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Mitigation of MHD phenomena in DCLL blankets by Flow Channel Inserts based on a SiC-sandwich material concept
Fusion Engineering and Design 151 (2020) 111381
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Mitigation of MHD phenomena in DCLL blankets by Flow Channel Inserts based on a SiC-sandwich material concept
T
C. Sotoa,b, S. Smolentsevc, C. García-Rosalesa,b,* a
Ceit-IK4 Technology Center, E-20018, San Sebastian, Spain Universidad de Navarra, Tecnun, E-20018, San Sebastian, Spain c Univerisity of California, Los Angeles, USA b
ABSTRACT
The DCLL blanket is an attractive concept for future fusion reactors. In order to mitigate MHD effects from the interaction between flowing PbLi and magnetic field, Flow Channel Inserts (FCIs) need to be developed. SiC-based materials are main candidates for high-temperature FCIs. In this work, the MHD interactions and their possible mitigation by FCIs consisting of a porous SiC core with a dense protective SiC coating are studied. The dependency between MHD effects and the FCIs’ properties is discussed under relevant conditions for the DCLL concept. The results show that with a porous-dense SiC-sandwich material, a pressure gradient of ∼120 Pa/m is predicted for a 4 T magnetic field, and of ∼300 Pa/m for 10 T, if an FCI with insulating porous core (< ∼1 S/m) is used. Relevant cases considering a PbLi infiltration in the porous SiC core due to possible damages in the protective coating are presented.
1. Introduction The Dual Coolant Lead Lihitum (DCLL) blanket is a promising concept for future nuclear fusion reactors, leading to potentially high efficiencies in the energy production [1]. This design is characterized by the use of liquid PbLi both as the main coolant and as tritium breeder; in the DCLL, the liquid metal flows through poloidal channels, heating up by the neutron flux from the fusion plasma while tritium is produced by the reaction between neutrons and the lithium in the alloy. The second coolant is pressurized helium, which cools down the structure of the blanket, made of a reduced activation ferritic-martensitic (RAFM) steel. Among attractive features of the DCLL is the high PbLi exit temperature, up to 700 °C in the case of a so-called hightemperature DCLL. However, despite the high thermal efficiency associated with this high temperature, a considerable level of R&D would be needed to effectively overcome the design challenges of the blanket, both considering the study of its unique operating conditions and the development of the necessary new materials and technologies. Key components of the DCLL concept are the so-called Flow Channel Inserts (FCIs), consisting of a thin-wall (∼5 mm) rectangular-shape structure loosely inserted in the host RAFM duct, so that the PbLi breeder flows inside the FCI and also in the thin (∼2 mm) gap between the FCI and the RAFM wall. The use of FCIs is required to electrically decouple the liquid metal from the blanket steel structure, since electromagnetic interactions may result in an unacceptably high pressure drop due to magnetohydrodynamic (MHD) effects. Apart from the
⁎
pressure drop, the MHD interactions may also cause a major disturbance in the PbLi flow, and to accurately predict the velocity profile of the PbLi is crucial for a proper design of the DCLL. In this concept, the liquid PbLi acts at the same time as primary coolant, breeder, and tritium carrier; major disturbances in the flow may affect key aspects defining the blanket performance, as may be the heat transfer inside the PbLi (e.g. the thermal efficiency), the temperature field in the steel structure (e.g. the mechanical integrity), or the production and extraction of tritium and/or residual He due to the appearance of areas with a near-stagnant PbLi flow due to the MHD effects. In the case of the high-temperature version of the DCLL, apart from the electrical insulation, the high temperatures of the PbLi require to consider FCIs with thermal insulation properties, in order to protect the steel structure from a possible overheating. The maximum safe temperature for the blanket steel structure is commonly considered to be 550 °C [2,3]; this temperature requirement, however, may be more severe in the zones where the steel is directly in contact with the flowing PbLi, being a lower temperature (∼470 °C) recommended in the literature to avoid corrosion issues [4,5]. The anti-corrosion requirements are also more severe in the case of the high-temperature DCLL, where the PbLi is flowing at higher velocities and at temperatures up to ∼700 °C inside the FCIs. To carry out the conceptual design of the DCLL avoiding some of the main technological difficulties, a near-term, low-temperature DCLL design is being developed in the framework of the EUROfusion Breeding Blanket Program for DEMO [3,6], leaded by CIEMAT. In this
Corresponding author. E-mail address: [email protected] (C. García-Rosales).
https://doi.org/10.1016/j.fusengdes.2019.111381 Received 31 May 2019; Received in revised form 22 August 2019; Accepted 22 October 2019 0920-3796/ © 2019 The Author(s). Published by Elsevier B.V. All rights reserved.
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design, based in a multi-module approach, the maximum PbLi temperature is limited to 550 °C, avoiding the need for thermal insulation and allowing the use of FCIs made of existing materials [6]. Despite the lower temperature of the PbLi, substantial progress has been made in terms of the achieved TBR, tritium extraction [7], neutronics [8] and the FCI design [9]. Apart from the developments in the EU, a DCLL blanket concept is being discussed in the framework of the development of the Fusion Nuclear Science Facility (FNSF) in the US [10,11]. This concept is based on a single-module approach, considering the use of long poloidal channels of 7-10 m length and keeping the PbLi temperature in a similar range than in the design proposed by CIEMAT. The characteristic magnetic field for the outboard module of the US DCLL is 5.5 T, raising to 10 T in the inboard module. Apart from this, further research involving the development of the DCLL concept is being carried out worldwide, for example in the China fusion program [12]. Even if the design of the DCLL is carried out, at first approach, from a low-temperature perspective, it is reasonable to consider a future upgrade of the concept allowing the achievement of higher PbLi temperatures, considering the advantages that this scenario would offer in terms of energy production. A main technological challenge that needs to be solved in the framework of a high-temperature DCLL is to develop an adequate material for FCIs, able to withstand the severe requirements associated to the application: the required electrical and thermal insulation, a good response to high temperatures and to high radiation, and suitability against possible corrosion issues. To this date, the main candidates for high-temperature FCIs are materials based on silicon carbide (SiC), a high-performance ceramic adequate for high temperature applications, with a promising response in high irradiation environments and with excellent chemical stability. The electrical and thermal conductivities of dense SiC, however, are relatively high, being necessary to develop a low-conductivity SiCbased insulating material to be applied in FCIs. Apart from the production of SiCf/SiC composites with the required properties [13], a possible approach consists in the development of a dense-porous SiC material, formed by a porous SiC core providing the insulating properties, and a dense SiC coating protecting from PbLi infiltration and possible corrosion. This last possibility has been explored in the US, with prototypes fabricated by Ultramet that were tested at the MaPLE PbLi loop in UCLA [14–16]. Besides, an alternative SiC-based material was developed and studied at CEIT (Spain), in the framework of the EUROfusion Enabling Research program [17–20]. Insulating porous SiC materials with porosities of 30-50%, candidates for the core of the FCI-SiC, were fabricated and characterized; as the outer layer of the material, a coating of dense SiC was deposited by Chemical Vapor Deposition (CVD). More details regarding the fabrication process, together with the characterization and testing of the material, can be found in [17,21,18], including experiments testing its response against hot flowing PbLi. To establish a range of recommended material properties for FCIs it is a necessary step in the proper development of the SiC-based material. Regarding specifically the electrical properties, to assure a good electrical insulation of the PbLi is crucial to avoid high pressure losses in the poloidal channels and major disturbances in the PbLi flow [22,23]; to that effect, the coupling between the properties of the FCIs and the MHD interactions must be studied. In this framework, and as a support to the previously mentioned experimental development of a candidate material for FCIs carried out at CEIT, an analysis of the MHD phenomena in the PbLi flow considering a SiC-based FCI was carried out under relevant conditions for the high-temperature DCLL. The results were used to discuss the recommended FCI properties to assure optimum performance of the blanket, establishing a range of values for the electrical conductivity of the porous SiC material and for its configuration, in terms of the thickness of the dense and porous layers. In the present work, the main results of the study discussing the possible mitigation of MHD phenomena by using a SiC-based sandwich
FCI are presented. In the first section, the dependency of the pressure drop values and the flow disturbances on the properties of the FCIs are addressed. In order to simplify the calculations, the FCI is at first modelled as a single-material channel, discussing the influence of the electrical properties of the material on the MHD phenomena. Then, the effect of including a dense SiC coating with respect to the electromagnetic interactions is analyzed as a function of its thickness and its electrical conductivity. Two intensities of the magnetic field, 4 and 10 T, were studied, as a reference for the expected magnetic field in the outboard and inboard modules of the blanket, respectively [10]. By last, a discussion is presented addressing the effect of a possible PbLi infiltration inside the FCIs. The values of the pressure gradient and the flow distribution in each scenario studied are presented, establishing a complete discussion with respect to the potential performance of a SiCbased material as electrical insulator in the poloidal channels of a hightemperature DCLL. 2. Methodology 2.1. Formulation The calculations were performed by MHD simulations using the software ANSYS-Fluent. The MHD module of ANSYS-Fluent is able to describe the problem by using two formulations, being the main variable either the electric potential or the induced magnetic field (B ). The last approach was the one used in this work, considered as a better option for the modelling of 2D problems with high Hartmann numbers, Ha [24,25] (the Hartmann number squared measures the ratio between the electromagnetic and viscous forces). In the induced magnetic field formulation, the generation of electric currents (j) is described by the Maxwell equations (equations 1, 2, 3 and 4) coupled with Ohm’s law, which, applied to the movement of a fluid with velocity U , adopts the form expressed in equation 5. (1)
·B = 0
xE =
B t
(2) (3)
· D = q being D = E xH = j + j =
j 1 being H = B t µ
(4) (5)
(E + U x B )
and µ denote the electric and magnetic permeability, respectively. The
induction equation (equation 6), in terms of B , is then obtained from the expressions above.
B 1 + (U · ) B = t µ
2B
+ (B · ) U
(6)
For solved B , the currents are determined by Ampère’s relation (equation 7). The combination between the Navier-Stokes equation, the momentum equation (equation 8) and the Lorentz forces associated to the electric currents (equation 9) determines the fluid movement, being P, and v the pressure, density and kinematic viscosity of the PbLi, respectively.
j =
1 µ
xB
U + (U · ) U = t 2
(7)
P
+v
2U
+F
(8)
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Table 1 Dimensions and parameters of the problem.
(9)
F = j xB
A 2D steady-state analysis was performed in order to simplify the problem, considering the flow as fully developed and studying the cross-section of the poloidal channel; a similar approach can be found in [26] and [27]. However, it should be mentioned that the flow in the long poloidal channels of the blanket may show significant 3D phenomena, as turbulence or buoyancy effects, that must be properly studied in future works in order to fully characterize the flow during operation. An external boundary condition for the induced field was applied, assuming B = 0 in the outer boundary of the problem domain. A coupled boundary condition was considered in the internal interfaces of the problem sub-domains, i.e. in the interfaces between the PbLi, the FCI and the steel wall, as there is an abrupt change in the electrical conductivity at all material interfaces. The imposition of a severe convergence criteria was necessary in order to properly solve some of the cases considered, especially those with higher Ha and conducting walls, varying the convergence criterion from 10-9 to 10-12 depending on the case considered. The computing time varied between 12 hours and several days.
Channel size
20 x 20 cm
FCI thickness Gap thickness Steel wall thickness PbLi mean velocity Mass flow rate Toroidal magnetic field
5 mm 2 mm 5 mm 0.1 m/s 36.5 kg/s 4, 10 T
Table 2 Properties of the materials.
PbLi EUROFER Porous SiC Dense SiC
Density (kg/m3)
µ (Pa·s)
9600.9 7625 variable 3210
0.001 -
(S/m) 739 447 884 956 variable 500
problem equal to the ones previously described. The intensity of the magnetic field was fixed to 4 T in these validation cases. As an example, a comparison between the results obtained by the code developed in UCLA and the one obtained with ANSYS-Fluent is shown in Fig. 2, including an FCI with two different values of the electrical conductivity, 10-4 and 100 S/m. For a better comparison of the results, the dimensionless flow rate factor (Q) is included for both dP cases, being - dz the pressure drop, U0 the main PbLi velocity, and b the characteristic dimension of the fluid domain:
2.2. Geometry A scheme showing the 2D geometry studied can be seen in Fig. 1, that includes the dimensions of the problem and the characteristics of the flow summarized in Table 1. The FCI was modelled as a 20 x 20 cm hollow channel of 5 mm thickness rounded at the corners, being the external radius 20 mm. A gap of 2 mm is included between the FCI and the blanket steel structure. The mean velocity imposed to the PbLi was 10 cm/s, a relevant value considering the high-temperature DCLL conditions [23]. For the geometry considered, this is equal to a mass flow rate of 36.5 kg/s. In Table 2, the properties of the materials implemented in the MHD model are shown.
Q=
4· U0· · v b2 ·(
dP ) dz
(10)
The results provided by ANSYS in terms of pressure drop are very similar to the solution of the UCLA code, with only slight differences in the velocity distribution. The higher discrepancies are found in the gap flow in the cases with a highly conducting FCI. Those discrepancies would probably be reduced if higher computation power was used in the case of the ANSYS simulations, since the computation time was found to be unacceptable to fully reproduce the flow in the gap in those cases. Nonetheless, these differences are considered as acceptable in terms of the discussion performed in the present work, mainly focused on the study of insulating FCIs.
2.3. Code validation The solution provided by the MHD module of ANSYS-Fluent was validated by comparing several study cases with the results obtained by the code developed by Dr. Smolentsev at UCLA. Details of the code can be found in [28]. For these simulations, the FCI was modelled as singlematerial channel with sharp corners, being the other parameters of the
2.4. Meshing The appropriate meshing of the problem domain is a crucial aspect in MHD simulations. The generated electric currents must be properly resolved, especially in the so-called Hartmann layers (of ∼1/Ha thickness, in the wall perpendicular to the magnetic field) and side layers (of ∼1/ Ha thickness, in the walls parallel to the field), the areas of the domain near the solid-liquid interfaces. The use of a nonuniform mesh is necessary to properly resolve the Hartmann and side layers, since the Hartmann layers are the most challenging zones; they need to include a minimum of 7-10 meshing points as recommended in [28]. A less severe requirement is suggested in [29]. The thickness of the Hartmann and side layers in the cases studied in the present work is shown in Table 3, together with the number of points included in the mesh. Due to the severe restrictions imposed by the 10 T field, it was necessary to reduce the number of elements in the Hartmann layers to get convergence. In all cases, the mesh included 100 × 100 points in the bulk PbLi, 20 elements across the dense conducting layers of the FCI, 20 elements across the core of the FCI, 20 elements in the PbLi gap and 10 across the steel wall. Details of the mesh geometry in the 4 and 10 T cases can be seen in Fig. 3 and Fig. 4.
Fig. 1. Geometry of the problem. 3
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Fig. 2. Cases calculated for the validation of the ANSYS-Fluent MHD module for high Hartmann numbers; comparison with the UCLA code.
3. Results
Table 3 Thickness of the Hartmann and side layers as a function of the intensity of the magnetic field and of the corresponding Hartmann number.
B (T) 4 10
Ha ∼ 10 333 ∼ 25 833
Thickness (mm)
Points in Ha layer
Ha layer ∼0.1 ∼0.04
Bulk 17 11
Side layer ∼10 ∼6
3.1. Single-material FCI To study the effect of the electrical conductivity of the FCI on the PbLi flow, a first set of results is presented, where the FCI is modelled as a single-material hollow channel. The cases corresponding to a magnetic field of 4 T will be presented first, discussing then the 10 T cases; the magnitude of the pressure drop expected in the poloidal channels of the blanket will be evaluated at the end of this section. The influence of including an outer dense coating in the material will be addressed in the
Gap 7 4
Fig. 3. Details of the mesh used in the 4 T cases. 4
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Fig. 4. Details of the mesh used in the 10 T cases.
next section. Despite being a well-known MHD case, the results considering the flow with no FCI are presented first, for an easier understanding of the influence of FCIs on the flow, and a better comparison between this and the other cases presented further in the text. The pressure gradient (dP/ dx) in this case, together with the intensity of the high-velocity jets formed near the side walls (illustrated by the velocity ratio Ujets/Ucore), are presented in Table 4 for the two intensities of the magnetic field considered. The use of FCIs is justified to avoid the high values of pressure drop together with the formation of high-velocity near-wall jets, as can be seen in the velocity profile schemed of Fig. 5. To analyze the effect of the FCI, a parametric study was performed in the flow with FCI, varying the value of its electrical conductivity in a range considered feasible for SiC-based materials [21][17][20]. The results considering a 4 T magnetic field are summarized in Table 5, as a function of the electrical conductivity of the FCI (σFCI). Illustrating the results, in Fig. 6 the pressure drop reduction factor (R, denoting the ratio between the pressure drop without FCI and the pressure drop with FCI) is represented as a function of the electrical conductivity of the FCI. As can be deduced from the results, the FCI provides an acceptable electrical insulation if its electrical conductivity is kept below ∼1 S/m, being the pressure drop rapidly increasing for FCIs with higher conductivities. The velocity profile if an insulating FCI is included can be seen in Fig. 7, corresponding to the flow distribution with a FCI of 0.1 S/m. Due to the presence of the insulating FCI, the electric currents formed by the electromagnetic interactions close their path inside the fluid domain, resulting in Lorentz forces with maximum intensity in the center of the bulk; this causes a characteristic flattering of the velocity profile in the PbLi core. With respect to the flow in the gap between the FCI and the steel structure, it presents a parabolic profile in the zones parallel to the magnetic field (side gap), with a lower main velocity if compared to the bulk flow. On the contrary, the PbLi in the areas perpendicular to the magnetic field (Hartmann gap) remains practically stagnant. If the electrical conductivity of the FCI increases, the formation of high-velocity jets near the side walls begins to be noticeable, as illustrated by the results shown in Fig. 8, corresponding to the flow with an FCI of 100 S/m. In this case, the electric currents cross the FCI, coupling the bulk and gap flows causing an increase of the PbLi velocity in the gap. To illustrate the influence of the intensity of the magnetic field in
Fig. 5. Velocity distribution in the flow with no FCI (4 T). Table 5 Pressure gradient as a function of the electrical conductivity of the FCI (singlematerial channel) (B = 4 T). σFCI (S/m)
dP/dx (Pa/m)
Table 4 Pressure gradient and intensity of the high-velocity jets near the side walls in the flow with no FCI, as a function of the intensity of the magnetic field.
dP/dx (Pa/m) Ujets/Ucore
10
59 253 12.6
361 021 20.3
0.1
1
10
100
4
123
126
171
4058
Fig. 6. Pressure drop reduction factor as a function of the electrical conductivity of the FCI (single-material channel) (B = 4 T).
B (T) 4
B (T)
the MHD phenomena, the pressure gradient considering a magnetic field of 10 T is represented in Fig. 9, as a function of the electrical conductivity of the FCI. The results of the 4 T cases are also included for a better comparison Higher pressure gradients are observed in the 10 T cases. Higher 5
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Fig. 7. Velocity distribution considering an insulating FCI (0.1 S/m, 4 T).
velocity jets were also noticed, as illustrated in Fig. 10, with the intensity of the high-velocity jets near the side walls as a function of the electrical conductivity of the FCI. Apart from the formation of the jets, it should be mentioned that considerable reverse flows were found in the gap corners for a 10 T field, even with insulating FCIs. The reverse flows are represented by the velocity projections of Fig. 11, with the velocity projected in the poloidal direction.
second batch of calculations, similar to the previously presented, were carried out simulating the FCI as a dense-porous-dense material. The porous core was considered as insulating in this study, being its electrical conductivity 0.1 S/m. 3.2.1. Influence of the thickness of the coating In these results, the electrical conductivity of the dense coating is fixed by 500 S/m, value in the range of the conductivity reported for dense SiC produced by CVD [30]. The influence of the thickness of the protective coating (δcoating) on the MHD effects is discussed in Table 6, where the variation of the pressure gradient with respect to the thickness of the coating is shown. The pressure drop reduction factor as a function of the coating thickness is represented in Fig. 12. The results obtained with an insulating FCI without coating, discussed in the previous section, are included for an easier comparison. These values show that, even if the pressure drop increases due to
3.2. SiC-FCI: porous SiC with protective dense SiC coating As mentioned in the introduction, the objective of the present work is to analyze the potential of a SiC-FCI as an electrical insulator in a high-temperature DCLL. In the proposed material, the insulation properties are provided by a core of porous SiC, which is coated with a dense SiC layer as a protection against PbLi. In order to discuss the possible influence of the dense SiC coating on the electrical insulation, a
Fig. 8. Velocity distribution considering a not-insulating FCI (100 S/m, 4 T). 6
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Table 6 Pressure gradient in a SiC-FCI as a function of the thickness of the protective dense coating, for the two values of the magnetic field (σcoating = 500 S/m, σcore = 0.1 S/m). δcoating
dP/dx (Pa/m)
B (T)
0
200 μm
500 μm
1 mm
4 10
123 305
128 341
137 384
151 475
Fig. 9. Pressure gradient as a function of the electrical conductivity of the FCI, for the two values of the magnetic field studied.
Fig. 12. Pressure drop reduction factor as a function of the thickness of the coating, for the two values of the magnetic field (σcoating = 500 S/m, σcore = 0.1 S/m).
coatings with moderate thicknesses and for lower intensities of the magnetic field Fig. 10. Intensity of the high-velocity jets near the side walls as a function of the electrical conductivity of the FCI, for the two values of the magnetic field studied.
3.2.2. Influence of the electrical conductivity of the protective coating Even if the electrical conductivity of dense SiC is not expected to be above 500 S/m, to consider the influence of the electrical conductivity of the coating may be relevant, especially if the use of alternative materials is contemplated in future designs of FCIs. This may be the case of the steel-Al2O3-steel FCI concept proposed for the low-temperature versions of the DCLL [3].
the presence of the conducting coating, its overall effect on the electrical insulation can be considered as negligible, if its properties are in the range of those attributed to dense SiC. This is especially true for
Fig. 11. Velocity projections illustrating the formation of reverse flows in the gap corner, for the two values of the magnetic field studied. 7
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3.3. Damaged FCI: effect of a PbLi infiltration
Table 7 Pressure gradient in a sandwich FCI as a function of the electrical conductivity of the protective coating (δcoating = 1 mm, σcore = 0.1 S/m, B = 4 T).
The above cases analyzed the effect of an undamaged FCI. In this section, the influence on the electrical insulation of a total or partial PbLi infiltration inside the porous core of the SiC-FCI due to damages in the protective coating will be analyzed. The electrical conductivity of the unfilled porous core is considered as 0.1 S/m in this section, being the magnetic field intensity fixed by 4 T.
σcoating (S/m) dP/dx (Pa/m)
500 151
5000 381
10 000 635
EUROFER 14 286
3.3.1. Total infiltration 3.3.1.1. In a single-material FCI. A first case modeling the FCI as a single-material is presented, simulating a total infiltration of a porous FCI by PbLi. To this effect, the FCI is modelled as a single material with an electrical conductivity equal to the one of PbLi, to address the worstcase scenario in terms of the electrical insulation. In this case, the presence of the FCI does not modify the path of the electrical currents formed, since its electrical conductivity equals that of the liquid metal; the currents close their path through the steel wall, generating high-velocity jets in the gap flow. The bulk PbLi presents a uniform velocity profile. This distribution is illustrated in Fig. 15. The insulating effect of the FCI in this case is almost negligible, being the pressure gradient of the order of ∼47 kPa/m. 3.3.1.2. With an undamaged protective coating of 1 mm. Even if the electrical conductivity of dense SiC is considerably high, it is still several orders of magnitude less conductive than the liquid metal. To study the possible electrically insulating role of the coating if the porous core is filled with PbLi, a scenario considering a damage in the FCI that would result in a full infiltration of PbLi into the porous core is presented, but considering the presence of a protective coating undamaged in the section studied. A failure case relevant for this scenario would be, for example, if no damages have occurred in most of the poloidal channel, but a PbLi infiltration is found through a crack in the inlet/outlet section of the FCI. To that effect, a case similar to the previous one was solved but including an undamaged dense coating of 1 mm, remaining the electrical conductivity of the porous core equal to the one of the PbLi. The conductivity of the dense SiC coating is fixed by 500 S/m. The results (Fig. 16) show a flow with high-velocity jets appearing both in the bulk and in the gap near the side walls, with a higher velocity in the gap compared to the bulk flow. Considerable reverse flows are formed in the gap and bulk corners. The pressure gradient (∼34 kPa/m), although reduced with respect to the previous case, remains at the same order of magnitude. It can be concluded that the insulating effect of the dense coating by itself, even if it remains undamaged, is not significant if the porous core is filled with PbLi.
Fig. 13. Pressure drop reduction factor as a function of the electrical conductivity of the protective coating (δcoating = 1 mm, σcore = 0.1 S/m, B = 4 T).
If the thickness of the coating is fixed by 1 mm (considering this as the worst-case scenario in terms of its influence on MHD effects), the pressure gradient if the electrical conductivity of the coating (σcoating) is raised up to values associated to the EUROFER steel is shown in Table 7 and represented in Fig. 13. These results correspond to a magnetic field of 4 T. It can be concluded that the influence of the conductive coating on the MHD effects starts to be relevant if its electrical conductivity raises to the order of 1000 S/m. Thus, if a material with a high conductivity is used as coating, the insulating properties of the FCI may be practically suppressed, even including an insulating core of 3 mm thickness. The velocity distribution illustrating the effects of a 1 mm steel coating is shown in Fig. 14 as an example
3.3.2. Partial infiltration As mentioned in the introduction, the discussion presented in this work is related to the experimental development of a SiC-based FCI with protective coating at CEIT. The porous core of the fabricated FCI presents a honeycomb-like porous structure of almost spherical pores surrounded by a dense SiC matrix [23]. The protective coating is needed to protect the porous core from PbLi infiltration; in case of damages in the dense coating, such a porosity distribution makes possible a partial infiltration of PbLi in the area surrounding the defect, instead of a complete filling of the porosity. To simulate the effect of a partial infiltration of PbLi in the FCI, some cases considering a PbLi infiltration in different areas of the channel were calculated. To simplify the computations, the FCI was simulated as a single material insulating channel, since the insulating effect of the dense coating has been shown to be not significant. 3.3.2.1. Partial infiltration in the corners. The appearance of cracks in the outer dense coating in the corner area is considered as the most probable case in terms of a coating failure, since the higher thermal
Fig. 14. Velocity distribution in the flow with a 1 mm EUROFER coating (4 T). 8
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Fig. 15. Velocity distribution considering a total infiltration of PbLi in a single material FCI (4 T).
stresses supported by the FCI are concentrated in this zone. This situation may derive in a partial infiltration of the porous core in the area near the corners of the channel. To simulate this scenario, a case considering the corners of the FCI with an electrical conductivity equal to that of the PbLi was calculated, remaining the central areas of the walls with the conductivity attributed to non-infiltrated porous SiC (0.1 S/m). A sketch of the problem can be seen in Fig. 17. If a PbLi infiltration occurs in all corners, the results (in Fig. 17) show a highly altered velocity profile, with the flow concentrated in the center of the channel and a reduced velocity in the front and back areas of the bulk, due to the electrical currents crossing the channel in the areas filled with PbLi. The global pressure gradient raises if compared to the case with no infiltration, although it remains in the order of Pa/m (Table 8). It can be pointed that a FCI partially filled with PbLi is still effective
in the reduction of the MHD pressure drop in the poloidal channels; the disturbed flow, however, may lead to additional issues that should be considered to assure an adequate blanket performance, as may be the alterations in the heat transfer in the blanket and the corresponding changes in the temperature profile, the tritium transport and extraction, or the formation and extraction of residual He. 3.3.2.2. Partial infiltration in the Hartmann walls. Even if a PbLi infiltration in the corners is considered as a more probable damage scenario for the FCI, the effect of an infiltration in the central area of the walls is discussed in this section, since a damage in the Hartmann walls is considered as the worst-case scenario with respect to the formation of electrical currents and their associated Lorentz forces. Similar to the previous case, the problem was solved considering the central area of the Hartmann walls with the electrical conductivity of the PbLi,
Fig. 16. Velocity distribution considering a PbLi infiltration in the porous core of a sandwich FCI, with an undamaged 1 mm-thick dense coating (4 T). 9
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Fig. 17. Velocity distribution in case of a partial infiltration of PbLi in the corners of the FCI (4 T). Table 8 Pressure gradient and pressure drop reduction factor considering a PbLi infiltration in the corners of the FCI (4 T). dP/dx (Pa/m) R
Table 9 Pressure gradient and pressure drop reduction factor considering a partial infiltration of PbLi in the center of the Hartmann walls (4 T).
430 138
dP/dx (Pa/m) R
remaining the rest of the FCI insulating. As in the previous case, and as can be observed in the results shown in Fig. 18 and in Table 9, the main effect of the MHD interactions in this case is related to the disturbance of the PbLi flow, remaining the overall pressure gradient below 200 Pa/m.
186 319
4. Pressure drop in the poloidal channels of a high-temperature DCLL As a summary of the cases presented before, the pressure drop in the poloidal channels of a high-temperature DCLL is evaluated for a SiC-FCI with and without a dense SiC protective coating. Considering the design proposed in [10], with a poloidal length for the inboard module (IB,
Fig. 18. Velocity distribution considering a partial infiltration of PbLi in the Hartmann walls (4 T). 10
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Table 10 Pressure drop in the poloidal channels of the IB and OB modules of a hightemperature FCI, as a function of the basic FCI features
No FCI Conducting FCI (100 S/m) Insulating FCI Totally infiltrated FCI FCI with protective Undamaged coating (1 mm) Core partially infiltrated (corners)
IB module (7 m, 10 T)
OB module (10 m, 4 T)
2.5 MPa 0.3 MPa 2.1 kPa 3.3 kPa -
0.6 MPa 0.04 MPa 1.2 kPa 0.5 MPa 1.5 kPa 4.3 kPa
Fusion Eng. Des. 109–111 (2016) pp. 1199–1206. [2] S.J. Zinkle, N.M. Ghoniem, Prospects for accelerated development of high performance structural materials, J. Nucl. Mater. 417 (2011) 2–8. [3] D. Rapisarda, et al., Status of the engineering activities carried out on the European DCLL, Fusion Eng. Des. 124 (2017) 876–881. [4] E. Platacis, A. Ziks, A. Poznjak, F. Muktepavela, Investigation of the Li-Pb flow corrosion attack on the surface of P91 steel in the presence of magnetic field, Magnetohydrodynamics 48 (2012) 343–350. [5] M.C. Gázquez, T. Hernández, F. Muktepavela, E. Platacis, A. Shishko, Magnetic field effect on the corrosion processes at the Eurofer-Pb-17Li flow interface, J. Nucl. Mater. 465 (2015) 633–639. [6] D. Rapisarda, et al., Overview of DCLL research activities in the EU / Spain, SOFE, 2015. [7] B. Garcinuño, D. Rapisarda, I. Fernández, C. Moreno, I. Palermo, Á. Ibarra, Design of a permeator against vacuum for tritium extraction from eutectic lithium-lead in a DCLL DEMO, Fusion Eng. Des. 117 (2017) 226–231. [8] I. Palermo, I. Fernández, D. Rapisarda, A. Ibarra, Neutronic analyses of the preliminary design of a DCLL blanket for the EUROfusion DEMO power plant, Fusion Eng. Des. 109–111 (2015) 13–19. [9] I. Fernández-Berceruelo, M. Gonzalez, I. Palermo, F.R. Urgorri, D. Rapisarda, Largescale behavior of sandwich-like FCI components within the EU-DCLL operational conditions, Fusion Eng. Des. (2018) 633–638. [10] S. Smolentsev, et al., MHD thermohydraulics analysis and supporting R&D for DCLL blanket in the FNSF, Fusion Eng. Des. 135 (2018) 314–323. [11] C.E. Kessel, et al., Overview of the fusion nuclear science facility, a credible break-in step on the path to fusion energy, Fusion Eng. Des. (2018) pp. 236-270. [12] Y. Wu, Conceptual design of the China fusion power plant FDS-II, Fusion Eng. Des. 83 (10–12) (2008) 1683–1689. [13] Y. Katoh, et al., Current status and recent research achievements in SiC/SiC composites, J. Nucl. Mater. 455 (2014) 387–397. [14] S. Sharafat, A. Aoyama, N. Ghoniem, B. Williams, Thermo-mechanical Analysis of a Prototypical SiC Foam-Based Flow Channel Insert, SOFE, 2009. [15] M. Gonzalez, D. Rapisarda, A. Ibarra, C. Courtessole, S. Smolentsev, M. Abdou, Material analyses of foam-based SiC FCI after dynamic testing in PbLi in MaPLE loop at UCLA, Fusion Eng. Des. 109–111 (2016) 93–98. [16] S. Smolentsev, C. Courtessole, M. Abdou, S. Sharafat, S. Sahu, T. Sketchley, Numerical modeling of first experiments on PbLi MHD flows in a rectangular duct with foam-based SiC flow channel insert, Fusion Eng. Des. 108 (2016) 7–20. [17] C. Soto, Development of a SiC-based material for Flow Channel Inserts in hightemperature DCLL blankets, PhD thesis (2018). [18] C. Soto, et al., SiC-based sandwich material for Flow Channel Inserts in DCLL blankets: Manufacturing, characterization, corrosion tests, Fusion Eng. Des. 124 (2017) 958–963. [19] C. Soto, J.M. Martínez-Esnaola, C. García-Rosales, Thermomechanical analysis of a Flow Channel Insert based on a SiC-sandwich material concept, Nucl. Mater. Energy 7 (2016) 5–11. [20] M. Malo, C. Soto, C. García-Rosales, T. Hernández, Stability of porous SiC based materials under relevant conditions of radiation and temperature, J. Nucl. Mater. 509 (2018) 54–61. [21] C. Soto, et al., Development, Characterization, and Testing of a SiC-Based Material for Flow Channel Inserts in High-Temperature DCLL Blankets, IEEE Trans. Plasma Sci. (2018). [22] S. Smolentsev, R. Moreau, M. Abdou, Characterization of key magnetohydrodynamic phenomena in PbLi flows for the US DCLL blanket, Fusion Eng. Des. 83 (2008) 771–783. [23] S. Smolentsev, N.B. Morley, M. a. Abdou, S. Malang, Dual-coolant lead–lithium (DCLL) blanket status and R&D needs, Fusion Eng. Des. 100 (2015) 44–54. [24] S. Smolentsev, A. Tananaev, Development of computer code for analysis of heat transfer in liquid metal MHD flows in ducts, Second International PAMIR Conference and Energy Transfer in Magnetohydrodynamic Flows, Aussois, France, 1994. [25] H. Araseki, A Self-Correcting Procedure for Computational Liquid Metal Magnetohydrodynamics, J. Comput. Phys. 110 (1994) 301–309. [26] S. Smolentsev, N.B. Morley, M. Abdou, Magnetohydrodynamic and thermal issues of the SiCf/SiC flow channel insert, Fusion Sci. Technol. 50 (2006) 107–119. [27] S. Smolentsev, Z. Xu, C. Pan, M.A. Abdou, Numerical and Experimental Studies of Mhd Flow in a Rectangular Duct With a Non-Conducting Flow Insert, Magnetohydrodynamics 46 (2010) 99–111. [28] S. Smolentsev, N. Morley, M. Abdou, Code development for analysis of MHD pressure drop reduction in a liquid metal blanket using insulation technique based on a fully developed flow model, Fusion Eng. Des. 73 (2005) 83–93. [29] S. Subramanian, P.K. Swain, A.V. Deshpande, P. Satyamurthy, Effect of Hartmann layer resolution for MHD flow in a straight, conducting duct at high Hartmann numbers, Sadhana - Acad. Proc. Eng. Sci. 40 (2015) 851–861. [30] Rohm and and Haas, CVD Silicon Carbide, (2008) https://nshosting.dow.com/docarchive/business/gt/advanced_ceramics/cvd_silicon_carbide/tds/cvd_silicon_ carbide.pdf.
10 T) of 7 m and for the outboard module (OB, 4 T) of 10 m, the pressure drop associated to the basic FCI features are summarized in Table 10. In the cases considering a PbLi infiltration, only the values corresponding to the outboard modules are shown. The pressure drop related to a 10 T magnetic field in these cases should be analyzed in future works. 5. Conclusions - With the conditions associated to a high-temperature DCLL, the FCIs provide an adequate mitigation of the MHD effects if their electrical conductivity is kept below ∼1 S/m for both inboard and outboard blankets. With the parameters considered and using an insulating FCI, the pressure drop in the poloidal channels is kept in the order of kPa. - Considerably higher pressure drops are predicted in the inboard blanket modules due to the higher magnetic field. If a properly insulating FCI is not considered, the pressure drop associated to a 10 T magnetic field is one order of magnitude higher than in the 4 T scenario. - A SiC-based sandwich FCI formed by a porous SiC core with an electrical conductivity below 1 S/m and a protective dense SiC coating is able to provide an adequate electrical insulation to the bulk PbLi. The effect of the protective coating on the MHD interactions can be considered as negligible if it is made of dense SiC. However, this is not true if coatings made of materials with higher electrical conductivities are considered; the use of a conducting dense coating may lead to a major disturbance of the flow, even considering an insulating core. - A major PbLi infiltration trough the porous core inhibits the insulating character of the FCI, even if the protective dense coating remains undamaged. - In case of a PbLi infiltration in localized areas of an insulating FCI, it is still effective in terms of the reduction of the pressure drop. The flow distribution will be, however, disturbed. Acknowledgments This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] L.V. Boccaccini, et al., Objectives and status of EUROfusion DEMO blanket studies,
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Mitigation of MHD phenomena in DCLL blankets by Flow Channel Inserts based on a SiC-sandwich material concept
T
C. Sotoa,b, S. Smolentsevc, C. García-Rosalesa,b,* a
Ceit-IK4 Technology Center, E-20018, San Sebastian, Spain Universidad de Navarra, Tecnun, E-20018, San Sebastian, Spain c Univerisity of California, Los Angeles, USA b
ABSTRACT
The DCLL blanket is an attractive concept for future fusion reactors. In order to mitigate MHD effects from the interaction between flowing PbLi and magnetic field, Flow Channel Inserts (FCIs) need to be developed. SiC-based materials are main candidates for high-temperature FCIs. In this work, the MHD interactions and their possible mitigation by FCIs consisting of a porous SiC core with a dense protective SiC coating are studied. The dependency between MHD effects and the FCIs’ properties is discussed under relevant conditions for the DCLL concept. The results show that with a porous-dense SiC-sandwich material, a pressure gradient of ∼120 Pa/m is predicted for a 4 T magnetic field, and of ∼300 Pa/m for 10 T, if an FCI with insulating porous core (< ∼1 S/m) is used. Relevant cases considering a PbLi infiltration in the porous SiC core due to possible damages in the protective coating are presented.
1. Introduction The Dual Coolant Lead Lihitum (DCLL) blanket is a promising concept for future nuclear fusion reactors, leading to potentially high efficiencies in the energy production [1]. This design is characterized by the use of liquid PbLi both as the main coolant and as tritium breeder; in the DCLL, the liquid metal flows through poloidal channels, heating up by the neutron flux from the fusion plasma while tritium is produced by the reaction between neutrons and the lithium in the alloy. The second coolant is pressurized helium, which cools down the structure of the blanket, made of a reduced activation ferritic-martensitic (RAFM) steel. Among attractive features of the DCLL is the high PbLi exit temperature, up to 700 °C in the case of a so-called hightemperature DCLL. However, despite the high thermal efficiency associated with this high temperature, a considerable level of R&D would be needed to effectively overcome the design challenges of the blanket, both considering the study of its unique operating conditions and the development of the necessary new materials and technologies. Key components of the DCLL concept are the so-called Flow Channel Inserts (FCIs), consisting of a thin-wall (∼5 mm) rectangular-shape structure loosely inserted in the host RAFM duct, so that the PbLi breeder flows inside the FCI and also in the thin (∼2 mm) gap between the FCI and the RAFM wall. The use of FCIs is required to electrically decouple the liquid metal from the blanket steel structure, since electromagnetic interactions may result in an unacceptably high pressure drop due to magnetohydrodynamic (MHD) effects. Apart from the
⁎
pressure drop, the MHD interactions may also cause a major disturbance in the PbLi flow, and to accurately predict the velocity profile of the PbLi is crucial for a proper design of the DCLL. In this concept, the liquid PbLi acts at the same time as primary coolant, breeder, and tritium carrier; major disturbances in the flow may affect key aspects defining the blanket performance, as may be the heat transfer inside the PbLi (e.g. the thermal efficiency), the temperature field in the steel structure (e.g. the mechanical integrity), or the production and extraction of tritium and/or residual He due to the appearance of areas with a near-stagnant PbLi flow due to the MHD effects. In the case of the high-temperature version of the DCLL, apart from the electrical insulation, the high temperatures of the PbLi require to consider FCIs with thermal insulation properties, in order to protect the steel structure from a possible overheating. The maximum safe temperature for the blanket steel structure is commonly considered to be 550 °C [2,3]; this temperature requirement, however, may be more severe in the zones where the steel is directly in contact with the flowing PbLi, being a lower temperature (∼470 °C) recommended in the literature to avoid corrosion issues [4,5]. The anti-corrosion requirements are also more severe in the case of the high-temperature DCLL, where the PbLi is flowing at higher velocities and at temperatures up to ∼700 °C inside the FCIs. To carry out the conceptual design of the DCLL avoiding some of the main technological difficulties, a near-term, low-temperature DCLL design is being developed in the framework of the EUROfusion Breeding Blanket Program for DEMO [3,6], leaded by CIEMAT. In this
Corresponding author. E-mail address: [email protected] (C. García-Rosales).
https://doi.org/10.1016/j.fusengdes.2019.111381 Received 31 May 2019; Received in revised form 22 August 2019; Accepted 22 October 2019 0920-3796/ © 2019 The Author(s). Published by Elsevier B.V. All rights reserved.
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design, based in a multi-module approach, the maximum PbLi temperature is limited to 550 °C, avoiding the need for thermal insulation and allowing the use of FCIs made of existing materials [6]. Despite the lower temperature of the PbLi, substantial progress has been made in terms of the achieved TBR, tritium extraction [7], neutronics [8] and the FCI design [9]. Apart from the developments in the EU, a DCLL blanket concept is being discussed in the framework of the development of the Fusion Nuclear Science Facility (FNSF) in the US [10,11]. This concept is based on a single-module approach, considering the use of long poloidal channels of 7-10 m length and keeping the PbLi temperature in a similar range than in the design proposed by CIEMAT. The characteristic magnetic field for the outboard module of the US DCLL is 5.5 T, raising to 10 T in the inboard module. Apart from this, further research involving the development of the DCLL concept is being carried out worldwide, for example in the China fusion program [12]. Even if the design of the DCLL is carried out, at first approach, from a low-temperature perspective, it is reasonable to consider a future upgrade of the concept allowing the achievement of higher PbLi temperatures, considering the advantages that this scenario would offer in terms of energy production. A main technological challenge that needs to be solved in the framework of a high-temperature DCLL is to develop an adequate material for FCIs, able to withstand the severe requirements associated to the application: the required electrical and thermal insulation, a good response to high temperatures and to high radiation, and suitability against possible corrosion issues. To this date, the main candidates for high-temperature FCIs are materials based on silicon carbide (SiC), a high-performance ceramic adequate for high temperature applications, with a promising response in high irradiation environments and with excellent chemical stability. The electrical and thermal conductivities of dense SiC, however, are relatively high, being necessary to develop a low-conductivity SiCbased insulating material to be applied in FCIs. Apart from the production of SiCf/SiC composites with the required properties [13], a possible approach consists in the development of a dense-porous SiC material, formed by a porous SiC core providing the insulating properties, and a dense SiC coating protecting from PbLi infiltration and possible corrosion. This last possibility has been explored in the US, with prototypes fabricated by Ultramet that were tested at the MaPLE PbLi loop in UCLA [14–16]. Besides, an alternative SiC-based material was developed and studied at CEIT (Spain), in the framework of the EUROfusion Enabling Research program [17–20]. Insulating porous SiC materials with porosities of 30-50%, candidates for the core of the FCI-SiC, were fabricated and characterized; as the outer layer of the material, a coating of dense SiC was deposited by Chemical Vapor Deposition (CVD). More details regarding the fabrication process, together with the characterization and testing of the material, can be found in [17,21,18], including experiments testing its response against hot flowing PbLi. To establish a range of recommended material properties for FCIs it is a necessary step in the proper development of the SiC-based material. Regarding specifically the electrical properties, to assure a good electrical insulation of the PbLi is crucial to avoid high pressure losses in the poloidal channels and major disturbances in the PbLi flow [22,23]; to that effect, the coupling between the properties of the FCIs and the MHD interactions must be studied. In this framework, and as a support to the previously mentioned experimental development of a candidate material for FCIs carried out at CEIT, an analysis of the MHD phenomena in the PbLi flow considering a SiC-based FCI was carried out under relevant conditions for the high-temperature DCLL. The results were used to discuss the recommended FCI properties to assure optimum performance of the blanket, establishing a range of values for the electrical conductivity of the porous SiC material and for its configuration, in terms of the thickness of the dense and porous layers. In the present work, the main results of the study discussing the possible mitigation of MHD phenomena by using a SiC-based sandwich
FCI are presented. In the first section, the dependency of the pressure drop values and the flow disturbances on the properties of the FCIs are addressed. In order to simplify the calculations, the FCI is at first modelled as a single-material channel, discussing the influence of the electrical properties of the material on the MHD phenomena. Then, the effect of including a dense SiC coating with respect to the electromagnetic interactions is analyzed as a function of its thickness and its electrical conductivity. Two intensities of the magnetic field, 4 and 10 T, were studied, as a reference for the expected magnetic field in the outboard and inboard modules of the blanket, respectively [10]. By last, a discussion is presented addressing the effect of a possible PbLi infiltration inside the FCIs. The values of the pressure gradient and the flow distribution in each scenario studied are presented, establishing a complete discussion with respect to the potential performance of a SiCbased material as electrical insulator in the poloidal channels of a hightemperature DCLL. 2. Methodology 2.1. Formulation The calculations were performed by MHD simulations using the software ANSYS-Fluent. The MHD module of ANSYS-Fluent is able to describe the problem by using two formulations, being the main variable either the electric potential or the induced magnetic field (B ). The last approach was the one used in this work, considered as a better option for the modelling of 2D problems with high Hartmann numbers, Ha [24,25] (the Hartmann number squared measures the ratio between the electromagnetic and viscous forces). In the induced magnetic field formulation, the generation of electric currents (j) is described by the Maxwell equations (equations 1, 2, 3 and 4) coupled with Ohm’s law, which, applied to the movement of a fluid with velocity U , adopts the form expressed in equation 5. (1)
·B = 0
xE =
B t
(2) (3)
· D = q being D = E xH = j + j =
j 1 being H = B t µ
(4) (5)
(E + U x B )
and µ denote the electric and magnetic permeability, respectively. The
induction equation (equation 6), in terms of B , is then obtained from the expressions above.
B 1 + (U · ) B = t µ
2B
+ (B · ) U
(6)
For solved B , the currents are determined by Ampère’s relation (equation 7). The combination between the Navier-Stokes equation, the momentum equation (equation 8) and the Lorentz forces associated to the electric currents (equation 9) determines the fluid movement, being P, and v the pressure, density and kinematic viscosity of the PbLi, respectively.
j =
1 µ
xB
U + (U · ) U = t 2
(7)
P
+v
2U
+F
(8)
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Table 1 Dimensions and parameters of the problem.
(9)
F = j xB
A 2D steady-state analysis was performed in order to simplify the problem, considering the flow as fully developed and studying the cross-section of the poloidal channel; a similar approach can be found in [26] and [27]. However, it should be mentioned that the flow in the long poloidal channels of the blanket may show significant 3D phenomena, as turbulence or buoyancy effects, that must be properly studied in future works in order to fully characterize the flow during operation. An external boundary condition for the induced field was applied, assuming B = 0 in the outer boundary of the problem domain. A coupled boundary condition was considered in the internal interfaces of the problem sub-domains, i.e. in the interfaces between the PbLi, the FCI and the steel wall, as there is an abrupt change in the electrical conductivity at all material interfaces. The imposition of a severe convergence criteria was necessary in order to properly solve some of the cases considered, especially those with higher Ha and conducting walls, varying the convergence criterion from 10-9 to 10-12 depending on the case considered. The computing time varied between 12 hours and several days.
Channel size
20 x 20 cm
FCI thickness Gap thickness Steel wall thickness PbLi mean velocity Mass flow rate Toroidal magnetic field
5 mm 2 mm 5 mm 0.1 m/s 36.5 kg/s 4, 10 T
Table 2 Properties of the materials.
PbLi EUROFER Porous SiC Dense SiC
Density (kg/m3)
µ (Pa·s)
9600.9 7625 variable 3210
0.001 -
(S/m) 739 447 884 956 variable 500
problem equal to the ones previously described. The intensity of the magnetic field was fixed to 4 T in these validation cases. As an example, a comparison between the results obtained by the code developed in UCLA and the one obtained with ANSYS-Fluent is shown in Fig. 2, including an FCI with two different values of the electrical conductivity, 10-4 and 100 S/m. For a better comparison of the results, the dimensionless flow rate factor (Q) is included for both dP cases, being - dz the pressure drop, U0 the main PbLi velocity, and b the characteristic dimension of the fluid domain:
2.2. Geometry A scheme showing the 2D geometry studied can be seen in Fig. 1, that includes the dimensions of the problem and the characteristics of the flow summarized in Table 1. The FCI was modelled as a 20 x 20 cm hollow channel of 5 mm thickness rounded at the corners, being the external radius 20 mm. A gap of 2 mm is included between the FCI and the blanket steel structure. The mean velocity imposed to the PbLi was 10 cm/s, a relevant value considering the high-temperature DCLL conditions [23]. For the geometry considered, this is equal to a mass flow rate of 36.5 kg/s. In Table 2, the properties of the materials implemented in the MHD model are shown.
Q=
4· U0· · v b2 ·(
dP ) dz
(10)
The results provided by ANSYS in terms of pressure drop are very similar to the solution of the UCLA code, with only slight differences in the velocity distribution. The higher discrepancies are found in the gap flow in the cases with a highly conducting FCI. Those discrepancies would probably be reduced if higher computation power was used in the case of the ANSYS simulations, since the computation time was found to be unacceptable to fully reproduce the flow in the gap in those cases. Nonetheless, these differences are considered as acceptable in terms of the discussion performed in the present work, mainly focused on the study of insulating FCIs.
2.3. Code validation The solution provided by the MHD module of ANSYS-Fluent was validated by comparing several study cases with the results obtained by the code developed by Dr. Smolentsev at UCLA. Details of the code can be found in [28]. For these simulations, the FCI was modelled as singlematerial channel with sharp corners, being the other parameters of the
2.4. Meshing The appropriate meshing of the problem domain is a crucial aspect in MHD simulations. The generated electric currents must be properly resolved, especially in the so-called Hartmann layers (of ∼1/Ha thickness, in the wall perpendicular to the magnetic field) and side layers (of ∼1/ Ha thickness, in the walls parallel to the field), the areas of the domain near the solid-liquid interfaces. The use of a nonuniform mesh is necessary to properly resolve the Hartmann and side layers, since the Hartmann layers are the most challenging zones; they need to include a minimum of 7-10 meshing points as recommended in [28]. A less severe requirement is suggested in [29]. The thickness of the Hartmann and side layers in the cases studied in the present work is shown in Table 3, together with the number of points included in the mesh. Due to the severe restrictions imposed by the 10 T field, it was necessary to reduce the number of elements in the Hartmann layers to get convergence. In all cases, the mesh included 100 × 100 points in the bulk PbLi, 20 elements across the dense conducting layers of the FCI, 20 elements across the core of the FCI, 20 elements in the PbLi gap and 10 across the steel wall. Details of the mesh geometry in the 4 and 10 T cases can be seen in Fig. 3 and Fig. 4.
Fig. 1. Geometry of the problem. 3
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Fig. 2. Cases calculated for the validation of the ANSYS-Fluent MHD module for high Hartmann numbers; comparison with the UCLA code.
3. Results
Table 3 Thickness of the Hartmann and side layers as a function of the intensity of the magnetic field and of the corresponding Hartmann number.
B (T) 4 10
Ha ∼ 10 333 ∼ 25 833
Thickness (mm)
Points in Ha layer
Ha layer ∼0.1 ∼0.04
Bulk 17 11
Side layer ∼10 ∼6
3.1. Single-material FCI To study the effect of the electrical conductivity of the FCI on the PbLi flow, a first set of results is presented, where the FCI is modelled as a single-material hollow channel. The cases corresponding to a magnetic field of 4 T will be presented first, discussing then the 10 T cases; the magnitude of the pressure drop expected in the poloidal channels of the blanket will be evaluated at the end of this section. The influence of including an outer dense coating in the material will be addressed in the
Gap 7 4
Fig. 3. Details of the mesh used in the 4 T cases. 4
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Fig. 4. Details of the mesh used in the 10 T cases.
next section. Despite being a well-known MHD case, the results considering the flow with no FCI are presented first, for an easier understanding of the influence of FCIs on the flow, and a better comparison between this and the other cases presented further in the text. The pressure gradient (dP/ dx) in this case, together with the intensity of the high-velocity jets formed near the side walls (illustrated by the velocity ratio Ujets/Ucore), are presented in Table 4 for the two intensities of the magnetic field considered. The use of FCIs is justified to avoid the high values of pressure drop together with the formation of high-velocity near-wall jets, as can be seen in the velocity profile schemed of Fig. 5. To analyze the effect of the FCI, a parametric study was performed in the flow with FCI, varying the value of its electrical conductivity in a range considered feasible for SiC-based materials [21][17][20]. The results considering a 4 T magnetic field are summarized in Table 5, as a function of the electrical conductivity of the FCI (σFCI). Illustrating the results, in Fig. 6 the pressure drop reduction factor (R, denoting the ratio between the pressure drop without FCI and the pressure drop with FCI) is represented as a function of the electrical conductivity of the FCI. As can be deduced from the results, the FCI provides an acceptable electrical insulation if its electrical conductivity is kept below ∼1 S/m, being the pressure drop rapidly increasing for FCIs with higher conductivities. The velocity profile if an insulating FCI is included can be seen in Fig. 7, corresponding to the flow distribution with a FCI of 0.1 S/m. Due to the presence of the insulating FCI, the electric currents formed by the electromagnetic interactions close their path inside the fluid domain, resulting in Lorentz forces with maximum intensity in the center of the bulk; this causes a characteristic flattering of the velocity profile in the PbLi core. With respect to the flow in the gap between the FCI and the steel structure, it presents a parabolic profile in the zones parallel to the magnetic field (side gap), with a lower main velocity if compared to the bulk flow. On the contrary, the PbLi in the areas perpendicular to the magnetic field (Hartmann gap) remains practically stagnant. If the electrical conductivity of the FCI increases, the formation of high-velocity jets near the side walls begins to be noticeable, as illustrated by the results shown in Fig. 8, corresponding to the flow with an FCI of 100 S/m. In this case, the electric currents cross the FCI, coupling the bulk and gap flows causing an increase of the PbLi velocity in the gap. To illustrate the influence of the intensity of the magnetic field in
Fig. 5. Velocity distribution in the flow with no FCI (4 T). Table 5 Pressure gradient as a function of the electrical conductivity of the FCI (singlematerial channel) (B = 4 T). σFCI (S/m)
dP/dx (Pa/m)
Table 4 Pressure gradient and intensity of the high-velocity jets near the side walls in the flow with no FCI, as a function of the intensity of the magnetic field.
dP/dx (Pa/m) Ujets/Ucore
10
59 253 12.6
361 021 20.3
0.1
1
10
100
4
123
126
171
4058
Fig. 6. Pressure drop reduction factor as a function of the electrical conductivity of the FCI (single-material channel) (B = 4 T).
B (T) 4
B (T)
the MHD phenomena, the pressure gradient considering a magnetic field of 10 T is represented in Fig. 9, as a function of the electrical conductivity of the FCI. The results of the 4 T cases are also included for a better comparison Higher pressure gradients are observed in the 10 T cases. Higher 5
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Fig. 7. Velocity distribution considering an insulating FCI (0.1 S/m, 4 T).
velocity jets were also noticed, as illustrated in Fig. 10, with the intensity of the high-velocity jets near the side walls as a function of the electrical conductivity of the FCI. Apart from the formation of the jets, it should be mentioned that considerable reverse flows were found in the gap corners for a 10 T field, even with insulating FCIs. The reverse flows are represented by the velocity projections of Fig. 11, with the velocity projected in the poloidal direction.
second batch of calculations, similar to the previously presented, were carried out simulating the FCI as a dense-porous-dense material. The porous core was considered as insulating in this study, being its electrical conductivity 0.1 S/m. 3.2.1. Influence of the thickness of the coating In these results, the electrical conductivity of the dense coating is fixed by 500 S/m, value in the range of the conductivity reported for dense SiC produced by CVD [30]. The influence of the thickness of the protective coating (δcoating) on the MHD effects is discussed in Table 6, where the variation of the pressure gradient with respect to the thickness of the coating is shown. The pressure drop reduction factor as a function of the coating thickness is represented in Fig. 12. The results obtained with an insulating FCI without coating, discussed in the previous section, are included for an easier comparison. These values show that, even if the pressure drop increases due to
3.2. SiC-FCI: porous SiC with protective dense SiC coating As mentioned in the introduction, the objective of the present work is to analyze the potential of a SiC-FCI as an electrical insulator in a high-temperature DCLL. In the proposed material, the insulation properties are provided by a core of porous SiC, which is coated with a dense SiC layer as a protection against PbLi. In order to discuss the possible influence of the dense SiC coating on the electrical insulation, a
Fig. 8. Velocity distribution considering a not-insulating FCI (100 S/m, 4 T). 6
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Table 6 Pressure gradient in a SiC-FCI as a function of the thickness of the protective dense coating, for the two values of the magnetic field (σcoating = 500 S/m, σcore = 0.1 S/m). δcoating
dP/dx (Pa/m)
B (T)
0
200 μm
500 μm
1 mm
4 10
123 305
128 341
137 384
151 475
Fig. 9. Pressure gradient as a function of the electrical conductivity of the FCI, for the two values of the magnetic field studied.
Fig. 12. Pressure drop reduction factor as a function of the thickness of the coating, for the two values of the magnetic field (σcoating = 500 S/m, σcore = 0.1 S/m).
coatings with moderate thicknesses and for lower intensities of the magnetic field Fig. 10. Intensity of the high-velocity jets near the side walls as a function of the electrical conductivity of the FCI, for the two values of the magnetic field studied.
3.2.2. Influence of the electrical conductivity of the protective coating Even if the electrical conductivity of dense SiC is not expected to be above 500 S/m, to consider the influence of the electrical conductivity of the coating may be relevant, especially if the use of alternative materials is contemplated in future designs of FCIs. This may be the case of the steel-Al2O3-steel FCI concept proposed for the low-temperature versions of the DCLL [3].
the presence of the conducting coating, its overall effect on the electrical insulation can be considered as negligible, if its properties are in the range of those attributed to dense SiC. This is especially true for
Fig. 11. Velocity projections illustrating the formation of reverse flows in the gap corner, for the two values of the magnetic field studied. 7
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3.3. Damaged FCI: effect of a PbLi infiltration
Table 7 Pressure gradient in a sandwich FCI as a function of the electrical conductivity of the protective coating (δcoating = 1 mm, σcore = 0.1 S/m, B = 4 T).
The above cases analyzed the effect of an undamaged FCI. In this section, the influence on the electrical insulation of a total or partial PbLi infiltration inside the porous core of the SiC-FCI due to damages in the protective coating will be analyzed. The electrical conductivity of the unfilled porous core is considered as 0.1 S/m in this section, being the magnetic field intensity fixed by 4 T.
σcoating (S/m) dP/dx (Pa/m)
500 151
5000 381
10 000 635
EUROFER 14 286
3.3.1. Total infiltration 3.3.1.1. In a single-material FCI. A first case modeling the FCI as a single-material is presented, simulating a total infiltration of a porous FCI by PbLi. To this effect, the FCI is modelled as a single material with an electrical conductivity equal to the one of PbLi, to address the worstcase scenario in terms of the electrical insulation. In this case, the presence of the FCI does not modify the path of the electrical currents formed, since its electrical conductivity equals that of the liquid metal; the currents close their path through the steel wall, generating high-velocity jets in the gap flow. The bulk PbLi presents a uniform velocity profile. This distribution is illustrated in Fig. 15. The insulating effect of the FCI in this case is almost negligible, being the pressure gradient of the order of ∼47 kPa/m. 3.3.1.2. With an undamaged protective coating of 1 mm. Even if the electrical conductivity of dense SiC is considerably high, it is still several orders of magnitude less conductive than the liquid metal. To study the possible electrically insulating role of the coating if the porous core is filled with PbLi, a scenario considering a damage in the FCI that would result in a full infiltration of PbLi into the porous core is presented, but considering the presence of a protective coating undamaged in the section studied. A failure case relevant for this scenario would be, for example, if no damages have occurred in most of the poloidal channel, but a PbLi infiltration is found through a crack in the inlet/outlet section of the FCI. To that effect, a case similar to the previous one was solved but including an undamaged dense coating of 1 mm, remaining the electrical conductivity of the porous core equal to the one of the PbLi. The conductivity of the dense SiC coating is fixed by 500 S/m. The results (Fig. 16) show a flow with high-velocity jets appearing both in the bulk and in the gap near the side walls, with a higher velocity in the gap compared to the bulk flow. Considerable reverse flows are formed in the gap and bulk corners. The pressure gradient (∼34 kPa/m), although reduced with respect to the previous case, remains at the same order of magnitude. It can be concluded that the insulating effect of the dense coating by itself, even if it remains undamaged, is not significant if the porous core is filled with PbLi.
Fig. 13. Pressure drop reduction factor as a function of the electrical conductivity of the protective coating (δcoating = 1 mm, σcore = 0.1 S/m, B = 4 T).
If the thickness of the coating is fixed by 1 mm (considering this as the worst-case scenario in terms of its influence on MHD effects), the pressure gradient if the electrical conductivity of the coating (σcoating) is raised up to values associated to the EUROFER steel is shown in Table 7 and represented in Fig. 13. These results correspond to a magnetic field of 4 T. It can be concluded that the influence of the conductive coating on the MHD effects starts to be relevant if its electrical conductivity raises to the order of 1000 S/m. Thus, if a material with a high conductivity is used as coating, the insulating properties of the FCI may be practically suppressed, even including an insulating core of 3 mm thickness. The velocity distribution illustrating the effects of a 1 mm steel coating is shown in Fig. 14 as an example
3.3.2. Partial infiltration As mentioned in the introduction, the discussion presented in this work is related to the experimental development of a SiC-based FCI with protective coating at CEIT. The porous core of the fabricated FCI presents a honeycomb-like porous structure of almost spherical pores surrounded by a dense SiC matrix [23]. The protective coating is needed to protect the porous core from PbLi infiltration; in case of damages in the dense coating, such a porosity distribution makes possible a partial infiltration of PbLi in the area surrounding the defect, instead of a complete filling of the porosity. To simulate the effect of a partial infiltration of PbLi in the FCI, some cases considering a PbLi infiltration in different areas of the channel were calculated. To simplify the computations, the FCI was simulated as a single material insulating channel, since the insulating effect of the dense coating has been shown to be not significant. 3.3.2.1. Partial infiltration in the corners. The appearance of cracks in the outer dense coating in the corner area is considered as the most probable case in terms of a coating failure, since the higher thermal
Fig. 14. Velocity distribution in the flow with a 1 mm EUROFER coating (4 T). 8
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Fig. 15. Velocity distribution considering a total infiltration of PbLi in a single material FCI (4 T).
stresses supported by the FCI are concentrated in this zone. This situation may derive in a partial infiltration of the porous core in the area near the corners of the channel. To simulate this scenario, a case considering the corners of the FCI with an electrical conductivity equal to that of the PbLi was calculated, remaining the central areas of the walls with the conductivity attributed to non-infiltrated porous SiC (0.1 S/m). A sketch of the problem can be seen in Fig. 17. If a PbLi infiltration occurs in all corners, the results (in Fig. 17) show a highly altered velocity profile, with the flow concentrated in the center of the channel and a reduced velocity in the front and back areas of the bulk, due to the electrical currents crossing the channel in the areas filled with PbLi. The global pressure gradient raises if compared to the case with no infiltration, although it remains in the order of Pa/m (Table 8). It can be pointed that a FCI partially filled with PbLi is still effective
in the reduction of the MHD pressure drop in the poloidal channels; the disturbed flow, however, may lead to additional issues that should be considered to assure an adequate blanket performance, as may be the alterations in the heat transfer in the blanket and the corresponding changes in the temperature profile, the tritium transport and extraction, or the formation and extraction of residual He. 3.3.2.2. Partial infiltration in the Hartmann walls. Even if a PbLi infiltration in the corners is considered as a more probable damage scenario for the FCI, the effect of an infiltration in the central area of the walls is discussed in this section, since a damage in the Hartmann walls is considered as the worst-case scenario with respect to the formation of electrical currents and their associated Lorentz forces. Similar to the previous case, the problem was solved considering the central area of the Hartmann walls with the electrical conductivity of the PbLi,
Fig. 16. Velocity distribution considering a PbLi infiltration in the porous core of a sandwich FCI, with an undamaged 1 mm-thick dense coating (4 T). 9
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Fig. 17. Velocity distribution in case of a partial infiltration of PbLi in the corners of the FCI (4 T). Table 8 Pressure gradient and pressure drop reduction factor considering a PbLi infiltration in the corners of the FCI (4 T). dP/dx (Pa/m) R
Table 9 Pressure gradient and pressure drop reduction factor considering a partial infiltration of PbLi in the center of the Hartmann walls (4 T).
430 138
dP/dx (Pa/m) R
remaining the rest of the FCI insulating. As in the previous case, and as can be observed in the results shown in Fig. 18 and in Table 9, the main effect of the MHD interactions in this case is related to the disturbance of the PbLi flow, remaining the overall pressure gradient below 200 Pa/m.
186 319
4. Pressure drop in the poloidal channels of a high-temperature DCLL As a summary of the cases presented before, the pressure drop in the poloidal channels of a high-temperature DCLL is evaluated for a SiC-FCI with and without a dense SiC protective coating. Considering the design proposed in [10], with a poloidal length for the inboard module (IB,
Fig. 18. Velocity distribution considering a partial infiltration of PbLi in the Hartmann walls (4 T). 10
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Table 10 Pressure drop in the poloidal channels of the IB and OB modules of a hightemperature FCI, as a function of the basic FCI features
No FCI Conducting FCI (100 S/m) Insulating FCI Totally infiltrated FCI FCI with protective Undamaged coating (1 mm) Core partially infiltrated (corners)
IB module (7 m, 10 T)
OB module (10 m, 4 T)
2.5 MPa 0.3 MPa 2.1 kPa 3.3 kPa -
0.6 MPa 0.04 MPa 1.2 kPa 0.5 MPa 1.5 kPa 4.3 kPa
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Ibarra, Design of a permeator against vacuum for tritium extraction from eutectic lithium-lead in a DCLL DEMO, Fusion Eng. Des. 117 (2017) 226–231. [8] I. Palermo, I. Fernández, D. Rapisarda, A. Ibarra, Neutronic analyses of the preliminary design of a DCLL blanket for the EUROfusion DEMO power plant, Fusion Eng. Des. 109–111 (2015) 13–19. [9] I. Fernández-Berceruelo, M. Gonzalez, I. Palermo, F.R. Urgorri, D. Rapisarda, Largescale behavior of sandwich-like FCI components within the EU-DCLL operational conditions, Fusion Eng. Des. (2018) 633–638. [10] S. Smolentsev, et al., MHD thermohydraulics analysis and supporting R&D for DCLL blanket in the FNSF, Fusion Eng. Des. 135 (2018) 314–323. [11] C.E. Kessel, et al., Overview of the fusion nuclear science facility, a credible break-in step on the path to fusion energy, Fusion Eng. Des. (2018) pp. 236-270. [12] Y. Wu, Conceptual design of the China fusion power plant FDS-II, Fusion Eng. Des. 83 (10–12) (2008) 1683–1689. [13] Y. 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10 T) of 7 m and for the outboard module (OB, 4 T) of 10 m, the pressure drop associated to the basic FCI features are summarized in Table 10. In the cases considering a PbLi infiltration, only the values corresponding to the outboard modules are shown. The pressure drop related to a 10 T magnetic field in these cases should be analyzed in future works. 5. Conclusions - With the conditions associated to a high-temperature DCLL, the FCIs provide an adequate mitigation of the MHD effects if their electrical conductivity is kept below ∼1 S/m for both inboard and outboard blankets. With the parameters considered and using an insulating FCI, the pressure drop in the poloidal channels is kept in the order of kPa. - Considerably higher pressure drops are predicted in the inboard blanket modules due to the higher magnetic field. If a properly insulating FCI is not considered, the pressure drop associated to a 10 T magnetic field is one order of magnitude higher than in the 4 T scenario. - A SiC-based sandwich FCI formed by a porous SiC core with an electrical conductivity below 1 S/m and a protective dense SiC coating is able to provide an adequate electrical insulation to the bulk PbLi. The effect of the protective coating on the MHD interactions can be considered as negligible if it is made of dense SiC. However, this is not true if coatings made of materials with higher electrical conductivities are considered; the use of a conducting dense coating may lead to a major disturbance of the flow, even considering an insulating core. - A major PbLi infiltration trough the porous core inhibits the insulating character of the FCI, even if the protective dense coating remains undamaged. - In case of a PbLi infiltration in localized areas of an insulating FCI, it is still effective in terms of the reduction of the pressure drop. The flow distribution will be, however, disturbed. Acknowledgments This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] L.V. Boccaccini, et al., Objectives and status of EUROfusion DEMO blanket studies,
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