- Email: [email protected]
MHD pressure drop measurement of PbLi flow in double-bended pipe
Fusion Engineering and Design xxx (xxxx) xxx–xxx
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Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
MHD pressure drop measurement of PbLi flow in double-bended pipe ⁎
Shoki Nakamuraa, Tomoaki Kunugia, , Takehiko Yokominea, Zensaku Kawaraa, Koji Kusumia, Akio Sagarab, Juro Yagib, Teruya Tanakab a b
Department of Nuclear Engineering, Kyoto University, Kyoto-Daigaku Katsura, Nishikyo-Ku, Kyoto, 615-8540, Japan National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Liquid blanket Experiment PbLi Oroshhi-2 facility Double-bended pipe MHD friction loss coefficient
The design of liquid metal cooling system for the liquid blanket concepts in magnetic fusion reactor requires the magnetohydrodynamics (MHD) friction loss coefficients for various pipes including pipes and bents to estimate the pressure drop of the whole blanket. The aim of this study is to reveal the MHD pressure drop of PbLi flow in a double-bended pipe. The experiments were conducted in the Oroshhi-2 loop having a super conducting magnet of 3T at NIFS in Japan. In this paper, the MHD pressure drops of the pipe under the magnetic field of 0.5T–3.0T, the ranges of Reynolds number (Re) of 2000–200,000 and Hartmann number (Ha) of 106–640 at the upstream, double-bended and downstream regions were measured. As the results, all the MHD friction loss coefficients in three regions were well correlated with the interaction parameter (Na = Ha2/Re) in the range of 0.1 < N < 100. Finally, the correlation equations of MHD friction loss coefficient against the interaction parameters at the upstream, double-bended and downstream regions of the pipe were obtained. Moreover, it was briefly discussed on the implementation to the liquid metal cooling system design for fusion reactor.
1. Introduction In various liquid blanket concepts in magnetic fusion reactor such as the dual-coolant lead-lithium (DCLL) and self-cooled lead lithium (SCLL) [1], helium-cooled lead-lithium (HCLL) [2] and water-cooled lithium-lead (WCLL) blankets [3], the design of liquid metal cooling system requires the magnetohydrodynamics (MHD) friction loss coefficients for various pipes including pipes and bents to estimate the MHD pressure drop of the whole blanket system. Many studies regarding the MHD pressure drop in various shape pipes and manifolds have been conducted, and the substantial summary until 1994 was reported in [4]. The liquid metals used in those studies were Sodium (Na), Sodium-Potasium (NaK), Lithium (Li), Mercury (Hg) and Galinstan (GaInSn). In the application for the fusion reactors, Li and Lead-Lithium (PbLi) are the candidates as the primary coolant because of tritium production. Li is firstly the best candidate, but its flammable nature is a big issue for the reactor safety. Although PbLi is a heavy metal and needs the high pumping power, it has less fire problem. So, PbLi is the better candidate material of liquid blanket coolant, but to our knowledge only three PbLi MHD pressure drop measurements in a straight pipe [5], a duct [6] and a rectangular curved duct [7] have been reported. As for the U-turn pipe, bent and manifold, several studies using Na, NaK, Hg and GaInSn were reported in [4], but no usage of Li and PbLi until today. ⁎
The aim of this experimental study is to reveal the MHD pressure drop characteristics of PbLi flow in a double-bended pipe. This doublebended pipe was installed in Oroshhi-2 (Operational Recovery Of Separated Hydrogen and Heat Inquiry-2) PbLi flow loop with 3T superconducting (SC) magnet [8]. At first, the pressure drops in the double-bended pipe without magnetic field were measured as the shakedown test. As the results, the non-MHD friction loss coefficients in the upstream and downstream regions were correlated to Reynolds number (Re = 2Ua/ν, U is mean velocity, a is pipe radius and ν is kinematic viscosity), but that in the double-bended region did not depend on Re, i.e., it kept constant caused by the centrifugal force. The MHD pressure drops of the pipe under the magnetic field B of 0.5T ∼ 3.0T, the ranges of Re (Re = Ua/ν, the characteristic length is a in case of MHD flow) of 2000–200,000 and Hartmann number (Ha = Ba (σ/ν)1/2 , σ is electrical conductivity) of 106–640 at the upstream, double-bended and downstream regions were measured, and were coincident to the theoretical value within around 20%, and those in the double-bended region were around 10% larger than the theoretical value except in case of 0.5T. Moreover, all MHD friction loss coefficients in three regions were well correlated with an interaction parameter N (the square of Hartmann number divided by Re: Ha2/Re) in the range of 2000 < Re < 200,000 and 0.1 < N < 100. The correlation equations of MHD friction loss coefficient against N at the upstream, double-bended and downstream regions of the pipe were obtained. At last, it was briefly discussed on the
Corresponding author. E-mail address: [email protected] (T. Kunugi).
https://doi.org/10.1016/j.fusengdes.2017.12.009 Received 8 November 2017; Received in revised form 7 December 2017; Accepted 9 December 2017 0920-3796/ © 2017 Elsevier B.V. All rights reserved.
Please cite this article as: Nakamura, S., Fusion Engineering and Design (2017), https://doi.org/10.1016/j.fusengdes.2017.12.009
Fusion Engineering and Design xxx (xxxx) xxx–xxx
S. Nakamura et al.
implementation to the liquid metal cooling system design for fusion reactor.
Table 1 Typical physical properties. Working fluid Density [kg m−3] Dynamic viscosity [Pa s] Kinematic viscosity [m2 s−1] Electrical conductivity (PbLi) [Ω−1 m−1] Electrical conductivity (SUS316) [Ω−1 m−1]
2. Experiments 2.1. Oroshhi-2 PbLi loop and test section The Oroshhi-2 PbLi loop [8] consists of a SC electromagnet (JASTEC, Japan), an electromagnetic (EM) pump, an EM flow meter, a PbLi flow loop, a melting/dump tank, a temperature control system: power supplies, heaters, and insulations. The PbLi main loop which is made of SUS316 has 40.8 mm of the inner diameter and the loop’s operational temperature is up to 320 °C. Maximum flow rates are 50 L min−1 without magnetic field and 18 L min−1 with magnetic field of 3.0 T, respectively. The horizontal penetration duct of the superconducting magnet was 210 mm × 165 mm, and the thermal insulator of pipe is composed of two materials: the first layer is a ceramic fiber blanket and the second layer is a rock wool. Since the superconducting magnet needs to be cooled at 5.1 K to generate 3.0 T, the surface temperature of test section must be kept at lower than 50 °C. This is the reason why the inner diameter of the pipe of 16.1 mm is designed by considering the insulator thickness. The Outer diameter (OD) of test section is 21.7 mm, the inner diameter of the double-bended pipe is 2a = 16.1 mm and that of the pressure-tap is 10.2 mm, which is quite large compared to the ordinal tap-diameter because the PbLi easily freezes at the pressure tap. The curvature radius of the bent is R = 38.1 mm. Fig. 1(a) shows the Orosshi-2 SC electromagnet, the test section including a double-bended pipe and four pressure taps (D-C: Upstream region: C-B: Double-bended region, B-A: Downstream region). The test section consists of five pipes denoted by the framed number 1–5 in Fig. 1(a). Frame # 1 and #5 pipes connects to the main loop of 40.8 mm in the inner diameter with a reducer and a diffuser, respectively. The pressure taps connect to the differential pressure gauge to measure the pressure drop. Fig. 1(b) shows the magnetic field profile and the locations of the pressure taps at B and C of doublebended pipe are indicated. The bore diameter is 745 mm and the double-bended region is located at the constant magnetic field region. On the other hand, the upstream and downstream parts of the test
PbLi at about 320 °C 9.50 × 103 at 300 °C 1.10 × 10−3 at 300 °C 1.15789 × 10−7 at 300 °C 7.70 × 105 at 300 °C 1.075 × 106 at300 °C
section have the fringe magnetic field, the magnetic field increasing in D-C and that decreasing in B-A. The experimental conditions were in the ranges of the magnetic field (B) from 0.5T to 3.0T, Re from 2000 to 200,000 (maximum flow rate was 18 Liters per min) and Ha from 106 to 640. Thus, N is the range from 0.1 to 100. The typical physical properties of the Oroshhi-2 PbLi loop are tabulated in Table 1. 2.2. Pressure drop measurement The measuring procedure of pressure drop was the same as Li’s method [5]. The diameter of differential pressure tap lines were ϕ12.7 mm × t1.24 mm (length about 2 m), and it connected to the differential pressure measurement-unit lines are ϕ6.35 mm × t0.89 mm (length about 8 m). The differential pressure tap and measurement-unit lines were firstly filled with Ar gas, and the levels of PbLi in each line were the same because of no-flow. When the flow starts, the liquid levels of PbLi in the upstream and downstream gas lines were different. So, the differential pressure of Ar between upstream and downstream lines were measured. The differential pressure measurement unit consisted of two differential pressure gauges: GC55 and GC50 (Nagano Keiki, Japan). The specifications of each differential pressure gauge are as follows: for GC55, the differential pressure measurement range (Δp) is −1.0 MPa–1.0 MPa, and the accuracy of ± (1.0%F. S. +1digit) , and for GC50, Δp is ± 10kPa, and the accuracy of ± (1.0%F. S. +1digit) . 3. Friction loss coefficient and MHD pressure gradient In this experiment, the friction loss coefficients of PbLi pipe flow were obtained and compared to the well-known Blasius’ correlation in case of no-magnetic field. Blasius’ correlation is expressed as,
f = 0.0791Re−0.25 (Re < 105)
(1)
and the friction loss coefficient of pipe is defined as,
f = d Δp /2ρLU 2
(2)
here, Δp, ρ, L are the pressure drop, the density and the flow length between the pressure taps, respectively. The theoretical estimation of MHD pressure drop (ΔpMHD) was derived by Miyazaki et al. [9],
Δp MHD = Kp
∫
σf UB2 (x ) dx
(3)
here, x is the streamwise coordinate, σf is an electrical conductivity of fluid, Kp is an effective load resistance and a function of the wall conductance ratio, C:
Kp = C/(1 + C ), C = σw (Ro2 − Ri 2)/ σf (Ro2 + Ri 2)
(4)
here, σw, Roand Ri are an electrical conductivity of wall, the outer and inner radius, respectively. Finally, the MHD pressure gradient (dp / dx ) MHD can be written as the function of B2 as follows:
(dp / dx ) MHD = Kp σf UB2
Fig. 1. (a) Orosshi-2 SC electromagnet, test section and pressure-tap locations (A-D) (b) Magnetic field profile and pressure taps of B & C of double-bended pipe.
In this study, the theoretical value of Kp is 0.287. 2
(5)
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Fig. 2. Relation between pressure drop and Re in (a) Upstream region, (b) Downstream region and (c) Double-bended region.
4. Results and discussions
According to Fig. 3(a), the friction loss coefficient correlation in the upstream region is similar to Blasius’ correlation of Eq. (1): it means the power of Re is the same, but the coefficient is twice larger. Because the size of the pressure taps is close to the test pipe diameter, the pressure loss coefficient became large. The friction loss coefficient correlation in the downstream region as shown in Fig. 3(b) is rather different from the Blasius’ correlation. This is because the friction loss coefficient in the double-bended region is kept constant as shown in Fig. 3(c). In the double-bended region, the flow receives a strong acceleration due to centrifugal force, so the pressure drop is caused by the
4.1. Shakedown results without magnetic field Fig. 2 (a–c) shows the relation under no-magnetic flied between the pressure drop and Re in the upstream, downstream and double-bended regions, respectively. The pressure drop in all regions are almost proportional to Re2. This means that the pressure drop (Δp) is proportional to the kinetic energy(ρU 2) is proportional, i.e., the pressure loss can be represented by the friction loss coefficient (f) as shown in Fig. 3.
Fig. 3. Relation between friction loss coefficients and Re in (a) Upstream region, (b) Downstream region and (c) Double-bended region.
3
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acceleration force, not the viscous drag. If the pressure gradient along the mainstream can balance to the acceleration force, the following relation for the 90° bent with the curvature (1/R) can be written:
Δp / L ∼ ρU 2/ R,
(6)
and the friction loss coefficient (f90° (2) as follows:
bent)
is expressed by using Eq.
f90obent = d Δp /2ρLU 2 ∼ d/2R f90°
(7)
The friction loss coefficient f of the double-bended region is twice of bent,
f = 2 × f90obent ∼ 2 × d/2R = d/ R
(8)
Finally, the friction loss coefficient in the double-bended region can be expressed as:
f = α (d/ R)
Fig. 5. B2-scaling trend of MHD pressure drops in double-bended region against Re.
(9)
According to Fig. 3(c), f = 0.013. Therefore, the coefficient α can be obtained about 0.03. However, this coefficient is not the universal value, so the experiments with various ratio of the pipe diameter to the curvature must be conducted in the future. 4.2. MHD pressure drop measurements Fig. 4 shows the pressure drop under the magnetic fields of from 0.5T to 3.0T in the double-bended region of the double-bended pipe against various Reynolds numbers. The pressure drops under each magnetic field condition linearly increase with increase of Reynolds number (i.e., volumetric flowrate). The increase rates of the pressure loss also increased with increase of the magnetic field strength, and eventually decreased the flowrate. This tendency is very different from the pressure loss of the ordinary bent pipe, which is caused by the centrifugal force due to the curved flow in the bent described in the previous section.
Δp MHD = Kp
∫
σf UB2 (x ) dx
Kp = C /(1 + C ), C = σw (Ro 2 − Ri 2)/ σf (Ro 2 + Ri 2) Finally, the MHD pressure gradient function of B2 as follows:
Fig. 6. Relation between measured pressure gradient and the theoretical value in doublebended region.
(10)
(dp / dx ) MHD
(11)
is 0.287. The MHD pressure gradient in the double-bended pipe showed a linear relationship to the product of mean velocity and a square of the magnetic field strength, and the effective load resistance Kp of the double-bended pipe was 25% larger than the theoretical value except in case of 0.5T (denoted the open circle).
can be written as the
(dp / dx ) MHD = Δp MHD / L = Kp σf UB2
(12)
The MHD pressure drops by B2-scaling (Δp MHD /B2) under various magnetic fields are very well correlated to Re as shown in Fig. 5. The measured MHD pressure drops are around 10% larger than the theoretical value obtained by Eq. (10) except in case of 0.5T (denoted the open circle). Fig. 6 shows the relation between the measured pressure gradient (dp / dx ) MHD = Δp MHD / L and the theoretical value of σfUB2 in the double-bended region. According to Eq. (11), the theoretical value of Kp
4.3. Correlations of MHD friction loss coefficient It is useful to evaluate a friction loss coefficient under the magnetic field compared to an ordinary (no magnetic field) friction loss coefficient for the pipe, because these coefficients are the non-dimensional quantity. In this paper, the Fanning’s formula is used to evaluate the MHD pressure drop as follows:
f MHD =
Δp a ⎛ ⎞, 2ρU 2 ⎝ L ⎠
(13)
here, f is MHD friction loss coefficient, ρ is density and L is pipe centerline length. The non-dimensional equation of motion for MHD flow are expressed as: MHD
∂u 1 2 Ha2 + (u·∇) u = −∇p + ∇u+ (J × B ) ∂t Re Re
(14)
The force balance between the pressure gradient and the Lorentz force if the velocity is small can be expressed as,
∇p ∼ Fig. 4. MHD pressure drop versus Re at double-bended region.
4
Ha2 (J × B ) Re
(15)
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Fig. 7. Relationships between fMHD and Re in (a) upstream region, (b) double-bended region and (c) Downstream region.
Therefore, the data were plotted against N as shown in Fig. 8. All the MHD friction loss coefficients fMHD were well correlated, and proportional to N. Finally, the correlations of MHD friction loss coefficient of the double-bended pipe were obtained as follows:
Thus, the MHD friction loss coefficient can be derived as,
f MHD
∼ ∇p/(J × B ) ∼
Ha2/Re
(16)
If the magnetic field is constant (Ha = constant), the above relation can be rewritten as:
f MHD ∼ 1/Re.
(17)
In the experiments, fMHD in three regions (upstream, double-bended and downstream) of the double-bended pipe against various Reynolds numbers were measured. Fig. 7 shows the relationships between fMHD and Re in (a) upstream region, (b) double-bended region and (c) downstream region, respectively. In the figure, fMHD seems to be inversely-proportional to Re in each constant magnetic field condition except the cases of higher magnetic fields (2.5T and 3.0T) and lower Re conditions (Re < 5000). These results under the constant magnetic field conditions confirmed Eq. (17) to be correct, and meant that the flow is a laminar flow and fMHD decreases with increase of Re. This tendency is like the ordinary laminar flow without magnetic field effect. According to the B2-scaling as shown in Fig. 5, Eq. (16) can be rewritten as,
f MHD ∼ Ha2/Re = N.
MHD fUpstream ∼ 0.05N in the upper stream region,
(19-1)
MHD f Double ∼ 0.075N in the double-bended region and, − bended
(19-2)
MHD f Downstream ∼ 0.05N in the downstream region.
(19-3)
According to these correlations, the MHD pressure loss in the double-bended region is 50% larger than that in the upstream and downstream regions. This is a very important information for the liquid metal cooling system design of fusion reactors. 4.4. Consideration on MHD flow characteristics in double-bended pipe As described in 4.2, the constant magnetic fields were applied in this experiment, and the increase rates of the MHD pressure loss increased with increase of the magnetic field strength, but decreased the flowrate (Re). The centrifugal force due to the curved flow in the double-bended
(18) 5
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Fig. 8. Relationships between fMHD and N in (a) upstream region, (b) double-bended region and (c) downstream region.
pipe caused the pressure drop in the bent pipe without the magnetic field. However, the MHD pressure drops in the double-bended pipe strongly depended on the flowrate (Re). Thus, it can be said that the centrifugal force may not be influenced on the MHD pressure drop in the double-bended pipe. According to Eq. (19), the MHD pressure loss coefficients fMHD in all regions are linearly proportional to N, so the thickness of Robert layer becomes thinner and the velocity becomes large with increase of Re if the magnetic field is constant. In other words, the fMHD linearly increases with increase of the magnetic field strength if the flowrate (Re) is constant. Therefore, the higher N causes the higher viscous drag in Roberts layer, so the fMHD in the doublebended pipe shows the linear relation to N, not independent to Re.
cooling system in the magnetic fusion reactors. To reduce the MHD pressure loss, it is necessary to use the electric insulation material for the pipes or the electric insulation coating on the inner wall of the pipes. However, the electric insulator has also less thermal conductivity, eventually the heat removal becomes a major problem. One of the design solutions is to prevent the current path across the flow channel, i.e., the electric insulator partially coats the inner pipe, such as the electric insulation coating on the half wall surface of the pipe, not the whole wall. It might be expected to reduce the MHD pressure loss and keep certain the heat removal capability.
5. Implementation to liquid metal cooling system design
In this paper, the MHD pressure drops of the pipe under the magnetic field of 0.5T-3.0T, Re = 2000–200,000 and Ha = 106–640 at the upstream, double-bended and downstream regions were measured. As the results, the MHD pressure gradient in the double-bended pipe showed a linear relationship to the product of mean velocity, and a square of the magnetic field strength, the effective load resistance Kp of the double-bended pipe was 25% larger than the theoretical value. All the MHD friction loss coefficients in three regions were well correlated with the interaction parameters (N= Ha2/Re) in the range of 0.1 < N < 100. Finally, the correlation equations of MHD friction loss coefficient fMHD against the interaction parameter N at the upstream, double-bended and downstream regions of the pipe were obtained. Based on the obtained data, the MHD flow characteristics in doublebended pipe were discussed. Moreover, it was briefly discussed on the implementation to the liquid metal cooling system design for fusion reactor.
6. Conclusions
The pressure loss coefficient in the double-bended region without magnetic field does not depend on Re and showed the constant as described in the Section 4.1:
f non − MHD =
Δp 2a ⎛ ⎞ = 0.013 2ρU 2 ⎝ L ⎠
(20)
The ratio of the MHD friction loss coefficient to the non-MHD one is,
f MHD / f non − MHD = 0.075N/(0.013/2) = 11.5N.
(21)
For example, the parameters of PbLi self-cooling liquid blanket are Re = 2.0 × 105 and Ha = 104, the interaction parameter will be N = 500. According to Eq. (21), the MHD pressure loss compared to the ordinary bent pipe is around 6000 times larger than the ordinary double-bended pipe. This is an inevitable problem of liquid metal 6
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Acknowledgement [5]
This work is performed with the support and under the auspices of the NIFS collaboration research program in Japan (NIFS16KERF035).
[6]
References [7] [1] S. Malang, M. Tillack, C.P.C. Wong, N. Morley, S. Smolentsev, Development of the lead lithium (DCLL) blanket concept, Fus. Sci. Technol. 60 (2011) 249–256. [2] G. Rampal, A. Li Puma, Y. Poitevin, E. Rigal, J. Szczepanski, C. Boudot, HCLL TBM for ITER-design studies, Fus. Eng. Des. 75–79 (2005) 917–922. [3] L. Giancarli, L. Baraer, P. Leroy, J. Mercier, E. Proust, Y. Severi, et al., Water-cooled lithium-lead blanket design studies for DEMO reactor: definition and recent developments of the box-shaped concept, Fus. Technol. 21 (1992) 2081–2088. [4] I.R. Kirillov, C.B. Reed, L. Barleon, K. Miyazaki, Present understanding of MHD and
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heat transfer phenomena for liquid metal blankets, Fus. Eng. Des. 27 (1994) 553–569. F.-C. Li, D. Sutevski, S. Smolentsev, M. Abdou, Experimental and numerical studies of pressure drop in PbLi flows in a circular duct under non-uniform transverse magnetic field, Fus. Eng. Des. 88 (2013) 3060–3071. Z. Meng, Z. Zhu, J. He, M. Ni, Experimental studies of MHD pressure drop of PbLi flow in rectangular pipes under uniform magnetic field, J. Fus. Energy 34 (2015) 759–764. S. Ivanov, MHD PbLi loop at IPUL, Proceedings of The 9-th International PAMIR Conference on Fundamental and Applied MHD, Thermo Acoustic Space Technol. Riga, Latvia, 2014. A. Sagara, T. Tanaka, J. Yagi, M. Takahashi, K. Miura, T. Yokomine, S. Fukada, S. Ishiyama, First operation of the Flinak/LiPb twin loop Orosh2i-2 with a 3T SC magnet for R and D of liquid blanket for fusion reactor, Fus. Sci. Technol. 68 (2015) 303–307. K. Miyazaki, S. Kotake, N. Yamaoka, S. Inoue, Y. Fujii-e, MHD pressure drop of NaK flow in stainless steel pipe, Nucl. Technol./Fusion 4 (September) (1983) 447–452.
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
MHD pressure drop measurement of PbLi flow in double-bended pipe ⁎
Shoki Nakamuraa, Tomoaki Kunugia, , Takehiko Yokominea, Zensaku Kawaraa, Koji Kusumia, Akio Sagarab, Juro Yagib, Teruya Tanakab a b
Department of Nuclear Engineering, Kyoto University, Kyoto-Daigaku Katsura, Nishikyo-Ku, Kyoto, 615-8540, Japan National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan
A R T I C L E I N F O
A B S T R A C T
Keywords: Liquid blanket Experiment PbLi Oroshhi-2 facility Double-bended pipe MHD friction loss coefficient
The design of liquid metal cooling system for the liquid blanket concepts in magnetic fusion reactor requires the magnetohydrodynamics (MHD) friction loss coefficients for various pipes including pipes and bents to estimate the pressure drop of the whole blanket. The aim of this study is to reveal the MHD pressure drop of PbLi flow in a double-bended pipe. The experiments were conducted in the Oroshhi-2 loop having a super conducting magnet of 3T at NIFS in Japan. In this paper, the MHD pressure drops of the pipe under the magnetic field of 0.5T–3.0T, the ranges of Reynolds number (Re) of 2000–200,000 and Hartmann number (Ha) of 106–640 at the upstream, double-bended and downstream regions were measured. As the results, all the MHD friction loss coefficients in three regions were well correlated with the interaction parameter (Na = Ha2/Re) in the range of 0.1 < N < 100. Finally, the correlation equations of MHD friction loss coefficient against the interaction parameters at the upstream, double-bended and downstream regions of the pipe were obtained. Moreover, it was briefly discussed on the implementation to the liquid metal cooling system design for fusion reactor.
1. Introduction In various liquid blanket concepts in magnetic fusion reactor such as the dual-coolant lead-lithium (DCLL) and self-cooled lead lithium (SCLL) [1], helium-cooled lead-lithium (HCLL) [2] and water-cooled lithium-lead (WCLL) blankets [3], the design of liquid metal cooling system requires the magnetohydrodynamics (MHD) friction loss coefficients for various pipes including pipes and bents to estimate the MHD pressure drop of the whole blanket system. Many studies regarding the MHD pressure drop in various shape pipes and manifolds have been conducted, and the substantial summary until 1994 was reported in [4]. The liquid metals used in those studies were Sodium (Na), Sodium-Potasium (NaK), Lithium (Li), Mercury (Hg) and Galinstan (GaInSn). In the application for the fusion reactors, Li and Lead-Lithium (PbLi) are the candidates as the primary coolant because of tritium production. Li is firstly the best candidate, but its flammable nature is a big issue for the reactor safety. Although PbLi is a heavy metal and needs the high pumping power, it has less fire problem. So, PbLi is the better candidate material of liquid blanket coolant, but to our knowledge only three PbLi MHD pressure drop measurements in a straight pipe [5], a duct [6] and a rectangular curved duct [7] have been reported. As for the U-turn pipe, bent and manifold, several studies using Na, NaK, Hg and GaInSn were reported in [4], but no usage of Li and PbLi until today. ⁎
The aim of this experimental study is to reveal the MHD pressure drop characteristics of PbLi flow in a double-bended pipe. This doublebended pipe was installed in Oroshhi-2 (Operational Recovery Of Separated Hydrogen and Heat Inquiry-2) PbLi flow loop with 3T superconducting (SC) magnet [8]. At first, the pressure drops in the double-bended pipe without magnetic field were measured as the shakedown test. As the results, the non-MHD friction loss coefficients in the upstream and downstream regions were correlated to Reynolds number (Re = 2Ua/ν, U is mean velocity, a is pipe radius and ν is kinematic viscosity), but that in the double-bended region did not depend on Re, i.e., it kept constant caused by the centrifugal force. The MHD pressure drops of the pipe under the magnetic field B of 0.5T ∼ 3.0T, the ranges of Re (Re = Ua/ν, the characteristic length is a in case of MHD flow) of 2000–200,000 and Hartmann number (Ha = Ba (σ/ν)1/2 , σ is electrical conductivity) of 106–640 at the upstream, double-bended and downstream regions were measured, and were coincident to the theoretical value within around 20%, and those in the double-bended region were around 10% larger than the theoretical value except in case of 0.5T. Moreover, all MHD friction loss coefficients in three regions were well correlated with an interaction parameter N (the square of Hartmann number divided by Re: Ha2/Re) in the range of 2000 < Re < 200,000 and 0.1 < N < 100. The correlation equations of MHD friction loss coefficient against N at the upstream, double-bended and downstream regions of the pipe were obtained. At last, it was briefly discussed on the
Corresponding author. E-mail address: [email protected] (T. Kunugi).
https://doi.org/10.1016/j.fusengdes.2017.12.009 Received 8 November 2017; Received in revised form 7 December 2017; Accepted 9 December 2017 0920-3796/ © 2017 Elsevier B.V. All rights reserved.
Please cite this article as: Nakamura, S., Fusion Engineering and Design (2017), https://doi.org/10.1016/j.fusengdes.2017.12.009
Fusion Engineering and Design xxx (xxxx) xxx–xxx
S. Nakamura et al.
implementation to the liquid metal cooling system design for fusion reactor.
Table 1 Typical physical properties. Working fluid Density [kg m−3] Dynamic viscosity [Pa s] Kinematic viscosity [m2 s−1] Electrical conductivity (PbLi) [Ω−1 m−1] Electrical conductivity (SUS316) [Ω−1 m−1]
2. Experiments 2.1. Oroshhi-2 PbLi loop and test section The Oroshhi-2 PbLi loop [8] consists of a SC electromagnet (JASTEC, Japan), an electromagnetic (EM) pump, an EM flow meter, a PbLi flow loop, a melting/dump tank, a temperature control system: power supplies, heaters, and insulations. The PbLi main loop which is made of SUS316 has 40.8 mm of the inner diameter and the loop’s operational temperature is up to 320 °C. Maximum flow rates are 50 L min−1 without magnetic field and 18 L min−1 with magnetic field of 3.0 T, respectively. The horizontal penetration duct of the superconducting magnet was 210 mm × 165 mm, and the thermal insulator of pipe is composed of two materials: the first layer is a ceramic fiber blanket and the second layer is a rock wool. Since the superconducting magnet needs to be cooled at 5.1 K to generate 3.0 T, the surface temperature of test section must be kept at lower than 50 °C. This is the reason why the inner diameter of the pipe of 16.1 mm is designed by considering the insulator thickness. The Outer diameter (OD) of test section is 21.7 mm, the inner diameter of the double-bended pipe is 2a = 16.1 mm and that of the pressure-tap is 10.2 mm, which is quite large compared to the ordinal tap-diameter because the PbLi easily freezes at the pressure tap. The curvature radius of the bent is R = 38.1 mm. Fig. 1(a) shows the Orosshi-2 SC electromagnet, the test section including a double-bended pipe and four pressure taps (D-C: Upstream region: C-B: Double-bended region, B-A: Downstream region). The test section consists of five pipes denoted by the framed number 1–5 in Fig. 1(a). Frame # 1 and #5 pipes connects to the main loop of 40.8 mm in the inner diameter with a reducer and a diffuser, respectively. The pressure taps connect to the differential pressure gauge to measure the pressure drop. Fig. 1(b) shows the magnetic field profile and the locations of the pressure taps at B and C of doublebended pipe are indicated. The bore diameter is 745 mm and the double-bended region is located at the constant magnetic field region. On the other hand, the upstream and downstream parts of the test
PbLi at about 320 °C 9.50 × 103 at 300 °C 1.10 × 10−3 at 300 °C 1.15789 × 10−7 at 300 °C 7.70 × 105 at 300 °C 1.075 × 106 at300 °C
section have the fringe magnetic field, the magnetic field increasing in D-C and that decreasing in B-A. The experimental conditions were in the ranges of the magnetic field (B) from 0.5T to 3.0T, Re from 2000 to 200,000 (maximum flow rate was 18 Liters per min) and Ha from 106 to 640. Thus, N is the range from 0.1 to 100. The typical physical properties of the Oroshhi-2 PbLi loop are tabulated in Table 1. 2.2. Pressure drop measurement The measuring procedure of pressure drop was the same as Li’s method [5]. The diameter of differential pressure tap lines were ϕ12.7 mm × t1.24 mm (length about 2 m), and it connected to the differential pressure measurement-unit lines are ϕ6.35 mm × t0.89 mm (length about 8 m). The differential pressure tap and measurement-unit lines were firstly filled with Ar gas, and the levels of PbLi in each line were the same because of no-flow. When the flow starts, the liquid levels of PbLi in the upstream and downstream gas lines were different. So, the differential pressure of Ar between upstream and downstream lines were measured. The differential pressure measurement unit consisted of two differential pressure gauges: GC55 and GC50 (Nagano Keiki, Japan). The specifications of each differential pressure gauge are as follows: for GC55, the differential pressure measurement range (Δp) is −1.0 MPa–1.0 MPa, and the accuracy of ± (1.0%F. S. +1digit) , and for GC50, Δp is ± 10kPa, and the accuracy of ± (1.0%F. S. +1digit) . 3. Friction loss coefficient and MHD pressure gradient In this experiment, the friction loss coefficients of PbLi pipe flow were obtained and compared to the well-known Blasius’ correlation in case of no-magnetic field. Blasius’ correlation is expressed as,
f = 0.0791Re−0.25 (Re < 105)
(1)
and the friction loss coefficient of pipe is defined as,
f = d Δp /2ρLU 2
(2)
here, Δp, ρ, L are the pressure drop, the density and the flow length between the pressure taps, respectively. The theoretical estimation of MHD pressure drop (ΔpMHD) was derived by Miyazaki et al. [9],
Δp MHD = Kp
∫
σf UB2 (x ) dx
(3)
here, x is the streamwise coordinate, σf is an electrical conductivity of fluid, Kp is an effective load resistance and a function of the wall conductance ratio, C:
Kp = C/(1 + C ), C = σw (Ro2 − Ri 2)/ σf (Ro2 + Ri 2)
(4)
here, σw, Roand Ri are an electrical conductivity of wall, the outer and inner radius, respectively. Finally, the MHD pressure gradient (dp / dx ) MHD can be written as the function of B2 as follows:
(dp / dx ) MHD = Kp σf UB2
Fig. 1. (a) Orosshi-2 SC electromagnet, test section and pressure-tap locations (A-D) (b) Magnetic field profile and pressure taps of B & C of double-bended pipe.
In this study, the theoretical value of Kp is 0.287. 2
(5)
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Fig. 2. Relation between pressure drop and Re in (a) Upstream region, (b) Downstream region and (c) Double-bended region.
4. Results and discussions
According to Fig. 3(a), the friction loss coefficient correlation in the upstream region is similar to Blasius’ correlation of Eq. (1): it means the power of Re is the same, but the coefficient is twice larger. Because the size of the pressure taps is close to the test pipe diameter, the pressure loss coefficient became large. The friction loss coefficient correlation in the downstream region as shown in Fig. 3(b) is rather different from the Blasius’ correlation. This is because the friction loss coefficient in the double-bended region is kept constant as shown in Fig. 3(c). In the double-bended region, the flow receives a strong acceleration due to centrifugal force, so the pressure drop is caused by the
4.1. Shakedown results without magnetic field Fig. 2 (a–c) shows the relation under no-magnetic flied between the pressure drop and Re in the upstream, downstream and double-bended regions, respectively. The pressure drop in all regions are almost proportional to Re2. This means that the pressure drop (Δp) is proportional to the kinetic energy(ρU 2) is proportional, i.e., the pressure loss can be represented by the friction loss coefficient (f) as shown in Fig. 3.
Fig. 3. Relation between friction loss coefficients and Re in (a) Upstream region, (b) Downstream region and (c) Double-bended region.
3
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acceleration force, not the viscous drag. If the pressure gradient along the mainstream can balance to the acceleration force, the following relation for the 90° bent with the curvature (1/R) can be written:
Δp / L ∼ ρU 2/ R,
(6)
and the friction loss coefficient (f90° (2) as follows:
bent)
is expressed by using Eq.
f90obent = d Δp /2ρLU 2 ∼ d/2R f90°
(7)
The friction loss coefficient f of the double-bended region is twice of bent,
f = 2 × f90obent ∼ 2 × d/2R = d/ R
(8)
Finally, the friction loss coefficient in the double-bended region can be expressed as:
f = α (d/ R)
Fig. 5. B2-scaling trend of MHD pressure drops in double-bended region against Re.
(9)
According to Fig. 3(c), f = 0.013. Therefore, the coefficient α can be obtained about 0.03. However, this coefficient is not the universal value, so the experiments with various ratio of the pipe diameter to the curvature must be conducted in the future. 4.2. MHD pressure drop measurements Fig. 4 shows the pressure drop under the magnetic fields of from 0.5T to 3.0T in the double-bended region of the double-bended pipe against various Reynolds numbers. The pressure drops under each magnetic field condition linearly increase with increase of Reynolds number (i.e., volumetric flowrate). The increase rates of the pressure loss also increased with increase of the magnetic field strength, and eventually decreased the flowrate. This tendency is very different from the pressure loss of the ordinary bent pipe, which is caused by the centrifugal force due to the curved flow in the bent described in the previous section.
Δp MHD = Kp
∫
σf UB2 (x ) dx
Kp = C /(1 + C ), C = σw (Ro 2 − Ri 2)/ σf (Ro 2 + Ri 2) Finally, the MHD pressure gradient function of B2 as follows:
Fig. 6. Relation between measured pressure gradient and the theoretical value in doublebended region.
(10)
(dp / dx ) MHD
(11)
is 0.287. The MHD pressure gradient in the double-bended pipe showed a linear relationship to the product of mean velocity and a square of the magnetic field strength, and the effective load resistance Kp of the double-bended pipe was 25% larger than the theoretical value except in case of 0.5T (denoted the open circle).
can be written as the
(dp / dx ) MHD = Δp MHD / L = Kp σf UB2
(12)
The MHD pressure drops by B2-scaling (Δp MHD /B2) under various magnetic fields are very well correlated to Re as shown in Fig. 5. The measured MHD pressure drops are around 10% larger than the theoretical value obtained by Eq. (10) except in case of 0.5T (denoted the open circle). Fig. 6 shows the relation between the measured pressure gradient (dp / dx ) MHD = Δp MHD / L and the theoretical value of σfUB2 in the double-bended region. According to Eq. (11), the theoretical value of Kp
4.3. Correlations of MHD friction loss coefficient It is useful to evaluate a friction loss coefficient under the magnetic field compared to an ordinary (no magnetic field) friction loss coefficient for the pipe, because these coefficients are the non-dimensional quantity. In this paper, the Fanning’s formula is used to evaluate the MHD pressure drop as follows:
f MHD =
Δp a ⎛ ⎞, 2ρU 2 ⎝ L ⎠
(13)
here, f is MHD friction loss coefficient, ρ is density and L is pipe centerline length. The non-dimensional equation of motion for MHD flow are expressed as: MHD
∂u 1 2 Ha2 + (u·∇) u = −∇p + ∇u+ (J × B ) ∂t Re Re
(14)
The force balance between the pressure gradient and the Lorentz force if the velocity is small can be expressed as,
∇p ∼ Fig. 4. MHD pressure drop versus Re at double-bended region.
4
Ha2 (J × B ) Re
(15)
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Fig. 7. Relationships between fMHD and Re in (a) upstream region, (b) double-bended region and (c) Downstream region.
Therefore, the data were plotted against N as shown in Fig. 8. All the MHD friction loss coefficients fMHD were well correlated, and proportional to N. Finally, the correlations of MHD friction loss coefficient of the double-bended pipe were obtained as follows:
Thus, the MHD friction loss coefficient can be derived as,
f MHD
∼ ∇p/(J × B ) ∼
Ha2/Re
(16)
If the magnetic field is constant (Ha = constant), the above relation can be rewritten as:
f MHD ∼ 1/Re.
(17)
In the experiments, fMHD in three regions (upstream, double-bended and downstream) of the double-bended pipe against various Reynolds numbers were measured. Fig. 7 shows the relationships between fMHD and Re in (a) upstream region, (b) double-bended region and (c) downstream region, respectively. In the figure, fMHD seems to be inversely-proportional to Re in each constant magnetic field condition except the cases of higher magnetic fields (2.5T and 3.0T) and lower Re conditions (Re < 5000). These results under the constant magnetic field conditions confirmed Eq. (17) to be correct, and meant that the flow is a laminar flow and fMHD decreases with increase of Re. This tendency is like the ordinary laminar flow without magnetic field effect. According to the B2-scaling as shown in Fig. 5, Eq. (16) can be rewritten as,
f MHD ∼ Ha2/Re = N.
MHD fUpstream ∼ 0.05N in the upper stream region,
(19-1)
MHD f Double ∼ 0.075N in the double-bended region and, − bended
(19-2)
MHD f Downstream ∼ 0.05N in the downstream region.
(19-3)
According to these correlations, the MHD pressure loss in the double-bended region is 50% larger than that in the upstream and downstream regions. This is a very important information for the liquid metal cooling system design of fusion reactors. 4.4. Consideration on MHD flow characteristics in double-bended pipe As described in 4.2, the constant magnetic fields were applied in this experiment, and the increase rates of the MHD pressure loss increased with increase of the magnetic field strength, but decreased the flowrate (Re). The centrifugal force due to the curved flow in the double-bended
(18) 5
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Fig. 8. Relationships between fMHD and N in (a) upstream region, (b) double-bended region and (c) downstream region.
pipe caused the pressure drop in the bent pipe without the magnetic field. However, the MHD pressure drops in the double-bended pipe strongly depended on the flowrate (Re). Thus, it can be said that the centrifugal force may not be influenced on the MHD pressure drop in the double-bended pipe. According to Eq. (19), the MHD pressure loss coefficients fMHD in all regions are linearly proportional to N, so the thickness of Robert layer becomes thinner and the velocity becomes large with increase of Re if the magnetic field is constant. In other words, the fMHD linearly increases with increase of the magnetic field strength if the flowrate (Re) is constant. Therefore, the higher N causes the higher viscous drag in Roberts layer, so the fMHD in the doublebended pipe shows the linear relation to N, not independent to Re.
cooling system in the magnetic fusion reactors. To reduce the MHD pressure loss, it is necessary to use the electric insulation material for the pipes or the electric insulation coating on the inner wall of the pipes. However, the electric insulator has also less thermal conductivity, eventually the heat removal becomes a major problem. One of the design solutions is to prevent the current path across the flow channel, i.e., the electric insulator partially coats the inner pipe, such as the electric insulation coating on the half wall surface of the pipe, not the whole wall. It might be expected to reduce the MHD pressure loss and keep certain the heat removal capability.
5. Implementation to liquid metal cooling system design
In this paper, the MHD pressure drops of the pipe under the magnetic field of 0.5T-3.0T, Re = 2000–200,000 and Ha = 106–640 at the upstream, double-bended and downstream regions were measured. As the results, the MHD pressure gradient in the double-bended pipe showed a linear relationship to the product of mean velocity, and a square of the magnetic field strength, the effective load resistance Kp of the double-bended pipe was 25% larger than the theoretical value. All the MHD friction loss coefficients in three regions were well correlated with the interaction parameters (N= Ha2/Re) in the range of 0.1 < N < 100. Finally, the correlation equations of MHD friction loss coefficient fMHD against the interaction parameter N at the upstream, double-bended and downstream regions of the pipe were obtained. Based on the obtained data, the MHD flow characteristics in doublebended pipe were discussed. Moreover, it was briefly discussed on the implementation to the liquid metal cooling system design for fusion reactor.
6. Conclusions
The pressure loss coefficient in the double-bended region without magnetic field does not depend on Re and showed the constant as described in the Section 4.1:
f non − MHD =
Δp 2a ⎛ ⎞ = 0.013 2ρU 2 ⎝ L ⎠
(20)
The ratio of the MHD friction loss coefficient to the non-MHD one is,
f MHD / f non − MHD = 0.075N/(0.013/2) = 11.5N.
(21)
For example, the parameters of PbLi self-cooling liquid blanket are Re = 2.0 × 105 and Ha = 104, the interaction parameter will be N = 500. According to Eq. (21), the MHD pressure loss compared to the ordinary bent pipe is around 6000 times larger than the ordinary double-bended pipe. This is an inevitable problem of liquid metal 6
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Acknowledgement [5]
This work is performed with the support and under the auspices of the NIFS collaboration research program in Japan (NIFS16KERF035).
[6]
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