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MHD pressure drop of imperfect insulation of liquid metal flow
Fusion Engineering and Design 51 – 52 (2000) 775 – 780 www.elsevier.com/locate/fusengdes
MHD pressure drop of imperfect insulation of liquid metal flow H. Horiike *, R. Nishiura 1, S. Inoue, K. Miyazaki Graduate School of Engineering, Osaka Uni6ersity, 2 -1, Yamadaoka, Suita City, Osaka 5650871, Japan
Abstract An experiment was performed to study magnetohydrodynamic (MHD) pressure gradient in the case of an imperfect electric insulation coating when using NaK loop. Test channels with uniform defects in their coating were made by painting inner surface with acrylic lacquer insulation. It was found that the exponent to B — which is 1 for insulated walls, and 2 for conducting ones, was very sensitive to crack fractions lower than 25%. The pressure gradient was found to increase almost linearly with the fraction. © 2000 Elsevier Science B.V. All rights reserved. Keywords: MHD pressure drop; Liquid metal; NaK; Electric insulation; Blanket
1. Introduction Self-cooled breeding blanket has been studied for long time, since the advantages of its design and concept were well recognized; they include simple structure, high breeding ratio, and high thermal conduction capability. A key consideration in the design of a liquid metal blanket is its magnetohydrodynamic (MHD) effects on the pressure gradient and the heat transfer. The pressure drop in liquid metal flow mainly originates from the net J ×B force, where the current loop in the case of conducting wall does not close * Corresponding author. Tel.: +81-6-68797884; fax: + 816-86797363. E-mail address: [email protected] (H. Horiike). 1 Present address: Mitsubishi Electric Co. Ltd., Osaka, Japan.
within the fluid, thus strongly retarding the flow direction. The current density and, hence, the pressure gradient depend on the electrical conductivities of the fluid and of the channel wall, as well as on the magnetic field strength, flow velocity, and channel geometry. A reduction method to bring down the MHD pressure drop to manageable levels, is an electrical insulation to be performed between the walls and the lithium fluid. Insulation could be achieved by a thin film or coating of some kind of electrically insulated materials, such as AlN, CaO, and MgO, in contact with lithium, which unfortunately are known to be fragile under fluid circulation and thermal cycling. The importance of an imperfect insulation was well recognized, and analytical studies were performed [1–3]. In the case of a rectangular channel we showed that the surface perpendicular to the field can be electrically conductive, in order to keep similar pressure gradi-
0920-3796/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 0 - 3 7 9 6 ( 0 0 ) 0 0 4 5 1 - 8
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H. Horiike et al. / Fusion Engineering and Design 51–52 (2000) 775–780
ents in the fully insulated one [4]. From these results it can be deduced that the allowable ratio of cracks of the insulation coating would not be very small, although no quantitative experimental data were reported so far. Thus, we performed a pressure drop measurement with crack-simulated
test channel on the NaK test loop [5]. Test channels were made of SS tubes, whose inner surface was insulated by an acrylic lacquer coating with defects. The experimental set up, and its results are discussed in the following chapters.
2. Experiments
Fig. 1. Structure of the test channel.
Fig. 2. Outline of the test channel.
The experiments are conducted in the NaK test loop constructed at the Osaka University. The structure of our test channel is shown in Fig. 1. A 1-m long stainless steel 316 tube 1 mm thick with inner diameter of 26 mm was half-cut along the axis, and the inner surface was coated by an acrylic resin paint. To simulate cracks, the acrylic coating was precisely cut off over an area of 2 mm in width and 50 mm in length by using many pieces of masking tape. These cuts were arranged in the form of a chequer-board in order to avoid the formation of long slits, and had to be uniform all over the whole surface of the test tube; by adjusting the number of cuts, a fixed ratio of the conducting to the non-conducting area should be achieved. Then, these two half-tubes were combined and inserted into outer stainless tube of 2.11 mm thick, with an inner diameter of 27.6 mm. Test channels of five different crack fractions were fabricated, namely 0, 15, 25, 40 and 60%. Considering the reliability of previously reported studies, a channel with 100% of cracks was not tested. Measurements were done by using the pressure taps and the potential taps indicated in Fig. 2. Pressure transducers were installed at the two points shown by solid circles; electrical potential taps are shown by the crosses. The sensor is a piezo-electrical semiconductor pressure sensor with a maximum rating of 0.2 MPa. The pressure taps are located at 5 cm from the edges of the flat magnetic field region. Therefore, the pressure drop data were obtained in a uniform magnetic field only. The magnet has a pole face of 15 cm wide and 50 cm high, with a gap length of 8 cm, which allowed the field of 2.0 T maximum, with exciting direct current of 310 A at 180 V, to be produced. A scheme of the NaK loop is indicated in Fig. 3. The loop was constructed with SS316 tubes of 25.4 mm outer diameter and 1.6 mm wall
H. Horiike et al. / Fusion Engineering and Design 51–52 (2000) 775–780
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down the fluid from the expansion tank to the storage tank. After switching to a new test channel, idling operation was conducted every time. This process is necessary to decrease electrical contact resistance between the fluid and the tube surface; it was found that 20 h of idle operation at a temperature of 60–70°C is necessary to sufficiently decrease contact resistance. Free surface was covered with argon at 0.12 MPa. The pressure sensors are calibrated by changing this pressure.
3. Results and discussions
Fig. 3. Schematic of the NaK loop.
In order to understand the effects of the partial electrical conduction, the exponent to the magnetic field intensity was noted. For fully developed flow with electrically insulated wall, the MHD drop shows a linear dependence of B, dp 8 suB dx where s is the liquid metal’s electrical conductivity, u is the average flow velocity, and B is the magnetic flux density. On the contrary, with an electrically conducting wall, the MHD drop is given by square of B, dp 8 suB 2 dx
Fig. 4. The MHD drop in the case of 25% of crack fraction.
thickness. The working fluid is NaK78, which is made of 22% of sodium and 78% of potassium. It was circulated by an AC-Faraday type electromagnetic pump of a maximum rating of 40 l/min for NaK78 and 100 l/min for sodium. The air cooling section was also provided in order to reduce fluid temperature against heat input due to pumping. The NaK was charged up into the loop upon vacuum evacuation of inner tube volume and connection space to the pressure taps. The electromagnetic flow meter was calibrated by blowing
Therefore, it was noted that the exponent to B is a good index to know whether the situation is near to perfect insulation or good conduction. Typical results are indicated in Fig. 4(a, b). These data show the MHD drop in the case of a 25% crack fraction. Fig. 4(a) shows the dependence from B linear and Fig. 4(b) the dependence from B square. Since all these data fell on the midway between perfect insulation and conduction, it was noted that the data were bending upwards in Fig. 4(a) and downwards in Fig. 4(b) according to the B increase. But, since all plots fell on a single curve in Fig. 4(b), it was observed that the MHD drop characteristic was fairly near to that in the perfect conduction. The other plotting showed that these data were proportional to the flow velocity.
H. Horiike et al. / Fusion Engineering and Design 51–52 (2000) 775–780
778
The second example is shown in Fig. 5(a, b), which belong to the 0% crack case. Here, all plots were seen to be depending on B linear, and not in agreement with the B square dependence. The data here are a good example of accuracy in our pressure measurements. The solid line in Fig. 5(a) shows the theoretical line for the round tube. The
Fig. 7. B exponent as a function of the crack fraction.
Fig. 5. MHD drop in the case of 0% crack.
Fig. 6. Semi-log plot of MHD drop. Table 1 Obtained exponent to B for five cases of the crack fraction Crack fraction
Exponent
0 15 25 40
0.98 1.64 1.81 1.86
present data are 1.8 times higher than the theoretical ones. In our previous tests the theory accuracy was verified by means of perfectly insulating test channels. The reason for this deviation is not clear, but one possibility lies in the construction of the present test channel, which consisted of two half-cut tubes and had two fitting lines neither glued nor blazed along the axis. Very low current might leak through these slits, thus causing additional pressure drop. However, these are very small as compared with MHD drops in the case of the conducting wall; this effect is negligible in the present estimation. Five cases of data were plotted in the semi-log plot shown in Fig. 6, in order to get the exponent to B from these data. The ordinate denotes the pressure gradient divided by the average flow velocity, and the abscissa the field intensity. The solid lines were obtained by means of the least square fit of the data. From this figure, the exponents to B were obtained and shown in Table 1 and Fig. 7 by means of open circles. It is clear that the exponent with no crack very well agrees with the perfect insulation case. It is also very significant that, with crack fractions higher than 25%, the MHD drop characteristics gradually approach those of the perfect electrical conduction, though the experimental data seem to be saturated at 1.85. We can see that most of the variation from insulation to conduction occurs within the fraction range of 0–25%.
H. Horiike et al. / Fusion Engineering and Design 51–52 (2000) 775–780
Fig. 8. Normalized pressure drop characteristics as a function of the crack fraction.
The solid line denotes an analytical solution obtained with two-dimensional MHD codes BIGMAC [6,7]. This code solves 2D MHD flow with the finite element Galerkin method for a circular geometry. The calculation was conducted for a quarter section of the tube cross section, by using 500 meshes with monolayer meshes of an electrical insulator between fluid region and wall. It was noted that the analytical and experimental results agree quite well, including the prediction of the shoulder value. We can conclude that the flow is
779
mostly characterized by being electrically conductive for the crack fraction of 25%. Pressure drop characteristics are represented in Fig. 8, where the MHD drop, normalized to fully conducting wall case, is plotted as a function of the crack fraction. The experimental results denoted by open circles fall slightly below the analytical results of the solid line, which was obtained by the same calculation as before. From this figure, the MHD drop is seen to mostly increase linearly from 0 to 100% of the fraction, while the analytical result is mostly saturated above 25%. Thus, we may conclude that the MHD drop behavior reaches a value very near to that of the full conducting case above the fraction of 25%. Finally, electric potential distributions around the tube circumference were indicated in Fig. 9, which were measured at the center of the test channel. These distributions were very close to cosine profile. The voltage appeared on the load resister of the tube wall, which was divided by resistance of the insulation layer. Therefore, it is equal to zero when the insulation is perfect. If this voltage could be precisely calibrated to the tube geometry under design, it could represent a good indicator of local crack formation, as far as its fraction is sufficiently large to affect the MHD pressure drop.
Fig. 9. Electrical potential around the channel.
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H. Horiike et al. / Fusion Engineering and Design 51–52 (2000) 775–780
4. Conclusion
References
The effect of crack formation on the MHD pressure drop was systematically studied for crack fractions of 0 – 60%. The MHD drop characteristics were tested in the name of the power exponent to the magnetic field. It was shown that the flow behavior quickly approaches that of conductive wall case for the crack fraction of 0–25%. The pressure drop measurement indicated that the drop mostly increases linearly from 0 to 100% of increase in the fraction, and that the flow behavior approaches that of conducting wall case for the crack fraction of 25%. The potential was measured on the outer surface of the tube. This voltage was shown to be used as an indicator of the crack formation.
[1] T.Q. Hua, Y. Gohar, MHD pressure drops and thermal hydraulic analysis for the ITER breeding blanket design, Fusion Eng. Design 27 (1995) 696 – 702. [2] I. Kirillov, MHD/HT study in channels with perfect insulation and controlled impurities, IEA workshop on insulator coating materials for liquid metal fusion blankets, Argonne National Laboratory, May 8 – 12, 1995. [3] A. Gaizer, UCLA effort in MHD modeling of the influence of insulator imperfections on the flow behavior, ibid. [4] C.B. Reed, K. Natesan, T.Q. Hua, I.R. Kirillov, I.V. Vitkovski, A.M. Anisimov, MHD pressure drop and surface voltage measurements in an Al2O3 coated round pipe, ibid. [5] K. Miyazaki et al., Fusion Technol. 19 (5) (1991), pp. 961 and 969. [6] K. Miyazaki et al., MHD pressure drop of NaK flow in a coaxial double circular duct and a plane-insulated duct under transverse magnetic fields, 4th Int’l Conf. on Liquid Metal Eng. & Technol. (LIMET88), Avignon, 437/1–10 Oct. 1988. [7] K. Miyazaki et al., Analysis and NAK experiment on electromagnetic flow coupler, Proc. Int’l Conf. Fast Breeder Systems: Experience Gained and Path to Economical Path to Power Generation, Richland, Washington, 12.9.1 – 10 Sept. 1987.
Acknowledgements The authors wish to acknowledge the assistance of N. Uda and A. Miyazawa for the data analysis.
.
MHD pressure drop of imperfect insulation of liquid metal flow H. Horiike *, R. Nishiura 1, S. Inoue, K. Miyazaki Graduate School of Engineering, Osaka Uni6ersity, 2 -1, Yamadaoka, Suita City, Osaka 5650871, Japan
Abstract An experiment was performed to study magnetohydrodynamic (MHD) pressure gradient in the case of an imperfect electric insulation coating when using NaK loop. Test channels with uniform defects in their coating were made by painting inner surface with acrylic lacquer insulation. It was found that the exponent to B — which is 1 for insulated walls, and 2 for conducting ones, was very sensitive to crack fractions lower than 25%. The pressure gradient was found to increase almost linearly with the fraction. © 2000 Elsevier Science B.V. All rights reserved. Keywords: MHD pressure drop; Liquid metal; NaK; Electric insulation; Blanket
1. Introduction Self-cooled breeding blanket has been studied for long time, since the advantages of its design and concept were well recognized; they include simple structure, high breeding ratio, and high thermal conduction capability. A key consideration in the design of a liquid metal blanket is its magnetohydrodynamic (MHD) effects on the pressure gradient and the heat transfer. The pressure drop in liquid metal flow mainly originates from the net J ×B force, where the current loop in the case of conducting wall does not close * Corresponding author. Tel.: +81-6-68797884; fax: + 816-86797363. E-mail address: [email protected] (H. Horiike). 1 Present address: Mitsubishi Electric Co. Ltd., Osaka, Japan.
within the fluid, thus strongly retarding the flow direction. The current density and, hence, the pressure gradient depend on the electrical conductivities of the fluid and of the channel wall, as well as on the magnetic field strength, flow velocity, and channel geometry. A reduction method to bring down the MHD pressure drop to manageable levels, is an electrical insulation to be performed between the walls and the lithium fluid. Insulation could be achieved by a thin film or coating of some kind of electrically insulated materials, such as AlN, CaO, and MgO, in contact with lithium, which unfortunately are known to be fragile under fluid circulation and thermal cycling. The importance of an imperfect insulation was well recognized, and analytical studies were performed [1–3]. In the case of a rectangular channel we showed that the surface perpendicular to the field can be electrically conductive, in order to keep similar pressure gradi-
0920-3796/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 0 - 3 7 9 6 ( 0 0 ) 0 0 4 5 1 - 8
776
H. Horiike et al. / Fusion Engineering and Design 51–52 (2000) 775–780
ents in the fully insulated one [4]. From these results it can be deduced that the allowable ratio of cracks of the insulation coating would not be very small, although no quantitative experimental data were reported so far. Thus, we performed a pressure drop measurement with crack-simulated
test channel on the NaK test loop [5]. Test channels were made of SS tubes, whose inner surface was insulated by an acrylic lacquer coating with defects. The experimental set up, and its results are discussed in the following chapters.
2. Experiments
Fig. 1. Structure of the test channel.
Fig. 2. Outline of the test channel.
The experiments are conducted in the NaK test loop constructed at the Osaka University. The structure of our test channel is shown in Fig. 1. A 1-m long stainless steel 316 tube 1 mm thick with inner diameter of 26 mm was half-cut along the axis, and the inner surface was coated by an acrylic resin paint. To simulate cracks, the acrylic coating was precisely cut off over an area of 2 mm in width and 50 mm in length by using many pieces of masking tape. These cuts were arranged in the form of a chequer-board in order to avoid the formation of long slits, and had to be uniform all over the whole surface of the test tube; by adjusting the number of cuts, a fixed ratio of the conducting to the non-conducting area should be achieved. Then, these two half-tubes were combined and inserted into outer stainless tube of 2.11 mm thick, with an inner diameter of 27.6 mm. Test channels of five different crack fractions were fabricated, namely 0, 15, 25, 40 and 60%. Considering the reliability of previously reported studies, a channel with 100% of cracks was not tested. Measurements were done by using the pressure taps and the potential taps indicated in Fig. 2. Pressure transducers were installed at the two points shown by solid circles; electrical potential taps are shown by the crosses. The sensor is a piezo-electrical semiconductor pressure sensor with a maximum rating of 0.2 MPa. The pressure taps are located at 5 cm from the edges of the flat magnetic field region. Therefore, the pressure drop data were obtained in a uniform magnetic field only. The magnet has a pole face of 15 cm wide and 50 cm high, with a gap length of 8 cm, which allowed the field of 2.0 T maximum, with exciting direct current of 310 A at 180 V, to be produced. A scheme of the NaK loop is indicated in Fig. 3. The loop was constructed with SS316 tubes of 25.4 mm outer diameter and 1.6 mm wall
H. Horiike et al. / Fusion Engineering and Design 51–52 (2000) 775–780
777
down the fluid from the expansion tank to the storage tank. After switching to a new test channel, idling operation was conducted every time. This process is necessary to decrease electrical contact resistance between the fluid and the tube surface; it was found that 20 h of idle operation at a temperature of 60–70°C is necessary to sufficiently decrease contact resistance. Free surface was covered with argon at 0.12 MPa. The pressure sensors are calibrated by changing this pressure.
3. Results and discussions
Fig. 3. Schematic of the NaK loop.
In order to understand the effects of the partial electrical conduction, the exponent to the magnetic field intensity was noted. For fully developed flow with electrically insulated wall, the MHD drop shows a linear dependence of B, dp 8 suB dx where s is the liquid metal’s electrical conductivity, u is the average flow velocity, and B is the magnetic flux density. On the contrary, with an electrically conducting wall, the MHD drop is given by square of B, dp 8 suB 2 dx
Fig. 4. The MHD drop in the case of 25% of crack fraction.
thickness. The working fluid is NaK78, which is made of 22% of sodium and 78% of potassium. It was circulated by an AC-Faraday type electromagnetic pump of a maximum rating of 40 l/min for NaK78 and 100 l/min for sodium. The air cooling section was also provided in order to reduce fluid temperature against heat input due to pumping. The NaK was charged up into the loop upon vacuum evacuation of inner tube volume and connection space to the pressure taps. The electromagnetic flow meter was calibrated by blowing
Therefore, it was noted that the exponent to B is a good index to know whether the situation is near to perfect insulation or good conduction. Typical results are indicated in Fig. 4(a, b). These data show the MHD drop in the case of a 25% crack fraction. Fig. 4(a) shows the dependence from B linear and Fig. 4(b) the dependence from B square. Since all these data fell on the midway between perfect insulation and conduction, it was noted that the data were bending upwards in Fig. 4(a) and downwards in Fig. 4(b) according to the B increase. But, since all plots fell on a single curve in Fig. 4(b), it was observed that the MHD drop characteristic was fairly near to that in the perfect conduction. The other plotting showed that these data were proportional to the flow velocity.
H. Horiike et al. / Fusion Engineering and Design 51–52 (2000) 775–780
778
The second example is shown in Fig. 5(a, b), which belong to the 0% crack case. Here, all plots were seen to be depending on B linear, and not in agreement with the B square dependence. The data here are a good example of accuracy in our pressure measurements. The solid line in Fig. 5(a) shows the theoretical line for the round tube. The
Fig. 7. B exponent as a function of the crack fraction.
Fig. 5. MHD drop in the case of 0% crack.
Fig. 6. Semi-log plot of MHD drop. Table 1 Obtained exponent to B for five cases of the crack fraction Crack fraction
Exponent
0 15 25 40
0.98 1.64 1.81 1.86
present data are 1.8 times higher than the theoretical ones. In our previous tests the theory accuracy was verified by means of perfectly insulating test channels. The reason for this deviation is not clear, but one possibility lies in the construction of the present test channel, which consisted of two half-cut tubes and had two fitting lines neither glued nor blazed along the axis. Very low current might leak through these slits, thus causing additional pressure drop. However, these are very small as compared with MHD drops in the case of the conducting wall; this effect is negligible in the present estimation. Five cases of data were plotted in the semi-log plot shown in Fig. 6, in order to get the exponent to B from these data. The ordinate denotes the pressure gradient divided by the average flow velocity, and the abscissa the field intensity. The solid lines were obtained by means of the least square fit of the data. From this figure, the exponents to B were obtained and shown in Table 1 and Fig. 7 by means of open circles. It is clear that the exponent with no crack very well agrees with the perfect insulation case. It is also very significant that, with crack fractions higher than 25%, the MHD drop characteristics gradually approach those of the perfect electrical conduction, though the experimental data seem to be saturated at 1.85. We can see that most of the variation from insulation to conduction occurs within the fraction range of 0–25%.
H. Horiike et al. / Fusion Engineering and Design 51–52 (2000) 775–780
Fig. 8. Normalized pressure drop characteristics as a function of the crack fraction.
The solid line denotes an analytical solution obtained with two-dimensional MHD codes BIGMAC [6,7]. This code solves 2D MHD flow with the finite element Galerkin method for a circular geometry. The calculation was conducted for a quarter section of the tube cross section, by using 500 meshes with monolayer meshes of an electrical insulator between fluid region and wall. It was noted that the analytical and experimental results agree quite well, including the prediction of the shoulder value. We can conclude that the flow is
779
mostly characterized by being electrically conductive for the crack fraction of 25%. Pressure drop characteristics are represented in Fig. 8, where the MHD drop, normalized to fully conducting wall case, is plotted as a function of the crack fraction. The experimental results denoted by open circles fall slightly below the analytical results of the solid line, which was obtained by the same calculation as before. From this figure, the MHD drop is seen to mostly increase linearly from 0 to 100% of the fraction, while the analytical result is mostly saturated above 25%. Thus, we may conclude that the MHD drop behavior reaches a value very near to that of the full conducting case above the fraction of 25%. Finally, electric potential distributions around the tube circumference were indicated in Fig. 9, which were measured at the center of the test channel. These distributions were very close to cosine profile. The voltage appeared on the load resister of the tube wall, which was divided by resistance of the insulation layer. Therefore, it is equal to zero when the insulation is perfect. If this voltage could be precisely calibrated to the tube geometry under design, it could represent a good indicator of local crack formation, as far as its fraction is sufficiently large to affect the MHD pressure drop.
Fig. 9. Electrical potential around the channel.
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H. Horiike et al. / Fusion Engineering and Design 51–52 (2000) 775–780
4. Conclusion
References
The effect of crack formation on the MHD pressure drop was systematically studied for crack fractions of 0 – 60%. The MHD drop characteristics were tested in the name of the power exponent to the magnetic field. It was shown that the flow behavior quickly approaches that of conductive wall case for the crack fraction of 0–25%. The pressure drop measurement indicated that the drop mostly increases linearly from 0 to 100% of increase in the fraction, and that the flow behavior approaches that of conducting wall case for the crack fraction of 25%. The potential was measured on the outer surface of the tube. This voltage was shown to be used as an indicator of the crack formation.
[1] T.Q. Hua, Y. Gohar, MHD pressure drops and thermal hydraulic analysis for the ITER breeding blanket design, Fusion Eng. Design 27 (1995) 696 – 702. [2] I. Kirillov, MHD/HT study in channels with perfect insulation and controlled impurities, IEA workshop on insulator coating materials for liquid metal fusion blankets, Argonne National Laboratory, May 8 – 12, 1995. [3] A. Gaizer, UCLA effort in MHD modeling of the influence of insulator imperfections on the flow behavior, ibid. [4] C.B. Reed, K. Natesan, T.Q. Hua, I.R. Kirillov, I.V. Vitkovski, A.M. Anisimov, MHD pressure drop and surface voltage measurements in an Al2O3 coated round pipe, ibid. [5] K. Miyazaki et al., Fusion Technol. 19 (5) (1991), pp. 961 and 969. [6] K. Miyazaki et al., MHD pressure drop of NaK flow in a coaxial double circular duct and a plane-insulated duct under transverse magnetic fields, 4th Int’l Conf. on Liquid Metal Eng. & Technol. (LIMET88), Avignon, 437/1–10 Oct. 1988. [7] K. Miyazaki et al., Analysis and NAK experiment on electromagnetic flow coupler, Proc. Int’l Conf. Fast Breeder Systems: Experience Gained and Path to Economical Path to Power Generation, Richland, Washington, 12.9.1 – 10 Sept. 1987.
Acknowledgements The authors wish to acknowledge the assistance of N. Uda and A. Miyazawa for the data analysis.
.