Modeling of thermal-hydraulic effects of AC losses in the ITER Central Solenoid Insert Coil using the M&M code
ABSTRACT During 2000, AC losses and the effects of possible ramp-rate limitation (RRL) were investigated on the International Thermonuclear Experimental Reactor (ITER) Central Solenoid Insert Coil (CSIC), at JAERI Naka, Japan. The CSIC was mounted inside the bore of the ITER Central Solenoid Model Coil (CSMC), at the maximum field of about 13 T and experiencing the largest magnetic field variations. The thermal-hydraulic response of the coil to different transport current scenarios was assessed by measuring the temperature increase and pressurization of the supercritical helium (SHe) coolant, together with the evolution of the mass-flow rate. Here we implement in the M&M code a detailed general model of AC losses, which is being validated for the first time. The resulting tool is then applied to the analysis of two CSIC tests, with different ramp-up of the transport current followed by the same dump, and used to qualitatively assess the major thermal-hydraulic effects of AC losses in the coil.
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ABSTRACT: The CS Insert Coil (CSIC), a well-instrumented 140 m long Nb3Sn solenoid wound one-in-hand and installed in the bore of the CS Model Coil, was tested during the summer of 2000 at JAERI Naka, Japan, within the framework of the International Thermonuclear Experimental Reactor large projects . The maximum transport current in the CSIC was 40 kA and the peak background field was 13 T. The coils were cooled by forced flow HeI nominally at 4.5 K and 0.6 MPa. An inductive heater was used to test stability and quench of the CSIC. In this second of two companion papers we concentrate on the analysis of quench initiation and propagation, based on the study of heater calibration and conductor stability presented in the first paper . The initiation and propagation of an inductively driven quench was tested here for the first time in a two-channel Nb3Sn conductor, for different transport currents, delay times of the dump, and temperature margins, and a selection of the corresponding results will be presented and discussed. We use the Mithrandir code  to analyze this problem and compare the simulation with the experimental results for the evolution of resistive voltage and quench propagation speed, of peak temperature and pressure, and of inlet and outlet mass-flow rate. © 2002 American Institute of Physics.AIP Conference Proceedings. 05/2002; 613(1):423-430.
Progress of the ITER central solenoid model coil program. 2001. Nucl. Fusion 41 645-651..
First test results for the ITER central solenoid model coil. 2001. Fus. Eng. Des 56-57..
1424IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO. 2, JUNE 2003
Modeling of Thermal-Hydraulic Effects of AC Losses
in the ITER Central Solenoid Insert Coil Using the
Roberto Zanino, Laura Savoldi Richard, and Elena Zapretilina
Abstract—During 2000, AC losses and the effects of possible
ramp-rate limitation (RRL) were investigated on the International
Thermonuclear Experimental Reactor (ITER) Central Solenoid
inside the bore of the ITER Central Solenoid Model Coil (CSMC),
at the maximum field of about 13 T and experiencing the largest
magnetic field variations. The thermal-hydraulic response of the
coil to different transport current scenarios was assessed by mea-
suring the temperature increase and pressurization of the super-
critical helium (SHe) coolant, together with the evolution of the
mass-flow rate. Here we implement in the M&M code a detailed
general model of AC losses, which is being validated for the first
time. The resulting tool is then applied to the analysis of two CSIC
tests, with different ramp-up of the transport current followed by
hydraulic effects of AC losses in the coil.
Index Terms—AC losses, computational thermal-hydraulics, fu-
sion reactors, ITER, superconducting coils.
heat source can lead to initiation of a normal zone and, possibly,
a significant part of the tests – performed during 2000 on
the intensity and effects of AC losses.
The CSIC is a Nb3Sn single-layer solenoid,
wound one-in-hand and positioned inside the bore of the ITER
CSMC, at the maximum field of
dual-channel structure typical of ITER .
In order to assess the major thermal-hydraulic effects of AC
losses in the CSIC, we implement here in the M&M code , a
validated tool already used for thermal-hydraulic analysis of the
ITER Model Coil experiments, a model for AC losses, already
used for the predictive analysis of the ITER magnets , but
validated here for the first time.
C LOSSES are an essential item in the design and opera-
tion of superconducting magnets, because the associated
140 m long,
13 T. The conductor is of the
was supported in part by the European Fusion Development Agreement and by
Associazione per lo Sviluppo Scientifico e Tecnologico del Piemonte.
R. Zanino and L. Savoldi Richard are with the Dipartimento di Energetica,
Politecnico, I-10129 Torino, Italy.
E. Zapretilina is with the ITER IT (as Visiting Personnel), Naka JWS, Japan,
on leave from the Scientific-Research Institute of Electro-Physical Apparatus
(NIIEFA, Efremov Institute), St. Petersburg, Russia (e-mail: zaprete@itergps.
Digital Object Identifier 10.1109/TASC.2003.812687
indicate temperature sensors, pressure taps, and flow meters, respectively.
Schematic view of the CSMC?CSIC hydraulic circuit. ?, ?, and ?
II. EXPERIMENTAL SETUP
The CSMC and CSIC tests are already described in detail
elsewhere –. While AC losses were investigated using a
standard trapezoidal cycle , the largest effects of these losses
were clearly seen in the RRL tests, where the stability of the
variation (actually even beyond the original goal of 0.4 T/s) up
to 13 T, using the power supplies of the JAERI tokamak JT-60
TheCSICis welldiagnosed from thethermal-hydraulic point
of view (see Fig. 1): the response of the coil to different sce-
narios of transport current variation can be assessed by mea-
suring the temperature “ ” and pressure “ ” increase at the
inlet, center and outlet of the conductor, together with the vari-
ation of the SHe coolant mass-flow rate at the inlet and outlet.
The whole cryogenic circuit (parallel) of CSIC CSMC, shown
in Fig. 1, will play an essential role in the assessment of the
thermal-hydraulic effects of AC losses in the CSIC.
A. Thermal-Hydraulic Model
The thermal-hydraulic model used here is that implemented
in the Multi-conductor Mithrandir (M&M) code . M&M al-
lows thesimulation of thermal-hydraulic transients in coils with
different complex topologies, e.g., layer wound as in the case of
the CSMC , or pancake wound as in the case of the ITER
Toroidal Field Model Coil . The single-conductor model on
which M&M is based, i.e., the Mithrandir model, was already
successfully applied in the past to the analysis of stability and
1051-8223/03$17.00 © 2003 IEEE
ZANINO et al.: MODELING OF THERMAL-HYDRAULIC EFFECTS OF AC LOSSES1425
Fig. 2.Hydraulic circuit model adopted in the M&M simulations.
quench tests in the CSIC , . However, in the case of longer
time-scale transients as those considered here, the role of all the
other channels, hydraulically in parallel with the CSIC, may be
very important, so that the Mithrandir model may be insuffi-
cient, and M&M is needed.
Different models with increasing sophistication of the
hydraulic circuit have been used here, from an open single
conductor with experimental inlet (
boundary conditions, to a closed circuit including the hydraulic
parallel of the CSIC, and of 8 conductors representing the four
innermost layers of the inner module of the CSMC, as shown
in Fig. 2. (In this case, also the thermal coupling between the
CSIC and its superconducting busbars is taken into account.)
In comparing the two approaches it may be said that the
experimental boundary conditions are simplest in principle,
but may in practice turn out to be too coarse (low sampling
rate data) or too noisy (high sampling rate data). On the other
hand, the full circuit model allows a more detailed analysis of
the effects of the hydraulic parallel, as well as a validation of
the predictive capabilities of the computational tool, although
some of the quantities to be modeled, e.g., the mass flow rate
evolution, can be very sensitive to parameters like the volume
of the manifolds in the circuit, which is in turn affected by
and) and outlet ( )
B. AC Losses Model
The approach to the CS Insert AC-loss modeling is very sim-
ilar totheone describedin,butthemodelis beingvalidated
used for the ITER magnets , . The conductor AC losses
are treated as the sum of two components—hysteresis and cou-
pling, each of which can be assessed independently. The mag-
is computed at a representative number of points
placed over the coil length (one point per turn in the case at
hand). Then the code analyzes field evolution and conductor
and the filament strain ) at each observation point, for thecom-
putation of the loss components.
The experimental database, provided by strand/cable manu-
facturers gives, in addition to the conductor geometrical data
(cable layout, strand diameter, Cu:non-Cu ratio, cross sections,
etc.), measured values of the noncopper critical current density
(at 12 T, 4.2 K,
%) and of the hysteresis loss energy
for a standard ( 3 T) pulse. For the CSIC witness strand, these
are 685 A/mm
and 92 mJ/cm
filament diameter estimated using these two characteristic
values, and used for the hysteresis loss assessment, is about
m. The hysteresis losses in the CSMC and CS Insert
conductors were measured during very slow current ramps
( 1 kA/min). During relatively fast test pulses (i.e., for dB/dt
0.3 T/s) the total losses in the CSIC are dominated by the
A convenient and common way to assess the coupling losses
in a coil is to employ the effective time constant (
ever, a definition of the time constant for a multistage cable is
not so obvious. It ranges from a scaling coefficient, which value
can be found from the linear part of the loss vs. frequency (field
rate) plot, to a function combining several dominant time con-
stants interacting by shielding with weighted volume fractions
. An accurate prediction of
more complicated. Estimations of
a series of loss measurements performed with short samples of
ITER sub- and full-size cables and ITER relevant coils before
behavior were observed.
— A single time constant could hardly give a good ac-
curacy of loss assessment over an extended range of
ITER-relevantfield rates (from 0 to 1–2 Hz frequency)
. In other words, the apparent time constant ap-
peared to be “field rate dependent” , .
— It was found  that the losses in a cable loaded with
mechanical pressure (or Lorentz force
until they finally settled at a certain level.
— Even the “settled”
sitive”: the larger was the transverse force applied, the
higher were the losses produced by a conductor under
a pulsed field .
To a certain extent all the above-mentioned effects were seen
during the CSMC and CS Insert test . Depending on the test
conditions, the estimated
values for the CSIC range from
15 ms —relatively fast pulse with the Insert carrying no
current, to over 50 ms —relatively slow discharge and rather
high current/field level.
The coupling losses are simulated here with a single
However, two approaches are suggested. The first approach is
to find a value of
that would give a good fit for the total loss
energy generated over the considered field pulse. As the se-
lected test conditions here are “relatively fast (
full current pulse” the probable
25–30 ms. The second one is an attempt to introduce a certain
“ -function,” which would reflect the major tendencies of the
behavior: field rate and transverse load depen-
dence. This is supposed to give a better picture of loss evolution
during the test pulse. For the first try we use the following
respectively. The effective
value for a cable is even
were carried out during
remained “transverse load sen-
figure should be around
force load history
1426IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO. 2, JUNE 2003
is a function of the field rate
ficient can be written as
and are correction coefficients responsible for the
(T/s). The transverse load coef-
history” coefficient (
T46 kA600 kN/m. The “load
) for the given case can be taken as 1.
-function can be written as
ms corresponds to the time constant at a “very
T/s, and is a fitting parameter.
C. Coupling Between Thermal-Hydraulic and AC Losses
The coupling between the two models must have in prin-
ciple an iterative structure, as the hysteresis losses depend on
the strand temperature, whose evolution is in turn due to the
total losses. However, in view of the above-mentioned limited
Therefore, we proceed as follows: a first space and time depen-
dence of the losses (W/m) is computed with the AC losses code
using a “reasonable” guessed evolution of the temperature pro-
file along the conductor; then, a full transient (up to the selected
final time) is computed with M&M, using the just computed
losses as the driver; new AC losses are then computed using the
temperature evolution computed by M&M at the previous itera-
tion, and the full transient is re-computed with M&M using the
new losses. These two steps are typically enough for conver-
gence, loss power variations between iterations being restricted
to the second or third digit for the case at hand.
IV. RESULTS AND DISCUSSION
We begin with the analysis of shot 301-1, a RRL test per-
formed on July 20, 2000, in a sense the most performing pulsed
shot of the CSIC test campaign. The CSIC and the CSMC were
connected in series, and the transport current
at a rate of
4.1 kA/s (equivalent to
a maximum current of
44.3 kA, see Fig. 3(a). As the plateau
was reached theCSMC quenchedand after
dump of the current was performed,but no quench was revealed
of the CSIC transient, covering the whole current pulse, so that
the direct effects of AC losses can be observed.
In the AC losses model we use
ms (equivalent to
in the CSMC . (For the “average” CSMC conductor the field
map of layer 1 is used.) The computed time evolution of the
losses near the center of the conductors is shown in Fig. 3(a).
The first thermal-hydraulic effects of the AC losses in the
CSIC strands are the heating of the conductor components and
the resulting pressurization of the SHe. A comparison between
computed and measured temperatures and pressures is shown in
Fig. 3(b), (c), respectively. The qualitative evolution is correctly
reproduced by the code, although the “final” values are some-
what overestimated. The overshoot of
T/s) up to
1 s delay a manual
in the CSIC, with
constant in terms
near the end of the
center of the CSIC and of the “average” CSMC conductor. (b) Computed and
measured CSIC temperatures. (c) Computed and measured CSIC pressures.
(a) Measured transport current scenario, and computed losses in the
ramp-up, as well as the overshoot of
of the dump, are both not captured by the simulation, possibly
indicating that the AC loss model might be inadequate during
The second thermal-hydraulic effect of AC losses on the
CSIC is to induce a repartition of the helium flow among
the different parallel channels, based on their different losses
and hydraulic characteristics. Let us first of all consider the
evolution of the sum of the inlet mass flow rates in all CSMC
inner module conductors (
), and the total inlet mass flow rate in the system
), as shown in Fig. 4(a). It is clearly seen that strong losses
in the inner module, where the field is higher, lead to a strong
and this, with a possibly approximately
, leads to a strong increase of
phase of the transient. As to the CSIC, the evolution of its inlet
mass flow rate
is shown in Fig. 4(b). After a small,
almost unnoticeable reduction,
phase of the ramp-up, somewhat contrary to intuition, and only
eventually it starts decreasing as expected, because of the losses
in the CSIC itself. The initial increase of
strong decrease of
the fact that in this phase the helium temperature
increasing [see Fig. 3(b)], possibly because of mixing with the
hot helium being expelled at the inlet of the innermost CSMC
layers. However, in this phase of the transient the variations
of the CSIC inlet mass flow rate (of the order of 1 g/s) come
from differences of much larger quantities (of the order of
100 g/s), see Fig. 4, and as such they are rather sensitive to
Toward the end of the ramp-up, a strong change in the slope
is observed (synchronous with the above-mentioned
) and backflow at the CSIC inlet is revealed
, near the beginning
), its counterpart in the outer
in the first
increases in the initial
is due to the
constant, as is confirmed by
ZANINO et al.: MODELING OF THERMAL-HYDRAULIC EFFECTS OF AC LOSSES1427
(CSV_FRT_CB40XB), at inner module (IM) inlet and at outer module (OM)
inlet. (b) Computed and measured at CSIC inlet and outlet.
Evolution of the mass-flow rate. (a) Measured totals at coil inlet
bythe flow meter. This change in slope is not observed in other,
similar CSIC shots with lower ramp rate (e.g., shot 250-1 at
0.4 T/s, see below, or shot 255-1 at 0.6 T/s), and can hardly
be explained in terms of normal coil operation. It might be re-
lated to different phenomena appearing at high ramp rate. As
and thendecreasesagainbecauseofthelosses intheCSICasso-
ciated with the current dump. The outlet mass flow rate
is also shown in Fig. 4(b) and quickly increases up to saturation
of the signal.
The computed evolution of
shown in Fig. 4(b). Although most of the qualitative features
of the transient are recovered, one cannot claim a quantitative
agreement. The computed
(overestimated with respect to the experiment) due to the losses
in the CSIC, then increases, as discussed above for the experi-
mental signal, until the losses in the CSIC do not prevail again,
leading to a further reduction (underestimated with respect to
the experiment). We see a change in slope in the mass flow
tively reproduces the dump phase of the transient.
puted using experimental boundary conditions (not shown) is
qualitatively similar (also in the disagreement with the experi-
appears to strongly underestimate the measured values,
and we cannot explain the curious asymmetric behavior mea-
sured with respect to the inlet.
The measured and computed transients at the inlet of the “av-
erage” CSMC inner layer conductor are compared in Fig. 5.
Both the computed
[see Fig. 5(a)] and the computed
Fig. 5(b)] are in qualitative agreement with the average of the
corresponding values, measured at the inlet of the innermost
To assess what of the previous qualitative features may
be related to the very fast ramp rate, we have also analyzed
shot 251-1, a RRL test completely analogous to shot 301-1,
T/s is much slower. The corresponding
current scenario and computed losses are shown in Fig. 6(a),
and of is also
shows an initial reduction
temperatures. (b) Computed and measured inlet mass flow rates.
Evolution of CSMC parameters. (a) Computed and measured inlet
losses in the center of the CSIC conductor. (b) Computed and measured mass
Shot 250-1. (a) Measured transport current scenario, and computed
and the comparison between measured and computed (with
experimental boundary conditions, but otherwise the same
input parameters) mass flow rates is shown in Fig. 6(b). It is
seen that the much lower losses during the ramp cause a much
smaller reduction of
, which is well reproduced by the
code, without change in slope.
strongly and somewhat unexplained, see also . The strong
inlet backflow due to the losses during the dump is also well
reproduced by the code, indicating that most of the unexplained
features during the ramp-up of shot 301-1 should indeed be
peculiar to the fast
. The central temperature evolution
(not shown) is a little underestimated by the code.
increases again very
V. CONCLUSION AND PERSPECTIVE
A detailed model for AC losses has been implemented in the
M&M code and the resulting tool has been applied for the first
time to an analysis of the most performing CSIC pulsed shot
(field ramp-up rate
1.2 T/s, followed by a fast manual dump
1428IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO. 2, JUNE 2003
with time constant of
of the AC losses are qualitatively reproduced by the code, while
quantitative agreement is very difficult to obtain particularly for
the mass flow rate. By comparison with a lower
it was shown that some qualitative features and difficulties for
the modeling appear indeed related to the high field rate, while
We plan to apply the same tool to the analysis of the thermal-
hydraulic effects of AC losses in the CSMC, and to the analysis
of the so-called “big” quench of the CSIC.
9 s). The main thermal-hydraulic effects
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