- Email: [email protected]
Determination of critical parameters in the EAST subcooled helium system
Fusion Engineering and Design 131 (2018) 84–89
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Determination of critical parameters in the EAST subcooled helium system Maofei Geng a b
a,b,⁎
a
a
a
a
, Yuntao Song , Anyi Cheng , Hansheng Feng , Qiyong Zhang , Qingfeng Jiang
T
a,b
Institute of Plasma Physics, Chinese Academy of Science, Hefei, 230031, People’s Republic of China University of Science and Technology of China, Hefei, 230026, People’s Republic of China
A R T I C LE I N FO
A B S T R A C T
Keywords: Subcooled helium Cryogenic Cold compressor
The cryogenic system at the Experimental Advanced Superconducting Tokamak (EAST) is designed for a capacity of 1050 W/3.5 K + 200 W/4.5 K + 13 g/s liquid helium+ 13 kW/80 K. The 3.5 K subcooled helium is obtained from an oil ring pump. The cryogenic system is now being upgraded with a centrifugal cold compressor that should reduce the helium-tank pressure and temperature. This article discusses the determination of critical parameters for the cold compressor, including the efficiency of heat exchange, the location of the thermal anchor, and the length of the tip clearance between the impeller and shroud. Developing the centrifugal cold compressor is a significant aspect of the EAST cryogenic system upgrades, and the preliminary tests reported herein demonstrate the promise of the retrofit project.
1. Introduction The Experimental Advanced Superconducting Tokamak (EAST), located in the Institute of Plasma Physics at the Chinese Academy of Sciences (ASIPP), is an advanced experimental device for steady-state plasma physics. The total cryogenic system at EAST is designed for a capacity of 1050 W/3.5 K + 200 W/4.5 K + 13 g/s liquid helium (LHe) +13 kW/80 K, the equivalent of 2 kW/4.5 K [1]. The subcooled helium at 3.5 K is obtained through an oil ring pump (ORP) at ambient temperature pumping saturated liquid helium (4.5 K). The centrifugal cold compressor (CC) will be used to pump saturated LHe, as it does not carry the ORP’s disadvantages due to low pressure in its piping and large flow. The comparison of OPR and CC is shown in Table 1. At present, many large-scale helium cryogenic systems have been built, and some of these systems are equipped with subcooled or superfluid helium systems. In 1988, a helium refrigerator with a capacity of 300 W/1.8 K was used in the TORE SUPRA to obtain superfluid helium by reducing the pressure of the supplied LHe from 120 to 1.5 kPa, and the superfluid helium system had 2 CCs and 2 ORP [2]. The cryogenic system at CERN-LHC in Geneva, with a capacity of 2.4 kW/ 1.8 K, was comprised of a warm compressor (WC) and 4 CCs [3–5]. The LHD cryogenic system pumped He from 120 to 47 kPa to reach subcooled helium at 50 g/s and 3.5 K in 2006 [6–8]. Many other subcooled or superfluid helium systems exist, but they are not listed because of space constraint [9–12]. This paper discusses the determination of critical parameters for a prospective CC to be installed at EAST, including the efficiency of heat exchanger (HX), the dimensions of a thermal anchor, and the optimum ⁎
tip clearance between the impeller and shroud. The efficiency of heat exchanger and the location of the thermal anchor are determined through theoretical calculations, and a numerical simulation is used to choose the optimal length of tip clearance between the impeller and shroud. It’s expected that an efficient and stable CC can be designed by determining these critical parameters. Furthermore, the theories in this paper can be used in the CC for superfluid helium (lower than 2.2 K). 2. The efficiency of heat exchanger As gas flows through the compressor, an impeller driven by three phase-asynchronous motors increases the pressure and velocity. Then, the gas flows through a diffuser and volute, and the gas velocity decreases while the gas pressure increases. If the outlet pressure is constant, the compressor can gradually reduce the input pressure for the liquid helium tank. A centrifugal CC produces subcooled helium by pumping helium gas from a saturated liquid tank. Heat is removed by the evaporation of liquid helium, thereby reducing the pressure and temperature of the liquid helium tank. The subcooled temperature of the tank reaches 3.5 K when the pressure drops to 0.47 bar. A flow chart for the subcooled helium system is shown in Fig. 1. Liquid helium in the saturated LHe tank is precooled as it flows through a HX into the subcooled LHe tank. The temperature of the subcooled LHe tank decreases when the CC pumps saturated helium gas. The gas helium flows through the HX, CC, and compressor in one cycle. To reach the subcooled temperature of 3.5 K, a one-stage CC can produce
Corresponding author at: Institute of Plasma Physics, Chinese Academy of Science, Hefei, 230031, People’s Republic of China. E-mail address: [email protected] (M. Geng).
https://doi.org/10.1016/j.fusengdes.2018.04.078 Received 28 December 2017; Received in revised form 20 March 2018; Accepted 19 April 2018 Available online 26 April 2018 0920-3796/ © 2018 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 131 (2018) 84–89
M. Geng et al.
Nomenclature
h P ε q0 q T UA NTU λ Q l
A D2 D0 d b2 N0 Mr m m* CC ORP LHe LN2 WC HX
Enthalpy [kJ/kg] Pressure [Pa] Heat exchanger efficiency Heat transfer per unit mass flow rate [kW/(kg/s)] Refrigeration capacity per unit mass flow rate [kW/(kg/s)] Temperature [K] Capacity of heat exchanger [W/K] Number of transfer units Thermal conductivity [W/m/K] Rate of heat transfer through [W] Length [mm]
HX. A JT HX clearly improves q, especially when the subcooled temperature is low. For example, compared with a system without an HX (ε = 0), q improves by 20.3% when the subcooled temperature is 3.5 K and ε is 1. When the subcooled temperature is higher, the effect is less dramatic. The HX efficiency has no effect on q when the subcooled temperature is 4.4 K. In general, when the subcooled temperature is low, a higher-efficiency HX is required. However, high-efficiency HXs are not cost-effective when the subcooled temperature is relatively high.
the required pressure ratio (about 2.13). Compared with a multistage CC, a one-stage CC works over a wider range of required pressures. Following the points marked in Fig. 1, the helium throttling process maintains constant enthalpy from point 2 to point 3, so that h2 = h3, where h is enthalpy. Typically, a maximum pressure drop of 100 Pa is acceptable, which corresponds to a few percent of the absolute saturation pressure for large cryogenic systems at 1.8 K. Under this condition, P1 = P2, P4 = P5, where P is pressure. Assuming that the HX does not cause any heat leakage (h1 − h2 = h5 − h4), the system is stable, so that the mass flow rates of cold and hot fluids are equal. When the refrigeration capacity is constant at 1050 W, the effects of subcooled temperature and HX efficiency on the volume flow rate are illustrated in Fig. 2. The volume flow rate clearly increases with decreasing subcooled temperature, so that increasing the HX efficiency will effectively reduce the flow rate. The volume flow rate through the currently installed WC is much higher than it is through the upgraded CC, which is one of the main reasons why ASIPP decided to improve the cryogenic system. ε, q0, and q are defined as
ε=
max(T1 − T2, T5 − T4 ) T1 − T4
Cross-sectional area [mm2] Impeller outlet diameter [mm] Impeller inlet diameter [mm] Hub diameter [mm] Impeller outlet tip width [mm] Rated speed [rpm] Reduced mass flow rate Mass flow rate [kg/s] Specific mass flow rate Cold compressor Oil ring pump Liquid helium Liquid nitrogen Warm compressor Heat exchanger
(1)
q0 = h1 − h2
(2)
q = h4 − h3
(3)
where T is the temperature at a point in the circuit, ε is the HX efficiency, q0 is the heat transfer per unit-mass-flow-rate in the HX, and q is refrigeration capacity divided by the unit mass flow rate. As shown in Fig. 3, heat transfer decreases with increasing subcooled temperature, and the relationship is almost linear. An increase in the subcooled temperature lowers the temperature difference, which decreases the rate of heat transfer. As the subcooled temperature decreases, HX efficiency has a more pronounced influence on heat transfer. As shown in Fig. 4, when ε = 1, the curve corresponds to the latent heat of vaporization of helium at different saturated temperatures. The effect of the HX is correlated with the subcooled temperature. The lower the subcooled temperature, the more obvious the impact of the Table 1 Comparison of ORP and CC. Parameters Volume flow mate (m /h) Input power (kW) Outlet temperature (K) Noise (dB) Weight (kg) Low pressure in piping 3
ORP
CC
3000 90 300 90 630 Yes
25.6 <2 ∼5 50 40 No
Fig. 1. Subcooled helium cryogenic system cycle. 85
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Fig. 4. Relationship between subcooled temperature and q for different ε values.
Fig. 5. UA and NTU with different ε.
such high-efficiency units uneconomical and substandard. These simulations show that an HX efficiency of 0.8 is reasonable when the desired subcooled temperature is 3.5 K, which is close to the temperature achieved by the HX at CERN’s LHC [13]. Compared with a system with no HX (ε = 0), q improves by 17.14% when the subcooled temperature is 3.5 K and ε is 0.8. UA with these parameters is 507 W/K, and NTU is 2.57, which are acceptable for the specifications needed at EAST.
Fig. 2. Volume flow rate versus subcooled temperature for different HX efficiencies (WC and CC).
3. Structure and heat leakage of the CC The structure of the proposed CC is shown in Fig. 6. A water-cooled motor operates at ambient temperature because of the electronics it requires. This means that a huge range of temperatures occur within the device (about 300 K, from 3.5 K to ambient temperature) because the impeller operates at less than 3.5 K. Thermal insulation is therefore crucial, as every 20 W of heat transfer decreases adiabatic efficiency by 1% [5]. To improve the insulation within the CC, several innovations are included. Special thermal-insulation materials lower the thermal conductivity to reduce the heat-transfer rate. A thermal anchor structure held at 80 K with LN2 effectively reduces heat leakage. The motor shaft is hollow and is manufactured as long as it can be within the specified vibration conditions. Fig. 7 shows a picture of the CC cartridge. The thermal anchor, cooled by LN2, intercepts heat on its way from the ambient environment to the cold gas, thereby improving the efficiency of the CC. The location of the thermal anchor obviously affects the heat leakage and the heat intercept. In this paper, the heat leakage and the heat intercept caused by varying locations of the thermal
Fig. 3. Subcooled temperature versus q0 for different ε values.
Increasing the HX efficiency improves the q value and decreases the mass-flow rate and power of the CC when the refrigeration capacity of the subcooled helium system remains constant. However, as shown in Fig. 5, the capacity of the HX (UA) and the number of transfer units (NTU) both increase rapidly with increasing HX efficiency. This increases the size of the unit and the pressure drop it causes, which makes 86
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Fig. 8. Size of G10 with a thermal anchor.
Fig. 6. Sectional drawing of the CC.
Fig. 9. Heat leakage and heat intercept with different l1/l ratios.
200 W of cooling capacity when cooled by LN2. Therefore, a thickness ratio of l1/l = 0.46 is chosen, which yields 11.66 W of heat leakage and 85.2 W intercepted. When l1/l > 0.5, the heat intercept increases quickly, but the heat leakage decreases slowly, which would unacceptably increase operating costs. The thermal anchor improves the heat insulation of the system by 70% over a G10 insulator without a thermal anchor (for which the heat leakage is 39.8 W).
Fig. 7. CC cartridge.
anchor are investigated. The size of G10 with a thermal anchor is shown in Fig. 8, where l0, l1, and l2 are the lengths of the thermal anchor, G10(1), and G10(2), respectively. D1 and D2 are the diameters of the G10(1) and G10(2) layers. The temperature of the thermal anchor, diameters of G10 and l are kept constant, the other dimensions are varied to optimize the system’s heat insulation capacity. The thermal conductivity of heat-insulating material (G10) changes with temperature, this relation is given as λ = f(t). The G10 material is separated into small layers along the direction of heat conduction, because the thermal conductivity of every piece is constant when the layers are sufficiently thin. Assuming that radiative heat leakage is negligibly small, heat transfer can be calculated according to the following equation:
Q = Aλi
λi = f (
ti + 1 − ti l
n
ti + 1 + ti )(1 ≤ i ≤ n) 2
(1 ≤ i ≤ n)
4. Tip clearance of the centrifugal compressor Compared with the compressor with closed impeller, there is a tip clearance between the blade and shroud in compressor with unshrouded impeller. In this work, various effects of mass flow and tip clearance on the EAST CC performance are investigated via CFD. As shown in Fig. 10, the impeller outlet diameter D2 is 100 mm, impeller inlet diameter D0 is 54 mm, impeller outlet tip width b2 is 6 mm, hub diameter d is 26 mm, the number of blades (includes splitter blades) is 18, and rated speed N0 = 18000 rpm. The tip clearance has values of 0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 mm. The density, dynamic viscosity and specific heat capacity of cold helium are redefined by the software Refprop. As depicted in Fig. 11, a single-passage steady state model is chosen for the numerical calculation model due to the circular symmetry of the impeller. A mesh generation software Turbo-grid is used to generate an H/J/C/L mixed grid, which is then imported to CFX to obtain the solution. The mesh number of the single-passage model is approximately 340,000. This is considered sufficiently reliable to ensure mesh independency by Fig. 12. The average y+ value is taken as 4 and a k-ε turbulence model is chosen to calculate the flow of cold helium. A special module Turbo-model in Ansys Workbench CFX is used to calculate the model. In the basic settings, the machine type is set as centrifugal compressor and the component type is set as a 18000 rpm rotating. The other basic settings are as follows:
(4) (5)
where Q is the rate of heat transfer through G10, A is the cross-sectional area, l is the length of G10, and λ is thermal conductivity. Eqs. (4) and (5) yield 2n independent equations, and if the number of unknown quantities(Q，ti(1 < i < = n), λi(1 < = i < = n))is no more than 2n, then Q can be calculated. Fig. 9 plots the heat leakage and heat intercepted by the thermal anchor for different ratios of l1/l. With increasing l1/l, the heat leakage decreases and the heat intercept increases. This means that as the thermal anchor intercepts more heat, heat insulation improves. However, the intercepted heat is limited by the size of the thermal anchor and the pressure drop. In reality, a thermal anchor can support less than
(1) Mass flow rate, total temperature, and no pre-whirl in inlet (2) Static pressure in outlet (3) No slip wall 87
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Fig. 10. Dimensions of impeller.
Fig. 13. Relationship between Mr and pressure ratio for different values of tip clearance.
Fig. 11. Single-passage steady state model of the impeller.
Fig. 14. Relationship between tip clearance and pressure ratio for different m*.
Pressure is highest around the design point when tip clearance is 0 mm. When deviating from the design point (Mr = 1), the performance curve for tip clearance of 0 mm is clearly seen to be steeper than other curves, with the result being a smaller stable operating range. The larger the tip clearance, the steeper the performance curve. Increasing clearance can delay the compressor entering the surge region when the mass flow rate is small. In the large mass flow rate region, the curves crosses due to compressor with 0 and smaller tip clearance more easily entering choke region, where the pressure ratio drops rapidly. A larger tip clearance can improve this situation, however, in general, an increase in tip clearance will result in the pressure ratio of the CC following a declining trend. For the CC and subcooled helium system, this means that the saturation pressure of the liquid helium tank increases with a corresponding increase in the subcooled temperature. As a result, the operational temperature required for EAST cannot be attained. The effect of various values of tip clearance on CC operation is depicted in Fig. 14. This figure illustrates pressure ratios with different values of m* as a function of tip clearance, where m* = m/m0, m* is the specific mass flow rate, m is mass flow rate, and m0 is mass flow rate at design point. When around the design mass flow(m* is 0.8–1.75), as shown is Fig. 14, pressure ratio decreases with an increase in tip clearance, and the relationship is nearly linear. In general, at design mass flow, when the tip clearance is increased by 0.1 mm the pressure ratio drops 2.5%. The tip clearance affects different compressors differently, so the data is accurate only for the sample CC. It should be noticed that curves are closer if CC deviates from the design point too much, especially when the tip clearance is small. It is difficult to effectively improve the
Fig. 12. Mesh independency investigation (pressure ratio and efficiency for different mesh number).
(4) Counter rotating wall on shroud (5) Tip clearance at shroud and no tip clearance at hub (6) Thermal insulating boundary conditions Convergence precision of all root mean square residuals is under 10E-5. Fig. 13 depicts the pressure ratio with different tip clearances as a function of reduced flow Mr defined as
Mr =
m m0
Tin Pin0 Tin0 Pin
(6)
Where m is the mass flow, Tin is the inlet temperature, Pin is the inlet pressure and the subscript 0 corresponds to the design conditions. 88
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intercepted by the thermal anchor is 85.2 W. A thermal anchor can therefore effectively improve the system’s thermal insulation. The CC performance with cold gas and warm gas is similar, and increasing the tip clearance decreases the pressure ratio. For the tested CC, when the tip clearance is increased by 0.1 mm, the pressure ratio and the polytropic efficiency drop by 2.5% and 1.64%, respectively. Considering safety, stability and economy, the value of tip clearance is 0.2 mm. This centrifugal CC will contribute significantly to improving the EAST cryogenic system, providing 3.5 K subcooled helium more efficiently than the currently installed oil ring pump. The design experience reported above can be drawn upon in the design of a larger cryogenic system in the future. Acknowledgment Fig. 15. Relationship between m* and polytropic efficiency for different values of tip clearance.
This work is supported by the Institute of Plasma Physics Foundation (NO. DSJJ-15-YY01)
pressure ratio when mass flow is smaller because of CC may entering surge region, especially when m* decreases from 0.806 to 0.639, the pressure ratio even decreases, unless there is bigger tip clearance. Fig. 14 further proves that tip clearance will improve the CC’s stability when the CC deviates from the design conditions. Fig. 15 depicts the polytropic efficiency versus m* for different values of tip clearance. Overall, polytropic efficiency decreases with increasing tip clearance. The structure of 0 mm tip clearance impeller and closed impeller are similar, but the polytropic efficiency of closed impeller is even lower than 0.1 mm impeller. Obviously, just like WC, a larger tip clearance will result in more flat performance curve but lower efficiency, they are irreconcilable. In general, at design mass flow (m* = 1), when the tip clearance is increased by 0.1 mm the polytropic efficiency drops 1.64%. In fact, the supplier promises that the vibration of the motor shaft is less than 0.15 mm in the axis direction and 0.06 mm in the radial direction. Compared with 0 tip clearance, when the tip clearance is 0.2 mm, the pressure ratio and the polytropic efficiency drop 5% and 3.28%, respectively, which is acceptable. It is not necessary to spend more money to buy a more sophisticated motor.
References [1] H.Y. Bai, Y.F. Bi, P. Zhu, et al., Cryogenics in EAST, Fusion Eng. Des. 81 (23) (2006) 2597–2603. [2] J.L. Duchateau, J.Y. Journeaux, F. Millet, Estimation of the recycled power associated with the cryogenic refrigeration power of a fusion reactor based on TORE SUPRA experiment and ITER design, Nucl. Fusion 46 (3) (2006) S94–S99. [3] B. Hilbert, G.M. Gistaubaguer, A. Caillaud, Air liquide 1.8 K refrigeration units for CERN LHC project, AIP Conf. Proc. 613 (1) (2002) 225–231. [4] F. Delcayre, J.C. Courty, F. Hamber, et al., Experimental results obtained with air liquide cold compression system: CERN LHC and SNS projects, AIP Conf. Proc. 823 (2006) 1829–1836. [5] G. Ferlin, L. Tavian, S. Claudet, et al., 5-year operation experience with the 1.8 K refrigeration units of the LHC cryogenic system, IOP Conf. Ser.: Mater. Sci. Eng. 101 (2015) 012141. [6] T. Mito, R. Maekawa, A. Iwamoto, et al., Performance of the LHD cryogenic system during cooling and excitation tests, IEEE Trans. Appl. Supercon. 10 (1) (2000) 1507–1510. [7] A. Komori, H. Yamada, O. Kaneko, et al., Overview of the large helical device, Plasma Phys. Contr. F 42 (11) (1999) 1165–1177. [8] S. Hamaguchi, T. Okamura, S. Imagawa, et al., Operation and control of helium subcooling system of LHD helical coils during change of rotational speed of cold compressors, IEEE Trans. Appl. Supercon. 20 (3) (2010) 2051–2053. [9] C.P. Dhard, M. Nagel, H. Bau, et al., Refrigerator operation during commissioning and first plasma operations of Wendelstein 7-X, Fusion Eng. Des. 123 (2017) 111–114. [10] C.H. Choi, H.S. Chang, D.S. Park, et al., Helium refrigeration system for the KSTAR, Fusion Eng. Des. 81 (2006) 2623–2631. [11] W.A. Maksoud, P. Bargueden, A. Bouty, et al., Status of the cold test facility for the JT-60SA tokamak toroidal field coils, Fusion Eng. Des. 96–97 (2015) 208–211. [12] V. Kalinin, E. Tada, F. Millet, et al., ITER cryogenic system, Fusion Eng. Des. 81 (2006) 2589–2595. [13] P. Roussel, A. Bézaguet, H. Bieri, et al., Performance tests of industrial prototype subcooling helium heat exchangers for the Large Hadron Collider, AIP Conf. Proc. 613 (1) (2002) 1429–1436.
5. Conclusion In comparison to a system without HXs, the per-unit mass flow of saturated liquid helium cooled by an HX can provide 17.14% more refrigeration capacity when the subcooled temperature is 3.5 K and ε is 80%. This increase in refrigeration capacity will obviously improve the overall system efficiency. When l1/l is 0.46, the heat leakage is 11.66 W and the heat
89
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Determination of critical parameters in the EAST subcooled helium system Maofei Geng a b
a,b,⁎
a
a
a
a
, Yuntao Song , Anyi Cheng , Hansheng Feng , Qiyong Zhang , Qingfeng Jiang
T
a,b
Institute of Plasma Physics, Chinese Academy of Science, Hefei, 230031, People’s Republic of China University of Science and Technology of China, Hefei, 230026, People’s Republic of China
A R T I C LE I N FO
A B S T R A C T
Keywords: Subcooled helium Cryogenic Cold compressor
The cryogenic system at the Experimental Advanced Superconducting Tokamak (EAST) is designed for a capacity of 1050 W/3.5 K + 200 W/4.5 K + 13 g/s liquid helium+ 13 kW/80 K. The 3.5 K subcooled helium is obtained from an oil ring pump. The cryogenic system is now being upgraded with a centrifugal cold compressor that should reduce the helium-tank pressure and temperature. This article discusses the determination of critical parameters for the cold compressor, including the efficiency of heat exchange, the location of the thermal anchor, and the length of the tip clearance between the impeller and shroud. Developing the centrifugal cold compressor is a significant aspect of the EAST cryogenic system upgrades, and the preliminary tests reported herein demonstrate the promise of the retrofit project.
1. Introduction The Experimental Advanced Superconducting Tokamak (EAST), located in the Institute of Plasma Physics at the Chinese Academy of Sciences (ASIPP), is an advanced experimental device for steady-state plasma physics. The total cryogenic system at EAST is designed for a capacity of 1050 W/3.5 K + 200 W/4.5 K + 13 g/s liquid helium (LHe) +13 kW/80 K, the equivalent of 2 kW/4.5 K [1]. The subcooled helium at 3.5 K is obtained through an oil ring pump (ORP) at ambient temperature pumping saturated liquid helium (4.5 K). The centrifugal cold compressor (CC) will be used to pump saturated LHe, as it does not carry the ORP’s disadvantages due to low pressure in its piping and large flow. The comparison of OPR and CC is shown in Table 1. At present, many large-scale helium cryogenic systems have been built, and some of these systems are equipped with subcooled or superfluid helium systems. In 1988, a helium refrigerator with a capacity of 300 W/1.8 K was used in the TORE SUPRA to obtain superfluid helium by reducing the pressure of the supplied LHe from 120 to 1.5 kPa, and the superfluid helium system had 2 CCs and 2 ORP [2]. The cryogenic system at CERN-LHC in Geneva, with a capacity of 2.4 kW/ 1.8 K, was comprised of a warm compressor (WC) and 4 CCs [3–5]. The LHD cryogenic system pumped He from 120 to 47 kPa to reach subcooled helium at 50 g/s and 3.5 K in 2006 [6–8]. Many other subcooled or superfluid helium systems exist, but they are not listed because of space constraint [9–12]. This paper discusses the determination of critical parameters for a prospective CC to be installed at EAST, including the efficiency of heat exchanger (HX), the dimensions of a thermal anchor, and the optimum ⁎
tip clearance between the impeller and shroud. The efficiency of heat exchanger and the location of the thermal anchor are determined through theoretical calculations, and a numerical simulation is used to choose the optimal length of tip clearance between the impeller and shroud. It’s expected that an efficient and stable CC can be designed by determining these critical parameters. Furthermore, the theories in this paper can be used in the CC for superfluid helium (lower than 2.2 K). 2. The efficiency of heat exchanger As gas flows through the compressor, an impeller driven by three phase-asynchronous motors increases the pressure and velocity. Then, the gas flows through a diffuser and volute, and the gas velocity decreases while the gas pressure increases. If the outlet pressure is constant, the compressor can gradually reduce the input pressure for the liquid helium tank. A centrifugal CC produces subcooled helium by pumping helium gas from a saturated liquid tank. Heat is removed by the evaporation of liquid helium, thereby reducing the pressure and temperature of the liquid helium tank. The subcooled temperature of the tank reaches 3.5 K when the pressure drops to 0.47 bar. A flow chart for the subcooled helium system is shown in Fig. 1. Liquid helium in the saturated LHe tank is precooled as it flows through a HX into the subcooled LHe tank. The temperature of the subcooled LHe tank decreases when the CC pumps saturated helium gas. The gas helium flows through the HX, CC, and compressor in one cycle. To reach the subcooled temperature of 3.5 K, a one-stage CC can produce
Corresponding author at: Institute of Plasma Physics, Chinese Academy of Science, Hefei, 230031, People’s Republic of China. E-mail address: [email protected] (M. Geng).
https://doi.org/10.1016/j.fusengdes.2018.04.078 Received 28 December 2017; Received in revised form 20 March 2018; Accepted 19 April 2018 Available online 26 April 2018 0920-3796/ © 2018 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 131 (2018) 84–89
M. Geng et al.
Nomenclature
h P ε q0 q T UA NTU λ Q l
A D2 D0 d b2 N0 Mr m m* CC ORP LHe LN2 WC HX
Enthalpy [kJ/kg] Pressure [Pa] Heat exchanger efficiency Heat transfer per unit mass flow rate [kW/(kg/s)] Refrigeration capacity per unit mass flow rate [kW/(kg/s)] Temperature [K] Capacity of heat exchanger [W/K] Number of transfer units Thermal conductivity [W/m/K] Rate of heat transfer through [W] Length [mm]
HX. A JT HX clearly improves q, especially when the subcooled temperature is low. For example, compared with a system without an HX (ε = 0), q improves by 20.3% when the subcooled temperature is 3.5 K and ε is 1. When the subcooled temperature is higher, the effect is less dramatic. The HX efficiency has no effect on q when the subcooled temperature is 4.4 K. In general, when the subcooled temperature is low, a higher-efficiency HX is required. However, high-efficiency HXs are not cost-effective when the subcooled temperature is relatively high.
the required pressure ratio (about 2.13). Compared with a multistage CC, a one-stage CC works over a wider range of required pressures. Following the points marked in Fig. 1, the helium throttling process maintains constant enthalpy from point 2 to point 3, so that h2 = h3, where h is enthalpy. Typically, a maximum pressure drop of 100 Pa is acceptable, which corresponds to a few percent of the absolute saturation pressure for large cryogenic systems at 1.8 K. Under this condition, P1 = P2, P4 = P5, where P is pressure. Assuming that the HX does not cause any heat leakage (h1 − h2 = h5 − h4), the system is stable, so that the mass flow rates of cold and hot fluids are equal. When the refrigeration capacity is constant at 1050 W, the effects of subcooled temperature and HX efficiency on the volume flow rate are illustrated in Fig. 2. The volume flow rate clearly increases with decreasing subcooled temperature, so that increasing the HX efficiency will effectively reduce the flow rate. The volume flow rate through the currently installed WC is much higher than it is through the upgraded CC, which is one of the main reasons why ASIPP decided to improve the cryogenic system. ε, q0, and q are defined as
ε=
max(T1 − T2, T5 − T4 ) T1 − T4
Cross-sectional area [mm2] Impeller outlet diameter [mm] Impeller inlet diameter [mm] Hub diameter [mm] Impeller outlet tip width [mm] Rated speed [rpm] Reduced mass flow rate Mass flow rate [kg/s] Specific mass flow rate Cold compressor Oil ring pump Liquid helium Liquid nitrogen Warm compressor Heat exchanger
(1)
q0 = h1 − h2
(2)
q = h4 − h3
(3)
where T is the temperature at a point in the circuit, ε is the HX efficiency, q0 is the heat transfer per unit-mass-flow-rate in the HX, and q is refrigeration capacity divided by the unit mass flow rate. As shown in Fig. 3, heat transfer decreases with increasing subcooled temperature, and the relationship is almost linear. An increase in the subcooled temperature lowers the temperature difference, which decreases the rate of heat transfer. As the subcooled temperature decreases, HX efficiency has a more pronounced influence on heat transfer. As shown in Fig. 4, when ε = 1, the curve corresponds to the latent heat of vaporization of helium at different saturated temperatures. The effect of the HX is correlated with the subcooled temperature. The lower the subcooled temperature, the more obvious the impact of the Table 1 Comparison of ORP and CC. Parameters Volume flow mate (m /h) Input power (kW) Outlet temperature (K) Noise (dB) Weight (kg) Low pressure in piping 3
ORP
CC
3000 90 300 90 630 Yes
25.6 <2 ∼5 50 40 No
Fig. 1. Subcooled helium cryogenic system cycle. 85
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Fig. 4. Relationship between subcooled temperature and q for different ε values.
Fig. 5. UA and NTU with different ε.
such high-efficiency units uneconomical and substandard. These simulations show that an HX efficiency of 0.8 is reasonable when the desired subcooled temperature is 3.5 K, which is close to the temperature achieved by the HX at CERN’s LHC [13]. Compared with a system with no HX (ε = 0), q improves by 17.14% when the subcooled temperature is 3.5 K and ε is 0.8. UA with these parameters is 507 W/K, and NTU is 2.57, which are acceptable for the specifications needed at EAST.
Fig. 2. Volume flow rate versus subcooled temperature for different HX efficiencies (WC and CC).
3. Structure and heat leakage of the CC The structure of the proposed CC is shown in Fig. 6. A water-cooled motor operates at ambient temperature because of the electronics it requires. This means that a huge range of temperatures occur within the device (about 300 K, from 3.5 K to ambient temperature) because the impeller operates at less than 3.5 K. Thermal insulation is therefore crucial, as every 20 W of heat transfer decreases adiabatic efficiency by 1% [5]. To improve the insulation within the CC, several innovations are included. Special thermal-insulation materials lower the thermal conductivity to reduce the heat-transfer rate. A thermal anchor structure held at 80 K with LN2 effectively reduces heat leakage. The motor shaft is hollow and is manufactured as long as it can be within the specified vibration conditions. Fig. 7 shows a picture of the CC cartridge. The thermal anchor, cooled by LN2, intercepts heat on its way from the ambient environment to the cold gas, thereby improving the efficiency of the CC. The location of the thermal anchor obviously affects the heat leakage and the heat intercept. In this paper, the heat leakage and the heat intercept caused by varying locations of the thermal
Fig. 3. Subcooled temperature versus q0 for different ε values.
Increasing the HX efficiency improves the q value and decreases the mass-flow rate and power of the CC when the refrigeration capacity of the subcooled helium system remains constant. However, as shown in Fig. 5, the capacity of the HX (UA) and the number of transfer units (NTU) both increase rapidly with increasing HX efficiency. This increases the size of the unit and the pressure drop it causes, which makes 86
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Fig. 8. Size of G10 with a thermal anchor.
Fig. 6. Sectional drawing of the CC.
Fig. 9. Heat leakage and heat intercept with different l1/l ratios.
200 W of cooling capacity when cooled by LN2. Therefore, a thickness ratio of l1/l = 0.46 is chosen, which yields 11.66 W of heat leakage and 85.2 W intercepted. When l1/l > 0.5, the heat intercept increases quickly, but the heat leakage decreases slowly, which would unacceptably increase operating costs. The thermal anchor improves the heat insulation of the system by 70% over a G10 insulator without a thermal anchor (for which the heat leakage is 39.8 W).
Fig. 7. CC cartridge.
anchor are investigated. The size of G10 with a thermal anchor is shown in Fig. 8, where l0, l1, and l2 are the lengths of the thermal anchor, G10(1), and G10(2), respectively. D1 and D2 are the diameters of the G10(1) and G10(2) layers. The temperature of the thermal anchor, diameters of G10 and l are kept constant, the other dimensions are varied to optimize the system’s heat insulation capacity. The thermal conductivity of heat-insulating material (G10) changes with temperature, this relation is given as λ = f(t). The G10 material is separated into small layers along the direction of heat conduction, because the thermal conductivity of every piece is constant when the layers are sufficiently thin. Assuming that radiative heat leakage is negligibly small, heat transfer can be calculated according to the following equation:
Q = Aλi
λi = f (
ti + 1 − ti l
n
ti + 1 + ti )(1 ≤ i ≤ n) 2
(1 ≤ i ≤ n)
4. Tip clearance of the centrifugal compressor Compared with the compressor with closed impeller, there is a tip clearance between the blade and shroud in compressor with unshrouded impeller. In this work, various effects of mass flow and tip clearance on the EAST CC performance are investigated via CFD. As shown in Fig. 10, the impeller outlet diameter D2 is 100 mm, impeller inlet diameter D0 is 54 mm, impeller outlet tip width b2 is 6 mm, hub diameter d is 26 mm, the number of blades (includes splitter blades) is 18, and rated speed N0 = 18000 rpm. The tip clearance has values of 0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 mm. The density, dynamic viscosity and specific heat capacity of cold helium are redefined by the software Refprop. As depicted in Fig. 11, a single-passage steady state model is chosen for the numerical calculation model due to the circular symmetry of the impeller. A mesh generation software Turbo-grid is used to generate an H/J/C/L mixed grid, which is then imported to CFX to obtain the solution. The mesh number of the single-passage model is approximately 340,000. This is considered sufficiently reliable to ensure mesh independency by Fig. 12. The average y+ value is taken as 4 and a k-ε turbulence model is chosen to calculate the flow of cold helium. A special module Turbo-model in Ansys Workbench CFX is used to calculate the model. In the basic settings, the machine type is set as centrifugal compressor and the component type is set as a 18000 rpm rotating. The other basic settings are as follows:
(4) (5)
where Q is the rate of heat transfer through G10, A is the cross-sectional area, l is the length of G10, and λ is thermal conductivity. Eqs. (4) and (5) yield 2n independent equations, and if the number of unknown quantities(Q，ti(1 < i < = n), λi(1 < = i < = n))is no more than 2n, then Q can be calculated. Fig. 9 plots the heat leakage and heat intercepted by the thermal anchor for different ratios of l1/l. With increasing l1/l, the heat leakage decreases and the heat intercept increases. This means that as the thermal anchor intercepts more heat, heat insulation improves. However, the intercepted heat is limited by the size of the thermal anchor and the pressure drop. In reality, a thermal anchor can support less than
(1) Mass flow rate, total temperature, and no pre-whirl in inlet (2) Static pressure in outlet (3) No slip wall 87
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Fig. 10. Dimensions of impeller.
Fig. 13. Relationship between Mr and pressure ratio for different values of tip clearance.
Fig. 11. Single-passage steady state model of the impeller.
Fig. 14. Relationship between tip clearance and pressure ratio for different m*.
Pressure is highest around the design point when tip clearance is 0 mm. When deviating from the design point (Mr = 1), the performance curve for tip clearance of 0 mm is clearly seen to be steeper than other curves, with the result being a smaller stable operating range. The larger the tip clearance, the steeper the performance curve. Increasing clearance can delay the compressor entering the surge region when the mass flow rate is small. In the large mass flow rate region, the curves crosses due to compressor with 0 and smaller tip clearance more easily entering choke region, where the pressure ratio drops rapidly. A larger tip clearance can improve this situation, however, in general, an increase in tip clearance will result in the pressure ratio of the CC following a declining trend. For the CC and subcooled helium system, this means that the saturation pressure of the liquid helium tank increases with a corresponding increase in the subcooled temperature. As a result, the operational temperature required for EAST cannot be attained. The effect of various values of tip clearance on CC operation is depicted in Fig. 14. This figure illustrates pressure ratios with different values of m* as a function of tip clearance, where m* = m/m0, m* is the specific mass flow rate, m is mass flow rate, and m0 is mass flow rate at design point. When around the design mass flow(m* is 0.8–1.75), as shown is Fig. 14, pressure ratio decreases with an increase in tip clearance, and the relationship is nearly linear. In general, at design mass flow, when the tip clearance is increased by 0.1 mm the pressure ratio drops 2.5%. The tip clearance affects different compressors differently, so the data is accurate only for the sample CC. It should be noticed that curves are closer if CC deviates from the design point too much, especially when the tip clearance is small. It is difficult to effectively improve the
Fig. 12. Mesh independency investigation (pressure ratio and efficiency for different mesh number).
(4) Counter rotating wall on shroud (5) Tip clearance at shroud and no tip clearance at hub (6) Thermal insulating boundary conditions Convergence precision of all root mean square residuals is under 10E-5. Fig. 13 depicts the pressure ratio with different tip clearances as a function of reduced flow Mr defined as
Mr =
m m0
Tin Pin0 Tin0 Pin
(6)
Where m is the mass flow, Tin is the inlet temperature, Pin is the inlet pressure and the subscript 0 corresponds to the design conditions. 88
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intercepted by the thermal anchor is 85.2 W. A thermal anchor can therefore effectively improve the system’s thermal insulation. The CC performance with cold gas and warm gas is similar, and increasing the tip clearance decreases the pressure ratio. For the tested CC, when the tip clearance is increased by 0.1 mm, the pressure ratio and the polytropic efficiency drop by 2.5% and 1.64%, respectively. Considering safety, stability and economy, the value of tip clearance is 0.2 mm. This centrifugal CC will contribute significantly to improving the EAST cryogenic system, providing 3.5 K subcooled helium more efficiently than the currently installed oil ring pump. The design experience reported above can be drawn upon in the design of a larger cryogenic system in the future. Acknowledgment Fig. 15. Relationship between m* and polytropic efficiency for different values of tip clearance.
This work is supported by the Institute of Plasma Physics Foundation (NO. DSJJ-15-YY01)
pressure ratio when mass flow is smaller because of CC may entering surge region, especially when m* decreases from 0.806 to 0.639, the pressure ratio even decreases, unless there is bigger tip clearance. Fig. 14 further proves that tip clearance will improve the CC’s stability when the CC deviates from the design conditions. Fig. 15 depicts the polytropic efficiency versus m* for different values of tip clearance. Overall, polytropic efficiency decreases with increasing tip clearance. The structure of 0 mm tip clearance impeller and closed impeller are similar, but the polytropic efficiency of closed impeller is even lower than 0.1 mm impeller. Obviously, just like WC, a larger tip clearance will result in more flat performance curve but lower efficiency, they are irreconcilable. In general, at design mass flow (m* = 1), when the tip clearance is increased by 0.1 mm the polytropic efficiency drops 1.64%. In fact, the supplier promises that the vibration of the motor shaft is less than 0.15 mm in the axis direction and 0.06 mm in the radial direction. Compared with 0 tip clearance, when the tip clearance is 0.2 mm, the pressure ratio and the polytropic efficiency drop 5% and 3.28%, respectively, which is acceptable. It is not necessary to spend more money to buy a more sophisticated motor.
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5. Conclusion In comparison to a system without HXs, the per-unit mass flow of saturated liquid helium cooled by an HX can provide 17.14% more refrigeration capacity when the subcooled temperature is 3.5 K and ε is 80%. This increase in refrigeration capacity will obviously improve the overall system efficiency. When l1/l is 0.46, the heat leakage is 11.66 W and the heat
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