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Evaluation of an existing helium liquefier in refrigerator and mixed-mode operation through exergy analysis
Cryogenics 103 (2019) 102977
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Evaluation of an existing helium liquefier in refrigerator and mixed-mode operation through exergy analysis
T
⁎
T.K. Maitia,b, , S. Pala,b, B. Kunduc, P. Ghoshd a
Variable Energy Cyclotron Centre, Kolkata 700064, India Homi Bhabha National Institute, Kolkata 700064, India c Department of Mechanical Engineering, Jadavpur University, Kolkata 700032, India d Cryogenic Engineering Centre, Indian Institute of Technology, Kharagpur 721302, India b
A R T I C LE I N FO
A B S T R A C T
Keywords: Helium Liquefier Mixed mode operation Exergy Specific power consumption
Present day, all small scale helium liquefiers operate in Claude cycle with two turbines in series arrangement. In this paper, an effort has been made to investigate the exergy characteristics of a small scale liquefier and its components at design and various off-design refrigeration and mixed mode operation under steady state condition. The variation of exergy efficiency, exergy destruction, exergy output-destruction interrelations, refrigeration- liquefaction capacity correlation, etc. have been evaluated by increasing refrigeration load in steps starting at pure liquefaction till pure refrigeration mode in the experiment. As the experimental data were not sufficient for complete analysis, Aspen Hysys software has been used to determine the remaining process parameters required to understand the thermodynamic cycle. The significance of the variation of exergy parameters at different modes of operation have been reported to establish the importance of the present study. Though the results are specific for the existing helium liquefier (model HELIAL 50 of Air Liquide DTA, France) with some associated constraints, the results may be useful to the designers of helium systems where flexibility of operation is a desirable feature.
1. Introduction Large and small scale helium plants are necessary for cryogenic applications in particle accelerators, like cyclotrons, synchrotrons, linacs, penning traps, etc., where three modes of operations exist, viz. liquefaction, refrigeration and liquefaction-refrigeration mixed mode. For cool down, steady state run, warm up, quenching, and breakdown situation of an accelerator superconducting magnet, a helium plant needs to run at all the modes of operation at maximum or part load capacity depending upon the type of loads and their operation. In pure liquefaction mode, liquid helium exits the system with both sensible and latent heat; whereas in pure refrigeration mode operating in closed loop, boil-off gas returns the compressor suction by only absorbing latent heat from external heat load when the sensible heat is conserved in heat exchangers; while in mixed mode, the component characteristics and parameters lie in between. Hence, a system designed for a particular mode, will not efficiently perform in other off-design modes, but it is necessary to predict the performance of the liquefier in other offdesign modes. Helium liquefiers are highly energy intensive system. To reduce the
⁎
consumption of power for cryogenic plants, exergetic performance criteria based on second law of thermodynamics, is a useful tool in design, evaluation, optimization and improvement of helium liquefier. By applying the exergy evaluation method, it is possible to locate and quantify the irreversibility source of each and every component of a system which in turn is helpful to predict the liquefier’s performance in other modes. In the available literature, there are a large number of papers on the exergy performance of thermal power plants operating in Rankine cycle, Brayton cycle and their various combinations and configurations [1–6]. But a few papers are available on exergy analysis of helium liquefaction systems. Thirumaleshwar [7] presented a theoretical exergetic analysis of an ideal isothermal and isobaric heat source of helium refrigeration systems working on modified Brayton cycle. Ahamed et al. [8] investigated the variation of exergy performance in vapour compression refrigeration cycle of air conditioning system by varying the several controlling parameters of the cycle. Thomas et al. [9,10] presented the design and optimization of a helium liquefier operating in Collins cycle using exergetic analysis
Corresponding author at: Variable Energy Cyclotron Centre, Kolkata 700064, India. E-mail address: [email protected] (T.K. Maiti).
https://doi.org/10.1016/j.cryogenics.2019.102977 Received 9 May 2019; Received in revised form 30 August 2019; Accepted 4 September 2019 Available online 06 September 2019 0011-2275/ © 2019 Elsevier Ltd. All rights reserved.
Cryogenics 103 (2019) 102977
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Compressor module
method with commercial process simulator Aspen Hysys. In the analysis, they assumed the fixed value of isothermal efficiency of compressor (55%), adiabatic efficiency of warm turbine (75%) and cold turbine (70%), and a fixed effectiveness value of all heat exchangers (97%). Exergy efficiency variation of the cycle, destruction of exergy at various components, with change of cycle pressure ratio and mass flow rate through turbines have been derieved. Thomas et al. [11–13] studied theoretically the effect of turbine and heat exchanger parameters on improvement and optimization of liquefaction capacity of Collins cycle. They assumed that all heat exchangers have equal effectiveness of 97% and all turbines have equal efficiency of 70%. Exergy analysis for optimization of different configurations of Collins cycle was carried out using intermediate pressure for large helium liquefiers. Kundu and Chowdhury [14] presented theoretical exergy analysis of large scale helium liquefier and refrigerator operating in Collins cycle at design and off-design mixed mode conditions using Aspen Hysys V7.0. Evaluation of some design parameters like optimum compressor discharge pressure, expander flow rate, UA of heat exchangers, specific work input was performed at maximum cold box exergy efficiency for liquefaction, refrigeration and mixed modes. It has been assumed that all heat exchangers have zero pressure drop and equal effectiveness (97%), turbines have equal isentropic efficiency (80%) and fixed compressor efficiency (55%). Cailland et al. [15] discussed on the evolution of fully automatic HELIAL models of Air Liquide DTA, France, the most widely used liquefier worldwide, since its inception in 1980s. The manufacturer has almost doubled the capacity of HELIAL range by design optimization of turbines, heat exchangers, automation and supervisory system. Turbines of this manufacturer have static gas bearings, characterized by mean time between failures (MTBF) higher than 150,000 h. This product also serves the multi-range turn-key projects of the customers, catering to specific requirements (pure liquefaction or pure refrigeration or mixed modes). A helium liquefier, which is coupled with cryogenic installations, needs to operate both at design and off-design operating modes in order to fulfil the need of cryogenic loads. From above literature survey, it is evident that in helium liquefaction/refrigeration systems, exergy and energy analyses have been addressed for liquefaction and refrigeration process of Collins cycle. And the analysis have been performed using commercial process simulator. Most of the studies in open literature [9–14] have considered pre-fixed constant values for effectiveness and negligible pressure drop of heat exchangers, efficiency of turbines and compressor, and zero heat in-leak into the system. There is dearth of literature available on the detailed study of exergy characteristics of different components and their variation trends in the off-design mixed modes for an actual small scale helium liquefier. The present study has been performed on a small scale existing helium liquefier and explored its exergetic characteristics in various modes of operation, such as designed pure liquefaction, off-design mixed and pure refrigeration modes. Some performance characteristics of major components have been analysed at different modes based on the experimental data of liquefier. The variation of the exergy efficiency and exergy output of a liquefier with the change of refrigeration load has been studied. Correlation between exergy output and exergy destruction of Claude cycle has been illustrated graphically. Evaluation has been carried out on the variation of exergy characteristics viz. percentage exergy destruction, exergy transfer load and exergy efficiency, of the major components like different heat exchangers, turbines, compressor, JT valve and flow control valve, when they are operated away from their designed conditions. Some study has been done on energy analysis of the heat exchangers working above and below 20 K. Below 20 K temperature range, there is sharp and substantial rise and fall of heat capacity of helium till liquefaction. Here, the cold stream which has minimum heat capacity at warm end of heat exchanger will have maximum heat capacity at cold end due to larger heat capacity at low temperature. This is true for helium streams at any
Buffer tank (BT) + turbine bearing + bypass 22
To bypass valve To turbine bearing (TB)
1
23
2
HX1 Flow control valve
3
HX2
5
4
6
Warm turbine
HX3 8
7
HX4
9
10
21
HX5 20
Cold turbine
12
11
19
HX6 Dewar heater
17
Q
18
13 JT Valve
15 14
16 f Liquid helium
Dewar
Fig. 1. Schematic of a small scale helium liquefier, consisting of a screw compressor, two turbines, six heat exchangers, a turbine flow control valve and a JT valve.
pressure working close to boiling point. The characteristics of two turbines in series have been assessed at all the operational modes. The results derived from exergy performance analysis, which are not available in any literature, will guide a designer to interpolate, extrapolate or predict the characteristics and performance of a helium plant in off-design conditions. 2. Process 2.1. Configuration of a helium liquefier under study and experimental procedure The schematic of a small scale liquefier is presented in Fig. 1. This configuration complied the standard product (model: HELIAL 50) of Air Liquide DTA, France, (manufacturer guaranteed liquefaction capacity without liquid nitrogen pre-cooling is 50 l/h), where l/h is litres/hour. This liquefier under the present study consists of three functional sections: 1. Compressor module (160 kW Siemens motor). The compressor runs at constant speed, hence, the discharge pressure, temperature and mass flow rate are constant for all the modes of operation. The discharge pressure (HP) and suction pressure (LP) are 1.40 MPa absolute (MPa) and 0.106 MPa repectively. A part of the compressor discharge flow is diverted for turbine static bearings (2.95 g/s) and remaining part, called hot stream (47.59 g/s) enters the cold box, where g/s is grams/second. 2. Cold box part, which comprises of two turbines (warm and cold turbine) in series with a heat exchanger in between, six plate-fin type heat exchangers, one JT valve. In this configuration, cold box inlet pressure and mass flow rate of process gas was constant for all modes of operation. The inlet mass flow rate of warm turbine is controlled by a flow control valve where pressure drop occur, hence the inlet pressure of warm turbine varies with change of turbine flow conditions. 2
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3. Liquid helium dewar. It is equipped with a Nichrome resistance heater. The cold helium LP stream returns through heat exchangers due to pressure difference between dewar and compressor suction end.
Table 2 . Temperature, pressure and mass flow rates of these nodes are recorded/observed during experiment (Fig. 1 is referred for nodes location).
Node
2.2. Measurement procedure In order to make the experimental study, the liquefier was operated at full capacity for all the modes of operation. To investigate the mixed modes, a certain refrigeration load was applied by a heater dipped in liquid helium within dewar and the increase in level of dewar was measured for assessing the liquefaction rate. This heater power was manually controlled by an auto-transformer and actual refrigeration load was calculated by monitoring current and voltage. The dewar pressure was maintained at 0.13 MPa and the dewar temperature was measured by CLTS sensor, maintained at 4.50 K during the entire experiment. For the investigation purpose in mixed modes, the refrigeration load was gradually increased by a step of 25 W beginning from pure liquefaction mode. Following this procedure, it was observed that at refrigeration load of 211.70 W, liquefaction rate got reduced to zero. At this stage, the liquid level in dewar remained constant and further refrigeration load increment resulted in reduction of dewar level. Liquid helium level in the dewar is measured in liters. Bypass valve always remains closed during experiments as the investigations were done at full capacity of the plant. Table 1 shows the experimental values of liquefaction and refrigeration capacity at different modes.
3.
4. 5. 6.
7.
2, 22, 23, 6, 9, 11, 13, 14, 15
1, TB, BT, f, bypass
As per manufacturer’s provided data, isentropic efficiency is equal for both the turbines at the design operating conditions. In addition, equal value of efficiency of warm and cold turbines is assumed in some reference literatures [10–13]. Average pressure drop of hot stream and cold stream of each heat exchanger is taken as of 50 × 102 Pa and 40 × 102 Pa respectively. This consideration is based on the experimental values obtained from the pressure transmitters located in the helium liquefier. Temperature and pressure of nodes 11, 19 and 20 are assumed to be same. Temperature and pressure of nodes 15 and 18 are same. The 3-stream heat exchanger, HX4, has been considered as 2-stream one by assuming equal temperatures for two warm flow inlets (nodes 7 and 8), and for two cold flow outlets (nodes 9 and10). Vapour fraction of node 18 is 1, as the co-axial transfer line between dewar and cold box is long.
2.4.1. Equation of state (EOS) The 32-term MBWR (Modified Benedict – Webb – Rubin) EOS developed by McCarty and Arp [16,17], a property package of Aspen Hysys, has been used here for generating thermo-physical properties of helium. MBWR EOS has very high accuracy for pure components. The thermo-physical properties of several cryogens generated by using MBWR correlation are also used in NIST property package, THERMOPACK property package software, HEPAK - a dedicated helium property package and commercial process simulator Aspen Hysys.
Table 1 Experimental readings of refrigeration load and liquefaction rate at different modes of operation.
2.201 g/s 26.13 W + 2.100 g/s 50.39 W + 1.877 g/s 74.42 W + 1.650 g/s 101.80 W + 1.300 g/s 122.90 W + 1.107 g/s 151.70 W + 0.774 g/s 174.40 W + 0.562 g/s 211.70 W
2, 3, 4, 7, 11, 13, 14
The liquefier under present investigation has limited number of sensors to gather information on the physical parameters (viz. pressure, temperature, mass flow rate, etc.) of the nodes (refer Fig. 1). These experimental data and some assumptions based on published references have been incorporated as input in the Aspen HYSYS v8.6 flowsheet program, to obtain the parameters of the remaining nodes as output. Using these basic physical parameters, the following functions have been calculated for cycle analysis, viz. exergy at each node; exergy efficiency of the total thermodynamic cycle; exergy efficiency and exergy destruction of each component; heat load, effectiveness, LMTD and UA of heat exchangers; adiabatic efficiency and power of turbines; isothermal efficiency of compressor; etc.
1. Analysis is done at steady state condition of the system. 2. Isentropic efficiency of both warm and cold turbines is taken as equal. This assumption is made based on the following facts:
Pure liquefaction Mixed Mixed Mixed Mixed Mixed Mixed Mixed Pure refrigeration
Mass flow rate
2.4. Analysis methodology
The experimental readings of the parameters of the nodes shown in Table 2 were recorded from sensors/transmitters located in helium liquefier during operation. Table 3 provides a brief specification of the measuring instruments. These physical parameters are the input of the study: Besides above, the other parameters obtained from experiment are dewar heater current and voltage, turbine rotational speed, bypass valve opening and compressor motor power. Figs. 2–4 shows input experimental data of temperature and pressure at different nodes; rate of dewar level variation, heater voltage and current, at different modes of operation. Liquid helium level, turbine bearings and buffer tank are denoted by Ldewar, TB, BT respectively. Dewar heater power is measured in Watt (W), warm and cold turbine rotational speed in revolutions per second (rps). The assumptions made for this study are as mentioned below: (nodal points of Fig. 1 are referred)
(Refrigeration load + Liquefaction rate*) @4.5 K
Pressure
The experimental data along with the assumptions which act as input parameters in this analysis have been summarised in Table 4.
2.3. Input experimental parameters recorded by sensors and assumptions
Mode of operation
Temperature
2.4.2. Exergy and energy analysis The basic principles and methodology of exergy analysis of a thermal system are well established and are widely available in the text books on thermodynamics. The exergy analysis of the operating liquefier is based on exergy balance in a flow system across a control volume, which is expressed as ·
·
∑ Ex flow + ∑ Q (1 − in
·
T0 )= Tj
·
·
Ex + W ∑ flow out
·
+ Ex D
(1)
·
where Ex = m × ex . The specific exergy in any state is expressed as
ex = (h − h 0) − T0 (s − s0)
* 1 g/s of LHe is equivalent to 30.28 l/h. 3
(2)
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Table 3 . Specification of instruments and uncertainty in the measurement of parameters in the experiment with the helium plant. Parameter
Instrument used
Overall uncertainty
Refrigeration power Level of liquid helium in dewar
Fluke digital multimeter, 17B (1) NbTi filament, 203 cm sensor active length (2) AMI monitor, model 135 (3) Eurotherm PLC, PC3000 1) Lakeshore Cernox sensor, model CX1050 2) Lakeshore temperature transmitter, model 234 3) Eurotherm PLC, PC3000 Keller make, model PA21
± 3% ± 0.85%
Temperature
Pressure
Exergy destruction in a turbine is the summation of exergy destructions in isentropic expansion (turbine work is not recovered in this case) and bearings. The exergy destruction of two turbines and adiabatic efficiency in steady flow process are expressed as:
And, irreversibility or exergy destruction or exergy loss is expressed as ·
·
Ex = m × exD = T0 × Δsgenerated
(3)
D
± 0.30% (for 4.20 K) ± 0.12% (for 77 K) ± 0.10% (for 300 K) ± 0.35%
·
·
·
where ex(J/g) represents specific exergy or exergy transfer per unit · · mass, Ex (W) is exergy transfer rate, m (g/s) is mass flow rate, h (J/g) is
ExD = m6(ex 6 + ex 9 − ex 7 − ex11) + mTB (exTB − ex22)
enthalpy per unit mass, s (J/g-K) is entropy. Q (W) is the rate of heat transfer across boundary at instantaneous temperature Tj (K). exD is the irreversibility associated with the process. h0 and s0 represents the enthalpy and entropy at reference state (T0, P0) respectively. The ambient condition of the environment is taken as reference state, where T0 = 300 K and P0 = 0.10 MPa. The helium compressor is the air cooled screw compressor, whose
ηad =
·
·
·
⎟
·
m (ex2 − ex22) + mTB (exTB − ex22)
(4)
2
·
·
·
Ex = abs [ m (exhot , in − exhot , out ) + m (ex cold, in − ex cold, out )]
Hence, exergy destruction in compressor = 160 kW − input exergy to cold box
(7)
In turbine flow control valve, pressure drop occurs in helium stream, resulting in the expansion of exit gas. This expansion causes the temperature rise of exit gas as inlet gas temperature is above the inversion temperature. In JT valve, the expansion of helium gas is isenthalpic (h13 = h14) and inlet gas temperature is below inversion temperature, hence there is drop of exit gas temperature. The exergy destruction of the following components are expressed as: for HX:
electrical exergy input is 160 kW ⎛ W ⎞. ⎝ comp⎠ Input exergy to the cold box relation is expressed as ⎜
Actual enthalpy drop due to expansion Theoretical enthalpy drop due to adiabatic expansion
(6)
D
hot
cold
(8)
for Turbine flow control valve:
(5)
·
Similarly, the exergy destruction of each major component of the liquefier is determined using exergy balance equation, Eq. (1).
·
ExD = m (ex5 − ex 6) 5
Fig. 2. Experimental temperature data of different nodes at different modes. 4
(9)
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Fig. 3. Experimental data of pressure and rate of liquefaction in dewar at different modes.
The first term of right hand side of Eq. (11) represents refrigeration output and second term expresses liquefaction output. Therefore, the exergy efficiency of the plant at any operational mode is expressed as:
for JT valve: ·
·
ExD = m (ex13 − ex14 ) 13
(10)
The exergy output of the helium liquefier operating in mixed mode = ·
·
·
m (ex16 − ex17) + m (exLHe − ex22)
·
m16(ex16 − ex17) + m (exLHe − ex22) LHe
ηcycle =
(11)
16
LHe ·
W comp
Fig. 4. Experimental data of heater voltage and current at different modes. 5
(12)
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of the existing liquefier at various modes. It is observed here that the system being liquefier, exergy efficiency and exergy output decreases above refrigeration load of 74.42 W and upto the pure refrigeration mode. Exergy efficiency and exergy output also decrease at pure liquefaction mode than subsequent 26.13 W mixed mode. This is due to the fact that, the turbine rotational speed is highest in pure liquefaction mode and is very near to threshold limit, so, for the safe operation of turbines, the speed of the turbines is not set at the best value. Consequently, the liquid production rate achieved in pure liquefaction mode is lower than the maximum possible capacity. But at off-design modes, the turbines are tuned to best possible efficiency as the speed reduces to optimum level. Fig. 6 reveals the same trend of variation of exergy efficiency and exergy output curves, which is due to the constant exergy input to the compressor at 160 kW. Fig. 7 shows that the relationship between exergy output and exergy destruction of a liquefier is linear. This correlation explains that pure refrigeration mode has minimum exergy output with maximum exergy destruction compared to any other modes, and the pure liquefaction mode is next in sequence. All mixed modes have larger exergy output and lesser exergy destruction than these two modes. Mixed mode output (74.42 W + 1.65 g/s) has least exergy destruction and maximum output. These results are corroborated by exergy efficiency distribution of Fig. 6. It is evident from Fig. 6, that the existing helium plant has maximum exergy efficiency at refrigeration load of 74.42 W, hence it can be rationally inferred that the system has been best tuned (designed) at this mode. As mentioned, at mixed mode refrigeration load of 74.42 W, the heat exchangers and turbines are set to operate at optimum level to provide maximum exergy efficiency. But as the system is operated away from the design mode, the exergy efficiency decreases as the output exergy gets reduced due to thermodynamic irreversibility or exergy loss associated with the process. Here, the exergy input at compressor is 160 kW. The decrease in exergy efficiency at off-design modes is due to increased irreversibility of cold box consisting of heat exchangers, turbines, flow control valve and JT valve. Percentage exergy destruction / loss of a component is the ratio of exergy destruction to exergy input to compressor. Figs. 8 and 9 display the quantitative value of percentage exergy loss of compressor, heat exchangers, turbines and valves at different modes. Irreversibility for compressor is constant for all modes; and for turbines, it declines with the increase of refrigeration load. The irreversibility of the system is related to the total entropy production in the system as explained in Eq. (3). The entropy generation in heat exchanger is largely due to heat transfer at finite differences of fluids temperature. Percentage exergy destruction / loss of a component is defined as the ratio of exergy destruction rate to input electrical power to compressor unit (motor power). Fig. 9 shows that minimum percentage exergy loss occur around 74.42 W refrigeration load at mixed mode for all the heat exchangers together and cold box respectively. Here, percentage exergy loss increases on both the left and right sides of the minimum point along x-axis. Fig. 8 shows that for two valves, the percentage exergy loss increases with refrigeration load. Hence, the resultant effect of the irreversibility characteristics of all these components determines the shape of exergy efficiency curve of Fig. 6.
Table 4 . List of input physical parameters. Input experimental data: 1. 2. 3. 4. 5. 6. 7. 8.
a. b. c. d. e. f.
Temperature of nodes 2, 3, 4, 7, 11, 13, 14, shown in Fig. 2 Pressure of nodes 2, 22, 23, 6, 9, 11, 13, 14, 15, presented in Fig. 3 Mass flow rate of nodes 1, TB, BT, f, bypass, shown in Section 2.1 Compressor motor input power, 160 kW Dewar heater current and voltage, shown in Fig. 4 Dewar level variation, shown in Fig. 3 Warm and cold turbine rotational speed, shown in Fig. 12 (Refrigeration load + Liquefaction rate) @ 4.50 K at pure liquefaction, mixed and pure refrigeration mode, displayed in Table 1 Assumptions: Equal isentropic efficiency for warm and cold turbines Average pressure drop of hot stream and cold stream of each heat exchanger is 50 × 102 Pa and 40 × 102 Pa respectively. Temperature and pressure of nodes 11, 19 and 20 are same. Temperature and pressure of nodes 15 and 18 are same. In HX4, equal temperatures for nodes 7 and 8, and, for nodes 9 and 10. Vapour fraction of node 18 is 1
subscripts TB, LHe and comp stands for turbine bearings, liquid helium and compressor respectively. Isothermal efficiency of a compressor is defined as the ratio of isothermal power to input power. ·
m × R × T23 × ln
isothermal efficiency =
23
(
input power
p1
p23
) (13)
where R denotes gas constant and input power is motor power. Isothermal efficiency of the screw compressor under present study has been determined as 50.83%. This value complies with the available literatures [9–12,14]. 3. Results and discussion 3.1. Helium liquefier cycle characteristics Fig. 5 depicts the relation between refrigeration load and liquefaction capacity of the liquefier at different modes. It is observed from this curve that experimental liquefaction capacity at mixed modes has positive variation within 45% from the linear line joining the maximum liquefaction capacity and refrigeration capacity for a certain refrigeration power applied. Fig. 6 presents the variation of exergy efficiency and exergy output
3.1.1. Specific power consumption of liquefier As cryogenic processes are potential energy demanding systems, Specific Power Consumption (SPC) parameter has been adopted as a performance indicator in the study of its energy assessment and it is one of the major concerns of liquefier manufacturers [15]. SPC is broadly defined as the energy used for producing a unit product. In the liquefier under the present study, the input compressor power is 160 kW, and product is Equivalent Carnot Refrigeration (ECR) at various modes of operation. Thermodynamic ideal cycle or Carnot cycle for liquefaction or
Fig. 5. Refrigeration load versus liquefaction capacity curve of the liquefier using experimental data. 6
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Fig. 6. Exergy efficiency and output exergy of helium liquefier at different modes.
Fig. 7. Exergy output versus exergy destruction at different modes.
refrigeration is a reversible cycle with maximum Coefficient of Performance (COP) for heat transfer process between two thermal reservoirs. Carnot work is the minimum input work requirement for a given heat transfer rate between two reservoirs. In the liquefier under present study, extraction of liquid helium or heat transfer to liquid takes place at temperature and pressure of 4.50 K and 0.13 MPa respectively in the dewar; and compressor suction temperature is 303 K. Therefore, thermodynamically ideal liquefaction system is working between thermal reservoirs at temperatures of 303 K and 4.50 K. The following equations concerning net ideal or Carnot work for helium liquefaction and refrigeration systems are obtained from the first law of thermodynamics for steady flow [20].
Ideal or Carnot work for liquefaction: −
Ẇ = Tsuction Δs − Δh ṁ
Fig. 8. Percentage exergy destruction of components with respect to electrical exergy input to compressor.
gas; suction temperature of compressor; entropy change due to reversible isothermal compression; and, enthalpy absorbed by saturated liquid helium at temperature and pressure of 4.50 K and 0.13 MPa respectively, to attain temperature of 303 K at the same pressure; respectively. ·
·
⎡Q ⎣R
W Carnot work for refrigeration: Carnot · m
= ⎡ ⎣
TC
·
m⎤
⎦
(TH − TC ) ⎤
⎦
(15)
·
W
Terms
(14)
Carnot · ,
m
·
Q , TC and TH stands for net work expended per unit R
mass of refrigerant, refrigeration effect or energy absorption rate at constant temperature TC, temperature of heat source, and temperature of heat sink, respectively.
Ẇ , ṁ
ṁ , Tsuction, Δs and Δh, denote net Carnot work required Terms − per unit mass of gas (this term is a positive quantity); mass flow rate of 7
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Fig. 9. Percentage exergy destruction at all heat exchangers together and cold box at different modes. ·
Applying Eqs. (14) and (15) in the present study, it is found that net Carnot work of 6671.76 W is required for 1 g/s @ 4.50 K, 0.13 MPa liquefaction; and 66.67 W for 1 W @ 4.50 K, 0.13 MPa refrigeration. Hence, on an equal Carnot work basis, 100.07 W of 4.50 K refrigeration is equivalent to 1 g/s of 4.50 K liquefaction. Specific power consumption [14] can also be explained on the basis of exergy output, which is the ratio of compressor power input to exergy output of the products at different modes. For illustration purpose, using input compressor power of 160 kW, Eq. (11) and liquefaction-refrigeration equivalence relation in the case of 74.42 W mixed mode, the parameters, Equivalent Carnot Refrigeration @ 4.50 K and 0.13 MPa, and exergy output, has been determined as 239.54 W and 15961.74 W respectively. The definition of Specific Power Consumption based on both ECR and exergy output yields the values 667.67 W/W and 10.024 W/W respectively. Fig. 10 presents SPC based on both ECR and exergy output at different modes. Fig. 10 reveals that SPC is lowest at 74.42 W mixed mode and increases with increasing refrigeration load till it reaches the maximum at pure refrigeration mode. SPC at pure liquefaction mode is higher than subsequent 25 W mixed mode, as ECR of former is less than the later one. Figs. 6 and 10, show that SPC is quantitatively reciprocal to exergy efficiency. Hence, at 74.42 W mixed mode, SPC is minimum when exergy efficiency is maximum; and, vice versa at pure refrigeration mode.
We ·
m
·
= (hin − hout ) +
mf
(hout − hf )
·
m
(16)
Applying the first law for steady flow to the same unit, in pure refrigeration mode, the expression follows as: ·
We ·
m
·
= (hin − hout ) + ·
mx ·
m
(hg − hf )
(17) ·
where We denotes total power output of the turbines, m denotes mass flow rate through compressor, hin and hout represents enthalpy of gas at the entry and exit of the unit, hf and hg represents enthalpy of saturated · gas and liquid at dewar pressure respectively, mf is liquid production · rate at dewar pressure at pure liquefaction mode, m x (hg – hf) denotes refrigeration load on the system within dewar. It is observed that second term of right hand side of Eq. (16) is much larger than that of Eq. (17), as hout is significantly greater than hg, which explains that, turbines power output per unit mass flow rate through compressor, is bigger for pure liquefaction than for pure refrigeration mode. Hence, in the mixed mode, the power output of the turbines decrease, with the decrease of liquefaction rate and increase of refrigeration load. In Fig. 11, the linear decrease of power of the turbines from pure liquefaction to pure refrigeration mode explains this phenomenon. In a liquefier, turbines are designed to work at maximum efficiency at pure liquefaction mode. So at this mode, mass flow and pressure drop in turbines are maximum, which causes the turbine to rotate at best speed. Due to unavailability of efficiency values of turbines at the experimental operating conditions from the manufacturer, the present study has been made to observe variations of isentropic efficiency at different modes. In the flow through turbines, pressure drop occurs across turbine inlet flow control valve and turbines. The output power of a turbine (Eturbine) or enthalpy drop is a function of pressure ratio across turbine (Pinlet/Poutlet), mass flow rate, flow inlet temperature and efficiency as evident from Eq. (18). The turbines speeds are controlled by a PID loop, actually manipulating mass flow through a control valve.
3.2. Turbine characteristics According to second law of thermodynamics, removal of heat at constant temperature from low temperature source to high temperature sink requires work on the thermodynamic system. The turbine system functions here as the refrigeration machine and compressor provide power to the thermodynamic cycle to operate. A basic Claude cycle consists of a compressor, heat exchangers, turbines, JT valve and dewar [20]. Applying the first law of thermodynamics for steady flow in pure liquefaction mode to the unit comprising of heat exchangers, turbines, JT valve and dewar, neglecting heat in-leaks from ambient, the following expression can be obtained, 8
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Fig. 10. Variation of Specific Power Consumption (SPC) at different modes. ·
Eturbine = mΔh =
·
m RTinlet (
turbine
γ−1 p γ )[1 − ( out )( γ ) ] ηturbine γ−1 pin
following equations: (18)
ηwarm turbine =
Turbine efficiency,
ηturbine =
Δhactual Δhisentropic
ηcold turbine =
(19)
For warm and cold turbines, the efficiencies are evaluated by
(h
(h 6 − h 7) 6 − hat p7 and s6) (h
(h
9
9 − h 11) − hat p11 and s9)
where s denotes entropy
Fig. 11. Temperature drop and power production by turbines at different modes. 9
(20)
(21)
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Fig. 12. Variation of efficiency and rotational speed of turbines at different modes.
From Eqs. (20) and (21), turbines efficiency is determined as 73% for pure liquefaction mode, 74% for 25 W mixed mode and 75% for all other remaining modes. It is observed from Fig. 12 that at pure liquefaction mode, both warm and cold turbines operate at lowest efficiency but highest speed. The reason for this behaviour is provided in the explanation of Fig. 6. With the increase of refrigeration load, the turbine efficiency increases initially and then becomes a constant. Data provided by the manufacturer shows that at design operating conditions of this liquefier, isentropic efficiency is 73% for both the warm and cold turbines, when refrigeration power generated are 3.11 kW and 1.06 kW respectively. Moreover, the literatures [10–13] comply the efficiency values evaluated by us. In the liquefier, with the gradual increase of the refrigeration load, requirement of cooling by expansion in the turbine reduces, thereby reduction of the mass flow rate through turbines by gradual closure of flow control valve. Hence, power and speed of both the turbines decrease linearly, which causes the temperature drop across each turbine to drop in a linear way, as found from Figs. 11 and 12. Fig. 13. Percentage exergy destruction of heat exchangers at various modes.
3.3. Heat exchanger characteristics
Exergy efficiency of a heat exchanger is defined as follows [19]:
In a heat exchanger working below the reference temperature, heat transfer takes place from hot stream to cold stream, whereas exergy transfer occurs from cold stream to hot stream [19]. Fig. 13 demonstrates that at pure liquefaction mode, exergy destruction rate of HX2 and HX4 are much higher than that of other heat exchangers, because the exergy transfer rate from cold stream to hot stream of these two heat exchangers are larger than others as expressed in Fig. 14. Here, exergy destruction rate of HX2, HX4; and HX1, HX3, HX5, HX6 are comparable. Fig. 13 shows that percentage exergy destruction of HX4 decreases and HX6 increases significantly from pure liquefaction to pure refrigeration mode, whereas for other heat exchangers there is marginal increase. This happens due to that, HX4 has substantial reduction and HX6 has significant increase of exergy transfer rate between cold stream and hot stream from pure liquefaction to pure refrigeration mode compared to other heat exchangers as shown in Fig. 14.
·
·
Ex − Ex ηHX =
C,O ·
C,I ·
when TC , I ⩾ Tref
Ex − Ex H ,I
H ,O
·
·
(22)
Ex − Ex ηHX =
H ,O ·
H ,I ·
when TC, I ⩽ Tref
Ex − Ex C,I
(23)
C,O
·
where ηHX andEx denote exergy efficiency of heat exchanger and exergy transfer rate of a stream respectively. Subscripts H, C, I, O stand for hot, cold, inlet and outlet respectively. Fig. 15 demonstrates that exergy efficiency of all heat exchangers increases from pure liquefaction to pure refrigeration mode. This is for the reason that the exergy destruction rate per unit exergy transferred 10
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In heat exchangers HX1, HX2, HX3 and HX4, the fluid properties do not vary appreciably with temperature in their operating range above 20 K. In heat exchangers, HX5 and HX6, helium temperature is below 20 K, where properties like specific heat capacity, thermal conductivity, density and viscosity, varies so widely that it affects the performance of the heat exchanger. The specific heat capacity of high pressure helium at 1.40 MPa, varies from 5.90 kJ/kg-K at 20 K to a maximum of 7.51 kJ/kg-K at 10 K and again drops down to 3.73 kJ/kg-K at 5.5 K. The low pressure stream at 0.13 MPa, varies from 5.26 kJ/kg-K at 20 K to 11.15 kJ/kg-K at 4.50 K and again drops sharply to 4.20 kJ/kg-K at liquid helium temperature of 4 K. The effectiveness of HX5 and HX6 has been determined by the modified relation following the enthalpy differential approach as mentioned in Barron [18]. The algebraic expressions of effectiveness at variable specific heat capacity zone are given as follows: H −H ε = hot, in hot*, out , H*out is the hot stream enthalpy at the cold stream Hhot , in − Hout
inlet temperature, for
Chot 〈Ccold
Fig. 14. Exergy transfer load from cold stream to hot stream at different modes.
ε=
(25)
Hcold, out − Hcold, in * −H Hout cold, in
, H*out is the cold stream enthalpy at hot stream
inlet temperature, for
Chot 〉Ccold
(26)
Variable heat capacity of low temperature helium is taken into consideration using enthalpy difference method for calculating ∊ of HX5 and HX6 using the relation:
mean specific heat capacity of a stream enthalpy difference between inlet and outlet of a stream = terminal temperature difference of that stream
As the temperature, mass flow, enthalpy, heat capacity of the inlet and outlet streams of a heat exchanger are available from Aspen Hysys as discussed in Section 2.4, effectiveness of all heat exchangers have been determined using Eqs. (22), (23), (25)–(27). Fig. 16 shows the variation of effectiveness of heat exchangers at pure liquefaction mode. Fig. 16 demonstrates that the effectiveness value of all heat exchangers is 90% or greater, which complies Barron [18] and literatures [10,12–14]. As shown in Fig. 17, at pure liquefaction mode, the calculated order of heat duty of the heat exchangers is as HX2 > HX1 > HX4 > HX3 > HX6 > HX5, and, this order is valid for any mode. It is
Fig. 15. Exergy efficiency of major components at different modes.
from cold stream to hot stream decreases with the increase of refrigeration load. Fig. 15 also states that in warm turbine, exergy efficiency decreases with increase of refrigeration load, whereas in cold turbine, exergy efficiency remains almost equal. For all modes, exergy efficiency is zero for flow control valve and JT valve i.e. valves contribute only exergy loss to the system. Therefore, a designer should take care on the number of valves used in a liquefier. The two most important thermodynamic parameters to represent a heat exchanger are effectiveness (∊) and UA, where U is overall heat transfer coefficient (W/m2 K) and A is heat transfer area (m2). UA signifies the heat transfer size of a heat exchanger which means the ability to transfer heat, while effectiveness is a measure of its thermal performance. Effectiveness of two stream counter flow heat exchanger is defined as the ratio of actual heat transfer rate to the maximum heat transfer rate possible theoretically having infinite surface area and no longitudinal wall conduction, and is expressed as ·
ε=
q ·
q max
=
Cp ΔT Cp,min ΔTmax
(27)
(24)
where Cp,min is the smaller of the two fluid’s heat capacities, ΔTmax is the difference of two inlet terminal temperatures of hot and cold streams.
Fig. 16. Effectiveness of heat exchangers at pure liquefaction mode. 11
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Fig. 17. Heat transfer from hot to cold stream (heat duty) at different modes.
percentage exergy output with respect to compressor motor power or exergy efficiency of this Claude cycle. Fig. 8 depicts that exergy destruction rate for compressor remain constant through all the modes; for turbines, exergy destruction rate decreases; and for flow control valve and JT valve, exergy destruction rate increases marginally from pure liquefaction to pure refrigeration mode. Decrease of exergy destruction rate in turbines occurs due to reduction of turbines work.
observed from Fig. 17 that heat duty of HX2 and HX4 are decreasing with the increase of refrigeration load. Heat exchangers, HX2 and HX4 are located on the downstream side of cold flow of HX3 and HX5 respectively. It is found from study that HX3 and HX5 are unbalanced heat exchangers. Due to increase of mass flow rate of both the streams, more cold is available in these heat exchangers with the increase of refrigeration load, resulting in increase of heat duty. Heat exchangers, HX2 and HX4 are getting balanced with the increase of refrigeration load, as hot stream mass flow remains constant in all modes. This results in decreasing heat duty of both HX2 and HX4 with increase in refrigeration load. Fig. 18 demonstrates that UA of HX5 and HX6 increases with refrigeration load, which is illustrated as follows. The heat duty of a heat exchanger is defined as:
4. Conclusion This investigation primarily aims at the behaviour of exergy characteristics of an existing helium liquefier (model HELIAL 50 of Air Liquide DTA, France) at off-design mixed mode operations. The exergy efficiency curve helps to infer the following: (1) Though sold as a liquefier, the machine works best at mixed mode with 74.42 W refrigeration load, (2) Exergy efficiency of the helium liquefier decreases with the increase of refrigeration load from its optimum point, (3) Exergy output at different modes bear a linear correlation with exergy destruction. The analysis is based on the experimental data archived from sensors equipped with the liquefier and basic characteristics of the components. The characteristics revealed in this investigation may be helpful to the process designer and operator for designing liquefiers and mixed mode refrigerators. Although this study has been performed on a specific liquefier model, the trends of the results could be helpful for the designers. The largest fraction of exergy is destroyed in the compressor. Hence, there is always a scope of improvement of compressor design and thereby, specific power consumption of the thermodynamic cycle could be improved. The trends of the UA values and exergy destruction in heat exchangers may be helpful in selecting their relative sizes.
·
Q = (U . A)ΔTLMTD
(28)
·
Q , U, A, ΔTLMTD denotes heat duty (W), overall heat transfer coefficient, heat transfer area (m2) and Logarithmic Mean Temperature Difference, LMTD (K), respectively. In present case, A remains constant for all modes. U is a function of convective heat transfer coefficient, h, of the fluids involved, which in turn depend on flow properties, fluid properties and surface geometry [18]. In general, h is a function of Reynold’s number, which increases with increasing mass flow rate. With the increase of refrigeration load, the mass flow rates of both hot and cold streams through HX5 and HX6 increase. Hence, the change of Reynold’s number increases U of the heat exchangers, resulting in higher heat duty as, observed in Eq. (28). 3.4. Exergy characteristics of other components From Figs. 8 and 9, it can be observed that at pure liquefaction mode, maximum exergy destruction occurs at compressor (49%). This is followed by six heat exchangers together (18.60%), two turbines together (15.20%), JT valve (4.84%) and turbine flow control valve (3%) sequentially which comprises of 90.77%. Remaining 9.20% is the
Declaration of Competing Interest The authors declared that there is no conflict of interest. 12
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Fig.18. Variation of UA and LMTD of heat exchangers at different modes.
Acknowledgements
[17] Thomas RJ, Dutta R, Ghosh P, Chowdhury K. Applicability of equations of state for modelling helium systems. Cryogenics 2012;52:375–81. [18] Barron RF. Cryogenic heat transfer. 1st ed. USA: Taylor & Francis; 1999. [19] Shah RK, Sekulic DP. Fundamentals of heat exchanger design. USA: John Wiley & Sons, Inc.; 2003. [20] Barron RF. Cryogenic systems. New York: Oxford University Press; 1985.
Authors gratefully acknowledge the constructive suggestions of the reviewers to improve the quality of this paper. References
Mr. Trijit K. Maiti received Masters in Mechanical Engineering from National Institute of Technology, Rourkela, India, in 2011. Currently he is working as Scientific Officer at Variable Energy Cyclotron Centre, Kolkata. His research area includes analysis of different thermal and cryogenic processes, development of helium refrigeration system and sub-systems; and development of cryo-sorption based gas purification system.
[1] Kaushik SC, Shiva Reddy V, Tyagi SK. Energy and exergy analysis of thermal power plants: a review. Renew Sustain Energy Rev 2011;15:1857–72. [2] Hafdhi F, Khir T, Yahyia AB, Brahim AB. Energetic and exergetic analysis of a steam turbine power plant in an existing phosphoric acid factory. Energy Convers Manage 2015;106:1230–41. [3] Erdem HH, Akkya AV, Cetin B, Dagdas A, Sevilgen SH, Sahin B, et al. Comparative energetic and exergetic performance analyses for coal fired thermal power plants in Turkey. Int J Therm Sci 2009;48:2179–86. [4] Yagli H, Koc Y, Koc A, Gorgulu A, Tandiroglu A. Parametric optimization and exergetic analysis comparison of subcritical and supercritical organic Rankine cycle (ORC) for biogas fuelled combined heat and power (CHP) engine exhaust gas waste heat. Energy 2016;111:923–32. [5] Khaliq A, Kaushik SC. Second law based thermodynamic analysis of Brayton/ Rankine combined power cycle with reheat. Appl Energy 2004;78:179–97. [6] Abuelnuor AAA, et al. Exergy analysis of Garri “2” 180 MW combined cycle power plant. Renew Sustain Energy Rev 2017;79:960–9. [7] Thirumaleshwar M. Exergy method of analysis and its application to a helium cryorefrigerator. Cryogenics 1979;19:355–61. [8] Ahamed JU, Saidur R, Masjuki HH. A review on exergy analysis of vapour compression refrigeration system. Renew Sustain Energy Rev 2011;15:1593–600. [9] Thomas RJ, Ghosh P, Chowdhury K. Exergy analysis of helium liquefaction systems based on modified claude cycle with two expanders. Cryogenics 2011;51:287–94. [10] Thomas RJ, Ghosh P, Chowdhury K. Application of exergy analysis in designing helium liquefiers. Energy 2012;37:207–19. [11] Thomas RJ, Ghosh P, Chowdhury K. Role of expanders in helium liquefaction cycles: parametric studies using Collins cycle. Fusion Eng Des 2011;86:318–24. [12] Thomas RJ, Ghosh P, Chowdhury K. Role of heat exchangers in helium liquefaction cycles: simulation studies using Collins cycle. Fusion Eng Des 2012;87:39–46. [13] Thomas RJ, Ghosh P, Chowdhury K. Optimum number of stages and intermediate pressure level for highest exergy efficiency in large helium liquefiers. Int J Refrig 2013;36:2438–57. [14] Kundu A, Chowdhury K. Evaluating performance of mixed mode multistage helium plants for design and off-design conditions by exergy analysis. Int J Refrig 2014;38:46–57. [15] Caillaud A, Crispel S, Grabie V, Delcayre F, Aigouy G. Evolution of the standard helium liquefier and refrigerator range designed by Air Liquide DTA, France. In: Proceedings of EPAC08, Genoa, Italy; 2008. p. 2497–99. [16] McCarty RD, Arp VD. A new wide range equation of state for helium. Adv Cryog Eng 1990;35:1465–75.
Dr. Sandip Pal received his PhD from University of Manchester, UK. Currently he is the Head of the Cryogenic Process and Instrumentation Section, Variable Energy Cyclotron Centre, Kolkata and Associate Professor of Homi Bhabha National University. His field of research includes development of new type of sensors, transducers and actuators; chemical species tomography, capacitance tomography, cryogenic process related instrumentationa and control.
13
Cryogenics 103 (2019) 102977
T.K. Maiti, et al. Prof. Balaram Kundu received his PhD from Indian Institute of Technology (IIT), Kharagpur, in 2000. Currently he is the Professor of the Department of Mechanical Engineering, Jadavpur University, India. His field of specialization includes analytical and computational heat transfer, flat plate solar collector, heat transfer in porous materials and fin and tube heat exchanger. He got two patents in 2016 on his work on subsonic flow in convergent-divergent nozzle and fin heat transfer with internal generation subject to nonlinear surface heat exchange.
Prof. Parthasarathi Ghosh received his PhD from Indian Institute of Technology (IIT), Kharagpur. Currently he is the Associate Professor and Head of the Department of Cryogenic Engineering, IIT, Kharagpur. He is the author and co-author of several publications on cryogenic process and equipments. His research field include low temperature processes, large scale helium liquefiers and cryogenic turboexpanders.
14
Contents lists available at ScienceDirect
Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Evaluation of an existing helium liquefier in refrigerator and mixed-mode operation through exergy analysis
T
⁎
T.K. Maitia,b, , S. Pala,b, B. Kunduc, P. Ghoshd a
Variable Energy Cyclotron Centre, Kolkata 700064, India Homi Bhabha National Institute, Kolkata 700064, India c Department of Mechanical Engineering, Jadavpur University, Kolkata 700032, India d Cryogenic Engineering Centre, Indian Institute of Technology, Kharagpur 721302, India b
A R T I C LE I N FO
A B S T R A C T
Keywords: Helium Liquefier Mixed mode operation Exergy Specific power consumption
Present day, all small scale helium liquefiers operate in Claude cycle with two turbines in series arrangement. In this paper, an effort has been made to investigate the exergy characteristics of a small scale liquefier and its components at design and various off-design refrigeration and mixed mode operation under steady state condition. The variation of exergy efficiency, exergy destruction, exergy output-destruction interrelations, refrigeration- liquefaction capacity correlation, etc. have been evaluated by increasing refrigeration load in steps starting at pure liquefaction till pure refrigeration mode in the experiment. As the experimental data were not sufficient for complete analysis, Aspen Hysys software has been used to determine the remaining process parameters required to understand the thermodynamic cycle. The significance of the variation of exergy parameters at different modes of operation have been reported to establish the importance of the present study. Though the results are specific for the existing helium liquefier (model HELIAL 50 of Air Liquide DTA, France) with some associated constraints, the results may be useful to the designers of helium systems where flexibility of operation is a desirable feature.
1. Introduction Large and small scale helium plants are necessary for cryogenic applications in particle accelerators, like cyclotrons, synchrotrons, linacs, penning traps, etc., where three modes of operations exist, viz. liquefaction, refrigeration and liquefaction-refrigeration mixed mode. For cool down, steady state run, warm up, quenching, and breakdown situation of an accelerator superconducting magnet, a helium plant needs to run at all the modes of operation at maximum or part load capacity depending upon the type of loads and their operation. In pure liquefaction mode, liquid helium exits the system with both sensible and latent heat; whereas in pure refrigeration mode operating in closed loop, boil-off gas returns the compressor suction by only absorbing latent heat from external heat load when the sensible heat is conserved in heat exchangers; while in mixed mode, the component characteristics and parameters lie in between. Hence, a system designed for a particular mode, will not efficiently perform in other off-design modes, but it is necessary to predict the performance of the liquefier in other offdesign modes. Helium liquefiers are highly energy intensive system. To reduce the
⁎
consumption of power for cryogenic plants, exergetic performance criteria based on second law of thermodynamics, is a useful tool in design, evaluation, optimization and improvement of helium liquefier. By applying the exergy evaluation method, it is possible to locate and quantify the irreversibility source of each and every component of a system which in turn is helpful to predict the liquefier’s performance in other modes. In the available literature, there are a large number of papers on the exergy performance of thermal power plants operating in Rankine cycle, Brayton cycle and their various combinations and configurations [1–6]. But a few papers are available on exergy analysis of helium liquefaction systems. Thirumaleshwar [7] presented a theoretical exergetic analysis of an ideal isothermal and isobaric heat source of helium refrigeration systems working on modified Brayton cycle. Ahamed et al. [8] investigated the variation of exergy performance in vapour compression refrigeration cycle of air conditioning system by varying the several controlling parameters of the cycle. Thomas et al. [9,10] presented the design and optimization of a helium liquefier operating in Collins cycle using exergetic analysis
Corresponding author at: Variable Energy Cyclotron Centre, Kolkata 700064, India. E-mail address: [email protected] (T.K. Maiti).
https://doi.org/10.1016/j.cryogenics.2019.102977 Received 9 May 2019; Received in revised form 30 August 2019; Accepted 4 September 2019 Available online 06 September 2019 0011-2275/ © 2019 Elsevier Ltd. All rights reserved.
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Compressor module
method with commercial process simulator Aspen Hysys. In the analysis, they assumed the fixed value of isothermal efficiency of compressor (55%), adiabatic efficiency of warm turbine (75%) and cold turbine (70%), and a fixed effectiveness value of all heat exchangers (97%). Exergy efficiency variation of the cycle, destruction of exergy at various components, with change of cycle pressure ratio and mass flow rate through turbines have been derieved. Thomas et al. [11–13] studied theoretically the effect of turbine and heat exchanger parameters on improvement and optimization of liquefaction capacity of Collins cycle. They assumed that all heat exchangers have equal effectiveness of 97% and all turbines have equal efficiency of 70%. Exergy analysis for optimization of different configurations of Collins cycle was carried out using intermediate pressure for large helium liquefiers. Kundu and Chowdhury [14] presented theoretical exergy analysis of large scale helium liquefier and refrigerator operating in Collins cycle at design and off-design mixed mode conditions using Aspen Hysys V7.0. Evaluation of some design parameters like optimum compressor discharge pressure, expander flow rate, UA of heat exchangers, specific work input was performed at maximum cold box exergy efficiency for liquefaction, refrigeration and mixed modes. It has been assumed that all heat exchangers have zero pressure drop and equal effectiveness (97%), turbines have equal isentropic efficiency (80%) and fixed compressor efficiency (55%). Cailland et al. [15] discussed on the evolution of fully automatic HELIAL models of Air Liquide DTA, France, the most widely used liquefier worldwide, since its inception in 1980s. The manufacturer has almost doubled the capacity of HELIAL range by design optimization of turbines, heat exchangers, automation and supervisory system. Turbines of this manufacturer have static gas bearings, characterized by mean time between failures (MTBF) higher than 150,000 h. This product also serves the multi-range turn-key projects of the customers, catering to specific requirements (pure liquefaction or pure refrigeration or mixed modes). A helium liquefier, which is coupled with cryogenic installations, needs to operate both at design and off-design operating modes in order to fulfil the need of cryogenic loads. From above literature survey, it is evident that in helium liquefaction/refrigeration systems, exergy and energy analyses have been addressed for liquefaction and refrigeration process of Collins cycle. And the analysis have been performed using commercial process simulator. Most of the studies in open literature [9–14] have considered pre-fixed constant values for effectiveness and negligible pressure drop of heat exchangers, efficiency of turbines and compressor, and zero heat in-leak into the system. There is dearth of literature available on the detailed study of exergy characteristics of different components and their variation trends in the off-design mixed modes for an actual small scale helium liquefier. The present study has been performed on a small scale existing helium liquefier and explored its exergetic characteristics in various modes of operation, such as designed pure liquefaction, off-design mixed and pure refrigeration modes. Some performance characteristics of major components have been analysed at different modes based on the experimental data of liquefier. The variation of the exergy efficiency and exergy output of a liquefier with the change of refrigeration load has been studied. Correlation between exergy output and exergy destruction of Claude cycle has been illustrated graphically. Evaluation has been carried out on the variation of exergy characteristics viz. percentage exergy destruction, exergy transfer load and exergy efficiency, of the major components like different heat exchangers, turbines, compressor, JT valve and flow control valve, when they are operated away from their designed conditions. Some study has been done on energy analysis of the heat exchangers working above and below 20 K. Below 20 K temperature range, there is sharp and substantial rise and fall of heat capacity of helium till liquefaction. Here, the cold stream which has minimum heat capacity at warm end of heat exchanger will have maximum heat capacity at cold end due to larger heat capacity at low temperature. This is true for helium streams at any
Buffer tank (BT) + turbine bearing + bypass 22
To bypass valve To turbine bearing (TB)
1
23
2
HX1 Flow control valve
3
HX2
5
4
6
Warm turbine
HX3 8
7
HX4
9
10
21
HX5 20
Cold turbine
12
11
19
HX6 Dewar heater
17
Q
18
13 JT Valve
15 14
16 f Liquid helium
Dewar
Fig. 1. Schematic of a small scale helium liquefier, consisting of a screw compressor, two turbines, six heat exchangers, a turbine flow control valve and a JT valve.
pressure working close to boiling point. The characteristics of two turbines in series have been assessed at all the operational modes. The results derived from exergy performance analysis, which are not available in any literature, will guide a designer to interpolate, extrapolate or predict the characteristics and performance of a helium plant in off-design conditions. 2. Process 2.1. Configuration of a helium liquefier under study and experimental procedure The schematic of a small scale liquefier is presented in Fig. 1. This configuration complied the standard product (model: HELIAL 50) of Air Liquide DTA, France, (manufacturer guaranteed liquefaction capacity without liquid nitrogen pre-cooling is 50 l/h), where l/h is litres/hour. This liquefier under the present study consists of three functional sections: 1. Compressor module (160 kW Siemens motor). The compressor runs at constant speed, hence, the discharge pressure, temperature and mass flow rate are constant for all the modes of operation. The discharge pressure (HP) and suction pressure (LP) are 1.40 MPa absolute (MPa) and 0.106 MPa repectively. A part of the compressor discharge flow is diverted for turbine static bearings (2.95 g/s) and remaining part, called hot stream (47.59 g/s) enters the cold box, where g/s is grams/second. 2. Cold box part, which comprises of two turbines (warm and cold turbine) in series with a heat exchanger in between, six plate-fin type heat exchangers, one JT valve. In this configuration, cold box inlet pressure and mass flow rate of process gas was constant for all modes of operation. The inlet mass flow rate of warm turbine is controlled by a flow control valve where pressure drop occur, hence the inlet pressure of warm turbine varies with change of turbine flow conditions. 2
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3. Liquid helium dewar. It is equipped with a Nichrome resistance heater. The cold helium LP stream returns through heat exchangers due to pressure difference between dewar and compressor suction end.
Table 2 . Temperature, pressure and mass flow rates of these nodes are recorded/observed during experiment (Fig. 1 is referred for nodes location).
Node
2.2. Measurement procedure In order to make the experimental study, the liquefier was operated at full capacity for all the modes of operation. To investigate the mixed modes, a certain refrigeration load was applied by a heater dipped in liquid helium within dewar and the increase in level of dewar was measured for assessing the liquefaction rate. This heater power was manually controlled by an auto-transformer and actual refrigeration load was calculated by monitoring current and voltage. The dewar pressure was maintained at 0.13 MPa and the dewar temperature was measured by CLTS sensor, maintained at 4.50 K during the entire experiment. For the investigation purpose in mixed modes, the refrigeration load was gradually increased by a step of 25 W beginning from pure liquefaction mode. Following this procedure, it was observed that at refrigeration load of 211.70 W, liquefaction rate got reduced to zero. At this stage, the liquid level in dewar remained constant and further refrigeration load increment resulted in reduction of dewar level. Liquid helium level in the dewar is measured in liters. Bypass valve always remains closed during experiments as the investigations were done at full capacity of the plant. Table 1 shows the experimental values of liquefaction and refrigeration capacity at different modes.
3.
4. 5. 6.
7.
2, 22, 23, 6, 9, 11, 13, 14, 15
1, TB, BT, f, bypass
As per manufacturer’s provided data, isentropic efficiency is equal for both the turbines at the design operating conditions. In addition, equal value of efficiency of warm and cold turbines is assumed in some reference literatures [10–13]. Average pressure drop of hot stream and cold stream of each heat exchanger is taken as of 50 × 102 Pa and 40 × 102 Pa respectively. This consideration is based on the experimental values obtained from the pressure transmitters located in the helium liquefier. Temperature and pressure of nodes 11, 19 and 20 are assumed to be same. Temperature and pressure of nodes 15 and 18 are same. The 3-stream heat exchanger, HX4, has been considered as 2-stream one by assuming equal temperatures for two warm flow inlets (nodes 7 and 8), and for two cold flow outlets (nodes 9 and10). Vapour fraction of node 18 is 1, as the co-axial transfer line between dewar and cold box is long.
2.4.1. Equation of state (EOS) The 32-term MBWR (Modified Benedict – Webb – Rubin) EOS developed by McCarty and Arp [16,17], a property package of Aspen Hysys, has been used here for generating thermo-physical properties of helium. MBWR EOS has very high accuracy for pure components. The thermo-physical properties of several cryogens generated by using MBWR correlation are also used in NIST property package, THERMOPACK property package software, HEPAK - a dedicated helium property package and commercial process simulator Aspen Hysys.
Table 1 Experimental readings of refrigeration load and liquefaction rate at different modes of operation.
2.201 g/s 26.13 W + 2.100 g/s 50.39 W + 1.877 g/s 74.42 W + 1.650 g/s 101.80 W + 1.300 g/s 122.90 W + 1.107 g/s 151.70 W + 0.774 g/s 174.40 W + 0.562 g/s 211.70 W
2, 3, 4, 7, 11, 13, 14
The liquefier under present investigation has limited number of sensors to gather information on the physical parameters (viz. pressure, temperature, mass flow rate, etc.) of the nodes (refer Fig. 1). These experimental data and some assumptions based on published references have been incorporated as input in the Aspen HYSYS v8.6 flowsheet program, to obtain the parameters of the remaining nodes as output. Using these basic physical parameters, the following functions have been calculated for cycle analysis, viz. exergy at each node; exergy efficiency of the total thermodynamic cycle; exergy efficiency and exergy destruction of each component; heat load, effectiveness, LMTD and UA of heat exchangers; adiabatic efficiency and power of turbines; isothermal efficiency of compressor; etc.
1. Analysis is done at steady state condition of the system. 2. Isentropic efficiency of both warm and cold turbines is taken as equal. This assumption is made based on the following facts:
Pure liquefaction Mixed Mixed Mixed Mixed Mixed Mixed Mixed Pure refrigeration
Mass flow rate
2.4. Analysis methodology
The experimental readings of the parameters of the nodes shown in Table 2 were recorded from sensors/transmitters located in helium liquefier during operation. Table 3 provides a brief specification of the measuring instruments. These physical parameters are the input of the study: Besides above, the other parameters obtained from experiment are dewar heater current and voltage, turbine rotational speed, bypass valve opening and compressor motor power. Figs. 2–4 shows input experimental data of temperature and pressure at different nodes; rate of dewar level variation, heater voltage and current, at different modes of operation. Liquid helium level, turbine bearings and buffer tank are denoted by Ldewar, TB, BT respectively. Dewar heater power is measured in Watt (W), warm and cold turbine rotational speed in revolutions per second (rps). The assumptions made for this study are as mentioned below: (nodal points of Fig. 1 are referred)
(Refrigeration load + Liquefaction rate*) @4.5 K
Pressure
The experimental data along with the assumptions which act as input parameters in this analysis have been summarised in Table 4.
2.3. Input experimental parameters recorded by sensors and assumptions
Mode of operation
Temperature
2.4.2. Exergy and energy analysis The basic principles and methodology of exergy analysis of a thermal system are well established and are widely available in the text books on thermodynamics. The exergy analysis of the operating liquefier is based on exergy balance in a flow system across a control volume, which is expressed as ·
·
∑ Ex flow + ∑ Q (1 − in
·
T0 )= Tj
·
·
Ex + W ∑ flow out
·
+ Ex D
(1)
·
where Ex = m × ex . The specific exergy in any state is expressed as
ex = (h − h 0) − T0 (s − s0)
* 1 g/s of LHe is equivalent to 30.28 l/h. 3
(2)
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Table 3 . Specification of instruments and uncertainty in the measurement of parameters in the experiment with the helium plant. Parameter
Instrument used
Overall uncertainty
Refrigeration power Level of liquid helium in dewar
Fluke digital multimeter, 17B (1) NbTi filament, 203 cm sensor active length (2) AMI monitor, model 135 (3) Eurotherm PLC, PC3000 1) Lakeshore Cernox sensor, model CX1050 2) Lakeshore temperature transmitter, model 234 3) Eurotherm PLC, PC3000 Keller make, model PA21
± 3% ± 0.85%
Temperature
Pressure
Exergy destruction in a turbine is the summation of exergy destructions in isentropic expansion (turbine work is not recovered in this case) and bearings. The exergy destruction of two turbines and adiabatic efficiency in steady flow process are expressed as:
And, irreversibility or exergy destruction or exergy loss is expressed as ·
·
Ex = m × exD = T0 × Δsgenerated
(3)
D
± 0.30% (for 4.20 K) ± 0.12% (for 77 K) ± 0.10% (for 300 K) ± 0.35%
·
·
·
where ex(J/g) represents specific exergy or exergy transfer per unit · · mass, Ex (W) is exergy transfer rate, m (g/s) is mass flow rate, h (J/g) is
ExD = m6(ex 6 + ex 9 − ex 7 − ex11) + mTB (exTB − ex22)
enthalpy per unit mass, s (J/g-K) is entropy. Q (W) is the rate of heat transfer across boundary at instantaneous temperature Tj (K). exD is the irreversibility associated with the process. h0 and s0 represents the enthalpy and entropy at reference state (T0, P0) respectively. The ambient condition of the environment is taken as reference state, where T0 = 300 K and P0 = 0.10 MPa. The helium compressor is the air cooled screw compressor, whose
ηad =
·
·
·
⎟
·
m (ex2 − ex22) + mTB (exTB − ex22)
(4)
2
·
·
·
Ex = abs [ m (exhot , in − exhot , out ) + m (ex cold, in − ex cold, out )]
Hence, exergy destruction in compressor = 160 kW − input exergy to cold box
(7)
In turbine flow control valve, pressure drop occurs in helium stream, resulting in the expansion of exit gas. This expansion causes the temperature rise of exit gas as inlet gas temperature is above the inversion temperature. In JT valve, the expansion of helium gas is isenthalpic (h13 = h14) and inlet gas temperature is below inversion temperature, hence there is drop of exit gas temperature. The exergy destruction of the following components are expressed as: for HX:
electrical exergy input is 160 kW ⎛ W ⎞. ⎝ comp⎠ Input exergy to the cold box relation is expressed as ⎜
Actual enthalpy drop due to expansion Theoretical enthalpy drop due to adiabatic expansion
(6)
D
hot
cold
(8)
for Turbine flow control valve:
(5)
·
Similarly, the exergy destruction of each major component of the liquefier is determined using exergy balance equation, Eq. (1).
·
ExD = m (ex5 − ex 6) 5
Fig. 2. Experimental temperature data of different nodes at different modes. 4
(9)
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Fig. 3. Experimental data of pressure and rate of liquefaction in dewar at different modes.
The first term of right hand side of Eq. (11) represents refrigeration output and second term expresses liquefaction output. Therefore, the exergy efficiency of the plant at any operational mode is expressed as:
for JT valve: ·
·
ExD = m (ex13 − ex14 ) 13
(10)
The exergy output of the helium liquefier operating in mixed mode = ·
·
·
m (ex16 − ex17) + m (exLHe − ex22)
·
m16(ex16 − ex17) + m (exLHe − ex22) LHe
ηcycle =
(11)
16
LHe ·
W comp
Fig. 4. Experimental data of heater voltage and current at different modes. 5
(12)
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of the existing liquefier at various modes. It is observed here that the system being liquefier, exergy efficiency and exergy output decreases above refrigeration load of 74.42 W and upto the pure refrigeration mode. Exergy efficiency and exergy output also decrease at pure liquefaction mode than subsequent 26.13 W mixed mode. This is due to the fact that, the turbine rotational speed is highest in pure liquefaction mode and is very near to threshold limit, so, for the safe operation of turbines, the speed of the turbines is not set at the best value. Consequently, the liquid production rate achieved in pure liquefaction mode is lower than the maximum possible capacity. But at off-design modes, the turbines are tuned to best possible efficiency as the speed reduces to optimum level. Fig. 6 reveals the same trend of variation of exergy efficiency and exergy output curves, which is due to the constant exergy input to the compressor at 160 kW. Fig. 7 shows that the relationship between exergy output and exergy destruction of a liquefier is linear. This correlation explains that pure refrigeration mode has minimum exergy output with maximum exergy destruction compared to any other modes, and the pure liquefaction mode is next in sequence. All mixed modes have larger exergy output and lesser exergy destruction than these two modes. Mixed mode output (74.42 W + 1.65 g/s) has least exergy destruction and maximum output. These results are corroborated by exergy efficiency distribution of Fig. 6. It is evident from Fig. 6, that the existing helium plant has maximum exergy efficiency at refrigeration load of 74.42 W, hence it can be rationally inferred that the system has been best tuned (designed) at this mode. As mentioned, at mixed mode refrigeration load of 74.42 W, the heat exchangers and turbines are set to operate at optimum level to provide maximum exergy efficiency. But as the system is operated away from the design mode, the exergy efficiency decreases as the output exergy gets reduced due to thermodynamic irreversibility or exergy loss associated with the process. Here, the exergy input at compressor is 160 kW. The decrease in exergy efficiency at off-design modes is due to increased irreversibility of cold box consisting of heat exchangers, turbines, flow control valve and JT valve. Percentage exergy destruction / loss of a component is the ratio of exergy destruction to exergy input to compressor. Figs. 8 and 9 display the quantitative value of percentage exergy loss of compressor, heat exchangers, turbines and valves at different modes. Irreversibility for compressor is constant for all modes; and for turbines, it declines with the increase of refrigeration load. The irreversibility of the system is related to the total entropy production in the system as explained in Eq. (3). The entropy generation in heat exchanger is largely due to heat transfer at finite differences of fluids temperature. Percentage exergy destruction / loss of a component is defined as the ratio of exergy destruction rate to input electrical power to compressor unit (motor power). Fig. 9 shows that minimum percentage exergy loss occur around 74.42 W refrigeration load at mixed mode for all the heat exchangers together and cold box respectively. Here, percentage exergy loss increases on both the left and right sides of the minimum point along x-axis. Fig. 8 shows that for two valves, the percentage exergy loss increases with refrigeration load. Hence, the resultant effect of the irreversibility characteristics of all these components determines the shape of exergy efficiency curve of Fig. 6.
Table 4 . List of input physical parameters. Input experimental data: 1. 2. 3. 4. 5. 6. 7. 8.
a. b. c. d. e. f.
Temperature of nodes 2, 3, 4, 7, 11, 13, 14, shown in Fig. 2 Pressure of nodes 2, 22, 23, 6, 9, 11, 13, 14, 15, presented in Fig. 3 Mass flow rate of nodes 1, TB, BT, f, bypass, shown in Section 2.1 Compressor motor input power, 160 kW Dewar heater current and voltage, shown in Fig. 4 Dewar level variation, shown in Fig. 3 Warm and cold turbine rotational speed, shown in Fig. 12 (Refrigeration load + Liquefaction rate) @ 4.50 K at pure liquefaction, mixed and pure refrigeration mode, displayed in Table 1 Assumptions: Equal isentropic efficiency for warm and cold turbines Average pressure drop of hot stream and cold stream of each heat exchanger is 50 × 102 Pa and 40 × 102 Pa respectively. Temperature and pressure of nodes 11, 19 and 20 are same. Temperature and pressure of nodes 15 and 18 are same. In HX4, equal temperatures for nodes 7 and 8, and, for nodes 9 and 10. Vapour fraction of node 18 is 1
subscripts TB, LHe and comp stands for turbine bearings, liquid helium and compressor respectively. Isothermal efficiency of a compressor is defined as the ratio of isothermal power to input power. ·
m × R × T23 × ln
isothermal efficiency =
23
(
input power
p1
p23
) (13)
where R denotes gas constant and input power is motor power. Isothermal efficiency of the screw compressor under present study has been determined as 50.83%. This value complies with the available literatures [9–12,14]. 3. Results and discussion 3.1. Helium liquefier cycle characteristics Fig. 5 depicts the relation between refrigeration load and liquefaction capacity of the liquefier at different modes. It is observed from this curve that experimental liquefaction capacity at mixed modes has positive variation within 45% from the linear line joining the maximum liquefaction capacity and refrigeration capacity for a certain refrigeration power applied. Fig. 6 presents the variation of exergy efficiency and exergy output
3.1.1. Specific power consumption of liquefier As cryogenic processes are potential energy demanding systems, Specific Power Consumption (SPC) parameter has been adopted as a performance indicator in the study of its energy assessment and it is one of the major concerns of liquefier manufacturers [15]. SPC is broadly defined as the energy used for producing a unit product. In the liquefier under the present study, the input compressor power is 160 kW, and product is Equivalent Carnot Refrigeration (ECR) at various modes of operation. Thermodynamic ideal cycle or Carnot cycle for liquefaction or
Fig. 5. Refrigeration load versus liquefaction capacity curve of the liquefier using experimental data. 6
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Fig. 6. Exergy efficiency and output exergy of helium liquefier at different modes.
Fig. 7. Exergy output versus exergy destruction at different modes.
refrigeration is a reversible cycle with maximum Coefficient of Performance (COP) for heat transfer process between two thermal reservoirs. Carnot work is the minimum input work requirement for a given heat transfer rate between two reservoirs. In the liquefier under present study, extraction of liquid helium or heat transfer to liquid takes place at temperature and pressure of 4.50 K and 0.13 MPa respectively in the dewar; and compressor suction temperature is 303 K. Therefore, thermodynamically ideal liquefaction system is working between thermal reservoirs at temperatures of 303 K and 4.50 K. The following equations concerning net ideal or Carnot work for helium liquefaction and refrigeration systems are obtained from the first law of thermodynamics for steady flow [20].
Ideal or Carnot work for liquefaction: −
Ẇ = Tsuction Δs − Δh ṁ
Fig. 8. Percentage exergy destruction of components with respect to electrical exergy input to compressor.
gas; suction temperature of compressor; entropy change due to reversible isothermal compression; and, enthalpy absorbed by saturated liquid helium at temperature and pressure of 4.50 K and 0.13 MPa respectively, to attain temperature of 303 K at the same pressure; respectively. ·
·
⎡Q ⎣R
W Carnot work for refrigeration: Carnot · m
= ⎡ ⎣
TC
·
m⎤
⎦
(TH − TC ) ⎤
⎦
(15)
·
W
Terms
(14)
Carnot · ,
m
·
Q , TC and TH stands for net work expended per unit R
mass of refrigerant, refrigeration effect or energy absorption rate at constant temperature TC, temperature of heat source, and temperature of heat sink, respectively.
Ẇ , ṁ
ṁ , Tsuction, Δs and Δh, denote net Carnot work required Terms − per unit mass of gas (this term is a positive quantity); mass flow rate of 7
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Fig. 9. Percentage exergy destruction at all heat exchangers together and cold box at different modes. ·
Applying Eqs. (14) and (15) in the present study, it is found that net Carnot work of 6671.76 W is required for 1 g/s @ 4.50 K, 0.13 MPa liquefaction; and 66.67 W for 1 W @ 4.50 K, 0.13 MPa refrigeration. Hence, on an equal Carnot work basis, 100.07 W of 4.50 K refrigeration is equivalent to 1 g/s of 4.50 K liquefaction. Specific power consumption [14] can also be explained on the basis of exergy output, which is the ratio of compressor power input to exergy output of the products at different modes. For illustration purpose, using input compressor power of 160 kW, Eq. (11) and liquefaction-refrigeration equivalence relation in the case of 74.42 W mixed mode, the parameters, Equivalent Carnot Refrigeration @ 4.50 K and 0.13 MPa, and exergy output, has been determined as 239.54 W and 15961.74 W respectively. The definition of Specific Power Consumption based on both ECR and exergy output yields the values 667.67 W/W and 10.024 W/W respectively. Fig. 10 presents SPC based on both ECR and exergy output at different modes. Fig. 10 reveals that SPC is lowest at 74.42 W mixed mode and increases with increasing refrigeration load till it reaches the maximum at pure refrigeration mode. SPC at pure liquefaction mode is higher than subsequent 25 W mixed mode, as ECR of former is less than the later one. Figs. 6 and 10, show that SPC is quantitatively reciprocal to exergy efficiency. Hence, at 74.42 W mixed mode, SPC is minimum when exergy efficiency is maximum; and, vice versa at pure refrigeration mode.
We ·
m
·
= (hin − hout ) +
mf
(hout − hf )
·
m
(16)
Applying the first law for steady flow to the same unit, in pure refrigeration mode, the expression follows as: ·
We ·
m
·
= (hin − hout ) + ·
mx ·
m
(hg − hf )
(17) ·
where We denotes total power output of the turbines, m denotes mass flow rate through compressor, hin and hout represents enthalpy of gas at the entry and exit of the unit, hf and hg represents enthalpy of saturated · gas and liquid at dewar pressure respectively, mf is liquid production · rate at dewar pressure at pure liquefaction mode, m x (hg – hf) denotes refrigeration load on the system within dewar. It is observed that second term of right hand side of Eq. (16) is much larger than that of Eq. (17), as hout is significantly greater than hg, which explains that, turbines power output per unit mass flow rate through compressor, is bigger for pure liquefaction than for pure refrigeration mode. Hence, in the mixed mode, the power output of the turbines decrease, with the decrease of liquefaction rate and increase of refrigeration load. In Fig. 11, the linear decrease of power of the turbines from pure liquefaction to pure refrigeration mode explains this phenomenon. In a liquefier, turbines are designed to work at maximum efficiency at pure liquefaction mode. So at this mode, mass flow and pressure drop in turbines are maximum, which causes the turbine to rotate at best speed. Due to unavailability of efficiency values of turbines at the experimental operating conditions from the manufacturer, the present study has been made to observe variations of isentropic efficiency at different modes. In the flow through turbines, pressure drop occurs across turbine inlet flow control valve and turbines. The output power of a turbine (Eturbine) or enthalpy drop is a function of pressure ratio across turbine (Pinlet/Poutlet), mass flow rate, flow inlet temperature and efficiency as evident from Eq. (18). The turbines speeds are controlled by a PID loop, actually manipulating mass flow through a control valve.
3.2. Turbine characteristics According to second law of thermodynamics, removal of heat at constant temperature from low temperature source to high temperature sink requires work on the thermodynamic system. The turbine system functions here as the refrigeration machine and compressor provide power to the thermodynamic cycle to operate. A basic Claude cycle consists of a compressor, heat exchangers, turbines, JT valve and dewar [20]. Applying the first law of thermodynamics for steady flow in pure liquefaction mode to the unit comprising of heat exchangers, turbines, JT valve and dewar, neglecting heat in-leaks from ambient, the following expression can be obtained, 8
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Fig. 10. Variation of Specific Power Consumption (SPC) at different modes. ·
Eturbine = mΔh =
·
m RTinlet (
turbine
γ−1 p γ )[1 − ( out )( γ ) ] ηturbine γ−1 pin
following equations: (18)
ηwarm turbine =
Turbine efficiency,
ηturbine =
Δhactual Δhisentropic
ηcold turbine =
(19)
For warm and cold turbines, the efficiencies are evaluated by
(h
(h 6 − h 7) 6 − hat p7 and s6) (h
(h
9
9 − h 11) − hat p11 and s9)
where s denotes entropy
Fig. 11. Temperature drop and power production by turbines at different modes. 9
(20)
(21)
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Fig. 12. Variation of efficiency and rotational speed of turbines at different modes.
From Eqs. (20) and (21), turbines efficiency is determined as 73% for pure liquefaction mode, 74% for 25 W mixed mode and 75% for all other remaining modes. It is observed from Fig. 12 that at pure liquefaction mode, both warm and cold turbines operate at lowest efficiency but highest speed. The reason for this behaviour is provided in the explanation of Fig. 6. With the increase of refrigeration load, the turbine efficiency increases initially and then becomes a constant. Data provided by the manufacturer shows that at design operating conditions of this liquefier, isentropic efficiency is 73% for both the warm and cold turbines, when refrigeration power generated are 3.11 kW and 1.06 kW respectively. Moreover, the literatures [10–13] comply the efficiency values evaluated by us. In the liquefier, with the gradual increase of the refrigeration load, requirement of cooling by expansion in the turbine reduces, thereby reduction of the mass flow rate through turbines by gradual closure of flow control valve. Hence, power and speed of both the turbines decrease linearly, which causes the temperature drop across each turbine to drop in a linear way, as found from Figs. 11 and 12. Fig. 13. Percentage exergy destruction of heat exchangers at various modes.
3.3. Heat exchanger characteristics
Exergy efficiency of a heat exchanger is defined as follows [19]:
In a heat exchanger working below the reference temperature, heat transfer takes place from hot stream to cold stream, whereas exergy transfer occurs from cold stream to hot stream [19]. Fig. 13 demonstrates that at pure liquefaction mode, exergy destruction rate of HX2 and HX4 are much higher than that of other heat exchangers, because the exergy transfer rate from cold stream to hot stream of these two heat exchangers are larger than others as expressed in Fig. 14. Here, exergy destruction rate of HX2, HX4; and HX1, HX3, HX5, HX6 are comparable. Fig. 13 shows that percentage exergy destruction of HX4 decreases and HX6 increases significantly from pure liquefaction to pure refrigeration mode, whereas for other heat exchangers there is marginal increase. This happens due to that, HX4 has substantial reduction and HX6 has significant increase of exergy transfer rate between cold stream and hot stream from pure liquefaction to pure refrigeration mode compared to other heat exchangers as shown in Fig. 14.
·
·
Ex − Ex ηHX =
C,O ·
C,I ·
when TC , I ⩾ Tref
Ex − Ex H ,I
H ,O
·
·
(22)
Ex − Ex ηHX =
H ,O ·
H ,I ·
when TC, I ⩽ Tref
Ex − Ex C,I
(23)
C,O
·
where ηHX andEx denote exergy efficiency of heat exchanger and exergy transfer rate of a stream respectively. Subscripts H, C, I, O stand for hot, cold, inlet and outlet respectively. Fig. 15 demonstrates that exergy efficiency of all heat exchangers increases from pure liquefaction to pure refrigeration mode. This is for the reason that the exergy destruction rate per unit exergy transferred 10
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In heat exchangers HX1, HX2, HX3 and HX4, the fluid properties do not vary appreciably with temperature in their operating range above 20 K. In heat exchangers, HX5 and HX6, helium temperature is below 20 K, where properties like specific heat capacity, thermal conductivity, density and viscosity, varies so widely that it affects the performance of the heat exchanger. The specific heat capacity of high pressure helium at 1.40 MPa, varies from 5.90 kJ/kg-K at 20 K to a maximum of 7.51 kJ/kg-K at 10 K and again drops down to 3.73 kJ/kg-K at 5.5 K. The low pressure stream at 0.13 MPa, varies from 5.26 kJ/kg-K at 20 K to 11.15 kJ/kg-K at 4.50 K and again drops sharply to 4.20 kJ/kg-K at liquid helium temperature of 4 K. The effectiveness of HX5 and HX6 has been determined by the modified relation following the enthalpy differential approach as mentioned in Barron [18]. The algebraic expressions of effectiveness at variable specific heat capacity zone are given as follows: H −H ε = hot, in hot*, out , H*out is the hot stream enthalpy at the cold stream Hhot , in − Hout
inlet temperature, for
Chot 〈Ccold
Fig. 14. Exergy transfer load from cold stream to hot stream at different modes.
ε=
(25)
Hcold, out − Hcold, in * −H Hout cold, in
, H*out is the cold stream enthalpy at hot stream
inlet temperature, for
Chot 〉Ccold
(26)
Variable heat capacity of low temperature helium is taken into consideration using enthalpy difference method for calculating ∊ of HX5 and HX6 using the relation:
mean specific heat capacity of a stream enthalpy difference between inlet and outlet of a stream = terminal temperature difference of that stream
As the temperature, mass flow, enthalpy, heat capacity of the inlet and outlet streams of a heat exchanger are available from Aspen Hysys as discussed in Section 2.4, effectiveness of all heat exchangers have been determined using Eqs. (22), (23), (25)–(27). Fig. 16 shows the variation of effectiveness of heat exchangers at pure liquefaction mode. Fig. 16 demonstrates that the effectiveness value of all heat exchangers is 90% or greater, which complies Barron [18] and literatures [10,12–14]. As shown in Fig. 17, at pure liquefaction mode, the calculated order of heat duty of the heat exchangers is as HX2 > HX1 > HX4 > HX3 > HX6 > HX5, and, this order is valid for any mode. It is
Fig. 15. Exergy efficiency of major components at different modes.
from cold stream to hot stream decreases with the increase of refrigeration load. Fig. 15 also states that in warm turbine, exergy efficiency decreases with increase of refrigeration load, whereas in cold turbine, exergy efficiency remains almost equal. For all modes, exergy efficiency is zero for flow control valve and JT valve i.e. valves contribute only exergy loss to the system. Therefore, a designer should take care on the number of valves used in a liquefier. The two most important thermodynamic parameters to represent a heat exchanger are effectiveness (∊) and UA, where U is overall heat transfer coefficient (W/m2 K) and A is heat transfer area (m2). UA signifies the heat transfer size of a heat exchanger which means the ability to transfer heat, while effectiveness is a measure of its thermal performance. Effectiveness of two stream counter flow heat exchanger is defined as the ratio of actual heat transfer rate to the maximum heat transfer rate possible theoretically having infinite surface area and no longitudinal wall conduction, and is expressed as ·
ε=
q ·
q max
=
Cp ΔT Cp,min ΔTmax
(27)
(24)
where Cp,min is the smaller of the two fluid’s heat capacities, ΔTmax is the difference of two inlet terminal temperatures of hot and cold streams.
Fig. 16. Effectiveness of heat exchangers at pure liquefaction mode. 11
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Fig. 17. Heat transfer from hot to cold stream (heat duty) at different modes.
percentage exergy output with respect to compressor motor power or exergy efficiency of this Claude cycle. Fig. 8 depicts that exergy destruction rate for compressor remain constant through all the modes; for turbines, exergy destruction rate decreases; and for flow control valve and JT valve, exergy destruction rate increases marginally from pure liquefaction to pure refrigeration mode. Decrease of exergy destruction rate in turbines occurs due to reduction of turbines work.
observed from Fig. 17 that heat duty of HX2 and HX4 are decreasing with the increase of refrigeration load. Heat exchangers, HX2 and HX4 are located on the downstream side of cold flow of HX3 and HX5 respectively. It is found from study that HX3 and HX5 are unbalanced heat exchangers. Due to increase of mass flow rate of both the streams, more cold is available in these heat exchangers with the increase of refrigeration load, resulting in increase of heat duty. Heat exchangers, HX2 and HX4 are getting balanced with the increase of refrigeration load, as hot stream mass flow remains constant in all modes. This results in decreasing heat duty of both HX2 and HX4 with increase in refrigeration load. Fig. 18 demonstrates that UA of HX5 and HX6 increases with refrigeration load, which is illustrated as follows. The heat duty of a heat exchanger is defined as:
4. Conclusion This investigation primarily aims at the behaviour of exergy characteristics of an existing helium liquefier (model HELIAL 50 of Air Liquide DTA, France) at off-design mixed mode operations. The exergy efficiency curve helps to infer the following: (1) Though sold as a liquefier, the machine works best at mixed mode with 74.42 W refrigeration load, (2) Exergy efficiency of the helium liquefier decreases with the increase of refrigeration load from its optimum point, (3) Exergy output at different modes bear a linear correlation with exergy destruction. The analysis is based on the experimental data archived from sensors equipped with the liquefier and basic characteristics of the components. The characteristics revealed in this investigation may be helpful to the process designer and operator for designing liquefiers and mixed mode refrigerators. Although this study has been performed on a specific liquefier model, the trends of the results could be helpful for the designers. The largest fraction of exergy is destroyed in the compressor. Hence, there is always a scope of improvement of compressor design and thereby, specific power consumption of the thermodynamic cycle could be improved. The trends of the UA values and exergy destruction in heat exchangers may be helpful in selecting their relative sizes.
·
Q = (U . A)ΔTLMTD
(28)
·
Q , U, A, ΔTLMTD denotes heat duty (W), overall heat transfer coefficient, heat transfer area (m2) and Logarithmic Mean Temperature Difference, LMTD (K), respectively. In present case, A remains constant for all modes. U is a function of convective heat transfer coefficient, h, of the fluids involved, which in turn depend on flow properties, fluid properties and surface geometry [18]. In general, h is a function of Reynold’s number, which increases with increasing mass flow rate. With the increase of refrigeration load, the mass flow rates of both hot and cold streams through HX5 and HX6 increase. Hence, the change of Reynold’s number increases U of the heat exchangers, resulting in higher heat duty as, observed in Eq. (28). 3.4. Exergy characteristics of other components From Figs. 8 and 9, it can be observed that at pure liquefaction mode, maximum exergy destruction occurs at compressor (49%). This is followed by six heat exchangers together (18.60%), two turbines together (15.20%), JT valve (4.84%) and turbine flow control valve (3%) sequentially which comprises of 90.77%. Remaining 9.20% is the
Declaration of Competing Interest The authors declared that there is no conflict of interest. 12
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Fig.18. Variation of UA and LMTD of heat exchangers at different modes.
Acknowledgements
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Authors gratefully acknowledge the constructive suggestions of the reviewers to improve the quality of this paper. References
Mr. Trijit K. Maiti received Masters in Mechanical Engineering from National Institute of Technology, Rourkela, India, in 2011. Currently he is working as Scientific Officer at Variable Energy Cyclotron Centre, Kolkata. His research area includes analysis of different thermal and cryogenic processes, development of helium refrigeration system and sub-systems; and development of cryo-sorption based gas purification system.
[1] Kaushik SC, Shiva Reddy V, Tyagi SK. Energy and exergy analysis of thermal power plants: a review. Renew Sustain Energy Rev 2011;15:1857–72. [2] Hafdhi F, Khir T, Yahyia AB, Brahim AB. Energetic and exergetic analysis of a steam turbine power plant in an existing phosphoric acid factory. Energy Convers Manage 2015;106:1230–41. [3] Erdem HH, Akkya AV, Cetin B, Dagdas A, Sevilgen SH, Sahin B, et al. Comparative energetic and exergetic performance analyses for coal fired thermal power plants in Turkey. Int J Therm Sci 2009;48:2179–86. [4] Yagli H, Koc Y, Koc A, Gorgulu A, Tandiroglu A. Parametric optimization and exergetic analysis comparison of subcritical and supercritical organic Rankine cycle (ORC) for biogas fuelled combined heat and power (CHP) engine exhaust gas waste heat. Energy 2016;111:923–32. [5] Khaliq A, Kaushik SC. Second law based thermodynamic analysis of Brayton/ Rankine combined power cycle with reheat. Appl Energy 2004;78:179–97. [6] Abuelnuor AAA, et al. Exergy analysis of Garri “2” 180 MW combined cycle power plant. Renew Sustain Energy Rev 2017;79:960–9. [7] Thirumaleshwar M. Exergy method of analysis and its application to a helium cryorefrigerator. Cryogenics 1979;19:355–61. [8] Ahamed JU, Saidur R, Masjuki HH. A review on exergy analysis of vapour compression refrigeration system. Renew Sustain Energy Rev 2011;15:1593–600. [9] Thomas RJ, Ghosh P, Chowdhury K. Exergy analysis of helium liquefaction systems based on modified claude cycle with two expanders. Cryogenics 2011;51:287–94. [10] Thomas RJ, Ghosh P, Chowdhury K. Application of exergy analysis in designing helium liquefiers. Energy 2012;37:207–19. [11] Thomas RJ, Ghosh P, Chowdhury K. Role of expanders in helium liquefaction cycles: parametric studies using Collins cycle. Fusion Eng Des 2011;86:318–24. [12] Thomas RJ, Ghosh P, Chowdhury K. Role of heat exchangers in helium liquefaction cycles: simulation studies using Collins cycle. Fusion Eng Des 2012;87:39–46. [13] Thomas RJ, Ghosh P, Chowdhury K. Optimum number of stages and intermediate pressure level for highest exergy efficiency in large helium liquefiers. Int J Refrig 2013;36:2438–57. [14] Kundu A, Chowdhury K. Evaluating performance of mixed mode multistage helium plants for design and off-design conditions by exergy analysis. Int J Refrig 2014;38:46–57. [15] Caillaud A, Crispel S, Grabie V, Delcayre F, Aigouy G. Evolution of the standard helium liquefier and refrigerator range designed by Air Liquide DTA, France. In: Proceedings of EPAC08, Genoa, Italy; 2008. p. 2497–99. [16] McCarty RD, Arp VD. A new wide range equation of state for helium. Adv Cryog Eng 1990;35:1465–75.
Dr. Sandip Pal received his PhD from University of Manchester, UK. Currently he is the Head of the Cryogenic Process and Instrumentation Section, Variable Energy Cyclotron Centre, Kolkata and Associate Professor of Homi Bhabha National University. His field of research includes development of new type of sensors, transducers and actuators; chemical species tomography, capacitance tomography, cryogenic process related instrumentationa and control.
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T.K. Maiti, et al. Prof. Balaram Kundu received his PhD from Indian Institute of Technology (IIT), Kharagpur, in 2000. Currently he is the Professor of the Department of Mechanical Engineering, Jadavpur University, India. His field of specialization includes analytical and computational heat transfer, flat plate solar collector, heat transfer in porous materials and fin and tube heat exchanger. He got two patents in 2016 on his work on subsonic flow in convergent-divergent nozzle and fin heat transfer with internal generation subject to nonlinear surface heat exchange.
Prof. Parthasarathi Ghosh received his PhD from Indian Institute of Technology (IIT), Kharagpur. Currently he is the Associate Professor and Head of the Department of Cryogenic Engineering, IIT, Kharagpur. He is the author and co-author of several publications on cryogenic process and equipments. His research field include low temperature processes, large scale helium liquefiers and cryogenic turboexpanders.
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