- Email: [email protected]
Mhd enhancement of heat transfer and its relevance to fusion reactor blanket design
Fusion Engineering and Design North-Holland. Amsterdam
8 (1989)
MI-ID ENHANCEMENT REACTOR BLANKET
S. SUKORIANSKY, Center for MHD
277-282
OF HEAT TRANSFER DESIGN
D. KLAIMAN,
Studies,
211
Ben-Gurion
University
AND ITS RELEVANCE
TO FUSION
H. BRANOVER of the Negev,
P.O.
Box 653, Beer-Shevo
84105,
Israel
E. GREENSPAN Atomic
Energy
Commission,
P.O. Box 7061, Tel-Aviv,
61070,
Israel
The effect of a uniform magnetic field on the heat transfer of liquid metal forced flows in straight rectangular channels subjected to a uniform heat flux on one of the walls parallel to the field is experimentally studied. The experiments covered the domain 3.8 Q U d 18 cm/s; 0 d B d 0.9 T; 0 d M d 300 and 4 X 10’ Q Re < 2 X 104. It is found that the application of the magnetic field improves the heat transfer in channels made of both non-conducting walls and of conducting walls. Whereas in the former case this improvement results from the creation of enhanced anisotropic turbulence across he entire channel, in the conducting channel the improvement results from an increase in the velocity near the heated wall as well as enhancement of turbulence in the vicinity of this wall.
1. Introduction Heat transfer experiments recently initiated at the Ben-Gurion University (BGU) Center for MHD Studies (CMHDS) [l] clearly demonstrated that in a channel made of nearly non-conducting walls (to be referred to as a non-conducting channel) a transverse magnetic field can significantly enhance the Nusselt number of liquid metal forced flows. This heat transfer enhancement is attributed [l] to the establishment, by the magnetic field, of a strongly anisotropic turbulent flow. The resulting heat transfer enhancement can have significant implications on the design and performance of self-cooled liquid metal blankets for fusion reactors
WI. The creation of the anisotropic turbulence is attributed by Branover and Sukoriansky [3,4] to an inverse energy cascade process in which small scale vortices, whose axes of rotation are parallel to the field direction, grow into large scale vortices. The field suppresses the velocity fluctuations in the field direction. The resulting anisotropic turbulence causes no substantial momentum transfer (i.e. no pressure drop enhancement). The creation and maintenance of the enhanced anisotropic turbulence requires the injection of turbulent energy (having vorticity components in the field direction). In non-conducting channels this energy injection 0920-3796/89/$03.50
0 Elsevier
Science
Publishers
is established by inserting into the channel a grid of bars whose axes are parallel to the field direction. Most of the magnetic field enhanced heat transfer experiments performed thus far at the BGU CMHDS were carried out in non-conducting channels. Preliminary measurements performed in conducting channels also indicated heat transfer enhancement [l]. Surprisingly, no external turbulence-inducing means were found necessary in conducting channels. The injection of turbulent energy in these channels appears to come from flow instabilities created by strong velocity gradients in the vicinity of the channel walls [l].
The purpose of the present work is to report results from additional measurements recently carried out in a conducting channel as well as to present as yet unpublished results for non-conducting channels. Among other results, this work presents for the first time temperature profiles measured across a flow channel subjected to a magnetic field.
2. Description
of the experiments
All the measurements were performed with using the experimental set-up described in ref. only difference is the addition of a fixture to thin thermocouple (OS-mm thick epoxy B.V.
mercury [l].
The
move a coated
S. Sukorianksy et al. / MHD enhancement of heat transfer
218 Thefmocoup!es,
Heating Elemenl
6bB
:iZ:-;l
2b = 5.6 cm
Grid
Fig.
1. Schematic
diagram
of the flow channel used for heat transfer measurements.
chromel-alumel) across the flow channel, at the end of the heated section, as illustrated in fig. 1. The heating element (70 cm X 2.65 cm) provides a uniform heat flux to the upper face of the channel. The thermally insulated channel is located inside the bore of an electromagnet having an 80-cm pole length. The charmel is made of stainless steel walls, l-mm thick on top and 2-mm thick elsewhere. As the wetting of steel by mercury is poor, the measurements carried with this flow channel correspond to liquid metal flows in nonconducting channels. In order to study MHD effects in liquid metal flows in conducting channels, a tin plated copper sleeve was inserted inside the stainless steel channel. The thickness of the sleeve walls are 3 mm and 1.5 mm in the faces parallel and perpendicular to the field dire&ion, respectively. In addition to the variable position thermocouple described above, fixed position thermocouples are used to measure the liquid metal temperature prior to the entrance into the test section,
on the surface of the heated wall in contact with the liquid metal (T,), and downstream of the heating section ( Tb) where a uniform temperature is re-established across the charmel (see fig. 1). All the experiments reported in this work were performed using a total heating power of 500 W. The heat transfer coefficient (or Nusselt number) deduced from the temperature difference measurements was found, as expected, to be independent of the heating power level. All the measurements pertaining to the non-conducting charmel reported in this work were performed using a grid consisting of lo-mm thick rods spaced 4 mm apart.
3. Results 3.1. Non-conducting
channel
Typical raw temperature measurement are illustrated
data obtained in a single in fig. 2. The effect of the
-40
rk 17400
I
NU
Rezs8all
30 20
Re.4400
10 k
TPC)
Fig. 2. An illustration of the raw temperature data recorded in the nonconducting channel subjected to three values of magnetic field strength: (a) no field; (b) 0.22 T, and (c) 0.6 T. Lime 1 records the bulk liquid metal temperature at the channel entrance. The dots represent the temperature reading of the liquid metal in contact with the heated surface.
01
. I
1
10 N+l
100
Fig. 3. Effect of the magnetic field on the Nusselt number for liquid metal flow velocity of 15.1 cm/s (A); 7.6 cm/s (U); 3.8 cm/s (+I.
S. Sukorianksy
7”
et al. / MHD
279
of heat transfer 10
GRID BARS ORIENTATI II B
N”
enhancement
l
6
A
B = 0.0 T (M = 0) B=06T(M=166)
35
25 LB
I 10
20
0
10
Distance
M/Re’lO”
Fig. 4. Effect of the turbulence inducing grid orientation on the magnetic field effect on heat transfer. Liquid metal flow velocity is 15.1 cm/s (Re = 17400).
magnetic field on the heat transfer is illustrated in fig. 3. Shown in the figure is the Nusselt number (Nu a heat transfer coefficient) as a function of the interaction parameter (N a B*/U) for three. flow velocities. The minimum of the Nu number is the outcome of two competing effects of the magnetic field; suppression of the isotropic turbulence prevailing in the zero field regime (N = O(1)) and the buildup of anisotropic turbulence. This buildup, and the corresponding Nu number, increase up to the maximum interaction parameter attainable in the present experimental setup. The Nu number arrived at with the maximum magnetic field is significantly higher than the Nu number corresponding to no field, and even more so, to field suppressed turbulence flow regime. Fig. 4 illustrates the effect of the grid orientation on the Nusselt number. It is observed that whereas the grid
= A
Fig. 6. Effect
20 30 40 from heated wall [mm]
of magnetic field on the velocity the conducting channel.
t
distribution
in
is aligned parallel to the field direction, the increase in the magnetic field strength can significantly enhance the Nu number, when the grid is aligned with its bars perpendicular to the field direction the magnetic field has only a very small effect. In fact, with the perpendicular orientation the grid has practically no effect on the attainable Nu number. Presently we have no clear explanation for the Nu number tendency to increase at the high field regime; it may be due to small turbulence induced at the entrance to the channel. The above observations appear to be consistent, as a general trend, with the corresponding effect of the magnetic field on the turbulence structure and on the turbulence intensity [3,41. 3.2. Conducting
channel
The effect of the magnetic field on the temperature, velocity and turbulence intensity measured across the
S-O.OT S-0.6T +
0
10 distance
20 40 30 from bottom wall [mm]
Fig. 5. Effect of magnetic field on the temperature across the conducting channel. ~7= 2.7 W/cm*; (Re = 17200).
50
0 distribution U = 18 cm/s
Fig. 7. Effect
2.0
10
distance
from wall [mm]
of magnetic field on turbulence intensity conducting channel. U = 18 cm/s.
in the
280
S. Sukorianksy
t-1 al. / h4HD
conducting channel is illustrated in figs. 5-7. The velocities were measured using hot film thermoanemometric probes. The interaction of the magnetic field with the liquid metal flow in the conducting channel makes it very difficult to accurately calibrate these probes. Also, the adherence of impurities on the probe as well as small temperature drifts introduce experimental errors in velocity measurements. Therefore, the velocity results should be taken as indicating a general trend rather than as providing accurate absolute values. Ah the temperature measurements performed so far in the conducting channel show that the application of the magnetic field improves the heat transfer; the stronger the field the steeper the temperature gradient and the lower the wall temperature. The improvement in the heat transfer with the application of (and increase in) the magnetic field may be due to the enhancement of turbulence and/or to an increase in the liquid metal velocity near the heated wall. Figs. 6 and 7 indicate that both phenomena take place in our system. The M-shaped velocity profile created by the field (fig. 6) brings about a significant increase in the velocity near the heated wall which could explain, qualitatively, the change of the temperature profile (fig. 5). Nevertheless, fig.7 clearly shows that the application of the magnetic field also significantly enhances the turbulence intensity in the vicinity of the channel wall. The spatial dependence of the turbulence intensity appears to indicate that it is excited by flow instabilities in the vicinity of the peaks of the M-shaped velocity profile (see fig. 6). Another illustration of the turbulence enhancement by the magnetic field is provided by fig. 8. These oscilloscope
enhancement
o/heat
transfer
>
0
I
1
2.0
1.5
1 2
r’
;
I
3
I
4
1.0
I-
0.5
1 6
11 0.0 I
I
I
I
I
10
14
18
22
26
T (“Cl Fig. 9. Raw data of the temperature profile across the channel with conducting walls. Line (1) is the bulk liquid metal temperature at the channel entrance. Line (2) is the temperature at different wall distances with the 0.6. T field alternately turned on (B) and off (0).
Fig. 8. Oscilloscope view of turbulence pulsations in the conducting channel without (left) and with (right) the magnetic field (0.6 T).
S. Sukorianksy
et al. / MHD
pictures of turbulent pulsations show that the field significantly increases the amplitude of the pulsations and decreases their frequency. It appears that the field enhances the heat transfer in conducting channels both by “M-shaping” the velocity profile and by enhancing turbulence. The relative contribution of the two phenomena is yet to be determined. Additional insight to the effect of the field on the liquid metal temperature is provided by fig. 9. Shown in the figure are raw temperature data measured at selected points across the channel with and without the field. Notice that the bulk liquid metal temperature drift was negligible during the temperature measurements at a given point. In addition to a reduction of the liquid metal temperature, the application of the field is seen to reduce the temperature fluctuations. This trend is opposite to that observed for the non-conducting channel (see fig. 2). The interpretation of these phenomena is not yet clear.
4. Relevance to previous experiments We are aware of only a limited number of experimental studies of the effect of a transverse magnetic field on liquid metal heat transfer [5-91. None of these experiments was designed to provide the conditions (such as turbulence inducing means) required for the establishment of enhanced turbulence. Moreover, even if they were to establish enhanced turbulence, at least several of these experiments did not have the directionality in the heat transfer that is required for its enhancement. Thus, for example, the test section in the experiments by Gardner et al. [5,6] was heated uniformly all around, whereas in the present experiments only one of the channel walls parallel to the field direction was heated. Due to the directionality of the flow vortices established in the experiment we do not expect heat transfer enhancement in the direction perpendicular to the field direction. Miyazaki et al. [9] used an annular flow channel with a heating element at its center. This geometry introduces complicated three-dimensional effects making it difficult to analyze. It is interesting to note, though, that whereas in the directions parallel to the magnetic field the increase in the field strength caused a general decrease in the Nu number, in the perpendicular direction (which is the direction considered in our experiments), the Nu number tended to increase with the increase in the field strength. This trend is in general agreement with our observations.
enhancement
of heat transfer
281
5. Relevance to fusion reactor blanket conditions Fig. 10 shows the domain in the Hartmann (M)-Reynolds (Re) number space covered by the present experiments (using mercury) at BGU and the domain that will shortly be accessible to us by using a NaK facility. Also shown in the figure are four M-Re values corresponding to design points of two fusion reactor blanket concepts: the poloidal/ toroidal tokamak blanket designed as part of the Blanket Comparison and Selection Study (BCSS) [lo], and a poloidal blanket recently suggested for the compact. reversed field pinch reactor TITAN [ll]. The dimensionless parameters accessible by our experiments correspond to the channel half-width in the field direction and to the hydraulic radius for, respectively, rectangular and circular channels. Two of the designs are characterized by an interaction parameter (N) which is in the range already accessed by the BGU experiments although at a Re which is significantly higher. However, the experimental evidence shows that the higher the Re, the stronger becomes the heat transfer enhancement. Moreover, we expect [l] that an increase in N and M by 2 to 3 orders of magnitude (needed for extending the domain reached so far to the design points of the other two blankets) will not eliminate the possibility of creating and maintaining enhanced anisotropic turbulence. The effect of almost two orders of magnitude increase in Non enhanced turbulence and heat transfer could be experimentally tested at the BGU NaK facility. This facility will also allow the study of MHD effects in flows parallel to the field.
Fig. 10. The domain in the M-Re space covered (using Hg) and to be covered (using NaK) by the BGU experiments in comparison with design points of representative self-cooled
liquid metal blankets.
S. Sukorionksy
282
6. Concluding
et al. / MHD
remarks
The experimental evidence accumulated so far at the BGU CMHDS clearly indicates that the application of a uniform transverse magnetic field to a liquid metal flow in a rectangular channel can enhance turbulence and improve the heat transfer from the walls parallel to the field direction in both conducting and non-conducting channels. In the non-conducting channel the fieldenhanced turbulence is highly anisotropic and spans over the entire channel cross-section. In the conducting channel, on the other hand, the enhanced turbulence strongly peaks near the regions close to the walls parallel to the field direction; its nature is not yet fully understood. Whereas there is clear evidence that the field-enhanced anisotropic turbulence is responsible for the heat transfer improvement in the non-conducting channel, the contribution of the enhanced turbulence to the observed improvement of heat transfer in the conducting channel is yet to be determined. The experimental set-up used for the measurements closely simulates the first wall conditions in many fusion reactor designs. Moreover, the interaction parameter obtained so far in our experiments is of relevance to a number of specific designs suggested. The BGU CMHDS experimental data accumulated so far provide no evidence to suggest that the enhanced heat transfer will not persist to the higher Hartmann and Reynolds numbers typical of common designs of fusion reactors. Nevertheless, many more experiments and theoretical analyses are required in order to thoroughly understand the creation of a magnetic field-enhanced turbulence and heat transfer. These experiments should cover a large domain of flow conditions, channel geometry and conductivity, magnetic field intensity and direction, as well as of turbulence inducing means.
Acknowledgements This work was supported by Solmecs (Israel) Ltd.. Many thanks are due to Charles Henoch and Ilya
enhoncemenr
of heat rransfer
Zilberman for their help in the preparation of the experiments.
and running
References [I]
S. Sukoriansky, H. Branover, D. KIaiman and E. Greenspan, Heat transfer enhancement possibilities and imphcations for Liquid metal blanket design, Proc. 12th IEEE Symp. on Fusion Engineering, Monterey, CA (Oct. 1987). [Z] H. Branover, E. Greenspan, S. Sukoriansky and G. Tahnage, Turbulence and the feasibility of self-cooled liquid metal blankets for fusion reactors, Fusion Technol. 10 (1986) 822. and S. Sukoriansky, MHD turbulence with ]31 H. Branover inverse energy cascade and enhanced heat transfer, Proc. 25th Symp. on Engineering Aspects of Magnetohydrodynamics, Bethesda, Maryland (1987). pp. 6.4.1-6.4.15. and H. Branover, Turbulent flows with 141 S. Sukoriansky inverse energy cascade realizable in a laboratory, J. Fluid Mech. (submitted). K.L. Uherka and P.S. Lykoudis, Influence ]51 R.A. Gardner, of a transverse magnetic field on forced convection Iiquid-metal heat transfer, AIAA J. 4 (1966) 848. [61R.A. Gardner and P.S. Lykoudis, Magneto-fluid-mechanic pipe flow in a transverse magnetic field, Part 2: Heat transfer, J. Fluid Mech. 48 (1971) 129. The effect of a transverse magnetic 171 E.Yu. Krasil’nikov, field upon convective heat transfer in magnetohydrodynamic channel flows, Magnetohydrodynamics 1 (1965) 26. 181E.Ya Blum, Effect of magnetic field on heat transfer in the turbulent flow of a conducting liquid, High Temp. 5 ]91
WI
(1967) 68. K. Miyazaki
et al., Heat transfer and temperature fluctuation of lithium flowing under transverse magnetic field, J. Nucl. Sci. Technol. 23 (1986) 582. D.L. Smith et al., Blanket comparison and selection study
- final report, Argonne ANL/FPP-84-l The TITAN 1111
National
(1984). research group,
The
Laboratory TITAN
Report
reversed-field
pinch fusion reactor study, The collection of papers presented at IEEE 12th Symp. on Fusion Engineering, Monterey, CA, 12-16 Oct. 1987. University of California LA Report UCLA-PPG-1110 (Oct. 1987).
8 (1989)
MI-ID ENHANCEMENT REACTOR BLANKET
S. SUKORIANSKY, Center for MHD
277-282
OF HEAT TRANSFER DESIGN
D. KLAIMAN,
Studies,
211
Ben-Gurion
University
AND ITS RELEVANCE
TO FUSION
H. BRANOVER of the Negev,
P.O.
Box 653, Beer-Shevo
84105,
Israel
E. GREENSPAN Atomic
Energy
Commission,
P.O. Box 7061, Tel-Aviv,
61070,
Israel
The effect of a uniform magnetic field on the heat transfer of liquid metal forced flows in straight rectangular channels subjected to a uniform heat flux on one of the walls parallel to the field is experimentally studied. The experiments covered the domain 3.8 Q U d 18 cm/s; 0 d B d 0.9 T; 0 d M d 300 and 4 X 10’ Q Re < 2 X 104. It is found that the application of the magnetic field improves the heat transfer in channels made of both non-conducting walls and of conducting walls. Whereas in the former case this improvement results from the creation of enhanced anisotropic turbulence across he entire channel, in the conducting channel the improvement results from an increase in the velocity near the heated wall as well as enhancement of turbulence in the vicinity of this wall.
1. Introduction Heat transfer experiments recently initiated at the Ben-Gurion University (BGU) Center for MHD Studies (CMHDS) [l] clearly demonstrated that in a channel made of nearly non-conducting walls (to be referred to as a non-conducting channel) a transverse magnetic field can significantly enhance the Nusselt number of liquid metal forced flows. This heat transfer enhancement is attributed [l] to the establishment, by the magnetic field, of a strongly anisotropic turbulent flow. The resulting heat transfer enhancement can have significant implications on the design and performance of self-cooled liquid metal blankets for fusion reactors
WI. The creation of the anisotropic turbulence is attributed by Branover and Sukoriansky [3,4] to an inverse energy cascade process in which small scale vortices, whose axes of rotation are parallel to the field direction, grow into large scale vortices. The field suppresses the velocity fluctuations in the field direction. The resulting anisotropic turbulence causes no substantial momentum transfer (i.e. no pressure drop enhancement). The creation and maintenance of the enhanced anisotropic turbulence requires the injection of turbulent energy (having vorticity components in the field direction). In non-conducting channels this energy injection 0920-3796/89/$03.50
0 Elsevier
Science
Publishers
is established by inserting into the channel a grid of bars whose axes are parallel to the field direction. Most of the magnetic field enhanced heat transfer experiments performed thus far at the BGU CMHDS were carried out in non-conducting channels. Preliminary measurements performed in conducting channels also indicated heat transfer enhancement [l]. Surprisingly, no external turbulence-inducing means were found necessary in conducting channels. The injection of turbulent energy in these channels appears to come from flow instabilities created by strong velocity gradients in the vicinity of the channel walls [l].
The purpose of the present work is to report results from additional measurements recently carried out in a conducting channel as well as to present as yet unpublished results for non-conducting channels. Among other results, this work presents for the first time temperature profiles measured across a flow channel subjected to a magnetic field.
2. Description
of the experiments
All the measurements were performed with using the experimental set-up described in ref. only difference is the addition of a fixture to thin thermocouple (OS-mm thick epoxy B.V.
mercury [l].
The
move a coated
S. Sukorianksy et al. / MHD enhancement of heat transfer
218 Thefmocoup!es,
Heating Elemenl
6bB
:iZ:-;l
2b = 5.6 cm
Grid
Fig.
1. Schematic
diagram
of the flow channel used for heat transfer measurements.
chromel-alumel) across the flow channel, at the end of the heated section, as illustrated in fig. 1. The heating element (70 cm X 2.65 cm) provides a uniform heat flux to the upper face of the channel. The thermally insulated channel is located inside the bore of an electromagnet having an 80-cm pole length. The charmel is made of stainless steel walls, l-mm thick on top and 2-mm thick elsewhere. As the wetting of steel by mercury is poor, the measurements carried with this flow channel correspond to liquid metal flows in nonconducting channels. In order to study MHD effects in liquid metal flows in conducting channels, a tin plated copper sleeve was inserted inside the stainless steel channel. The thickness of the sleeve walls are 3 mm and 1.5 mm in the faces parallel and perpendicular to the field dire&ion, respectively. In addition to the variable position thermocouple described above, fixed position thermocouples are used to measure the liquid metal temperature prior to the entrance into the test section,
on the surface of the heated wall in contact with the liquid metal (T,), and downstream of the heating section ( Tb) where a uniform temperature is re-established across the charmel (see fig. 1). All the experiments reported in this work were performed using a total heating power of 500 W. The heat transfer coefficient (or Nusselt number) deduced from the temperature difference measurements was found, as expected, to be independent of the heating power level. All the measurements pertaining to the non-conducting charmel reported in this work were performed using a grid consisting of lo-mm thick rods spaced 4 mm apart.
3. Results 3.1. Non-conducting
channel
Typical raw temperature measurement are illustrated
data obtained in a single in fig. 2. The effect of the
-40
rk 17400
I
NU
Rezs8all
30 20
Re.4400
10 k
TPC)
Fig. 2. An illustration of the raw temperature data recorded in the nonconducting channel subjected to three values of magnetic field strength: (a) no field; (b) 0.22 T, and (c) 0.6 T. Lime 1 records the bulk liquid metal temperature at the channel entrance. The dots represent the temperature reading of the liquid metal in contact with the heated surface.
01
. I
1
10 N+l
100
Fig. 3. Effect of the magnetic field on the Nusselt number for liquid metal flow velocity of 15.1 cm/s (A); 7.6 cm/s (U); 3.8 cm/s (+I.
S. Sukorianksy
7”
et al. / MHD
279
of heat transfer 10
GRID BARS ORIENTATI II B
N”
enhancement
l
6
A
B = 0.0 T (M = 0) B=06T(M=166)
35
25 LB
I 10
20
0
10
Distance
M/Re’lO”
Fig. 4. Effect of the turbulence inducing grid orientation on the magnetic field effect on heat transfer. Liquid metal flow velocity is 15.1 cm/s (Re = 17400).
magnetic field on the heat transfer is illustrated in fig. 3. Shown in the figure is the Nusselt number (Nu a heat transfer coefficient) as a function of the interaction parameter (N a B*/U) for three. flow velocities. The minimum of the Nu number is the outcome of two competing effects of the magnetic field; suppression of the isotropic turbulence prevailing in the zero field regime (N = O(1)) and the buildup of anisotropic turbulence. This buildup, and the corresponding Nu number, increase up to the maximum interaction parameter attainable in the present experimental setup. The Nu number arrived at with the maximum magnetic field is significantly higher than the Nu number corresponding to no field, and even more so, to field suppressed turbulence flow regime. Fig. 4 illustrates the effect of the grid orientation on the Nusselt number. It is observed that whereas the grid
= A
Fig. 6. Effect
20 30 40 from heated wall [mm]
of magnetic field on the velocity the conducting channel.
t
distribution
in
is aligned parallel to the field direction, the increase in the magnetic field strength can significantly enhance the Nu number, when the grid is aligned with its bars perpendicular to the field direction the magnetic field has only a very small effect. In fact, with the perpendicular orientation the grid has practically no effect on the attainable Nu number. Presently we have no clear explanation for the Nu number tendency to increase at the high field regime; it may be due to small turbulence induced at the entrance to the channel. The above observations appear to be consistent, as a general trend, with the corresponding effect of the magnetic field on the turbulence structure and on the turbulence intensity [3,41. 3.2. Conducting
channel
The effect of the magnetic field on the temperature, velocity and turbulence intensity measured across the
S-O.OT S-0.6T +
0
10 distance
20 40 30 from bottom wall [mm]
Fig. 5. Effect of magnetic field on the temperature across the conducting channel. ~7= 2.7 W/cm*; (Re = 17200).
50
0 distribution U = 18 cm/s
Fig. 7. Effect
2.0
10
distance
from wall [mm]
of magnetic field on turbulence intensity conducting channel. U = 18 cm/s.
in the
280
S. Sukorianksy
t-1 al. / h4HD
conducting channel is illustrated in figs. 5-7. The velocities were measured using hot film thermoanemometric probes. The interaction of the magnetic field with the liquid metal flow in the conducting channel makes it very difficult to accurately calibrate these probes. Also, the adherence of impurities on the probe as well as small temperature drifts introduce experimental errors in velocity measurements. Therefore, the velocity results should be taken as indicating a general trend rather than as providing accurate absolute values. Ah the temperature measurements performed so far in the conducting channel show that the application of the magnetic field improves the heat transfer; the stronger the field the steeper the temperature gradient and the lower the wall temperature. The improvement in the heat transfer with the application of (and increase in) the magnetic field may be due to the enhancement of turbulence and/or to an increase in the liquid metal velocity near the heated wall. Figs. 6 and 7 indicate that both phenomena take place in our system. The M-shaped velocity profile created by the field (fig. 6) brings about a significant increase in the velocity near the heated wall which could explain, qualitatively, the change of the temperature profile (fig. 5). Nevertheless, fig.7 clearly shows that the application of the magnetic field also significantly enhances the turbulence intensity in the vicinity of the channel wall. The spatial dependence of the turbulence intensity appears to indicate that it is excited by flow instabilities in the vicinity of the peaks of the M-shaped velocity profile (see fig. 6). Another illustration of the turbulence enhancement by the magnetic field is provided by fig. 8. These oscilloscope
enhancement
o/heat
transfer
>
0
I
1
2.0
1.5
1 2
r’
;
I
3
I
4
1.0
I-
0.5
1 6
11 0.0 I
I
I
I
I
10
14
18
22
26
T (“Cl Fig. 9. Raw data of the temperature profile across the channel with conducting walls. Line (1) is the bulk liquid metal temperature at the channel entrance. Line (2) is the temperature at different wall distances with the 0.6. T field alternately turned on (B) and off (0).
Fig. 8. Oscilloscope view of turbulence pulsations in the conducting channel without (left) and with (right) the magnetic field (0.6 T).
S. Sukorianksy
et al. / MHD
pictures of turbulent pulsations show that the field significantly increases the amplitude of the pulsations and decreases their frequency. It appears that the field enhances the heat transfer in conducting channels both by “M-shaping” the velocity profile and by enhancing turbulence. The relative contribution of the two phenomena is yet to be determined. Additional insight to the effect of the field on the liquid metal temperature is provided by fig. 9. Shown in the figure are raw temperature data measured at selected points across the channel with and without the field. Notice that the bulk liquid metal temperature drift was negligible during the temperature measurements at a given point. In addition to a reduction of the liquid metal temperature, the application of the field is seen to reduce the temperature fluctuations. This trend is opposite to that observed for the non-conducting channel (see fig. 2). The interpretation of these phenomena is not yet clear.
4. Relevance to previous experiments We are aware of only a limited number of experimental studies of the effect of a transverse magnetic field on liquid metal heat transfer [5-91. None of these experiments was designed to provide the conditions (such as turbulence inducing means) required for the establishment of enhanced turbulence. Moreover, even if they were to establish enhanced turbulence, at least several of these experiments did not have the directionality in the heat transfer that is required for its enhancement. Thus, for example, the test section in the experiments by Gardner et al. [5,6] was heated uniformly all around, whereas in the present experiments only one of the channel walls parallel to the field direction was heated. Due to the directionality of the flow vortices established in the experiment we do not expect heat transfer enhancement in the direction perpendicular to the field direction. Miyazaki et al. [9] used an annular flow channel with a heating element at its center. This geometry introduces complicated three-dimensional effects making it difficult to analyze. It is interesting to note, though, that whereas in the directions parallel to the magnetic field the increase in the field strength caused a general decrease in the Nu number, in the perpendicular direction (which is the direction considered in our experiments), the Nu number tended to increase with the increase in the field strength. This trend is in general agreement with our observations.
enhancement
of heat transfer
281
5. Relevance to fusion reactor blanket conditions Fig. 10 shows the domain in the Hartmann (M)-Reynolds (Re) number space covered by the present experiments (using mercury) at BGU and the domain that will shortly be accessible to us by using a NaK facility. Also shown in the figure are four M-Re values corresponding to design points of two fusion reactor blanket concepts: the poloidal/ toroidal tokamak blanket designed as part of the Blanket Comparison and Selection Study (BCSS) [lo], and a poloidal blanket recently suggested for the compact. reversed field pinch reactor TITAN [ll]. The dimensionless parameters accessible by our experiments correspond to the channel half-width in the field direction and to the hydraulic radius for, respectively, rectangular and circular channels. Two of the designs are characterized by an interaction parameter (N) which is in the range already accessed by the BGU experiments although at a Re which is significantly higher. However, the experimental evidence shows that the higher the Re, the stronger becomes the heat transfer enhancement. Moreover, we expect [l] that an increase in N and M by 2 to 3 orders of magnitude (needed for extending the domain reached so far to the design points of the other two blankets) will not eliminate the possibility of creating and maintaining enhanced anisotropic turbulence. The effect of almost two orders of magnitude increase in Non enhanced turbulence and heat transfer could be experimentally tested at the BGU NaK facility. This facility will also allow the study of MHD effects in flows parallel to the field.
Fig. 10. The domain in the M-Re space covered (using Hg) and to be covered (using NaK) by the BGU experiments in comparison with design points of representative self-cooled
liquid metal blankets.
S. Sukorionksy
282
6. Concluding
et al. / MHD
remarks
The experimental evidence accumulated so far at the BGU CMHDS clearly indicates that the application of a uniform transverse magnetic field to a liquid metal flow in a rectangular channel can enhance turbulence and improve the heat transfer from the walls parallel to the field direction in both conducting and non-conducting channels. In the non-conducting channel the fieldenhanced turbulence is highly anisotropic and spans over the entire channel cross-section. In the conducting channel, on the other hand, the enhanced turbulence strongly peaks near the regions close to the walls parallel to the field direction; its nature is not yet fully understood. Whereas there is clear evidence that the field-enhanced anisotropic turbulence is responsible for the heat transfer improvement in the non-conducting channel, the contribution of the enhanced turbulence to the observed improvement of heat transfer in the conducting channel is yet to be determined. The experimental set-up used for the measurements closely simulates the first wall conditions in many fusion reactor designs. Moreover, the interaction parameter obtained so far in our experiments is of relevance to a number of specific designs suggested. The BGU CMHDS experimental data accumulated so far provide no evidence to suggest that the enhanced heat transfer will not persist to the higher Hartmann and Reynolds numbers typical of common designs of fusion reactors. Nevertheless, many more experiments and theoretical analyses are required in order to thoroughly understand the creation of a magnetic field-enhanced turbulence and heat transfer. These experiments should cover a large domain of flow conditions, channel geometry and conductivity, magnetic field intensity and direction, as well as of turbulence inducing means.
Acknowledgements This work was supported by Solmecs (Israel) Ltd.. Many thanks are due to Charles Henoch and Ilya
enhoncemenr
of heat rransfer
Zilberman for their help in the preparation of the experiments.
and running
References [I]
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