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Investigation on gradient thermal cycle for power and refrigeration cogeneration
Accepted Manuscript Title: Investigation on gradient thermal cycle for power and refrigeration cogeneration Author: L. Jiang, R.Z. Wang, L.W. Wang, P. Gao, F.Q. Zhu PII: DOI: Reference:
S0140-7007(17)30038-5 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.01.018 JIJR 3530
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
2-9-2016 16-1-2017 19-1-2017
Please cite this article as: L. Jiang, R.Z. Wang, L.W. Wang, P. Gao, F.Q. Zhu, Investigation on gradient thermal cycle for power and refrigeration cogeneration, International Journal of Refrigeration (2017), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.01.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Investigation on gradient thermal cycle for power and refrigeration cogeneration L. Jiang, R.Z. Wang*, L.W. Wang, P. Gao, F.Q. Zhu Institute of Refrigeration and Cryogenics, Key Laboratory of Power Machinery and Engineering of Ministry of
Education, Shanghai Jiao Tong University, Shanghai, 200240, China * Corresponding author. Email: [email protected]; Tel. +86-21-34206548; Fax. + 86-21-34206548
Highlights
A novel gradient thermal cycle for power and refrigeration cogeneration is proposed.
ENG-TSA as the additive improves the heat and mass performance of composite adsorbent.
The maximum power and cooling effect can be obtained as 204 W and 0.91 kW, respectively.
The exergy efficiency of heat utilization ranges from 18.8% to 24%.
Abstract: In order to improve energy utilization efficiency of low grade heat, a novel gradient thermal cycle for power and refrigeration cogeneration is proposed. The cycle is cascaded with two stages based on different thermal driven temperature. The first stage is pumpless Organic Rankine Cycle (PRC) while the second stage is two-stage sorption refrigerator. R245fa is selected as the working fluid of PRC whereas CaCl2-BaCl2-NH3 working pair is chosen for two-stage sorption refrigerator. Different heat source temperature from 80oC to 95oC are adopted for analysis and comparison. Results indicate that the highest average power output and cooling effect are able to reach 204 W and 0.91 kW under the condition of 95oC heat source temperature and 10oC refrigeration temperature. For different heat source temperature, total energy and exergy efficiency of the gradient thermal cycle for power and refrigeration cogeneration range from 9.49% to 9.9% and 10.9% to 11.8%, respectively. For gradient thermal cycle exergy efficiency of heat utilization ranges from 24% to 18.8%, which is 126.5% and 70.9% higher than the PRC and two-stage sorption refrigerator, respectively when the heat source temperature is 80oC.
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Keywords Pumpless Organic Rankine Cycle (PRC); Sorption; Exergy efficiency; Gradient thermal cycle 1
1
This paper was presented at SET2016
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Nomenclature c
Specific heat (kJ·kg-1·oC-1)
COP
Coefficient of performance
E
Exergy (kW)
h
Enthalpy (kJ·kg-1)
HTS
High temperature salt
HX
Heat exchanger
LTS
Low temperature salt
m
Mass flowrate (kg·s-1)
M
Mass (kg)
PRC
Pumpless Organic Rankine Cycle
Q
Heat (kW)
R
Gas constant (J·mol-1·K-1)
SCP
Specific cooling power (W·kg-1)
t
Time (s)
T
Temperature (K)
W
Power output (W)
Greek letters η
Efficiency
Subscripts ads
Sorbent
ave
Average
cool
Cooling water
chilled
Chilled water
cycle
Gradient thermal cycle
des
Desorption
En
Energy
eva
Evaporation
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Ex
Exergy
exp
Expander
H
Heat
hx
Heat exchanger
L
Liquid
PRC
Pumpless Organic Rankine Cycle
ref
Refrigeration
tot
Total
V
Vapor
1. Introduction Thermal driven power generation and refrigeration are two major technologies to recover the low grade heat source, which have been drawn a burgeoning number of attentions in recent years (Han et al., 2014; Wang et al., 2016). To further improve the efficiency of low temperature heat source, especially for that lower than 100oC, power and refrigeration cogeneration cycle has been proposed with many forms (Chaiyat and Kiatsiriroat, 2015; Yang et al., 2016). Among them, gradient thermal cycle is desirable to have a big temperature drop at the inlet and outlet of the cogeneration system. Selection of power generation and refrigeration cycles for gradient thermal cycle are usually critical. For power generation part, it always requires relatively higher driven temperature, which is suitable for the construction as the first stage (Yue et al., 2016). As one major kind of thermal driven power generation type for low temperature heat utilization, Organic Rankine Cycle (ORC) take advantages of simplicity and flexibility. Various researchers investigated ORC systems for efficient utilization of waste heat. Working fluid and external boundary conditions are two main research hotspots for improving thermal efficiency. Kaska et al. (Kaşka, 2014) conducted both energy and exergy analysis on ORC system driven by steel industrial waste heat. Simulation results indicated that the energy efficiency and exergy efficiency of the system were 10.2% and 48.5%, respectively. Peris et al.(Peris et al., 2015) investigated the performance of an ORC module. The maximum gross electrical efficiency obtained was able to reach 12.32% when heat source temperature was about 155oC, and
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outlet waste heat was dissipated to the ambient directly. However, considering small-scale ORC systems, working fluid pump acted as main components will consume a large part of power resulting in the loss of energy efficiency and compactness of the system(Yamada et al., 2013). Therefore, one innovative idea is to regard the possibility of eliminating the pump so that the system efficiency for small ORC system can be further improved. One approach is to use the gravity of working fluid to drive small ORC system. Although working fluid pump could be replaced by this method, the required height would be the bottleneck of this novel design(Li et al., 2013). After that, a novel PRC (pumpless Organic Rankine Cycle) prototype was considered to be alternative solution(Yamada et al., 2011). Experimental results demonstrated that the novel cycle had capability of producing power. Nonetheless, the maximum shaft power obtained was very small, which was lower than 50 W. Later, Gao et al.(Gao et al., 2015) investigated a PRC system, trying to gain a relative higher electricity output. The results indicated a potential for better power output. For refrigeration part, sorption refrigeration tends to be selected as the second stage since it is one perspective method of thermal driven refrigeration for recovering low temperature heat source(Li et al., 2014). As one commercial system, silica gel-water sorption refrigeration has been designed as the second stage of cascading cycle for power and refrigeration cogeneration(Wang, 2014) since silica gel-water sorption chiller has been extensively investigated. Khan et al.(Khan et al., 2007) studied a three-stage silica-gel/water sorption chiller that could generate cooling power with the lowest heat source temperature of 50oC and the coolant temperature of 30oC. Shanghai Jiao Tong University successfully developed a silica gel-water sorption chiller with modular adsorbers (Pan et al.). However, due to the property limitation of water, working pair of silica gel-water cannot be applied for freezing conditions. Under this scenario, two-stage sorption refrigeration will be one good solution to both air conditioning and freezing condition since it has flexibility to adapt to heat source with different temperatures. Even if the outlet temperature of the PRC is relatively low and severe environmental condition when condensing temperature is higher than 40 oC, two-stage sorption cycle is still able to reach the reasonable performance, which is the reason why it is selected as the second stage of the gradient thermal cycle. Wang et al.(Wang et al., 2013) established a two-stage sorption chiller by means of composite sorbents of CaCl2 and BaCl2. Results showed that the optimal coefficient of performance (COP) and specific cooling power (SCP) are 0.127 and 100 W·kg-1 under 15oC refrigeration temperature. Later, this energy conversion technology was investigated for the possibility
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to apply into a refrigerated truck, and it proved that maximum refrigerating capacity of 1.25 kW and COP of 0.143 were obtained at a resorption time of 120 min when the hot air temperature and refrigerating temperature were 230oC and 5oC, respectively (Gao et al., 2016a; Gao et al., 2016b). Two-stage sorption refrigeration with two sorption beds are intermittent refrigeration. Comparably, PRC system is able to generate the power in most phases of cycle. Therefore, cascading these two cycles will achieve power and cooling output in one cycle. In this paper, an innovative gradient thermal cycle for power and refrigeration cogeneration is proposed, and concerning system is designed and established. Heat source temperature from 80oC to 95oC and evaporation temperature from 5oC to 10oC are employed for overall investigation, and results are analyzed and compared.
2. Design of gradient thermal cycle Design of gradient thermal cycle for power and refrigeration cogeneration is shown in Fig.1, and two parts are included. The first part is PRC while the second part is CaCl2/BaCl2 two-stage sorption refrigeration cycle. R245fa is selected as the refrigerant for PRC which proves to be one good working fluid for low temperature heat source (Ghim and Lee, 2016), and ammonia is utilized for two-stage sorption refrigeration cycle. As it shows in Fig.1, two different cycles are connected with water pipelines. One hot water line and one cooling water line are included, which serve as heat source and cooling source, respectively. Hot water first flows into PRC, and then goes through two-stage sorption refrigeration cycle. Under this scenario, the low temperature heat is able to be recovered successively, which further improves the efficiency of heat utilization. The power and cooling effect could be obtained in this working process. Ethanol water solution in chilled water tank is used for transporting the cooling capacity out of the evaporator. PRC part mainly consists of two heat exchangers i.e. heat exchanger 1(HX1) and heat exchanger 2 (HX2), one expander, one generator and other auxiliary equipment. Two-stage sorption refrigeration cycle, which is composed of two sorption beds i.e. High temperature salts (HTS) bed and Low temperature salts (LTS) bed, one condenser, one evaporator and ammonia valves. CaCl2 is selected as the HTS whereas BaCl2 is chosen for the LTS. The thermochemical reaction process of CaCl2 and BaCl2 with ammonia can be referred to the equations 1-3. The reasons of selecting CaCl2-BaCl2-NH3 as
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the working pairs lie in thermal driven temperature and the match of different chlorides. As stated above, the inlet temperature of the two-stage sorption refrigerator is the outlet temperature of the PRC, which is lower than 95oC. Taking 85oC thermal driven temperature and 25oC environmental temperature into consideration, according to the Chaperon lines of common chlorides, PbCl 2, SnCl2, NH4Cl and BaCl2 could be selected as LTS while CaCl2 and SrCl2 can be chosen for HTS. PbCl2 and SnCl2 have the disadvantage of relatively low cycle quantity whereas NH4Cl is easy to be condensed since it is closed to the ammonia line. Similarly, CaCl2 has the higher cycle sorption quantity than that of SrCl2. Therefore, CaCl2 and BaCl2 are more suitable for HTS and LTS. The more details could be referred to our previous work (Hu et al., 2011). C aC l 2 4 N H 3 4 N H 3 C aC l 2 8 N H 3 4 H C aC l 2
(1)
B aC l 2 8 N H 3 B aC l 2 8 N H 3 8 H B aC l 2
(2)
N H 3 (gas) N H 3 (liq) H cond
(3)
Fig.2 indicates the thermodynamic diagram for T-S diagram of PRC and P-T diagram of two-stage sorption refrigeration cycle, which are manifested in Fig.2a and Fig.2b, respectively. The working processes of gradient thermal cycle consist of four processes in one cycle, which are as follows: Preheating process: HX1 serves as an evaporator, and HX2 acts as a condenser. Hot water flows into the HX1 for preheating. Pressure of the HX1 increases gradually until it reaches an almost constant value which is quite close to saturation pressure of R245fa. Simultaneously the cooling water flows into the HX2 for cooling through the cooling tower. Power generation process: As the pressure of the HX1 climbs to be constant, the high-pressure refrigerant inside the HX1 flows into the expander, generating power until no pressure difference happens between the HX1 and HX2, which is 1-2 in Fig.2a. At this moment the heating process inside HX1 is an isobaric heating process, which is 4-1 in Fig.2a. The expanded refrigerant enters the HX2, and it. After first power generation process, HX1 replaces the role as a condenser, and HX2 exchanges the role as an evaporator. Hot water begins to heat HX2 and cooling water begins to cool HX1 Sorption process of HTS bed: In this process, HTS bed is cooled by the cooling water. HTS bed adsorbs the ammonia from the evaporator, which is E-F in Fig.2b. The evaporation process of the 7 Page 7 of 27
ammonia inside the evaporator provides the cooling effect. Meanwhile LTS bed is heated by the hot water, which is the outlet temperature of PRC cycle. The ammonia is desorbed from the LTS bed. The desorbed ammonia will be condensed in the condenser, which is C-D in Fig.2b. Resorption process: HTS bed is heated by the hot water and desorbs ammonia to LTS bed, which is A-B in Fig.2b. The LTS bed is cooled by the cooling water to facilitate sorption of LTS bed. Sorption process of HTS bed and resorption process will proceed with preheating and power generation processes. Under this scenario, the gradient thermal cycle is able to supply refrigeration and cooling power sequentially.
Fig.3 shows photograph of gradient thermal system, in which Fig.3a is the photo of power and refrigeration cogeneration system. As Fig.3a shows, two sorption beds, i.e. HTS and LTS bed are installed at the lower position of experimental rig. Two heat exchangers of PRC, i.e. HX1 and HX2 are placed at the higher position. The scroll expander and generator are in the middle position. Temperature of sorption bed and heat exchangers are adjusted by the hot water and cooling water. Temperature of evaporator is controlled by the by ethanol water tank. Composite sorbent of each tube weighs about 0.8kg. Composite BaCl2 is filled in the LTS bed, which contains seven unit tube. Each tube weighs about 0.96kg. Therefore, total mass of composite CaCl2 and BaCl2 are 5.6 kg and 6.72 kg, respectively. The mass ratio between salt and ENG-TSA is 5:1, which can ensure the better heat and mass transfer performance of sorbent (Wang et al., 2012). Fig.3b is the photo of cogeneration system with auxiliary equipment including hot water tank, cooling tower, power and refrigeration generation cogeneration part. Pressure sensors (full scale from 0 to 2.5 MPa with tolerance of ±0.1%) are placed at the inlet and outlet of the expander and in the sorption beds and the upper position of two heat exchangers. Pt100 thermal resistance temperature sensors with ±0.1oC accuracy are used. The flow rate meter is adopted with ±0.5% accuracy. All the measurement points are marked as P, T, m, W in Fig.1. Flowrate of the hot water is 2.4 m3·h-1 while flowrate of cooling water is 3 m3·h-1.
As far as traditional fin-tube sorption bed is concerned, the filled density of sorbent is no more
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than 450 kg m-3(Pan et al., 2015), which will lead to lower SCP and larger system volume. Comparably, the sorption bed in this cogeneration system considers the novel design of removing fins which is shown in Fig.4. As Fig.4 shows, since the mass transfer tunnel places in the middle of unit tube, the composite sorbent can be compressed to a larger density, which will result in the smaller volume of total sorption bed. The filled density of unit sorption bed is able to reach 600 kg m-3. The composite sorbent developed with the matrix of ENG-TSA is selected for the system, which could effectively enhance heat and mass transfer performance due to its porous structure. (Wang et al., 2012). Thermal conductivity of the composite sorbent is 18.7 W·m-1·K-1) with the packing density of 500 kg m-3 in the previous work(Jiang et al., 2014).
3. Performance evaluation The heat input of PRC: Q h1
1 M ref heva,m id hliq,sat t cycle
t cycle, 0
t pow er 0
m ref heva,out heva,m id d t M hx C hx Δ T hx
(4)
C w m w T h1,in T h1,out d t t cycle
where heva,mid is the enthalpy of the fluid at the point 4 in Fig.2a, heva,out is the enthalpy of the fluid at the point 1 in Fig.2a, hliq,sat is the enthalpy of the saturated liquid at the point 3 in Fig.2a, mw is mass flowrate of hot water, cw is the specific heat of hot water, Th1,in, Th1,out are inlet and outlet temperature of hot water of PRC; tcycle is the cycle time of gradient thermal system. Average power output of scroll expander: W ave
1 t cycle
t cycle 0
η exp m ref heva,out hexp,out d t
1 t cycle
t cycle 0
2π n N 60
dt
1 t cycle
t cycle 0
W dt
(5)
where heva,out is the outlet enthalpy of the evaporator, hexp,out is the outlet enthalpy of the expander, n is rotating speed of expander, N is torque meter, W is the instantaneous power output. The energy efficiency of the PRC system:
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PR C
W ave
(6)
Q h1
Heat exergy of PRC: T0 E ex1 Q h1 1 Th1, ave
(7)
where T0 is environmental temperature, Th1, ave is inlet and outlet average temperature of hot water. Exergy efficiency of PRC:
ex1
W ave
(8)
E ex1
The heat input of two-stage sorption refrigerator:
Q h2
t cycle 0
c w m w T h 2 , in T h 2 ,o u t d t
(9)
t cycle
where Th2,in and Th2,out are the inlet and outlet temperature of hot water of two-stage sorption refrigerator. The cooling power of the two-stage sorption refrigerator:
Q ref
c w ,ch i m w ,ch i Tch i,in Tch i,o u t d t
t cycle 0
(10)
t cycle
where mw,chi is the mass flowrate of chilled water of the evaporator; Tchi,in and Tchi,out are the inlet and outlet temperature of chilled water. COP of two-stage sorption refrigerator: COP
Q ref Q h2
(11)
The SCP per kilogram sorbent: SC P
Q ref M
(12)
to t
where Mtot is total mass of HTS and LTS composite sorbent, i.e. both the mass of chlorides and expanded natural graphite are considered.
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Heat exergy: E ex2 Q h2 (1
T0
)
(13)
T h2, ave
where Th2,ave is the average temperature of hot water inlet and outlet of the two-stage refrigerator. Refrigeration exergy:
T0 E ref Q ref 1 T eva,ave
(14)
where Teva,ave is the average temperature of chilled water inlet and outlet: The total energy efficiency and exergy efficiency of the gradient thermal system can be calculated as follows:
tot,en
tot,ex
Q ref W ave
(15)
Q h1 Q h2 E ref W ave
(16)
E ex1 E ex2
For the utilization of the low temperature heat source, since at the outlet heat of the system always go directly to waste, it will be desirable to have a big temperature drop between the inlet and outlet for efficient heat utilization. In order to evaluate the heat utilization efficiency of the gradient thermal system, the thermal exergy efficiency for heat utilization is analyzed for both cogeneration cycle and single cycle, the concerning equation is as follow: （ Tin T0） (1
heat source 1
T0
)
Tout
（ Tout T0 ) (1
T0
(17) )
Tin
4. Results and discussions In order to investigate the overall performance of gradient thermal system, different hot water temperature is employed from 75oC to 95oC with 5oC increment while the cooling water temperature is 25oC i.e. the environmental temperature. The cycle time of gradient thermal system is adopted for 40
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minutes. Two power generation processes will proceeds in a cogeneration cycle since it takes 10 minutes for PRC to complete one. Meanwhile one sorption refrigeration process will proceed in a cogeneration cycle. Since the temperature trends under different working conditions are similar, 95oC heat source temperature is selected as one example for further elaboration. Fig.5 manifests hot water, cooling water inlet and outlet temperature of the PRC part with the variation of time. As Fig.5 shows, trends of the temperature are similar between two heat exchangers, which indicates the good thermal stability. In the beginning of the heating process the hot water inlet and outlet temperature declines sharply. Hot water outlet temperature drops from 95oC to 57oC, and meanwhile the cooling water outlet temperature climbs from 25oC to 29.7oC. The reasons are explained as following expressions: when preheating process happens, the cooling water originally inside HX2 is required to be flow away. Then the heat is consumed for sensible heat. The heat accounts for heating the metal part of heat exchanger from low temperature to high temperature. Besides, the other certain amount of heat accounts for heating the sub-cooled refrigerant liquid of R245fa to saturated state.
Fig.6 demonstrates the maximum and average power output of the PRC under the condition different heat source temperature from 80oC to 95oC. The maximum power output is the highest value in the power generation process which keeps two-third of the total PRC cycle. Comparably, average power output takes both power generation and preheating processes into consideration. It can be seen that the maximum power output and average power output are 232 W and 204 W, respectively when the heat source temperature is 95oC. For different heat source temperature, the maximum power output ranges from 144 W to 232 W while the average power output ranges from 122 W to 204 W. When the heat source temperature increases, the evaporation pressure will accordingly increase, which leads to the higher power output of the system.
Fig.7 indicates the energy efficiency and exergy efficiency of the PRC under the condition 12 Page 12 of 27
different heat source temperature from 80oC to 95oC. As it shows, energy efficiency increases with the increment of heat source temperature. Exergy efficiency decreases gradually from 80oC to 90oC and increases at the end, which is because the power output of 95oC heat source temperature is relatively higher. The maximum energy efficiency is able to reach 2.4% on the condition of 95oC heat source temperature. The maximum exergy efficiency is about 13.7% when hot water temperature is 80oC. For different heat source temperature, the energy and exergy efficiency range from 2.09% to 2.4% and 12.2% to 13.7%, respectively.
Still 95oC heat source temperature is selected as an example for elaborating the temperature of hot water, cooling water, and HTS and LTS bed of the two-stage sorption refrigerator proceeding with the time, as shown in Fig.8. The temperature of the cooling water inlet are controlled steadily at 25oC whereas the inlet temperature of chilled ethanol solution is kept about 5oC. Since the inlet of the two-stage sorption refrigerator is the outlet of the PRC part, the inlet temperature of sorption refrigerator is about 5oC lower than that of PRC i.e. about 90oC as shown in Fig.8. The desorption process happens on the rising curves while the sorption process occurs on the declining curves. Temperature of HTS bed shows the opposite trend when compared with that of LTS bed. This is mainly because both of two sorption beds work in different modes in the working process. The ethanol solution is used to exchange the heat from the evaporator.
When the initial inlet temperature of the ethanol tank is controlled at 5oC, the ethanol inlet and outlet temperature of the evaporator is shown in Fig.9. Results indicate that at the beginning of
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refrigeration process the evaporator outlet temperature declines sharply due to high sorption rate. The inlet temperature also decreases with the same trend. The reason is mainly because the ethanol solution tank cannot balance the electrical heat inside the tank timely. It also indicates that the lowest outlet temperature of the adsorber is as low as 0.57oC and the maximum temperature difference between evaporator outlet and inlet is approximately 0.83oC. This demonstrates a huge potential of the system for refrigeration.
For two-stage sorption refrigeration, SCP and COP are two major parameters for evaluating the overall refrigeration performance. As Fig.10 shows, 5oC and 10oC evaporation temperature is selected as typical condition under the condition of different heat source temperature. COP and SCP both increase with the increment of evaporation temperature and heat source temperature. COP varies more obviously with the increment of heat source temperature than evaporation temperature. This is because sorption rate is more sensitive to the heat source temperature than evaporation temprature. When evaporation temperature is 5oC, COP climbs from 0.185 to 0.202 while SCP rises from 60 W·kg-1 to 72 W·kg-1. Comparably, for 10oC evaporation temperature COP and SCP range from 0.202 to 0.22 and from 80 W·kg-1 to 91 W·kg-1, respectively. It is interesting to note that the SCP of the system with novel sorption bed is not futher improved when compared with data in reference(Wang et al., 2013) since SCP is usually defined based on mass of chlorides. With regard to total mass of the system, cooling power per kilogram of the novel system is 3.5 times higher than the data of the reference.
Fig.11 shows total energy efficiency and exergy efficiency of gradient thermal system for power and refrigeration cogeneration. Results show that total energy efficiency decreases first and increases
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slightly with increase of heat source while exergy efficiency decreases with the increment of heat source. The reason is mainly because the input heating power of 80 oC is relatively low when compared with power output. When heat source temperature climbs from 80oC to 95oC, energy efficiency and exergy efficiency range from 9.49% to 9.9% and 10.9% to 11.8%, respectively.
The theoretical limit of the gradient thermal system is the combined effect of PRC and two-stage sorption refrigeration. Take 95oC heat source temperature as an example, the theoretical energy efficiency of PRC and two-stage sorption refrigerator are analyzed as follows: According to the experimental working conditions, the theoretical thermodynamic energy efficiency of PRC under the concerning condition is about 8%, which is concerned with equations 4-6. Also the theoretical energy efficiency of the two-stage sorption refrigerator is about 45% which is concerned with equations 9-12. The theoretical energy efficiency i.e. the theoretical limit of the gradient thermal system is about 0.265 under the condition of 95 oC heat source temperature. For the cogeneration system, the irreversibilities come from two main parts. One part is from the power generation process, in which the loss caused by scroll expander and generator will lead to the larger exergy loss when compared with the isentropic expansion and ideal work to power processes. The other part comes from the heat exchange of the sorption beds. The heat transfer temperature difference between the internal and external heat exchange fluid will result in the exergy loss for two-stage sorption refrigerator. If the isentropic efficiency, work to power efficiency and heat transfer temperature are all taken into consideration, the energy efficiency of PRC, two-stage sorption refrigerator and gradient thermal system will reach 2.95%, 24% and 13.5% which is quite closed to the experimental results as shown in Fig.11.
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The errors of the experiments are analyzed by the parameters shown in Table 1. Assuming that the testing value is unrelated, the error of total energy and exergy efficiency are calculated as the equation 15 and equation 16. Calculating results show that the largest error of tot energy efficiency and exergy efficiency are 10.56% and 11.88%, respectively, when the heat source temperature is 95oC.
( energy
energy W ave
(
( exergy
energy T h,in
exergy W ave
(
energy W ave ) Tchi,in T chi,in 2
2
T h,out
T h,out ) (
exergy W ave ) Tchi,in T chi,in
exergy T h,in
T h,in ) (
energy
2
T h,in ) ( 2
exergy T h,out
2
energy Tchi,out Tchi,ou t 2
energy m w
mw )
2
2
exergy m w
mw )
(15)
2
exergy Tchi,out Tchi,out
T h,out ) (
2
2
(16)
2
Fig.12 shows exergy efficiency of heat source under the condition of different heat source temperature for cogeneration cycle, single PRC and two stage sorption refrigerator. The exergy efficiency of heat utilization for single PRC and two-stage sorption refrigerator range from 10.9% to 8.3% and from 14.3% to 11%, separately. However, for gradient thermal cycle, the exergy efficiency of heat utilization ranges from 24% to 18.8%, which is 126.5% and 70.9% higher than the PRC and two-stage sorption refrigerator, respectively when the heat source temperature is 80oC. Even for the highest heat source temperature of 95oC, the improvement is still as high as 120% and 67.8%, separately, which indicates the high efficiency for the heat utilization by gradient thermal cycle for power and refrigeration cogeneration.
5. Conclusions
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A novel gradient thermal cycle for power and refrigeration cogeneration is proposed and analyzed with the heat driven temperature lower than 100oC. In this cycle, PRC is served as the first part to provide the power, and two-stage sorption refrigerator is utilized as the second part for refrigeration output. Conclusions are yielded as follows: [1] For PRC, the maximum power output ranges from 144 W to 232 W while average power output ranges from 122 W to 204 W when the heat source temperature range from 80 oC to 95oC. Energy efficiency increases with the increment of heat source temperature. Exergy
efficiency decreases gradually from 80oC to 90oC and increases at the end. For different heat source temperature, the energy and exergy efficiency range from 2.09% to 2.4% and 12.2% to 13.7%, respectively. [2] For two stage sorption refrigerator, COP and SCP increase with heat source temperature under 5oC and 10oC evaporation temperature. COP varies more obviously with heat source temperature than evaporation temperature. For different working conditions, COP rises from 0.185 to 0.22 while SCP ranges from 60 W·kg-1 to 91 W·kg-1. [3] Total energy efficiency decreases first and increases slightly with increase of heat source while exergy efficiency decreases with the increase of the heat source. When heat source temperature rises from 80oC to 95oC, energy efficiency and exergy efficiency range from 9.49% to 9.9% and 10.9% to 11.8%, respectively. [4] For gradient thermal cycle exergy efficiency of heat utilization ranges from 24% to 18.8%, which is 126.5% and 70.9% higher than the PRC and two-stage sorption refrigerator, respectively when the heat source temperature is 80oC. Even for the highest heat source temperature of 95oC, the improvement is still as high as 120% and 67.8%, separately, which indicates the high efficiency for the utilization of the heat by gradient thermal cycle for power and refrigeration cogeneration.
Acknowledgements: This research was supported by foundation for Innovative Research Groups of the National Natural 17 Page 17 of 27
Science Foundation of China (51521004), National Natural Science Foundation of China (51606118) and China Postdoctoral Science Foundation (15Z102060060).
References Chaiyat, N., Kiatsiriroat, T., 2015. Analysis of combined cooling heating and power generation from organic Rankine cycle and absorption system. Energy 91, 363-370. Gao, P., Wang, L.W., Wang, R.Z., Jiang, L., Zhou, Z.S., 2015. Experimental investigation on a small pumpless ORC (organic rankine cycle) system driven by the low temperature heat source. Energy 91, 324-333. Gao, P., Wang, L.W., Wang, R.Z., Zhang, X.F., Li, D.P., Liang, Z.W., Cai, A.F., 2016a. Experimental investigation of a MnCl2/CaCl2-NH3 two-stage solid sorption freezing system for a refrigerated truck. Energy 103, 16-26. Gao, P., Zhang, X.F., Wang, L.W., Wang, R.Z., Li, D.P., Liang, Z.W., Cai, A.F., 2016b. Study on MnCl2/CaCl2–NH3 two-stage solid sorption freezing cycle for refrigerated trucks at low engine load in summer. Energy Conversion and Management 109, 1-9. Ghim, G., Lee, J., 2016. Experimental evaluation of the in-tube condensation heat transfer of pure n-pentane/R245fa and their non-azeotropic mixture as an ORC working fluid. Applied Thermal Engineering 106, 753-761. Han, W., Chen, Q., Sun, L., Ma, S., Zhao, T., Zheng, D., Jin, H., 2014. Experimental studies on a combined refrigeration/power generation system activated by low-grade heat. Energy 74, 59-66. Hu, Y., Wang, L., Xu, L., Wang, R., Kiplagat, J., Wang, J., 2011. A two-stage deep freezing chemisorption cycle driven by low-temperature heat source. Frontiers in Energy 5, 263. Jiang, L., Wang, L.W., Wang, R.Z., 2014. Investigation on thermal conductive consolidated composite
18 Page 18 of 27
CaCl2 for adsorption refrigeration. International Journal of Thermal Sciences 81, 68-75. Kaşka, Ö., 2014. Energy and exergy analysis of an organic Rankine for power generation from waste heat recovery in steel industry. Energy Conversion and Management 77, 108-117. Khan, M.Z.I., Saha, B.B., Alam, K.C.A., Akisawa, A., Kashiwagi, T., 2007. Study on solar/waste heat driven multi-bed adsorption chiller with mass recovery. Renewable Energy 32, 365-381. Li, J., Pei, G., Li, Y., Ji, J., 2013. Analysis of a novel gravity driven organic Rankine cycle for small-scale cogeneration applications. Applied Energy 108, 34-44. Li, T.X., Wang, R.Z., Li, H., 2014. Progress in the development of solid–gas sorption refrigeration thermodynamic cycle driven by low-grade thermal energy. Progress in Energy and Combustion Science 40, 1-58. Pan, Q.W., Wang, R.Z., Wang, L.W., 2015. Comparison of different kinds of heat recoveries applied in adsorption refrigeration system. International Journal of Refrigeration 55, 37-48. Pan, Q.W., Wang, R.Z., Wang, L.W., Liu, D., Design and experimental study of a silica gel-water adsorption chiller with modular adsorbers. International Journal of Refrigeration. Peris, B., Navarro-Esbrí, J., Molés, F., Collado, R., Mota-Babiloni, A., 2015. Performance evaluation of an Organic Rankine Cycle (ORC) for power applications from low grade heat sources. Applied Thermal Engineering 75, 763-769. Wang, J., Wang, L.W., Luo, W.L., Wang, R.Z., 2013. Experimental study of a two-stage adsorption freezing machine driven by low temperature heat source. International Journal of Refrigeration 36, 1029-1036. Wang, L.W., 2014. Solar Powered Cascading Cogeneration Cycle with ORC and Adsorption Technology for Electricity and Refrigeration. Heat Transfer Engineering 35, 1028-1034.
19 Page 19 of 27
Wang, L.W., Metcalf, S.J., Critoph, R.E., Thorpe, R., Tamainot-Telto, Z., 2012. Development of thermal conductive consolidated activated carbon for adsorption refrigeration. Carbon 50, 977-986. Wang, R.Z., Xu, Z.Y., Pan, Q.W., Du, S., Xia, Z.Z., 2016. Solar driven air conditioning and refrigeration systems corresponding to various heating source temperatures. Applied Energy 169, 846-856. Yamada, N., Minami, T., Anuar Mohamad, M.N., 2011. Fundamental experiment of pumpless Rankine-type cycle for low-temperature heat recovery. Energy 36, 1010-1017. Yamada, N., Watanabe, M., Hoshi, A., 2013. Experiment on pumpless Rankine-type cycle with scroll expander. Energy 49, 137-145. Yang, X., Zheng, N., Zhao, L., Deng, S., Li, H., Yu, Z., 2016. Analysis of a novel combined power and ejector-refrigeration cycle. Energy Conversion and Management 108, 266-274. Yue, C., You, F., Huang, Y., 2016. Thermal and economic analysis of an energy system of an ORC coupled with vehicle air conditioning. International Journal of Refrigeration 64, 152-167.
20 Page 20 of 27
Fig.1-Gradient thermal cycle for power and refrigeration cogeneration.
180
140 120
o
Temperature ( C)
14.4
600 800 400 1000 200 1200 100 3 = 1400 kg/m 50 20 4 1
R245fa 160
14.0
1.06MPa
C D (30oC)
lnP (Pa)
100 80 60 40
NH3 BaCl2 (0-8) CaCl2 (4-8)
14.2
13.8 13.6
0.76MPa
B (55oC)
13.4 0.6MPa E 3
2
13.0 -3.8
0 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Entropy (kJ/(kg K))
B'
-3.6
-3.4
-3.2
o A (70 C)
o F(63 C)
(10oC)
13.2
20
A' (83oC)
-3.0
-2.8
-2.6
-1000/T (K)
(a) (b) Fig.2-Thermodynamic diagram. (a) T-S diagram of pumpless ORC, (b) P-T diagram of two-stage sorption system.
21 Page 21 of 27
(a)
(b)
Fig.3-Photograph of cogeneration system (a) Cogeneration system, (b) cogeneration system with auxiliary equipment.
(a)
(b)
Fig.4-The diagram of the unit tube. (a) Schematic, (b) photo.
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120
Temperature/oC
100 80 HX1
HX2
HX1
60 Hot water outlet Hot water inlet
40
Cooling water inlet Cooling water outlet
20 0
0
5
10
15
20
25
30
Time/min
Fig. 5-Hot water, cooling water inlet and outlet temperature.
250
Power output/W
200
Maximum power output
150 Average power output 100
50 75
80
85
90
95
100
o
Heat source temperature/ C
Fig.6-The maximum and average power output of the PRC vs. heat source temperature.
23 Page 23 of 27
0.030
0.24
0.16 0.020
0.12 0.08
Exergy efficiency
0.015
Exergy efficiency
Energy efficiency
0.20
Energy efficiency
0.025
0.04 0.010 75
80
85
90
95
0.00 100
Heat source temperature/oC
Fig.7-Energy and exergy efficiency of the PRC vs. heat source temperature.
120
Hot water inlet
Temperature/oC
100
LTS bed
80 60 40 20
Cooling water 0
0
20
HTS bed
40 60 Time/min Fig.8-Temperature of sorption beds, hot water and cooling water.
80
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6
Temperature/oC
5 Evaporator outlet
4
Evaporator inlet
3 2 1 0
0
5
10
15
20
25
Time/min
Fig.9-Inlet and outlet temperature of evaporator.
0.25
240 10 oC evaporation temperature 200
0.20
0.15
10 oC evaporation temperature
160 120 80
SCP/kW·kg-1
COP
5 oC evaporation temperature
0.10 5 oC evaporation temperature 0.05 75
80
85
90
95
40 0 100
Heat source temperature/oC
Fig.10-COP and SCP vs. different heat source temperature.
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0.16
0.20
Energy efficiency
0.10 0.08 0.05
Energy efficiency 0.04 75
80
85
90
95
Exergy efficiency
0.15
Exergy efficiency 0.12
0.00 100
Heat source temperature/oC
Fig.11-Total energy efficiency and exergy efficiency of gradient thermal system.
0.3
Exergy efficiency
Gradient thermal cycle
B C D
0.2 Two-stage refrigerator Single PRC
0.1
0.0 70
80
90
100
110
o
Heat source temperature/ C
Fig.12-Exergy efficiency of heat utilization vs. heat source temperature
26 Page 26 of 27
Table 1-Testing error of the apparatus for gradient thermal system. Apparatus
Type
Testing scope
Error
Dynamometer
HP9800
0-3kW
±0.2R
Temperature sensor
PT100
-50℃-200℃
±0.1℃
Pressure sensors
YSZK-311
0-2.5Mpa
±0.1%
Flow meter
LWGY-B15L
0.1-90oC
±0.5%
27 Page 27 of 27
S0140-7007(17)30038-5 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.01.018 JIJR 3530
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
2-9-2016 16-1-2017 19-1-2017
Please cite this article as: L. Jiang, R.Z. Wang, L.W. Wang, P. Gao, F.Q. Zhu, Investigation on gradient thermal cycle for power and refrigeration cogeneration, International Journal of Refrigeration (2017), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.01.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Investigation on gradient thermal cycle for power and refrigeration cogeneration L. Jiang, R.Z. Wang*, L.W. Wang, P. Gao, F.Q. Zhu Institute of Refrigeration and Cryogenics, Key Laboratory of Power Machinery and Engineering of Ministry of
Education, Shanghai Jiao Tong University, Shanghai, 200240, China * Corresponding author. Email: [email protected]; Tel. +86-21-34206548; Fax. + 86-21-34206548
Highlights
A novel gradient thermal cycle for power and refrigeration cogeneration is proposed.
ENG-TSA as the additive improves the heat and mass performance of composite adsorbent.
The maximum power and cooling effect can be obtained as 204 W and 0.91 kW, respectively.
The exergy efficiency of heat utilization ranges from 18.8% to 24%.
Abstract: In order to improve energy utilization efficiency of low grade heat, a novel gradient thermal cycle for power and refrigeration cogeneration is proposed. The cycle is cascaded with two stages based on different thermal driven temperature. The first stage is pumpless Organic Rankine Cycle (PRC) while the second stage is two-stage sorption refrigerator. R245fa is selected as the working fluid of PRC whereas CaCl2-BaCl2-NH3 working pair is chosen for two-stage sorption refrigerator. Different heat source temperature from 80oC to 95oC are adopted for analysis and comparison. Results indicate that the highest average power output and cooling effect are able to reach 204 W and 0.91 kW under the condition of 95oC heat source temperature and 10oC refrigeration temperature. For different heat source temperature, total energy and exergy efficiency of the gradient thermal cycle for power and refrigeration cogeneration range from 9.49% to 9.9% and 10.9% to 11.8%, respectively. For gradient thermal cycle exergy efficiency of heat utilization ranges from 24% to 18.8%, which is 126.5% and 70.9% higher than the PRC and two-stage sorption refrigerator, respectively when the heat source temperature is 80oC.
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Keywords Pumpless Organic Rankine Cycle (PRC); Sorption; Exergy efficiency; Gradient thermal cycle 1
1
This paper was presented at SET2016
2 Page 2 of 27
Nomenclature c
Specific heat (kJ·kg-1·oC-1)
COP
Coefficient of performance
E
Exergy (kW)
h
Enthalpy (kJ·kg-1)
HTS
High temperature salt
HX
Heat exchanger
LTS
Low temperature salt
m
Mass flowrate (kg·s-1)
M
Mass (kg)
PRC
Pumpless Organic Rankine Cycle
Q
Heat (kW)
R
Gas constant (J·mol-1·K-1)
SCP
Specific cooling power (W·kg-1)
t
Time (s)
T
Temperature (K)
W
Power output (W)
Greek letters η
Efficiency
Subscripts ads
Sorbent
ave
Average
cool
Cooling water
chilled
Chilled water
cycle
Gradient thermal cycle
des
Desorption
En
Energy
eva
Evaporation
3 Page 3 of 27
Ex
Exergy
exp
Expander
H
Heat
hx
Heat exchanger
L
Liquid
PRC
Pumpless Organic Rankine Cycle
ref
Refrigeration
tot
Total
V
Vapor
1. Introduction Thermal driven power generation and refrigeration are two major technologies to recover the low grade heat source, which have been drawn a burgeoning number of attentions in recent years (Han et al., 2014; Wang et al., 2016). To further improve the efficiency of low temperature heat source, especially for that lower than 100oC, power and refrigeration cogeneration cycle has been proposed with many forms (Chaiyat and Kiatsiriroat, 2015; Yang et al., 2016). Among them, gradient thermal cycle is desirable to have a big temperature drop at the inlet and outlet of the cogeneration system. Selection of power generation and refrigeration cycles for gradient thermal cycle are usually critical. For power generation part, it always requires relatively higher driven temperature, which is suitable for the construction as the first stage (Yue et al., 2016). As one major kind of thermal driven power generation type for low temperature heat utilization, Organic Rankine Cycle (ORC) take advantages of simplicity and flexibility. Various researchers investigated ORC systems for efficient utilization of waste heat. Working fluid and external boundary conditions are two main research hotspots for improving thermal efficiency. Kaska et al. (Kaşka, 2014) conducted both energy and exergy analysis on ORC system driven by steel industrial waste heat. Simulation results indicated that the energy efficiency and exergy efficiency of the system were 10.2% and 48.5%, respectively. Peris et al.(Peris et al., 2015) investigated the performance of an ORC module. The maximum gross electrical efficiency obtained was able to reach 12.32% when heat source temperature was about 155oC, and
4 Page 4 of 27
outlet waste heat was dissipated to the ambient directly. However, considering small-scale ORC systems, working fluid pump acted as main components will consume a large part of power resulting in the loss of energy efficiency and compactness of the system(Yamada et al., 2013). Therefore, one innovative idea is to regard the possibility of eliminating the pump so that the system efficiency for small ORC system can be further improved. One approach is to use the gravity of working fluid to drive small ORC system. Although working fluid pump could be replaced by this method, the required height would be the bottleneck of this novel design(Li et al., 2013). After that, a novel PRC (pumpless Organic Rankine Cycle) prototype was considered to be alternative solution(Yamada et al., 2011). Experimental results demonstrated that the novel cycle had capability of producing power. Nonetheless, the maximum shaft power obtained was very small, which was lower than 50 W. Later, Gao et al.(Gao et al., 2015) investigated a PRC system, trying to gain a relative higher electricity output. The results indicated a potential for better power output. For refrigeration part, sorption refrigeration tends to be selected as the second stage since it is one perspective method of thermal driven refrigeration for recovering low temperature heat source(Li et al., 2014). As one commercial system, silica gel-water sorption refrigeration has been designed as the second stage of cascading cycle for power and refrigeration cogeneration(Wang, 2014) since silica gel-water sorption chiller has been extensively investigated. Khan et al.(Khan et al., 2007) studied a three-stage silica-gel/water sorption chiller that could generate cooling power with the lowest heat source temperature of 50oC and the coolant temperature of 30oC. Shanghai Jiao Tong University successfully developed a silica gel-water sorption chiller with modular adsorbers (Pan et al.). However, due to the property limitation of water, working pair of silica gel-water cannot be applied for freezing conditions. Under this scenario, two-stage sorption refrigeration will be one good solution to both air conditioning and freezing condition since it has flexibility to adapt to heat source with different temperatures. Even if the outlet temperature of the PRC is relatively low and severe environmental condition when condensing temperature is higher than 40 oC, two-stage sorption cycle is still able to reach the reasonable performance, which is the reason why it is selected as the second stage of the gradient thermal cycle. Wang et al.(Wang et al., 2013) established a two-stage sorption chiller by means of composite sorbents of CaCl2 and BaCl2. Results showed that the optimal coefficient of performance (COP) and specific cooling power (SCP) are 0.127 and 100 W·kg-1 under 15oC refrigeration temperature. Later, this energy conversion technology was investigated for the possibility
5 Page 5 of 27
to apply into a refrigerated truck, and it proved that maximum refrigerating capacity of 1.25 kW and COP of 0.143 were obtained at a resorption time of 120 min when the hot air temperature and refrigerating temperature were 230oC and 5oC, respectively (Gao et al., 2016a; Gao et al., 2016b). Two-stage sorption refrigeration with two sorption beds are intermittent refrigeration. Comparably, PRC system is able to generate the power in most phases of cycle. Therefore, cascading these two cycles will achieve power and cooling output in one cycle. In this paper, an innovative gradient thermal cycle for power and refrigeration cogeneration is proposed, and concerning system is designed and established. Heat source temperature from 80oC to 95oC and evaporation temperature from 5oC to 10oC are employed for overall investigation, and results are analyzed and compared.
2. Design of gradient thermal cycle Design of gradient thermal cycle for power and refrigeration cogeneration is shown in Fig.1, and two parts are included. The first part is PRC while the second part is CaCl2/BaCl2 two-stage sorption refrigeration cycle. R245fa is selected as the refrigerant for PRC which proves to be one good working fluid for low temperature heat source (Ghim and Lee, 2016), and ammonia is utilized for two-stage sorption refrigeration cycle. As it shows in Fig.1, two different cycles are connected with water pipelines. One hot water line and one cooling water line are included, which serve as heat source and cooling source, respectively. Hot water first flows into PRC, and then goes through two-stage sorption refrigeration cycle. Under this scenario, the low temperature heat is able to be recovered successively, which further improves the efficiency of heat utilization. The power and cooling effect could be obtained in this working process. Ethanol water solution in chilled water tank is used for transporting the cooling capacity out of the evaporator. PRC part mainly consists of two heat exchangers i.e. heat exchanger 1(HX1) and heat exchanger 2 (HX2), one expander, one generator and other auxiliary equipment. Two-stage sorption refrigeration cycle, which is composed of two sorption beds i.e. High temperature salts (HTS) bed and Low temperature salts (LTS) bed, one condenser, one evaporator and ammonia valves. CaCl2 is selected as the HTS whereas BaCl2 is chosen for the LTS. The thermochemical reaction process of CaCl2 and BaCl2 with ammonia can be referred to the equations 1-3. The reasons of selecting CaCl2-BaCl2-NH3 as
6 Page 6 of 27
the working pairs lie in thermal driven temperature and the match of different chlorides. As stated above, the inlet temperature of the two-stage sorption refrigerator is the outlet temperature of the PRC, which is lower than 95oC. Taking 85oC thermal driven temperature and 25oC environmental temperature into consideration, according to the Chaperon lines of common chlorides, PbCl 2, SnCl2, NH4Cl and BaCl2 could be selected as LTS while CaCl2 and SrCl2 can be chosen for HTS. PbCl2 and SnCl2 have the disadvantage of relatively low cycle quantity whereas NH4Cl is easy to be condensed since it is closed to the ammonia line. Similarly, CaCl2 has the higher cycle sorption quantity than that of SrCl2. Therefore, CaCl2 and BaCl2 are more suitable for HTS and LTS. The more details could be referred to our previous work (Hu et al., 2011). C aC l 2 4 N H 3 4 N H 3 C aC l 2 8 N H 3 4 H C aC l 2
(1)
B aC l 2 8 N H 3 B aC l 2 8 N H 3 8 H B aC l 2
(2)
N H 3 (gas) N H 3 (liq) H cond
(3)
Fig.2 indicates the thermodynamic diagram for T-S diagram of PRC and P-T diagram of two-stage sorption refrigeration cycle, which are manifested in Fig.2a and Fig.2b, respectively. The working processes of gradient thermal cycle consist of four processes in one cycle, which are as follows: Preheating process: HX1 serves as an evaporator, and HX2 acts as a condenser. Hot water flows into the HX1 for preheating. Pressure of the HX1 increases gradually until it reaches an almost constant value which is quite close to saturation pressure of R245fa. Simultaneously the cooling water flows into the HX2 for cooling through the cooling tower. Power generation process: As the pressure of the HX1 climbs to be constant, the high-pressure refrigerant inside the HX1 flows into the expander, generating power until no pressure difference happens between the HX1 and HX2, which is 1-2 in Fig.2a. At this moment the heating process inside HX1 is an isobaric heating process, which is 4-1 in Fig.2a. The expanded refrigerant enters the HX2, and it. After first power generation process, HX1 replaces the role as a condenser, and HX2 exchanges the role as an evaporator. Hot water begins to heat HX2 and cooling water begins to cool HX1 Sorption process of HTS bed: In this process, HTS bed is cooled by the cooling water. HTS bed adsorbs the ammonia from the evaporator, which is E-F in Fig.2b. The evaporation process of the 7 Page 7 of 27
ammonia inside the evaporator provides the cooling effect. Meanwhile LTS bed is heated by the hot water, which is the outlet temperature of PRC cycle. The ammonia is desorbed from the LTS bed. The desorbed ammonia will be condensed in the condenser, which is C-D in Fig.2b. Resorption process: HTS bed is heated by the hot water and desorbs ammonia to LTS bed, which is A-B in Fig.2b. The LTS bed is cooled by the cooling water to facilitate sorption of LTS bed. Sorption process of HTS bed and resorption process will proceed with preheating and power generation processes. Under this scenario, the gradient thermal cycle is able to supply refrigeration and cooling power sequentially.
Fig.3 shows photograph of gradient thermal system, in which Fig.3a is the photo of power and refrigeration cogeneration system. As Fig.3a shows, two sorption beds, i.e. HTS and LTS bed are installed at the lower position of experimental rig. Two heat exchangers of PRC, i.e. HX1 and HX2 are placed at the higher position. The scroll expander and generator are in the middle position. Temperature of sorption bed and heat exchangers are adjusted by the hot water and cooling water. Temperature of evaporator is controlled by the by ethanol water tank. Composite sorbent of each tube weighs about 0.8kg. Composite BaCl2 is filled in the LTS bed, which contains seven unit tube. Each tube weighs about 0.96kg. Therefore, total mass of composite CaCl2 and BaCl2 are 5.6 kg and 6.72 kg, respectively. The mass ratio between salt and ENG-TSA is 5:1, which can ensure the better heat and mass transfer performance of sorbent (Wang et al., 2012). Fig.3b is the photo of cogeneration system with auxiliary equipment including hot water tank, cooling tower, power and refrigeration generation cogeneration part. Pressure sensors (full scale from 0 to 2.5 MPa with tolerance of ±0.1%) are placed at the inlet and outlet of the expander and in the sorption beds and the upper position of two heat exchangers. Pt100 thermal resistance temperature sensors with ±0.1oC accuracy are used. The flow rate meter is adopted with ±0.5% accuracy. All the measurement points are marked as P, T, m, W in Fig.1. Flowrate of the hot water is 2.4 m3·h-1 while flowrate of cooling water is 3 m3·h-1.
As far as traditional fin-tube sorption bed is concerned, the filled density of sorbent is no more
8 Page 8 of 27
than 450 kg m-3(Pan et al., 2015), which will lead to lower SCP and larger system volume. Comparably, the sorption bed in this cogeneration system considers the novel design of removing fins which is shown in Fig.4. As Fig.4 shows, since the mass transfer tunnel places in the middle of unit tube, the composite sorbent can be compressed to a larger density, which will result in the smaller volume of total sorption bed. The filled density of unit sorption bed is able to reach 600 kg m-3. The composite sorbent developed with the matrix of ENG-TSA is selected for the system, which could effectively enhance heat and mass transfer performance due to its porous structure. (Wang et al., 2012). Thermal conductivity of the composite sorbent is 18.7 W·m-1·K-1) with the packing density of 500 kg m-3 in the previous work(Jiang et al., 2014).
3. Performance evaluation The heat input of PRC: Q h1
1 M ref heva,m id hliq,sat t cycle
t cycle, 0
t pow er 0
m ref heva,out heva,m id d t M hx C hx Δ T hx
(4)
C w m w T h1,in T h1,out d t t cycle
where heva,mid is the enthalpy of the fluid at the point 4 in Fig.2a, heva,out is the enthalpy of the fluid at the point 1 in Fig.2a, hliq,sat is the enthalpy of the saturated liquid at the point 3 in Fig.2a, mw is mass flowrate of hot water, cw is the specific heat of hot water, Th1,in, Th1,out are inlet and outlet temperature of hot water of PRC; tcycle is the cycle time of gradient thermal system. Average power output of scroll expander: W ave
1 t cycle
t cycle 0
η exp m ref heva,out hexp,out d t
1 t cycle
t cycle 0
2π n N 60
dt
1 t cycle
t cycle 0
W dt
(5)
where heva,out is the outlet enthalpy of the evaporator, hexp,out is the outlet enthalpy of the expander, n is rotating speed of expander, N is torque meter, W is the instantaneous power output. The energy efficiency of the PRC system:
9 Page 9 of 27
PR C
W ave
(6)
Q h1
Heat exergy of PRC: T0 E ex1 Q h1 1 Th1, ave
(7)
where T0 is environmental temperature, Th1, ave is inlet and outlet average temperature of hot water. Exergy efficiency of PRC:
ex1
W ave
(8)
E ex1
The heat input of two-stage sorption refrigerator:
Q h2
t cycle 0
c w m w T h 2 , in T h 2 ,o u t d t
(9)
t cycle
where Th2,in and Th2,out are the inlet and outlet temperature of hot water of two-stage sorption refrigerator. The cooling power of the two-stage sorption refrigerator:
Q ref
c w ,ch i m w ,ch i Tch i,in Tch i,o u t d t
t cycle 0
(10)
t cycle
where mw,chi is the mass flowrate of chilled water of the evaporator; Tchi,in and Tchi,out are the inlet and outlet temperature of chilled water. COP of two-stage sorption refrigerator: COP
Q ref Q h2
(11)
The SCP per kilogram sorbent: SC P
Q ref M
(12)
to t
where Mtot is total mass of HTS and LTS composite sorbent, i.e. both the mass of chlorides and expanded natural graphite are considered.
10 Page 10 of 27
Heat exergy: E ex2 Q h2 (1
T0
)
(13)
T h2, ave
where Th2,ave is the average temperature of hot water inlet and outlet of the two-stage refrigerator. Refrigeration exergy:
T0 E ref Q ref 1 T eva,ave
(14)
where Teva,ave is the average temperature of chilled water inlet and outlet: The total energy efficiency and exergy efficiency of the gradient thermal system can be calculated as follows:
tot,en
tot,ex
Q ref W ave
(15)
Q h1 Q h2 E ref W ave
(16)
E ex1 E ex2
For the utilization of the low temperature heat source, since at the outlet heat of the system always go directly to waste, it will be desirable to have a big temperature drop between the inlet and outlet for efficient heat utilization. In order to evaluate the heat utilization efficiency of the gradient thermal system, the thermal exergy efficiency for heat utilization is analyzed for both cogeneration cycle and single cycle, the concerning equation is as follow: （ Tin T0） (1
heat source 1
T0
)
Tout
（ Tout T0 ) (1
T0
(17) )
Tin
4. Results and discussions In order to investigate the overall performance of gradient thermal system, different hot water temperature is employed from 75oC to 95oC with 5oC increment while the cooling water temperature is 25oC i.e. the environmental temperature. The cycle time of gradient thermal system is adopted for 40
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minutes. Two power generation processes will proceeds in a cogeneration cycle since it takes 10 minutes for PRC to complete one. Meanwhile one sorption refrigeration process will proceed in a cogeneration cycle. Since the temperature trends under different working conditions are similar, 95oC heat source temperature is selected as one example for further elaboration. Fig.5 manifests hot water, cooling water inlet and outlet temperature of the PRC part with the variation of time. As Fig.5 shows, trends of the temperature are similar between two heat exchangers, which indicates the good thermal stability. In the beginning of the heating process the hot water inlet and outlet temperature declines sharply. Hot water outlet temperature drops from 95oC to 57oC, and meanwhile the cooling water outlet temperature climbs from 25oC to 29.7oC. The reasons are explained as following expressions: when preheating process happens, the cooling water originally inside HX2 is required to be flow away. Then the heat is consumed for sensible heat. The heat accounts for heating the metal part of heat exchanger from low temperature to high temperature. Besides, the other certain amount of heat accounts for heating the sub-cooled refrigerant liquid of R245fa to saturated state.
Fig.6 demonstrates the maximum and average power output of the PRC under the condition different heat source temperature from 80oC to 95oC. The maximum power output is the highest value in the power generation process which keeps two-third of the total PRC cycle. Comparably, average power output takes both power generation and preheating processes into consideration. It can be seen that the maximum power output and average power output are 232 W and 204 W, respectively when the heat source temperature is 95oC. For different heat source temperature, the maximum power output ranges from 144 W to 232 W while the average power output ranges from 122 W to 204 W. When the heat source temperature increases, the evaporation pressure will accordingly increase, which leads to the higher power output of the system.
Fig.7 indicates the energy efficiency and exergy efficiency of the PRC under the condition 12 Page 12 of 27
different heat source temperature from 80oC to 95oC. As it shows, energy efficiency increases with the increment of heat source temperature. Exergy efficiency decreases gradually from 80oC to 90oC and increases at the end, which is because the power output of 95oC heat source temperature is relatively higher. The maximum energy efficiency is able to reach 2.4% on the condition of 95oC heat source temperature. The maximum exergy efficiency is about 13.7% when hot water temperature is 80oC. For different heat source temperature, the energy and exergy efficiency range from 2.09% to 2.4% and 12.2% to 13.7%, respectively.
Still 95oC heat source temperature is selected as an example for elaborating the temperature of hot water, cooling water, and HTS and LTS bed of the two-stage sorption refrigerator proceeding with the time, as shown in Fig.8. The temperature of the cooling water inlet are controlled steadily at 25oC whereas the inlet temperature of chilled ethanol solution is kept about 5oC. Since the inlet of the two-stage sorption refrigerator is the outlet of the PRC part, the inlet temperature of sorption refrigerator is about 5oC lower than that of PRC i.e. about 90oC as shown in Fig.8. The desorption process happens on the rising curves while the sorption process occurs on the declining curves. Temperature of HTS bed shows the opposite trend when compared with that of LTS bed. This is mainly because both of two sorption beds work in different modes in the working process. The ethanol solution is used to exchange the heat from the evaporator.
When the initial inlet temperature of the ethanol tank is controlled at 5oC, the ethanol inlet and outlet temperature of the evaporator is shown in Fig.9. Results indicate that at the beginning of
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refrigeration process the evaporator outlet temperature declines sharply due to high sorption rate. The inlet temperature also decreases with the same trend. The reason is mainly because the ethanol solution tank cannot balance the electrical heat inside the tank timely. It also indicates that the lowest outlet temperature of the adsorber is as low as 0.57oC and the maximum temperature difference between evaporator outlet and inlet is approximately 0.83oC. This demonstrates a huge potential of the system for refrigeration.
For two-stage sorption refrigeration, SCP and COP are two major parameters for evaluating the overall refrigeration performance. As Fig.10 shows, 5oC and 10oC evaporation temperature is selected as typical condition under the condition of different heat source temperature. COP and SCP both increase with the increment of evaporation temperature and heat source temperature. COP varies more obviously with the increment of heat source temperature than evaporation temperature. This is because sorption rate is more sensitive to the heat source temperature than evaporation temprature. When evaporation temperature is 5oC, COP climbs from 0.185 to 0.202 while SCP rises from 60 W·kg-1 to 72 W·kg-1. Comparably, for 10oC evaporation temperature COP and SCP range from 0.202 to 0.22 and from 80 W·kg-1 to 91 W·kg-1, respectively. It is interesting to note that the SCP of the system with novel sorption bed is not futher improved when compared with data in reference(Wang et al., 2013) since SCP is usually defined based on mass of chlorides. With regard to total mass of the system, cooling power per kilogram of the novel system is 3.5 times higher than the data of the reference.
Fig.11 shows total energy efficiency and exergy efficiency of gradient thermal system for power and refrigeration cogeneration. Results show that total energy efficiency decreases first and increases
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slightly with increase of heat source while exergy efficiency decreases with the increment of heat source. The reason is mainly because the input heating power of 80 oC is relatively low when compared with power output. When heat source temperature climbs from 80oC to 95oC, energy efficiency and exergy efficiency range from 9.49% to 9.9% and 10.9% to 11.8%, respectively.
The theoretical limit of the gradient thermal system is the combined effect of PRC and two-stage sorption refrigeration. Take 95oC heat source temperature as an example, the theoretical energy efficiency of PRC and two-stage sorption refrigerator are analyzed as follows: According to the experimental working conditions, the theoretical thermodynamic energy efficiency of PRC under the concerning condition is about 8%, which is concerned with equations 4-6. Also the theoretical energy efficiency of the two-stage sorption refrigerator is about 45% which is concerned with equations 9-12. The theoretical energy efficiency i.e. the theoretical limit of the gradient thermal system is about 0.265 under the condition of 95 oC heat source temperature. For the cogeneration system, the irreversibilities come from two main parts. One part is from the power generation process, in which the loss caused by scroll expander and generator will lead to the larger exergy loss when compared with the isentropic expansion and ideal work to power processes. The other part comes from the heat exchange of the sorption beds. The heat transfer temperature difference between the internal and external heat exchange fluid will result in the exergy loss for two-stage sorption refrigerator. If the isentropic efficiency, work to power efficiency and heat transfer temperature are all taken into consideration, the energy efficiency of PRC, two-stage sorption refrigerator and gradient thermal system will reach 2.95%, 24% and 13.5% which is quite closed to the experimental results as shown in Fig.11.
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The errors of the experiments are analyzed by the parameters shown in Table 1. Assuming that the testing value is unrelated, the error of total energy and exergy efficiency are calculated as the equation 15 and equation 16. Calculating results show that the largest error of tot energy efficiency and exergy efficiency are 10.56% and 11.88%, respectively, when the heat source temperature is 95oC.
( energy
energy W ave
(
( exergy
energy T h,in
exergy W ave
(
energy W ave ) Tchi,in T chi,in 2
2
T h,out
T h,out ) (
exergy W ave ) Tchi,in T chi,in
exergy T h,in
T h,in ) (
energy
2
T h,in ) ( 2
exergy T h,out
2
energy Tchi,out Tchi,ou t 2
energy m w
mw )
2
2
exergy m w
mw )
(15)
2
exergy Tchi,out Tchi,out
T h,out ) (
2
2
(16)
2
Fig.12 shows exergy efficiency of heat source under the condition of different heat source temperature for cogeneration cycle, single PRC and two stage sorption refrigerator. The exergy efficiency of heat utilization for single PRC and two-stage sorption refrigerator range from 10.9% to 8.3% and from 14.3% to 11%, separately. However, for gradient thermal cycle, the exergy efficiency of heat utilization ranges from 24% to 18.8%, which is 126.5% and 70.9% higher than the PRC and two-stage sorption refrigerator, respectively when the heat source temperature is 80oC. Even for the highest heat source temperature of 95oC, the improvement is still as high as 120% and 67.8%, separately, which indicates the high efficiency for the heat utilization by gradient thermal cycle for power and refrigeration cogeneration.
5. Conclusions
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A novel gradient thermal cycle for power and refrigeration cogeneration is proposed and analyzed with the heat driven temperature lower than 100oC. In this cycle, PRC is served as the first part to provide the power, and two-stage sorption refrigerator is utilized as the second part for refrigeration output. Conclusions are yielded as follows: [1] For PRC, the maximum power output ranges from 144 W to 232 W while average power output ranges from 122 W to 204 W when the heat source temperature range from 80 oC to 95oC. Energy efficiency increases with the increment of heat source temperature. Exergy
efficiency decreases gradually from 80oC to 90oC and increases at the end. For different heat source temperature, the energy and exergy efficiency range from 2.09% to 2.4% and 12.2% to 13.7%, respectively. [2] For two stage sorption refrigerator, COP and SCP increase with heat source temperature under 5oC and 10oC evaporation temperature. COP varies more obviously with heat source temperature than evaporation temperature. For different working conditions, COP rises from 0.185 to 0.22 while SCP ranges from 60 W·kg-1 to 91 W·kg-1. [3] Total energy efficiency decreases first and increases slightly with increase of heat source while exergy efficiency decreases with the increase of the heat source. When heat source temperature rises from 80oC to 95oC, energy efficiency and exergy efficiency range from 9.49% to 9.9% and 10.9% to 11.8%, respectively. [4] For gradient thermal cycle exergy efficiency of heat utilization ranges from 24% to 18.8%, which is 126.5% and 70.9% higher than the PRC and two-stage sorption refrigerator, respectively when the heat source temperature is 80oC. Even for the highest heat source temperature of 95oC, the improvement is still as high as 120% and 67.8%, separately, which indicates the high efficiency for the utilization of the heat by gradient thermal cycle for power and refrigeration cogeneration.
Acknowledgements: This research was supported by foundation for Innovative Research Groups of the National Natural 17 Page 17 of 27
Science Foundation of China (51521004), National Natural Science Foundation of China (51606118) and China Postdoctoral Science Foundation (15Z102060060).
References Chaiyat, N., Kiatsiriroat, T., 2015. Analysis of combined cooling heating and power generation from organic Rankine cycle and absorption system. Energy 91, 363-370. Gao, P., Wang, L.W., Wang, R.Z., Jiang, L., Zhou, Z.S., 2015. Experimental investigation on a small pumpless ORC (organic rankine cycle) system driven by the low temperature heat source. Energy 91, 324-333. Gao, P., Wang, L.W., Wang, R.Z., Zhang, X.F., Li, D.P., Liang, Z.W., Cai, A.F., 2016a. Experimental investigation of a MnCl2/CaCl2-NH3 two-stage solid sorption freezing system for a refrigerated truck. Energy 103, 16-26. Gao, P., Zhang, X.F., Wang, L.W., Wang, R.Z., Li, D.P., Liang, Z.W., Cai, A.F., 2016b. Study on MnCl2/CaCl2–NH3 two-stage solid sorption freezing cycle for refrigerated trucks at low engine load in summer. Energy Conversion and Management 109, 1-9. Ghim, G., Lee, J., 2016. Experimental evaluation of the in-tube condensation heat transfer of pure n-pentane/R245fa and their non-azeotropic mixture as an ORC working fluid. Applied Thermal Engineering 106, 753-761. Han, W., Chen, Q., Sun, L., Ma, S., Zhao, T., Zheng, D., Jin, H., 2014. Experimental studies on a combined refrigeration/power generation system activated by low-grade heat. Energy 74, 59-66. Hu, Y., Wang, L., Xu, L., Wang, R., Kiplagat, J., Wang, J., 2011. A two-stage deep freezing chemisorption cycle driven by low-temperature heat source. Frontiers in Energy 5, 263. Jiang, L., Wang, L.W., Wang, R.Z., 2014. Investigation on thermal conductive consolidated composite
18 Page 18 of 27
CaCl2 for adsorption refrigeration. International Journal of Thermal Sciences 81, 68-75. Kaşka, Ö., 2014. Energy and exergy analysis of an organic Rankine for power generation from waste heat recovery in steel industry. Energy Conversion and Management 77, 108-117. Khan, M.Z.I., Saha, B.B., Alam, K.C.A., Akisawa, A., Kashiwagi, T., 2007. Study on solar/waste heat driven multi-bed adsorption chiller with mass recovery. Renewable Energy 32, 365-381. Li, J., Pei, G., Li, Y., Ji, J., 2013. Analysis of a novel gravity driven organic Rankine cycle for small-scale cogeneration applications. Applied Energy 108, 34-44. Li, T.X., Wang, R.Z., Li, H., 2014. Progress in the development of solid–gas sorption refrigeration thermodynamic cycle driven by low-grade thermal energy. Progress in Energy and Combustion Science 40, 1-58. Pan, Q.W., Wang, R.Z., Wang, L.W., 2015. Comparison of different kinds of heat recoveries applied in adsorption refrigeration system. International Journal of Refrigeration 55, 37-48. Pan, Q.W., Wang, R.Z., Wang, L.W., Liu, D., Design and experimental study of a silica gel-water adsorption chiller with modular adsorbers. International Journal of Refrigeration. Peris, B., Navarro-Esbrí, J., Molés, F., Collado, R., Mota-Babiloni, A., 2015. Performance evaluation of an Organic Rankine Cycle (ORC) for power applications from low grade heat sources. Applied Thermal Engineering 75, 763-769. Wang, J., Wang, L.W., Luo, W.L., Wang, R.Z., 2013. Experimental study of a two-stage adsorption freezing machine driven by low temperature heat source. International Journal of Refrigeration 36, 1029-1036. Wang, L.W., 2014. Solar Powered Cascading Cogeneration Cycle with ORC and Adsorption Technology for Electricity and Refrigeration. Heat Transfer Engineering 35, 1028-1034.
19 Page 19 of 27
Wang, L.W., Metcalf, S.J., Critoph, R.E., Thorpe, R., Tamainot-Telto, Z., 2012. Development of thermal conductive consolidated activated carbon for adsorption refrigeration. Carbon 50, 977-986. Wang, R.Z., Xu, Z.Y., Pan, Q.W., Du, S., Xia, Z.Z., 2016. Solar driven air conditioning and refrigeration systems corresponding to various heating source temperatures. Applied Energy 169, 846-856. Yamada, N., Minami, T., Anuar Mohamad, M.N., 2011. Fundamental experiment of pumpless Rankine-type cycle for low-temperature heat recovery. Energy 36, 1010-1017. Yamada, N., Watanabe, M., Hoshi, A., 2013. Experiment on pumpless Rankine-type cycle with scroll expander. Energy 49, 137-145. Yang, X., Zheng, N., Zhao, L., Deng, S., Li, H., Yu, Z., 2016. Analysis of a novel combined power and ejector-refrigeration cycle. Energy Conversion and Management 108, 266-274. Yue, C., You, F., Huang, Y., 2016. Thermal and economic analysis of an energy system of an ORC coupled with vehicle air conditioning. International Journal of Refrigeration 64, 152-167.
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Fig.1-Gradient thermal cycle for power and refrigeration cogeneration.
180
140 120
o
Temperature ( C)
14.4
600 800 400 1000 200 1200 100 3 = 1400 kg/m 50 20 4 1
R245fa 160
14.0
1.06MPa
C D (30oC)
lnP (Pa)
100 80 60 40
NH3 BaCl2 (0-8) CaCl2 (4-8)
14.2
13.8 13.6
0.76MPa
B (55oC)
13.4 0.6MPa E 3
2
13.0 -3.8
0 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Entropy (kJ/(kg K))
B'
-3.6
-3.4
-3.2
o A (70 C)
o F(63 C)
(10oC)
13.2
20
A' (83oC)
-3.0
-2.8
-2.6
-1000/T (K)
(a) (b) Fig.2-Thermodynamic diagram. (a) T-S diagram of pumpless ORC, (b) P-T diagram of two-stage sorption system.
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(a)
(b)
Fig.3-Photograph of cogeneration system (a) Cogeneration system, (b) cogeneration system with auxiliary equipment.
(a)
(b)
Fig.4-The diagram of the unit tube. (a) Schematic, (b) photo.
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120
Temperature/oC
100 80 HX1
HX2
HX1
60 Hot water outlet Hot water inlet
40
Cooling water inlet Cooling water outlet
20 0
0
5
10
15
20
25
30
Time/min
Fig. 5-Hot water, cooling water inlet and outlet temperature.
250
Power output/W
200
Maximum power output
150 Average power output 100
50 75
80
85
90
95
100
o
Heat source temperature/ C
Fig.6-The maximum and average power output of the PRC vs. heat source temperature.
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0.030
0.24
0.16 0.020
0.12 0.08
Exergy efficiency
0.015
Exergy efficiency
Energy efficiency
0.20
Energy efficiency
0.025
0.04 0.010 75
80
85
90
95
0.00 100
Heat source temperature/oC
Fig.7-Energy and exergy efficiency of the PRC vs. heat source temperature.
120
Hot water inlet
Temperature/oC
100
LTS bed
80 60 40 20
Cooling water 0
0
20
HTS bed
40 60 Time/min Fig.8-Temperature of sorption beds, hot water and cooling water.
80
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6
Temperature/oC
5 Evaporator outlet
4
Evaporator inlet
3 2 1 0
0
5
10
15
20
25
Time/min
Fig.9-Inlet and outlet temperature of evaporator.
0.25
240 10 oC evaporation temperature 200
0.20
0.15
10 oC evaporation temperature
160 120 80
SCP/kW·kg-1
COP
5 oC evaporation temperature
0.10 5 oC evaporation temperature 0.05 75
80
85
90
95
40 0 100
Heat source temperature/oC
Fig.10-COP and SCP vs. different heat source temperature.
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0.16
0.20
Energy efficiency
0.10 0.08 0.05
Energy efficiency 0.04 75
80
85
90
95
Exergy efficiency
0.15
Exergy efficiency 0.12
0.00 100
Heat source temperature/oC
Fig.11-Total energy efficiency and exergy efficiency of gradient thermal system.
0.3
Exergy efficiency
Gradient thermal cycle
B C D
0.2 Two-stage refrigerator Single PRC
0.1
0.0 70
80
90
100
110
o
Heat source temperature/ C
Fig.12-Exergy efficiency of heat utilization vs. heat source temperature
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Table 1-Testing error of the apparatus for gradient thermal system. Apparatus
Type
Testing scope
Error
Dynamometer
HP9800
0-3kW
±0.2R
Temperature sensor
PT100
-50℃-200℃
±0.1℃
Pressure sensors
YSZK-311
0-2.5Mpa
±0.1%
Flow meter
LWGY-B15L
0.1-90oC
±0.5%
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