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Research Paper

Characteristics of air cooling for cold storage and power recovery of compressed air energy storage (CAES) with inter-cooling Xinghua Liu a,b, Yufeng Zhang a, Jiang Shen b, Sheng Yao a,⇑, Ziqiang Zhang c a

School of Architecture, Tianjin University, Tianjin 300072, PR China School of Mechanical Engineering, Tianjin University of Commerce, Tianjin 300134, PR China c CECEP Industrial Energy Conservation Co., Ltd, Beijing 100082, PR China b

h i g h l i g h t s A combined cooling and power system (CCP) is proposed. The air cooling is the by-product of the air expander for CAES. The air temperature entering the cold storage is controlled by inter-cooling. Air discharge from the cold storage is used as the heat sink of inter-cooling.

a r t i c l e

i n f o

Article history: Received 30 April 2016 Revised 8 June 2016 Accepted 9 June 2016 Available online 21 June 2016 Keywords: Combined cooling and power Compressed air energy storage Air compression refrigeration cycle refrigeration Air cooling Thermodynamic analysis Inter-cooling

a b s t r a c t A combined cooling and power (CCP) system driven by the compressed air energy storage (CAES) with inter-cooling is presented, and the air cooling is compared with that of an air compression refrigeration cycle (ACRC). The main objective of this paper is to evaluate the system performance, such as the volumetric flow ratio (VFR), the size parameter (SP), the ambient temperature, the temperature at the expander inlet, the power consumption of the compressor, and the power output of the air expander. The air discharge from the cold storage is used as the heat sink for air inter-cooling. Results show that the air expander can recover most of the power consumed by the air compressor. The air temperature at the expander outlet can be controlled by adjusting the air temperature difference (ATD) between the compressor outlet and the expander inlet, and the ATD is one of the main factors that influence the power output of the air expander and the net power consumption. To realize the air cooling for the cold storage, most of the power consumption of the compressor can be simultaneously recovered by the air expander. Compared with the ACRC, the air cooing by the air expander is superior for the ATD higher than 36 °C. Overall, the CCP can recover most of the power consumption of the air compressor and realize the air cooling as a by-product for cold storage, which can be popularized in engineering applications. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction The rapid social progress and the improvement of people’s living standard have stimulated the global demand for energy, which leads to a significant increase of the fossil fuel consumption. Moreover, the coal-dominated energy structure has also aroused serious environmental issues in China, such as the global warming, the ozone depletion, the acid rain, the pollutant emission. In this context, the utilization of the renewable energies, including the solar energy [1], geothermal energy [2], wind energy [3,4] and so on and the recovery of the kinds of waste heat [5,6] have been ⇑ Corresponding author. E-mail address: [email protected] (S. Yao). http://dx.doi.org/10.1016/j.applthermaleng.2016.06.064 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

attracted more and more attention in order to reduce the fossil fuel consumption and improve the energy structure and increase the energy efficiency. Compared with the wide public concern of the renewable energy utilization and the waste energy recovery, the compressed air energy storage (CAES) is also a promising technology. To enhance the air temperature, the conventional CAES systems require additional energy consumption [7–10]. Moreover, an adiabatic compressed air energy storage (A-CAES) was also presented to avoid the additional energy consumption [11,12]. Onishi et al. [13] presented a new mathematical model for the heat exchanger networks retrofit with pressure recovery to enhance the heat integration, and the results show that the pressure recovery of streams is efficient for energy savings and, consequently, for

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X. Liu et al. / Applied Thermal Engineering 107 (2016) 1–9

Nomenclature h I m p s t W Dt

specific enthalpy (kJ/kg) irreversibility rate (kW) mass flow rate (kg/s) pressure (MPa) specific entropy (kJ/(kg °C)) temperature (°C) power (kW) temperature difference (°C)

Greek symbols g efficiency (%)

decreasing the heat exchanger networks retrofit total cost especially in sub-ambient processes. Yang et al. [14] conducted a theoretical formula of the maximum pressure recovery coefficient, and they found that the derived theoretical equation can be employed in the supersonic separation process to improve the design efficiency. Dong et al. [15] studied the recovery of the heat and work in the hydrogen flows to raise the effective utilization rate of the energy, and the recovery of heat is realized by the heat exchanger, with the recovery of the work realized by rotary work exchanger composed of several compressors and turbines. The authors found the pressure and heat recovery can reduce the energy consumption and economic cost simultaneously. Lin et al. [16] used the Computational Fluid Dynamics (CFD) technique to investigate the optimum geometry parameters of the adjustable ejector used in variable cooling loads conditions for the performance of pressure recovery in a multi-evaporator refrigeration system using R134a as the refrigerant, and the results indicate that the pressure recovery ratio can be efficiently improved after the geometries optimization which is very sensitive to the nozzle diverging angle and the length of the constant-pressure mixing section. Lin et al. [17] first validated the developed CFD model by actual experimental data from an ejector-based multi-evaporator refrigeration system. The results indicate that pressure recovery ratio is very sensitive to the varying primary and secondary flow cooling loads, with the maximum pressure recovery ratio of 60% at the varied cooling loads. Moreover, in order to keep the system stable, the primary and secondary cooling loads should be maintained within ±5% and ±10%, respectively, in which case the pressure recovery ratio will have a maximum ratio of 32.8%. Lin et al. [18] found that the adjustable ejector using spindle to adjust the throat area of primary nozzle is an efficient solution to control the primary operating pressure in constant for system stability, and the pressure recovery ratio is sensitive to the varying of cooling loads. Opgenorth et al. [19] improved the performance by enhanced mixing through flow instability by adding lobes to the circular nozzle design, combined with the profiling of the mixing channel, with the objective to determine the impact of the aspect ratio and total perimeter of the lobes on system pressure recovery and the entrainment ratio. And the authors found that increasing the perimeter beyond this value drives the frictional losses along the wall surfaces to dominate the process and the recovered pressure reduces back to the circular nozzle. From the above analysis, it can be found that no literature has been found to recover the power consumption of the compressor for air cooling to realize the combined cooling and power (CCP). The power output by the air expander is used to offset the power consumption of the air compressor and the air cooling is for the cold storage is a byproduct of the air expander. In this paper, a CCP system is proposed in order to recover the power consumption of the air compressor for a CAES system, with

Subscripts com air compressor exp air expander g generator m mechanical net net s isentropic 0 environment 1, 2, 3, 4, 5 state points

the air cooling as a by-product. The cooling performance of the air expander is also compared with that of an air compression refrigeration cycle (ACRC). The objective is to analyze the influencing parameters including the volumetric flow ratio (VFR), the ambient temperature, and the temperature at the expander inlet, on the system performances. The power output of the air expander, the power consumption of the air compressor and the power consumption of the ACRC are emphatically calculated and compared with each other. Moreover, the size parameter and the volumetric flow ratio of the air expander will be also calculated.

2. System description Fig. 1 shows the flow diagram of the combined cooling and power system to recover the residual pressure of the air compressor for the ACRC system, which is mainly composed of an air compressor, a dry filter, a storage tank, an air expander, and a cold storage. Fig. 2 is the T-s diagram of the proposed system. The air (Figs. 1 and 2, state 0) coming from the environment is first pressurized to a fixed pressure (Figs. 1 and 2, state 1), and then the moisture in the air is absorbed and the impurities are also prevented from going through by the drier filter (Figs. 1 and 2, state 2). Afterwards, the air is flowed into the storage tank. The air from the storage tank (Figs. 1 and 2, state 3) pours into the air expander and its enthalpy drop is converted into shaft work to drive the generator. Finally, the air at the expander outlet (Figs. 1 and 2, state 4) reaching the requirement of the temperature is sent into the cold storage. The exhaust air is discharged by the exhaust fans.

3. Mathematical modelling The thermodynamic analysis based on the first and second laws of thermodynamics were carried out for the system shown in Fig. 1. The flow chart of the numerical model in this paper is illustrated in Fig. 3. To simplify the analysis, the following hypotheses were made: (1) The system operates in a steady-state condition. (2) There are 5% pressure loss between the tank and the air expander including the drier filter, the storage tank, and the pipes. (3) The kinetic and potential energy changes are negligible. (4) The water content in the air is assumed to be 0, and no condensate water separates out. The mathematical model for the system is expressed by the following equations:

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X. Liu et al. / Applied Thermal Engineering 107 (2016) 1–9

7 Air compressor

Drier filter

1

Tank

2

Air cooler

3

4

Air expander

5 0

Cold storage 6

Fig. 1. Flow diagram of the CCP system driven by CAES with inter-cooling.

T

Start

1

2 Input data p0, p1, p3, mair, T0, ηcom, ηexp, ηm, ηg

3

4 0

Parameter optimization T

7 5(6)

Calculation output Wcom, Wexp, Icom, Iexp, Wnet, T, T5, Rrec, SP

s Fig. 2. T-s diagram of the CCP system driven by CAES with inter-cooling.

T=

3.1. Air compressor

T-1

No

The air from the environment is compressed by the air compressor, and then it passes through the drier filter. Finally, the compressed air is stored in the air storage tank. The inlet temperature of the air compressor, T0, is the ambient temperature, which is:

T 0 ¼ T amb

ð2Þ

where tamb is the ambient temperature.

p1 ¼ ep0

Yes Output T= Topt

ð1Þ

where Tamb is the ambient temperature. The inlet pressure of the air compressor, p0, is the ambient pressure, which is expressed as follows:

p0 ¼ pamb

T5

ð3Þ

where e is the pressure ratio of the air compressor, and it equals to the ratio of the pressure at the compressor outlet to that at the compressor inlet.

End Fig. 3. Flow chart of the optimization procedure.

gcom ¼ ðh1 h0 Þ=ðh1;s h0 Þ

ð4Þ

where g and h denote the efficiency and the specific enthalpy, respectively; the subscript com stands for the air compressor, and s means the isentropic process; the difference value of h1 and h0 is the specific power consumption of the actual compression pro-

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X. Liu et al. / Applied Thermal Engineering 107 (2016) 1–9

cess, and the difference value of h1,s and h0 is the specific power consumption of the isentropic compression process.

W com ¼ mair ðh1 h0 Þ=ðgg gm Þ

ð5Þ

where W and m represent the power and the mass flow rate, respectively; gg and gm are the efficiency of the generator and the mechanical efficiency, respectively.

Icom ¼ T 0 mair ðs1 s0 Þ

The drier filter is used to catch impurities and absorb water in the air. Considering the pressure loss in the drier filter, 5% pressure drop is assumed.

ð7Þ

As a result of a relatively high velocity in the drier filter, the air temperature is assumed to be a constant value.

ð8Þ

3.3. Tank The air tank is used to store the compressed air, and the air temperature in the tank is reduced due to the heat exchange between the tank and its surroundings, so the tank can be regarded as a precooler. As the pressure drop is very small, no pressure loss is considered. DT1 is the air temperature drop in the air tank.

p3 ¼ p2 T 3 ¼ T 2 DT 1

ð9Þ ð10Þ

The mass balance equation of the air storage tank is:

dm ¼ m2 m3 ds

In order to evaluate the inter-cooling effect of the air between the outlet of the air compressor and the inlet of the air expander, the air temperature difference (ATD), DT, can be expressed as follows:

DT ¼ T 1 T 4

ð17Þ

3.5. Air expander The isentropic efficiency of the air expander is as follows:

gexp ¼ ðh4 h5 Þ=ðh4 h4;s Þ

3.2. Drier filter

T2 ¼ T1

ð16Þ

ð6Þ

where I and s stand for the irreversible loss and the specific entropy, respectively; T0 means the ambient temperature.

p2 ¼ 0:95p1

T 4 ¼ T 3 DT 2

ð11Þ

ð18Þ

where the subscripts exp and s stand for the air expander and an isentropic process; the difference value of h4 and h5 is the specific power output of the actual expansion process, and the difference value of h4 and h4,s is the specific power output of the isentropic expansion process. The power output of the air expander can be calculated as:

W exp ¼ mðh4 h5 Þgg gm

ð19Þ

where gm and gg are the conversion efficiency of the mechanical energy and the efficiency of the generator, respectively. The irreversible loss of the air expander is:

Iexp ¼ T 0 mðs5 s4 Þ

ð20Þ

3.6. System performance The net power consumption is the difference between the power consumption of the air compressor and the power output of the air expander:

W net ¼ W com W exp

ð21Þ

The recovery ratio, Rrec, is a dimensionless ratio of the power output of the air expander to the power consumption of the air compressor:

Rrec ¼ W exp =W com

ð22Þ

where m is the air stored in the air storage tank, s is time, m2 is the mass flow rate of the air entering the air storage tank, and m3 is the mass flow rate of the air leaving the air storage tank. Based on the first law of thermodynamics [20], it can be got:

For the energy conversion, the system economic performance of the air expander is largely influenced by its parameters, such as the volumetric flow ratio (VFR), the size parameter (SP). The VFR is as follows:

dðmuÞ ¼ m2 h2 m3 h3 Q loss ds

VFR ¼ V exp;out =V exp;in

ð12Þ

where u and h are the specific internal energy and the specific enthalpy of the air, and Qloss is the thermal loss from the air storage tank to the environment.

Q loss ¼ m3 cp DT 1

ð13Þ

3.4. Air cooler The air discharge from the cold storage is used as the heat sink to cool down the air from the tank. Strictly, the component of the air from the cold storage is different with that of air from the tank, but there is no evident difference between their specific heats and specific volumes. The mass flow rate and the specific heat are the same.

h3 h4 ¼ h7 h6

ð14Þ

No pressure loss exists in the air cooler.

p4 ¼ p3

ð15Þ

ð23Þ

where Vexp,out stands for the volumetric flow rate of the working fluids at the outlet of the air expander, and Vexp,in stands for the volumetric flow rate of the working fluids at the inlet of the air expander. The SP is defined as follows [21]:

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ V exp;out ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ SP ¼ p 4 DHis

ð24Þ

where His is the enthalpy drop of the air expander experiencing an isentropic process. 4. Validation Considering that no actual system is reported in the open literature, the power output performance of an air expander is numerically simulated, and the numerical values are compared with the experimental results. The numerical results of the power output of the air expander are validated by the experimental data of the power output of an air expander under the same operating conditions. The simulation results of the present solutions showed a

5

X. Liu et al. / Applied Thermal Engineering 107 (2016) 1–9 Table 1 Validation of the numerical model with the experimental data of the power output of an air expander. Substance

mair, kg/h

tex,in, °C

tex,out, °C

pex,in, kPa

pex,out, MPa

Wcom, kW

Sources

Air Air Air Air Air Air Air Air Air Air

1.07 1.07 1.12 1.12 1.11 1.11 1.09 1.09 1.06 1.06

29.10 29.10 29.06 29.06 29.04 29.04 29.04 29.04 29.09 29.09

28.76 28.76 28.80 28.80 28.80 28.80 28.80 28.80 28.80 28.80

283.27 283.27 284.72 284.72 285.24 285.24 285.54 285.54 285.98 285.98

100.44 100.44 100.47 100.47 100.48 100.48 100.48 100.48 100.47 100.47

61.75 65.11 64.87 67.61 63.95 67.37 63.29 66.81 61.30 64.95

Present Experiment Present Experiment Present Experiment Present Experiment Present Experiment

very good agreement with the experimental data as shown in Table 1, which illustrates the accuracy of the simulation results. It can be evidently seen that the experimental data is higher than the simulation results of the power output of an air expander. The highest absolute difference in power output of an air expander is only 3.96 kW, with the highest relative difference of 6.48%. The differences mainly arise from the measuring error of the temperature, the pressure, and the mass flow rate of the air. 5. Results and discussion 5.1. Effect of ambient temperature on compressor Fig. 4 shows the power consumption and irreversible loss of the air compressor with the ambient temperature at a pressure ratio of 4. It can be seen that an obvious inversely-proportional relationship exists between the power consumption and irreversible loss of the air compressor and the ambient temperature. The power consumption depends on the mass flow rate of air and the specific power. Corresponding to the ambient temperature ranging from 10 to 40 °C, the mass flow rate of air decreases from 0.1115 to 0.09363 kg/s, with a relative reducing rate of 16.03%. It should be noted that the pressure ratio of the air compressor is constant and the specific volume of air augments with the ambient temperature, so the mass flow rate of air reduces. The specific power consumption increases from 84.20 to 100.80 kJ/kg, with a relative increasing rate of 19.71%. Evidently, compared with the mass flow rate of air, the specific power consumption plays a more significant role in the power consumption. Moreover, the specific irreversible loss of the air compressor is increased from 43.78 to 51.70 kJ/kg, with the relative increasing rate of 15.32%. Similar to the power consumption, the irreversible loss is more dependent with the air mass flow rate.

5.2. Effect of ambient temperature and ATD on system performance In this section, the pressure ratio of the compressor is fixed to be 4. Fig. 5 illustrates the power output of the air expander with the ambient temperature and the (ATD between the compressor outlet and the expander inlet. Compared with the ambient temperature, the power output of the air expander is more sensitive to the ATD between the compressor outlet and the expander inlet. Under the same ambient temperature, there is an inversely-proportional relationship between the power output of the air expander and the ATD between the compressor outlet and the expander inlet, which shows that a higher air temperature at the expander inlet is beneficial to output more power. Taken the ambient temperature of 0 °C as an example, corresponding to the ATD between the compressor outlet and the expander inlet from 0 to 50 °C, the specific enthalpy at the expander inlet reduces from 360.80 to 310.20 kJ/kg, and the absolute difference reaches 50.60 kJ/kg. However, the specific enthalpy at the expander outlet reduces from 284.30 to 244.40 kJ/kg, and the absolute difference reaches 39.90 kJ/kg. Therefore, the power output of the air expander decreases with the ATD between the compressor outlet and the expander inlet under the same ambient temperature. On the other hand, under the same ATD between the compressor outlet and the expander inlet, the power output of the air expander increases little, but the increasing rate becomes larger with the ATD. Fig. 6 shows the air temperature at the expander outlet as a function of the ambient temperature and the ATD between the compressor outlet and the expander inlet. The air temperature at the expander outlet is increased with the increase of the ambient temperature and the decrease of the ATD. For a fixed ambient temperature, a higher ATD represents a lower specific enthalpy of air at the expander inlet, resulting in a lower air temperature (or specific W

50

4.885 10.81 W

4.880

I

4.875

40

10.78 4.860

10.77

4.855

10.76

4.850

30

4.845

10.75 -5

0

5

10

15

20

25

30

35

4.840 40

tsur Fig. 4. Power consumption and irreversible loss of air compressor with ambient temperature.

25

Δt

4.865

-10

35

4.870

10.79

Icom (kW)

Wcom (kW)

com

(kW)

6.135 6.267 6.399 6.531 6.662 6.794 6.926 7.058 7.190

45

com

10.80

exp

20 15 10 5 0 -10

-5

0

5

10

15

20

25

30

35

40

tsur Fig. 5. Power output of air expander with ambient temperature and temperature difference of T1 and T4.

X. Liu et al. / Applied Thermal Engineering 107 (2016) 1–9

t exp,out

50

-39.25 -27.72 -16.19 -4.656 6.875 18.41 29.94 41.47 53.00

45 40 35 30

Δt

25 20 15 10 5 0 -10

-5

0

5

10

15

20

25

30

35 40

tsur Fig. 6. Air temperature at the expander outlet with ambient temperature and temperature difference of T1 and T4.

enthalpy) at the expander inlet. On the other hand, for a fixed ATD, the air temperature at the expander inlet is completely dependent on the ambient temperature, and the air temperature at the expander outlet is proportional to that at the expander inlet. Within the range of this paper, the air temperature at the expander outlet is from 39.18 to 50.83 °C. From the above analysis, it should be pointed out that for a combined cooling and power system, the air temperature at the expander outlet can be adjusted by changing the air temperature at the expander inlet in order to satisfy the air temperature requirement. The net power consumption is the difference between the power consumed by the air compressor and the power output by the air expander, and it is a function of the ambient temperature and the ATD is plotted in Fig. 7. Combining Figs. 6 and 7, it can be obtained that the air temperature at the expander outlet is similar with the net power consumption, which is due to that under the fixed isentropic efficiency of the air expander and the same air temperature at the expander inlet, the power output by the air expander is inversely proportional to the air temperature at the expander outlet. On the other hand, the ATD has nothing to do with the power consumption of the compressor, but it is related with the ambient temperature. Therefore, a higher ambient temperature and a lower ATD between the compressor outlet

50

W

40 35 30

Δt

25 20

40 35 30 25 20 15

10

10

5

5 -5

0

5

10

15

20

25

30

35

40

tsur Fig. 7. Net power output with ambient temperature and temperature difference of T1 and T4.

0.5710 0.5832 0.5954 0.6076 0.6198 0.6319 0.6441 0.6563 0.6685

45

15

0 -10

R rec

50 (kW)

net 3.560 3.691 3.823 3.954 4.085 4.216 4.347 4.479 4.610

45

and the expander inlet leads to a higher air temperature at the expander outlet. Within the scope of this study, the net power consumption is from 3.562 to 4.450 kW. From this sense, the air temperature at the expander outlet can be controlled by changing the ATD and the ambient temperature. However, it should be noted that the ambient temperature is often uncontrolled, so changing the ATD between the compressor outlet and the expander inlet and the ambient temperature can be implemented in engineering applications, with the air discharge from the cold storage as the heat sink in the air-cooler. In order to analyze the effect of the compression and expansion, a dimensionless parameter, the recovery ratio of the power output by the air expander to the power consumed by the air compressor, is defined to quantitatively evaluate the system performance. As shown in Fig. 8, the recovery ratio is evidently influenced with the ambient temperature and the ATD between the compressor outlet and the expander inlet. Combined Figs. 4, 5 and 8, it can be concluded that a higher ambient temperature and a lower ATD between the compressor outlet and the expander inlet is beneficial to lower the net power consumption, whereas a lower ambient temperature and a higher ATD between the compressor outlet and the expander inlet is detrimental. Form the point of view of the net power output, the thermal insulation of the air between the compressor outlet and the expander inlet is essential to keep a higher air temperature at the expander inlet, and this case is only under the condition that the cooling system has no specific requirement of the air temperature at the expander outlet. Once the air temperature at the expander outlet is defined, the ATD between the compressor outlet and the expander inlet should be adjusted to make the air temperature at the expander outlet within the scope of the requirement. As far as this paper is concerned, the recovery ratio ranges from 0.571 to 0.668. The effect of the VFR on the system performance will be discussed in the following section. The SP value of the expander can be a manifestation of the initial investment to a great extent. The SP is concerned with the ambient temperature and the ATD between the compressor outlet and the expander inlet, which is shown in Fig. 9. It can be obtained that the SP is mainly influenced by the ATD between the compressor outlet and the expander inlet, and the ambient temperature only plays a secondary role in the SP. Apparently, for a fixed temperature drop between the compressor outlet and the expander inlet, the SP remains unchanged or changes very little, which is because the volumetric flow rate of the air compressor is constant, so the enthalpy drop of the air expe-

Δt

6

0 -10

-5

0

5

10

15

20

25

30

35

40

tsur Fig. 8. Ratio of power consumption of compressor to power output of expander with ambient temperature and temperature difference of T1 and T4.

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X. Liu et al. / Applied Thermal Engineering 107 (2016) 1–9

SP 0.1501 0.1509 0.1516 0.1524 0.1532 0.1539 0.1547 0.1554 0.1562

50 45 40 35 30

Δt

25 20 15 10 5 0 -10 -5

0

5

10

15

20

25

30

35

40

tsur Fig. 9. SP with ambient temperature and temperature difference of T1 and T4.

riencing an isentropic process is a decisive element to the value of the SP, and it is a function of the mass flow rate and the specific enthalpy drop of the air experiencing an isentropic process. It can be achieved that the mass flow rate is inversely proportional to the ambient temperature, however, the specific enthalpy drop of the air experiencing an isentropic process increases with the ambient temperature and the ATD between the compressor outlet and the expander inlet. Therefore, the value of the SP parameter ranges from 0.1517 to 0.1578.

portional to the VFR, within the range of 1.034 to 130.80 kW, which suggests that the power output of the air expander with a lower VFR cannot offset the power consumption of the air compressor. From this sense, a higher VFR leads to consume more net power. The VFR is dependent on the air pressure at the compressor outlet and at the expander outlet. In addition, the air pressure at the expander outlet should be higher than the atmospheric pressure. More possibly, the air pressures at the expander outlet should be at a certain pressure in order to meet the requirement of the air temperature for the cold storage to overcome the friction loss and the pressure head of the air terminal devices of the cooling subsystem. Fig. 11 demonstrates the irreversible losses of the air compressor and the air expander as a function of the VFR. Similar with the power consumption of the air compressor and the power output of the air expander shown in Fig. 8, both the irreversible losses of the air compressor the air expander are proportional to the VFR, and this is due to that a higher VFR leads to a higher irreversibility, resulting in a higher irreversible loss. The irreversible loss of the air compressor presents a upward bending whereas the irreversible loss of the air compressor is downward bending. At a VFR of 50, the irreversible losses of the air compressor and the air expander are 194.7 and 143.8 kW. The SP and the recovery ratio as a function of the VFR are illustrated in Fig. 12. It can be seen from Fig. 12 that the value of the SP parameter first sharply decreases and then gradually increases with the increment of the VFR, and there exists the lowest value

180

Icom

180

160

Iexp

160

140

140

120

120

100

100

80

80

60

60

40

40

20

20

0

0

5

10

15

20

25

30

35

40

45

Wcom

Fig. 11. Irreversible losses of compressor and expander with VFR.

0.62

150

150

100

100

50

50

0

5

10

15

20

25

30

35

40

45

0 50

R rec

200

R rec

0.20

SP 0.19 0.18

0.61 0.17

0.60

0.16

0.59 0.58

SP

200

Wexp (kW)

0.63

0

0.21

0.64

250

250

Wcom (kW)

300

Wexp

0 50

VFR

0.65 300

Iexp (kW)

Icom (kW)

5.3. Effect of VFR on system performance In this section, another important parameter, the effect of the VFR, on the power consumption of the air compressor and the power output of the air expander is analyzed. The power consumption of the air compressor and the power output of the air expander as a function of the VFR are shown in Fig. 10. Both the power consumption of the air compressor and the power output of the air expander are increased with the VFR, and the power consumption of the air compressor presents an upward bending whereas the power output of the air expander is downward bending. At a VFR of 50, the power consumption of the air compressor is 303.30 kW, and the power output of the air expander 178.60 kW. The difference between the power consumption of the air compressor and the power output of the air expander is directly pro-

200

200

5

10

15

20

25

30

35

40

45

0.15 50

VFR

VFR

Fig. 10. Power consumption of compressor and power output of expander with the VFR.

Fig. 12. SP and ratio of power consumption of compressor to power output of expander with VFR.

X. Liu et al. / Applied Thermal Engineering 107 (2016) 1–9

of 0.1541 when the VFR is 4. For the VFR lower than 2.0, the SP value is extremely high, which is due to that the volumetric flow rate remains constant. But the enthalpy drop of the air experiencing an isentropic process is pretty small correspondingly, and this will result in a very high value of the SP parameter. The recovery ratio always remains a continuous increase with the VFR, and a higher VFR means that more net power can be input. However, the VFR should not be too high, and most importantly, the air temperature at the expander outlet often limits the value of the VFR.

50

W /W net

45

ACRC

0.4900 0.6325 0.7750 0.9175 1.060 1.202 1.345 1.488 1.630

40 35 30 25

Δt

8

20 15

5.4. Air cooling performance comparison with the ACRC

10

From the above analysis, the air temperature at the air expander outlet is quite low, and such low temperature air contains a considerable cooling capacity, which is at the cost of the net power consumption for the air compressor and the air expander. In order to evaluate the cooling performance, an ACRC is used as a basis of comparison. Considering the low coefficient of performance (COP) of the ACRC system and the working condition, the COP of the ACRC is assumed to be 0.35 from the data provided by Liu et al. [22]. The difference between the net power consumption and the power consumption of the ACRC, Wnet WACRC, represents the cooling performance. The cooling provided by the air expander is superior to the ACRC for Wnet < WACRC whereas the ACRC is more preferable for Wnet < WACRC. From Fig. 13, it cam be evidently found out that the Dt plays a more significant role than the ambient temperature to Wnet WACRC, as the variation range of (Wnet WACRC) is much larger at a fixed ambient temperature than that at a fixed Dt, and this is owning to that a larger Dt results in a lower air temperature at the air expander inlet and outlet. Moreover, the cooling load of air is inversely proportional to the air temperature at the air expander outlet. For a fixed COP of the ACRC, the power consumption of the ACRC is completely dependent on the cooling load of the ACRC. It should be pointed out that a lower Dt leads to a relatively high air temperature at the air expander outlet, which may be higher than the ambient temperature corresponding to a negative value of the cooling load of the ACRC. Combining Figs. 5 and 11, WACRC increases faster than Wnet with Dt under a constant ambient temperature, so a lower ambient temperature and a higher Dt makes (Wnet WACRC) to become lower. (Wnet WACRC) ranges from 4.748 to 3.617 kW in this study, and the cooling provided by the air expander is superior to the ACRC for Dt > 36 °C. Fig. 14 shows the ratio of the net power consumption to the power consumption of the ACRC. For Dt < 12 °C, there is no cooling

50

W

-WACRC (kW)

net

45 -4.750 -3.669 -2.588 -1.506 -0.4250 0.6562 1.737 2.819 3.900

40 35 30 Δt

25 20 15 10 5 0 -10

-5

0

5

10

15

20

25

30

35

40

tsur Fig. 13. Difference of the net power consumption and the power consumption of the ACRC with ambient temperature and temperature difference of T1 and T4.

5 0 -10

-5

0

5

10

15

20

25

30

35

40

tsur Fig. 14. Ratio of the net power consumption to the power consumption of the ACRC with ambient temperature and temperature difference of T1 and T4.

load for the ACRC due to that the air temperature at the air expander outlet is higher than the ambient temperature. Moreover, for 12 < Dt < 28 °C, the power consumption of the ACRC is low to lead to a high ratio of the net power consumption to the power consumption of the ACRC, so Fig. 14 only illustrates the variation trend for Dt > 28 °C in order to facilitate the observation. The cooling provided by the air expander is superior to the ACRC for Wnet/ WACRC > 1. The value of Wnet/WACRC is from 0.4925 to 1.629 for Dt > 28 °C. Therefore, the cooling performance provided by the air expander is superior to the ACRC for Dt > 36 °C, and the air temperature at the air expander outlet can be adjustable by controlling the temperature drop between the compressor outlet and the expander inlet. 6. Conclusions The air compressed energy storage (CAES) system with intercooling is presented. The air cooling for cold storage by the air expander and power recovery of the compressor are investigated, and the air cooling by the air expander is compared with an air compression refrigeration cycle (ACRC). The main conclusions that can be drawn from the present study are summarized as follows: (1) The air expander can recover the most of the power consumption of the air compressor, and a lower ambient temperature and a lower air temperature difference (ATD) between the compressor and the expander leads to reduce the net power consumption. (2) The air temperature at the cold storage inlet can be controlled by adjusting the ATD between the compressor outlet and the expander inlet. (3) The air discharge from the cold storage is used as the heat sink of the inter-cooling for the compressed air to meet the air temperature requirement of the cold storage. (4) The CAES can realize the air cooling as a companying byproduct, which is at the cost of a portion of the net power consumption, and it is superior to the ACRC for the ATD higher than 36 °C (5) The combined cooling and power driven by a CAES system is suitable for the places where there is a need for cooling, which can be popularized in engineering applications.

X. Liu et al. / Applied Thermal Engineering 107 (2016) 1–9

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