liquefier for LHD

Cryogenics 45 (2005) 199–211 www.elsevier.com/locate/cryogenics

Dynamic simulation of the helium refrigerator/liquefier for LHD Ryuji Maekawa

a,*

, Kouki Ooba a, Minoru Nobutoki b, Toshiyuki Mito

a b

a

National Institute for Fusion Science, Toki, Gifu 509-5292, Japan Nippon Sanso Corporation, Kawasaki, Kanagawa 210-0861, Japan

Received 19 April 2004; received in revised form 30 September 2004; accepted 9 October 2004

Abstract A real-time dynamic simulation has been carried out for the 10 kW class helium refrigerator/liquefier of Large Helical Device (LHD) at National Institute for Fusion Science (NIFS). The refrigerator consists of eight screw compressors, seven expansion turbines, fourteen heat exchangers and a 20 m3 liquid helium reservoir. A simulation model was implemented to Cryogenic Process REal-time SimulaTor (C-PREST), developed as a platform for the plant process study and optimization. Validity of the simulation model has been confirmed based on the design values as well as the results of commissioning tests. This paper describes the cooldown process and expansion turbine trips during the operation. Difficulties of dynamic simulation for the large cryoplant are also discussed. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Dynamic simulation (C); Claude cycle (E); Heat exchangers (E); Fusion magnets (F)

1. Introduction Large Helical Device (LHD) is an experimental fusion apparatus to study current-less steady-state plasmas and utilizes superconducting coil systems to generate magnetic field for confining and controlling [1]. This is the largest superconducting apparatus for the experimental fusion research and has the dimensions of 13.5 m in diameter with 9.1 m height and the cold mass of approximately 850 tons. Two types of superconducting coil systems have been developed; a pair of pool boiling helical coil; three pairs of forced-flow poloidal coils. Further, the fabrication of flexible superconducting bus–line system to connect the LHD with power supplies satisfies the space constraint and considerably reduces the operating cost [2]. After eight years of the

*

Corresponding author. Tel.: +81 572 58 2136; fax: +81 572 58 2616. E-mail address: [email protected] (R. Maekawa). 0011-2275/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2004.10.001

development stage, plasma experiments have been conducted since 1998 and showed progress of plasma parameters, its diagnostic technique with theoretical prediction and support. To cooldown and maintain superconducting state of the coil systems, the helium (He) refrigeration plant required to possess fairly large refrigeration capacity and complex thermodynamic process to provide four different cooling schemes to the LHD; a pool boiling, a forced flow cooling for both supercritical helium and cold gaseous helium (GHe), and a two-phase flow cooling. Since the reliabilities of components of the refrigerator, i.e. a gas bearing turbine, a compressor, an adsorber, have been considerably improved; the main focus is set for the intensive thermodynamic analyses to pursue high efficiency of the refrigeration plant. Continuous operation of the plant requires substantially higher cost than the fabrication of the plant itself. As increasing the complexity of a refrigeration plant process, its control system has to be very reliable to have high availability of plant operation. In addition to this,

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the system has to provide a user-friendly operating environment; which only requires knowledge of control dynamics rather than profound programming technique. The control system adopts spatial redundancy to have high reliability and availability of the system. The system itself has been developed based on an ‘‘open system’’, a computer design system that is compatible with any similar type of system, so that its flexibility ensures the expandability for future developments. For the past 5-year of operating periods, the cryogenic system has been experienced not only predictable disturbances but also unpredictable disturbances. The plant operation suffered devastating loss of GHe which leaded to a few days of recovery operation to reestablish the normal operating condition and relatively large financial losses. A part of these failures was caused by the erratic dynamic response of the plant. Even though the sequence programs were implemented for the predictable disturbances, some of the programs are not suitable enough for the recovery operation. Based on these experiences, the process control programs have been modified to avoid any damage to the plant operation [3]. However, we were convinced that it is almost impossible to anticipate the dynamic response of the variables such as, massflow, temperature and pressure, as a result of interaction in the plant process. The demand to develop a dynamic simulator has been considered as a very important issue at the early stage of the cryogenic system operation. Nobutoki et al. [4] conducted the dynamic simulation of the helium refrigerator/liquefier, using SPEEDUPTM. This is based on the mathematical modeling of the process plant and could not be used as a real time basis.

Recently, a dynamic simulator has been utilized as a powerful tool to model the chemical plant because of the advancement of PC and simulation software. Possibility to use this type of advanced software is a key to develop a simulation environment for the refrigeration plant. We have been working on the development of a real-time dynamic simulator as a platform to study the control strategy and to train operators [5]. The validity of specific model has been confirmed by the dynamic simulation of a Brayton cycle refrigerator and a He liquefier [6]. The final stage of development is to model the He refrigerator/liquefier of LHD. This paper describes the dynamic simulation of a large scale He refrigerator/liquefier, operated from 300 to 4.4 K and discusses its validity of the model compared with the actual refrigerator. Performances and difficulties of process calculation under different conditions are also discussed.

2. Specification of helium refrigerator The He refrigerator/liquefier design demands for the specific refrigeration process which allowed to improv-

Table 1 Specification of He refrigerator/liquefier for the LHD

Refrigeration capacity at 4.4 K Liquefaction rate Refrigeration capacity at 40 K < T < 80 K

Design value

Measured value

5670 W 650 L/h 20,600 W

5770 W 704 L/h 20,770 W

Fig. 1. Simplified P&ID for the helium refrigerator/liquefier. Solid circle indicates the data points for thermophysical property of He calculation.

R. Maekawa et al. / Cryogenics 45 (2005) 199–211

ing overall thermodynamic efficiency of the refrigeration plant. Based on its design requirements, the extensive study had been carried out to achieve a relatively high Carnot efficiency of 19.8% [7]. Table 1 shows a specification of the He refrigerator/liquefier and the equivalent refrigeration capacity at 4.4 K is estimated to be 9.7 kW, which possesses the largest refrigeration capacity of operating He refrigeration plants in Japan. Fig. 1 shows simplified process and instrumentation diagram (P&ID) of He refrigerator/liquefier, which consists of eight oil-injected screw type compressors, seven gas-bearing expansion turbines (ET), 14 multi-stream aluminum plate-fin type heat exchangers and a 20 m3 liquid helium (LHe) reservoir. Since the refrigeration process was specifically designed for LHD operation to have a high thermodynamic efficiency, which results in rather complicated process. The part of this complexity is caused by the fact that refrigeration power to the thermal radiation shields is supplied by ET4&ET5. 2.1. Refrigeration cycle description A T–S diagram for the He refrigerator/liquefier is shown in Fig. 2, which represents a nominal operating condition, data points were taken during the commissioning of the refrigerator conducted in 1995 [8]. Compressors are comprised of two units, ‘‘A’’ and ‘‘B’’, working at different suction pressures. Each unit has the two compression stages; unit ‘‘A’’ consists of four parallel compressors at first stage which connects to two parallel compressors at second stage, while unit ‘‘B’’ has two compressors connected in series. Unit ‘‘A’’ is designed to generate helium massflow rate of 750 g/s with suction and discharge pressure of 0.10 and

201

1.94 MPa, respectively. The unit ‘‘B’’ generates the designed mass flow rate of 210 g/s with suction and discharge pressure of 0.20 and 1.94 MPa, respectively and is responsible for the operation of first precooling cycle, ET1–ET3 connected in series, which eliminates utilization of LN2. After the compressed helium mass flow is divided at ET1 circuit, some portion of the Joule Thomson (JT) stream is split to ET4 and ET5: second precooling cycle, which provides refrigerant to the thermal radiation shields with its capacity of 20.6 kW at 40– 80 K. The rest of JT stream is used for two expansion turbines ET6 and ET7, operated in parallel at different temperature levels, producing supercritical helium at 1 MPa which is used to cool poloidal coils and/or to produce LHe in the reservoir after expansion at the JT valve. The discrepancy in the total massflow rates, Fig. 2, compared with design values were caused by the operating condition of ETs and the accuracy of massflow meters which was originated by the temperature reading from thermometers. The configuration at the cold end of refrigerator was adapted to improve thermodynamic efficiency. Non-linearity of specific heat, Cp(T, P), of GHe becomes significant at low temperature regime, which leads to a large exergy loss at the cold end of heat exchangers. This is primarily caused by the substantial differences in the enthalpy changes in the high and low pressure side of heat exchanger. To balance the variation of enthalpy changes in each heat exchanger, Barton et al. [9] introduced two supercritical expansion turbines operated in a parallel configuration with different temperature levels. This refrigeration cycle had also been adopted to improve the efficiency at the cold end of He refrigerator such as, 6 kW He refrigerator for LEP in CERN [10].

500 Unit A 1.84MPa

Unit B 0.21MPa

0.11MPa

ET1

Temperature (K)

160.5g/s

100

ET2 ET3 ET4

225.3g/s

ET5 113.2g/s

ET6 164.2g/s

ET7

10

4 4000

203.8g/s

8000

3. Description of C-PREST

12000 16000 20000 24000 28000 32000 36000 Entropy (J/kg-K)

Fig. 2. T–S diagram showing a result of the commissioning.

The development of C-PREST is completed and its configuration is almost identical to the LHD cryogenic control system [3]. Fig. 3 shows an illustration of the C-PREST, which consists of an integrated controller with two subsystems; a He refrigerator/liquefier system; a superconducting coil system, operating consoles (FAPPTM) and a PC workstation for dynamic simulations. The hardware architectures for each system are Versa Module EuropeÕs (VMEs) with a PC for advanced control programming, whereas the dynamic simulation PC workstation has the specification of 2.8 GHz dual CPU, 2 GB Memory, 140 GB HD, Windows 2000 ProfessionalTM and a solid state flash drive. To interact the process data of the simulation PC with VMEs, dynamic data marshalling is realized by a PCI-bus with reflective memory boards in each system via optical fibers. Synchronization of the PC with VMEs is achieved with a communication program written by Visual C++ [5].

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Fig. 3. Illustration of C-PREST.

The simulator can be used for the start-up and the shut down operations and its versatilities allow saving snap shots at certain plant processes and restarting the simulation from the particular point. Further the dynamic simulation speed can be accelerated up to four times faster than the real-time basis, depending on the workload to the CPU of the simulation PC. The dynamic simulation software for the helium cryogenic plant has been developed, customizing Visual ModelerTM (VM) which is a powerful software tool, developed by Omega Simulation, to simulate the chemical plants such as, the petroleum refining plant, utility boiler plant [11]. The VM is module-type software and the model plant is configured with combining these modules with stream lines on the PC. In the case of He refrigerator, basic modules are a heat exchanger, an ET, a pneumatic control valve, a compressor and a LHe reservoir. Each module is described by algebraic and differential equations and is solved with the mass, pressure and heat balances. The pressure–massflow rate balance between each module is obtained by solving the number of linear and/or quadratic equations, simultaneously. To acquire physical data such as, temperature, massflow rate, pressure, from simulation model, the signal line is used to connect the instruments such as, temperature and pressure sensors, to the stream lines. These physical data are shared with VME controller for loop and/or sequence controls. 3.1. Simulation model approach The safety and reliability are primary concern for the cryogenic plant. To achieve this goal, sequence programs were implemented to the control system to protect the hardware from ‘‘improper’’ operating command or procedure. Therefore, the most hardware components are operated with restricted inter-locks to insure the operation security. Even though the design

philosophy of a dynamic simulation system was to duplicate the identical operating scenario, these interlocks sometimes halt the automatic start-up of the plant because of lack of digital return signals from the hardware to confirm their operation status. To avoid these conflicts, some signals are added to clear some of inter-locks. After these minor modifications of the control programs, the dynamic simulation was conducted as the same as the real refrigeration plant operation. According to the P&ID of the He refrigeration plant, the simulation model has been implemented on the PC workstation. Most of the sequence and feedback control programs for the real He refrigerator/liquefier are applied for the simulation system. However, the modifications of process control programs are inevitable to permit the process engineer to interrupt the operation or adjust Proportional-plus-Integral-plus-Derivative (PID) parameters of control valves. After these modifications, the control program was stored in the PC and down-loaded to the VME of the He refrigerator/liquefier system as indicated in Fig. 3. Table 2 summarizes the number of I/O for the simulator. 3.1.1. Heat exchanger The He refrigerator has 14 aluminum plate-fin multifluid type heat exchangers. To build-up each heat exchanger module, parameters to define each heat exchanger are the heat transfer coefficient, the heat transfer area, the pressure drop with a fluid density at the design condition and the total weight. The heat transfer coefficient has a dependency on the massflow rate and is expressed with its power function of n, where n is a Table 2 I/O list for the dynamic simulation of He refrigerator/liquefier

Simulation model (I/O)

AI

AO

DI

DO

PID

Sequence

396

86

158

33

16

38

R. Maekawa et al. / Cryogenics 45 (2005) 199–211

203

Table 3 Specification of aluminum plate-fin type heat exchanger HX-#

ETa

Heat transfer area (m2) b

HX-1 HX-2 HX-3 HX-4 HX-5 HX-6 HX-7 HX-8 HX-9 HX-10 HX-11 HX-12 HX-13 HX-14 a b c d

644 233

c

HP

MP

LP

985 108 202 97 53 94 145 444 235 111 141 74

275 30 236 27 68 121 183 920

800 87 688 78 233 21 32 248 234 115 139 131 80 156

55 83 107

Heat transfer coefficient for LP side (W/m2 K)

Weight (kg)

203 177 155 130 237 192 183 215 373 261 255 248 238 333

3880 425 3510 400 1290 525 800 1700 580 285 350 410 250 470

d

Expansion turbine circuit. High pressure. Medium pressure. Low pressure.

constant decimal [6]. Specifications for the heat exchangers are summarized in Table 3 and values are calculated based on the steady-state conditions with axial conduction. Equations for the heat exchanger module are solved by the space discretization and 20 spatial divisions are applied from HX-1 to HX-7, while 50 spatial divisions are selected for HX-8 through HX-14. The heat capacity changes for the GHe inside the heat exchangers are neglected in the model in order to have faster calculation. 3.1.2. LHe reservoir A flash-tank module is applied for the 20 m3 LHe reservoir [6]. The module accounts for the dynamic mass and heat balance of the liquid and vapor phases. The accumulation of energy and mass in each phase is also calculated. Mass transfer between liquid phase and gaseous phase is evaluated based on the evaporation and/or condensation rates, which are estimated from the assumed mass transfer coefficient. Parameters to specify the LHe reservoir are configuration, size, weight, heat capacity, mass transfer coefficient, the heat leak to the surrounding environment.

integrated brake circuit that controls the turbine-speed. Specification of turbines is listed in Table 4. Conversion of power extracted by turbine impeller is realized by a brake circuit which dissipates the heat with a watercooled heat exchanger. An expansion turbine module was developed based on the algebraic equations; a St. VenantÕs equation for isentropic ideal-gas flow through a nozzle; adiabatic efficiency and speed equation; an equation to represent the performance of the brake circuit [6]. Required parameters to simulate the performance of turbine module are the impeller size, the cross-sectional area of the nozzle inlet, the maximum isentropic efficiency and the optimal speed. 3.1.4. Control valves Pneumatic control valves are simulated based on the maximum Cv value and the opening (lift). On-off valve can be set to have a limit switch to inform operator that the operation of the valve is valid. For a two-phase expansion valve such as the JT valve, the fluid density is calculated as a homogeneous mixture of gas and liquid. 3.2. Cooldown Scenario

3.1.3. Expansion turbine The expansion turbine, TGL series supplied by Linde Kryotechnik AG, consists of a radial-inward-flow impeller and a centrifugal-brake compressor with an

The cooldown control program comprises of threeblock-operation—Precooling A, B and C: a compressor operation, an expansion turbine operation and a

Table 4 Specification of expansion turbine

Model Impeller diameter (mm) Max. efficiency (%) Rated speed (rps)

ET-1

ET-2

ET-3

ET-4

ET-5

ET-6

ET-7

TGL45 45 73.55 1650

TG45 45 73.68 1650

TG45 45 76.81 1650

TGL32 32 77.26 2450

TGL45 40 79.26 1650

TGL32 18 77.63 1800

TGL32 18 69.07 1500

204

START UP 2 Pre-cooling B

Pre-cooling A Compressor operation

3

4

5

6

Operation of ET1-3

Operation of ET4&5

Operation of ET6

Operation of ET7

Liquefaction

Startup Compressor UNIT A

Startup Compressor UNIT B

Startup ET1-3

Startup ET4,5

Startup ET6

Startup ET7

LPIC2014=0.12MPa

Control discharge pressure around 1.8MPa

Control suction pressure at 0.207MPa

Ramp open LCV2101

Ramp open LCV2008

Ramp open LCV2009

Ramp open LCV2011

Control suction pressure to 0.15MPa and 0.105MPa

Control discharge pressure at 1.83MPa

ET6>1800rps

ET7>1900rps

Ramp close LCV2023

Warmup operation for 10 min.

Warmup operation for 10 min.

LCV2011>=70% & LCV2023=0

SIC for ET6

SIC for ET7

5

6

Set bypass valve LPDIC2043

Ramp open LCV2001 ET1-3=1400rps ET4>2000rps or ET5>1400rps Slide valve open 100%

Ramp open slide valve to 100%

Discharge pressure at 1.8MPa

Confirmation of discharge pressure and suction pressure

Warmup operation for 10 min. Warmup operation for 10 min. Setup the rated rotation speeds

LPIC2014=0.10MPa

Rated rotation speeds for each turbine

Check the purity of N2<20ppm and H2O<10ppm

Control heat input to simulate thermal radiation shields

Connection to the cold box

LPDIC2043=0.26MPa

1

2

3

4

END

Fig. 4. Flowchart of automatic cooldown operation. Initiation of sub-program is controlled by the operator.

R. Maekawa et al. / Cryogenics 45 (2005) 199–211

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R. Maekawa et al. / Cryogenics 45 (2005) 199–211

gram was initiated. The JT bypass valve was ramped close, while the JT valve was ramped open. However, the sequence operation was controlled by the HX-14 temperature: if the temperature increased, the program was interrupted. At the same time, the pressure at the inlet of JT valve has to be maintained larger than 0.80 MPa, while changing the flow passage. Therefore, the opening and/or closing of valve need to be adjusted to satisfy these conditions. Once the opening of JT valve becomes 80%, the JT bypass is fully closed for the liquefaction process. The cooldown process of the He refrigerator/liquefier is completed at this point. Since the initial cooldown is performed with a closure of JT valve, which results in the co-current flow condition at HX-14, the JT valve is opened and HX-14 is operated as a counter-current flow mode, after the cooldown of the cold-box. This flexibility is one of our great interests if the module base simulator can handle a multi-fluid heat exchanger which allows co-current and counter-current flow heat exchanger operation.

4. Results and discussion 4.1. Cooldown operation from 300 to 4.4 K The dynamic simulation of the cooldown operation was conducted, using the automatic sequence programs as stated earlier. Fig. 5 shows the cooldown curve of the dynamic simulation results compared with the actual data obtained during the commissioning in June 1995. The dynamic simulation is well described the commissioning situation; however, the time to reach the liquefaction is much faster for the simulation. This set back 350 HX-14_sim HX-14 ET3_out_sim ET3_out

300 250 Temperature (K)

liquefaction, respectively. Fig. 4 shows the flowchart of operations, which summarizes a part of indispensable conditions. The cooldown process is initiated with a Precooling A, however, the modeling of compressor unit was left out because of higher CPU load for the process calculation. Therefore, the compressed GHe, 1.8 MPa at 300 K, is generated by the feed line, while suction lines of compressor units are substituted by the two outflow lines from the cold box with pressures, 0.12 and 0.2 MPa, respectively. In this case, the simulator is simply generating the operating status signals of compressor units to satisfy the conditions to proceed to the next sequential operations. As connecting the compressor units with a cold box, the flow passage in the cold box is automatically set for the cooldown. The bypass valve (LCV2021) for ET6&ET7 is opened for 38%, while the JT bypass valve (LCV2023) is opened for 50%. Precooling B, the expansion turbine operation, is composed of four programs with an almost identical startup procedure for ET1–ET7. Once the program is executed, the brake valves are opened and the inlet valve is ramped open. As the rotation speed of turbine increases and reaches at the specified value, a 10 min warmup operation takes over with a momentary interrupt the ramp-up. The sequence program is resumed to ramp up the inlet valve, while maintaining the outlet pressure of expansion turbine. The sequence operation is completed as the inlet valve attains the rated opening and the rotation speed. In the case of ET4 and ET5, however, a part of the control program is different from others since they are designed to provide the refrigeration to the thermal radiation shields. The operation requires adjusting the pressure difference between an outlet pressure of ET4 and an inlet pressure of ET5, which determines the flow rate to the radiation shields. In addition to this, the appropriate magnitude of heat load has to be applied to control the outlet temperature at the heater to 80 K, which is loop-controlled with LTIC2023. As ETs reached their rated rotation speed, the steady state heat load of 20.6 kW is applied for a steady-state operating condition. During the cooldown process, LCV2021 is used to regulate the refrigeration produced at ET1 circuit, which balances the massflow rate of a JT stream to prevent too much cooling at the outlet of ET3. As the temperature of HX-14 reached around 100 K, the JT valve (LCV2011) is opened for 40% to start the precooling of the transfer line and the LHe reservoir, while the pressure in the reservoir is controlled automatically by LCV2014 and LCV2025 at 0.12 MPa. LCV2021 is closed for the ET6 startup, as the HX-14 temperature became less than 90 K. At this point, the JT stream is adjusted by the opening of ET7 bypass valve (LCV2022), which takes over the function of LCV2021. After the operation of ET6&ET7 and the HX-14 temperature became 10 K the liquefaction sequence pro-

205

200 150 100 50 0 0

5

10

15

20

25

30

35

40

Time (hr)

Fig. 5. Cooldown curve compared with the commissioning test which took place in June 1995. Solid lines indicate simulation results, while dotted lines indicate the data from the refrigerator operation.

R. Maekawa et al. / Cryogenics 45 (2005) 199–211

for the actual plant was primarily associated with the expansion turbine trips before starting up of ET6&ET7. Since the overall dynamic plant behavior was not fully understood at the time of commissioning, the sequence program to operate the expansion turbines was too straightforward, which will be discussed later. The simulation results are also compared with the results of performance test in October 1995, as shown in Fig. 6. The sequence program to control the ET6&ET7 startup was adjusted to prevent the trips experienced during the commissioning. The first precooling circuit was warmed up to prevent the ETs trip at t = 7 h, which affect the relatively large temperature discrepancy at the cold end of heat exchangers such as, HX-14. As proceeding the cooldown process, from t = 15 to 19 h, the similarities in temperature profiles of HX-14 were apparent. The results proved that the adjusted program actually prevent the turbine trips. The discrepancies in the temperature profile of HX-14 from t = 20 to 32 h was due to the standby operation for an overnight, the startup operation of ET6 were faster for the simulator, around t = 18 h, than that of actual refrigerator at t = 30 h, as shown in Fig. 7. Cooldown time is almost identical if one could merge or neglect the standby operation period. Consequently, comparison of dynamic simulation result with these two different operations of actual refrigeration plant ensures the fidelity of the process calculation. 4.1.1. Process calculation speed dependency The C-PREST was designed to perform the process calculation, solving the mass and pressure balance in the entire plant, as a real-time basis since the process-control VMEs are generally operated as 1 s interval. Although the flexibility of C-PREST allows accelerating 350 300

HX-14_sim HX-14 ET3_out_sim ET3_out

Temperature (K)

250 200 150

Standby operation during the night

100 Warmup operation to prevent ETs trip

50 0 0

5

10

15 20 Time (hr)

25

30

35

Fig. 6. Cooldown curve compared with the performance evaluation in October 1995.

2500

T ur bi ne R otation Speed (r ps)

206

2000

1500 ET3 ET4 ET6 ET3_sim ET4_sim ET6_sim

1000 ETs ref. trip

Initiation of ET6_sim

500 Initiation of ET6_ref.

0 0

4

8

12

16

20

24

28

32

Time (hr)

Fig. 7. Startup operation of turbines compared with the performance evaluation. ET6 operation was 12 h faster for the simulation than that of the actual refrigerator since it did not include any standby operation during the night.

the computational speed up to 0.5 s, the set back of computational speed was inevitable as increasing the complexities of the plant process associated with the cooldown-temperature. At the initial stage of cooldown, the computational speed was fairly first, approximately 0.5 s, up to the nominal operation of ET1–ET3. Once the startup of ET4&ET5 was initiated, the speed was slow down to 1 s. The workload to the CPU was increased further as operating ET6&ET7 and the processing time was set back to 1.7 s at the onset of two-phase flow after JT expansion. The time delay was extended further as the liquid helium started to accumulate in the reservoir: at this point, the processing speed became 2 s. As decreasing the temperature of GHe, the temperature gradients within the heat exchangers became smaller, especially at the cold end. In addition to this, nonlinearity of thermal property of GHe is aggravated. As a result, the inadequate spatial divisions of heat exchangers leaded to the divergence behavior in the calculation: the rapid growth of high frequency oscillation. To compensate the effect, the spatial divisions were increased from 20 to 50 for the HX-8 to HX-14. These modifications became tremendous workload to the CPU. The calculation of non-equilibrium state of gas and liquid in the reservoir is the other factor to affect the speed. Mass transfer between the liquid and gaseous phase is calculated based upon the evaporation and condensation rates which are considered to proportional to the difference between the equilibrium and the gaseous phase pressure. As qualitatively described the process calculation, two dominant factors to increase the workload to the CPU are considered as the iterations within the heat exchangers and the dynamic balance calculation in the reservoir.

R. Maekawa et al. / Cryogenics 45 (2005) 199–211

4.2. Nominal operation After the refrigerator was cooldown to 4.4 K, LHe was started to accumulate in the reservoir. The next step was to establish the nominal operating condition; 5.6 kW refrigeration capacity at 4.4 K. The heat input to the reservoir was gradually increased to compensate the refrigeration process. The temperatures of heat exchangers were decreased as increasing the evaporation rate from the reservoir. As the temperature of HX-11 at a low pressure side was decreased approximately to 11 K, the computational error was occurred. To satisfy the criteria for the computational stability and accuracy, the flexibility of C-PREST allowed adjusting the calculation time step size, Dt. Although the step size Dt was varied from 1/70 to 1/200 s, the occurrence of computational error was consistent with the temperature. This instability is assumed to be caused by the variation of GHe specific heat which has a peak around 11 K at 1.8 MPa. One way to solve the problem was to suppress the excessive cooling of heat exchangers at the cold end. A part of evaporated LHe from the reservoir was returned to the high temperature side of the cold box: HX-8 and HX-4 with LCV2020, LCV2017 and LCV2018 (see Fig. 1). Fig. 8 shows a process to apply 5.6 kW to the LHe reservoir. ET3&ET4 outlet temperatures were decreased as increasing the heat input: t = 26– 31 h. Similarly the HX-11 temperature was changed from 19 to 13 K but it was maintained above the ‘‘critical’’ temperature of 11 K, at which the computational instability would take place. As the heat input to the res-

ervoir was reached at the nominal value 5.6 kW, approximately 20% in Fig. 8, the flow passage to the high temperature side of the cold box was closed with LCV2020 to validate the nominal operating condition (see Fig. 9). The graph indicates the substantial temperatures increase of ET3&ET4 outlets, while the outlet temperatures of ET5–ET7 were not affected by the closure of bypass valve, LCV2020. The refrigeration power produced by the first and second precooling circuits was apparently decreased, as losing the cold GHe flow from the reservoir. Fig. 10 supports the idea of insufficient cooling at precooling circuits. GHe return from the reservoir was increased from 396 to 403 g/s as closing LCV2020, while the massflow rate of JT stream was almost constant. The liquefaction rate was estimated to be 350 l/h which is approximately 54% of that of the actual liquefaction rate. The possible explanation for this discrepancy is caused by the fact that the incoming JT stream was not cooled sufficiently at the high temperature region of cold box. Consequently, the deterioration of liquid yield after JT expansion was observed. To look into the detail of refrigeration process, dynamic simulation results were compared with those of commissioning, using T–S diagram as shown in Fig. 11. Data points enclosed in circles are operation results of ETs, while other points are selected from process points of heat exchangers. As one can see clearly that the temperature of simulation results are higher than those of commissioning. This temperature deviation of the simulation results is originated by the simple heat exchanger model which neglects axial heat conduction and

ET3 ET4 ET5 ET6 ET7

Heater LCV2020

70

35

80

60

30

70

50

25

40

20 Heat input to the reservoir

30

15 Bypass valve:LCV2020

20

10

10

5

0

0 24

25

26

27

28

29

30

Outlet Temperature (K)

40

LCV2020 Heater

30

25

60 20

50 Temp. increase due to the loss of cold GHe through LCV2020

40 30

10

20 5

10

31

Time (h)

Closing LCV2020

0

0 29

Fig. 8. A graph shows the process to applying 5.6 kW heat input to the LHe reservoir. The change of mass flow rates are proportional to the heat input, whereas the temperature profile of turbines and heat exchangers are in-proportional.

15

LCV2020 (%), Heater (%)

80

H e at e r ( % ) , L C V 2 0 2 0 ( % )

Temperautre (K)

ET3_outlet ET4_outlet HX11_LP

207

30

31

32

33

34

35

36

37

Time (h) Fig. 9. Closing a bypass valve LCV2020 to the high temperature side of cold box to establish the nominal operating condition.

208

R. Maekawa et al. / Cryogenics 45 (2005) 199–211 From LHe reservoir JT_massflow

Heater LCV2020

50

420

Ma s s fl o w Ra te ( g/ s)

40 Massflow rate increase from a LHe reservoir

380

30 360 20 340 Bypass valve closed for nominal operation

320

10

H e a t e r ( % ) , V al v e O p e ni ng ( % )

400

0

300 26

28

30

32 Time (h)

34

36

Fig. 10. Deterioration of liquid helium production after JT expansion.

320

Temperature (K)

ET4 ET2&3

ET5

10

HX14

HX8

HX_H_sim. HX_H_com. HX_L_sim. HX_L_com. ET_sim. ET_com.

HX11

ET6&7

In the previous section, LHe production with CPREST was estimated to be less than that of the actual refrigerator because of higher temperature distributions in the cold box. To understand the cause of this deterioration, the exergy for each heat exchanger was evaluated. The concept of exergy gives an idea of which part of the composed components has a key to the primary source of irreversible losses. The exergy loss in each stream of heat exchanger can be expressed as

HX14

ð1Þ

where m is massflow rate, h is enthalpy, s is entropy and 0 denotes ambient condition. Based on Eq. (1), the exergy loss in the multi-flow type heat exchanger was evaluated with neglecting the heat loss. In this case, the exergy loss is defined as the difference between the exergy lost in the low pressure streams and the exergy gained by the high pressure streams of heat exchanger, which can be expressed as X ELHX ¼ m_ i ½ðhi;in
hi;out Þ
T 0 ðsi;in
si;out ÞLP

100

HX11

4.3. Exergy analyses and LHe production deficiency

ELi ¼ m_ i ½ðhi;in
hi;out Þ
T 0 ðsi;in
si;out Þ

ET1

HX8

cess, including special condition of HX-14, can be simulated with rather simple assumptions such as, ignoring the heat exchanger fin dependency with massflow rate and temperatures. To understand the efficiency of each heat exchanger module and expansion turbine, their operations are thermodynamically analyzed in the next section. In general, the simple assumptions of the model cause relatively large discrepancies as compared with the actual data but they have given more valuable information, which is more significant than the high accuracy.

i




X

 
 m_ j hj;in
hj;out
T 0 ðsj;in
sj;out Þ HP

j

2 0

5000

10000

15000

20000

25000

30000

35000

ð2Þ

Entropy (J/kg-K)

Fig. 11. T–S diagram shows the dynamic simulation results, which compared with the performance test.

thermal property variation of GHe within the heat exchanger [11]. As a result, the deterioration of LHe production was inevitable and 46% discrepancy of liquefaction rate was confirmed. This tendency is inherent from the previous study; however, the instability in the massflow return from the reservoir, the irregular zigzag patterns, was not observed [11]. The fluctuation appears to be transmitted from the low pressure side to the high pressure side of the cold box and is considered as the results of dynamic calculation between liquid and vapor phase within the reservoir. The mechanism of this fluctuation is still unknown at this point. Performance of C-PREST proves that the dynamic behaviors of the large and sophisticated cryogenic pro-

where subscript LP and HP denote a low and a high pressure side of heat exchanger, respectively. Fig. 12 shows variations of exergy losses in 14 heat exchangers, which indicate the higher temperature distribution in the cold box than those of actual refrigerator. The discrepancies were appeared to be originated from the large exergy losses of HX-1, -3, -8 and -9. Although HX-14 has the largest exergy loss, this is caused by the massflow imbalance and the large enthalpy difference of a high and a low pressure side of heat exchanger: non-linearity of Cp(T, P) is significant at the cold end. Therefore, this is not considered as a primary factor to have lower liquefaction rate. Based on the exergy loss of each heat exchanger, its efficiency was evaluated as; exergy gained by the high pressure sides divided by the total exergy loss of heat exchanger. As shown in Fig. 13, the warm end of cold box possesses relatively lower efficiency, especially HX-1.

R. Maekawa et al. / Cryogenics 45 (2005) 199–211 80000 70000

Exergy Loss (W)

60000 50000 40000 30000 20000 10000 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

HX #

Fig. 12. Exergy loss of heat exchangers under the nominal operating condition.

209

tual refrigerator. Since the HX-1 has the largest volume with the large temperature gradient across it, the spatial discretization has to be large enough to obtain accurate temperature gradient. However, the main focus of simulation was set at the low temperature regime which caused inadequate modeling at the high temperature side of cold box. Therefore, the temperature distributions in the cold box are not entirely similar to the test results, deteriorating LHe production rate after JT expansion. As increasing the spatial division of HX-1 from 20 to 50 would improve the accuracy of temperature distribution in the cold box. Although there is a discrepancy for the LHe production rate, the fidelity of the C-PREST was confirmed from the cooldown and the nominal operation. 4.4. Dynamic response of simulator with an expansion turbine trip

1.0 0.9 0.8

Efficiency

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

HX #

Fig. 13. Efficiencies of heat exchangers under the nominal operating condition.

The large exergy loss at the HX-1 combined with its low efficiency result in the higher inlet temperature of first precooling circuit than the actual refrigerator. Furthermore, HX-3 has comparable exergy loss as that of HX1, which deteriorates overall refrigeration performance for a first precooling circuit. Both HX-8 and HX-9 also possess large exergy losses, which are other factors to affect the production of refrigerant at the second precooling circuit. As a result, the inefficiency at the first precooling circuit affects the overall refrigeration performance, resulting in the less LHe production after JT expansion. Since the simulation result of HX-1 revealed the worst performance within heat exchangers, its operating condition was compared with the design values. To obtain the simulated condition of HX-1, the total length required to establish the temperature gradients were turned out as only 30% of the actual length. This discrepancy reveals the accuracy of calculation was not good enough to obtain comparable results with the ac-

One way to verify the fidelity of the simulator is how well it could predict the dynamic response of the plant during the off-design operation. The He refrigerator/liquefier experienced the ET trips during the commissioning test because of decreasing their outlet temperatures. As stated earlier, the ET operations were too straightforward, neglecting dynamic response of overall process. Originally, the startup operations of ET6&ET7 were followed by the closure of LCV2021 from 20% to 0% in 60 s, which brought about the JT stream flow reduction during this time period. This has the equivalent effect to decrease the heat load to the cold box. As a result, ETs could not maintain their outlet temperature at the same level since they produced the same amount of refrigeration power with lower heat load. To prevent ET trips, the sequence program was implemented to adjust the refrigeration power production by ETs associated with the JT stream flow reduction. To reproduce the same dynamic response as the ET6&ET7 startup and to verify the implemented program, LCV2021 was closed manually, as shown in Fig. 14. At this point, ET1–ET5 were in operation and ET4 and ET5 were in the warmup operating condition (see Fig. 4). As observed during the commissioning test, the outlet temperatures of ETs were decreased, corresponding to the closure of LCV2021. The effect was more significant for the ET5 outlet than that of ET3. The temperature of ET5 outlet dropped from 45 to 12 K, which was also related with the startup process of ET4 (and ET5) circuit, ramp-opening the inlet valve of ET4 (LCV2001) from 40% to 60% at t = 1500 s in Fig. 15. As decreasing the ET5 outlet temperature, LCV2001 was started to ramp-closed, regulating the outlet temperature from t = 3000 s. This particular operation demonstrated the dynamic response of a cold box as reducing the JT flow and the effectiveness of a turbine trip protection program.

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R. Maekawa et al. / Cryogenics 45 (2005) 199–211

ET6,7_bypass

70

60

50

60

50

50

30

40

20

30

ET5_outlet_Temp

50

40

40 30 30 20 20

Regulation of outlet temp.

10

20

10

0

10 1000 1500 2000 2500 3000 3500 4000 Time (s)

0

Temperature (K)

40

Valv e Ope ning (% )

60

Temperature (K)

ET6 ,7_bypass(LCV2021) Opening (%)

ET6,7_bypass JT_bypass JT_valve

ET3_outlet ET4_outlet ET5_outlet

10 ET5 trip

0

500

Fig. 14. Temperature profile of ET5 outlet with closing the ET6, 7 bypass valve.

0

4000

6000

0 10000

8000

Time (s)

Fig. 16. Temperature profile of ET5 outlet with closing the ET6, 7 bypass, the JT bypass and the JT valve.

70

2500 ET1_Inlet ET4_Inlet

60

2000 Rotation Speed (rps)

50 V al ve O pe ning (%)

2000

40 Outlet temp. regulation

30

Warm up operation

1500 ET1 ET2 ET3 ET4 ET5

1000

ET5 trip

20 500

10 0

0 0

500

1000

1500

2000

2500

3000

3500

4000

0

2000

4000 6000 Time (s)

8000

10000

Time (s)

Fig. 15. Regulation of ET4 inlet valve to prevent ET5 trip.

Fig. 17. ET5 trips because of exceeding the trip temperature, resulting from the JT flow reduction.

To invoke the ET trips, LCV2001 was set at the manual control to prevent the ET5 outlet temperature regulation. The operating conditions for ET1–ET5 were the same as before and ET6&ET7 were also not operated. The outlet temperature of ET5 was dropped rapidly after closing LCV2021, the temperature was somehow stabilized above 9 K as shown in Fig. 16. Since the ET4&ET5 were in the warmup condition, the refrigeration power produced was not sufficient to lower the ET5 outlet temperature than 9 K. Therefore, the massflow rate for the JT stream was reduced further with closing the JT bypass and the JT valve. The outlet temperature

of ET5 was dropped below 9 K as closing the JT valve and ET5 was finally tripped as shown in Fig. 17. In general, the most of simulation programs would crash as the massflow rates of turbine circuits become zero; however, the C-PREST is robust enough to sustain the process calculation. According to these simulations, the flexibility of the C-PREST provided valuable information to understand the dynamic response of the whole plant. Note that the comparison of commissioning data was impossible since the data acquisition period was only set at 1 min intervals which were not enough to describe the dynamic response of ET trip processes.

R. Maekawa et al. / Cryogenics 45 (2005) 199–211

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5. Conclusion

References

The dynamic simulation of the large scale He refrigerator/liquefier has been conducted. The validity of simulation has been confirmed under cooldown operations. The versatility of C-PREST showed the dynamic computation of the ET trips without inducing any computational error. Throughout these studies, the C-PREST proved their vigorous performance for a dynamic simulation of a small scale to a large scale He refrigeration plant. Consequently, the C-PREST can be applicable to investigate the dynamic response of the plant, to design new process, to develop advanced control algorithm and to train operators. One drawback is the simulation performance is not achieved as a real-time due to the complexity of the process and the large variation of thermophysical property of He at low temperature. Alternative approach to model a liquid helium reservoir and heat exchangers is necessary to accomplish the real time simulation. Still, we are confident to extend C-PREST to the entire LHD cryogenic system, which includes superconducting coil systems and their supporting structures.

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Acknowledgments The authors would like to express our gratitude to Mr. T. Fukano for his precious guidance and encouragement for the project. Many thanks to S. Takami for programming support and to A. Kato for preparation of view graphs for the paper.