, X, thus decreases, and so too does the concentration exergy of the solution. Fig. 14(a) shows the thermal, humid, and concentration exergy of the solution and humid air. Transfer loss between the humid air and equivalent state is demonstrated in Fig. 14(b). The solution offers two parts of thermal exergy, dExh,S,1, with sensible heat, dQ, and dExh,S,2 with latent heat, rdD, as demonstrated in Fig. 14(a) and (c). dExh,S,1 flows through the equivalent air film and then part of it is lost through thermal exergy destruction. The rest is obtained by humid air. dExh,S,2 is first converted to the humid exergy of the air film together with the concentration exergy, dExC,S, supplied by the solution, as shown by Fig. 14(c) and 14(d) and Eq. (22). Part of dExm,e flows to the humid air and the rest is destroyed. The equivalent air film is also a medium for exergy flow. Fig. 14(d) and Eq. (23) demonstrate the exergy balance in this process. The two terms on the left in Eq. (23) are the total supplied exergy and total obtained exergy, respectively, while the term on the right is the total exergy destruction.
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between humid air and the equivalent air film is demonstrated in Fig. 15(a). The humid air offers its thermal exergy, dExh,a, and humid exergy, dExm,a. Part of dExh,a is destroyed through thermal exergy destruction, the remainder flowing to the solution through the equivalent air film. Part of dExm,a is destroyed and the rest flows to the equivalent air film. Then, dExm,e is divided into two parts: one part becomes the concentration exergy of the solution and the other part is converted into the thermal exergy of the solution, as demonstrated in Fig. 15(b) and Eq. (24). Fig. 15(c) and Eq. (25) demonstrate the exergy balance in this process. The three terms in Eq. (25) are the total supplied exergy, the total obtained exergy, and the total exergy destruction, respectively.
dExm;e ¼ dExC;S þ dExh;S;2
dExh;a þ dExm;a dExh;S;1 þ dExh;S;2 þ dExC;S
¼ dExd;h þ dExd;m
(24) (25)
4.2.4. Case study The regeneration process at standard atmospheric pressure is taken as an example. Table 3 gives detailed values, which exactly satisfy Eq. (24) and Eq. (25).
5. Conclusions This work theoretically analyzes the direct contact process between humid air and water/LD solution using exergy theory. The following is a summary of the conclusions:
Fig. 15. Exergetic analysis of the transfer and conversion processes of regeneration process.
dExC;S þ dExh;S;2 ¼ dExm;e
(22)
dExh;S;1 þ dExh;S;2 þ dExC;S dExh;a þ dExm;a ¼ dExd;h þ dExd;m
(23)
4.2.3. Regeneration process Humid air with a lower temperature and lower humidity ratio is used to cool and concentrate the solution during the regeneration process. dQ is thus transferred from the solution to humid air. Meanwhile, liquid dD first evaporates into the equivalent state and then is transferred to humid air, with latent heat, rdD. The solution concentration, X, thus increases, and so too does the concentration exergy of solution. The transfer loss, in other words, the exergy destruction,
(1) Exergy flow and exergy destruction of heat transfer and mass transfer between two air states can be expressed in a unified expression (as in Eqs. (10) and (16)), in which the heat transfer and mass transfer are expressed by dry-bulb temperatures and dew point temperatures, respectively. (2) The equivalent air film of water or a solution is a medium not only for the transfer of heat and mass but also for exergy and is thus used to determine the supplied exergy or obtained exergy of the water/solution. Accordingly, the concentration exergy of the solution can be defined as the exergy difference between the two equivalent air films. (3) During direct evaporative cooling between humid air and water, humid air provides its thermal exergy and humid exergy, which flow through the equivalent air film, except for the exergy destruction part. Then, the rest all become the thermal exergy of the water. In condensation dehumidification, the preceding processes are reversed. (4) In dehumidification between humid air and solution, the solution supplies its thermal exergy and concentration exergy to complete the exergy flow from solution to water. In the regeneration process, the humid exergy supplied by humid air, except for the exergy destruction part, is divided into two parts: one becomes the concentration exergy of the solution and the other is converted into the thermal exergy of the solution.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 51708104) and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20160669).
L. Zhang et al. / Energy 187 (2019) 115976
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Nomenclature a nv 1:608,u Mv ,u B¼ ,B ¼ ,B n 1 þ 1:608,u 1 þ Ma , u
M
A cp D Ex ex Exh Exm Exd,h Exd,m LD m M n P B Q r R Rv Ra T T0 V W X
u u0 a am
4
DT Du Subscripts a dp e S s v w
Pv ¼
Heat and mass transfer area (m2) Specific heat (kJ/(kgK)) Mass flux (kg/s) Exergy (kW) Exergy per mass flow rate (kJ/kg) Thermal exergy (kW) Humid exergy (kW) Thermal exergy destruction (kW) Humid exergy destruction (kW) Liquid desiccant Mass flow rate (kg/s) Molar mass (kg/mole) Number of moles (mole) Pressure (Pa) Atmospheric pressure (Pa) Heat (kW) Latent heat of vaporization (kJ/kg) General gas constant (kJ/(kgK)) Gas constant of vapor (kJ/(kgK)) Gas constant of dry air (kJ/(kgK)) Temperature (ºC) Reference temperature (ºC) Volume (m3) Work (kW) Concentration (%) Humidity ratio (g/kg) Reference humidity ratio (g/kg) Heat transfer coefficient (W/m2K) Mass transfer coefficient (kg/m2s) Relative humidity (%) Temperature difference (ºC) Moisture difference (g/kg)
(A4)
Mv
Humid exergy destruction during the mass transfer between two air states, as shown in Fig. A1, can be expressed in Eq. (A5):
dExd;m u1 u2 ¼ 1:608Ra T0 ln ln dD 1 þ 1:608u1 1 þ 1:608u2
(A5)
u1 and u2 are the humidity ratios of the two air states; TB and TA are the corresponding temperatures of u1 and u2, respectively, along the relative humidity line, 4; and TC and TD are the corresponding dew point temperatures of u1 and u2, respectively. According to Eq. (A4), Eq. (A5) can be rewritten as:
dExd;m P ¼ 1:608Ra T0 ln 1 dD P2
(A6)
The Clapeyron equation shows the relationship between any temperature and its saturated vapor pressure, as expressed in Eq. (A7):
lnPs ¼
r þ A0 Rv T
(A7)
where A0 and Rv are a constant and gas constant of vapor, respectively, r denotes the latent heat of vaporization, and Ps is the saturated vapor pressure. P1 and P2 can be thus expressed using the dew point temperature, TC, and TD separately. The following equation can then be obtained:
ln
P1 r 1 1 ¼ P2 Rv TD TC
(A8)
For any iso-relative humidity, 4, according to Eq. (A9), Eq. (A7) can be rewritten as Eq. (A10):
Air Dew point Equivalent air film Solution Saturation state Vapor Water
P ¼ fPs ln P ¼
(A9) r þ A0 ln f Rv T
(A10)
The temperatures at the same iso-relative humidity line, TB and TA, can thus be used to express P1 and P2, respectively:
Appendix A
ln Both the dry air and vapor in the humid air can be regarded as an ideal gas, so Eq. (A1) and (A2) can be obtained:
Pv V ¼ nv RT
(A1)
BV ¼ nRT
(A2)
P1 r 1 1 ¼ P2 Rv TA TB
(A11)
Eq. (A6) is rewritten as:
dExd;m r 1 1 r 1 1 ¼ 1:608Ra T0 ¼ 1:608Ra T0 Rv TD TC Rv TA TB dD
(A12)
where V denotes the volume, R is the general gas constant, B is the atmospheric pressure, and n is the total number of moles of dry air and vapor. Eq. (A1) is divided by Eq. (A2), shown as Eq. (A3):
where Rv/Ra ¼ 1.608, according to the molar masses of dry air and vapor, and the ideal gas thermodynamics state equation; thus Eq. (A12) can be rewritten as:
Pv nv ¼ B n
dExd;m 1 1 1 1 ¼ T0 ,r ¼ T0 ,r TD TC TA TB dD
(A3)
1 kg of dry air and u kg of vapor constitute the humid air, so 1 kmol of dry air corresponds to Ma/Mv$u kmol of vapor. Eq. (A3) can thus be rewritten as Eq. (A4):
(A13)
The humid exergy destruction is expressed by dew point temperatures or temperatures when they are exactly located at the same iso-relative humidity line.
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Conflict of interest statement No conflicts of interest exist in the submission of this manuscript, and it has neither been published before nor been submitted to another journal for consideration. All authors listed have approved the enclosed manuscript for publication. I hereby declare that the work described in this manuscript was original research.
Fig. A.1 Mass transfer between two air states.
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