MHD thermofluid issues of liquid-metal blankets: Phenomena and advances

Fusion Engineering and Design 85 (2010) 1196–1205

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MHD thermofluid issues of liquid-metal blankets: Phenomena and advances Sergey Smolentsev a,∗ , René Moreau b , Leo Bühler c , Chiara Mistrangelo c a

University of California, Los Angeles, CA, USA Laboratoire SIMAP, Groupe EPM, Grenoble-INP, France c Forschungszentrum Karlsruhe, Germany b

a r t i c l e

i n f o

Article history: Available online 26 March 2010 Keywords: Liquid-metal blanket Magnetohydrodynamic flow Heat transfer

a b s t r a c t The major accomplishments in the MHD thermofluid area over the last few years are reviewed for liquidmetal blankets. After summarizing basic liquid-metal blanket concepts, such as self-cooled blankets and in particular those to be tested in ITER, namely the dual-coolant and the helium-cooled lead–lithium blanket modules, we consider the most important MHD phenomena and discuss their impact on heat and mass transfer during blanket operation with special emphasis placed on underlying flow physics. Among them are: MHD pressure drop, three-dimensional flows, MHD instability and turbulence, buoyancydriven flows, electromagnetic coupling, and interfacial phenomena associated with hydrodynamic slip. Published by Elsevier B.V.

1. Introduction Using pure lithium (Li) or Li-containing liquids (e.g. eutectic alloy lead–lithium, PbLi) in fusion blankets as breeder and/or as coolant is a very attractive option due to potentially higher thermal efficiency compared to solid breeder blankets. Typical examples of liquid-breeder blankets are DCLL (dual-coolant lead–lithium) [1], HCLL (helium-cooled lead–lithium) [2], and selfcooled lithium/vanadium [3] blankets. All liquid-metal blankets have special features associated with the nature of liquid breeders, including their high chemical reactivity, and especially interaction with the plasma-confining magnetic field that results in various magnetohydrodynamic (MHD) phenomena [4], which have to be carefully studied. The MHD effects, being coupled with heat and mass transfer, have a profound impact on the blanket performance, operation and safety, which can be either positive or negative depending on the specific issue. In fact, MHD and heat/mass transfer considerations are primary drivers of any liquid-metal blanket design. A better understanding and prediction of MHD effects during normal blanket operation and off-normal conditions could, therefore, allow significant improvements of fusion blanket systems. For decades, liquid-metal blankets were designed using simplified models based on limited experimental data, starting from a slug-flow approximation, followed by a more advanced “core flow” approach. Presently, sophisticated numerical codes and more complete mathematical models are used but the progress in studying

∗ Corresponding author. Tel.: +1 310 7945366. E-mail address: [email protected] (S. Smolentsev). 0920-3796/$ – see front matter. Published by Elsevier B.V. doi:10.1016/j.fusengdes.2010.02.038

MHD flows under real blanket conditions is still limited due to the complexity of the blanket geometry (i.e., manifolds, bends, contractions, expansions, etc.) and high up to 12 T multi-component magnetic fields. The main goal of this paper (similarly to previous reviews, e.g. [5]) is to overview current trends and advances in studying MHD flows for blanket relevant conditions over the last few years. Focus is placed on generic MHD issues and underlying flow physics as well as specific issues for two particular blanket concepts, which are presently considered for testing in ITER and for further implementation in a DEMO reactor, namely the US DCLL and European HCLL blankets. The paper is organized as follows: Section 2 introduces the three already mentioned basic liquid-metal blanket concepts and describes general MHD problems in these applications. Sections 3–10 address particular MHD issues, including MHD pressure drop, flows in fringing magnetic fields, buoyancy effects, MHD instabilities and turbulence, flows in complex geometries followed by flow balancing, electromagnetic coupling, and interfacial phenomena. Conclusions are formulated in Section 11. This order is based on requirements for engineering issues of liquid-metal blankets. 2. Basic liquid-metal blanket concepts and general definition of MHD problem 2.1. DCLL blanket The DCLL blanket concept evolved from the original ARIES studies [6] is considered in the US for testing in ITER and as a primary candidate for a DEMO reactor [7,8]. In this blanket (Fig. 1), PbLi circulates slowly (∼10 cm/s) through long poloidal channels for

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Fig. 1. Basic sketch of the US DCLL ITER TBM.

power conversion and tritium breeding. Reduced activation ferritic steel is foreseen as structural material and helium is used to cool the first wall and the blanket structure. The overall geometry of the blanket modules in ITER and DEMO is similar but the number of poloidal ducts and cross-sectional dimensions are different. The poloidal length in both cases is about 2 m, while the radial depth is smaller in the ITER test blanket module (TBM). The liquid metal enters the inlet manifold at the back of the module, from where it is distributed into poloidal ducts. At the exit of the module, the liquid is collected and leaves the module through the outlet manifold. The key element of the DCLL concept is the flow channel insert (FCI) made of silicon carbide (SiC), which serves as electrical insulator to reduce the impact from the MHD pressure drop of the circulating liquid metal. The FCIs serve further as thermal insulators to separate the high temperature PbLi from the ferritic structure. Using FCIs allows for high exit temperature (700 ◦ C or even higher) which leads to high blanket efficiency. A desirable blanket configuration requires minimization of heat leakages from the PbLi flows into helium streams as well as minimization of the MHD pressure drop, while keeping the interface temperature between the PbLi and the ferritic structure and the temperature drop across the FCI below the allowable limits. Meeting all these requirements places special limitations on the FCI design and SiC properties, such as electrical and thermal conductivity as discussed in [9]. All MHD related issues of the DCLL blanket concept are to a major degree affected by the presence of the insulating flow insert [10,11]. 2.2. HCLL blanket In Europe, a helium-cooled lead–lithium blanket is considered as a design option for applications in fusion power reactors. This concept relies on available structural materials and fabrication techniques and therefore it is highly attractive and was chosen as the European reference design for a liquid-metal blanket to be tested in ITER [12]. In contrast to other liquid-metal blankets, here, PbLi serves exclusively as a breeder material while the entire thermal power released in the blanket is removed by a helium cooling system. Therefore, from a thermal point of view, there is no liquidmetal flow required for heat transfer. Only a weak purge flow is foreseen for a slow (0.1–1 mm/s) circulation of the breeder towards external ancillary systems for tritium separation and liquid-metal

Fig. 2. View into the European HCLL TBM for ITER designed by CEA.

purification. A view on the designed blanket geometry is shown in Fig. 2. The HCLL blanket module is subdivided by a helium-cooled stiffening grid into an array of rectangular breeder units (BUs). Each of them is supplied with a number of cooling plates for efficient heat removal. Since the liquid-metal velocity in BUs is very small, the interaction of the electrically conducting PbLi with the plasmaconfining magnetic field is weak and MHD pressure drop in BUs is not an issue. However, in a blanket module, as foreseen for ITER and for a DEMO reactor, a number of BUs is combined in columns and fed by a single system of pipes and manifolds. In these components, velocities may reach considerable values, so that MHD effects become important and cannot be ignored any longer. For safe removal of tritium it has to be ensured that MHD effects do not lead to unbalanced mass flux in different BUs or to stagnant regions. Major MHD issues of the HCLL blanket concept are also reviewed and summarized in the earlier work [13]. 2.3. Self-cooled blanket The self-cooled lithium/vanadium blanket was considered in the US in the past as the most promising blanket concept as the same liquid is used as tritium breeder and coolant (see, e.g. [3]). There are, however, severe constraints of using lithium related to the limited lithium–vanadium interface temperature, high reactivity of lithium with air and water, and in particular to high MHD pressure drop. The last issue requires implementation of special approaches to minimize the MHD pressure drop by using either insulating coatings [14] or high aspect ratio (slotted) ducts [15]. In the reference US self-cooled blanket design, which sometimes is referred to as a “toroidal-poloidal” blanket, the liquid metal flows along magnetic field lines through relatively small toroidal channels in the first wall to remove the surface heat flux and a significant part of the volumetric heating. Then it turns to the poloidal manifold where it is heated mainly by neutrons. A large cross-sectional area is maintained for the poloidal manifold to keep the velocity low to reduce the MHD pressure drop. The flows in the manifold are the main contributors to the overall MHD pressure drop, which

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can be as high as 3 MPa for the inboard blanket. In spite of a significant interest to this design in 80s, further efforts in the US were discontinued due to the unresolved issues with insulating coatings. The self-cooled lithium blanket is still considered in Russian Federation as a promising concept for testing in ITER [16] and some R&D for this type of blanket is performed in Japan [17]. The progress towards highly efficient self-cooled blankets in the last decade is however limited since no practical solution for effective electrical insulation has been obtained yet.

2.4. Essence of MHD problems for blanket applications The full set of MHD equations for liquid-metal flows in a fusion reactor blanket consists of Navier–Stokes/Maxwell equations, which are coupled with the equations for heat and mass transport. These equations are often written in the inductionless approximation, i.e. the magnetic field is considered as given, without being affected by the fluid flow (see, e.g. [4] for details). In particular, the momentum equation takes the following form





∂v  + (v · ∇ )v = −∇ p + ∇ 2 v + j × B + f. ∂t

(1)

Here, v, B, j, p, and t are the fluid velocity, applied magnetic field, electric current density, pressure, and time, whereas  denotes the density,  the kinematic viscosity, and  the electrical conductivity of the liquid metal. Frequently, variables in Eq. (1) are expressed in dimensionless form by using characteristic scales, such as U0 for velocity, B0 for magnetic field, and L as a length scale. In such a formulation, the balance of momentum is fully characterized by two dimensionless groups. One is the Hartmann number

 Ha = LB0

 , 

the square of which represents the ratio of electromagnetic to viscous forces. The other is the hydrodynamic Reynolds number Re =

U0 L , 

which measures the ratio of inertial to viscous forces. Their combinations, such as the interaction parameter or Stuart number N = Ha2 /Re and the parameter R = Re/Ha are also used in various studies to characterize inertial effects, including the onset of MHD instabilities, turbulence, and the impact of inertia on MHD pressure drop. The term f on the right-hand side of the momentum equation denotes a volumetric force different from the electromagnetic one, which typically represents the gravitational force. For applications in fusion with variations of the fluid density due to strong temperature gradients, f stands for the buoyant force. The contribution of buoyancy with respect to viscous forces, is described by the Grashof number Gr = gˇTL3 /2 , where ˇ is the volumetric thermal expansion coefficient, g is acceleration of gravity, and T is a characteristic temperature difference in the fluid. For MHD flows in ducts made of electrically conducting materials, electric currents find additional paths for their closure through the conducting walls. In addition to the parameters mentioned above, such flows depend on the relative conductance of the walls in comparison with the conductance of the bulk fluid, characterized by the so-called wall conductance ratio C = w tw /L, where w and tw denote the electrical conductivity and the thickness of the wall. In the simplest case of a 1D fully developed Hartmann flow, the pressure gradient in the core is balanced by the Lorentz force (for

Ha  1):

∇p U0 B02

≈

jcore C + 1/Ha ≈ . U0 B0 C +1

(2)

If C  1, the whole electric current closes through the walls, which behave as being perfectly conducting. The electric current density scales as U0 B0 , and the MHD pressure gradient become proportional to U0 B02 . For ducts with thin walls, where Ha−1 << C << 1, the core current is limited in magnitude by the resistance of the walls and becomes proportional to w U0 B0 tw /L. As a consequence the pressure gradient reduces to values ∼w U0 B02 tw /L, depending preferentially on the conductivity of the walls and their thickness, independent of the conductivity of the fluid. In another particular case, when C  1/Ha, the conductance of the walls becomes so poor that they can be considered as insulating. In this case, the induced current loops close preferentially through the viscous Hartmann layers. For these conditions, the current density is much smaller (by factor 1/Ha compared with the perfectly conducting case), resulting in the MHD pressure gradient proportional to U0 B02 /Ha, i.e. proportional to B0 . The significant difference in the MHD pressure gradient among these cases has stimulated many studies in the past and is still the key reason for development of insulating coatings and insulating flow inserts mentioned above. The real blanket flows are, however, much more complex than the Hartmann flow in a separate channel. Namely, the flow geometry is often 3D; the ducts are electrically coupled; the use of different structural and functional materials results in pronounced changes in the electrical conductance, etc. As a result, scaling laws may vary significantly depending on particular flow conditions. From the physical point of view, these differences indicate the complexity of MHD phenomena, including turbulence, buoyancyinduced flows, and formation of internal shear layers, in addition to Hartmann and side layers. Internal layers provide another path for a current short-circuit and their resistance affects the current magnitude and the pressure drop. For general 3D applications, the pressure drop depends on C and Ha and its inertial contributions may scale with powers of Re, R, or N. More examples of scaling laws for inertial MHD flows are given in subsequent sections. The choice of proper scales and constructing adequate scaling laws for MHD phenomena in blanket flows is one of the most important R&D goals. Generally it is a very difficult task, especially if inertial effects need to be taken into account for more complex 3D blanket elements like manifolds, or regions with global electric coupling through common conducting walls, which give rise to three-dimensional current circuits. Table 1 summarizes typical values of the most important dimensionless parameters for the DCLL, HCLL and self-cooled blankets. In the calculations of these parameters for a generic self-cooled blanket we use B0 = 10 T, U0 = 0.5 m/s and L = 0.05 m, heat loads typical to a DEMO reactor, and physical properties of lithium at 450 ◦ C. The calculations for the DCLL and HCLL blankets are based on the parameters for the ITER test blanket modules. Based on our current understanding of MHD flows, the main issues associated with MHD flows in liquid-breeder blankets and their importance for the three reference liquid-metal blanket concepts are summarized in Table 2. In self-cooled blankets, where velocities are high ∼0.5 m/s, the most critical MHD issue is the MHD pressure drop that requires electrical insulation of the whole blanket, e.g. using thin insulating coatings. In practice, this problem has not been resolved yet. In the DCLL blanket, the velocity is significantly lower (∼0.1 m/s for the outboard and ∼0.01 m/s for the inboard blanket) such that electric insulation can be provided using SiC FCI. The associated heat transfer problem is tightly coupled with the MHD flow requiring detailed analysis of MHD turbulence and buoyancy effects. In the breeder units of HCLL blankets, the veloc-

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Table 1 Typical values of the dimensionless MHD flow parameters for three blanket concepts. Blanket type

Ha

Re

DCLL (ITER TBM [11]) HCLL (ITER TBM [18,19]) Self-cooled blanket (DEMO)

6.5 × 10 1.1 × 104 4.5 × 104

4

ity of the liquid-metal purge flow is very small (less than 1 mm/s), and the corresponding MHD pressure drop is significantly lower compared to other blankets. The liquid is, however, far from being stagnant due to buoyant convection. Table 2 Summary of MHD related issues and their importance for three blanket concepts. MHD related issues

Importance

1. MHD pressure drop (Including 3D MHD pressure drops due to complex geometry, fringing fields, etc., and pressure drops in nearly fully developed flows.)

Self-cooled blanketa

DCLLb HCLLb 2. Electrical insulation (Needed for reduction of MHD pressure drop in the poloidal flows, and to some degree in 3D flows using insulating flow inserts or coatings.)

N

3.0 × 10 670 3.2 × 104

3

Self-cooled blanketa

1.4 × 10 1.8 × 105 6.0 × 104 3

R

Gr

4.6 0.06 0.7

7.0 × 109 1.0 × 109 2.0 × 1012

In addition to purely MHD and closely related heat transfer issues, we have to mention another group of important transport phenomena, namely mass transfer processes (not reviewed here in detail), which are also affected by MHD flows. Corrosion of structural and functional materials is another blanket feasibility issue, which includes complex physical–chemical interactions at the liquid/solid interface, including electromigration, as well as the bulk transport of corrosion products in the moving fluid. A corrosion experiment on washing EUROFER steel samples by hot 550 ◦ C PbLi [20] shows that the corrosion rate in the presence of a magnetic field is significantly higher than that without a magnetic field. A noticeable feature is that the corroded samples exhibit periodic grooves on the surface, which seem to be a footprint of vortical structures that appear in the Hartmann layer. 3. MHD pressure drop

b

DCLL HCLLc 3. Flow in a fringing magnetic field (Flows in a fringing magnetic field cause 3D MHD pressure drop.)

Self-cooled blanketa

DCLLa HCLLb 4. Buoyant flows (Buoyancy-induced flows compete with the forced flows and thus are more important in those blankets where the breeder/coolant forced flow is lower.)

Self-cooled blanketb

DCLLa HCLLa 5. MHD instabilities and turbulence (May change significantly transport properties of the flow with a significant effect on heat and mass transfer.)

Self-cooled blanketa

DCLLa HCLLc 6. Complex geometry flow and flow balancing (Flow imbalance can be associated with the design complexity and/or magnetic field asymmetry, cracked insulation, etc.)

Self-cooled blanketa

DCLLa HCLLa 7. Electromagnetic coupling (If ducts are not insulated, flows are coupled as electric currents can flow from one to another duct. This causes changes in the flow partitioning and pressure drop.)

Self-cooled blanketa

DCLLb HCLLa 8. Thermal insulation (For DCLL blanket to reduce heat losses from PbLi into cooling helium streams.)

Self-cooled blanketc

DCLLa HCLLc 9. Interfacial phenomena (Interfacial slip, electrical and thermal contact resistance may change the flow and through these changes there will be an effect on heat and mass transfer.)

Self-cooled blanketa

DCLLa HCLLc a b c

Very important. Important. Not applicable or low importance.

3.1. MHD pressure drop in the DCLL blanket Two major sources of the MHD pressure drop in the DCLL blanket are those due to the cross-sectional currents in the near fully developed poloidal flows and those associated with the 3D currents in complex geometry flows or flows in a fringing magnetic field. The MHD pressure drop associated with the cross-sectional currents can be reduced by orders of magnitude through a proper choice of SiC by lowering its electrical conductivity or by making the FCI thicker. As shown in [10] for a DEMO outboard blanket, near-ideal electrical insulation can be achieved with a 5 mm FCI if  SiC < 1 S/m. For the inboard DEMO blanket, a similar analysis suggests that ideal insulation requires  SiC < 0.1 S/m [21]. In practice, such low values of  SiC are not necessary since reasonable reduction of the MHD pressure drop in poloidal flows can be achieved at significantly higher values of  SiC ∼ 10 S/m for the inboard blanket [10] and ∼100 S/m for the outboard blanket [21]. Recent experiments show that the through-thickness conductivity can be maintained at ∼10 S/m for 2D composites, unirradiated or irradiated, up to 800 ◦ C [22]. Lower values ∼1 S/m seem to be achievable, if necessary, using SiC foams as suggested in [23]. In the inlet or outlet manifold or access pipes in the fringing magnetic field region, the flow is essentially three-dimensional. Providing the poloidal channels are properly insulated, most of the MHD pressure drop in the DCLL module arises due to threedimensional flows. In these flows, the 3D axial currents close their circuit mostly in the flow domain. Thus, in those blanket elements where the flow is essentially three-dimensional, the MHD drag can hardly be reduced by using insulating flow inserts or other insulating techniques. The FCI then serves mainly as thermal insulator decoupling hot PbLi from the ferritic structure. The estimates of the total MHD pressure drop in the DCLL blanket have been performed for outboard [10] and inboard [21] blankets. Flows in the long poloidal channels, including those in the module itself and in the access pipes were analyzed using a finitedifference numerical code based on a fully developed flow model [24]. The 3D MHD pressure drop was estimated using an empirical correlation, P3D = (1/2)U02 , where  is the local pressure drop coefficient. Experimental data suggest  = kN, where k is an empirical coefficient that depends strongly on the flow geometry. Typically, 0.25 < k < 2 [25–28]. In the calculations, higher k values

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Fig. 4. Mock-up of the HCLL blanket in front of the magnet, covered with insulating plates that carry sensors for measuring electric potential.

Fig. 3. View into the scaled mock-up of the HCLL blanket formed by four breeder units. Each unit is divided by cooling plates into a number of sub-channels.

are used for the flows in the inlet/outlet manifolds due to their complexity. The overall MHD pressure drop for the outboard blanket is about 0.4 MPa, while it is about 1.4 MPa for the inboard position, i.e. both values are below 2 MPa, usually considered as the maximum allowable MHD pressure drop. 3.2. MHD pressure drop in HCLL blanket In the past theoretical analyses for single geometric elements of HCLL blankets have been performed and the results have been combined for a first estimation of the overall performance [29]. The real situation, however, is far more complex because electric currents are not confined to these separated elements. Since all walls are electrically conducting currents may circulate along large-scale paths involving many neighboring fluid domains thus coupling them electrically in a strong way. A complete theoretical analysis therefore has to consider electrically coupled fluid domains, to resolve all viscous boundary layers along walls and to model the conducting walls simultaneously during numerical simulation of MHD flows. Using assumptions of fully established flow in a symmetry plane of the module such calculations are possible with available numerical tools even for quite general orientations of the magnetic field [30]. The electrically coupled 3D regions in which the major MHD effects are present, i.e. connections between pipes, manifolds, contractions, expansions and bends are still far from being treatable by numerical methods. Therefore, in order to get a better idea about the performance of 3D fully electrically coupled MHD flows in a blanket module, and in particular to predict the MHD pressure drop, experiments are required. For this purpose a scaled mock-up of the HCLL TBM has been fabricated and inserted into the liquid-metal loop of the MEKKA laboratory at the Forschungszentrum Karlsruhe, where NaK is used as a model fluid. The mock-up shown in detail in Fig. 3 consists of 4 BUs with internal walls simulating the cooling plates. They are connected by a system of manifolds for feeding and draining the liquid metal. The test section is instrumented with 600 sensors for recording the distribution of electric potential on its surface and with a system for measuring pressure differences among 30 pressure taps (see Fig. 4). First experiments in a strong transverse magnetic field showed that the major part of the pressure drop occurs in feeding and

draining pipes, in manifolds and in gaps that distribute the fluid to the breeder units [31,32]. As expected, the pressure losses inside the BUs themselves remain quite small and negligible in comparison with the before mentioned contributions. As an important result of these first measurements, scaling laws for pressure drop of the MHD flow in the entire electrically coupled system have been derived. It has been found that the inertial part of the total pressure drop scales inversely proportional to the interaction parameter N. This result shows a different dependence on N compared with MHD flows in other more simple 3D geometries investigated in the past [33,34]. 4. Flows in a fringing magnetic field This 3D problem has been studied intensively for the last two decades both from the academic point of view (see, e.g. [35] for references), and as an important blanket problem using the straight magnetic field assumption and inertialess approximation. In particular, numerical results based on the inertialess flow model [36] have demonstrated a fair agreement with the ALEX experimental data for both pipe and rectangular duct flows in a strong magnetic field. However, other experiments for flows in a slotted duct at high Re ∼ 105 and moderate Ha ∼ 102 demonstrate strong inertial effects [37], which cannot be explained using inertialess models. The effect of inertia in this type of flows was analyzed recently [38] under conditions similar to those in [37] (i.e., small aspect ratio ε = L/a  1 insulated rectangular ducts, where L is the “shorter” duct dimension in the magnetic field direction and a is the “longer” one). The suggested model includes inertial terms and is based on a realistic div- and curl-free applied magnetic field. As shown, the role of inertia is characterized by the parameter ε2 R. In the regime with weak inertia (ε2 R  1), the disturbance caused by the magnetic field gradient diffuses upstream over a length of the order of a few duct widths a, while the downstream variations towards the fully developed flow occur within a thin transverse layer whose thickness scales as L; both lengths are almost Ha-independent. Similar to previous studies, two high velocity jets are observed on both sides of the almost motionless core. In the inertial regime (ε2 R  1), on the contrary, the upstream length becomes quite small, whereas the downstream evolution of the velocity profile occurs over a long distance of the order of ε2 Re/Ha (Fig. 5). The current exchange between the axial loop and the Hartmann layers is found to be important in the inertialess regime, but almost negligible in the inertial one. The pressure gradient scales as ∂p/∂x ≈ B02 U0 N −1 ≈ U02 /L, demonstrating purely hydrodynamic behavior independent of the magnetic field, a tendency similar to the recent measurements of the MHD pressure drop in the manifold of the mock-up of the HCLL TBM (see Section 3.2).

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Fig. 5. Axial velocity in the flow in a fringing magnetic field. (a) Inertialess regime: Ha = 2000, Re = 500 and ε = 0.2. (b) Inertial regime: Ha = 200, Re = 100,000 and ε = 0.2.

5. Buoyancy effects Another important aspect of MHD flows under blanket conditions is related to non-uniform volumetric heating by fusion neutrons causing buoyant flows, which may influence or even dominate the performance of HCLL and DCLL blankets. In both blanket concepts, the buoyancy forces affect the velocity profiles significantly and create recirculating flows, whose magnitude of velocity can even overcome that of the forced flow. The effect of buoyancy forces on the blanket operation should be addressed separately for both types of blankets since their geometries and operation parameters are very different. In DCLL blankets buoyant flows establish in very long poloidal channels as studied, e.g., in [39,40]. In the poloidal ducts, the buoyant flow superimposes on the average forced flow resulting in mixed convection (Fig. 6). Under some conditions such flows demonstrate inflectional instability and eventually become turbulent (Fig. 7). A concern associated with the buoyancy effects in the DCLL blanket is the risk of locally reversed flows and associated “hot

Fig. 6. Typical basic velocity profiles in the upward (left) and downward (right) flows associated with mixed convection in poloidal ducts of DCLL blanket.

spots” at the solid wall, which may occur in those ducts where the forced and buoyant flows are opposite as shown in [11]. Tritium accumulation in the near-wall regions where the liquid is about stagnant is another concern. In the HCLL blanket, buoyancy-driven flows occur in thin liquidmetal layers between cooling plates. Since the pressure-driven purge flow is so weak, buoyant MHD flows could become significant for mass transfer problems of dissolved species like tritium or corrosion products. In the ITER test blanket module the liquid gaps in breeder units are essentially horizontal, a fact that reduces but not excludes buoyant convection in comparison with other orientations. A stronger influence is expected for DEMO applications where even vertical gaps are foreseen in upper poloidal positions [12,41].

Fig. 7. Q2D MHD turbulence (vorticity field is shown) in upward mixed convection flow caused by volumetric heating: Ha = 100, Re = 104 , Gr = 4 × 108 .

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Fig. 8. Map of flow regimes. Different regions are separated by Rec1 and Rec2 depending on Ha.

Fig. 9. Mixed convection. Neutral stability curves for different Gr at Re = 10,000 for the upward flows. Here, ˛ is the wave number.

7. MHD turbulence 6. MHD instabilities Instabilities of pressure-driven MHD channel flows as they may occur in conducting rectangular ducts of fusion blankets have been investigated several years ago for a square and for a small aspect ratio duct [42,43]. It has been found that for sufficiently high Reynolds numbers the laminar high-speed jets along the side walls aligned with the magnetic field become unstable. In those references the onset of instabilities in terms of a critical Reynolds number was only weakly dependent on Ha and at least one order of magnitude higher than theoretically predicted [44]. In a more recent experiment, the stability problem was revisited for flows in a high aspect ratio duct [45]. For this case velocity data were obtained from signals of a traversable potential probe. As in previous experiments the first onset of instability was observed at a critical Reynolds number Rec1 practically independent of Ha. The measured small fluctuations remain confined to narrow regions close to the side walls, leaving the major part of the core unaffected and laminar. By increasing further the flow rate this behavior persists until a second critical Reynolds number Rec2 is reached, above which perturbations amplify quickly by one or more orders of magnitude. Under these conditions strong intermittent fluctuations are observable even at larger distance from the side walls. As a result the mean flow exhibits thicker side layers with smaller jet velocities. In contrast to Rec1 that is more or less independent of the strength of the magnetic field, it is found that Rec2 depends strongly on Ha as can be seen from the map of flow regimes shown in Fig. 8. Instabilities have been also investigated for mixed convection flows under DCLL blanket conditions. A description of this problem can be found in [11]. The Orr–Sommerfeld theory is applied to upward (buoyancy-assisted) poloidal blanket-type flows assuming ideal electrical and thermal insulation [46]. Depending on the flow parameters Re, Ha and Gr, different instability regimes have been identified, associated with either Shercliff layers at the duct wall parallel to the magnetic field or with inflectional instability. This analysis also suggests that in the range of Re and Gr relevant to the DCLL blanket, the buoyant flows become stable if Ha > Hacr ∼ 200 (Fig. 9). The ongoing studies of downward (buoyancy-opposed) flows show that these flows in the blanket conditions are much more unstable as the corresponding critical Hartmann numbers are significantly higher. It should be noted that results based on linear stability analysis usually over-predict the critical parameters. In practice, one can expect that the flow remain unstable at much higher Ha compared to the linear theory predictions due to development of finite-amplitude perturbations.

Two types of turbulence can be observed in electrically conducting fluids in the presence of a magnetic field as illustrated in the Ha–Re diagram (Fig. 10). In this diagram plotted for fully developed MHD flows in a non-conducting rectangular duct, the straight line R = Const ≈ 200 [47] separates two characteristic turbulence regions. In this context, the parameter R can be interpreted as the Reynolds number based on the thickness of the laminar Hartmann layer and the straight line shown in the diagram represents the onset of instability of the Hartmann layer. All liquid-metal blankets (under simplifying conditions of insulated ducts with no electromagnetic coupling) fall on the sub-region below the separation line, where MHD turbulence exists in a very specific quasi-two-dimensional (Q2D) form [48]. The Q2D turbulent structures appear as large columnar-like vortices aligned with the field direction and are subject to the inverse energy cascade. Their intensity is a result of the balance between the Joule and viscous dissipation in the Hartmann layers, on the one hand, and the feeding mechanism associated with the instability of parallel internal shear layers or buoyancy effects, on the other hand, as described in Section 6. Such Q2D eddies can be highly energetic, occupy the whole cross-section of the duct and persist over many eddy turnovers. This Q2D MHD turbulence (see Fig. 7) is mostly foreseen in long poloidal ducts resulting in a strong increase of

Fig. 10. Ha–Re diagram showing two distinctive turbulence regions in blanket flows. IB and OB denote inboard and outboard blankets.

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Fig. 11. Experimental study of flow distribution in three parallel channels of the inlet manifold.

heat and mass transfer. To our knowledge, until now a very limited number of attempts have been made to develop a turbulence model relevant to this range of flow parameters [49,50]. Most of the available models are in fact limited to molten salt (MS) blankets, where the energy containing eddies remain 3D, inducing a significant current and are therefore subject to significant Joule damping even in the core flow (see, e.g. [50] for references). Recent experiments [51] also show that turbulence properties of MHD flows in ducts can be strongly affected by the magnetic field gradients. Namely, the turbulent flow seems to be efficiently laminarized when turbulent eddies coming from upstream enter the magnetic field space. A theoretical explanation based on high dissipation losses when turbulent eddies cross the so-called “characteristic” surfaces [52] is given in [53]. As applied to blanket flows, this mechanism suggests that all turbulent pulsations in access pipes are damped when the liquid crosses the field gradient region at the entry and exit of the blanket, so that all turbulence is generated in the blanket itself. 8. Complex geometry flows and flow distribution Uniform coolant/breeder flow distribution is one of the ultimate goals of any blanket design to provide stable blanket characteristics and to eliminate a risk of locally high MHD pressure drops and “hot spots” at the liquid–solid interface. This problem is, for example, one of the important issues in the design of the inlet manifold of the DCLL blanket, where the liquid metal from the radial inlet access pipe is distributed into three poloidal ducts. On the other hand, a manifold is a typical example of complex geometry where flows are essentially three-dimensional. A series of experiments [54] was carried out recently to understand the mechanisms that determine flow distribution in such a complex geometry. For values of the interaction parameter N > 90, the flow was found to be uniformly distributed (Fig. 11) (the maximum imbalance among three parallel ducts is only 5%). The experimental results on the flow distribution are in qualitative agreement with numerical computations [55]. Almost uniform flow distribution seems to be related to the well-known tendency of MHD flows to become Q2D once a strong enough magnetic field is applied. The observed tendency mitigates significantly the manifold design as no any special flow routers are required. Flows in complex elements of HCLL blankets like entrance and exit manifolds, their connections with the breeder units and feed-

ing and draining pipes are responsible for the major part of total pressure drop [31]. The “symmetric” design of these manifolds as shown in Fig. 3 ensures a uniform flow distribution in breeder units. Moreover, the strong electromagnetic coupling of fluid layers within individual BUs favors in addition uniform distributions inside the units [30] as discussed in more detail in Section 9. Other complex geometric elements form the recently redesigned connections of couples of BUs near the first wall, where several but very narrow penetrations are foreseen, that exclude any Q2D flows. As a result one should expect an increase in pressure drop near the first wall in comparison with the previous design. For that reason these elements require further investigation in future. 9. Electromagnetic coupling Electromagnetic coupling of flow in neighboring fluid domains occurs if the blanket ducts are not ideally electrically insulated. It results from an exchange of electric currents through common walls that can lead to modifications of flow distribution and pressure drop compared to that in separated channels. The increase in MHD pressure drop in parallel ducts due to the multi-channel effect (Madarame effect) has been known starting from the pioneering study [56]. In the past, fully developed MHD flow has been investigated in assemblies formed by three electrically conducting channels coupled at Hartmann walls [57] and in ducts connected at walls parallel to the magnetic field [58]. The relevance of these effects to blanket flows is clearly more important for those concepts where electrical insulation is not foreseen like in the case of an HCLL blanket. Recently numerical studies have been performed to investigate MHD flows in a middle crosssection of a HCLL blanket module by assuming fully developed flow conditions [30]. Mock-up experiments [59] confirmed the validity of this assumption for intense magnetic fields. In the case of a pure toroidal applied magnetic field, currents induced in the cores of the slender sub-channels that form one BU cross the cooling plates (side walls in MHD terminology) and couple strongly the flow in adjacent ducts. As a result, in these channels the observed velocity profiles resemble the one in a duct with perfectly conducting side walls. Therefore this strong electric coupling ensures a quite uniform flow distribution in sub-channels of BUs. Instead, in the grid plates separating the breeding boxes, currents flow preferentially in tangential direction resulting in a parabola-like potential distribution along these walls. This leads to

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an increased velocity in the parallel layers at the grid plates compared to that at the internal side walls. The presence of these jets could help reducing tritium permeation towards helium cooling channels in these walls. The electric coupling between neighboring BUs is weak as shown by the fact that no current is exchanged between adjacent boxes across the common dividing grid plates. This situation is related to concomitant conditions, i.e. the imposed magnetic field is purely toroidal, the BUs are connected at side walls with counter-current flows on different sides of grid plates. When an additional poloidal field component is applied, solutions for velocity and electric potential become oriented along the magnetic field lines due to the formation of internal layers aligned with magnetic field direction. This yields a stronger electric coupling between the breeder units. In addition, locally reversed flow regions are present in the corners next to the grid plates suggesting the possibility of closed flow recirculation. The latter ones could be an issue in terms of tritium accumulation and local hot spots. The combination of experimental and numerical outcomes shows that electric flow coupling in the HCLL blanket can be regarded as a positive feature to be exploited for supporting homogeneous flow partitioning in the BUs and in columns of a blanket module. 10. Slip effect In most of the cooling applications where a viscous fluid flows in contact with a solid wall, for example in heat exchangers, a common assumption is a good wettability at the liquid–solid interface. When such is the case, the so-called hydrodynamic “no-slip” boundary condition is usually applied. In contrast, in some special applications, e.g., in microfluidic and nanofluidic devices, where the surface-to-volume ratio is large, the slip behavior is more typical, and the mixed “slip” hydrodynamic boundary condition is usually used. Recent experimental studies for PbLi flows in the presence of SiC [60–62] demonstrate that poor wetting will most likely occur in the DCLL blanket conditions, which is a direct indication of interfacial slip. The effect of interfacial slip has recently been addressed for three classic MHD problems: (i) Hartmann flow; (ii) fully developed flow in a rectangular duct; and (iii) Q2D turbulent flow [63]. The first two problems have been solved analytically. Additionally to the Hartmann number, a new dimensionless parameter S, the ratio of the slip length to the thickness of the Hartmann layer, has been identified. One of the most important conclusions is that duct flows with slip still exhibit Hartmann layers, whose thickness scales as 1/Ha, while the thickness of the side layers is a function of both Ha and S. In the case of Q2D flows, a new expression for the Hartmann braking time has been derived showing its increase at Ha  1 by factor (1 + S). Numerical simulations performed for a flow with the “M-shaped” velocity profile show that in the presence of the slip, a Q2D flow becomes more irregular as vortical structures experience less Joule and viscous dissipation in the Hartmann layers. A direct implication of the slip phenomena for blanket flows is a further reduction of the MHD pressure drop in ducts with insulation and a strong effect on heat and mass transfer via changes in the velocity field. 11. Concluding remarks Concluding this paper, we would like to emphasize that the MHD thermofluid phenomena under various blanket conditions are very rich in their physical nature and differ significantly among various blanket concepts and designs. It is very unlikely that universal scaling laws can ever be developed covering the variety of all phenomena that may occur in liquid-metal MHD flows under blanket conditions, ranging from the low-velocity HCLL blanket to

high-velocity self-cooled blankets. Among other concerns related to liquid-metal blankets, reduction of MHD pressure drop still remains one of the most important issues, stimulating new ideas and efforts on decoupling the electrically conducting wall from the fluid. Current studies are, however, more focusing on the detailed structure of MHD flows in the blanket, including various 3D and unsteady effects associated with the flow instability, MHD turbulence and buoyancy-driven convection. These flow phenomena can affect the transport properties in a drastic way and, therefore, have a profound impact on blanket operation and performance. In spite of significant success in advancing our knowledge of blanket flows within last decades, the relevant phenomena are not fully understood yet. For example, the mass transport in the blanket (e.g., tritium permeation and corrosion/deposition processes) is closely coupled with MHD flows and heat transfer, requiring much better knowledge of MHD thermofluid phenomena compared to relatively simple pressure drop predictions. Therefore, the key to the development of advanced liquid-metal blankets for future power plants lies in a better understanding of complex MHD flows, both laminar and turbulent, via developing validated numerical tools and physical experiments. Compared to the recent past, current advances in MHD thermofluid area are to a large degree related to a more intensive use of complete physical models and of more sophisticated predictive capability tools, including full 3D numerical codes and prototypic experiments. These tendencies are really important and need to be enhanced in the future. References [1] S. Malang, E. Bojarsky, L. Bühler, H. Deckers, U. Fischer, P. Norajitra, et al., Dual coolant liquid metal breeder blanket, in: Proceedings of the 17th Symposium on Fusion Technology, Rome, Italy, September 14–18, 1992, pp. 1424–1428. [2] G. Rampal, A. Li Puma, Y. Poitevin, E. Rigal, J. Szczepanski, C. Boudot, HCLL TBM for ITER-design studies, Fusion Eng. Des. 75–79 (2005) 917–922. [3] D.L. Smith, C.C. Baker, D.K. Sze, G.D. Morgan, M.A. Abdou, S.J. Piet, et al., Overview of the blanket comparison and selection study, Fusion Technol. 8 (1985) 10–113. [4] R. Moreau, Magnetohydrodynamics, Kluwer, 1990. [5] N. Morley, S. Malang, I. Kirillov, Thermofluid magnetohydrodynamic issues for liquid breeders, Fusion Sci. Technol. 47 (2005) 488–501. [6] D.K. Sze, M. Tillack, L. El-Guebaly, Blanket system selection for the ARIES-ST, Fusion Eng. Des. 48 (2000) 371–378. [7] C.P.C. Wong, S. Malang, M. Sawan, M. Dagher, S. Smolentsev, B. Merrill, et al., An overview of dual coolant Pb-17Li breeder first wall and blanket concept development for the US ITER-TBM design, Fusion Eng. Des. 81 (2006) 461–467. [8] C.P.C. Wong, S. Malang, M. Sawan, S. Smolentsev, S. Majumdar, B. Merrill, et al., Assessment of first wall and blanket options with the use of liquid breeder, Fusion Sci. Technol. 47 (2005) 502–509. [9] S. Smolentsev, N.B. Morley, C. Wong, M. Abdou, MHD and heat transfer considerations for the US DCLL blanket for DEMO and ITER TBM, Fusion Eng. Des. 83 (2008) 1788–1791. [10] 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. [11] 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. [12] J.-F. Salavy, G. Aiello, O. David, F. Gabriel, L. Giancarli, C. Girard, et al., The HCLL test blanket module system: present reference design, system integration in ITER and R&D needs, Fusion Eng. Des. 83 (2008) 1162–1167. [13] J. Reimann, L. Bühler, C. Mistrangelo, S. Molokov, Magneto-hydrodynamic issues of the HCLL blanket, Fusion Eng. Des. 81 (2006) 625–629. [14] I.R. Kirillov, RF DEMO team, Lithium cooled blanket of RF DEMO reactor, Fusion Eng. Des. 49–50 (2000) 457–465. [15] I.V. Lavrent’ev, MHD-flow at high Rm, N and Ha, in: J. Lielpetris, R. Moreau (Eds.), Liquid Metal Magnetohydrodynamics, Kluwer, 1989, pp. 21–43. [16] I.R. Kirillov, G.E. Shatalov, Yu.S. Strebkov, The RF TBM Team, RF TBMs for ITER tests, Fusion Eng. Des. 81 (2006) 425–432. [17] K. Abe, A. Kohyama, S. Tanaka, C. Namba, T. Terai, T. Kunugi, et al., Development of advanced blanket performance under irradiation and system integration through JUPITER-II project, Fusion Eng. Des. 83 (2008) 842–849. [18] L. Bühler, H.-J. Brinkmann, S. Horanyi, K. Starke, Magnetohydrodynamic flow in a mock-up of a HCLL Blanket. Part II Experiments, Technical Report FZKA 7424, Forschungszentrum Karlsruhe, 2008. [19] S. Molokov, L. Bühler, Three-dimensional buoyant convection in a rectangular box with thin conducting walls in a strong horizontal magnetic field, Technical Report FZKA 6817, Forschungszentrum Karlsruhe, 2003.

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