- Email: [email protected]
Influence of corrugation topology on thermohydraulic performance of cold dielectric counter cooled high temperature superconducting cable
Physica C: Superconductivity and its applications 566 (2019) 1353525
Contents lists available at ScienceDirect
Physica C: Superconductivity and its applications journal homepage: www.elsevier.com/locate/physc
Influence of corrugation topology on thermohydraulic performance of cold dielectric counter cooled high temperature superconducting cable
T
Mohit Kalsia, Raja Sekhar Dondapati
⁎
School of Mechanical Engineering, Lovely Professional University, Phagwara, 144401, India
ARTICLE INFO
ABSTRACT
Keywords: Corrugation topology Cold dielectric Counter flow HTS cable Turbulent kinetic energy Boundary layer separation
Fluid flow, pressure drop and heat transfer across the long length cold dielectric counter cooled High Temperature Superconducting (HTS) cables are significantly influenced by the different corrugation (rectangular, circular and triangular) topologies. Thus, in this present work, thermal and hydraulic characteristics of turbulent LN2 flow in counter cooled HTS cable with various corrugation topologies are computationally investigated. The 2-D axisymmetric model of HTS cable with counter flow cooling system is considered by changing the corrugation shapes for Reynolds number ranging from 3.0 × 104 to 6.0 × 104. Heat flux from ambient temperature on outer corrugated pipe and heat generation from A.C. losses in the HTS tapes are also considered in the present simulations. In addition, distribution of the velocity, temperature and turbulent kinetic energy (TKE) of liquid nitrogen (LN2) in the HTS cable with various corrugations are estimated using computational fluid dynamics (CFD) technique. Finite volume method is adapted to solve the governing equations (continuity, momentum and energy) using Semi-Implicit Pressure Linked Equations (SIMPLE) scheme with k turbulence model and enhanced wall treatment. The results reveal that the corrugation topologies (rectangular, circular and triangular) have significant effect on heat transfer and pressure drop. The corrugated pipes with different topologies exhibit different friction factors due to the variations in the contact of wall surfaces with the LN2. Moreover, the calculated friction factors for all the three corrugation topologies are compared with the experimental results available in the literature. Further, the results of temperature difference between outlet and inlet temperatures of LN2 are validated with the available experimental measurements. Finally, it was concluded that the effect of heat flux and AC Losses on cooling capacity and heat transfer is found to be significant as compared that on friction factor and pumping power.
1. Introduction High temperature superconducting (HTS) power cables have been developing as a solution of increasing power demand due to their advantages of lower losses, large transmission capability, light weight and smaller diameter with higher ampacity. The HTS cables exhibit various kind of losses such as AC losses in the superconductor, dielectric losses in dielectric material, the heat influx through the cryogenic enclosure wall from ambient temperature and pressure losses in LN2 flowing through corrugated pipes. In order to encounter such losses in the HTS cable, thermal and hydraulic analysis of LN2 is necessary. After years of research, the HTS cables have been acknowledged to be installed in the grids for large scale power transmission. However, the efficient cooling system and flow system in HTS cable is still one of the major issues for the researcher and manufacturers. Therefore, several studies on cooling mechanism (thermal) and flow system (hydraulic) in corrugated pipe
⁎
HTS cables have been carried out and published so far. Kottonau et al. [1] has analyzed the pressure drop and heat transfer for four various cooling concepts in three phase concentric HTS cable. The HTS cable may also have other different cooling arrangements such as single flow cooling and counter flow cooling systems. When LN2 flows through either inner or annular flexible corrugated pipe to reduce the temperature rise in HTS cable, termed as single flow cooling system. The thermohydraulic analysis of HTS cable using single flow cooling system is described by [2–10]. The influence of corrugation pitch and depth on pressure drop and heat transfer in warm dielectric HTS cable with single flow cooling systems using computer simulations have been investigated by Lee et al. [4] and Dondapati et al. [6]. Whereas, the thermal and fluid characteristics of LN2 in annular channel in the HTS cable have been investigated by Sasaki et al. [7] and Maruyama et al. [5]. However, there are few reports on the thermohydraulic behavior of the non-cryogenic fluid flowing through corrugated pipes with single
Corresponding author. E-mail address: [email protected] (R.S. Dondapati).
https://doi.org/10.1016/j.physc.2019.1353525 Received 4 July 2019; Received in revised form 19 August 2019; Accepted 5 September 2019 Available online 05 September 2019 0921-4534/ © 2019 Elsevier B.V. All rights reserved.
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 1. (a) flowchart of thermohydraulic analysis of HTS cable (b) Schematic of Counter flow arrangement.
flow cooling systems [11–15]. On the other hand, counter flow cooling system [16–24] has its own advantage of compact size due to elimination of separate LN2 return pipe and efficient cooling of HTS cables. The research work on counter flow cooling system in the HTS cables is done so far either using analytical approach or experimental approach. Moreover, nobody has reported computational work on counter cooled HTS cable with various corrugation topologies. Hence, in the present work, counter-flow cooling system with various corrugation topologies have been proposed and analyzed the heat transfer and pumping power computationally in order to design the long length HTS cables.
Table 1 Parameters for conceptual design of HTS cable.
2. Solution procedure of computational method
Parameters
Details
Diameter of Inner region (mm) Equivalent Diameter of Annular region (mm) Thickness of corrugated pipe, g (mm) Thickness of HTS tape (mm) Thickness of Dielectric material (mm) Corrugation pitch, p (mm) Corrugation depth, s (mm) Heat Flux from ambient/exterior, Qe (W/m2) Heat from HTS tapes/A.C loss, QAC (W/m) Inlet temperature, To (K) Inlet Pressure, P1 (bar) Volumetric flow, V (L/min)
40 37.5 1 0.02 0.1 8 4 4–10 1–2.5 65 3 20–35
3. Computational modeling of HTS cable
The solution process of computational method used for thermohydraulic analysis of HTS cable is shown in Fig. 1(a). The method involves the creation of geometry, mesh (grid) and few significant solver settings to obtain the desired results. Referring the method, geometries with various corrugation shapes are modelled using ANSYS Design Modeler with physical parameters as discussed in Table 1. The modelled HTS cable with various corrugation topologies are further meshed using ANSYS Meshing and the mesh size varies for each of geometry depending upon the wall corrugation surface. The meshed geometries are further exported to the ANSYS Fluent in order to define boundary conditions, material properties, turbulence model and pressure-velocity coupling scheme. The solver will stop the calculation once the solution criteria for the continuity, x, y and z velocities, the kinetic energy k, and the dissipation of energy ɛ is satisfied. The mesh geometries are refined for the grid independent analysis to achieve more accurate results. Using post-processing tool of the ANSYS Fluent, the required results for the defined model can be retrieved.
The single phase coaxial cold dielectric HTS cable using (singlesided cooling with internal coolant return flow) counter flow cooling was proposed in our previous study with circular corrugations [24]. In the present model the various corrugation topologies were chosen to investigate the thermal and hydraulic performance of LN2. Fig. 1(b) depicts the counter flow cooling arrangement in which liquid nitrogen (LN2) is used to cool the HTS cable, which is circulated through inner corrugated pipe (inner region) and exits from the annular outer corrugated pipe (annular region). The HTS cable comprises of inner corrugated pipe, HTS tapes, Dielectric material, and outer corrugated pipe with cable shield. HTS tape comprises of different layers of solid materials such as silver/copper (protective layer), YBCO (superconducting layer), buffer layer and metal substrate with total thickness of ≤0.2 mm. Polypropylene laminated paper (PPLP) is commonly used as an insulation material for superconducting device applications with an
2
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 2. Schematic and structural parameters of 2-D axisymmetric HTS cable with various corrugation shapes and respective typical mesh (a) rectangular (b) circular (c) triangular.
advantage of low dielectric losses. The corrugated pipes used in the HTS cable are mainly of stainless steel (SS) material with cryogenic compatible grades such SS316L. Fig. 2 shows the 2-D axisymmetric model of HTS cable with various corrugation topologies (rectangular, circular and triangular) having a computational length of 504 mm with their respective mesh. The physical parameters such as inner corrugated pipe of 40 mm in diameter and an annular outer corrugated pipe with diameter of 37.5 mm is considered for the present work. The thickness of HTS tape and dielectric material (solid domain) is <1% of the diameter of corrugated pipe as can be seen in Table 1. Therefore, due to the lesser thickness of HTS tape and dielectric material than fluid domain, the thickness of HTS tapes and dielectric material is worth neglecting for the present CFD analysis. During operation with alternating current (A.C), the HTS tapes cause electrical power dissipation (W/m) that indicates an internal heat source (W/m3). Therefore, the effect of heat generation (W/m3) in the HTS tapes due to electrical dissipation power is considered and assumed to be equal in the inner corrugated pipe of 1 mm thickness for the present analysis. Moreover, the exterior heat–in-leak (W/m) from the ambient temperature on the outer corrugated pipe is converted into heat flux (W/ m2) and worth considered for the analysis. The present study involves the effect of heat-in-leak of (4–10 W/m2) and A.C. losses of (1–2.25 W/ m) on pressure drop and heat transfer analysis of the HTS model. The heat generated (W/m3) in the HTS tapes due to electrical dissipation power can be estimated using Eq. (1).
=
Q AC ASC
3.1. Grid independent study The grid independent analysis of modeled HTS cable with various corrugation topology is shown in Fig. 3. It can be concluded from the results that the pressure drop is grid independent after further refinement of the mesh with element size of 0.6 mm, 0.58 mm and 0.7 mm for rectangular, circular and triangular corrugations respectively. Therefore, in order to avoid long computational time and solution instability, mesh with element size of 0.6 mm for rectangular corrugation, 0.58 mm for circular corrugation and 0.7 mm for triangular corrugation was adopted for the further thermohydraulic analysis of HTS cable. The number of nodes corresponding to the element size are compiled in the Table 2 given below. 3.2. Boundary conditions The boundary conditions of counter cooled HTS cable with various corrugation shapes are discussed below. (a) Steady state and incompressible flow of LN2 with the temperature dependent thermophysical properties is considered for the analysis. (b) The LN2 inlet conditions such as inlet temperature of 65 K, inlet mass flow rate ranges from 20 L/min to 35 L/min [19], the turbulence intensity of I = 5% and the hydraulic diameter of 40 mm are considered for the present analysis. (c) The outlet boundary is assigned as outflow, a turbulence intensity of I = 5% and the hydraulic diameter of 37.5 mm. (d) Inner corrugated pipe (solid) of thickness 1 mm is considered as heat source and allocated as heat generation of (396 W/m3 to 986 W/m3) corresponding to the A.C. losses. (e) The wall boundary conditions at outer corrugated wall is assigned as heat flux of (4 W/m2–10 W/m2). No slip boundary condition is imposed on the walls of corrugated pipe surfaces. (f) The k-epsilon turbulent model with enhanced wall treatment and pressure based solver is used in the simulation. The solver uses
(1)
where, ω is the heat generated by power dissipation in HTS phase (W/ m3). QAC is known as the AC losses in superconducting phase (W/m) and Asc is the cross-sectional area of the HTS phase (W/m2). The analytical process of estimating flow characteristics such as pressure drop, friction factor and pumping power in the HTS cable is discussed by Kalsia et al. [24]. 3
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 3. Pressure drop for various element sizes in the HTS cable with different corrugation (a) Rectangular (b) Circular (c) Triangular.
follows: X-momentum
Table 2 Number of nodes for various element size. Corrugation Shape
Rectangular
Circular
Triangular
Element Size (mm) Number of Nodes
0.6 60,945
0.58 63,508
0.7 56,031
u u u +u +v t x y
p +µ u x
= FY
p +µ v y
uu uv + x y
(3)
Y-momentum
v v v +u +v t x y
SIMPLE algorithm for pressure and velocity coupling. 4. Governing equations
Where, u = (
The velocity and the pressure fields were acquired from the numerical solution of the mass momentum and energy conservation equations under incompressible and steady-state conditions, in the domain of the finite volume CFD approach. Since flow is turbulent in all cases due to the corrugation topologies, the simulations are obtained using general Reynolds averaged Navier-Stokes (RANS) equations [24]. The time-averaged conservation of mass for 2-D flow can be written as:
u v + =0 x y
= FX
(
(µ
ui xj
ui u j xj
2u
x2
+
2u
y2
+
2u
z2
uv vv + x y
) and v = (
2v
x2
+
2v
y2
+
(4) 2v
z2
)
) is termed as Reynolds stress or turbulent shear stress and
ui uj ) is known as total shear stress τij.
Fx, Fy and Fz are the body forces, which are neglected for the present simulations The time-averaged energy equation can be written as:
CP u
T T +v x y
=
x
k
T x
CP u T
+
y
k
T y
CP v T (5)
(2)
where, u is the momentary velocity component, u is the time-averaged velocity and u′is the fluctuating velocity. The time-averaged conservation of momentum equations are as
5. Results and discussion In this study the thermohydraulic analysis of HTS cable with 4
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 4. (a). Validation of friction factor from present investigation with experimental results obtained by Li et al. [27] (b) Comparison of temperature difference between outlet and inlet of LN2 in counter flow HTS cable (present work) with that of LN2 estimated by Dondapati et al. [28] and with the experimental results performed by Ivanov et al. [29] (c) validation of obtained pressure drop (present work) with experimental and simulation results performed by Li et al. [27].
different corrugation topology was carried out using k realizable turbulence model with enhanced wall treatment due to the extra benefit of improved performance for the complex flow involving swirl/vortices/rotation, adverse pressure gradient, flow separation and recirculation [14,25,26]. Furthermore, the results of friction factor, temperature difference and pressure drop for the present work are validated with the experimental and numerical published results. In addition, the effect of various heat in leaks and A.C. losses on the thermohydraulic performance of HTS cable are also presented in this section.
Moreover, the friction factors found to be reduced at higher Reynolds numbers ranges as can be observed in the Fig. 4(a). So far, no correlation is established for the calculation of friction losses in the corrugated annular pipe. Therefore, the foremost reason for the higher friction factor in the HTS cable of different corrugation topologies, may be due to the combined effect of LN2 interaction with the walls of inner corrugated pipe and outer (annular) corrugated pipe simultaneously [24]. Fig. 4(b) demonstrates the comparison of temperature difference between outlet and inlet of counter flow HTS cable using LN2 estimated by Dondapati et al., [28] and that estimated by Ivanov et al., [29]. It can be seen from the results that the temperature difference between outlet and inlet for LN2 in the counter flow HTS cable of different corrugation topologies is lower than the other HTS cable system (singleway cooling). Hence, long length counter flow HTS cables can be cooled effectively without losing the superconductivity. Fig. 4(c) represents the validation of pressure drop estimated computationally for the counter cooled HTS cable with the experimental and calculated data available for Single (annular) flow cooling system of HTS cable. Analyzing the pressure drop in counter cooled HTS cable with different
5.1. Validation The results obtained from the present computational investigation are validated with the experimental results computed by Li et al. [27] (annulus flow through centrally placed smooth pipe enveloped by a corrugated pipe) with the present work (employing counter flow through corrugated pipes placed centrally as well as externally) as shown in Fig. 4. The results show that the topology of corrugation would affect the friction factors at various Reynolds numbers. 5
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
corrugation topologies, it was found that the pressure drop (Pa/m) in the counter flow cooling system (present work) is larger than the single flow cooling system (annulus flow through centrally placed smooth pipe enveloped by a corrugated pipe) [27]. This difference in pressure drop in the counter flow cooling system (present work) may be due to the variation in corrugation topology of the pipes (inner and annular) along with expected turbulent characteristics such as swirl, separation and recirculation as discussed in Section 5.4.
temperature distribution profile of LN2 in counter cooled HTS cable at flow rate of 25 L/min and heat flux of 6 W/m2 is shown in Fig. 6(g). The maximum temperature of LN2 is found to be 65.018 K in triangular shaped HTS cable at the location of 0.150 m from the inlet. The radial temperature profile is divided into three domains such as inner region (fluid), superconducting phase (solid) and annular region (fluid). The temperature rise can easily be measured in each of the domain through the temperature profile.
5.2. Effect of heat flux and corrugation topology on thermohydraulic characteristics
5.3. Effect of heat generation and corrugation topologies on thermohydraulic characteristics
The influence of various heat fluxes and corrugation topologies on thermohydraulic characteristics of HTS cable are presented in this section. The effect of exterior heat flux (4 W/m2–10 W/m2) due to the ambient temperature encountered by the outer corrugated pipe is significantly affecting the thermohydraulic performance of the HTS cable. Also, the effect of various corrugation topologies (rectangular, circular and triangular) is significant on the thermohydraulic behavior of HTS cable.
The effect of various heat generation and corrugation topologies on pressure drop and heat transfer analysis of counter cooled HTS cable is revealed in this section. The heat generation is the form of heat source produced through the HTS tapes while transferring the alternating current (A.C.). The actual A.C. losses in the HTS cable as (1–2.25 W/m) and the corresponding heat generation as (396 W/m3 to 986 W/m3) are considered for the present analysis. 5.3.1. Hydraulic studies The effect of heat sources and corrugation topologies on hydraulic characteristics of counter cooled HTS cable is presented in this section. Fig. 7 shows the effect of corrugation topologies and heat generation on friction factor, pumping power and the velocity profile obtained in the counter cooled HTS cable. It can be observed from the results that there is no significant difference between effect of heat flux and heat generation on the hydraulic performance of the HTS cable. Therefore, the present analysis concludes that the hydraulic performance of counter cooled HTS cable is independent of heat flux or heat generation.
5.2.1. Hydraulic studies The effect of various heat fluxes and corrugation topologies on friction factor, pumping power and velocity profile is discussed in this section to describe the hydraulic behavior of LN2. The pressure drop behavior in terms of friction factor in the HTS cable with various corrugation shapes is displayed in Fig. 5(a)–(c) for the Reynolds number range of 30,000–60,000. It can be concluded that the friction factor for the triangular corrugation is significantly high as compared with the rectangular and circular corrugations. The pumping power follows the increasing trend at various volumetric flow rates as can be seen in Fig. 5(d)–(f). The high pumping power is required to circulate the liquid nitrogen in triangular corrugation shape counter cooled HTS cable as compared to rectangular and circular corrugation. Moreover, the pumping power in all the corrugation shaped HTS cable for various heat fluxes will be quite similar at different flow rates. The velocity profiles of all three corrugation shapes in inner region and annular region at 0.150 m from the inlet of the HTS cable are shown in Fig. 5(g). The triangular corrugation shaped HTS cable has attained a maximum velocity of 0.44 m/s at the axis of the model. The negative sign indicates the direction of flow in the annular region of the HTS cable and the maximum velocity attained in this region is 0.2 m/s. it can be seen from the results that fully developed velocity profiles are not observed as also reported earlier [24]. In order to achieve the fully developed flow at inlet in the HTS cable, the domain needs to extend up to a distance called entry length. The estimated entry lengths for each Reynolds numbers are compiled in Table 3.
5.3.2. Thermal studies This section reveals the influence of various corrugation topologies and heat generation on heat transfer mechanism of counter cooled HTS cable. Fig. 8(a)–(c) represents the effect of various A.C. losses and corrugation shapes on the cooling capacity of LN2. It can be seen from the results that with increase in the A.C. loss the cooling capacity also increases and with high flow rates the required cooling capacity will be higher. The maximum required cooling capacity were found in rectangular corrugation. The enhancement of heat transfer in rectangular corrugation shaped HTS cable is an evident from increase in the Nusselt number as shown in Fig. 8(d)–(f). With increase in the Reynolds number, the Nusselt number also increases can be observed from the results. Similarly, the A.C. losses increases, the average nusselt number for the various corrugation shapes HTS cable increases. Also, the highest Nusselt number values were presented by rectangular corrugation shaped HTS cable. The radial temperature distribution profile of LN2 in counter cooled HTS cable at flow rate of 25 L/min and A.C. loss of 1.5 W/m is shown in Fig. 8(g). The maximum temperature in the counter cooled HTS cable at the location of 0.150 m from the inlet is found to be 65.012 K.
5.2.2. Thermal studies The effect of various heat fluxes and corrugation topologies on heat transfer analysis in counter cooled HTS cable is presented in this section. Heat transfer analysis in the form of the cooling capacity, Nusselt number and the temperature profile of LN2 inside a counter cooled HTS cable is discussed. It can be observed from the Fig. 6(a)–(c) that with increase in the flow rates, the required cooling capacity of LN2 also increases and with maximum heat flux, the required cooling capacity will be higher. Moreover, the highest required cooling capacity were presented by rectangular corrugation shaped HTS cable. Average Nusselt number at Reynolds number range of 30,000–60,000 for different corrugation topologies is presented in Fig. 6(d)–(f). It can be noted that as Reynolds number increases, the Nusselt number for the various corrugation shapes also increases. Whereas, the heat flux reduces, the Nusselt number for the various corrugation shapes in the HTS cable increases. The highest Nusselt number values were presented by rectangular corrugation shaped HTS cable due to the presence of high recirculation and thin boundary layer. The radial
5.4. Comparison of thermohydarulic performance of HTS cable with different corrugation topologies Fig. 9(a)–(c) shows the boundary layer separation, recirculation and vortex appearance in each of the corrugation topology for inner and annular region. The separated boundary layer in both the regions attempt to develop and reattach when the fluid flow past the each corrugation topology. The separation of boundary layer and reattachment occurs for an instance due to the continuation of upper and lower corrugations in both the regions of the HTS cable. The continuation of boundary layer separation in the corrugations increase the boundary layer thickness which leads to an additional resistance and flow reversal. An adverse pressure gradient produces vortices and eddies, results in the formation of turbulence and more pressure drop across the 6
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 5. Effect of Heat Flux on cooling capacity (a) Rectangular Corrugations (b) Circular Corrugations (c) Triangular Corrugations, Effect of Heat Flux on pumping power (d) Rectangular Corrugations (e) Circular Corrugations (f) Triangular Corrugations and (g) Radial velocity distribution counter cooled HTS cable.
flow. Fig. 9(d)–(f). The effect of various heat-in-leaks and A.C. losses are studied simultaneously in order to analyze the thermal behavior of LN2. The inner region of each corrugation topology seems with an almost
constant temperature gradient whereas, the high temperature gradient is found around the walls of outer corrugated pipe in annular region. The maximum thermal boundary layer thickness occurs near the separation point, whereas the minimum thermal boundary layer thickness near the reattachment point in the corrugations [12]. The temperature distribution in each of the corrugation topology of HTS cable is shown in It can be observed from the contours that the heat flux dominates more than the A.C. losses to raise the temperature of LN2. The
Table 3 Estimated approximate entry lengths at various Reynolds numbers. Reynolds Number Entry Length (m)
32,450 0.99
40,563 1.03
48,675 1.06
56,788 1.09
7
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 6. Effect of Heat flux on cooling capacity (a) Rectangular Corrugations (b) Circular Corrugations (c) Triangular Corrugations, Effect of Heat Flux on Nusselt Number (d) Rectangular Corrugations (e) Circular Corrugations (f) Triangular Corrugations and (g) Radial Temperature distribution counter cooled HTS cable.
minimum temperature in each of the corrugation topology is 65 K. And the maximum temperature reaches 65.077 K, 65.0283 K and 65.03537 K in rectangular, circular and triangular corrugations respectively. Hence, the maximum temperature in rectangular corrugation indicates the higher Nusselt number than that of other corrugations. TKE is a standout amongst the most significant factors in a boundary layer and flow attributes, and it is a proportion of the turbulence intensity, which is explicitly identified with the velocity profile of the fluid. High TKE along the fluid stream way contributes to the strong flow mixing and enhanced heat transfer, whereas the TKE layers indicate the intensity of flow mixing from the corrugated wall surfaces to the flow zone. Influence of various corrugation topologies on TKE are shown in Fig. 9(g)–(i). It is observed that the magnitude of TKE is much higher near the side wall and tube wall of all corrugated shapes. This shows the strong intensity of flow mixing from side wall and corrugated walls to the core
flow zone, which leads to an enormous heat transfer performance. It is also concluded that rectangular corrugation shape have higher TKE near side wall than circular and triangular corrugation shapes. 6. Conclusions In this paper, the influence of three various corrugation topologies (rectangular, circular and triangular) on thermohydraulic performance of turbulent flow LN2 was studied using CFD method. Moreover, the influence of heat-in-leak losses and A.C. losses on thermal and hydraulic characteristics of LN2 were also considered in the present work. The following conclusion can be drawn from the present simulation results: i Pressure drop in the triangular corrugation shaped HTS cable is significantly larger than the circular and rectangular corrugation due to the higher intensity of the vortices appearing in the both 8
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 7. Effect of AC Losses on friction factor with (a) Rectangular Corrugations (b) Circular Corrugations (c) Triangular Corrugations, Effect of AC Losses on pumping power with (d) Rectangular Corrugations (e) Circular Corrugations (f) Triangular Corrugations and (g) Radial velocity distribution counter cooled HTS cable.
inner and annular region. ii The obtained friction factor results for each corrugation shapes are compared with other experimental results. In addition, the obtained friction factor for the present work is significantly larger due to the counter flow arrangement with corrugated pipes. iii The Nusselt number obtained from the rectangular corrugation has increased which indicates the higher heat transfer rate than that of
other two corrugation shapes. Moreover, the intensity of the turbulent kinetic energy is found to be higher in rectangular corrugation shaped HTS cable. iv The effect of various heat-in-leak losses (heat flux) and A.C. losses (heat generation) on the hydraulic performance of LN2 is found to be similar. Whereas, the thermal performance of LN2 was significantly affected by heat-in-leak losses and A.C. losses. 9
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 8. Effect of AC Losses on cooling capacity with (a) Rectangular Corrugations (b) Circular Corrugations (c) Triangular Corrugations, Effect of AC Losses on Nusselt Number with (d) Rectangular Corrugations (e) Circular Corrugations (f) Triangular Corrugations and (g) Radial Temperature distribution counter cooled HTS cable.
10
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 9. Velocity vectors in (a) Rectangular Corrugations (b) Circular Corrugations (c) Triangular Corrugations, Temperature Distribution in (d) Rectangular Corrugations (e) Circular Corrugations (f) Triangular Corrugations and Turbulent Kinetic Energy Distribution in (g) Rectangular Corrugations (h) Circular Corrugations (i) Triangular Corrugations across the HTS cable.
Acknowledgements
[3] Y.V. Ivanov, H. Watanabe, M. Hamabe, J. Sun, T. Kawahara, S. Yamaguchi, Circulation pump power for 200 m cable experiment, Phys. C Supercond. 471 (21–22) (2011) 1308–1312. [4] C.H. Lee, C.D. Kim, K.S. Kim, D.H. Kim, I.S. Kim, Performance of heat transfer and pressure drop in superconducting cable former, Cryogenics (Guildf) 43 (2003) 583–588. [5] O. Maruyama, T. Ohkuma, T. Izumi, Numerical analysis of heat transfer and fluid characteristics in long distance HTS cable, Phys. Procedia 45 (Jan. 2013) 285–288. [6] R.S. Dondapati, V.V. Rao, Pressure drop and heat transfer analysis of long length internally cooled HTS cables, Appl. Supercond. IEEE Trans. 23 (3) (2013) 2–5. [7] A. Sasaki, Y. Ivanov, S. Yamaguchi, LN2 circulation in cryopipes of superconducting power transmission line, Cryogenics (Guildf) 51 (9) (Sep. 2011) 471–476. [8] S. Thadela, V.V. Rao, R. Agarwal, R.S. Dondapati, Computational investigation on thermohydraulic characteristics of high-temperature superconducting (HTS) power cables, Phys. C Supercond. Appl. 559 (2019) 25–31. [9] M. Kalsia, R.S. Dondapati, P. Rao, Statistical correlations for thermophysical properties of supercritical argon (SCAR) used in cooling of futuristic high temperature superconducting (HTS) cables, Phys. C Supercond. Appl. 536 (2017) 30–34. [10] O. Maruyama, T. Mimura, Fluid characteristic of liquid nitrogen flowing in HTS
The authors gratefully acknowledge the suggestions of the reviewers which helped in enhancing standard of the manuscript. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.physc.2019.1353525. References [1] D. Kottonau, W.T.B. De Sousa, J. Bock, M. Noe, Design comparisons of concentric three-phase HTS cables, IEEE Trans. Appl. Supercond. 29 (6) (2019). [2] J. He, Y. Tang, B. Wei, J. Li, L. Ren, J. Shi, K. Wang, X. Li, Y. Xu, S. Wang, Thermal analysis of HTS power cable using 3-D fem model, IEEE Trans. Appl. Supercond. 23 (3) (2013) 1–4.
11
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati cable, J. Phys. Conf. Ser. 1054 (2018). [11] M. Ahsan, Numerical analysis of friction factor for a fully developed turbulent flow using k e ε turbulence model with enhanced wall treatment, Beni-Suef Univ. J. Basic Appl. Sci. 3 (4) (2014) 269–277. [12] X. Chen, H. Han, K. Lee, B. Li, Y. Zhang, Turbulent heat transfer enhancement in a heat exchanger using asymmetrical outward convex corrugated tubes, Nucl. Eng. Des. 350 (January) (2019) 78–89. [13] S. Song, X. Yang, F. Xin, T.J. Lu, S. Song, X. Yang, F. Xin, T.J. Lu, Modeling of surface roughness effects on stokes flow in circular pipes modeling of surface roughness effects on stokes flow in circular pipes, Phys. fluids 30 (2) (2018). [14] A. Kaood, H. Eltahan, M.A. Yehia, E.E. Khalil, Numerical investigation of heat transfer and friction characteristics for turbulent flow in various corrugated tubes, J. Power Energy 233 (2018) 1–19. [15] A.T. Franco, S.L.M. Junqueira, M.A.L. Gonc, Turbulent flow in D-Type corrugated pipes: flow pattern and friction factor, J. Fluids Eng. 134 (December 2012) (2016) 1–9. [16] J.A. Demko, J.W. Lue, M.J. Gouge, J.P. Stovall, U. Sinha, R.L. Hughey, Practical ac loss and thermal considerations for HTS power transmission cable systems, IEEE Trans. Appl. Supercond. 11 (1) (2001) 1789–1792. [17] J.A. Demko, J.W. Lue, M.J. Gouge, P.W. Fisher, D. Lindsay, M. Roden, Analysis of a liquid nitrogen-cooled tri-axial High- Temperature superconducting cable system, Am. Inst. Phys. 49 (2004) 913–920. [18] J.A. Demko, R.C. Duckworth, Cooling configuration design considerations for longlength HTS cables, IEEE Trans. Appl. Supercond. 19 (3) (2009) 1752–1755. [19] S. Fuchino, M. Furuse, N. Higuchi, Longitudinal temperature distribution in superconducting power cables with counter-Flow cooling, IEEE Trans. Appl. Supercond. 12 (1) (2002) 1339–1342. [20] M. Furuse, S. Fuchino, N. Higuchi, Counter flow cooling characteristics with liquid nitrogen for superconducting power cables, Cryogenics (Guildf) 42 (2002)
405–409. [21] M. Furuse, S. Fuchino, N. Higuchi, Investigation of structure of superconducting power transmission cables with LN2 counter-flow cooling, Phys. C Supercond. 386 (2003) 474–479. [22] T. Masuda, T. Kato, H. Yumura, M. Watanabe, Y. Ashibe, K. Ohkura, Verification tests of a 66 kV HTSC cable system for practical use (first cooling tests), Phys. C Supercond. 381 (2002) 1174–1180. [23] E. Shabagin, C. Heidt, S. Strauß, S. Grohmann, Modelling of 3D temperature profiles and pressure drop in concentric three-phase HTS power cables, Cryogenics (Guildf) 81 (2017) 24–32. [24] M. Kalsia, R.S. Dondapati, Thermohydraulic analysis of cold dielectric high temperature superconducting cable with counter-flow cooling, Phys. C Supercond. its Appl. 564 (2019) 59–67. [25] M. Pisarenco, Friction factor estimation for turbulent flows in corrugated pipes with rough walls, J. Offshore Mech. Arct. Eng. 133 (February) (2011) 1–9. [26] H. Benzenine, R. Saim, Comparative study of the thermo-convective behavior of a turbulent flow in a rectangular duct in the presence of three planar baffles and/or corrugated (waved), J. Eng. Sci. Technol. 13 (1) (2018) 35–47. [27] Z. Li, Y. Li, W. Liu, J. Zhu, M. Qiu, Comparison of liquid nitrogen flow resistance in corrugated pipe with smooth pipe for HTS cable, IEEE Trans. Appl. Supercond. 25 (3) (2015). [28] R.S. Dondapati, J. Ravula, S. Thadela, P.R. Usurumarti, Analytical approximations for thermophysical properties of supercritical nitrogen (SCN) to be used in futuristic high temperature superconducting (HTS) cables, Phys. C Supercond. its Appl. 519 (2015) 53–59. [29] Y. Ivanov, H. Watanabe, M. Hamabe, T. Kawahara, J. Sun, Observation of the thermosiphon effect in the circulation of liquid nitrogen in HTS cable cooling system, Phys. Procedia 27 (2012) 368–371.
12
Contents lists available at ScienceDirect
Physica C: Superconductivity and its applications journal homepage: www.elsevier.com/locate/physc
Influence of corrugation topology on thermohydraulic performance of cold dielectric counter cooled high temperature superconducting cable
T
Mohit Kalsia, Raja Sekhar Dondapati
⁎
School of Mechanical Engineering, Lovely Professional University, Phagwara, 144401, India
ARTICLE INFO
ABSTRACT
Keywords: Corrugation topology Cold dielectric Counter flow HTS cable Turbulent kinetic energy Boundary layer separation
Fluid flow, pressure drop and heat transfer across the long length cold dielectric counter cooled High Temperature Superconducting (HTS) cables are significantly influenced by the different corrugation (rectangular, circular and triangular) topologies. Thus, in this present work, thermal and hydraulic characteristics of turbulent LN2 flow in counter cooled HTS cable with various corrugation topologies are computationally investigated. The 2-D axisymmetric model of HTS cable with counter flow cooling system is considered by changing the corrugation shapes for Reynolds number ranging from 3.0 × 104 to 6.0 × 104. Heat flux from ambient temperature on outer corrugated pipe and heat generation from A.C. losses in the HTS tapes are also considered in the present simulations. In addition, distribution of the velocity, temperature and turbulent kinetic energy (TKE) of liquid nitrogen (LN2) in the HTS cable with various corrugations are estimated using computational fluid dynamics (CFD) technique. Finite volume method is adapted to solve the governing equations (continuity, momentum and energy) using Semi-Implicit Pressure Linked Equations (SIMPLE) scheme with k turbulence model and enhanced wall treatment. The results reveal that the corrugation topologies (rectangular, circular and triangular) have significant effect on heat transfer and pressure drop. The corrugated pipes with different topologies exhibit different friction factors due to the variations in the contact of wall surfaces with the LN2. Moreover, the calculated friction factors for all the three corrugation topologies are compared with the experimental results available in the literature. Further, the results of temperature difference between outlet and inlet temperatures of LN2 are validated with the available experimental measurements. Finally, it was concluded that the effect of heat flux and AC Losses on cooling capacity and heat transfer is found to be significant as compared that on friction factor and pumping power.
1. Introduction High temperature superconducting (HTS) power cables have been developing as a solution of increasing power demand due to their advantages of lower losses, large transmission capability, light weight and smaller diameter with higher ampacity. The HTS cables exhibit various kind of losses such as AC losses in the superconductor, dielectric losses in dielectric material, the heat influx through the cryogenic enclosure wall from ambient temperature and pressure losses in LN2 flowing through corrugated pipes. In order to encounter such losses in the HTS cable, thermal and hydraulic analysis of LN2 is necessary. After years of research, the HTS cables have been acknowledged to be installed in the grids for large scale power transmission. However, the efficient cooling system and flow system in HTS cable is still one of the major issues for the researcher and manufacturers. Therefore, several studies on cooling mechanism (thermal) and flow system (hydraulic) in corrugated pipe
⁎
HTS cables have been carried out and published so far. Kottonau et al. [1] has analyzed the pressure drop and heat transfer for four various cooling concepts in three phase concentric HTS cable. The HTS cable may also have other different cooling arrangements such as single flow cooling and counter flow cooling systems. When LN2 flows through either inner or annular flexible corrugated pipe to reduce the temperature rise in HTS cable, termed as single flow cooling system. The thermohydraulic analysis of HTS cable using single flow cooling system is described by [2–10]. The influence of corrugation pitch and depth on pressure drop and heat transfer in warm dielectric HTS cable with single flow cooling systems using computer simulations have been investigated by Lee et al. [4] and Dondapati et al. [6]. Whereas, the thermal and fluid characteristics of LN2 in annular channel in the HTS cable have been investigated by Sasaki et al. [7] and Maruyama et al. [5]. However, there are few reports on the thermohydraulic behavior of the non-cryogenic fluid flowing through corrugated pipes with single
Corresponding author. E-mail address: [email protected] (R.S. Dondapati).
https://doi.org/10.1016/j.physc.2019.1353525 Received 4 July 2019; Received in revised form 19 August 2019; Accepted 5 September 2019 Available online 05 September 2019 0921-4534/ © 2019 Elsevier B.V. All rights reserved.
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 1. (a) flowchart of thermohydraulic analysis of HTS cable (b) Schematic of Counter flow arrangement.
flow cooling systems [11–15]. On the other hand, counter flow cooling system [16–24] has its own advantage of compact size due to elimination of separate LN2 return pipe and efficient cooling of HTS cables. The research work on counter flow cooling system in the HTS cables is done so far either using analytical approach or experimental approach. Moreover, nobody has reported computational work on counter cooled HTS cable with various corrugation topologies. Hence, in the present work, counter-flow cooling system with various corrugation topologies have been proposed and analyzed the heat transfer and pumping power computationally in order to design the long length HTS cables.
Table 1 Parameters for conceptual design of HTS cable.
2. Solution procedure of computational method
Parameters
Details
Diameter of Inner region (mm) Equivalent Diameter of Annular region (mm) Thickness of corrugated pipe, g (mm) Thickness of HTS tape (mm) Thickness of Dielectric material (mm) Corrugation pitch, p (mm) Corrugation depth, s (mm) Heat Flux from ambient/exterior, Qe (W/m2) Heat from HTS tapes/A.C loss, QAC (W/m) Inlet temperature, To (K) Inlet Pressure, P1 (bar) Volumetric flow, V (L/min)
40 37.5 1 0.02 0.1 8 4 4–10 1–2.5 65 3 20–35
3. Computational modeling of HTS cable
The solution process of computational method used for thermohydraulic analysis of HTS cable is shown in Fig. 1(a). The method involves the creation of geometry, mesh (grid) and few significant solver settings to obtain the desired results. Referring the method, geometries with various corrugation shapes are modelled using ANSYS Design Modeler with physical parameters as discussed in Table 1. The modelled HTS cable with various corrugation topologies are further meshed using ANSYS Meshing and the mesh size varies for each of geometry depending upon the wall corrugation surface. The meshed geometries are further exported to the ANSYS Fluent in order to define boundary conditions, material properties, turbulence model and pressure-velocity coupling scheme. The solver will stop the calculation once the solution criteria for the continuity, x, y and z velocities, the kinetic energy k, and the dissipation of energy ɛ is satisfied. The mesh geometries are refined for the grid independent analysis to achieve more accurate results. Using post-processing tool of the ANSYS Fluent, the required results for the defined model can be retrieved.
The single phase coaxial cold dielectric HTS cable using (singlesided cooling with internal coolant return flow) counter flow cooling was proposed in our previous study with circular corrugations [24]. In the present model the various corrugation topologies were chosen to investigate the thermal and hydraulic performance of LN2. Fig. 1(b) depicts the counter flow cooling arrangement in which liquid nitrogen (LN2) is used to cool the HTS cable, which is circulated through inner corrugated pipe (inner region) and exits from the annular outer corrugated pipe (annular region). The HTS cable comprises of inner corrugated pipe, HTS tapes, Dielectric material, and outer corrugated pipe with cable shield. HTS tape comprises of different layers of solid materials such as silver/copper (protective layer), YBCO (superconducting layer), buffer layer and metal substrate with total thickness of ≤0.2 mm. Polypropylene laminated paper (PPLP) is commonly used as an insulation material for superconducting device applications with an
2
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 2. Schematic and structural parameters of 2-D axisymmetric HTS cable with various corrugation shapes and respective typical mesh (a) rectangular (b) circular (c) triangular.
advantage of low dielectric losses. The corrugated pipes used in the HTS cable are mainly of stainless steel (SS) material with cryogenic compatible grades such SS316L. Fig. 2 shows the 2-D axisymmetric model of HTS cable with various corrugation topologies (rectangular, circular and triangular) having a computational length of 504 mm with their respective mesh. The physical parameters such as inner corrugated pipe of 40 mm in diameter and an annular outer corrugated pipe with diameter of 37.5 mm is considered for the present work. The thickness of HTS tape and dielectric material (solid domain) is <1% of the diameter of corrugated pipe as can be seen in Table 1. Therefore, due to the lesser thickness of HTS tape and dielectric material than fluid domain, the thickness of HTS tapes and dielectric material is worth neglecting for the present CFD analysis. During operation with alternating current (A.C), the HTS tapes cause electrical power dissipation (W/m) that indicates an internal heat source (W/m3). Therefore, the effect of heat generation (W/m3) in the HTS tapes due to electrical dissipation power is considered and assumed to be equal in the inner corrugated pipe of 1 mm thickness for the present analysis. Moreover, the exterior heat–in-leak (W/m) from the ambient temperature on the outer corrugated pipe is converted into heat flux (W/ m2) and worth considered for the analysis. The present study involves the effect of heat-in-leak of (4–10 W/m2) and A.C. losses of (1–2.25 W/ m) on pressure drop and heat transfer analysis of the HTS model. The heat generated (W/m3) in the HTS tapes due to electrical dissipation power can be estimated using Eq. (1).
=
Q AC ASC
3.1. Grid independent study The grid independent analysis of modeled HTS cable with various corrugation topology is shown in Fig. 3. It can be concluded from the results that the pressure drop is grid independent after further refinement of the mesh with element size of 0.6 mm, 0.58 mm and 0.7 mm for rectangular, circular and triangular corrugations respectively. Therefore, in order to avoid long computational time and solution instability, mesh with element size of 0.6 mm for rectangular corrugation, 0.58 mm for circular corrugation and 0.7 mm for triangular corrugation was adopted for the further thermohydraulic analysis of HTS cable. The number of nodes corresponding to the element size are compiled in the Table 2 given below. 3.2. Boundary conditions The boundary conditions of counter cooled HTS cable with various corrugation shapes are discussed below. (a) Steady state and incompressible flow of LN2 with the temperature dependent thermophysical properties is considered for the analysis. (b) The LN2 inlet conditions such as inlet temperature of 65 K, inlet mass flow rate ranges from 20 L/min to 35 L/min [19], the turbulence intensity of I = 5% and the hydraulic diameter of 40 mm are considered for the present analysis. (c) The outlet boundary is assigned as outflow, a turbulence intensity of I = 5% and the hydraulic diameter of 37.5 mm. (d) Inner corrugated pipe (solid) of thickness 1 mm is considered as heat source and allocated as heat generation of (396 W/m3 to 986 W/m3) corresponding to the A.C. losses. (e) The wall boundary conditions at outer corrugated wall is assigned as heat flux of (4 W/m2–10 W/m2). No slip boundary condition is imposed on the walls of corrugated pipe surfaces. (f) The k-epsilon turbulent model with enhanced wall treatment and pressure based solver is used in the simulation. The solver uses
(1)
where, ω is the heat generated by power dissipation in HTS phase (W/ m3). QAC is known as the AC losses in superconducting phase (W/m) and Asc is the cross-sectional area of the HTS phase (W/m2). The analytical process of estimating flow characteristics such as pressure drop, friction factor and pumping power in the HTS cable is discussed by Kalsia et al. [24]. 3
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 3. Pressure drop for various element sizes in the HTS cable with different corrugation (a) Rectangular (b) Circular (c) Triangular.
follows: X-momentum
Table 2 Number of nodes for various element size. Corrugation Shape
Rectangular
Circular
Triangular
Element Size (mm) Number of Nodes
0.6 60,945
0.58 63,508
0.7 56,031
u u u +u +v t x y
p +µ u x
= FY
p +µ v y
uu uv + x y
(3)
Y-momentum
v v v +u +v t x y
SIMPLE algorithm for pressure and velocity coupling. 4. Governing equations
Where, u = (
The velocity and the pressure fields were acquired from the numerical solution of the mass momentum and energy conservation equations under incompressible and steady-state conditions, in the domain of the finite volume CFD approach. Since flow is turbulent in all cases due to the corrugation topologies, the simulations are obtained using general Reynolds averaged Navier-Stokes (RANS) equations [24]. The time-averaged conservation of mass for 2-D flow can be written as:
u v + =0 x y
= FX
(
(µ
ui xj
ui u j xj
2u
x2
+
2u
y2
+
2u
z2
uv vv + x y
) and v = (
2v
x2
+
2v
y2
+
(4) 2v
z2
)
) is termed as Reynolds stress or turbulent shear stress and
ui uj ) is known as total shear stress τij.
Fx, Fy and Fz are the body forces, which are neglected for the present simulations The time-averaged energy equation can be written as:
CP u
T T +v x y
=
x
k
T x
CP u T
+
y
k
T y
CP v T (5)
(2)
where, u is the momentary velocity component, u is the time-averaged velocity and u′is the fluctuating velocity. The time-averaged conservation of momentum equations are as
5. Results and discussion In this study the thermohydraulic analysis of HTS cable with 4
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 4. (a). Validation of friction factor from present investigation with experimental results obtained by Li et al. [27] (b) Comparison of temperature difference between outlet and inlet of LN2 in counter flow HTS cable (present work) with that of LN2 estimated by Dondapati et al. [28] and with the experimental results performed by Ivanov et al. [29] (c) validation of obtained pressure drop (present work) with experimental and simulation results performed by Li et al. [27].
different corrugation topology was carried out using k realizable turbulence model with enhanced wall treatment due to the extra benefit of improved performance for the complex flow involving swirl/vortices/rotation, adverse pressure gradient, flow separation and recirculation [14,25,26]. Furthermore, the results of friction factor, temperature difference and pressure drop for the present work are validated with the experimental and numerical published results. In addition, the effect of various heat in leaks and A.C. losses on the thermohydraulic performance of HTS cable are also presented in this section.
Moreover, the friction factors found to be reduced at higher Reynolds numbers ranges as can be observed in the Fig. 4(a). So far, no correlation is established for the calculation of friction losses in the corrugated annular pipe. Therefore, the foremost reason for the higher friction factor in the HTS cable of different corrugation topologies, may be due to the combined effect of LN2 interaction with the walls of inner corrugated pipe and outer (annular) corrugated pipe simultaneously [24]. Fig. 4(b) demonstrates the comparison of temperature difference between outlet and inlet of counter flow HTS cable using LN2 estimated by Dondapati et al., [28] and that estimated by Ivanov et al., [29]. It can be seen from the results that the temperature difference between outlet and inlet for LN2 in the counter flow HTS cable of different corrugation topologies is lower than the other HTS cable system (singleway cooling). Hence, long length counter flow HTS cables can be cooled effectively without losing the superconductivity. Fig. 4(c) represents the validation of pressure drop estimated computationally for the counter cooled HTS cable with the experimental and calculated data available for Single (annular) flow cooling system of HTS cable. Analyzing the pressure drop in counter cooled HTS cable with different
5.1. Validation The results obtained from the present computational investigation are validated with the experimental results computed by Li et al. [27] (annulus flow through centrally placed smooth pipe enveloped by a corrugated pipe) with the present work (employing counter flow through corrugated pipes placed centrally as well as externally) as shown in Fig. 4. The results show that the topology of corrugation would affect the friction factors at various Reynolds numbers. 5
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
corrugation topologies, it was found that the pressure drop (Pa/m) in the counter flow cooling system (present work) is larger than the single flow cooling system (annulus flow through centrally placed smooth pipe enveloped by a corrugated pipe) [27]. This difference in pressure drop in the counter flow cooling system (present work) may be due to the variation in corrugation topology of the pipes (inner and annular) along with expected turbulent characteristics such as swirl, separation and recirculation as discussed in Section 5.4.
temperature distribution profile of LN2 in counter cooled HTS cable at flow rate of 25 L/min and heat flux of 6 W/m2 is shown in Fig. 6(g). The maximum temperature of LN2 is found to be 65.018 K in triangular shaped HTS cable at the location of 0.150 m from the inlet. The radial temperature profile is divided into three domains such as inner region (fluid), superconducting phase (solid) and annular region (fluid). The temperature rise can easily be measured in each of the domain through the temperature profile.
5.2. Effect of heat flux and corrugation topology on thermohydraulic characteristics
5.3. Effect of heat generation and corrugation topologies on thermohydraulic characteristics
The influence of various heat fluxes and corrugation topologies on thermohydraulic characteristics of HTS cable are presented in this section. The effect of exterior heat flux (4 W/m2–10 W/m2) due to the ambient temperature encountered by the outer corrugated pipe is significantly affecting the thermohydraulic performance of the HTS cable. Also, the effect of various corrugation topologies (rectangular, circular and triangular) is significant on the thermohydraulic behavior of HTS cable.
The effect of various heat generation and corrugation topologies on pressure drop and heat transfer analysis of counter cooled HTS cable is revealed in this section. The heat generation is the form of heat source produced through the HTS tapes while transferring the alternating current (A.C.). The actual A.C. losses in the HTS cable as (1–2.25 W/m) and the corresponding heat generation as (396 W/m3 to 986 W/m3) are considered for the present analysis. 5.3.1. Hydraulic studies The effect of heat sources and corrugation topologies on hydraulic characteristics of counter cooled HTS cable is presented in this section. Fig. 7 shows the effect of corrugation topologies and heat generation on friction factor, pumping power and the velocity profile obtained in the counter cooled HTS cable. It can be observed from the results that there is no significant difference between effect of heat flux and heat generation on the hydraulic performance of the HTS cable. Therefore, the present analysis concludes that the hydraulic performance of counter cooled HTS cable is independent of heat flux or heat generation.
5.2.1. Hydraulic studies The effect of various heat fluxes and corrugation topologies on friction factor, pumping power and velocity profile is discussed in this section to describe the hydraulic behavior of LN2. The pressure drop behavior in terms of friction factor in the HTS cable with various corrugation shapes is displayed in Fig. 5(a)–(c) for the Reynolds number range of 30,000–60,000. It can be concluded that the friction factor for the triangular corrugation is significantly high as compared with the rectangular and circular corrugations. The pumping power follows the increasing trend at various volumetric flow rates as can be seen in Fig. 5(d)–(f). The high pumping power is required to circulate the liquid nitrogen in triangular corrugation shape counter cooled HTS cable as compared to rectangular and circular corrugation. Moreover, the pumping power in all the corrugation shaped HTS cable for various heat fluxes will be quite similar at different flow rates. The velocity profiles of all three corrugation shapes in inner region and annular region at 0.150 m from the inlet of the HTS cable are shown in Fig. 5(g). The triangular corrugation shaped HTS cable has attained a maximum velocity of 0.44 m/s at the axis of the model. The negative sign indicates the direction of flow in the annular region of the HTS cable and the maximum velocity attained in this region is 0.2 m/s. it can be seen from the results that fully developed velocity profiles are not observed as also reported earlier [24]. In order to achieve the fully developed flow at inlet in the HTS cable, the domain needs to extend up to a distance called entry length. The estimated entry lengths for each Reynolds numbers are compiled in Table 3.
5.3.2. Thermal studies This section reveals the influence of various corrugation topologies and heat generation on heat transfer mechanism of counter cooled HTS cable. Fig. 8(a)–(c) represents the effect of various A.C. losses and corrugation shapes on the cooling capacity of LN2. It can be seen from the results that with increase in the A.C. loss the cooling capacity also increases and with high flow rates the required cooling capacity will be higher. The maximum required cooling capacity were found in rectangular corrugation. The enhancement of heat transfer in rectangular corrugation shaped HTS cable is an evident from increase in the Nusselt number as shown in Fig. 8(d)–(f). With increase in the Reynolds number, the Nusselt number also increases can be observed from the results. Similarly, the A.C. losses increases, the average nusselt number for the various corrugation shapes HTS cable increases. Also, the highest Nusselt number values were presented by rectangular corrugation shaped HTS cable. The radial temperature distribution profile of LN2 in counter cooled HTS cable at flow rate of 25 L/min and A.C. loss of 1.5 W/m is shown in Fig. 8(g). The maximum temperature in the counter cooled HTS cable at the location of 0.150 m from the inlet is found to be 65.012 K.
5.2.2. Thermal studies The effect of various heat fluxes and corrugation topologies on heat transfer analysis in counter cooled HTS cable is presented in this section. Heat transfer analysis in the form of the cooling capacity, Nusselt number and the temperature profile of LN2 inside a counter cooled HTS cable is discussed. It can be observed from the Fig. 6(a)–(c) that with increase in the flow rates, the required cooling capacity of LN2 also increases and with maximum heat flux, the required cooling capacity will be higher. Moreover, the highest required cooling capacity were presented by rectangular corrugation shaped HTS cable. Average Nusselt number at Reynolds number range of 30,000–60,000 for different corrugation topologies is presented in Fig. 6(d)–(f). It can be noted that as Reynolds number increases, the Nusselt number for the various corrugation shapes also increases. Whereas, the heat flux reduces, the Nusselt number for the various corrugation shapes in the HTS cable increases. The highest Nusselt number values were presented by rectangular corrugation shaped HTS cable due to the presence of high recirculation and thin boundary layer. The radial
5.4. Comparison of thermohydarulic performance of HTS cable with different corrugation topologies Fig. 9(a)–(c) shows the boundary layer separation, recirculation and vortex appearance in each of the corrugation topology for inner and annular region. The separated boundary layer in both the regions attempt to develop and reattach when the fluid flow past the each corrugation topology. The separation of boundary layer and reattachment occurs for an instance due to the continuation of upper and lower corrugations in both the regions of the HTS cable. The continuation of boundary layer separation in the corrugations increase the boundary layer thickness which leads to an additional resistance and flow reversal. An adverse pressure gradient produces vortices and eddies, results in the formation of turbulence and more pressure drop across the 6
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 5. Effect of Heat Flux on cooling capacity (a) Rectangular Corrugations (b) Circular Corrugations (c) Triangular Corrugations, Effect of Heat Flux on pumping power (d) Rectangular Corrugations (e) Circular Corrugations (f) Triangular Corrugations and (g) Radial velocity distribution counter cooled HTS cable.
flow. Fig. 9(d)–(f). The effect of various heat-in-leaks and A.C. losses are studied simultaneously in order to analyze the thermal behavior of LN2. The inner region of each corrugation topology seems with an almost
constant temperature gradient whereas, the high temperature gradient is found around the walls of outer corrugated pipe in annular region. The maximum thermal boundary layer thickness occurs near the separation point, whereas the minimum thermal boundary layer thickness near the reattachment point in the corrugations [12]. The temperature distribution in each of the corrugation topology of HTS cable is shown in It can be observed from the contours that the heat flux dominates more than the A.C. losses to raise the temperature of LN2. The
Table 3 Estimated approximate entry lengths at various Reynolds numbers. Reynolds Number Entry Length (m)
32,450 0.99
40,563 1.03
48,675 1.06
56,788 1.09
7
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 6. Effect of Heat flux on cooling capacity (a) Rectangular Corrugations (b) Circular Corrugations (c) Triangular Corrugations, Effect of Heat Flux on Nusselt Number (d) Rectangular Corrugations (e) Circular Corrugations (f) Triangular Corrugations and (g) Radial Temperature distribution counter cooled HTS cable.
minimum temperature in each of the corrugation topology is 65 K. And the maximum temperature reaches 65.077 K, 65.0283 K and 65.03537 K in rectangular, circular and triangular corrugations respectively. Hence, the maximum temperature in rectangular corrugation indicates the higher Nusselt number than that of other corrugations. TKE is a standout amongst the most significant factors in a boundary layer and flow attributes, and it is a proportion of the turbulence intensity, which is explicitly identified with the velocity profile of the fluid. High TKE along the fluid stream way contributes to the strong flow mixing and enhanced heat transfer, whereas the TKE layers indicate the intensity of flow mixing from the corrugated wall surfaces to the flow zone. Influence of various corrugation topologies on TKE are shown in Fig. 9(g)–(i). It is observed that the magnitude of TKE is much higher near the side wall and tube wall of all corrugated shapes. This shows the strong intensity of flow mixing from side wall and corrugated walls to the core
flow zone, which leads to an enormous heat transfer performance. It is also concluded that rectangular corrugation shape have higher TKE near side wall than circular and triangular corrugation shapes. 6. Conclusions In this paper, the influence of three various corrugation topologies (rectangular, circular and triangular) on thermohydraulic performance of turbulent flow LN2 was studied using CFD method. Moreover, the influence of heat-in-leak losses and A.C. losses on thermal and hydraulic characteristics of LN2 were also considered in the present work. The following conclusion can be drawn from the present simulation results: i Pressure drop in the triangular corrugation shaped HTS cable is significantly larger than the circular and rectangular corrugation due to the higher intensity of the vortices appearing in the both 8
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 7. Effect of AC Losses on friction factor with (a) Rectangular Corrugations (b) Circular Corrugations (c) Triangular Corrugations, Effect of AC Losses on pumping power with (d) Rectangular Corrugations (e) Circular Corrugations (f) Triangular Corrugations and (g) Radial velocity distribution counter cooled HTS cable.
inner and annular region. ii The obtained friction factor results for each corrugation shapes are compared with other experimental results. In addition, the obtained friction factor for the present work is significantly larger due to the counter flow arrangement with corrugated pipes. iii The Nusselt number obtained from the rectangular corrugation has increased which indicates the higher heat transfer rate than that of
other two corrugation shapes. Moreover, the intensity of the turbulent kinetic energy is found to be higher in rectangular corrugation shaped HTS cable. iv The effect of various heat-in-leak losses (heat flux) and A.C. losses (heat generation) on the hydraulic performance of LN2 is found to be similar. Whereas, the thermal performance of LN2 was significantly affected by heat-in-leak losses and A.C. losses. 9
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 8. Effect of AC Losses on cooling capacity with (a) Rectangular Corrugations (b) Circular Corrugations (c) Triangular Corrugations, Effect of AC Losses on Nusselt Number with (d) Rectangular Corrugations (e) Circular Corrugations (f) Triangular Corrugations and (g) Radial Temperature distribution counter cooled HTS cable.
10
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati
Fig. 9. Velocity vectors in (a) Rectangular Corrugations (b) Circular Corrugations (c) Triangular Corrugations, Temperature Distribution in (d) Rectangular Corrugations (e) Circular Corrugations (f) Triangular Corrugations and Turbulent Kinetic Energy Distribution in (g) Rectangular Corrugations (h) Circular Corrugations (i) Triangular Corrugations across the HTS cable.
Acknowledgements
[3] Y.V. Ivanov, H. Watanabe, M. Hamabe, J. Sun, T. Kawahara, S. Yamaguchi, Circulation pump power for 200 m cable experiment, Phys. C Supercond. 471 (21–22) (2011) 1308–1312. [4] C.H. Lee, C.D. Kim, K.S. Kim, D.H. Kim, I.S. Kim, Performance of heat transfer and pressure drop in superconducting cable former, Cryogenics (Guildf) 43 (2003) 583–588. [5] O. Maruyama, T. Ohkuma, T. Izumi, Numerical analysis of heat transfer and fluid characteristics in long distance HTS cable, Phys. Procedia 45 (Jan. 2013) 285–288. [6] R.S. Dondapati, V.V. Rao, Pressure drop and heat transfer analysis of long length internally cooled HTS cables, Appl. Supercond. IEEE Trans. 23 (3) (2013) 2–5. [7] A. Sasaki, Y. Ivanov, S. Yamaguchi, LN2 circulation in cryopipes of superconducting power transmission line, Cryogenics (Guildf) 51 (9) (Sep. 2011) 471–476. [8] S. Thadela, V.V. Rao, R. Agarwal, R.S. Dondapati, Computational investigation on thermohydraulic characteristics of high-temperature superconducting (HTS) power cables, Phys. C Supercond. Appl. 559 (2019) 25–31. [9] M. Kalsia, R.S. Dondapati, P. Rao, Statistical correlations for thermophysical properties of supercritical argon (SCAR) used in cooling of futuristic high temperature superconducting (HTS) cables, Phys. C Supercond. Appl. 536 (2017) 30–34. [10] O. Maruyama, T. Mimura, Fluid characteristic of liquid nitrogen flowing in HTS
The authors gratefully acknowledge the suggestions of the reviewers which helped in enhancing standard of the manuscript. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.physc.2019.1353525. References [1] D. Kottonau, W.T.B. De Sousa, J. Bock, M. Noe, Design comparisons of concentric three-phase HTS cables, IEEE Trans. Appl. Supercond. 29 (6) (2019). [2] J. He, Y. Tang, B. Wei, J. Li, L. Ren, J. Shi, K. Wang, X. Li, Y. Xu, S. Wang, Thermal analysis of HTS power cable using 3-D fem model, IEEE Trans. Appl. Supercond. 23 (3) (2013) 1–4.
11
Physica C: Superconductivity and its applications 566 (2019) 1353525
M. Kalsia and R.S. Dondapati cable, J. Phys. Conf. Ser. 1054 (2018). [11] M. Ahsan, Numerical analysis of friction factor for a fully developed turbulent flow using k e ε turbulence model with enhanced wall treatment, Beni-Suef Univ. J. Basic Appl. Sci. 3 (4) (2014) 269–277. [12] X. Chen, H. Han, K. Lee, B. Li, Y. Zhang, Turbulent heat transfer enhancement in a heat exchanger using asymmetrical outward convex corrugated tubes, Nucl. Eng. Des. 350 (January) (2019) 78–89. [13] S. Song, X. Yang, F. Xin, T.J. Lu, S. Song, X. Yang, F. Xin, T.J. Lu, Modeling of surface roughness effects on stokes flow in circular pipes modeling of surface roughness effects on stokes flow in circular pipes, Phys. fluids 30 (2) (2018). [14] A. Kaood, H. Eltahan, M.A. Yehia, E.E. Khalil, Numerical investigation of heat transfer and friction characteristics for turbulent flow in various corrugated tubes, J. Power Energy 233 (2018) 1–19. [15] A.T. Franco, S.L.M. Junqueira, M.A.L. Gonc, Turbulent flow in D-Type corrugated pipes: flow pattern and friction factor, J. Fluids Eng. 134 (December 2012) (2016) 1–9. [16] J.A. Demko, J.W. Lue, M.J. Gouge, J.P. Stovall, U. Sinha, R.L. Hughey, Practical ac loss and thermal considerations for HTS power transmission cable systems, IEEE Trans. Appl. Supercond. 11 (1) (2001) 1789–1792. [17] J.A. Demko, J.W. Lue, M.J. Gouge, P.W. Fisher, D. Lindsay, M. Roden, Analysis of a liquid nitrogen-cooled tri-axial High- Temperature superconducting cable system, Am. Inst. Phys. 49 (2004) 913–920. [18] J.A. Demko, R.C. Duckworth, Cooling configuration design considerations for longlength HTS cables, IEEE Trans. Appl. Supercond. 19 (3) (2009) 1752–1755. [19] S. Fuchino, M. Furuse, N. Higuchi, Longitudinal temperature distribution in superconducting power cables with counter-Flow cooling, IEEE Trans. Appl. Supercond. 12 (1) (2002) 1339–1342. [20] M. Furuse, S. Fuchino, N. Higuchi, Counter flow cooling characteristics with liquid nitrogen for superconducting power cables, Cryogenics (Guildf) 42 (2002)
405–409. [21] M. Furuse, S. Fuchino, N. Higuchi, Investigation of structure of superconducting power transmission cables with LN2 counter-flow cooling, Phys. C Supercond. 386 (2003) 474–479. [22] T. Masuda, T. Kato, H. Yumura, M. Watanabe, Y. Ashibe, K. Ohkura, Verification tests of a 66 kV HTSC cable system for practical use (first cooling tests), Phys. C Supercond. 381 (2002) 1174–1180. [23] E. Shabagin, C. Heidt, S. Strauß, S. Grohmann, Modelling of 3D temperature profiles and pressure drop in concentric three-phase HTS power cables, Cryogenics (Guildf) 81 (2017) 24–32. [24] M. Kalsia, R.S. Dondapati, Thermohydraulic analysis of cold dielectric high temperature superconducting cable with counter-flow cooling, Phys. C Supercond. its Appl. 564 (2019) 59–67. [25] M. Pisarenco, Friction factor estimation for turbulent flows in corrugated pipes with rough walls, J. Offshore Mech. Arct. Eng. 133 (February) (2011) 1–9. [26] H. Benzenine, R. Saim, Comparative study of the thermo-convective behavior of a turbulent flow in a rectangular duct in the presence of three planar baffles and/or corrugated (waved), J. Eng. Sci. Technol. 13 (1) (2018) 35–47. [27] Z. Li, Y. Li, W. Liu, J. Zhu, M. Qiu, Comparison of liquid nitrogen flow resistance in corrugated pipe with smooth pipe for HTS cable, IEEE Trans. Appl. Supercond. 25 (3) (2015). [28] R.S. Dondapati, J. Ravula, S. Thadela, P.R. Usurumarti, Analytical approximations for thermophysical properties of supercritical nitrogen (SCN) to be used in futuristic high temperature superconducting (HTS) cables, Phys. C Supercond. its Appl. 519 (2015) 53–59. [29] Y. Ivanov, H. Watanabe, M. Hamabe, T. Kawahara, J. Sun, Observation of the thermosiphon effect in the circulation of liquid nitrogen in HTS cable cooling system, Phys. Procedia 27 (2012) 368–371.
12