HT-7UTF Superconducting MagnetSystem 4. Thermal analysis of TF System
4 Thermal Analysis
4.1 System Description
Toroidal field magnet system is one of the important part of HT-7U superconducting tokamak. The conductor used in the TF coils is NbTi cable-in-conductor (CICC) cooled by forced flow supercritical helium. Each of the sixteen D-shaped windings is made from double pancakes with the helium inlet located at the outermost turn nearby the joint-box of the case. The steel case is cooled by a separate cooling circuit consisting of a series of channels supplied in parallel and located in the exterior of surface of TF casing. The cross-section dimension of cooling channel is 22mm×8mm, and its wall thickness is 1.5mm, seeing fig.1. Several heat sources such as: radiation, conduction, nuclear heat, eddy currents for the case, joint resistance heat for the winding pack , and so on, are deposited on the TF coil. Most of these contributions have been calculated based on a set of parameters related to a size of HT-7U device, and an assessment of the heat power deposition on a TF coil during a regular pulse has been made. These results show that the heat deposition yielded by eddy currents for the case is the main heat source acting on the TF coil.
Fig.1 The distrubtion of cooling channels of the TF coil case
Most of the magnet cold structures are designed to carry the large electromagnetic loads arising during machine operation and, therefore, they are massive stainless steel structures, sometime of rather complicated shape, with low voltage insulating barriers incorporated into mechanical joints to reduce the level of the eddy current heating. But the TF coil case is a closed thick wall high-strengthen case surrounding the TF coil winding. The walls of the case do not have any insulation breaks, which allows eddy currents to flow around the case cross-section as well as along the case perimeter (i.e. parallel to the TF conductor), if suitable Db/dt conditions occur. These currents, when they flow through resistive structures, cause energy dissipation (eddy current losses).
The TF conductor is designed to satisfy the usual three design criteria (temperature margin, cryogenic stability and hot spot temperature) for the most sever combination (current - magnetic field - temperature – stain), the conductor gets warmer and a higher operation temperature must be assumed in the TF coil design to maintain the design temperature margin.
4.2 Thermal Analysis in TF Coil for the Case of Plasma Disruption
HT-7U tokamak is a fusion experiment device with a major radius of 1.7 m and a minor radius of 0.4 m. The magnets of the tokamak consist of 16 D-shaped coils for the toroidal field (TF), 6 coils for the central solenoid, and other 6 coils for divertor, shaping and equilibrium fields. All HT-7U coils will be wound in CIC type with NbTi/Cu as superconductor/stabilizer and supercritical helium at pressure of 4 bar and temperature of 4.2 K (recently this operation temperature was reduced to be 3.8 K), as the coolant.
For the TF coils, cases which embrace each winding pack are applied to withstand the electromagnetic force and to maintain the integrity. The case must be cooled because there is heat deposition on the cases due to thermal radiation, nuclear heating and the eddy current heating arising from the magnetic field variation. The highest heating rate on the cases occurs during the phase of the plasma disruption. By a simplified model, in the case of plasma current of 1 MA disrupting at a time constant of 3 ms, the total eddy current heat dissipation on HT-7U TF cases will be 87.5 KJ within a time of several tens’ millisecond. This amount of heat dissipation will increase the case temperature up by several degrees Kelvin and the heat would be transferred to the winding pack causing the CICC temperature margin to be reduced.
To evaluate the heat removal rate and the influence on the winding pack of HT-7U TF coils, the eddy heat evaluation and the thermal analysis by the program ANSYS have been done during the phase of major centered plasma disruption. A 1/16 solid and finite element model of the whole magnetic system is established for the integrated analysis of the electromagnetic, structural and thermal fields. In section 4.2.1, the models for the electromagnetic and thermal analysis are outlined. Using these models, we then evaluate the eddy current heating and the heat removal behavior of HT-7U TF cases. We also discuss the coupling loss in CICC due to plasma disruption. The loss rate is applied to the code GANDALF for thermal transient calculation to evaluate the stability behavior of the conductors. The results and discussion are given in section 4.2.2.
4.2.1 Finite Element Models
Because of cyclic symmetry, the whole system can be modeled by a 1/16 section of the whole toroidal direction. The 1/16 solid model is shown on the left side of fig.2. This solid model is thus meshed which is outlined on the right side of Fig 2. Due to the requirements for the electromagnetic modeling, the surrounding or filled air is also meshed. Half of the finite element model of the solid components which include vacuum vessel, case and wedges, is shown in Fig.2 in detail. In ANSYS, the coupled multi-physics coupled modeling is possible, the model shown in the figure can be used for electromagnetic, thermal and structural calculations by applying relevant physical environments.
The material used for vacuum vessel, TF case and wedges is SS-316LN. The material of the ground insulation is glass epoxy (G-10). All the material properties are temperature dependent which come from ITER database.
For the thermal-hydraulic modeling in CICC, 1-D gandalf code was used. The electromagnetic field and external heat input are coming from ANSYS calculation.
Fig.2 Solid(left) and finite element(right) models of 1/16 HT-7U magnet system
Fig. 3 Finite element model (1/32) of TF case, wedge block and vacuum vessel
4.2.1.1 Electromagnetic model, load and boundary conditions
For the electromagnetic calculation, MVP(magnetic vector potential) method is used. All the regions including the surrounding air or filled air are modeled with SOLID97 elements (hexahedral, 8 nodes). For the non-conducting regions and PF coils including plasma column, TF winding pack and ground insulation layer, only magnetic vector potential is used for DOF (the Degree Of Freedom). For the solid regions where the eddy current will appear, an extra DOF, VOLT is used. The far field elements, INFIN111, are generated by extruding the outer air surface of the modeled region to model electromagnetic far field.
In this calculation, the coupling of the PF coils is not taken into account because the decay of plasma current is very fast and the response of the PF coils is rather slow.
On the center axis, parallel magnetic flux condition is applied because only poloidal field by plasma current is modeled. The operating current at normal operation is Ip=1.5 MA. In the case of a major plasma condition, the plasma current decays at a time constant of tconst of 3 ms. The plasma current during the plasma disruption can be expressed as:
(1)
The cyclic symmetry condition is modeled by coupling all DOFs at each node on one symmetry surface (=-360/32) to the relevant one on the opposite surface (=360/32).
It is noted that there is electric insulation between adjacent cases. To ensure this insulation, thin insulation layers are put attached on the case surfaces at toroidal angles of =-360/32 and 360/32.
4.2.1.2 Thermal model, load and boundary conditions
Fig.4 Left: Cross section view of case, ground insulation and cooling channels (half model)
Right: Cross section view of a TF winding pack (whole cross section)
Because of the symmetry, the TF case together with ground insulation layer and wedges is further divided half. SOLID70 (hexahedral, 8 nodes) elements which are compatible with SOLID97 elements, are used for all the solid regions. Fig. 4 gives a cross section view of the TF case with embedded cooling channels. The cooling channel run poloidally. The flowing channels are modeled with 1-D flowing pipe element type (in geometry, it is 3-D), FLUID116. The convection heat transfer between the case and cooling channels is modeled by SURF152 attached on the channel surfaces, with the nodes of FLUID116 at relevant position as their extra nodes. The effects of the case heating on the winding pack are modeled in a similar way. The heat transferred from the case through the ground insulation layer between the winding pack and case is assumed to heat up directly the coolant in CICC of the winding pack. Two positions are selected to consider this effect. One is the corner inner turn (position A in Fig.4) and the other is middle inner turn (position B in Fig.4).
Except the surfaces modeled with SURF152, all the other surfaces connecting the insulation layer and winding pack are assumed to keep a constant temperature, i.e., 4 K. All the outer surfaces of the case (including wedges) are assumed adiabatic because of symmetry and much smaller radiated heat compared with eddy current heating. The case coolant flowing diagram is shown in fig.5. The coolant at a mass flow rate of 260/32 g/s and temperature of 4 K firstly enters in parallel the channels in the inner side, then flow out the inner side and enters the channels in the outside and finally cools the back side of the case.
Fig.5 Flow diagram of coolant in TF case
4.2.1.3 Thermal-hydraulic transient model by GANDLF
For the evaluation of the stability behavior under coupling loss heating to strands induced by the magnetic field variation after plasma disruption, we use 1-D calculation by GANDALF code .
Table 1 Main parameters of HT-7U TF coil cable
Dimension / 20.7 mm * 20.7 mm/(2SC+2Cu)*3*4*5(without center cooling hole)
SC strands / NbTi/copper / Cu/NbTi ratio in SC strands / 1.38
Diameter of SC / 0.87 mm / Number of SC strands / 120
Diameter of Cu / 1.06 mm / Number of Cu strands / 120
RRR of Cu / 100
Jacket / SS-316 / Thickness of jacket / 1.5 mm
Porosity / 0.37
Coolant / Helium/3.8K/4bar / Maximum B / 5.8 T
Table 1 summarizes the cable parameters. According to the test made in SULTAN [5], there exists degradation of the cable performance. Current sharing temperature is reduced to 5.83 K, and the critical current density in NbTi strand was reduced to 71% of the theoretical value. The coupling loss on the CICC strands is mainly transverse coupling loss. It can be evaluated by the following formula:
(2)
where Bn is the magnetic flux component normal to the winding direction. For the TF CICC, according to the test[5] in SULTAN the coupling time constant was derived as 37 ms. After a plasma disruption, magnetic field variation is mostly distributed in the straight leg and it mostly occurs in the period of 50 ms after plasma disruption. The worst place is on the corner turn of a TF coil winding so in GANDALF modeling, only this turn was modeled. Figure 9 shows the integration of d2Bn/dt2 on the corner turn which is derived from the electromagnetic calculation in this paper.
4.3 The Results of Analysis
Fig. 6 gives the distribution of magnetic field generated by plasma current before the plasma disruption. The results agree well with other calculations, i.e. the calculation by EFFI. After the plasma disruption, eddy currents establish on the vacuum vessel which absorbs most of the magnetic energy. The eddy heating on the vacuum vessel at 15 ms is shown in Fig.7 (left) while the eddy heating on the cases at the same time is shown in Fig.7 (right). The heat dissipation on the cases shows large gradients on the poloidal direction. Most of the heat deposits are on the inner straight leg where largest magnetic variation takes place and the thickness of the wall is thin. The overall eddy heat dissipation rate is shown in Fig.8. The eddy current heating on the cases reaches a maximum at about 12 ms after plasma disruption because of the shielding effect of the vacuum vessel. After a major centered disruption of HT-7U, the total dissipated heat on TF cases is 212 kJ.
Fig.6 Magnetic field (unit: Tesla) by Ip before plasma disruption
Fig.7 Eddy current heating(unit: W/m3) in TF case and vacuum vessel at time of 15 ms
after plasma disruption
Fig.8 Eddy current heating history of TF case
Table 2 summarizes the results of the thermal calculation. The peak temperature on the cases is 19.4 K which occurs at middle of the inner straight leg at 70 ms after plasma disruption. After 2 s, the coolant of the cases reaches its maximum temperature of about 8.8 K at the middle of the inner straight leg. The temperature rise of the liquid helium in the CIC bundles is a little slower than the coolant in TF case because the ground insulation layer plays a role in thermal shielding. The peak temperature history of helium in CICC is shown in Fig.9. The peak temperature increase of the helium in the CIC bundles reaches about 0.4 K at leg lower part of corner turn in the inner straight at time of about 15 s, but during the first 2 seconds, the peak temperature of helium in CICC is less than 0.1 K. The calculation also shows that the case temperature can recover within 3 minutes after a major plasma disruption.
Table. 2 Peak temperatures of TF case and coolants
(nominal initial temperature and the helium inlet temperature were both set to 4 K)
Case / Coolant of case / He in CICCPeak temperature (K) / 19.4 / 8.8 / 4.4
Occur time (s) / 0.07 / 2 / 10-15
Occur position / Middle of inner straight leg / Lower part of inner straight leg / middle of the inner straight leg
Recover time (min.) / 3
Fig.9 Temperature rise of the coolant in CICC of the inner corner turn due to
case heating under plasma disruption.
ANSYS calculation shows that the magnetic field variation on CIC conductors mostly occurs in a period of 50 ms after a plasma disruption. Figure 10 shows the d2Bn/dt2 distribution on a corner turn and middle turn of a TF coil. It can be seen that the variation of magnetic field on the straight leg is much larger than the one at other positions. The coupling heat loss on cable is thus evaluated by applying formula (2) and the results are applied into GANDALF calculation. In order to see the effects of the coupling to the temperature margin, we can assume a higher operation temperature. When the coupling loss is applied in the thermal transient calculation as the only heating source and the operation temperature is adjusted to a the point just leading to coil quench, the reduction of the temperature margin by the coupling loss can be evaluated. The GANDALF calculation shows when the inlet/initial temperature of helium in CICC is set up to 5.2 K, the sc conductor can still recover within 0.1 s and remains stable if only this coupling heat loss is considered. This means that the coupling heat loss induced by the plasma disruption could reduce the temperature margin of the conductor by 0.63 K(The current sharing temperature of the conductor is 5.83 K). Due to the fact that magnetic field variation on CICC occurs mostly within a period of 50 ms after plasma disruption and case heating to CICC helium during this period is less than 0.1 K, we can conclude that we still have a temperature margin of 1.3 K for other events except plasma disruption if the normal operation temperature of CICC is 3.8 K.
Fig.10 Integration of d2Bn/dt2 over 50 ms after plasma disruption, half
of straight leg has a length of 0.917 m on the vertical direction
In a ward, after a center plasma disruption when the operation plasma current is 1.5 MA, the TF coil case can be heated up significantly and the peak temperature rise on TF case is about 15 K. The heat deposited in TF case would heat up helium in CICC by 0.4 K temperature increase 15 s after plasma disruption. Up to 2 seconds after plasma disruption, the temperature increase is not so significant, it is less than 0.1 K. The magnetic field variation occurs mostly in a period of 50 ms and the induced coupling heat loss in CIC bundles would reduce the CICC temperature margin by 0.63 K. So the reduction of the temperature due to a plasma disruption is within an extent 0.63-0.73 K and it is mostly caused by the coupling loss in the cables. We still have a temperature margin of 1.3 K to withstand other events except plasma disruption if the normal operation temperature of CICC is 3.8 K.
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