Two-temperature Model Research Articles

Dependence of interfacial mixing for thermally induced magnetization switching in Gd/Fe multilayers

The use of femtosecond laser pulses for ultrafast triggering of magnetization switching is of great interest in multilayer systems with great tunability. At present, the impact of interfacial mixing on magnetization switching has not been thoroughly investigated. In this paper, the impact of interfacial mixing on magnetization dynamics in multilayer systems is investigated by a combination of atomic spin dynamics and two-temperature models. Our results show that interfacial mixing in multilayer systems not only reduces the energy density required for magnetization switching but also expands the range of pulse durations that can trigger magnetization switching. In addition, we have investigated the dependence of the switching time on the interfacial mixing in multilayer systems. The results show that interfacial mixing can accelerate the process of magnetization dynamics, thus providing a theoretical basis for the design of faster speed optically controlled magnetic tunnel junctions.

A hybrid mesoscale-continuum approach to understand and predict melting kinetics of Al powders during laser processing

Abstract Laser interaction with metallic powders during additive manufacturing (AM) leads to fast heating and cooling rates that can affect the quality of the final products due to the formation of defects. One of the first steps towards predicting microstructures generated during AM, therefore, requires an accurate understanding of the laser energy deposition mechanisms that determine the melting kinetics at the level of individual powders. The critical challenge, however, is the availability of computational methods that can model the laser energy absorption, heat transfer, and the related microstructure evolution in individual metal powders at the length and time scales of AM. This manuscript demonstrates the capability of a novel scale-bridging methodology that combines the mesoscale quasi-coarse-grained dynamics (QCGD) simulations with a continuum two-temperature model (TTM) to account for the atomistic mechanisms of laser energy deposition and microstructure evolution and predict the kinetics of melting of individual powders at the experimental time and length scales. The scale-bridging capability of the hybrid QCGD-TTM simulations is demonstrated here by investigating the laser-induced microstructure evolution in aluminum powders with various sizes ranging from 200 nm to 20 µm. The analysis of the evolution of temperature, pressure, phase fraction, and melt fronts suggests the melting mechanism is heterogeneous due to the interaction with a laser, and the melting time is observed to decrease exponentially as the laser intensity increases. The solid-liquid interface velocity can be quantified to identify correlations with interface temperatures, and the predicted values satisfy the theoretically reported limits of crystal stability of metals against homogeneous melting. In addition, the pre-melting is found at the grain boundaries of 20 µm polycrystalline aluminum powder, while a minute contribution to melting is observed. This manuscript demonstrates the capability of the QCGD-TTM method to capture laser-powder interaction and allow the investigation of the kinetics of laser melting.

Capturing non-equilibrium in hypersonic flows: Insights from a two-temperature model in polyatomic rarefied gases

The study utilizes a two-temperature model to analyze non-equilibrium in normal shocks within hypersonic flows in polyatomic rarefied gases. Derived from the extended second law of thermodynamics, this model separates translational and internal temperatures in polyatomic gases, providing a more accurate depiction of non-equilibrium gas flow compared to classical theories like the Navier–Stokes and Fourier (NSF) system. Notably, the analysis reveals that the two-temperature model incorporates an additional contribution to the heat flux due to the gradient of the dynamic temperature, resulting in improved accuracy, especially for high Mach numbers. Results show that the model gives satisfactory shock density and temperature profiles up to Mach 10, with very good agreement observed up to Mach 6.1 compared to the classical NSF model. We conduct an order of magnitude analysis on the dynamic temperature and heat flux gradients appearing in the new constitutive equation using the Mott-Smith method. This analysis highlights the impact of these terms on accurately modeling polyatomic gas behavior in high-speed flows. The effects of bulk viscosity and incoming temperature on shock profiles are also investigated, contributing to a better understanding of shock wave structures in polyatomic gases and their implications for hypersonic flow dynamics.

Simulation and experimental study of femtosecond laser ablation mechanisms of NiCoCrAlY coatings

To enhance the adhesion of turbine blade thermal barrier coating systems using the LST method, a thorough understanding of the ablation mechanism of NiCoCrAlY bond coat material by femtosecond laser systems is essential for producing high-quality textured grooves. This study systematically investigates the ablation mechanisms of NiCoCrAlY material, exploring the effects of laser energy density, laser scanning speed, and the number of laser scans on the ablation of NiCoCrAlY. Numerical simulations based on the two-temperature model were conducted, providing a comprehensive analysis of thermal effects, heat accumulation, and material response during the laser ablation process. The experimental results indicate that 1) the ablation phenomenon caused by heat accumulation becomes evident as the laser energy density increases from 1.948 J/cm2 to 4.521 J/cm2, with the accumulated heat reaching 1525.2 K, leading to distinct melting residues and heat-affected zones on the groove walls. 2) The change in laser scanning speed also affects heat accumulation. Using a laser scanning speed of 800 mm/s results in a high material removal rate, smooth machined walls, and a uniform surface with no significant heat-affected zones. 3) Excessively high numbers of laser scans shift the laser focus to the bottom of the groove. The high concentration of laser energy causes intense localized ablation, forming sharp bases with numerous cracks and melting residues. To achieve efficient and high-quality laser ablation, it is necessary to ensure that the number of scans remains below 40.

Impacting factors and operation thresholds of electron transpiration cooling-based thermal protection system

Electron transpiration cooling (ETC) is a spontaneous endothermic process that occurs during thermionic emission, which shows great potential in ultra-high-temperature thermal protection systems (TPS). Herein, we systematically analyze the main influencing factors on the cooling effect of ETC, such as incoming flow velocity, geometry, and material work function. A two-dimensional finite element model, based on Navier-Stokes equations coupled with the 11-species air reaction model and two-temperature model, is developed to solve the thermal interaction between ETC and the non-equilibrium flow field. Three operational thresholds for ETC are identified. Lower work functions enhance electron emission, thereby reducing wall temperature. With a 2.0 eV work function, ETC significantly outperforms blackbody radiation at 1360 K, and its cooling efficiency increases with temperature. For flow velocities above Mach 9.0, ETC is effective at the leading edge with a 2.4 eV work function and a 5 mm radius. However, it loses effectiveness with a 300 mm leading edge radius, even at Mach 16.0. Notably, at Mach 19.6, with a 2.0 eV work function and a 5 mm radius, ETC reduces surface temperature by up to 48.1 %. These findings highlight the considerable potential of ETC for applications in ultra-high-temperature TPS. These findings highlight the considerable potential of ETC for applications in ultra-high-temperature TPS.

Improving a shell-tube latent heat thermal energy storage unit for building hot water demand using metal foam inserts at a constant pumping power

The phase transition heat transfer during the melting and solidification processes of phase change materials (PCMs) was modeled in a shell-tube thermal energy storage unit. For the first time, special attention was dedicated to the heat transfer enhancement on the heat transfer fluid (HTF) side by placing metal foam (MF) inserts in the HTF tube. The MF inserts on the HTF side were placed next to the fin bases to produce the maximum heat transfer enhancement. A two-temperature local thermal non-equilibrium model was applied to accurately model the transient heat transfer in the MF domains. To perform a fair heat transfer analysis and consider the hydrodynamic aspects of heat transfer, the pumping power for driving the HTF fluid was kept fixed. The finite element method with automatic time-step control was used to integrate the model equations. Results show that the insertion of the MF in the HTF tube enhances conduction heat transfer but reduces flow for a constant pump power. Using a small amount of MF provides a good flow rate and a convective heat transfer while using a large amount of MF provides good conduction heat transfer but a poor flow rate and convection. A moderate amount of MF inserts results in poor conduction and a poor flow rate, notably increasing the phase transition time. A 5 % MF insert could provide about a 13 % shorter solidification time compared to a 25 % MF insert. Thus, a well-designed and engineered MF insert configuration on the HTF side can reduce the phase transition time and improve the energy storage power.

Study on the flow characteristics of double-cone in hypersonic flows

Reusable spacecraft is one of the hot topics in the field of aerospace, attracting wide attention from researchers. Due to the high-Mach-number flight of re-entry, the air near the wall exhibits significant thermochemical nonequilibrium effects. Besides, the existing shock wave/boundary layer interaction (SWBLI) leads to severe aerodynamic heating issues. This study utilizes the two-temperature model to conduct simulations of hypersonic laminar flows around a canonical 25°/55° double-cone with low and high enthalpy. By varying the wall temperature and the aft cone angle, the evolution mechanism of the flow under the high-enthalpy and hypersonic freestream is explored. Our findings illustrate that while the thermodynamic nonequilibrium model closely reflects the separation zone evidenced in the experiments, it habitually overpredicts the peak heat transfer, particularly under high-enthalpy conditions. For the thermochemical nonequilibrium model, the flow field structure appears more uniform, with a reduced standoff distance of the detached shock. An incremental rise in wall temperature correlates with a proportional augmentation of the separation bubble, though its impact on the overall flow field is negligible. Increasing the aft cone angle intensifies the shock/shock interaction (SSI), transitioning from a lower-intensity Type VI to a more intense Type IV shock interplay. The examination reveals that the increase in temperature and cone angle amplifies the interaction between the separation region and shock waves, drastically escalating the peak heat transfer and fostering a secondary peak. The hypersonic flow of the double-cone demonstrates a multifaceted interaction of phenomena, notably SWBLI and SSI, with our analyses providing pivotal insights for the aerodynamic and thermal protection design of the high-Mach-number spacecraft.

Laser-initiated electron and heat transport in gold-skutterudite CoSb3 bilayers resolved by pulsed x-ray scattering

Abstract Electron and lattice heat transport have been investigated in bilayer thin films of gold and CoSb3 after photo-excitation of the nanometric top gold layer through picosecond x-ray scattering in a pump-probe setup. The kinetics of heat transfer are detected by thermal lattice expansion and compared to simulations based on the two-temperature model of coupling of electron and phonon degrees of freedom. The unexpected observation of a larger portion of the deposited heat being detected in the underlying CoSb3 layer before the topmost gold layer is heated supports the picture of transport of the photo-excited electrons from gold to the underlying layer to be converted into lattice heat. The change of partition of heat between the gold and CoSb3 layer with laser fluence and wavelength (either exciting intraband transitions or additionally interband transitions) is rooted in the amplitude of electron temperature. Higher electron temperatures result in a longer equilibration time with the lattice and thus a larger proportion of ballistic electron transport across the interface.

Two-temperature thermochemical nonequilibrium model based on the coarse-grained treatment of molecular vibrational states.

Although the high-fidelity state-to-state (StS) model accurately describes high-temperature thermochemical nonequilibrium flows, its practical application is hindered by the prohibitively high computational cost. In this paper, we develop a reduced-order model that leverages the widelyused two-temperature (2T) framework and a coarse-grained treatment of molecular vibrational states to achieve accuracy comparable to the StS model while ensuring computational efficiency. We observe that the multigroup coarse-grained model (CGM), lumping vibrational energy levels into several groups, yields results close to the StS model for the high-temperature postshock oxygen flows, even using only two groups. However, theone-group CGM (CGM-1G), equivalent to the 2T model but using the StS kinetics, fails to approximate the StS results. Analysis of microscopic group properties reveals that the failure of the CGM-1G stems from the inability to capture the non-Boltzmann effects of mid-to-high vibrational levels, overestimating apparent dissociation rates and vibrational energy loss in the dissociation-dominated region. We then propose an analytical distribution function of vibrational groups by incorporating Treanor-like terms and an additional linear term (addressing the dissociation depletion of high-lying levels). Building upon this algebraic group distribution function and reconstructing vibrational levels within each group using the vibrational temperature, we develop a new 2T model called CG2T, which demonstrates accuracy much closer (than the CGM-1G) to the StS results for the postshock oxygen flows with varying degrees of thermochemical nonequilibrium. Moreover, a fullyconnected neural network is pretrained to substitute the module for the mass and vibrational energy source terms to enhance computational efficiency, achieving about 30-fold speedup in the CG2T model without sacrificing accuracy.

On ablation characteristics based on two-temperature model involving a multivariate lattice heat capacity by ultrashort laser-irradiated in zirconia

To explore the mechanism of material removal, this paper conducts a systematic study on picosecond laser processing of zirconia by using both theory and experiment. Comparing the multivariate lattice heat capacity of the Einstein and Debye models, two-temperature model (TTM) is developed to improve the accuracy of the temperature field. Then, to verify the effectiveness of TTM proposed, ablation experiments are performed by single-pulse picosecond laser on zirconia at different laser energy density. The results show that the measured craters profiles are well agree with the simulated melting/vaporization temperature distribution. Micro-morphology is significantly affected by phase transition induced by temperature rise. Moreover, the results confirmed that increased temperature can lead to transition in zirconia crystal structure and oxygen vacancies. Finally, the effect of coupling temperature variations on the elemental and physical phase variations are focused to investigate, which can help to optimize the processing quality due to crystalline phase transitions. This study provides guidance for optimizing picosecond laser processing of zirconia.

A study on the combined effects of variable viscosity and thermal conductivity on forced convection in bidisperse porous medium

This research focuses on exploring the flow and temperature distribution of forced convection in a channel of horizontally placed parallel plate under the existence of a bidisperse porous medium (BDPM) emphasizing the consequences of viscous dissipation. The temperature-dependent thermal conductivity and viscosity are considered while maintaining the momentum slip and constant wall temperature at the channel walls. Analysis of the dynamics of fluid flow and the temperature distributions in both the fluid and solid phases is conducted by following the two-velocity and two-temperature models in this work. The model governing equations are non-dimensionalized following the relevant dimensionless parameters and the study calculates the temperature and velocity profiles for each phase using the Homotopy Analysis Method (HAM). The obtained temperature and velocity are discussed and explained with the help of graphs. Certain fluids exhibit varying behaviors at different temperatures. Therefore, it is crucial to consider the temperature-dependent physical properties of the fluid for specific applications. This highlights the importance of implementing temperature-dependent physical properties in the analysis. Throughout the investigation, it is discovered that the viscosity parameter has a greater influence on velocity as compared to temperature, the same for thermal conductivity on temperature. The impact of physical parameters including skin friction, volume flow rate, and Nusselt number on both plates are also examined in this study. The findings are discussed, and tables displaying numerical values for various physical characteristics are provided for both the liquid and solid phases. The results obtained were also compared with existing literature, revealing a strong alignment between them.

Optimization of GeSn nanostructures via tuning of femtosecond laser parameters

Semiconductor nanostructures are known to exhibit interesting electrical and optical properties, as well as functionalities that are significantly different from their bulk counterparts. These unique characteristics can be attributed to their quantum confinement effects, and large surface-to-volume ratios, along with the fact that their compositions can be tuned. This study proposes a new method for tuning the properties of GeSn nanostructures on a silicon substrate using femtosecond laser direct writing. A series of GeSn nanostructures with different compositions of Sn ranging from nanodots, nanoholes, nanostrips, nanogaps, and nano-cauliflowers were successfully prepared via tuning of femtosecond laser parameters. The morphology, composition of Sn, and crystalline properties of the formed nanostructures were also greatly influenced by the laser fluence and the effective pulse number. The femtosecond laser/GeSn interaction mechanism was thoroughly investigated based on the two-temperature Drude model. This work provides a novel strategy for tuning the bandgap and morphology of GeSn nanostructures, through which the properties of GeSn-based devices can be tailored according to the requirements of practical applications in the fields of microelectronics and photonics.

A study of an X-ray flare on the solar analogue V895 Tau

Using observations with XMM-Newton, we study the characteristics of a flare emanating from a solar analogous V895 Tau. At the peak of the flare, its luminosity reached 3.3×1030ergs−1, which is ∼ 600 times more energetic than the X10 class flare on the Sun. The quiescent state corona of V895 Tau is depicted by a two-temperature plasma model with temperatures of 3.9 and 11 MK. The flare’s evolution was carefully scrutinized through time-resolved X-ray spectroscopy, unveiling the variations in temperature, emission measure, abundance and luminosity during the flare. The temperature peaked at 36.1 MK, which is approximately four times higher than the pre-flare temperature. Employing a hydrodynamic loop model, we have estimated the half length of the flaring loop to be 5.9×1010 cm. Using the loop scaling laws, other loop parameters like density, pressure, volume, and minimum magnetic field are also estimated, and are found to be similar to those of other flares from similar type of stars.

Single photon detection up to 2 µm in pair of parallel microstrips based on NbRe ultrathin films

Superconducting microstrip single photon detectors (SMSPDs) are increasingly attracting the interest of the scientific community as a new platform for large area detectors with unprecedented advantaged in terms of fabrication. However, while their operativity at the telecommunication wavelength was achieved, working beyond 1.55 µm is challenging. Here, we experimentally demonstrate single-photon operation of NbRe microstrips at wavelengths of 1.55 and 2 µm. The devices are structured as pairs of parallel microstrips with widths ranging from 1.4 to 2.2 μm and lengths from 5 to 10 μm. This innovative design may assure large sensitive areas, without affecting the kinetic inductance, namely the time performance of the detectors. The results are discussed in the framework of the hot-spot two-temperature model.

Numerical study of shock-induced thermochemical nonequilibrium effects in a high Mach flow field

As Mach number increases, thermochemical nonequilibrium is recognized as potentially affecting the flow field structure, as well as mixing and combustion characteristics, where shock-induced thermochemical nonequilibrium is a common and crucial phenomenon in compressible flow fields. A numerical study of shock-induced thermochemical nonequilibrium effects within a high Mach flow field of the electre vehicle is conducted by employing a two-temperature model-based solver hy2foam. The validation through experimental and simulation data confirms that hy2foam coupled with Park's two-temperature model and Park's five-species mechanism correctly predicts the flow structure and nonequilibrium characteristics. Four regime cases of thermochemical equilibrium, thermal nonequilibrium, chemical nonequilibrium, and thermochemical nonequilibrium are designed for comparison. First, the mechanism of shock-induced nonequilibrium is revealed. The shock induces the thermal nonequilibrium to occur instantly, and then the equilibrium is reestablished by undergoing the relaxation process. However, chemical nonequilibrium works delayed after the shock, and the high temperature induced by the shock motivates deviation from the chemical equilibrium by turning on chemical reactions. Further comparison of the four cases reveals that thermodynamic nonequilibrium significantly affects both shock position and intensity. In contrast, chemical nonequilibrium only significantly affects the distance to the shock detachment. Furthermore, it is found that thermodynamic and chemical nonequilibria behave in a complex coupling relationship after the shock.

Effect of multi-temperature models on heat transfer and electron behavior in hypersonic flows

In hypersonic computational fluid dynamics, the two-temperature (2-T) model is widely used to simulate thermochemical nonequilibrium. The 2-T model incorporates translational-rotational and electron-electronic-vibrational energies, assuming that the integrated energies have the equivalent temperature. In this study, multi-T models are constructed to accurately predict the effects on heat flux and free electrons due to the separation of energy modes under hypersonic environments. The three-temperature (3-T) model separates the electron-electronic energy from the electron-electronic-vibrational energy of the 2-T model. The 3-T model can accurately predict the distribution and temperature of free electrons by separating the energy of free electrons, which has different characteristics from heavy particles. The four-temperature model treats rotational energy as a nonequilibrium energy mode, distinct from translational-rotational energy. While the rotational temperature reaches equilibrium rapidly at low temperatures, at high-temperature regime rotational temperature shows a relaxation time similar to that of vibrational temperature, which cannot be ignored. To develop multi-T models, electron-vibrational relaxation and translational-rotational relaxation, which are omitted in the 2-T model, are considered. Various flight test and ground facility conditions are analyzed to verify the effects of electron and heat flux under circumstances that include shock, expansion, and shock wave boundary layer interaction. The results of the multi-T models show significant differences in electron temperature and distribution caused by electron-electronic nonequilibrium. Additionally, rotational nonequilibrium increases the shock standoff distance and alters the electron distribution at high altitudes. The heat flux difference across multi-T models is found to be negligible, except in the high degree of ionization condition.

A shell-tube latent heat thermal energy storage: Influence of metal foam inserts in both shell and tube sides

Enhancing heat transfer in latent heat thermal energy storage systems is of utmost importance to facilitate the efficient absorption and release of thermal energy. The primary objective of the current study is to investigate the influence of a metal foam layer on heat transfer enhancement in both the heat transfer fluid side and the shell side. The research explores the incorporation of a fixed 30 % foam layer, which can either extend along the tube wall or penetrate deeper into the shell, moving away from the heat transfer fluid tube. A local thermal non-equilibrium two-temperature heat equation model is utilized to mathematically model the interactions within the metal foam embedded in the heat transfer fluid tube and the phase change material domain. The governing equations are solved using the finite element method. The results indicate that adjustments to the inlet pressure and the metal foam shape parameter (FL) can significantly reduce the melting time, with a variation of approximately 40 %. Specifically, at a constant inlet pressure of 750 Pa, the energy storage power at a 90 % charging increases from 32.2 W (FL = 0.75) to 48.7 W (FL = 1.37). A modification of FL shape parameter increased the power output by 34 %.

Molecular dynamics simulations of neutron induced collision cascades in Zr — Statistical modelling of irradiation damage and potential applications

Understanding irradiation damage involves a multi-scale and multi-physics approach, integrating data from experiments, simulations and phenomenological models. This paper focuses on its early stages, specifically neutron-induced collision cascades in zirconium, as nuclear-grade zirconium alloys are widely used in fuel assemblies. We have gathered and analysed a significant sample of results from high-fidelity, large-scale molecular dynamics (MD) simulations, employing existing interatomic potentials and the two-temperature model to account for electron–phonon coupling. Our data can be directly applied to higher-scale methods.Furthermore, we carried out a comprehensive statistical analysis of the features associated with the defect production, including the number of defects, their distribution and size of the affected area. As a result, we developed a generative model of collision cascades that is parametric, hierarchical and stochastic, i.e. it takes into account a statistical nature of the phenomenon, is interpretable and shareable. This model has been developed with three primary objectives: to provide a sufficient descriptor of a cascade, to interpolate data obtained from high-fidelity simulations, and to demonstrate that the statistical model can produce representative distributions of primary irradiation defects. The results can be used to generate synthetic inputs for models at longer length and time scales, to provide fast approximations that take into account the morphology of introduced defects, and in general to serve as a powerful analytical tool.

Near-Field-Regulated Ultrafast Laser Supra-Wavelength Structuring Directly on Ultrahard Metallic Glasses.

The ultrafast-laser-matter interactions enable "top-down" laser surface structuring, especially for materials difficult to process, with "bottom-up" self-organizing features. The subwavelength scenarios of laser-induced structuring are improved in defects and long-range order by applying positive/negative feedbacks. It is still hardly reported for supra-wavelength laser structuring more associated with complicated thermo/hydro-dynamics. For the first time to the knowledge, the near-field-regulated ultrafast-laser lithography of self-arrayed supra-wavelength micro/nano-pores directly on ultra-hard metallic glass is developed here. The plasmonic hot spots on pre-structures, as the positive feedback, clamped the lateral geometries (i.e., position, size). Simultaneously, it drilled and self-organized into micro/nano-pore arrays by photo-dynamic plasma ablation and Marangoni removal confined under specific femtosecond-laser irradiation, as the negative feedback. The mechanisms and finite element modeling of the multi-physical transduction (based on the two-temperature model), the far-field/near-field coupling, and the polarization dependence during laser-matter interactions are studied. Large-area micro/nano-pore arrays (centimeter scale or larger) aremanufactured with tunable periods (1-5µm) and geometries (e.g., diameters of 500 nm-6µm using 343, 515, and 1030 lasers, respectively). Consequently, the mid/far-infrared reflectivity at 2.5-6.5µm iss decreased from ≈80% to ≈5%. The universality of multi-physical coupling and near-field enhancements makes this approach widely applicable, or even irreplaceable, in various applications.

Radiation RMHD Accretion Flows around Spinning AGNs: A Comparative Study of MAD and SANE State

In our study, we examine a 2D radiation, relativistic, magnetohydrodynamics accretion flow around a spinning supermassive black hole. We begin by setting an initial equilibrium torus around the black hole, with an embedded initial magnetic field inside the torus. The strength of the initial magnetic field is determined by the plasma beta parameter, which is the ratio of the gas pressure to the magnetic pressure. In this paper, we perform a comparative study of the magnetically arrested disc (MAD) and standard and normal evolution (SANE) states. We observe that the MAD state is possible for comparatively high initial magnetic field strength flow. Additionally, we also adopt a self-consistent two-temperature model to evaluate the luminosity and energy spectrum for our model. We observe that the total luminosity is mostly dominated by bremsstrahlung luminosity compared to the synchrotron luminosity due to the presence of a highly dense torus. We also identify similar quasi-periodic oscillations for both MAD and SANE states based on power-density spectrum analysis. Furthermore, our comparative study of the energy spectrum does not reveal any characteristic differences between MAD and SANE states. Last, we note that the MAD state is possible for both prograde and retrograde accretion flow.