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Hydraulic analysis of liquid nitrogen flow through concentric annulus with corrugations for High Temperature Superconducting power cable
Cryogenics 103 (2019) 102950
Contents lists available at ScienceDirect
Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Research paper
Hydraulic analysis of liquid nitrogen flow through concentric annulus with corrugations for High Temperature Superconducting power cable
T
Ipsita Das , V.V Rao ⁎
Cryogenic Engineering Centre, Indian Institute of Technology, Kharagpur 721302, India
ARTICLE INFO
ABSTRACT
Keywords: HTS cable Annular flow Subcooled liquid nitrogen Friction factor CFD Corrugation pitch and depth
A hydraulic analysis for turbulent flow of subcooled liquid nitrogen through an annulus within the HTS cable is numerically investigated in terms of friction factor and flow pattern. The control volume for the investigation is confined to the annular space between outer smooth surface of cable core and inner surface of corrugated cryopipe. The corrugation geometries i.e pitch and depth affect the friction factor and thus the pressure drop and pumping power of liquid nitrogen. Nine different geometries of corrugated cryostats with various combinations of pitches (6, 10 and 14 mm) and depths (5, 7 and 9 mm) are considered and compared with smooth (noncorrugated) pipe. The results are useful in selecting the cryostat configuration and the associated fluid pumping system for cooling HTS power cables.
1. Introduction One of the major concerns in recent days is the conservation of energy and the quest to develop any alternative solution to the existing system, with minimum losses. High Temperature Superconducting (HTS) power cables can address this issue very well, as it has the ability to transmit huge electrical power in compact size with minimum Joule loss. Since the discovery of high temperature superconductivity [1], many researchers have been working on different applications in power sector including HTS power cable. Moreover, various projects [2–9] on HTS cables worldwide have been successfully tested to introduce the technology into real grid operation. HTS cables require to operate below a certain temperature (critical temperature, Tc) in order to maintain superconductivity. Subcooled liquid nitrogen (LN2) is mostly used as coolant in HTS cable. Further, researchers have also adopted some other possible alternatives as coolants. Demko and Hassenzahl [10] investigated with liquid air and Pamidi et al. [11] have used cold helium gas, Kephart et al. [12] have conducted experiment with gaseous cryogen (air and nitrogen). Ashworth and Reagor [13] have used ‘Distributed Cooling’ method for HTS cable. Further, various heat loads like internal heat generation due to AC loss, heat-in-leak from the surrounding and frictional heat loss are inherent in a HTS cable. The frictional heating is mainly dependent on flow velocity and is not so significant at small flow rates and in short length cables. However, with increase in cable length, frictional heat load increases, which is one of the major issues of concern in operation of HTS cable. Hence, the effect
⁎
of corrugated flexible cryostat on frictional heat load needs a realistic evaluation under various operating and geometric conditions. In open literature, there is some debate on how the corrugations in the inner cryostat wall of HTS cable affect the flow pattern and friction factor of LN2. Fuchino et al. [14] measured the pressure drop across a 10 m corrugated pipe with different flow rates to evaluate the friction factor. The friction factor in corrugated pipes is larger than that in smooth pipes. It is also reported that, the pressure drop in corrugated pipe is four times as high as that of smooth pipe [15]. Li et al.[16] have experimentally measured the flow resistance for both smooth and corrugated pipes. They have reported that the friction factor in corrugated pipes is three times that of smooth pipe. Chevtchenko et al. [17] have considered different cryostat sections (three straight and two corrugated) with a dummy cable for their experiment to investigate the flow behavior of LN2 through different sections. Few researchers have numerically analyzed the effect of corrugations on the friction factor of LN2 in case of corrugated pipes [18,19] and also analyzed the LN2 flow behavior within the cryostat depending on the positioning of cable core [20,21]. Ivanov et al. [22] have conducted an experiment considering smooth cryo-pipe with cable in it, to measure the pressure drop along the length of pipe. Further, they have extended their research to finalize one optimum set of cryostats [23] from a combination of different sets of cryostats (one for cable and another for LN2return line). Many researchers [24,25] have developed correlations for friction factor considering the results available from experimental and numerical analysis. Zajaczkowski et al. [26] have calculated the pressure drop along the
Corresponding author. E-mail address: [email protected] (I. Das).
https://doi.org/10.1016/j.cryogenics.2019.05.010 Received 11 December 2018; Received in revised form 21 May 2019; Accepted 28 May 2019 Available online 04 June 2019 0011-2275/ © 2019 Elsevier Ltd. All rights reserved.
Cryogenics 103 (2019) 102950
I. Das and V.V. Rao
Nomenclature A Di dh Do Dm fi fo f
k L ΔP Pw p v ρ τw µ
cross-sectional area of the flow (mm2) inner diameter of annulus (mm) hydraulic diameter(4A/Pw) (mm) outer diameter of annulus (mm) mean diameter (mm) friction factor of smooth wall friction factor of corrugated wall friction factor of annulus.
HTS cable using the friction factor obtained from Colebrook–White–Barr (CWB) formula [27] for inner pipe and friction factor obtained from numerical result of Lee at al. [18] for outer annular duct. However, an extensive study of literature shows that there is still some uncertainty about the fact that how the corrugation dimensions affect the flow behavior. The present analysis is focused on the effects of various realistic corrugated geometries (pitches and depths) on flow pattern and friction factor in the fully developed turbulent flow region. The friction factor obtained in case of corrugated cryostat is further compared with the same of smooth cryostat. The calculations are made with constant properties of LN2 in subcooled region. The analysis is performed numerically using CFD fluent. The outcome of the present investigation has practical significance, as the friction factor plays an important role in calculating the pressure drop and pumping power of LN2 flow in case of long distance cooling of HTS power cables requiring intermittent re-cooling.
corrugation depth (mm) length of pipe (mm) pressure drop (pa/m) Wetted perimeter (mm) corrugation pitch (mm) flow velocity (m/s) density of subcooled LN2(kg/m3) wall shear stress (Pa) viscosity (Pa·s)
2.2. Operating range of LN2 The subcooled LN2 is considered as coolant in HTS cable as its heat capacity is quite high and also to avoid two phase flow. The operating temperature range can be increased by increasing the pressure (Fig. 1). However, the increase in operating temperature reduces the critical current. Thus the operating range of LN2 should be decided considering the electromagnetic properties of HTS tapes and thermodynamic properties of LN2. 3. Flow model In the present work, it is considered that the cable core is housed within a flexible corrugated cryostat along its centerline, as shown Fig. 2(a). Subcooled LN2 flows through the annular space between outer surface of cable core (smooth wall) and inner surface of corrugated cryostat (corrugated wall).The inner and outer diameter of annulus considered for the present analysis is mentioned in Table 1 [21]. The annular section of the cable is modeled with three different pitches and three different depths (Table 1). Further, the analysis is also made for smooth cryostat without any corrugations. The flow velocity of LN2 is assumed to be within 0.18 to 0.34 m/s and the flow is turbulent with corresponding Reynolds number range 9582-30,632. The hydraulic diameters of the annulus having depths of 5, 7 and 9 mm are 18.5, 20.5 and 22.5 mm respectively. The length of cable for the present analysis (0.8 m) is calculated by taking the sum of entrance length (0.23 m), length of fully developed turbulent flow (0.5 m) and outlet length (0.07 m). Further, the directions of LN2 flow and heat loads into the annulus are also shown in Fig. 2(i)–(ii).
2. HTS cable geometry and operating range of LN2 2.1. HTS cable geometry A cold dielectric (CD) HTS cable is made out of copper former, HTS conductor layer, dielectric (PPLP) layer, HTS and copper shield layers. Further, all these layers are arranged co-axially around the former and are housed within a double walled cryostat for cooling the HTS cable. The cable cryostat is mostly made up of corrugated pipes to absorb the thermal shrinkage, bending stress and to ensure flexibility.
3.1. Corrugated annular section geometry The schematic of cable annulus, investigated in the present analysis is shown in Fig. 2. The outer wall of annulus (i.e inner surface of corrugated cryostat) consists of a series of corrugations with pitch “p” and depth “k” as shown in Fig. 2(i). Nine different geometric configurations are studied, with three different pitches and three different depths at different Reynolds numbers. In order to calculate Reynolds number (Re) for the annulus, hydraulic diameter is calculated by:
Fig. 1. Operating range of LN2 for HTS cable operation.
dh =
4 4A = Pw
Re =
vDh µ
2 (Di ) 2} = (Do Do + Di
4 {(Do )
Di )
(1) (2)
Table 1 Geometric specifications of cable. Annulus
Diameter (mm)
Length (mm)
Pitch (mm)
Depth (mm)
Inner diameter (smooth) (Di) Outer diameter (corrugated) (Do)
85 98.5
800 800
– 6, 10, 14
– 5, 7, 9
2
Cryogenics 103 (2019) 102950
I. Das and V.V. Rao
4. CFD model
Table 2 Geometric specifications of corrugated cryostat used in numerical calculations (p, k, dh). Geometry sets
Configuration
p/dh
k/dh
k/p
Set-1
p1k1 p1k2 p1k3 p2k1 p2k2 p2k3 p3k1 p3k2 p3k3
0.333 0.3 0.273 0.555 0.5 0.455 0.777 0.7 0.636
0.278 0.35 0.409 0.278 0.35 0.409 0.278 0.35 0.409
0.833 1.167 1.5 0.5 0.7 0.9 0.357 0.5 0.642
Set-2 Set-3
The LN2 flow within the annulus of HTS cable is considered as incompressible and turbulent. The CFD method helps us to obtain wall shear stress of the present complicated geometries numerically. The velocity distributions of LN2 flow are investigated using FLUENT®. As per the model shown in Fig. 2(a), an axisymmetric CFD model is prepared for the analysis. The details of geometric specifications, used in CFD formulation are mentioned in Table 2. Simulation is carried out at five different Reynolds numbers within the ranges for each (p and k) combination, in order to reflect its effect on friction factor and velocity distribution. The numerical mesh is used in the analysis, is shown in Fig. 2(c). For turbulent flow analysis, one has to properly take the
Fig. 2. The simplified model of annulus. (i) (a) Schematic of HTS cable (annular section with corrugated cryostat), (b) Corrugation showing Pitch and depth, (c) Meshed model and zoomed portion showing the details of meshing. (ii) HTS cable (annular section with smooth cryostat).
The range of Reynolds number for different corrugation depths are (9582–18,100), (13,268–25,062), (14,742–27,847), (16,217–30,632) for smooth cryostat and corrugated cryostat with 5, 7 and 9 mm depths respectively. The annular section has inner diameter Di and outer diameter Do. For the annulus with smooth cryopipe (Fig. 2ii) the outer diameter is Do and for corrugated cryopipe it is Dm. Table 2 shows the dimensions of the aforementioned nine geometries; pitch (p1, p2, p3) and depth (k1, k2, k3).
Table 3 Details of Meshing, Boundary condition and CFD formulation. Meshing Details
Boundary conditions
Number of nodes: 379,181 Inlet: Velocity inlet (0.18–0.34 m/s) Number of elements: 371,716 Outlet: Outflow Type of element: Quadrilateral Wall: Inner wall and Corrugated wall with Minimum size of the element: uniform heat load of 0.4 W/m and 1.4 W/m 4.0128e-4 respectively [21] CFD Formulation Pressure based Navier Stokes, 2D axis-symmetric, steady flow, Turbulent realizable k-ε Model with enhanced wall treatment
3.2. Theoretical analysis For a long length HTS power cable, pressure drop is an important aspect in estimating various parameters such as length of cable, cryogen pumping power. The pressure drop of subcooled LN2 flow is explained using Darcy-Weisbach equation.
P=
fL v 2 2dh
(3)
In order to calculate pressure drop along the length of cable, friction factor has to be evaluated. In case of fully developed flow, the pressure force balances the wall shear force. Hence after balancing both the forces the friction factor can be expressed as
f=
8
w
v2
(4)
The friction factor in the annular space is estimated by considering the existence of two types of wall surfaces (i.e. smooth surface of cable outer and the corrugated surface of cryostat’s inner wall). Hence the friction factor is evaluated as the sum of the contributions from both the walls, which are proportional to their wetted perimeters and can be expressed as [28]
f=
fi Di + fo Do Di + Do
Fig. 3. Validation of the present model.
(5)
3
Cryogenics 103 (2019) 102950
I. Das and V.V. Rao
viscous sublayer (the near wall laminar flow) into account. The grids are stretched to cluster grids near the wall and are adjusted for every Reynolds number in order to ensure the dimensionless distance, y+ within 5. A mesh sensitive test is conducted for all nine different investigated geometries. The best suitable meshing is considered for the analysis as per the mesh convergence. However, the number of elements in the meshed model differs due to change in geometries. The tabulated number of elements and nodes in Table 3 are for the axissymmetric meshed model shown in Fig. 2(c), taken for the p = 10 mm and k = 7 mm configuration. During simulation, the “velocity inlet” condition is used for inlet boundary condition and “outflow” boundary condition for the outlet. The numerical friction factor is then derived
from the wall shear stress using Eq. (4). The details of the mesh formulation and boundary conditions are mentioned in Table 3. 5. Results and discussion The wall shear stress is obtained from the CFD simulation along the length of annular section, in the fully developed turbulent flow region. The values of wall shear stresses for all pitch and depth combinations at different Reynolds’s numbers are obtained for both smooth (cable side) and corrugated (cryostat side) surfaces of the annular section through which subcooled LN2 is flowing. Moreover, the friction factor is calculated using average shear stress in fully developed flow region. The
Fig. 4. Friction factors as a function of flow rate at varied pitch with fixed depths (a, b, c) and at varied, depths with fixed pitch (d, e, f). 4
Cryogenics 103 (2019) 102950
I. Das and V.V. Rao
Fig. 5. Streamlines from CFD for all nine geometries at a particular flow velocity of 0.22 m/s (with Re = 16217.14, 18019.04, 19820.951 for k = 5, 7 and 9 mm respectively). All p and k are in mm.
friction factors for both the surfaces are calculated using Eqs. (4) and (5). The numerical formulation considered for the present simulation model is first validated with the results obtained from Ivanov et al. [23] as shown in Fig. 3. The simulated result of pressure drop shows very good agreements with the results of Ivanov et al. [23]. The pressure drop is estimated from the friction factor using Darcy-Weisbach formulation (Eq. (3)). Thereafter, validated numerical formulation is used for current nine corrugated models. All six plots in Fig. 4 correspond to the values of friction factor at three different pitches (p1, p2, p3) and three depths (k1, k2, k3) within the Reynolds number range. It can be observed from Fig. 4(a)–(c) that the friction factor tends to decrease with the increase in corrugation pitch at constant corrugation depth. Similarly, Fig. 4(d)–(f) show that friction factor increases as corrugation depth increases with constant pitch. All six plots of Fig. 4 also show the friction factor variation of smooth cryostat with flow rates. The values of friction factor in smooth cryostat are smaller than that of corrugated cryostats. Further, the friction factors are low at larger Reynolds numbers as compared to those for smaller Reynolds numbers. The flow patterns of LN2 inside the corrugations of the annulus, for all combinations of pitches and depths are shown in Fig. 5. The results correspond to a particular flow velocity of 0.22 m/s. The obtained flow patterns vary with respect to k/p ratio. In smaller k/p ratios (Fig. 5(a), (d)–(i)), a single vortex tends to fill up the whole corrugation space, whereas for higher k/p ratios (Fig. 5(b) and (c)), two sets of vortices are observed within the corrugation space.
6. Conclusions The friction factor and the flow pattern of subcooled liquid nitrogen flowing within the annulus of HTS cable are investigated numerically using RANS turbulence model, for nine different corrugation geometries. From these investigations, it can be concluded that smaller k/p ratios (k/p ≤ 0.5) are preferred for getting lesser friction factor and thereby lesser LN2 pumping power to maintain thermally stable operation of HTS cable. The HTS cable with a pitch of 10 mm and depth of 5 mm shows the minimum pressure drop of 76.57 Pa/m for 28.69 L/ min. Further the CFD analysis gives an insight into flow visualization with breaking of vortices. This study can provide an useful guideline to the engineers and manufactures of flexible HTS cable while selecting the depth and pitch of corrugated pipes and designing the flexible cryostat with minimum pressure drop of liquid nitrogen. Declaration of Competing Interest The authors declared that there is no conflict of interest. References [1] Bednorz JG, Müller KA. Possible high TC superconductivity in the BaLaCuO system. Z Physik B 1986;64:189–93. [2] Takigawa H, Yumura H, Masuda T, Watanabe M, Ashibe Y, Itoh H, et al. The installation and test results for Albany HTS cable project. Physica C 2007;463–467:1127–31. [3] Mukoyama S, Maruyama S, Yagi M, Yagi Y, Ishii N, Sato O, et al. Development of 500 m HTS power cable in Super-ACE project. Cryogenics 2005;45:11–5.
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I. Das and V.V. Rao [4] Maguire JF, Schmidt F, Bratt S, Welsh TE, Yuan J. Installation and testing results of long Island transmission level HTS cable. IEEE Trans Appl Supercond 2009;19:1692–7. [5] Yang HS, Kim DL, Sohn SH, Lim JH, Choi HO, Choi YS, et al. Long term performance test of KEPCO HTS power cable. IEEE Trans Appl Supercond 2009;19:1782–4. [6] Yumura H, Ashibe Y, Ohya M, Itoh H, Watanabe M, Yatsuka K, et al. Test results of a 30-m HTS cable pre-demonstration system in Yokohama project. Physica C 2010;470:1558–62. [7] Xin Y, Hou B, Bi Y, Xi H, Zhang Y, Ren A, et al. Introduction of China’s first live grid installed HTS power cable system. IEEE Trans Appl Supercond 2005;15:1814–7. [8] Yagi M, Mukoyama S, Amemiya N, Ishiyama A, Wang X, Aoki Y, et al. Progress of 275 kV–3 kA YBCO HTS cable. Physica C 2011;471:1274–8. [9] Shabagin E, Heidt C, Strauß S, Grohmann S. Modeling of 3D temperature profiles and pressure drop in concentric three-phase HTS power cables. Cryogenics 2017;81:24–32. [10] Demko J, Hassenzahl W. Liquid air as a coolant for thermal management of longlength HTS cable systems. AIP Conf Proc 2012;1434(1):273–82. [11] Pamidi S, Kim CH, Kim JH, Crook D, Dale S. Cryogenic helium gas circulation system for advanced characterization of superconducting cables and other devices. Cryogenics 2012;52:315–20. [12] Kephart JT, Fitzpatrick BK, Ferrara P, Pyryt M, Miller J, Nadig C. Flow resistance experiments in HTS cable form. IEEE Trans Appl Supercond 2013;23(3):5401304. [13] Ashworth SP, Reagor DW. A novel cooling scheme for superconducting power cables. Cryogenics 2011;51:161–7. [14] Fuchino S, Tamada N, Ishii I, Higuchi N. Hydraulic characteristics in superconducting power transmission cable. Physica C 2001;354:125–8. [15] Weisend II JG, Van Sciver SW. Pressure drop from flow of cryogens in corrugated bellows. Cryogenics 1990;30:935–41. [16] Li Z, Li Y, Liu W, Zhu J, Qiu M. Comparison of liquid nitrogen flow resistance in corrugated pipe with smooth pipe. IEEE Trans Appl Supercond
2015;25(3):5401304. [17] Chevtchenko O, Zuijderduin R, Smit J, Willén D, Lentge H, Thidemann C, et al. Low friction cryostat for HTS power cable of Dutch project. Phys Procedia 2012;36:1309–12. [18] Lee CH, Kim CH, Kim KS, Kim DH, Kim IS. Performance of heat transfer and pressure drop in superconducting cable. Cryogenics 2003;43:583–8. [19] Dondapati RS, Rao VV. Pressure drop and heat transfer analysis of long length cooled HTS cables. IEEE Trans Appl Supercond 2013;23(3):5400604. [20] Sasaki A, Hamabe M, Famakinwa T, Yamaguchi S, Radovinsky A, Okumura H, et al. Cryogenic fluid dynamics for DC superconducting power transmission line. IEEE Trans Appl Supercond 2007;17:1748–51. [21] Maruyama O, Ohkuma T, Izumi T, Shiohara Y. Numerical calculation of advection heat transfer and fluid flow dynamics. IEEE Trans Appl Supercond 2015;25(3):5401505. [22] Ivanov Y, Watanabe H, Hamabe M, Kawahara T, Sun J, Yamaguchi S. Design study of LN2 circulation in a long SC power transmission lines. Phys Procedia 2012;36:1372–7. [23] Ivanov YV, Romashov MA, Bemert SE, Sytnikov VE. Choice of flexible cryostat for 2.5 km DC HTS cable to be laid in St. Petersburg. AIP Conference Proceedings, vol. 1573. 2014. p. 887. [24] Koh D, Yeom H, Hong Y, Lee K. Performance tests of HTS power cable cooling system. IEEE Trans Appl Supercond 2004;14(2):1747. [25] Sasaki A, Ivanov Y, Yamaguchi S. LN2 circulation in cryopipes of superconducting power transmission line. Cryogenics 2011;51(9):471–6. [26] Zajaczkowski B, Giesbers AJM, Holtrust M, Haenen E, Heijer R. Feasibility of inline cooling in long distance HTS power line. Cryogenics 2011;51(4):180–6. [27] Barr DIH. Two additional methods of direct solution of the Colebrook-White function. Proc Inst Civ Eng 1976;61:489–97. [28] Ivanov YV, Watanabe H, Hamabe M, Sun J, Kawahara T, Yamaguchi S. Circulation pump power for 200 m cable experiment. Physica C 2011;471:1308–12.
6
Contents lists available at ScienceDirect
Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Research paper
Hydraulic analysis of liquid nitrogen flow through concentric annulus with corrugations for High Temperature Superconducting power cable
T
Ipsita Das , V.V Rao ⁎
Cryogenic Engineering Centre, Indian Institute of Technology, Kharagpur 721302, India
ARTICLE INFO
ABSTRACT
Keywords: HTS cable Annular flow Subcooled liquid nitrogen Friction factor CFD Corrugation pitch and depth
A hydraulic analysis for turbulent flow of subcooled liquid nitrogen through an annulus within the HTS cable is numerically investigated in terms of friction factor and flow pattern. The control volume for the investigation is confined to the annular space between outer smooth surface of cable core and inner surface of corrugated cryopipe. The corrugation geometries i.e pitch and depth affect the friction factor and thus the pressure drop and pumping power of liquid nitrogen. Nine different geometries of corrugated cryostats with various combinations of pitches (6, 10 and 14 mm) and depths (5, 7 and 9 mm) are considered and compared with smooth (noncorrugated) pipe. The results are useful in selecting the cryostat configuration and the associated fluid pumping system for cooling HTS power cables.
1. Introduction One of the major concerns in recent days is the conservation of energy and the quest to develop any alternative solution to the existing system, with minimum losses. High Temperature Superconducting (HTS) power cables can address this issue very well, as it has the ability to transmit huge electrical power in compact size with minimum Joule loss. Since the discovery of high temperature superconductivity [1], many researchers have been working on different applications in power sector including HTS power cable. Moreover, various projects [2–9] on HTS cables worldwide have been successfully tested to introduce the technology into real grid operation. HTS cables require to operate below a certain temperature (critical temperature, Tc) in order to maintain superconductivity. Subcooled liquid nitrogen (LN2) is mostly used as coolant in HTS cable. Further, researchers have also adopted some other possible alternatives as coolants. Demko and Hassenzahl [10] investigated with liquid air and Pamidi et al. [11] have used cold helium gas, Kephart et al. [12] have conducted experiment with gaseous cryogen (air and nitrogen). Ashworth and Reagor [13] have used ‘Distributed Cooling’ method for HTS cable. Further, various heat loads like internal heat generation due to AC loss, heat-in-leak from the surrounding and frictional heat loss are inherent in a HTS cable. The frictional heating is mainly dependent on flow velocity and is not so significant at small flow rates and in short length cables. However, with increase in cable length, frictional heat load increases, which is one of the major issues of concern in operation of HTS cable. Hence, the effect
⁎
of corrugated flexible cryostat on frictional heat load needs a realistic evaluation under various operating and geometric conditions. In open literature, there is some debate on how the corrugations in the inner cryostat wall of HTS cable affect the flow pattern and friction factor of LN2. Fuchino et al. [14] measured the pressure drop across a 10 m corrugated pipe with different flow rates to evaluate the friction factor. The friction factor in corrugated pipes is larger than that in smooth pipes. It is also reported that, the pressure drop in corrugated pipe is four times as high as that of smooth pipe [15]. Li et al.[16] have experimentally measured the flow resistance for both smooth and corrugated pipes. They have reported that the friction factor in corrugated pipes is three times that of smooth pipe. Chevtchenko et al. [17] have considered different cryostat sections (three straight and two corrugated) with a dummy cable for their experiment to investigate the flow behavior of LN2 through different sections. Few researchers have numerically analyzed the effect of corrugations on the friction factor of LN2 in case of corrugated pipes [18,19] and also analyzed the LN2 flow behavior within the cryostat depending on the positioning of cable core [20,21]. Ivanov et al. [22] have conducted an experiment considering smooth cryo-pipe with cable in it, to measure the pressure drop along the length of pipe. Further, they have extended their research to finalize one optimum set of cryostats [23] from a combination of different sets of cryostats (one for cable and another for LN2return line). Many researchers [24,25] have developed correlations for friction factor considering the results available from experimental and numerical analysis. Zajaczkowski et al. [26] have calculated the pressure drop along the
Corresponding author. E-mail address: [email protected] (I. Das).
https://doi.org/10.1016/j.cryogenics.2019.05.010 Received 11 December 2018; Received in revised form 21 May 2019; Accepted 28 May 2019 Available online 04 June 2019 0011-2275/ © 2019 Elsevier Ltd. All rights reserved.
Cryogenics 103 (2019) 102950
I. Das and V.V. Rao
Nomenclature A Di dh Do Dm fi fo f
k L ΔP Pw p v ρ τw µ
cross-sectional area of the flow (mm2) inner diameter of annulus (mm) hydraulic diameter(4A/Pw) (mm) outer diameter of annulus (mm) mean diameter (mm) friction factor of smooth wall friction factor of corrugated wall friction factor of annulus.
HTS cable using the friction factor obtained from Colebrook–White–Barr (CWB) formula [27] for inner pipe and friction factor obtained from numerical result of Lee at al. [18] for outer annular duct. However, an extensive study of literature shows that there is still some uncertainty about the fact that how the corrugation dimensions affect the flow behavior. The present analysis is focused on the effects of various realistic corrugated geometries (pitches and depths) on flow pattern and friction factor in the fully developed turbulent flow region. The friction factor obtained in case of corrugated cryostat is further compared with the same of smooth cryostat. The calculations are made with constant properties of LN2 in subcooled region. The analysis is performed numerically using CFD fluent. The outcome of the present investigation has practical significance, as the friction factor plays an important role in calculating the pressure drop and pumping power of LN2 flow in case of long distance cooling of HTS power cables requiring intermittent re-cooling.
corrugation depth (mm) length of pipe (mm) pressure drop (pa/m) Wetted perimeter (mm) corrugation pitch (mm) flow velocity (m/s) density of subcooled LN2(kg/m3) wall shear stress (Pa) viscosity (Pa·s)
2.2. Operating range of LN2 The subcooled LN2 is considered as coolant in HTS cable as its heat capacity is quite high and also to avoid two phase flow. The operating temperature range can be increased by increasing the pressure (Fig. 1). However, the increase in operating temperature reduces the critical current. Thus the operating range of LN2 should be decided considering the electromagnetic properties of HTS tapes and thermodynamic properties of LN2. 3. Flow model In the present work, it is considered that the cable core is housed within a flexible corrugated cryostat along its centerline, as shown Fig. 2(a). Subcooled LN2 flows through the annular space between outer surface of cable core (smooth wall) and inner surface of corrugated cryostat (corrugated wall).The inner and outer diameter of annulus considered for the present analysis is mentioned in Table 1 [21]. The annular section of the cable is modeled with three different pitches and three different depths (Table 1). Further, the analysis is also made for smooth cryostat without any corrugations. The flow velocity of LN2 is assumed to be within 0.18 to 0.34 m/s and the flow is turbulent with corresponding Reynolds number range 9582-30,632. The hydraulic diameters of the annulus having depths of 5, 7 and 9 mm are 18.5, 20.5 and 22.5 mm respectively. The length of cable for the present analysis (0.8 m) is calculated by taking the sum of entrance length (0.23 m), length of fully developed turbulent flow (0.5 m) and outlet length (0.07 m). Further, the directions of LN2 flow and heat loads into the annulus are also shown in Fig. 2(i)–(ii).
2. HTS cable geometry and operating range of LN2 2.1. HTS cable geometry A cold dielectric (CD) HTS cable is made out of copper former, HTS conductor layer, dielectric (PPLP) layer, HTS and copper shield layers. Further, all these layers are arranged co-axially around the former and are housed within a double walled cryostat for cooling the HTS cable. The cable cryostat is mostly made up of corrugated pipes to absorb the thermal shrinkage, bending stress and to ensure flexibility.
3.1. Corrugated annular section geometry The schematic of cable annulus, investigated in the present analysis is shown in Fig. 2. The outer wall of annulus (i.e inner surface of corrugated cryostat) consists of a series of corrugations with pitch “p” and depth “k” as shown in Fig. 2(i). Nine different geometric configurations are studied, with three different pitches and three different depths at different Reynolds numbers. In order to calculate Reynolds number (Re) for the annulus, hydraulic diameter is calculated by:
Fig. 1. Operating range of LN2 for HTS cable operation.
dh =
4 4A = Pw
Re =
vDh µ
2 (Di ) 2} = (Do Do + Di
4 {(Do )
Di )
(1) (2)
Table 1 Geometric specifications of cable. Annulus
Diameter (mm)
Length (mm)
Pitch (mm)
Depth (mm)
Inner diameter (smooth) (Di) Outer diameter (corrugated) (Do)
85 98.5
800 800
– 6, 10, 14
– 5, 7, 9
2
Cryogenics 103 (2019) 102950
I. Das and V.V. Rao
4. CFD model
Table 2 Geometric specifications of corrugated cryostat used in numerical calculations (p, k, dh). Geometry sets
Configuration
p/dh
k/dh
k/p
Set-1
p1k1 p1k2 p1k3 p2k1 p2k2 p2k3 p3k1 p3k2 p3k3
0.333 0.3 0.273 0.555 0.5 0.455 0.777 0.7 0.636
0.278 0.35 0.409 0.278 0.35 0.409 0.278 0.35 0.409
0.833 1.167 1.5 0.5 0.7 0.9 0.357 0.5 0.642
Set-2 Set-3
The LN2 flow within the annulus of HTS cable is considered as incompressible and turbulent. The CFD method helps us to obtain wall shear stress of the present complicated geometries numerically. The velocity distributions of LN2 flow are investigated using FLUENT®. As per the model shown in Fig. 2(a), an axisymmetric CFD model is prepared for the analysis. The details of geometric specifications, used in CFD formulation are mentioned in Table 2. Simulation is carried out at five different Reynolds numbers within the ranges for each (p and k) combination, in order to reflect its effect on friction factor and velocity distribution. The numerical mesh is used in the analysis, is shown in Fig. 2(c). For turbulent flow analysis, one has to properly take the
Fig. 2. The simplified model of annulus. (i) (a) Schematic of HTS cable (annular section with corrugated cryostat), (b) Corrugation showing Pitch and depth, (c) Meshed model and zoomed portion showing the details of meshing. (ii) HTS cable (annular section with smooth cryostat).
The range of Reynolds number for different corrugation depths are (9582–18,100), (13,268–25,062), (14,742–27,847), (16,217–30,632) for smooth cryostat and corrugated cryostat with 5, 7 and 9 mm depths respectively. The annular section has inner diameter Di and outer diameter Do. For the annulus with smooth cryopipe (Fig. 2ii) the outer diameter is Do and for corrugated cryopipe it is Dm. Table 2 shows the dimensions of the aforementioned nine geometries; pitch (p1, p2, p3) and depth (k1, k2, k3).
Table 3 Details of Meshing, Boundary condition and CFD formulation. Meshing Details
Boundary conditions
Number of nodes: 379,181 Inlet: Velocity inlet (0.18–0.34 m/s) Number of elements: 371,716 Outlet: Outflow Type of element: Quadrilateral Wall: Inner wall and Corrugated wall with Minimum size of the element: uniform heat load of 0.4 W/m and 1.4 W/m 4.0128e-4 respectively [21] CFD Formulation Pressure based Navier Stokes, 2D axis-symmetric, steady flow, Turbulent realizable k-ε Model with enhanced wall treatment
3.2. Theoretical analysis For a long length HTS power cable, pressure drop is an important aspect in estimating various parameters such as length of cable, cryogen pumping power. The pressure drop of subcooled LN2 flow is explained using Darcy-Weisbach equation.
P=
fL v 2 2dh
(3)
In order to calculate pressure drop along the length of cable, friction factor has to be evaluated. In case of fully developed flow, the pressure force balances the wall shear force. Hence after balancing both the forces the friction factor can be expressed as
f=
8
w
v2
(4)
The friction factor in the annular space is estimated by considering the existence of two types of wall surfaces (i.e. smooth surface of cable outer and the corrugated surface of cryostat’s inner wall). Hence the friction factor is evaluated as the sum of the contributions from both the walls, which are proportional to their wetted perimeters and can be expressed as [28]
f=
fi Di + fo Do Di + Do
Fig. 3. Validation of the present model.
(5)
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viscous sublayer (the near wall laminar flow) into account. The grids are stretched to cluster grids near the wall and are adjusted for every Reynolds number in order to ensure the dimensionless distance, y+ within 5. A mesh sensitive test is conducted for all nine different investigated geometries. The best suitable meshing is considered for the analysis as per the mesh convergence. However, the number of elements in the meshed model differs due to change in geometries. The tabulated number of elements and nodes in Table 3 are for the axissymmetric meshed model shown in Fig. 2(c), taken for the p = 10 mm and k = 7 mm configuration. During simulation, the “velocity inlet” condition is used for inlet boundary condition and “outflow” boundary condition for the outlet. The numerical friction factor is then derived
from the wall shear stress using Eq. (4). The details of the mesh formulation and boundary conditions are mentioned in Table 3. 5. Results and discussion The wall shear stress is obtained from the CFD simulation along the length of annular section, in the fully developed turbulent flow region. The values of wall shear stresses for all pitch and depth combinations at different Reynolds’s numbers are obtained for both smooth (cable side) and corrugated (cryostat side) surfaces of the annular section through which subcooled LN2 is flowing. Moreover, the friction factor is calculated using average shear stress in fully developed flow region. The
Fig. 4. Friction factors as a function of flow rate at varied pitch with fixed depths (a, b, c) and at varied, depths with fixed pitch (d, e, f). 4
Cryogenics 103 (2019) 102950
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Fig. 5. Streamlines from CFD for all nine geometries at a particular flow velocity of 0.22 m/s (with Re = 16217.14, 18019.04, 19820.951 for k = 5, 7 and 9 mm respectively). All p and k are in mm.
friction factors for both the surfaces are calculated using Eqs. (4) and (5). The numerical formulation considered for the present simulation model is first validated with the results obtained from Ivanov et al. [23] as shown in Fig. 3. The simulated result of pressure drop shows very good agreements with the results of Ivanov et al. [23]. The pressure drop is estimated from the friction factor using Darcy-Weisbach formulation (Eq. (3)). Thereafter, validated numerical formulation is used for current nine corrugated models. All six plots in Fig. 4 correspond to the values of friction factor at three different pitches (p1, p2, p3) and three depths (k1, k2, k3) within the Reynolds number range. It can be observed from Fig. 4(a)–(c) that the friction factor tends to decrease with the increase in corrugation pitch at constant corrugation depth. Similarly, Fig. 4(d)–(f) show that friction factor increases as corrugation depth increases with constant pitch. All six plots of Fig. 4 also show the friction factor variation of smooth cryostat with flow rates. The values of friction factor in smooth cryostat are smaller than that of corrugated cryostats. Further, the friction factors are low at larger Reynolds numbers as compared to those for smaller Reynolds numbers. The flow patterns of LN2 inside the corrugations of the annulus, for all combinations of pitches and depths are shown in Fig. 5. The results correspond to a particular flow velocity of 0.22 m/s. The obtained flow patterns vary with respect to k/p ratio. In smaller k/p ratios (Fig. 5(a), (d)–(i)), a single vortex tends to fill up the whole corrugation space, whereas for higher k/p ratios (Fig. 5(b) and (c)), two sets of vortices are observed within the corrugation space.
6. Conclusions The friction factor and the flow pattern of subcooled liquid nitrogen flowing within the annulus of HTS cable are investigated numerically using RANS turbulence model, for nine different corrugation geometries. From these investigations, it can be concluded that smaller k/p ratios (k/p ≤ 0.5) are preferred for getting lesser friction factor and thereby lesser LN2 pumping power to maintain thermally stable operation of HTS cable. The HTS cable with a pitch of 10 mm and depth of 5 mm shows the minimum pressure drop of 76.57 Pa/m for 28.69 L/ min. Further the CFD analysis gives an insight into flow visualization with breaking of vortices. This study can provide an useful guideline to the engineers and manufactures of flexible HTS cable while selecting the depth and pitch of corrugated pipes and designing the flexible cryostat with minimum pressure drop of liquid nitrogen. Declaration of Competing Interest The authors declared that there is no conflict of interest. References [1] Bednorz JG, Müller KA. Possible high TC superconductivity in the BaLaCuO system. Z Physik B 1986;64:189–93. [2] Takigawa H, Yumura H, Masuda T, Watanabe M, Ashibe Y, Itoh H, et al. The installation and test results for Albany HTS cable project. Physica C 2007;463–467:1127–31. [3] Mukoyama S, Maruyama S, Yagi M, Yagi Y, Ishii N, Sato O, et al. Development of 500 m HTS power cable in Super-ACE project. Cryogenics 2005;45:11–5.
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I. Das and V.V. Rao [4] Maguire JF, Schmidt F, Bratt S, Welsh TE, Yuan J. Installation and testing results of long Island transmission level HTS cable. IEEE Trans Appl Supercond 2009;19:1692–7. [5] Yang HS, Kim DL, Sohn SH, Lim JH, Choi HO, Choi YS, et al. Long term performance test of KEPCO HTS power cable. IEEE Trans Appl Supercond 2009;19:1782–4. [6] Yumura H, Ashibe Y, Ohya M, Itoh H, Watanabe M, Yatsuka K, et al. Test results of a 30-m HTS cable pre-demonstration system in Yokohama project. Physica C 2010;470:1558–62. [7] Xin Y, Hou B, Bi Y, Xi H, Zhang Y, Ren A, et al. Introduction of China’s first live grid installed HTS power cable system. IEEE Trans Appl Supercond 2005;15:1814–7. [8] Yagi M, Mukoyama S, Amemiya N, Ishiyama A, Wang X, Aoki Y, et al. Progress of 275 kV–3 kA YBCO HTS cable. Physica C 2011;471:1274–8. [9] Shabagin E, Heidt C, Strauß S, Grohmann S. Modeling of 3D temperature profiles and pressure drop in concentric three-phase HTS power cables. Cryogenics 2017;81:24–32. [10] Demko J, Hassenzahl W. Liquid air as a coolant for thermal management of longlength HTS cable systems. AIP Conf Proc 2012;1434(1):273–82. [11] Pamidi S, Kim CH, Kim JH, Crook D, Dale S. Cryogenic helium gas circulation system for advanced characterization of superconducting cables and other devices. Cryogenics 2012;52:315–20. [12] Kephart JT, Fitzpatrick BK, Ferrara P, Pyryt M, Miller J, Nadig C. Flow resistance experiments in HTS cable form. IEEE Trans Appl Supercond 2013;23(3):5401304. [13] Ashworth SP, Reagor DW. A novel cooling scheme for superconducting power cables. Cryogenics 2011;51:161–7. [14] Fuchino S, Tamada N, Ishii I, Higuchi N. Hydraulic characteristics in superconducting power transmission cable. Physica C 2001;354:125–8. [15] Weisend II JG, Van Sciver SW. Pressure drop from flow of cryogens in corrugated bellows. Cryogenics 1990;30:935–41. [16] Li Z, Li Y, Liu W, Zhu J, Qiu M. Comparison of liquid nitrogen flow resistance in corrugated pipe with smooth pipe. IEEE Trans Appl Supercond
2015;25(3):5401304. [17] Chevtchenko O, Zuijderduin R, Smit J, Willén D, Lentge H, Thidemann C, et al. Low friction cryostat for HTS power cable of Dutch project. Phys Procedia 2012;36:1309–12. [18] Lee CH, Kim CH, Kim KS, Kim DH, Kim IS. Performance of heat transfer and pressure drop in superconducting cable. Cryogenics 2003;43:583–8. [19] Dondapati RS, Rao VV. Pressure drop and heat transfer analysis of long length cooled HTS cables. IEEE Trans Appl Supercond 2013;23(3):5400604. [20] Sasaki A, Hamabe M, Famakinwa T, Yamaguchi S, Radovinsky A, Okumura H, et al. Cryogenic fluid dynamics for DC superconducting power transmission line. IEEE Trans Appl Supercond 2007;17:1748–51. [21] Maruyama O, Ohkuma T, Izumi T, Shiohara Y. Numerical calculation of advection heat transfer and fluid flow dynamics. IEEE Trans Appl Supercond 2015;25(3):5401505. [22] Ivanov Y, Watanabe H, Hamabe M, Kawahara T, Sun J, Yamaguchi S. Design study of LN2 circulation in a long SC power transmission lines. Phys Procedia 2012;36:1372–7. [23] Ivanov YV, Romashov MA, Bemert SE, Sytnikov VE. Choice of flexible cryostat for 2.5 km DC HTS cable to be laid in St. Petersburg. AIP Conference Proceedings, vol. 1573. 2014. p. 887. [24] Koh D, Yeom H, Hong Y, Lee K. Performance tests of HTS power cable cooling system. IEEE Trans Appl Supercond 2004;14(2):1747. [25] Sasaki A, Ivanov Y, Yamaguchi S. LN2 circulation in cryopipes of superconducting power transmission line. Cryogenics 2011;51(9):471–6. [26] Zajaczkowski B, Giesbers AJM, Holtrust M, Haenen E, Heijer R. Feasibility of inline cooling in long distance HTS power line. Cryogenics 2011;51(4):180–6. [27] Barr DIH. Two additional methods of direct solution of the Colebrook-White function. Proc Inst Civ Eng 1976;61:489–97. [28] Ivanov YV, Watanabe H, Hamabe M, Sun J, Kawahara T, Yamaguchi S. Circulation pump power for 200 m cable experiment. Physica C 2011;471:1308–12.
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