Appendix C FIRE Coil Cooling Calculations

Appendix C FIRE Coil Cooling Calculations November 11, 2001, Rev 1 FIRE Coil Thermal Distributions, EOF Peter H. Titus, http://psfc.mit.edu/vc/titus/home.html, titus@psfc.mit.edu Stone & Webster Engineering Corporation, Under Contract To Massachusetts Institute of Technology - Plasma Science and Fusion Center Cambridge, MA 1

Table of Contents Introduction 3 Summary of Results 5 References 6 Materials 6 TF Cool-Down ANSYS Simulation with Good LN2/Copper Heat Transfer 7 Contoured (Shaped) TF Heat-Up and Cool-down 53 TF Cool-down With Convective Heat Transfer 10 Operating Rep Rate 11 (Rev 1) TF Thermal Energy after the Pulse 13 Volumes and Areas for Cooling System Analyses 14 CS Cooldown 20 (Rev 1) 2

Introduction The toroidal field coil system of the FIRE tokamak utilizes LN 2 cooled, copper alloy Bitter plate type magnets. They produce a field on axis (R 0 =2.0 m) of 10T with a flat top time of >10 s.. The magnet details evolved from the BPX and BPXAT design studies. The baseline TF coil configuration is wedged. C17510 high strength, high conductivity beryllium copper alloy conductor developed for BPX is proposed for the conductor. The characteristics of the TF coil pertinent to its thermal design are listed in the table below. Number of TF Coils 16 Max Field Ripple 1% (edge) Bt, Tesla 10, (12 as an upgrade) Pulse Rep Rate, /hr 0.5 Flat-top, s 21 (minimum) Coil Initial Temp 80 K Life Pulses at Full Field 3000 Full Performance, 30000 2/3 (Ip and Bt) Coil Max Temp 373 K These design choices were made after considering a number of alternative structural concepts and a variety of conductor materials. Bucked and wedged designs generally produce reduced TF coil stress and would permit the use of other conductors such as work hardened copper or work hardened copper steel reinforced copper plates like those used in C-Mod s Inner leg. Results of coupled electromagnetic-thermal diffusion analyses of the TF coil are presented along with parametric studies of the pulse length in Appendix B. These analyses set the starting point for the cooldown calculations TF cooling is by tubes soldered on the plasma side of the TF coil plates. The tubes run along the inner leg and pass up - and down through low stressed regions of the horizontal legs. The CS is envisioned as being cooled in a manner similar to that developed for CIT/BPX. The pancake to pancake insulation is grooved radially to communicate with a plenum at the OD of the CS. LN2 is fed from the outside to limit radial tensile stresses. The BPX CS cooling design was qualified by analysis and test [4]. The layout of the BPX central solenoid is shown on the following page. This drawing includes notations showing the LN2 flow. 3

BPX CS Cross Section - Similar LN2 Cooling Paths are Planned for FIRE 4

Summary of Results A one dimensional transient heat conduction analysis is used to investigate cooldown capabilities in the TF. This analysis is conservative in that it considers cooling only from the plasma side, and does not consider conduction poloidally. From the results of this analysis, OFHC copper TF coils would cool in 2 hours, BeCu coils will take longer to cool, up to 3 hours, because of the lower thermal conduction of this material. Cooling from both sides will reduce this to about an hour, but the space for cooling tubes at the CS side of the TF has not been provided, and the centimeter needed for the extra cooling tube will reduce the flat top time by a second. CS cooling time is estimated to be a little over an hour. In all these analyses, the details of the flow and pressure drops in the channels and manifolds has not been evaluated. The ANSYS current diffusion analysis with the lower thermal conductivity of BeCu was run. It had minimal effect on the peak temperature in the min section of the TF inner leg. During the pulse, in the minimum section of the inner leg, conduction for copper or BeCu is not sufficient to distribute the heat away from the equatorial plane. There should be no effect on the pulse length, but given the larger times available between shots, poloidal conduction may help to improve the cool-down times. Thermal Energy of 16 coils after each Pulse, 80 Start. (Energy to be removed during cool-down) Peak Temp after Pulse 292 313 370 TF Coil Thermal Energy 9.958GJ 11.0543 GJ 14.079GJ 5

References [1] Fusion Ignition Research Experiment Structural Design Criteria; Doc. No. 11_FIRE_DesCrit _IZ_022499.doc; February, 1999. [2] R. Leonard Myatt & Peter H. Titus, 3D, Coupled Electromagnetic, Thermal, Current Diffusion in the Finger Joints of the Alcator C-Mod Toroidal Field Coils, Presented at the IEEE 17th Symp. Fusion Engineering, San Diego, CA, Oct. 1998. [3] Transient Coupled Electromagnetic Thermal Diffusion Analysis of the Alcator C-Mod TF Coil System, Felt Metal Review, May 6 1998 [4] Preliminary Report on BPX Cooling Channel Testing and Analysis P. Winn, J, Maguire, Applied Engineering Technologies, Ltd 5-31-91 [5] Analysis Status - TF Cooldown P.Titus, March 31 1999 [6] PF coil currents derived from equilibrium calculations, for the Ip=7.7 MA and Bt=12 T scenario. Charles Kessel [ckessel@pppl.gov] Mon 6/21/99 4:23 PM [7] PF coil currents for a 250 s flattop, corresponding to the long pulse Ip=2 MA, Bt=4 T mode.charles Kessel [ckessel@pppl.gov] Thu 6/17/99 10:50 AM [8] PF coil currents for our SUPER-UPDATED 21 s flattop, including the +1.8 V-s additional advancing of the flux state everywhere as recommended by Woolley's optimization. Wed 6/9/99 8:55 PM [9]The fiducial equilibrium coil currents for : 1) 5 V-s advanced flux state everywhere, 2) 1 V-s additional added to the IM state to provide for breakdown and, early plasma current rampup to 100 ka (this created a higher pre-bias), 3) 21 second flattop which requires 1 V-s additional consumption, Tue 6/8/99 9:06 AM Charles Kessel [10] ANSYS Structural Analysis Program, Revision 5.5 Swanson Analysis Systems, Houston Pa. [11] Evaluation of Insulation Shear Stresses in the ITER Central Solenoid IEEE Symposium on Fusion Engineering, October 1997, San Diego California, Peter Titus, Anatoly Panin, Efremov Institute, St. Petersburg Russia and Alexey I. Borovkov, St. Petersburg State Technical University, Russia [12] IGNITOR Program General Report, Volume II, Engineering Design Description B. Coppi and the Ignitor Project Group RLE Report No. PTP 96/03 December 1996 [13] "MHD and Fusion Magnets, Field and Force Design Concepts", R.J.Thome, John Tarrh, Wiley Interscience, 1982 [14]"Non- Axisymmetric Behavior of the Central Solenoid Spiral Cut Pancakes for the Burning Plasma Experiment", P.H. Titus, 14th Symposium on Fusion Engineering, October 1991, San Diego California [15] Effects of Damaged Felt Metal in C-Mod s TF Coil Finger Joints Memo, L. Myatt, 12-10-96 [16] Cryogenic Properties of Copper, and Copper Alloys, Reed and Simon 1987, t=412-.664*t+2.73*cw-.00695*cw^2,t2=230+3.14*cw-.00962*cw^2! at RT [17] Handbook of Superconducting Machinery [18] TIBB data sheet, informally provided. Similar copper data in [18] page 38 [19]" Feasibility Studies of the IGNITOR Experiment" Scuola Normale Superiore, May1982 [20] Work hardened copper- c15500,t60 (per 12-20-85 conversation with H. Becker of MIT) [21] Ip=7.7 MA and Bt=12 T scenario. shifted flux state everywhere back by 5 V-s Charles Kessel [ckessel@pppl.gov] Tue 6/29/99 10:43 AM [21] Revised Precharge Currents for the 7.7MA 12 T Scenario [21]T 7.7 MA plasma case with 5 Charles Kessel [ckessel@pppl.gov] Thu 7/1/99 9:30 PM Materials Material Ref Heat Capacity J/kg-K @ 80 Heat Capacity j/kg-k @ 273 K Thermal Conductivity W/m-K @ 80 K C10100 1 181 386 500 390 C10100, 3 202 380 600 400 CW C15500 T60 1 181 384 387 347 C17510 RT 1 205 384 147 233 C17510 2 134.8 231.3 Thermal Conductivity W/m-K @ 273 6

[1] Nov 25 1985 Meeting in Austin TX as reported by H. Becker, C17510 RT Yield=760 [2] Eqn. from NIST as reported by Wooley [3] "Cryogenic Properties of Copper and Copper Alloys" NIST Boulder CO, 4-15-88 7

TF Cool-down Transient Conduction Assuming Good Heat Transfer Between LN2 and Copper The coupled electromagnetic - thermal conduction solution can be continued after the end of pulse with only the thermal diffusion cooldown behavior modeled by extending the thermal part of the ANSYS solution. At the beginning of the cooldown, boundary conditions which model certain cooling schemes can be added. In this analysis the annular space between the TF and CS is assumed flooded with sufficient liquid nitrogen to force the local nose temperature to 80 deg. K. A similar assumption is made at the outer edge of the outer leg of the TF. The analysis of the cooldown is a transient conduction solution starting with the temperature distribution at the end of pulse - and, although it has not yet been done, it allows starting analysis of a second pulse with the residual temperature distribution from the previous cooldown. After an hour, the inner and outer legs of the TF are adequately cooled. The horizontal legs, which in this model have not had direct cooling, remain well above liquid nitrogen temperatures. The simplistic conclusion is to provide full perimeter edge cooling, but starting the second pulse with this initial temperature distribution, may be acceptable, and in fact may be better in that it may offer a means of obtaining more wedge pressure in the corners of the inner leg. The cooling scheme described here is similar to that used by C-Mod. The 5.6 Tesla shots cooldown to less than 90 deg K in all the thermocouples in less than 15 min. Other inner leg contours are being investigated to improve the structural response or to make room for the divertor. The straight inner leg design has peak temperature of 340 K, up from 323 K for the nominal 20 sec flattop. No nuclear heat has been included. 8

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Temperatures of Models with Contoured Inner Legs, 20 sec Fattop, No Nuclear Heat 28 sec 55 sec comments Baseline Shape 215 323 Contoured for Divertor 247 385 Straight Inner Leg 241 340 (Intended to Improve Wedging Pressure) 10

TF Cool-down With Convective Heat Transfer This analysis is based on convective heat transfer to LN2 and transient conduction through the copper. The convective heat transfer coefficient is based on CIT/BPX tests. Ninety K is chosen as the target temp after a shot. C-Mod cool-down is used as a benchmark for the analysis. C-Mod is cooled from both sides, whereas FIRE is cooled from one side. For C-Mod, with coolant grooves machined in the OD, following an 8 Tesla Shot, 470 sec, or 8 min is required. For FIRE, with some form of similar cooling fin detail on the ID, 6000 sec, or 1 Hr and 40 min is required. C-Mod is currently allowing 15 min between 5.6 T shots. The ANSYS current/thermal diffusion analysis considered the response of the FIRE TF coil to simple assumptions as to the cooldown characteristics, but with the temperature distribution resulting form the current/temperature diffusion analysis. The cooling assumption was that the LN2 in contact with the copper would impose a surface temperature of 80 deg k. In this section, the convective heat transfer behavior is included, but in a simplified transient conduction model. The TF inner leg assembly of both FIRE and C-Mod represents a thick cylinder cooled from both the inside and outside in the case of C-Mod and just from the outside in the case of FIRE. The convective heat transfer coefficient is taken from work done by Winn [4] during the BPX project. Heat transfer and pressure drop in a channel were measured in a detail that was proposed for cooling the central solenoid. The following relation produced a good fit to the data: hc= 4.215e7*t wall^(-2.2)! Heat transfer Coefficient LN2 to Wall [4] Use of this relation for the cooling behavior of both C-Mod and FIRE TF coils is an assumption. Multiphase flow of the nitrogen is complicated, but previous BPX work found the relation good over a range of flow conditions. A numerical, one dimensional finite difference integration scheme is used to simulate the conduction through the thick cylinder. The numerical solution allows addition of the convective behavior of the surfaces, and allows adjustments for the conduction areas, packing fractions and inclusion of reinforcement steel. The heat transfer area communicating with the LN2 in C-Mod is increased with grooves machined in the OD of the turns. The initial distribution of temperature can be fit to the electromagnetic/thermal diffusion solution with the discrete numerical approach. The temperature after the pulse is nearly uniform for FIRE. In C-Mod, the temperature on the outside of the inner leg is 100 deg., K greater than the ID This is shown in the next figure from Myatt s analysis of May 1998[3]. 11

Temp distribution in joint region at time of T max Ti=80K, t=2.82s, discretization. T max =228K, T=148K [3] The results of the transient conduction analysis of C-Mod are shown in the next figure. The temperature profile across the width of the inner leg is plotted at a number of time points throughout the cooling process. The initial linear distribution is flattened relatively quickly via conduction. The inclination of the temperature profile showing preferential cooling towards the outside is a consequence of the increased conduction areas in the copper for the outer radii, which is exaggerated by the effects of the steel reinforcement, and the increased area exposed to the LN2 at the outside. Convergence of the finite difference scheme must be investigated by adjusting the time and dimension 12

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Operating Rep Rate Curves are labeled for their field, TF inner leg material, and max coil temperature at the end of the pulse. 370K is the allowed, 292K is recommended for the more numerous lower power shots. The radial build of FIRE is.488m. The radial build of FIRE* is actually slightly smaller than FIRE but by only 6mm. To keep constant current density, the current and conduction area must increase by 7% to obtain the same Bo for the 7% linear geometric scaleup, The retention of the same current density makes the flat-top times identical for the two versions of FIRE for the same TF field. (neglecting some third order current diffusion effects). Since the radial builds are similar, the cooldown times will be almost identical. In answering your questions, I made a few simplifications. I used the same pair of transient conduction solutions - one for 68% BeCu and one for OFHC Cu, both are included at the end of this memo. They both are actually for an initial temp of 322K, and I use them for both the 370 and RT initial temps, so the results tabulated should be considered semiquantitative. Most of the "lesser power" shots require a little over an hour to cool down. One second flat top shots which are fizzles, conditioning shots, or are investigating start-up would require about a half hour. A full power shot would best be scheduled after an evening or an operating pause because it would need to start at LN2 temps, prior to which the 3 Hr cooldown is needed. (2 Hr for OFHC). Using a cooling scheme that cools from both the ID and OD of the TF inner leg reduced the cooldown times by a factor of 1/3. This is attractive, and doable certainly in the wedged machine, and possibly in the B&W machine ( Bucked CIT had a plenum at the CS/TF interface which could be used as a CS vent or a TF feed) In both cases a loss of about 1cm worth of conductor would be needed to make room for the channel or tube. I estimate that this would subtract a fraction of a second from the 20 sec FIRE* nominal flat top time. 14

You can operate to minimize power or operate to maximize pulse repetition rate. To obtain the fastest cooldown times you want to run the TF at the higher temperatures, and cool down only enough so that the next shot brings you to your allowable max temp. The higher temperature operation means a bigger delta T with respect to the cooling medium of LN2, greater heat flux and shorter cool-down times. In the plots at the end of the memo, you have to count down temp profile lines, each of which is 100 sec to get the time to reach a given temp. I used the CS side temp - which is actually on the right hand side of the plots. These plots assume cooling from one side, and although they are labeled 10 T shots, the analysis doesn't know what field produced the initial temp. I would recommend that for the 30,000 lower power shots that you plan to keep the max temp to RT. A case has been made not to operate at the stress limits of the machine for the many low power shots. A similar case can be made to operate with some thermal margin. 68% IACS BeCu, Bo = 10, Ip = 7.7 MA, Pf = 150 MW Flat Top Time Start Temp Final Temp Cool-Down Time sec 20 sec 80 370 10000 2.7 15 sec 125 370 6000 1.67 10 sec 165 370 4400 1.22 5 sec 210 370 3100.86 OFHC Cu, Bo = 10, Ip = 7.7 MA, Pf = 150 MW Flat Top Time Start Temp Final Temp Cool-Down Time sec 29 sec 80 292 6000 1.67 20 sec 125 292 4800 1.333 15 sec 150 292 4100 1.13 10 sec 175 292 3500.97 5 sec 210 292 2900.81 Cool-Down Time Hrs Cool-Down Time Hrs 68% IACS BeCu, Bo = 6.7 T, Ip = 5.1 MA, Pf = 37 MW Start Temp K Final Temp K flat top time sec Time to cool sec 90 292 42 10000 2.77 150 292 25 4500 1.25 175 292 18 3900 1.08 200 292 12 3400.944 250 292 1 2300.64 OFHC Cu, Bo = 6.7 T, Ip = 5.1 MA, Pf = 37 MW Start Temp K Final Temp K flat top time sec Time to cool sec 90 292 83 6000 1.67 150 292 49 4100 1.14 175 292 37 3600 1.00 200 292 25 3100.86 225 292 15 2600.7222 250 292 6 1900.53 275 300 1 1300.36 Time to cool Hrs Time to cool Hrs 15

OFHC Inner Leg With cooling on both sides, and an initial temperature of 322 K, it takes 3300 sec to get to 90 degk, compared with 10000 sec for the one sided cooling arrangement. The time is found in this plot by counting 100 second temp profiles. The end condition of the transient conduction simulation was 90K at the center. Temperature Profiles for cooling from both sides. 16

TF Thermal Energy After the Pulse The current diffusion ANSYS analyses, discussed in Appendix B, provide the temperature distributions for the structural analyses. The results from the electromagnetic/thermal analysis are, converted to a temperature load file for the finer structural mesh in a FORTRAN program outside ANSYS. The temperature and coil geometry data (shown at left) can be used to sum the stored energy accumulated in the coil during the pulse. All that is needed is a volumetric specific heat. For copper a simple bilinear relation is used, the coding for which follows:: IF(tc<=105.5555) then CP= 2.62328*(tc-27.77)/77.77 IF(tc>=105.5555) then CP= 2.62382+.002176*(tc-105.555) This is in Joules/cm^3. For BeCu the specific heat has been derived from the available G function data. Thermal Energy of 16 coils after each Pulse, 80 Start Peak Temp after Pulse 292 313 370 Copper Thermal Energy 9.96GJ 11.05 GJ 14.08GJ BeCu Thermal Energy 10.66GJ 11.8 GJ 15.06GJ Comparing the BeCu specific heat and copper specific heat in the range of 80 to 300 K, the BeCu specific heat is 7% higher than for copper. The copper CP was used in the code because it was available, and then the results were multiplied by 1.07 for BeCu. The current diffusion analysis used for the structural calculations actually has a 323 peak temp at the end of pulse, and only EOF files which had a peak of 313 were available. To get the stored energy of specific end temperatures. the temperatures were scaled from the 313 data, using an 80 start temp. The stored energy of the coil was found by summing the energy of the individual elements in the finite element model. Preliminary estimates of the TF thermal energy are given in the following table: Summing over the inner leg (Mat 6 in the structural model, the wedged region of the coil,) the inner leg thermal energy was found to be 62% of the total. Inner Leg Cooling Tube Dimensions 17

Volumes and Areas for Cooling System Analyses Surface areas are calculated from a mesh formed on the outside of the un-reinforced case and the TF and structure which faces the vessel. A half section of two surfaces are shown below: TF and Structure Facing Cryostat (full section) TF and Structure Facing Vessel (full section) 262.6m^2 120.4m^2 Volumes are computed from the structural model segments Baseline Case Reinforced Case with Ring 1/16 Coil Volume PF and TF 4.822 m^3 4.822m^3 1/16 Case and Tierod 2.48m^3 4.576m^3 Total for 1/16 sector 7.302m^3 9.398m^3 Total for Tokamak 116.8m^3 150.4 m^3 Total kg at 8020kg/m^3.937e6kg 1.21e6kg 18

CS Cooldown Cooldown of the TF has been assumed as limiting because of the relatively large conduction distance along the width of the bitter plate. In the CS, cooling channels are provided every other pancake, or on the top and bottom surface of the double pancake assembly. Heat must be conducted through a full turn thickness, and through ground wrap to the thin CS Cooling Arrangements: Channels are Cut in Pancake to Pancake Insulation Sheets Which are Bonded between Double Pancakes. While conduction is through insulation, the wetted area is larger, and the conduction path is lower than in the TF. channels that communicate with the LN2 feed in the bore of the central solenoid. In the 2D cooldown analysis, Nitrogen is assumed mostly liquid. It is modeled as solid elements in the channel that are held to 80 K (red elements at right). The convective heat transfer coefficient is the same as that used for the TF, but is modeled as a temperature dependent thermal conductivity in a solid element layer (dark blue) the light blue area is copper conductor and the magenta area is G-10-like insulation. All four sides of the model represent adiabatic symmetry planes. The geometry is not precise because details of the CS winding and insulation have not been finalized. The ~4000 sec. cooldown time is 1/3 to 1/2 that of the TF, if it is cooled from one side. If the TF is cooled from both sides, the cooldown times for the TF and CS would be comparable. In both the TF and CS cooldown calculations, the flow behavior of the coolant channels is not addressed. It is assumed that there is adequate flow in the channels and pipes to support the selection of the convective heat transfer coefficient that was used. The temperature contour plots show almost all the gradient to occur across the insulation. CS Cooldown Conduction Model Temperature at the warmest point in the model vs. time. 19

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