Radial Thermal Gradients Research Articles

Distribution of the electrical resistivity of a n-type 4H-SiC crystal

Nitrogen is commonly doped to obtain n-type 4H-SiC crystals, which have been commercialized for the development of power electronics in recent years. Now the uniformity of electrical resistivity becomes an important issue for the growth of n-type 4H-SiC crystals. In this work, the effects of the radial thermal gradient and growth facet on the distribution of the electrical resistivity were investigated for a n-type 4H-SiC crystal with a diameter of 150 mm during its physical-vapor-transport growth. It is found that the resistivity at the center of the crystal is low in the early growth stage. As the crystal grows, the growth facet expands, accompanied by a reduction in the resistivity of this facet. The change in the distribution of the resistivity in the crystal is initially governed by the radial thermal gradient and then influenced by the spiral growth mode of the growth facet. In the non-facet region of the crystal step-flow growth occurs, where the doping of nitrogen is primarily affected by the temperature and C/Si ratio. In the facet region, the volume fraction of nitrogen in the mixture of argon and nitrogen input into the growth system mainly governs the doping of nitrogen during the spiral growth. The insights gained in the current work may help the fabrication of n-type 4H-SiC crystals with uniform resistivity.

Frequency-domain axisymmetric and thermomechanical viscoelastic analysis of thermoplastic composite pipe

ABSTRACT Thermoplastic composite pipe (TCP), composed of polymers and composite laminates, shows significant potential for deep-water offshore oil field development due to its lightweight and high strength. However, current mechanical studies primarily focus on the elastic domain, ignoring the critical viscoelasticity of non-metallic materials. To solve this, we introduce a comprehensive theoretical model that incorporates viscoelastic properties under both axisymmetric and thermal loads, considering radial convective thermal gradients and axial heat conduction. This model accurately predicts TCP's mechanical behavior by using stiffness coefficients, differential geometry, and radial-axial temperature transfer curves. By applying the principle of elastic-viscoelastic correspondence, we obtain viscoelastic solutions in the frequency domain, showing strong agreement with Finite Element (FE) models particularly under cyclic loading. Viscoelasticity introduces larger equivalent axial stiffness and viscoelastic damping within complex structures, which become more obvious with temperature fluctuations.

Radial Thermoelectric Model for Stranded Transmission Line Conductors.

Bare-stranded conductors play a critical role in the efficiency and safe operation of transmission lines. The heat generated in the interior of the conductor is conducted radially to the outer surface, creating a radial thermal gradient. The radial temperature gradient between the core and the surface depends on multiple factors, such as stranding, number of layers, current level, electrical resistance and the effective radial thermal conductivity. Therefore, the radial temperature model must be considered when developing accurate conductor models. Such models are particularly important in the development of dynamic line rating (DLR) approaches to allow the full current carrying capacity of the conductor to be utilized while ensuring safe operation. This paper develops a radial one-dimensional thermoelectric model for bare-stranded conductors used in transmission lines. The accuracy of the proposed model is determined by experimental tests performed on three conductors.

On the migration of a droplet driven by thermocapillary action in a wettability-confined track

We report a study of the thermocapillary migration of droplets under a radial thermal gradient and in a wettability-confined track. A three-dimensional mathematical model is established based on the lubrication approximation. By considering the contact-line dynamics, a method for determining the velocity of the contact line in different directions is proposed for a three-dimensional droplet. Numerical simulations are performed to investigate the variations in the droplet profile, contact angle, and contact line. Three substrate-wettability cases are considered: uniform, temperature-dependent, and track-dependent wettability. The results show that when the substrate wettability is uniform, the droplet height initially decreases rapidly, and its center becomes concave and then gradually evolves into a ring-like morphology. Reducing the temperature sensitivity of the liquid–gas interfacial tension or increasing the temperature sensitivity of the liquid–solid interfacial tension decreases the equilibrium contact angle and accelerates thermocapillary migration. When a droplet spreads in a wettability-confined track, a wave-like peak is formed on each side of the droplet along the track direction until it finally separates into two distinct parts. As the track width is decreased, the time taken for a droplet to split into two smaller droplets advances, and the separation time presents a linear relationship with the track width.

Design and optimization of superconducting CUSP electromagnetic field structure based on a COMSOL-GMDH-MOSO hybrid strategy

As the semiconductor industry gains momentum, there is a significant focus on producing high-quality silicon wafers with larger diameters. However, the preparation of major-diameter, high-quality silicon single-crystal has encountered challenges such as intense convection inside the melt and high oxygen impurity concentration at the interface between the fluid and solid phases. To tackle these problems, the external superconducting CUSP electromagnetic field structure was designed to optimize the crystal growth parameters. A hybrid strategy of the multiphysics field coupling method, Group Method of Data Handling (GMDH) type neural network identification, and the Multiple Objective Snake Optimizer (MOSO) algorithm was proposed to optimize the superconducting CUSP electromagnetic field structure. A two-dimensional axisymmetric model was established for 18-inch silicon single-crystal preparation using the Magnet system Applied Czochralski (MCZ) method. The amount of longitudinal plies of superconducting CUSP electromagnetic field coils, coil spacing, and the thickness of magnetic shields were selected as design variables, and the radial electromagnetic induction intensity at the graphite crucible inner wall and the superconducting magnet volume were used as dual objective functions. The required samples for GMDH training were provided by COMSOL Multiphysics (COMSOL) numerical calculations, and polynomial mathematical equations were established with the radial electromagnetic induction intensity at the graphite crucible inner wall and the superconducting magnet volume as the dual objective functions. Then the Pareto optimal solution for the electromagnetic field structure design variables was obtained using the dual objective function optimized by MOSO. With the hybrid strategy, numerical simulations and theoretical analysis of the crystal preparation process parameters under the effect of the superconducting electromagnetic field with the optimal structure were carried out. The results displayed that the added superconducting CUSP electromagnetic field reduced the crystal radial and axial thermal gradients and greatly suppressed the melt convection. As a result, the heat distribution inside the hot fused silicon was more even, the thermal gradient at the solid–liquid interface was reduced by 68.4%, and the oxygen impurity content was reduced by 82.1%, which effectively improved the crystal quality. The thermal field simulation results verified that the proposed hybrid strategy provided a new numerical calculation method for obtaining the optimal superconducting electromagnetic field structure.

Characterization of Prismatic Slip in SiC Crystals by Chemical Etching Method

In 4H-silicon carbide crystals, basal plane slip is the predominant deformation mechanism. However, prismatic slip is often observed in single crystals grown by the physical vapor transport method as the diameter expands to 6 inches or larger. Thermal modeling has shown that occurrence of prismatic slip is attributed to increased radial thermal gradients. While X-ray topography can be used to characterize the presence and extent of prismatic slip, the feasibility of using the chemical etching method to assess the extent of prismatic slip in an industrial setting is investigated. The distribution of scallop shaped etch pits oriented along the directions that correspond to prismatic dislocations, correlate well with the results of the thermal model that predicts the occurrence of prismatic slip dislocations. This capability of the etch pit method to characterize prismatic slip can be used to manage radial thermal gradients during PVT growth.

Numerical investigations of turbulent heat transfer enhancement in circular tubes via modified internal profiles

Convective heat transfer enhancement in turbulent pipe flows via patterned surface textures is studied numerically via large eddy simulation (LES). The Reynolds and Prandtl numbers of the flow are 90,000 and 0.836, respectively. The patterned surface textures consist of ellipsoidal inward-facing elements, a wire coil, and spiral corrugations. The governing equations are solved on three-dimensional grids with the finite volume method using second-order temporal and spatial schemes. The mean Nusselt number and friction factor are calculated in each textured pipe and compared to an untextured baseline configuration. The inward-facing ellipsoidal elements showed the best performance yielding 22 − 42 % heat transfer enhancement with 41 − 97 % pressure loss penalty. The mechanisms driving convective heat transfer enhancement are examined via order-of-magnitude analysis of the first and second laws of thermodynamics. An effective convective mixing parameter is defined to reflect the interplay between the radial turbulence and local thermal gradients. The best enhancement technique yields 46% larger effective convective mixing with 26% lower turbulent kinetic energy compared to the least efficient case. The analysis shows that high heat transfer enhancement is promoted by inducing strong radial turbulent fluctuations in high-temperature-gradient regions while keeping other regions undisturbed. • Heat transfer enhancement via surface textures is studied via large eddy simulation. • Inward ellipsoids yield 22% higher heat transfer rate and 41% larger pressure drop. • The process driving heat transfer enhancement is explained via total energy budgets. • Near-wall radial fluctuations contribute the most towards enhancing heat transfer. • Axial vortices yield the best heat transfer enhancement and low entropy generation.

On the double-diffusive layer formation in the vertical annulus driven by radial thermal and salinity gradients

We employ the Chebyshev tau-qz algorithm developed by Straughan and co-workers (1996, 2013) to investigate the stability of the double-diffusive convection in a vertical annulus, in which the inner cylinder maintains cold and fresh and the outer cylinder warm and salty. Results show that the double-diffusive layer may form through a successive generation of vortices induced by the interaction between the radial thermal and salinity gradients. The competition of the two gradients leads to three different types of double-diffusive instabilities: thermal, salt-finger, and diffusive. The axisymmetric mode is generally the most unstable, and its instability enhances when the annular gap width is larger. The non-axisymmetric mode becomes more stable for the annulus with a larger gap width, and its stability enhances when the mode has a smaller azimuthal wavelength. Finally, we show through a simulated experiment that the HDDL thickness is of a scale about the gap width.

Buoyant flow instability induced by a uniform internal heat source in a vertical annular porous layer

The buoyancy–induced parallel flow in a vertical cylindrical porous layer with annular cross–section is analysed. A radial thermal gradient caused by a uniformly distributed heat source is assumed to induce the buoyant flow. The layer boundaries are modelled as isothermal and permeable to an external fluid reservoir. The onset of the convective instability is analysed by linearising the governing equations for the perturbations. The governing parameters driving the instability are the heat–source Rayleigh number and the ratio between the internal radius and the external radius. Neutral stability curves and the critical values of the Rayleigh number, the perturbation wave number and the angular frequency are computed numerically. It is shown that axisymmetric modes form the most dangerous type of instability.

Thermodynamic Modeling of the Uranium–Tellurium System: Estimation of the Uncertainties by a Bayesian Approach

Under irradiation, the formation of fission products in the (U,Pu)O2 fuel with time has a substantial effect on its chemistry. In particular, migration of the most volatile fission products (Cs, Te, I, Mo) from the center to the periphery of the fuel pellet is induced by the large radial thermal gradient. To predict the thermodynamic properties of the irradiated fuel, thermodynamic modeling of the complex multi-component (Cs-I-Te-Mo)–(U-Pu)–O system is performed using the CALPHAD method. In this work, the thermodynamic assessment of the U–Te sub-system is performed. The literature review reveals a lack of experimental data as well as scattering and inconsistency of some of the data. In particular, no thermodynamic data exist on the liquid. From this review, input thermodynamic and phase diagram data are carefully selected. The Gibbs energy functions are then adjusted by fitting these data. An overall good agreement is obtained with all the selected data except for the enthalpy of formation for UTe which is underestimated by 13% by our model. This could be due to an inconsistency between the enthalpy of formation and vapor pressure data. In a second step, the uncertainties on the thermodynamic parameters and their propagation on the calculated thermodynamic and phase diagram data are estimated using a Bayesian approach. The analysis shows that there are too many parameters (22) for too few data points (120 points). The uncertainties are thus large on some of the calculated data. Moreover the inconsistency of some of the data and the lack of thermodynamic data for the liquid makes the model uncertain. New experimental data such as heat capacity, enthalpy of formation for the compounds, and chemical potentials or activities for the liquid phase would improve the reliability of our model. Measurements of phase diagram data in the U–UTe2 region are also required. However this work provides the first detailed uncertainty analysis of the U–Te CALPHAD model. Moreover our approach, contrary to other Bayesian methods, provides an analytical posterior probability distribution and analytical credible intervals for the calculated thermodynamic quantities. It also speeds up the simulation of the uncertainty estimations on the phase diagram.

Characterization of prismatic slip in PVT-grown AlN crystals

The most frequently observed deformation mechanism in wurtzite aluminum nitride (AlN) grown by the physical vapor transport (PVT) method is basal plane slip. However, prismatic slip also takes place in such crystals. In this study, prismatic slip is observed in a 50 mm commercial AlN substrate wafer, leading to a sixfold symmetric BPD pattern in the wafer. Prismatic dislocations cross slip on to basal plane and multiply there, increasing the dislocation density of the wafer. A radial thermal model is established to explore the origin of the unevenly distributed dislocations. The unevenly distributed resolved shear stress across the whole radial area of the boule during PVT growth caused by radial thermal gradients offers driving force for the activation of the three sets of prismatic slip systems, producing nonuniform dislocation distribution in the boule and thus the wafer. Both experimental observations and theoretical calculations of the critical resolved shear stress (CRSS) correlate well with the model results, revealing that controlling radial thermal gradients is critical for lowering dislocation density and enhancing the crystal quality using PVT growth method.

High Throughput UHPLC-MS-Based Lipidomics Using Vacuum Jacketed Columns.

Reversed-phase UHPLC-MS is extensively employed for both the profiling of biological fluids and tissues to characterize lipid dysregulation in disease and toxicological studies. With conventional LC-MS systems the chromatographic performance and throughput are limited due to dispersion from the fluidic connections as well as radial and longitudinal thermal gradients in the LC column. In this study vacuum jacketed columns (VJC), positioned at the source of the mass spectrometer, were applied to the lipidomic analysis of plasma extracts. Compared to conventional UHPLC, the VJC-based methods offered greater resolution, faster analysis, and improved peak intensity. For a 5 min VJC analysis, the peak capacity increased by 66%, peak tailing reduced by up to 34%, and the number of lipids detected increased by 30% compared to conventional UHPLC. The narrower peaks, and thus increased resolution, compared to the conventional system resulted in a 2-fold increase in peak intensity as well a significant improvement in MS and MS/MS spectral quality resulting in a 22% increase in the number of lipids identified. When applied to mouse plasma samples, reproducibility of the lipid intensities in the pooled QC ranged from 1.8-12%, with no related drift in tR observed.

Magnetic field effects on laser energy deposition and filamentation in magneto-inertial fusion relevant plasmas

We report on experimental measurements of how an externally imposed magnetic field affects plasma heating by kJ-class, nanosecond laser pulses. The experiments reported here took place in gas cells analogous to magnetized liner inertial fusion targets. We observed significant changes in laser propagation and energy deposition scale lengths when a 12T external magnetic field was imposed in the gas cell. We find evidence that the axial magnetic field reduces radial electron thermal transport, narrows the width of the heated plasma, and increases the axial plasma length. Reduced thermal conductivity increases radial thermal gradients. This enhances radial hydrodynamic expansion and subsequent thermal self-focusing. Our experiments and supporting 3D simulations in helium demonstrate that magnetization leads to higher thermal gradients, higher peak temperatures, more rapid blast wave development, and beam focusing with an applied field of 12T.

Prismatic Slip in AlN Crystals Grown By PVT

Aluminum nitride (AlN) single crystals are desired as substrates for nitride based electronic and optoelectronic applications[1]. A low density of dislocations and other structural defects in bulk AlN substrates is in demand to grow high-quality heteroepitaxial epilayers. Physical vapor transport (PVT) grown AlN crystals possess low density dislocations and other structural defects[2]. In AlN crystals grown by PVT, basal plane slip is the most frequently observed deformation mechanism. However, prismatic slip takes place as well in such crystals [3, 4].When the diameter of AlN wafers expands to 50 mm and larger, managing the thermal gradients in the PVT growth chamber becomes critical for reducing thermal stresses that cause deformation. Recent synchrotron X-ray topography [5] studies of 50 mm diameter AlN wafers showed that while most wafers contained few to no basal plane dislocations (BPDs), some wafers possessed a 6-fold BPD dislocation pattern [2] which was aligned along the <11-20> directions. This configuration indicated that prismatic slip had likely occurred. Screw typed prismatic dislocations cross slipped from the prismatic plane onto the basal plane, and underwent basal plane slip, leading to dislocation multiplication. To investigate the origins of prismatic slip, a radial thermal gradient model was established showing[6] the resolved shear stress across the entire area of the crystal boule during growth. The results from the model were compared with experimental observations to investigate the role of radial thermal gradients in the nucleation of prismatic slip in AlN during bulk growth. This insight will help guide efforts to minimize structural defects in PVT AlN.

Prismatic Slip in AlN Crystals Grown By PVT

Basal plane slip is the most frequently observed deformation mechanism in hexagonal aluminum nitride (AlN) crystals grown by the physical vapor transport (PVT) method. However, prismatic slip can also take place in such crystals. In this study, slip in the three prismatic slip systems with nonuniform distributions, observed in a commercial 50 mm AlN substrate wafer, was investigated. The nonuniformity was attributed to the distribution of resolved shear stress in each prismatic slip system caused by radial thermal gradients in the growing crystal boule. A radial thermal model was established to quantitively estimate the thermal stress across the area of the crystal boule during PVT growth. The model results correlated well with both the experimental observations and theoretical calculations of the critical resolved shear stress, revealing that radial thermal gradients play a key role in activating prismatic slip during AlN bulk growth.

A Numerical Study of Cirrus Bands and Low Static-stability Layers associated with Tropical Cyclone Outflow

AbstractProminent cirrus cloud banding occurred episodically within a northern cirrus canopy of Typhoon Talim (2017) during its recurvature. The generation mechanisms of the cirrus bands and low static-stability layers that support the bands are investigated using a numerical simulation with the Advanced Research Weather Research and Forecasting Model. Inspection of model output reveals that thin layers of near-neutral to weakly unstable static stability are persistently present in the upper and lower parts of the upper-level outflow, and shallow convection aligned along the vertical shear vector is prevalent in these layers. The cirrus banding occurs as the lowered outflow from the weakening storm ascends slantwise over a midlatitude baroclinic zone, and updrafts of the preexisting shallow convection in the upper part of the outflow layer become saturated. It is shown that the strong outflow resulting from violation of gradient-wind balance in the core region, by itself, creates the low static-stability layers. Analyses of potential temperature and static stability budgets show that the low static-stability layers are created mainly by the differential radial advection of radial thermal gradients on the vertical edges of the outflow. The radial thermal gradients occur in response to the outward air parcel acceleration in the core region and deceleration in the outer region, which, by inducing compensating vertical mass transport into and out of the outflow, act to tilt the isentropes within the shear layers. The effects of environmental flow and cloud radiative forcing on the cirrus banding are also addressed.

Analyzing and relieving the thermal issues caused by fabrication details of a deuterium cryogenic target

In inertial confinement fusion experiments, fuel quality is determined mainly by the thermal environment of the capsule in the layering procedure. Owing to the absence of a radial thermal gradient, formed deuterium–deuterium (DD) ice shells in the capsule are thermally instable. To obtain a solid DD layer with good quality and long lifetime, stringent demands must be placed on the thermal performance of cryogenic targets. In DD cryogenic target preparation, two issues arise, even after the capsule’s temperature uniformity has been improved by the use of thick aluminized films. The first is the inconsistent ice shape, which is related to the capsule’s thermal field. In this article, some typical fabrication details are investigated, including adhesive penetration during assembly, the presence of the fill tube, the optical properties of the hohlraum and film surfaces, the jacket–hohlraum connection, deviations in capsule location, and asymmetrical contact at the arm–jacket interfaces. Detailed comparisons of the thermal effects of these factors provide guidance for target optimization. The second issue is the instability of seeding crystals in the fill tube due to unsteadiness of the direction of the thermal gradient in the fill tube assembly. An additional thermal controller is proposed, analyzed, and optimized to provide robust controllability of tube temperature. The analysis results and optimization methods presented in this article should not only help in dealing with thermal issues associated with DD cryogenic targets, but also provide important references for engineering design of other cryogenic targets.

Thermal‐hydraulic analysis of UO2 and MOX fuel considering different cladding materials at various burnup levels in pressurized water reactor

AbstractThermal analysis of fuel elements with UO2 and mixed‐oxide (MOX) fuels at different fuel burnup levels has been performed analytically and by simulation using ANSYS. Results showed that UO2 incurred a lower fuel temperature than MOX under all conditions. Higher fuel element temperatures were obtained for higher levels of burnup for UO2 fuel. For MOX fuel, higher temperatures were obtained for low and high burnup fuel. Radial temperature, thermal gradient, and thermal heat flux were determined across reactor pressure vessel (RPV), demonstrating the highest value at the center of the RPV. The maximum linear power density was determined for UO2 and MOX, showing that using UO2 fuel at 2 at% burnup rendered the highest allowable linear power density. Furthermore, the transient analysis showed that there was a small rise in fuel temperature for a decrease in mass flow rate from 100% to 60% followed by a rapid increase in temperature for further reduction in flow rate.

Investigation of delayed formation of wax deposits in polyethylene pipe using a flow-loop

After the start of the flow in a home-built flow-loop, the thickness of a waxy layer deposited on a stainless steel (SS) test section was found to increase immediately, while deposition was delayed for around 4 h on a polyethylene (PE) test section. The radial thermal gradient, wax precipitation rate, radial diffusivity of wax, and shear stresses at the surface of the deposit layer were calculated, eliminating these factors as sources of different deposition behavior. However, the contact angles of oils containing precipitated wax crystals on PE surfaces were found to increase more with increasing wax content than those on SS surfaces. Consistent with this, while the wax contents of deposits were found to be around 18 wt % for both PE and SS pipes, the adhesion of the deposit on the PE surface was found to be much weaker than on the SS surface, as evidenced by the easier of removal of the deposit from PE than from SS pipes when heated in vertical orientation under gravity. These results point to pipe wall wettability as a significant factor in both initial growth of wax deposit, and ease of removal.

Investigation of thickness and wax content of wax deposits in polyethylene pipe using a flow loop

AbstractIn this study, the thickness and wax content of wax deposits were found to be thinner and lower in the polyethylene (PE) pipe than in the stainless steel (SS) pipe using a flow loop apparatus. The diffusivity of wax, radial thermal gradient, and wax precipitation rate in the PE and SS pipes were calculated and compared. It was found the diffusivity of wax in the PE pipe was higher and tended to enhance the wax deposition in the PE pipe, while the radial thermal gradient and wax precipitation rate were lower in the PE pipe and had the opposite effects. These factors are shown to be comparable with each other and the effect of the thermal gradient dominates the mass flux of wax from bulk to the oil‐deposit interface and into the deposits finally, thus causing differences in thickness and wax content of deposits between the PE and SS pipes.