Magnetohydrodynamic investigations of a self-cooled Pb-17Li blanket with poloidal-radial-toroidal ducts

ELSEVIER

Fusion Engineering and Design 27 (1995) 593-606

Fusion Engineering and Design

Magnetohydrodynamic investigations of a self-cooled Pb-17Li blanket with poloidal-radial-toroidal ducts J. Reimann ", L. Barleon a, I. Bucenieks b, L. Biihler a, L. Lenhart a, S. Malang a, S. M o l o k o v a, I. Platnieks b, R. Stieglitz " a Association K f K - E U R A T O M , Kernforschungszentrum Karlsruhe, IATF, Postfach 3640, D-76021 Karlsruhe, Germany b Latvian Academy of Sciences, IP: Salaspils 1, 229021 Riga, Latvia

Abstract

For self-cooled liquid metal blankets, the magnetohydrodynamic (MHD) pressure drop and velocity distributions are considered as critical issues. This paper summarizes M H D work performed for a DEMO-related P b - 1 7 L i blanket, where the coolant flows downwards in rear poloidal ducts; turns around by 180 ° at the blanket bottom; is diverted from poloidal ducts into short radial channels which feed to toroidal First wall coolant ducts; flows through the subsequent radial channels; is collected again in poloidal channels and leaves the blanket segment at the blanket top. To reduce the pressure drop and to decouple electrically parallel channels, flow channel inserts are used for all the ducts except the first wall ducts. A previous pressure drop assessment resulted in significant values for duct geometries with flow distribution or collection, and multichannel effects for the system of U-bends. As a result of the uncertainty of these assessments, corresponding investigations were carried out recently. Characteristic results are presented in this paper. It is shown that, for both geometries, the pressure drops are considerably lower than those previously assessed. First results from experiments on the velocity distribution in a r a d i a l - t o r o i d a l - r a d i a l U-bend are also presented. Here, it is shown that, with an increasing interaction parameter, the liquid preferentially flows close to the First wall. Additionally, a pair of strong vortices was observed in a toroidal duct. Both effects are supposed very favourable for heat transfer.

1. Introduction

It has to be shown for self-cooled liquid metal blankets that magnetohydrodynamic (MHD) pressure drops do not result in unacceptable mechanical stresses, and that M H D velocity distributions ensure the heat transfer from the first wall without exceeding maximum allowable temperatures. This paper summarizes the M H D work performed for the development of a P b -

17Li blanket for the European fusion DEMO reactor [1-3] shown in Fig. 1. There are 48 outboard blanket segments, where the liquid metal enters at the top end, flows down in poloidal ducts at the rear side, turns around by 180 ° at the bottom, and flows up in the poloidal direction at the front side. The liquid metal is diverted into radial ducts and then into toroidal ducts, where the heat is transferred from the first wall. After flowing through

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J. Reimann et al. / Fusion Engineering and Design 27 (1995) 593-606

594

meander-type ducts, the flow is again combined in a poloidal channel. The characteristic feature of the p o l o i d a l - r a d i a l toroidal flow concept, first proposed in another study [4], is that, in the F W toroidal ducts, being parallel to the main component of the magnetic field B, high velocities can be achieved with moderate pressure drops. In contrast, in ducts with electrical-conducting walls perpendicular to B, the velocity must be small. The pressure drop Ap in these ducts can be approximated by A p = LB2vcrw(tw/a) = L B 2 v c r C

with the wall conductance ratio C given by C - twOw

(1)

Here, L is the duct length, o w and a are the electric conductivities of the walls and liquid metal, tw is the wall thickness, v is the liquid metal velocity, a is the half-width of the duet in the field direction, and b is the half-width perpendicular to B. Eq. (1) shows that the pressure drop is proportional to tw. It can be easily shown that the blanket is not feasible without any electrical decoupling of the loadcarrying walls from the liquid metal. One method to achieve this is the use of 'flow channel inserts' (FCI), which consist of a thin ceramic layer between steel sheets that are welded at all edges to avoid any contact between the insulator material and the liquid metal [2]. They are fitted loosely into the ducts and allow for pressure equalization between the flow region and the duct wall.

aft

Upper Inboard Blanket Upper Divertor

\ /

Outboard Blanket Segment

Breedin PbLi B Shieldir Structu

Lower Divertol Lower Inboard Blanket

Fig. l(a)

7---

Breeding PbLi Blanket

595

J. Reimann et al. / Fusion Engineering and Design 27 (1995) 593-606

Pb-17Li Outlet Inlet

Poloidal Duct

Jct

(b) Fig. 1. MHD issues of self-cooled Pb-17Li blanket considered.

The other method to achieve this insulation is the use of insulating layers on all duct surfaces in contact with the liquid metal. This method is believed to be a more aggressive engineering approach, in the present design, it is assumed that all the ducts in the blanket (except the first-wall ducts) are equipped with FCIs with a steel liner thickness of tw = 0.5 mm. Another important effect of FCIs (or direct insulation) is that interactions between parallel channels (multichannel effects; MCEs) are minimized (see Section 3.2).

2. M I l D issues of the P b - 1 7 L i blanket and pressure drop assessments Table 1 summarizes the blanket related M H D issues, contains results of a previously performed pressure drop assessment [1,2] (when specific investigations for several issues did not exist) and gives references of

related work. For the issues (a) and (b) numerous publications exist, though only a few characteristic examples are cited. The work by Btihler [5] was selected because this calculation method can be easily applied for all subitems of issue (a). Issues ( a ) - ( d ) are mainly of interest with respect to the pressure drop, while issue (e) refers to heat transfer from first wall. The total pressure drop of the outboard blanket was 3.4MPa (inboard blanket 3.1 MPa). The maximum liquid metal pressure at the torus mid-plane was about 2.5 MPa (consisting of 1 MPa of static pressure and less than 1.5 MPa between the torus mid-plane and coolant outlet). For a maximum allowable pressure of 6.5 MPa, the safety margin was then about 4 MPa which is a high value for absorbing additional loads, such as those caused by plasma disruptions. The pressure drops in single-duct flows contributed by more than 50% to the total pressure drop. The accuracy of the prediction methods for these flow geometries was estimated to be fairly high. Larger uncertainties existed for issues (c) and (d). For the inlet and

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J. Reimann et al. / Fusion Engineering and Design 27 (1995) 593-606

Table 1 MHD issues of the Pb 17Li blanket MHD issues (a) Liquid metal flow in single ducts perpendicular to the magnetic fields (al) with varying field strength in flow direction (inlet and outlet pipes) (a2) with varying duct cross-section (transition from inlet or outlet pipes to poloidal ducts) (a3) with constant thin conducting walls (poloidal, radial ducts) (a4) with varying wall conductance (region of overlapping FCIs) (a5) with changing flow direction (bends of inlet or outlet pipes, U-bend of poloidal pipes)

Ap (MPa) a

Related work

[5] 0.05

[6,7]

0.05

[8,91

1.61

[8,10-12]

0.23 b

[131

0.036

[2,14]

0.06 0.22

[15-18] [21

(e) Liquid metal flow in manifolds: (cl) inlet or outlet manifolds (e2) poloidal-radial distributor and radial-poloidal collector

0.06 0.64; 0.1 °

[191 [201

(d) Liquid metal flow interaction in multichannel ducts: multichannel U-bend system (radial- toroidal- radial ducts)

0.78; ~0 c

[12, 21-25]

(b) Liquid metal flow in single ducts with changing direction to the magnetic field: (bl) radial-toroidal-radial U-bend (b2) U-bend in meander-type channels

(e) Velocity distribution in the toroidal duct

[17,26,27]

a values for the outboard blanket assessment performed in 1991. b value not included in previous assessment.

outlet manifolds (four poloidal tubes arranged in B direction, connected to the flow expansion of the inlet or outlet tube), a very low pressure drop was assessed. This value agrees qualitatively with the statement of a recent theoretical investigation [9] that " M H D effects related to manifolds of this type can be neglected during the blanket conceptual design phase". An issue which was not considered previously is that of the pressure drop resulting from overlapping FCIs [13]. For FCI pieces about 1 m long with an overlapping length of about 6 cm, an additional pressure drop of 0.22 MPa is calculated for the poloidal channels. For the multichannel U-bend (issue (d)) quite a high pressure drop was assessed, assuming that the FCIs ended at the entrance into the toroidal channels. This pressure drop should be much smaller if the FCIs extend up to the first wall, which should not complicate manufacturing. The experiments described in Section

3.2 refer to this modification. A considerable pressure drop was also assessed for the poloidal-radial manifolds (issue (c2)). As a result of these high values and the uncertainty of the predictions, corresponding investigations [20-25] have been performed; characteristic results are presented below. For issue (e), there was the concern [26] that the liquid in the toroidal channel is preferentially transported close to the second wall, which would result in hot spots at the first wall. Again, first results from recent investigations [17,27]. 3. Results from recent investigations 3.1. Pressure drop in the poloidal-radial manifolds [20] Radial ducts with small cross-sections are connected to a much larger poloidal duct, (see Fig. 1). The duct

J. Reimann et al. / Fusion Engineering and Design 27 (1995) 593-606 dimensions in the direction of the magnetic field (at, ap) differ significantly, which gives rise to three-dimensional electrical currents and, hence, a three-dimensional pressure drop. (In "ideal" M H D flow almost no additional pressure drop occurs for ar = ap.) The pressure drop is affected by the wall conductance ratio C, the Hartmann number M, and the interaction parameter N, defined by

Table 2 Characteristic values for the manifolds

Blanket a (mm) M N C k

M = a B ( ~r ~ °s \pv / N=

a~rB2 pv

Experiments a (mm) Mmax

where p and v are the liquid metal density and kinematic viscosity respectively. Table 2 shows that M, N and the number of radial ducts (k) differ significantly between blanket conditions and experiments. Therefore, an important feature is the extrapolation of the experimental results. Screening tests were performed with Hg as liquid metal in the Institute of Physics of the Latvian Academy of Sciences (LAS). Fig. 2 shows schematically the investigated flow duct geometries. The test section consisted of a poloidal duct with a cross-section of 125 mm × 125 mm, and five perpendicular radial ducts each with dimensions 25mm × 25mm. The radial ducts were electrically insulated from each other (simulating the use of FCIs in the blanket). The cross-section of the poloidal duct could be reduced by inserts to an area of 2 5 m m × 125mm. Three configurations were investigated as follows: (a) with insert; B parallel to the small side of the poloidal duct (two-dimensional flow);

Nma x

C k

Poloidal duct

Radial duct

80 7600 300 0.01 --

37 3900 200 0.02 38

62.5; 12.5 1800 200 0; 0.004; 0.008

I us

(~) magnetic field B

12.5 360 40 0; 0.025; 0.05 5

(b) with insert; B parallel to the large side of the poloidal duct (three-dimensional flow); (c) without insert. Configuration (c) is the most relevant for the blanket; for configuration (b), it was expected that the pressure drops are even larger than for (c) (conservative case); for configuration (a), a negligible pressure drop was expected (and observed). The wall conductance ratios shown in Table 2 were realized by using non-conducting duct walls, with and without appropriate stainless steel sheets glued on them. The experiments were performed with both distributing flow, as indicated in Fig. 2, and combining flow (reversed flow directions).

poloidal duct u,-

597

\ \|

j3d flow

t B

Fig. 2. Schematic diagram of manifold test sections.

l

598

J, Reimann et al. / Fusion Engineering and Design 27 (1995) 593 606 p [mbar] 249 j

poloidal duct - - - - - - -~-

247 I

--

-- --

239

number of radial radial ducts: k = 5 vi = c o n s t = 7 cm/s 237 . . . . 0 50 1 O0 150

4z

-"-~-"---~=-"-----.~ - " - ! i=1

.

i=2

i=3

i=4

i=5

. 200

i

250

300

350

flow length [mm]

Fig. 3. Pressure distribution for distributing flow: C = 0.05; k = 5; configuration (b).

The pressure distributions were measured both along the axis of the poloidal channel and along the radial channels. The manifold pressure drop Ap was obtained by extrapolating the undisturbed pressure gradients to the junctions, as shown schematically in Fig. 3, for the case of flow distribution with equal flow rates through five radial ducts. Fig. 4 shows the effect of the number of radial channels (k) for configuration (b) with distributing flow (the results for combining flow are very similar). With

increasing values of k, the pressure drop (normalized with araB 2) increases. For large values of k, an asymptotic value is expected. Fig. 5 depicts the dependence on the interaction parameter N. A distinct increase is observed for N < 5. In this range, the first pressure measurement in the radial duct indicated a recirculation zone resulting from inertia effects. The values for configuration (c) are slightly lower than those for configuration (b). The wall conductance ratio C did not exhibit a significant effect on the pressure drop. To extrapolate the results to blanket conditions, a correlation of the type Ap = a i M -°'5 + aaN -°'333 + ApM,U~o~

(2)

was used [16], where ApM, N~oo is the value for inertialess flow calculated by the core flow approximation (CFA). For the present case, Eq. (2) cannot be used quantitatively. If the value of the channel with the highest measured pressure drop at N - - 4 0 and M = 360 is assumed to be valid for blanket related conditions, a pressure drop of 0.07 MPa is obtained (for both manifolds), which is about one-tenth of the value given in Table 1.

0,25

0.2

0.15

0.1

2.2. Pressure drop in the multichannel U-bends k=3

0.05

[22-251

k=2 >k=l

0

I

I

I

I

2

3

4

5

radial d u c t i

Fig. 4. Manifold pressure drop (distributing flow): effect of channel number k for configuration (b): C = 0.04 T; N = 18; M = 340.

The first theoretical estimation that very high pressure drops can occur in electrically coupled U-bends was performed about 10 years ago by Madarame [21]. This result was taken into account in the blanket design, by decoupling electrically the radial parts of the U-bends by FCIs (cf. Section 2). To obtain a more fundamental insight into these M C E s experimental investigations were carried out,

599

J. Reimann et al. / Fusion Engineering and Design 27 (1995) 593-606 0.5

g

AP

0.4 [3

0.3

0

Conf. B

n i=1

<> i = 2

J' i = 3

x i=4

o i=5

Conf. C

• i=1

* i=2

•

x i=4

• i=5

i=3

0.2

•

0.1

~

•

0 0

o

• il o nnum o

I

I

I

I

I

I

t

5

10

15

20

25

30

35

•

I

L

40

45

Fig. 5. Manifold pressure drop (distributing flow): effect of interaction parameter N: C = 0.047; k = 5; M = 180 360.

which also included fully electrically coupled U-bends. Theoretical analyses were restricted to the latter case. Screening tests were performed at the LAS, using a simple experimental set-up which allowed easy variation of the channel geometries. The measurements were restricted for flow rates and pressure drops over the single U-bends. More detailed experiments were performed at KfK. Here, the aim was to provide data for code validation. Detailed pressure measurements were performed (29 positions) and 255 probes were used to measure the electric wall potentials. Similar test sections with five parallel channels were used in both experi-

ments. Fig. 6 shows schematically the test section for the detailed experiments. Table 3 contains characteristic values. Table 4 illustrates the channel geometries investigated. Fig. 7 shows the individual U-bend pressure drops (normalized with the single U-bend pressure drop, determined for M = N ~ oo) for different channel numbers k and flow geometries. For electrically coupled ducts, the pressure drop increases with increasing k, with minimum values in the outer ducts. Fig. 8 contains detailed experiment results for the middle channel (exhibiting the largest pressure drop)

symmetry plane S 1

symmetry plane $2

YY ~<

*x O,,

t,

.... / ~ - - - "

out,et

Y

Y

y:0

II 1

4

B

:

Fig. 6. Test section for multichannel U-bend experiments (detailed experiments).

inlet

600

J. Reimann et al. / Fusion Engineering and Design 27 (1995) 593-606

for the case of electrically coupled channels with thin conducting outer walls. Again, the increase in pressure drop with channel number k is seen. With increasing N, the values become smaller, however; even for N ~ 38 000, the values determined by the C F A method are not reached (the difference is negligible for k = 1 but increases with k). Therefore, the C F A method is only of limited value to predict these MCEs. Both the C F A and the experiments showed that the pressure drop increases linearly with k; no asymptotic value for large k is predicted by the CFA, in contrast to previous estimations [21]. Fig. 7 also contains the results for the blanket-related geometry: n o remarkable MCE is observed, with each channel of the multichannel system behaving like a completely separated duct. Therefore, electrical decoupling of the ducts in the toroidal part is not required. It should be mentioned that, for the case of electrically decoupled radial dividing walls, but with an electrical connection over the Hartmann walls, a pronounced MCE is still found. To conclude this section, it can be said that the use of FCIs in the radial ducts (extended up to the first wall) does not give rise to increased pressure drops caused by MCEs. The previous pressure drop assessment was greatly over-conservative.

channel were performed at the LAS [27], using traversing electric potential and hot wire probes, and Hg as liquid metal. The velocity distribution was predicted using C F A [17]. The predicted result is that, in the toroidal channel, transport of the liquid metal in the toroidal direction (x-axis) occurs only in layers close to the walls; in the bulk of the duct, the velocity component in the x direction is zero, but the velocity components in the other directions are non-zero. Fig. 9 illustrates the coordinate system used; Table 5 contains characteristic experimental parameters. Fig. 10 shows the velocity distributions obtained by the potential probe in the radial duct for a U-bend with thin con-

Table 3 Characteristic values for the U-bend

a (mm) M N C Lr/a Lt/a Channel Geometry a

3.3. Velocity distribution in the U-bend

The measurement of the velocity distribution in the radial duct, in the bend region and in the toroidal

Blanket

Screening tests

Detailed experiments

40 3000 200 0.028 6 25 III

12.5 300-1600 50-10 000 0; 0.068 12 32 I, II, III, IV

13 0-2400 0-40 000 0.038 20 24 II, III b

See Table 4. b Electrical connection over Hartmann walls. a

----

DE ST

Apmeas

Aps¢ =5

3-

k=3 2-

+|!1 m

~//~/,a k= 3

1- I m m~m~

k=l

|k=2|~

~ ) ~

O1 a)

2

34

1 b)

2

34

5

1 2 3 4 5 ¢)

Fig. 7. Multichannel effect for different channel geometries: (a) channel geometry I: (b) channel geometry II; (c) channel geometry III; Qi = constant; M ~ 1600; N ~ 3000 (see Table 4).

601

J. Reimann et aL/ Fusion Engineering and Design 27 (1995) 593 606

2.0

experiments N=1169 [] N=5154

///~

o N=38077

//"

'~ CVA:rn~tichannel calculation

1.5

/~/

/0

1.0 rr//// 0.5

o

i

corresponding aspect ratio

2

k

8

4

5

6

Fig. 8. Pressure drop (detailed experiments) in middle channel as a function of channel number k: (M = 2400); Q~= constant.

Table 4 Channel geometries investigated Channel geometry I: non-conducting outside walls; conducting dividing walls; number of channels k = 1, 2, 3, 5 Channel geometry II: conducting outside walls; conducting dividing walls; number of channels k = 1, 3, 5 Channel geometry III: conducting outside walls; non-conducting dividing walls in radial part; conducting dividing walls in toroidal part; number of channels k = 5 Channel geometry IV: non-conducting outside walls; conducting dividing walls in first half of test section; non-conducting dividing walls in second half; number of channels k = 5

ducting walls and non-conducting walls. Approaching the bend, the liquid metal is characteristically pushed towards the side walls. This effect is much more apparent for C = 0 than for C = 0.06. Fig. 11 shows the velocity distributions (hot wire probe) in the toroidal duct for three different values of

the interaction parameter. F o r purely hydrodynamic flow, the characteristic recirculation zone is seen down stream of the inner bend corner. F o r N = 17, this recirculation zone no longer exists. With increasing N, the liquid is pushed towards the side walls, and highest signals are observed close to the first wall as predicted by C F A . Surprisingly, the hot wire signals depict a maximum at y = 0 in the bulk of the toroidal duct.

Table 5 Test section characteristics (all lengths in millimetres) Geometry

a

b

d

a0

C~

Mma× a

Nmax~

(a) (b) (c) (d)

18 9 9 10

18 18 18 20

17 17 17 19

9 9 9 10

0.06 0.122 0.122 b 0

~460 ~230 ~230 ~255

~70 ~35 ~35 ~38

a Values based on the quantities in the radial channel. b Wall conductivity at first wall ten times larger than at other walls.

Fig. 12 shows for C = 0.122 a similar distribution of the mean velocity, measured by the hot wire probe, and the corresponding distribution of the fluctuating velocity. As a result of these surprising signal distributions, additional measurements with potential probes for measurement of the v~ and vx velocity components were performed. All the measurements indicate the existence of a pair of strong vortices with axes parallel to the

602

J. Reimann et al. / Fusion Engineering and Design 27 (1995) 593-606

First ~

d

0

1

duct

U/i

.0, -Z

i - - - - 2b

Radial duct Fig. 9. Coordinate system.

magnetic field (see Fig. 13), which probably are caused by the M-shaped velocity profile at the entrance to the toroidal duct. From the present measurements, it is not clear if these vortices exist for blanket-related conditions. If these vortices do not exist, then the expected velocity distribution with high values close to the first wall is still very favourable for heat transfer.

4. Conclusions

The M H D issues of a self-cooled Pb-17Li blanket with poloidal-radial-toroidal ducts, based on the use of FCIs, were investigated. Recent experimental and theoretical investigations show that previous assumptions of the total pressure drop were too conservative (although the old values resulted in a high safety margin).

For the velocity distribution in the first-wall ducts, it was shown that the distributions are very favourable for heat transfer. First, it was found that the velocity close to the first wall increases with increasing interaction parameter; secondly, a pair of vortices was identified, which is even more favourable for heat transfer, because they transport the heat into the bulk of the flow cross-section. If such vortices exist at high values of M and N, the flow rates could be reduced and the design could be essentially simplified. The work summarized in this survey paper was restricted to ducts with thin conducting walls (resulting from the use of the FCIs). For non-conducting walls (use of insulating coatings on the duct walls), the M H D pressure drops would be much lower. Work on MHD questions related to non-conducting walls is summarized in another paper [28]. In this paper, another blanket concept is considered, i.e. the so-called "Dual coolant blanket" [29]. This blanket has

J. Reimann et al. / Fusion Engineering and Design 27 (1995) 593-606

603

t~

~..

~.

""

z

"~"

z

z =-34 m m

"',-,; ~ .

z = - 2 1 mm

"~ " ' ~ - ~ " "

-"

°.

%,

.~ ~o

z=-Smm

oQ"

z---5

..~

.

Fig. 10. Velocity distributions in the radial duct: (a) thin conducting walls (C = 0.06, M = 460, N = 17); (b) non-conducting walls (C = 0).

been selected since about 1 year ago as the reference self-cooled blanket option for the European D E M O reactor. However, it must be pointed out that this

decision was not required, because of critical M H D problems of the old blanket design, as demonstrated in this paper, but because of reliability and safety reasons.

~c)

xE E

'

e,

qb ~

~,

o,

~

~

'

~

4

"7,

~

J~

I/

¢

i

•

#'

¢

'

o,

¢

~

cr~

II

0

.

-'"~"

-~ ~ il

605

J. Reimann et al. ] Fusion Engineering and Design 27 (1995) 593-606

Fig. 12. Velocity and velocity fluctuations in the toroida] duct: C = 0.122; configuration (b).

-17-15-13-11 I ~4 / I / V I . , , ~

c

-9 I

I

P~l

-7

-5

-3

I

I ~-.._~.

I

-1 I

I

1

3

I'~.1

I'~AJ

5 I.,~"l

7 I

9

~ 1

11 I

I

13

15

I X ~

17 I

•

,.

4

-17-15-13-11

-9

-7

-5

-3

-1

!

) )

1

3

5

7

9

11

13

15

17

Y Fig. 13. Curves of constant velocity (from hot wire probe), indicating vortex system in toroidal channel.

Acknowledgements

This work was performed in the framework of the Nuclear Fusion Project of the Kernforschungszentrum Karlsruhe, and is supported by the European Communities within the European Fusion Technology Programme.

[3]

[4]

References [5] [1] S. Malang, J. Reimann and H. Sebening (eds.), Status report. KfK contribution to the development of DEMOrelevant test blankets for NET/ITR, part 1: Self-cooled liquid metal breeder blanket, vol. 1, Summary, Rep. KfK-4907, Karlsruhe Nuclear Research Centre, 1991. [2] H. John, S. Malang and H. Sebening (eds!), Status report, KfK contribution to the development of DEMO-relevant

[6]

test blankets for NET/ITER, part 1: Self-cooled liquid metal breeder blanket, vol. 2, Detailed Version, Rep. KfK-4908, Karlsruhe Nuclear Research Centre, 1991. S. Malang, L. Barleon, L. Biihler, H. Deckers, S. Molokov, U. MiNer, P. Norajitra, J. Reimann, H. Reiser and R. Stieglitz, MHD work on self-cooled liquid-metal blankets under development at the Nuclear Research Centre, Karlsruhe, Perspect. Energy (1992) 303-312. D. L. Smith, Blanket comparison and selection study (final report), Rep. ANL/FPP-84-1, vol. 1-3 Argonne National Laboratory, Argonne, IL, 1984. L. Biihler, Liquid metal flow in arbitrary thin-walled channels under a strong transverse variable magnetic field, Fusion Eng. Des. 17 (1991) 215-220. C. B. Reed, B. F. Picologlou, T. Q. Hua and J. S. Walker, ALEX results--a comparison of measurements from a round and a rectangular duct with 3-D code predictions, Proc. 12th Symp. on Fusion Engineering, Monterey, CA, IEEE, New York. 1987, pp. 1267-1270.

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J. Reimann et al. / Fusion Engineering and Design 27 (1995) 593-606

[7] T. Q. Hua, J. S. Walker, B. F. Picologlou and C. B. Reed, Three-dimensional MHD flows in rectangular ducts of liquid-metal-cooled blankets, Fusion Technol. 14(3) (1988). [8] J. S. Walker, Magnetohydrodynamic flows in rectangular ducts with thin conducting walls, J. Mecan. 20(1) (1981) 79-112. [9] B. F. Picologlou, C. B. Reed, T. Q. Hua, L. Barleon, H. Kreuzinger and J. S. Walker, Experimental investigations of MHD flow tailoring for first wall coolant channels of self-cooled blankets, Fusion Technol. 15 (1989) 11801185. [10] M. Tillack, MHD-flow in rectangular ducts, design equations for pressure drop and flow quantity, Rep. UCLAFNT-41, 1990. [11] L. Barleon, V. Casal and L. Lenhart, MHD flow in liquid metal cooled blankets, Fusion Eng. Des. 14 (1991) 401412. [12] S. Molokov, Fully developed liquid-metal flow in multiple rectangular ducts in a strong uniform magnetic field, Euro. J. Mech., B 12(3) (1993) 769-787. [13] L. Biihler, Additional magnetohydrodynamic pressure drop at junctions of flow channel inserts, Proc. 18th SOFT Symp. on Fusion Technology, Rome, September, 1992, pp. 14-18. [14] J. S. Walker, Liquid metal flow through a thin walled elbow in a plane perpendicular to a uniform magnetic field, Int. J. Eng. Sci. 24(11) (1986). [15] T. J. Moon, J. S. Walker and T. Q. Hua, Liquid-metal flow a backward elbow in the plane of a strong magnetic field, J. Fluid Mech. 227 (1990) 273-292. [16] L. Barleon, L. Bfihler, S. Molokov and R. Stieglitz, Magnetohydrodynamic flow through a right angle bend, Proc. 7th Beer-Sheva Int. Seminar on MHD Flows and Turbulence, Israel, 14-18 February 1993. [17] S. Molokov and L. Biihler, Liquid metal flow in a U-bend in a strong uniform magnetic field, J. Fluid Mech., in press. [18] O. Lielausis, Liquid metal in a strong magnetic field, in J. Lielpeteris and R. Moreau (eds.), Liquid Metal Magnetohydrodynamics, Kluwer, Dordrecht, 1989, pp. 3-12.

[19] T. Q. Hua and B. F. Picologlou, Magnetohydrodynamic flow in a manifold and multiple rectangular coolant ducts of self-cooled blankets, Fusion Technol. 19 (1991). [20] J. Reimann, I. Bucenieks, A. Flerov, L. Heller and I. Platnieks, Experiments on pressure drop of MHD flow in manifolds, Proc. 2nd Int. Conf. on Energy Transfer in Magnetohydrodynamic Flows (PAMIR), Aussois, France, 26-30 September, 1994. [21] H. Madarame, MHD fluid flow and pressure drop, FINESSE Interim Rep. G-821 UCLA-ENG-84-30, vol. 3. 1984, pp. 6.9-6.109. [22] J. Reimann, S. Molokov, I. Platnieks and E. Platacis, MHD-flow in multichannel U-bends: Screening experiments and theoretical analysis, Rep. KfK 5102, February 1993. [23] J. Reimann, S. Molokov, I. Platnieks and E. Platacis, MHD-flow in multichannel U-bends: screening experiments and theoretical analysis, Proc. 17th SOFT Symp. on Fusion Technology, Rome, Italy, September 1992. [24] R. Stieglitz, S. Molokov, L. Barleon, J. Reimann, and K.-J. Mack, MHD-flows in electrically coupled bends, Proc. 2nd Int. Conf. on Energy Transfer in Magnetohydrodynamic flows, Aussois, France, 26-30 September 1994. [25] S. Molokov and R. Stieglitz, Liquid-metal flow in a system of electrically coupled U-bends in a strong uniform magnetic field, to be published. [26] J. C. R. Hunt and R. J. Holroyd, Applications of laboratory and theoretical MHD duct flow studies in fusion reactor technology, Rep. CLM-R-169, 1977. [27] J. Reimann, I. Bucenieks, S. Dementer, A. Flerov, S. Molokov and I. Platnieks, MHD-velocity distributions in U-bends partly parallel to the magnetic field, Proc. 2nd Int. Conf. on Energy Transfer in Magnetohydrodynamic Flows, Aussois, France, 26-30 September, 1994. [28] L. Barleon, L. Biihler, L. Lenhart, S. Malang, S. Molokov, J. Reimann and R. Stieglietz, MHD issues of the dual coolant blanket concept, Proc. SOFT 94 Conf. [29] S. Malang, E. Bojarsky, L. Bfihler, H. Deckers, U. Fischer, P. Norajitra and H. Reiser, Dual coolant liquid metal breeder blanket, Fusion Technol. (1992) 1424-1428.