Transverse heat transfer coefficients on a full size dual channel CICC ITER conductor

Dual channel Cable-In-Conduit Conductors (CICC) provide low hydraulic resistance and faster central channel circulation, limiting superconductors temperature rise. The Poloidal Field Insert Sample (PFIS) was tested in the SULTAN facility to evaluate the thermal coupling between the CICC channels upon an experimental heat transfer coefficient assessment. Simple assumptions on the flow – homogeneous central and annular temperatures, no jacket conduction, no steel inertia and diffusivity – lead to a one-dimensional thermal model fully solved in its transient response to a Heavyside temperature evolution at the inlet, using a Laplace transformation. Transient temperature step data fitted with the analytical resolution provide heat transfer coefficients as a function of mass flow rate, compared to crude predictions. The transient measurements provided consistent measurements on the full range of mass flow rate in both vertical flow directions, whereas steady state homogenization characteristic length measures pursuing the same goal suffer from annular isothermal assumption. Recommendations are made for the thermohydraulic instrumentation of future conductor samples.     

Using the HELIOS facility for assessment of bundle-jacket thermal coupling in a CICC

In a Cable In Conduit Conductor (CICC) cooled by forced circulation of supercritical helium, the heat exchange in the bundle region can play a significant role for conductor safe operation, while remaining a quite uncertain parameter. Heat exchange between bundle and jacket depends on the relative contributions of convective heat transfer due to the helium flow inside the bundle and of thermal resistance due to the wrappings between the cable and the conduit.In order to qualify this thermal coupling at realistic operating conditions, a dedicated experiment on a 1.2 m sample of ITER Toroidal Field (TF) dummy conductor was designed and performed in the HELIOS test facility at CEA Grenoble. Several methods were envisaged, and the choice was made to assess bundle-jacket heat transfer coefficient by measuring the temperature of a solid copper cylinder inserted over the conductor jacket and submitted to heat deposition on its outer surface.The mock-up was manufactured and tested in spring 2015. Bundle-jacket heat transfer coefficient was found in the range 300–500 W m⁻² K⁻¹. Results analysis suggests that the order of magnitude of convective heat transfer coefficient inside bundle is closer to Colburn–Reynolds analogy than to Dittus–Boelter correlation, and that bundle-jacket thermal coupling is mainly limited by thermal resistance due to wrappings. A model based on an equivalent layer of stagnant helium between wraps and jacket was proposed and showed a good consistency with the experiment, with relevant values for the helium layer thickness.     

Three dimensional CFD analysis of Cable-in-Conduit Conductors (CICCs) using porous medium approach

Thermohydraulic studies based on porous medium analogy, pertinent to dual channel Cable-in-Conduit Conductors (CICCs) used in International Thermonuclear Experimental Reactor (ITER), are explored in the present work. Dual channel CICC used in Toroidal Field (TF) Coil consists of a circular jacket in which superconducting cable bundles are placed in the annular channel separated from the central channel by a spiral. The cable bundle in the annular channel can be considered as saturated porous medium and the central channel can be viewed as clear region for thermohydraulic studies. In the present work, a 3D Computational Fluid Dynamics (CFD) analysis is performed on CICC by considering dual channel CICC as partially filled saturated porous medium. The 3D geometry was developed and meshed in GAMBIT-2.1.6, and exported to a commercial solver FLUENT -6.3.26 for further analysis. The effect of mass flow rate ( 6 - 10 g/s) of supercritical helium (SHe) on the velocity and pressure gradient distributions (axial and radial) in the transverse plane is presented. These studies resulted in estimating the mass flow repartition between the two channels and pumping power required to pump the SHe in CICC. In addition, the present CFD analysis brings a clear perspective of the phenomena of flow and heat transfer in complex geometries such as CICC.     

CFD model of ITER CICC. Part VI: Heat and mass transfer between cable region and central channel

Dual-channel cable-in-conduit conductors (CICC) are used in the superconducting magnets for the International Thermonuclear Experimental Reactor (ITER). As the CICC axial/transverse size ratio is typically ∼1000, 1D axial models are customarily used for the CICC, but they require constitutive relations for the transverse fluxes. A novel approach, based on Computational Fluid Dynamics (CFD), was recently proposed by these authors to understand the complex transverse thermal-hydraulic processes in an ITER CICC from first principles. Multidimensional (2D, 3D) Reynolds-Averaged Navier-Stokes models implemented in the commercial CFD code FLUENT were validated against compact heat exchanger and ITER-relevant experimental data, and applied to compute the friction factor and the heat transfer coefficient in fully turbulent spiral rib-roughened pipes, mimicking the central channel of an ITER CICC. That analysis is extended here to the problem of heat and mass transfer through the perforated spiral separating the central channel from the cable bundle region, by combining the previously developed central channel model with a porous medium model for the cable region. The resulting 2D model is used to analyze several key features of the transport processes occurring between the two regions including the relation between transverse mass transfer and transverse pressure drop, the influence of transverse mass transfer on axial pressure drop, and the heat transfer coefficient between central channel and annular cable bundle region.     

Transverse heat transfer coefficient in the dual channel ITER TF CICCs: Part I: Analysis of steady state temperature profiles resulting from annular heating

Two ITER TF dual channel Cable-in-Conduit Conductors (CICCs) have been tested in the SULTAN test facility. The samples were heated either by foil heaters mounted on the outside of the conductor jacket or by induced AC losses. The steady-state temperature response of several thermometers installed on the jacket surface as well as inside the cable were analyzed using the two-channel analytical model proposed by Renard et al. to obtain the equivalent transverse heat transfer coefficient between the bundle and central channel as a function of the mass flow rate. In addition, on the basis of the measured pressure drop and helium flow velocities, the friction factors for helium flow in the bundle and in the central channel were determined. The obtained results may serve as a reference for these cables.     

Using the Vincenta code to analyse pressure increases in helium during the quench of a superconducting magnet

The Vincenta code is used to simulate the pressure increases in helium in case of a quench in the superconducting coils. We focus on two classes of coil in which helium is in direct contact with the conductor: coils consisting of cable-in-conduit conductors (as in ITER or JT-60SA), in which supercritical helium is forced through long channels; and bath-cooled coils, in which static helium is confined in short channels perpendicular to the conductor and opening into a bath (as in Tore Supra or Iseult). Various physical phenomena are responsible for the pressure increases in helium, which is subjected to strong heat flux in the conductor during a quench: at the local level, i.e. in the heated channels, the inertial forces that must be overcome to expel the fluid and the friction forces due to the induced velocity; at the global level, i.e. throughout the cryogenic system, the adiabatic compression of non-heated volumes hydraulically connected to the heated channels. Here we analyse the thermohydraulic behaviour of helium to highlight the dominant phenomena, according to the geometry of the helium flow paths. The results are applied to numerical simulation of the pressure rise in case of quench in a JT-60SA cable-in-conduit conductor (CICC) and in the bath-cooled Iseult coil.     

Effect of sub-cooling channel in an ITER 13 T-40 kA Nb3Sn coil (CS insert) on stability

This paper analyzes the stability of a center solenoid (CS) insert and describes the effects a sub-cooling channel (central channel) at the center cross section of a cable-in-conduit (CIC) conductor has on stability. First, the calculation results are compared with test results in a center solenoid (CS) insert, and the effectiveness of the calculation is verified. Next, the effects of central channel on stability are examined by comparing the energy margin between a case in which perforations exist between the bundle region and the central channel, such as a CS insert, to allow the fluid to migrate and a case in which perforations are blocked to prevent the coolant from migrating. The following points are clarified: (1) if most of the thermal disturbance is applied to the jacket, the case with perforations is more stable than the case without perforations, thus the central channel contributes to the improvement of stability; (2) if thermal disturbance is applied only to the cable and is produced for about 20 ms, the central channel hardly has any effect on the stability. If the thermal disturbance is produced for about 400 ms, the central channel contributes to the stability; (3) the effect of cooling the bundle region by means of heat conduction through the central channel wall is very small, and it hardly affects the stability at all.     

Thermo-hydraulic analysis of the gradual cool-down to 80 K of the ITER toroidal field coil

A time-dependent thermo-hydraulic simulation for an ITER toroidal field (TF) coil gradual cool-down to 80 K has been performed using a new FORTRAN code. The code is based on a 1D helium flow and 1D multi-region solid heat conduction model. The whole TF coil is simulated taking into account thermal conduction between winding pack and case, which are cooled down separately. To limit coil mechanical stresses and coolant pressure drop in the cooling channels, an improved cool-down mode has been developed based on the analysis. Typical and gradual cool-down temperature distributions of TF coil and case are presented. The results indicate that gradual cool-down to 80 K can be achieved in 3 weeks.     

A multi-scale model for coupled heat conduction and deformations of viscoelastic functionally graded materials

An integrated micromechanical-structural framework is presented to analyze coupled heat conduction and deformations of functionally graded materials (FGM) having temperature and stress dependent viscoelastic constituents. A through-thickness continuous variation of the thermal and mechanical properties of the FGM is approximated as an assembly of homogeneous layers. Average thermo-mechanical properties in each homogeneous medium are computed using a simplified micromechanical model for particle reinforced composites. This micromechanical model consists of two isotropic constituents. The mechanical properties of each constituent are time–stress–temperature dependent. The thermal properties (coefficient of thermal expansion and thermal conductivity) of each constituent are allowed to vary with temperature. Sequentially coupled heat transfer and displacement analyses are performed, which allow analyzing stress/strain behaviors of FGM having time and temperature dependent material properties. The thermo-mechanical responses of the homogenized FGM obtained from micromechanical model are compared with experimental data and the results obtained from finite element (FE) analysis of FGMs having microstructural details. The present micromechanical-modeling approach is computationally efficient and shows good agreement with experiments in predicting time-dependent responses of FGMs. Our analysis forecasts a better design for creep resistant materials using particulate FGM composites.     

A review of thermal-hydraulic issues in ITER cable-in-conduit conductors

Problems related to cable-in-conduit conductors (CICC) are intrinsically multi-physics involving coupled electro-magnetic/mechanical/thermal-hydraulic fields. Here we concentrate on the thermal-hydraulic issues because, although the CICC was first proposed for the low-T_C superconducting coils of the International Thermonuclear Experimental Reactor (ITER) many years ago, CICC thermal-hydraulics alone is less understood than could be expected. Some of the difficulties are due to the multi-channel nature of the ITER CICC, where strands containing the superconducting filaments are twisted in multi-stage sub-bundles (petals) delimited by wrappings and concentrated in an annular (porous-medium like) region, while a central channel, delimited by a spiral, provides lower hydraulic impedance and pressure relief to the flow of the supercritical helium coolant. Other difficulties are related to the multi-scale nature of this problem, with length scales relevant for thermal-hydraulics ranging from the strand diameter (<∼10⁻³ m), to the CICC length in a coil (up to several 10² m). On the other hand, taking advantage of this length-scale separation, the models presently used for CICC simulations are typically 1D (along the conductor) but they need constitutive relations (like friction and heat transfer coefficients) for the transverse mass, momentum and energy transport processes occurring between different conductor elements. The database for the transverse transport coefficients, unfortunately, does not appear complete, or free of internal contradictions, often because the smallness of the transverse scales makes even an experimental assessment of these processes difficult. Here we discuss these issues and possible strategies for overcoming some of the difficulties are proposed.     

梯度复合材料热传导分析的梯度单元法

给出了一种适用于梯度复合材料热传导分析的梯度单元, 采用细观力学方法描述材料变化的热物理属性, 通过线性插值和高阶插值温度场分别给出了4节点和8节点梯度单元随空间位置变化的热传导刚度矩阵。推导了在温度梯度载荷和热流密度载荷作用下, 矩形梯度板的稳态温度场和热通量场精确解。基于该精确解对比了连续梯度模型和传统的离散梯度模型的热传导有限元计算结果, 验证了梯度单元的有效性, 并讨论了相关参数对梯度单元的影响。结果表明, 梯度单元和均匀单元得到的温度场基本一致; 当热载荷垂直于材料梯度方向时, 梯度单元能够给出更加精确的局部热通量场; 当热载荷平行于材料梯度方向时, 4节点梯度单元性能恶化, 8节点梯度单元和均匀单元的计算结果与精确解吻合很好。     

Hydraulic behavior of forced-flow cooled superconducting coils for the large helical device

The large helical device (LHD) has been operated since 1998 and the 13th experimental campaign was conducted in 2009. Before final assembling, cool-down and excitation tests for the Inner Vertical (IV) field coil, which is one of the LHD poloidal field coils, were carried out in 1995. This coil, which consists of a cable-in-conduit conductor, (CICC) is cooled by the forced-flow of supercritical helium. During the tests of the IV coil, hydraulic characteristics, such as flow distribution among cooling channels and friction factors, were measured. In this paper, the consistency of the behavior of the IV coil will be presented and comparison with other fusion devices using superconducting coils will also be made at not only cryogenic temperatures but also at room temperature.     

Effect of flow mal-distribution on effective NTU in multi-channel counter-flow heat exchanger of single body

Most heat exchangers in services belong to multi-channel heat exchangers. The working fluid is distributed among the multiple channels. This kind of heat exchangers usually has a flow distribution problem. In general, the flow is not evenly distributed and, as a result, the thermal performance of the heat exchanger degrades due to it. In this paper, such flow distribution effect in a single body multi-channel heat exchanger is evaluated in an analytic way. Transverse conduction through the heat exchanger body which is caused by the mal-distributed flow is formulated and included in NTU evaluation. The NTU relationship between the well-balanced flow distribution and the ill-balanced one is obtained. According to the analysis result, the heat exchanger has the best performance in case of the well-balanced flow distribution, as is expected, and has the performance degradation in case of the ill-balanced flow. The performance degradation is very severe in the heat exchanger with poor transverse conduction.     

Probabilistic multiconstraints optimization of cooling channels in ceramic matrix composites

This paper presents a computational reliable optimization approach for internal cooling channels in Ceramic Matrix Composite (CMC) under thermal and mechanical loadings. The algorithm finds the optimal cooling capacity of all channels (which directly minimizes the amount of coolant needed). In the first step, available uncertainties in the constituent material properties, the applied mechanical load, the heat flux and the heat convection coefficient are considered. Using the Reliability Based Design Optimization (RBDO) approach, the probabilistic constraints ensure the failure due to excessive temperature and deflection will not happen. The deterministic constraints restrict the capacity of any arbitrary cooling channel between two extreme limits. A “series system” reliability concept is adopted as a union of mechanical and thermal failure subsets. Having the results of the first step for CMC with uniformly distributed carbon (C-) fibers, the algorithm presents the optimal layout for distribution of the C-fibers inside the ceramic matrix in order to enhance the target reliability of the component. A sequential approach and B-spline finite elements have overcome the cumbersome computational burden. Numerical results demonstrate that if the mechanical loading dominates the thermal loading, C-fibers distribution can play a considerable role towards increasing the reliability of the design.     

Analysis of transverse heat transfer coefficient in CICC’s with central cooling channel

This paper describes a new method to determine the equivalent transverse heat transfer coefficient between the helium flow in the cable bundle and the flow in the central space of a CICC’s with parallel cooling channel. The method is based on the analysis of the temperature traces during a heat pulse experiment. The equations for the average temperature distribution in the cable are solved analytically to obtain a closed-form expression of the characteristic rise time of the temperature front as a function of the transverse heat transfer coefficient. The value of the equivalent transverse heat transfer coefficient from the bundle to the hole is then obtained as the best fit of the experimental rise time. We show the results of the method by application to short cable sample experiments in SULTAN.     

Gas gap thermal switches using neon or hydrogen and sorption pump

The very low pressure obtained thanks to adsorption phenomenon at low temperature can be used to build cryogenic heat switches, which offer the possibility to make or break thermal contact between two parts of a cryogenic system. The ON (conducting) and OFF (insulating) states of the switch are obtained by varying the gas pressure between two copper blocks separated by a gap of 100 μm. This pressure is controlled by acting upon the temperature of a small sorption pump (activated charcoal) connected to the gap space. For a “high” sorption pump temperature, the gas previously adsorbed in the sorption pump is released to the gap between the two blocks, allowing a good thermal conduction through the gas (ON state). On the opposite, cooling the sorption pump allows a very good vacuum between the copper blocks, which efficiently break the thermal contact (OFF state). Experimental thermal characteristics (Conductance in the ON and OFF state, ON-OFF switching temperature) of such a “Gas Gap Heat Switch” are described using hydrogen or neon as exchange gas and are compared with theoretical calculations.     

Conversion of methane to hydrogen in a reversible flow superadiabatic inert porous medium reactor

Using the analysis of the experimental data on partial oxidation of methane as an example, we have shown that the chemical processes in the inert medium of a reciprocating flow reactor can be modeled with good accuracy by the standard kinetic scheme for homogeneous processes due to the fact that the gas flow in the region of combustion is described by two temperatures — the gas and framework temperatures. Such a modification of the chemical model requires neither changing the recognized mechanism of homogeneous chemistry nor correcting the volume heat transfer coefficient.     

Formation and Transport of Atomic Hydrogen in Hot-Filament Chemical Vapor Deposition Reactors

In this paper we focus on diamond film hot-filament chemical vapor deposition reactors where the only reactant is hydrogen so as to study the formation and transport of hydrogen atoms. Analysis of dimensionless numbers for heat and mass transfer reveals that thermal conduction and diffusion are the dominant mechanisms for gas-phase heat and mass transfer, respectively. A simplified model has been established to simulate gas-phase temperature and H concentration distributions between the filament and the substrate. Examination of the relative importance of homogeneous and heterogeneous production of H atoms indicates that filament-surface decomposition of molecular hydrogen is the dominant source of H and gas-phase reaction plays a negligible role. The filament-surface dissociation rates of H2 for various filament temperatures were calculated to match H-atom concentrations observed in the literature or derived from power consumption by filaments. Arrhenius plots of the filament-surface hydrogen dissociation rates suggest that dissociation of H2 at refractory filament surface is a catalytic process, which has a rather lower effective activation energy than homogeneous thermal dissociation. Atomic hydrogen, acting as an important heat transfer medium to heat the substrate, can freely diffuse from the filament to the substrate without recombination.     

Modelization of the thermal coupling between the ITER TF coil conductor and the structure cooling circuit

The ITER Toroidal Field (TF) coils are required not to quench during the most demanding event: a plasma disruption followed by a fast discharge of the Central Solenoid (CS), the Poloidal Field (PF) coils and the Correction Coils (CC). This event creates large heat deposition in the ITER magnet stainless steel structures in addition to the conductor AC losses. In order to prevent quench occurring in the TF conductor, cooling channels, implemented in the TF coil structure (TFCS), have to remove a large fraction of the heat deposited. The first integrated TF and structure mock-up has been manufactured and then tested in the HELIOS cryogenic test facility (CEA Grenoble) to determine the thermal coupling between the TFCS and the TF conductor, both actively cooled by supercritical helium at 4.4 K and 5 bar. It consists in a stainless steel casing, a cooling pipe glued with resin in the casing groove, winding pack (WP) ground insulation, a radial plate and a copper dummy cable-in-conduit-conductor (CICC). Steady state as well as transient thermal characterizations have been completed in May 2015. Simulation results by thermal hydraulic codes (VENECIA/SuperMagnet) and some of the experimental data are presented and discussed. The thermal coupling between the helium in the cooling tube and the TF coil structure is then modelled as an equivalent heat transfer coefficient in order to simplify the thermal hydraulic (TH) models. Comparison between simplified coupling and detailed coupling is presented.     

Application of Differential Transform Method to Thermoelastic Problem for Annular Disks of Variable Thickness with Temperature-Dependent Parameters

This article analyzes the one-dimensional steady temperature field and related thermal stresses in an annular disk of variable thickness that has a temperature-dependent heat transfer coefficient and is capable of temperature-dependent internal heat generation. The temperature dependencies of the thermal conductivity, Young’s modulus, and the coefficient of linear thermal expansion of the disk are considered, whereas Poisson’s ratio is assumed to be constant. The differential transform method (DTM) is employed to analyze not only the nonlinear heat conduction but also the resulting thermal stresses. Analytical solutions are developed for the temperature and thermal stresses in the form of simple power series. Numerical calculations are performed for an annular cooling/heating fin of variable thickness. Numerical results show that the sufficiently converged analytical solutions are in good agreement with the solutions obtained by the Adomian decomposition method and give the effects of the temperature-dependent parameters on the temperature and thermal stress profiles in the disk. The DTM is useful as a new analytical method for solving thermoelastic problems for a body with temperature-dependent parameters including material properties.