DEMO SAMPLE Cable in Conduit Conductor (CICC) quench modelling
This demo gives an example of quench simulation for a Central Solenoid (CS). CS is divided into geometrically identical sections (see Fig. ) wounded by Cable-in-Conduit Conductor (CICC). Each section consists of CICC double pancakes. CS cooling is provided by supercritical helium (SHe) flow in parallel for all pancakes. Helium inlet is at the innermost turn of each pancake and outlet is at outermost turn. Quench occurs in CICC s of section CSL. Figure. CS sections with lower/upper buffer zones
It is assumed that CSL quench is initiated in each innermost turns of CSL pancakes at 79s of a regular plasma pulse, when constant and maximal currents (~ka) excite different CS sections. The VENECIA model of CS includes CS and an external cooling circuit. CS is modelled as CICC pancakes (C-:-C+C87-:-C7), inlet (C-:-C3) and outlet (C3-:-C8) tubes, supply (C733-:-C738) and return (C77-:-C73) feeders. The external cooling circuit is modelled as SHe heat exchangers (C7, C7), circulator (P), control valves (A, A), supply/return cryolines (C739, C7, C7, C73), relief valves (A3-:- A) with opening pressure of MPa and a set of quench line tubes (C7-:-C7) with the quench tank (V89). Control valve A is used to mitigate pulsed heat load from CS on the cryoplant. Control valve A provides protection of a SHe circulator when the pressure difference between the outlet and inlet of the circulator is close to the design limit on the pressure head. In each pancake, CICC is individually modelled with pares of SHe flows in the bundle and central channel which interact through mass- heat exchange. The CS model includes individual descriptions for magnetic field B, strains, AC losses and currents I distribution in each of CICC. These space/time descriptions for CS section CICC are provided through inputs as external data. Electrical field in CICC is calculated using a tabular description of superconductor properties parameterized via B, db/dr,, I and temperature T.
Figure. Hydraulic scheme of CS cooling cirquit. An inter turn and inter pancake heat exchange in CICC is modelled by solving a D thermal diffusion problem over CS cross-sections normal to the cable axis. Each cross-section includes 33 (x) stainless steel cable conduits, inter turn and inter pancake insulation, intersection insulation and upper/lower buffer zones. cross-sections taken for the simulation are meshed with 3. million nodes in total.
Figure 3. Meshing over a D CS cross-section. 7, nodes
Figure. Extraction from CS hydraulic model: CSL cooling circuit with position for cross sections # and #
Figure. Hydraulic scheme of quench lines Hydraulic parameters of CS cooling circuit and quench lines are listed in Table and Table. Channels # Cross section area, mm Hydraulic ID, mm Length, m Table. Parameters of CS cooling circuit Comments C-C..7 Cable space C87-C7 3. 9.7 Central pipe C-C3 78. Supply tubes C3-C8 78. Return tubes C77-C73 3 Return feeders C733-C738 3 Supply feeders C7,C73 3 8 39 Cryolines C7, C739 3 8 9 Cryolines C7, C7 3 SHEXs
Channels # Cross section area, mm Hydraulic ID, mm Length, m Table. Parameters of quench lines Comments C7 3 L3 lines С7 3 8 L3 lines C77 3 L3 lines C78 3 L3 lines C79 3 3 L3 lines C7 77 3 3 L3 lines C7 3 8 L3 lines C7 3 8 B lines С73 3 9 B lines C7 3 B lines C7 3 B lines C7 3 B lines C77 3 B lines C78 3 B lines C79 3 9 B lines C7 3 B lines C7 3 Blines C7 3 7 B lines С73 77 3 3 Line between L3 & B levels C7 9 3 Common line to quench tank C7 9 3 Common line to quench tank Volume V89 models a 8K quench tank of 7 m 3. This demo example is aimed to show VENECIA capabilities in modelling complex thermal hydraulic processes associated with CICC quench in CS, in particular - assessment of a minimum heat pulse energy for quench initiation; - simulation of normal zone evolution resulted in temperature (T) and helium pressure (P) rise caused by Joule heat deposited during quench; - investigation of protection strategy against overpressure in a cryogenic circuit via controlled opening of relief valves and evaluation of instant parameters of helium flows released from the CS; - prediction of temperature & pressure rise along quench lines. Simulation of CSL conductors quench allows revealing the conditions for helium release from CS through the relief valves and the maximum helium parameters along the quench lines. The demo simulation is only illustrative and has certain limitations due to taken for consideration the simplified quench scenario. Simulated CS behaviour is reduced to a s quench at constant currents in CS sections that corresponds to overheat conditions without quench protection and fast energy discharge. Modelling of complex phenomena occurred in a cryomagnetic system in case of quench and CICC protection against overheating requires more detailed description beyond demo purposes and is a subject of contractual investigations.
Initial conditions for modelling The quench is initiated by a uniform heat pulse applied to innermost turns of CSL CICC s when the other CICCs of CS have zero currents. A W/m heat pulse with a.s duration is applied at the end of plasma pulse (79s) when a s plateau of constant maximum currents in sections (~ ka) is supported. The magnetic field in the fired innermost turns is close to the maximal value of T. As initial thermal-hydraulic conditions for CS quench simulation, pre-determined data are used from input files CS3.BS and HEATD_.BAS that gathered in a CS simulation at normal operation. For illustration, the plots below shows CS behaviour at normal operation for a 8s regular plasma pulse..8. Temperature, K...8... 8 8 x, m Figure. Variation of CICC temperature in middle double pancakes of six CS sections CS3L, CSL, CSL, CSU, CSU, CS3U during a 8 s plasma pulse. Normal operation
Temperature, K.. 8.7 7.8 (8) s 8 3 8 8 38 8 8 8 89 9 39. x, m Figure 7. Temperature variation along pancake # (middle of CSL). Normal operation The full set of inputs for the demo quench simulation is available in the input files DEMO.IN and HEATD_.IN. Files VENECIA.MAT and ETABD_.IN describe thermal properties of different materials in the CS assembly and electrical properties of CICC, correspondingly.
Basic simulated results for CS quench started in CSL section Temperatura, K 3 3. s.. 3 3... 7 8 9 N N3 x, m Temperature evolution of CICC bundle for adjacent pancakes # and # of quenched CS section CSL
Temperatura, K 3 3. s.. 3 3... 7 8 9 N N3 x, m Helium temperature evolution in central channel for adjacent pancakes # and # of quenched CS section CSL
Pressure, MPa 8. s.. 3 3... 7 8 9 N N3 8 x, m Helium pressure in cable space for adjacent pancakes # and # of quenched CS section CSL
Velocity, m/s N. s.. 3 3... 7 8 9 N x, m Helium velocity in cable space for adjacent pancakes # and # of quenched CS section CSL
3 N N Mass flow rate, g/s 3 x, m. s.. 3 3... 7 8 9 Helium mass flow rate in cable space for adjacent pancakes # and # of quenched CS section CSL
N N Mass flow rate, g/s x, m. s.. 3 3... 7 8 9 Helium mass flow rate in central channel for adjacent pancakes # and # of quenched CS section CSL
Temperature map for cross section # of CS model in vicinity of adjacent sections CS3L and CSL at t=.s
Temperature map for cross section # of CS model in vicinity of adjacent sections CS3L and CSL at t=.s
Temperature map for cross section # of model in vicinity of adjacent CS sections CS3L and CSL at t=.s (zoom-in of marked region from previous plot)
Temperature, K 3 3. s.. 3 3... 7 8 9 3 9 38 x, m Helium temperature variation in inlet feeders (C733, C73, C73, C73, C737, C738, each 3 m in length) for six CS sections: CS3L, CSL, CSL, CSU, CSU, CS3U
Pressure, MPa 7 3. s.. 3 3... 7 8 9 3 9 38 x, m Helium pressure variation in inlet feeders for six CS sections
Velocity, m/s 3 3. s.. 3 3... 7 8 9 3 9 38 x, m Helium velocity variation in inlet feeders for six CS sections
dm/dt, kg/s. s.. 3 3... 7 8 9 3 9 38 x, m Helium mass flow rate variation in inlet feeders for six CS sections
3 N # & # N 9 8 B, T 7 3 x, m Local distribution of magnetic field B along CICC in pancakes # & #
.73.7.7.7 Strain.77.78.79.8 # & #.8 x, m Local distribution of strain along CICC in pancakes # & #
ExI, W/m N N. s.. 3 3... 7 8 9.8... 8 x, m Variation of Joule heat along CICC in pancakes # & # at constant current of ka. NOTE: Plateau of Joule heat at a level ~8kW/m is explained by limited input data on CICC property in file ETABD_.IN, where the tabulated maximal temperature is given as 3K, so for T>3K electric field E(T, B, db/dr,, I)= E(3K, B, db/dr,, I).
.. A A A8 dm/dt, kg/s.8... 3 7 8 9 t, s Helium mass flow rate at inlets of relief valves A, A, A8 7 A3 A A7 dm/dt, kg/s 3 3 7 8 9 t, s Helium mass flow rate at inlets of relief valves A3, A, A7
.3.3 A A A. dm/dt, kg/s.... 3 7 8 9 t, s Helium mass flow rate at inlets of relief valves A, A, A 7 A A A8 Opening, mm^ 3 3 7 8 9 t, s Variation of opening for relief valves A, A, A8
. P_open.8. Pressure, MPa...8. V9 (A3,A,A7) V (A9,A,A3). V (A,A,A8) V (A,A,A). 3 7 8 9 t, s Helium pressure at inlets of the safety relief valves 3 3 V9 (A3,A,A7) V (A9,A,A3) V (A,A,A8) V (A,A,A) Temperature, K 3 7 8 9 t, s Helium temperature at inlets of the safety relief valves
.. P T. Pressure, MPa.3 98 Temperature, K. 9. 8. 8 3 7 8 9 t, s Evolution of helium pressure and temperature inside quench tank V89 due to helium release via safety valves
3 C7-C7, 73, 7, 7 3 T, K. s.. 3 3... 7 8 9 x, m Evolution of temperature along selected portion of quench lines (see total layout of quench lines in Fig. )
P, MPa.....3.3. C7-C7, 73, 7, 7. s.. 3 3... 7 8 9.... x, m Evolution of pressure along selected portion of quench lines (see total layout of quench lines in Fig. )
3. P 3. dm/dt, kg/s.. 8 t, s Flow rate variation of circulator P in accordance with its characteristic m - P.9 P.8.7 DP, MPa....3 3 7 8 9 t, s Pressure head variation in circulator P limited by control valve A opening
A Opening, mm^ 3 3 7 8 9 t, s Variation of control valve A opening A dm/dt, kg/s 3 7 8 9 t, s Variation of control valve A mass flow rate