Thermal Accommodation Research Articles

TriPoD: Tri-Population size distributions for Dust evolution

Context. Dust coagulation and fragmentation impact the structure and evolution of protoplanetary disks and set the initial conditions for planet formation. Dust grains dominate the opacities, they determine the cooling times of the gas via thermal accommodation in collisions, they influence the ionization state of the gas, and the available grain surface area is an important parameter for the chemistry in protoplanetary disks. Therefore, dust evolution is an effect that should not be ignored in numerical studies of protoplanetary disks. Available dust coagulation models are, however, too computationally expensive to be implemented in large-scale hydrodynamic simulations. This limits detailed numerical studies of protoplanetary disks, including these effects, mostly to one-dimensional models. Aims. We aim to develop a simple – yet accurate – dust coagulation model that can be easily implemented in hydrodynamic simulations of protoplanetary disks. Our model shall not significantly increase the computational cost of simulations and provide information about the local grain size distribution. Methods. The local dust size distributions are assumed to be truncated power laws. Such distributions can be fully characterized by only two dust fluids (large and small grains) and a maximum particle size, truncating the power law. We compare our model to state- of-the-art dust coagulation simulations and calibrate it to achieve a good fit with these sophisticated numerical methods. Results. Running various parameter studies, we achieved a good fit between our simplified three-parameter model and DustPy, a state-of-the-art dust coagulation software. Conclusions. We present TriPoD, a sub-grid dust coagulation model for the PLUTO code. With TriPoD, we can perform twodimensional, vertically integrated dust coagulation simulations on top of a hydrodynamic simulation. Studying the dust distributions in two-dimensional vortices and planet-disk systems is thus made possible.

Investigation of iron oxide nanoparticle formation in a spray-flame synthesis process using laser-induced incandescence

In this work, iron-oxide nanoparticle formation in the spray-flame synthesis (SFS) process of the standardized SpraySyn 2.0 burner was investigated in situ using laser-induced incandescence (LII). For the evaluation of these measurements, prior LII-experiments within iron-oxide aerosols (Fe3O4 and α-Fe2O3) with known primary particle size distribution and morphological properties were performed to determine the thermal accommodation coefficient (TAC) α, which led to approx. α = 0.08. The applicability of the TAC results within the flame was validated using spectrally and temporally resolved measurements in the flame at 65 mm HAB employing a spectrograph. Data for a bimodal particle size distribution, obtained from Transmission Electron Microscopy (TEM), were used in the LII-evaluation. The validated TAC was then used to evaluate the primary particle size evolution from in situ Time-Resolved (TiRe) LII-measurements using PMTs along the centre axis of the burner, ranging from 10 mm to 50 mm HAB. These measurements reveal a relatively constant effective particle diameter along HAB with dp,eff ≈ 300 nm. To further investigate particle formation in SFS, 2-dimensional time-resolved LII-measurements in the SFS flame were performed, showing a clear particle formation region up to approx. 30 mm HAB, from where on a constant particle mass is observed.

Measurement of the thermal accommodation coefficient of helium on a crystalline silicon surface at low-temperatures

Abstract Proposals for next-generation gravitational wave observatories include cryogenically cooled 200 kg test mass mirrors suspended from pendulums and made of a crystalline material such as crystalline silicon. During operation of the observatories, these mirrors undergo heating due to the absorption of laser radiation of up to a watt. Low noise cooling techniques need to be developed. Low-pressure helium exchange gas at 5 K might contribute to the challenging task. Here, we report the measurement of the helium accommodation coefficient α ( 11 K < T < 30 K ) , which is the probability that a helium atom thermalises with a surface at a given temperature when reflected from it. We find α ( T ) > 0.7 for temperatures < 20 K, which increases the cooling power compared to recently used assumptions. The idea of free molecular flow helium gas cooling is thus supported and might find application in some observatory concepts.

Frictional pressure drop correlation of steam-water two-phase flow in helically coiled tubes

Helically coiled tubes are utilized as the heat transfer tubes for High-Temperature Gas-cooled Reactor (HTGR) steam generators due to their compactness, thermal expansion accommodation and high heat transfer coefficient. A clear understanding of the pressure drop characteristics is important for the design and operation of steam generators. In this study, experiments were conducted to investigate the frictional pressure drop characteristics in helically coiled tube with a very large curvature ratio of 0.109. The experiments were carried out in a steam quality range of 0.1–0.9, system pressure range of 3.5–7 MPa, mass flux range of 320–1100 kg/m2s. The results indicate that the frictional pressure drop increased with the increase of mass flux, decreased with the increase of system pressure. It first increased with the increase of steam quality, and reached a maximum value at a steam quality of approximately 0.8, then decreased until steam quality reached unity. Based on the present work and existing experimental database, 25 existing correlations are evaluated and none of them could satisfactorily fit all the data. Therefore, a new correlation based on the Martinelli and Nelson correlation was proposed. Compared with existing correlations, it has a broader range of applicability (operating pressure from 0.75 to 8 MPa, mass flux from 200 to 1100 kg/(m2·s), steam quality from 0.03 to 0.99, and curvature ratio from 0 to 0.109.), and higher accuracy (weighted mean MAPE of 8.92 % and arithmetic mean MAPE of 8.81 %). It also has better compatibility with straight tubes.

Vertical shear instability with dust evolution and consistent cooling times

Context. Gas in protoplanetary disks mostly cools via thermal accommodation with dust particles. Thermal relaxation is thus highly sensitive to the local dust size distributions and the spatial distribution of the grains. So far, the interplay between thermal relaxation and gas turbulence has not been dynamically modeled in hydrodynamic simulations of protoplanetary disks with dust. Aims. We aim to study the effects of the vertical shear instability (VSI) on the thermal relaxation times, and vice versa. We are particularly interested in the influence of the initial dust grain size on the VSI and whether the emerging turbulence is sustained over long timescales. Methods. We ran three axisymmetric hydrodynamic simulations of a protoplanetary disk including four dust fluids that initially resemble MRN size distributions of different initial grain sizes. From the local dust densities, we calculated the thermal accommodation timescale of dust and gas and used the result as the thermal relaxation time of the gas in our simulation. We included the effect of dust growth by applying the monodisperse dust growth rate and the typical growth limits. Results. We find that the emergence of the VSI is strongly dependent on the initial dust grain size. Coagulation also counteracts the emergence of hydrodynamic turbulence in our simulations, as shown by others before. Starting a simulation with larger grains (100 μm) generally leads to a less turbulent outcome. While the inner disk regions (within ∼70 au) develop turbulence in all three simulations, we find that the simulations with larger particles do not develop VSI in the outer disk. Conclusions. Our simulations with dynamically calculated thermal accommodation times based on the drifting and settling dust distribution show that the VSI, once developed in a disk, can be sustained over long timescales, even if grain growth is occurring. The VSI corrugates the dust layer and even diffuses the smaller grains into the upper atmosphere, where they can cool the gas. Whether the instability can emerge for a specific stratification depends on the initial dust grain sizes and the initial dust scale height. If the grains are initially ≳100 μm and if the level of turbulence is initially assumed to be low, we find no VSI turbulence in the outer disk regions.

Latent-to-sensible heat conversion kinetics during nanoparticle coalescence.

Coagulational growth in an aerosol is a multistep process; first particles collide, and then they coalesce with one another. Coalescence kinetics have been investigated in numerous prior studies, largely through atomistic simulations of nanoclusters (102-104 atoms). However, with a few exceptions, they have either assumed the process is completely isothermal or is a constant energy process. During coalescence, there is the formation of new bonds, decreasing potential energy, and correspondingly increasing internal kinetic (thermal) energy. Internal kinetic energy evolution is dependent not only on coalescence kinetics but also on heat transfer to the surrounding gas. Here, we develop and test a model of internal kinetic energy evolution in collisionally formed nanoclusters in the presence of a background gas. We find that internal kinetic energy dynamics hinge upon a power law relationship describing latent-to-sensible heat release as well as a modified thermal accommodation coefficient. The model is tested against atomistic models of 1.5-3.0nm embedded-atom gold nanocluster sintering in argon and helium environments. The model results are in excellent agreement with the simulation results for all tested conditions. Results show that nanocluster effective temperatures can increase by hundreds of Kelvin due to coalescence, but that the rise and re-equilibration of the internal kinetic energy is strongly dependent on the background gas environment. Interestingly, internal kinetic energy change kinetics are also found to be distinct from surface area change kinetics, suggesting that modeling coalescence heat release solely due to surface area change is inaccurate.

On the Statistical Mechanics of Mass Accommodation at Liquid-Vapor Interfaces.

We propose a framework for describing the dynamics associated with the adsorption of small molecules to liquid-vapor interfaces using an intermediate resolution between traditional continuum theories that are bereft of molecular detail and molecular dynamics simulations that are replete with them. In particular, we develop an effective single particle equation of motion capable of describing the physical processes that determine thermal and mass accommodation probabilities. The effective equation is parametrized with quantities that vary through space away from the liquid-vapor interface. Of particular importance in describing the early time dynamics is the spatially dependent friction, for which we propose a numerical scheme to evaluate from molecular simulation. Taken together with potentials of mean force computable with importance sampling methods, we illustrate how to compute the mass accommodation coefficient and residence time distribution. Throughout, we highlight the case of ozone adsorption in aqueous solutions and its dependence on electrolyte composition.

Inferring primary particle size distribution and thermal accommodation coefficient of soot aggregate across diverse ambient temperatures using laser-induced incandescence

Laser-induced incandescence (LII) technique has proven to be a powerful tool for non-invasive, in-situ particle sizing of soot aggregates in flames, and the key lies in interpreting LII signals with a heat transfer model. However, the reliability of model-derived primary particle size distribution (PPSD) is sensitive to the uncertainty of thermal accommodation coefficient (TAC), which is typically regarded as a pre-determined parameter in the LII heat transfer model. To overcome this problem, we have proposed a trivariate inversion strategy, i.e., inferring two PPSD parameters and TAC simultaneously from LII signals, which has been theoretically validated at room temperature, but its feasibility in the flame case remains to be investigated. In this study, the trivariate inversion strategy is extensively evaluated over a wide distribution of both ambient temperature and laser fluence. For different cases ranging from room temperature to flame temperature, numerical tests show that the inversion results of all three variables exhibit significantly high accuracy and low uncertainty with proper selection of laser fluence. Furthermore, our study shows that the trivariate inversion strategy can maintain robust performance in ambient temperature fluctuation caused by spatial inhomogeneity of the flame. All these results indicate that this trivariate inversion strategy has a promising application in combustion scenarios.

An Experimental Investigation of a Flexible Sintered Silver Joint for Micro-Joining Based on a Design of Experiments

The increasing electrification of vehicles requires the use of ever higher voltages and electrical power. The thermal stresses to which the assembly joints of electronic chips are subjected are becoming increasingly severe. As a result, thermal stresses acting on the electronic assembly, and particularly on the electrical interconnections, are becoming increasingly severe. The objective of this study is to create, characterize and optimize the structure and properties of a porous silver sintered joint using the design of experiments (DoE) method. Joints consisting of a porous network of silver particles are obtained, showing remarkable flexibility allowing for thermal stresses accommodation and having sufficient tensile strength to ensure a correct bonding of the components. Depending on the selected levels for the sintering process parameters, the microscopy analysis shows a transition of the mode of rupture from the silver layer to the intermetallic compounds forming at the interface with the substrate.

Simultaneous Inversion of Particle Size Distribution, Thermal Accommodation Coefficient, and Temperature of In-Flame Soot Aggregates Using Laser-Induced Incandescence.

Measuring the size distribution and temperature of high-temperature dispersed particles, particularly in-flame soot, holds paramount importance across various industries. Laser-induced incandescence (LII) stands out as a potent non-contact diagnostic technology for in-flame soot, although its effectiveness is hindered by uncertainties associated with pre-determined thermal properties. To tackle this challenge, our study proposes a multi-parameter inversion strategy-simultaneous inversion of particle size distribution, thermal accommodation coefficient, and initial temperature of in-flame soot aggregates using time-resolved LII signals. Analyzing the responses of different heat transfer sub-models to temperature rise demonstrates the necessity of incorporating sublimation and thermionic emission for accurately reproducing LII signals of high-temperature dispersed particles. Consequently, we selected a particular LII model for the multi-parameter inversion strategy. Our research reveals that LII-based particle sizing is sensitive to biases in the initial temperature of particles (equivalent to the flame temperature), underscoring the need for the proposed multi-parameter inversion strategy. Numerical results obtained at two typical flame temperatures, 1100 K and 1700 K, illustrate that selecting an appropriate laser fluence enables the simultaneous inversion of particle size distribution, thermal accommodation coefficient, and initial particle temperatures of soot aggregates with high accuracy and confidence using the LII technique.

How Does the Thermal Environment Affect the Exosphere/Surface Interface at Mercury?

The fate of Mercury’s exospheric volatiles and, in a lesser way, of the refractory particles absorbed in the first few centimeters of the surface both depend highly on the temperature profile with depth and its diurnal variation. In this paper, we review several mechanisms by which the surface temperature might control the surface/exosphere interface. The day/night cycle of the surface temperature and its orbital variation, the temperature in the permanent shadow regions, and the subsurface temperature profiles are key thermal properties that control the fate of the exospheric volatiles through the volatile ejection mechanisms, the thermal accommodation, and the subsurface diffusion. Such properties depend on the solar illumination from large to small scales but also on the regolith structure. The regolith is also space-weathered by the thermal forcing and by the thermal-mechanical processing. Its composition is changed by the thermal conditions. We conclude by discussing key characteristics that need to be investigated theoretically and/or in the laboratory: the dependency of the surface spectra with respect to temperature, the typical diffusion timescale of the volatile species, and the thermal dependency of their ejection mechanisms.

Effect of Fe-O ReaxFF on Liquid Iron Oxide Properties Derived from Reactive Molecular Dynamics.

As iron powder nowadays attracts research attention as a carbon-free, circular energy carrier, molecular dynamics (MD) simulations can be used to better understand the mechanisms of liquid iron oxidation at elevated temperatures. However, prudence must be practiced in the selection of a reactive force field. This work investigates the influence of currently available reactive force fields (ReaxFFs) on a number of properties of the liquid iron-oxygen (Fe-O) system derived (or resulting) from MD simulations. Liquid Fe-O systems are considered over a range of oxidation degrees ZO, which represents the molar ratio of O/(O + Fe), with 0 < ZO < 0.6 and at a constant temperature of 2000 K, which is representative of the combustion temperature of micrometric iron particles burning in air. The investigated properties include the minimum energy path, system structure, (im)miscibility, transport properties, and the mass and thermal accommodation coefficients. The properties are compared to experimental values and thermodynamic calculation results if available. Results show that there are significant differences in the properties obtained with MD using the various ReaxFF parameter sets. Based on the available experimental data and equilibrium calculation results, an improved ReaxFF is required to better capture the properties of a liquid Fe-O system.

Thermal strain relaxation of GaAs overgrown on nanovoid based Ge/Si substrate

The integration of high quality III-V materials-based devices on the Si platform is considered as an enabling path towards achieving the long-standing goal of creating low-cost/high-performance devices. However, the heteroepitaxy of III-V compounds on a Si substrate generates high stress due to the difference in thermal expansion coefficient leading notably to crack generation. Here, we report on the reduction of the thermal strain of GaAs and Ge deposited on a Si substrate. The method is based on the formation of buried high density nanovoids by electrochemical etching of Ge/Si virtual substrate followed by direct epitaxial growth of Ge and GaAs. The thermal strain has been investigated for GaAs epilayer by High-Resolution X-Ray Diffraction and Raman spectroscopy showing a 30% decrease in strain. The strain reduction relies on the nanovoids-mediated thermal strain accommodation. Furthermore, photoluminescence measurements showed a 10-fold increase of the intensity, resulting in an improved optical and crystalline quality, making this virtual substrate promising for III-V based devices on Silicon.

Origin of residual strain in heteroepitaxial films

Heterogeneous integration of diverse materials structures is critical to the scaling of electronic and photonic integrated circuits. For a model system of Ge-on-Si, we experimentally examine the roles of lattice misfit and thermal expansion misfit in determining the residual strain in as-grown and annealed heteroepitaxial films. We present data for Ge-on-Si growth from 400 to 730 °C followed by heat treatment from 500–900 °C. We show that strain fluctuations of 5.02% enable misfit dislocation formation, and we propose a comprehensive model for the conversion of compressive misfit strain to tensile elastic strain. The model is expressed in terms of three regimes: (1) misfit control for the low temperature growth regime at 400 °C; (2) point defect control via annealing in the point defect recovery regime at 500–650 °C; and (3) thermal expansion control for growth or anneal at T &amp;gt; 650 °C in the dislocation recovery regime. Growth from 400 to 730 °C exhibits near complete misfit strain relief by misfit dislocations leaving a consistent residual compressive strain of 0.09%. Growth at 400 °C followed by post growth heat treatment at 600 °C results in vertical threading dislocation density reduction via a point defect-mediated climb mechanism that gives minimal strain relief. Anneal above 650 °C promotes strain relief by dislocation glide. Temperature excursions at T &amp;gt; 730 °C followed by cooling to room temperature yield plastic strain in the Ge film that cannot be further relieved by thermal expansion misfit accommodation. Growth at 400–730 °C retains a residual compressive strain that represents the nucleation threshold for misfit dislocations.

On the surface chemisorption of oxidizing fine iron particles: Insights gained from molecular dynamics simulations

Molecular dynamics (MD) simulations are performed to investigate the thermal and mass accommodation coefficients (TAC and MAC, respectively) for the combination of iron(-oxide) and air. The obtained values of TAC and MAC are then used in a point-particle Knudsen model to investigate the effect of chemisorption and the Knudsen transition regime on the combustion behavior of (fine) iron particles. The thermal accommodation for the interactions of Fe with N2 and FexOy with O2 is investigated for different surface temperatures, while the mass accommodation coefficient for iron(-oxide) with oxygen is investigated for different initial oxidation stages ZO, which represents the molar ratio of O/(O+Fe), and different surface temperatures. The MAC decreases fast from unity to 0.03 as ZO increases from 0 to 0.5 and then diminishes as ZO further increases to 0.57. By incorporating the MD-informed accommodation coefficients into the single iron particle combustion model, the oxidation beyond ZO=0.5 (from stoichiometric FeO to Fe3O4) is modeled. A new temperature evolution for single iron particles is observed compared to results obtained with previously developed continuum models. Specifically, results of the present simulations show that the oxidation process continues after the particle reaching the peak temperature, while previous models predicting that the maximum temperature was attained when the particle is oxidized to ZO=0.5. Since the rate of oxidation slows down as the MAC decreases with an increasing oxidation stage, the rate of heat loss exceeds the rate of heat release upon reaching the maximum temperature, while the particle is not yet oxidized to ZO=0.5. Finally, the effect of transition-regime heat and mass transfer on the combustion behavior of fine iron particles is investigated and discussed.

Experimental Verification of and Physical Interpretation for Adsorption-Dependent Squeeze-Film Damping

The squeeze-film-damping effect is one of the main limits in many precision experiments, especially in the study of short-range interactions, and its physical mechanism is still not very clear. We develop a torsion pendulum to measure the damping effects caused by the thermal motion of residual gas between a cubic test mass and a pair of symmetric movable plates. The measured results are consistent with the model that synthesized the elastic and inelastic collisions by introducing a thermal accommodation coefficient (TAC). In our research, the pressure dependence of the TAC, which can be expressed as an exponential decay function, is also observed. This dependence may imply that the elastic collisions correspond to the simple bouncing of residual gas molecules, while the inelastic collisions correspond to the adsorption and desorption cycle of gas molecules on the surface. The method in this work and the discovered TAC pressure dependence are instructive for the analysis of residual-gas effects in weak-force measurements, as well as the deviation correction of rarefied gas pressure measurements based on the squeeze-film-damping effect.

Two-dimensional computational fluid dynamics modeling of slip-flow heat transfer in the hot filament chemical vapor deposition process

The computational fluid dynamics (CFD) modeling on the hot filament chemical vapor deposition (HFCVD) process used to produce a diamond film has been conducted to anticipate the heat transfer and calculate the generation of H. The effect in the slip-flow regime owing to the low-pressure process should be considered to simulate the heat transfer accurately. In addition, a heterogeneous reaction occurring on the filament should be included to calculate the generation of H. The parameters to simulate such microscopic phenomena were applied in the present work and validated by comparing the results with the previous work. The thermal accommodation coefficient (TAC) for H2 was determined as 0.3, at which the calculated mass fraction and H concentration showed good agreement. In addition, It was confirmed that the value could be applied over various filament temperatures and operating pressure. Further, the behavior of H is analyzed above the substrate; the analysis results indicate that there is a correlation between the gas temperature and the gradient of H concentration on the substrate. The high gas temperature caused a severe gradient; thus, a non-uniform film may be deposited. The developed modeling method suggested that microscopic phenomena could be simulated without experimental materials. This fact implied that it is possible to anticipate the temperature and H concentration regardless of the structural design.

A modified Cercignani–Lampis model with independent momentum and thermal accommodation coefficients for gas molecules scattering on surfaces

To accurately predict the aerodynamic forces and heating of hypersonic vehicles, an elaborate gas–surface interaction (GSI) model is essential to describe the rarefied gas effect at the interface. By far, the Cercignani–Lampis (CL) model is the most sophisticated GSI model, but it has not been systematically examined under hypersonic conditions where the gas flow possesses large velocity and temperature differences relative to the boundary surface. In this work, the accuracy of the CL model is first assessed by comparing with molecular dynamics simulation results under a variety of conditions of temperature and velocity differences, surface temperature, and surface roughness. It is found that the tangential scattering kernel of CL model is perfect only when the surface is smooth and the gas kinetic energy is close to the surface kinetic energy. To accurately capture the momentum and temperature of the reflected gas molecules, a modified CL model with independent momentum and thermal accommodation coefficients is developed. A hybrid diffusive and modified CL model is further proposed to account for the adsorption phenomenon. With these modifications, the new GSI model can accurately describe the scattering of gas molecules in a wider range of hypersonic rarefied gas flows.

Thermal Energy Transfer between Helium Gas and Graphene Surface According to Molecular Dynamics Simulations and the Monte Carlo Method.

The scattering of gases on solid surfaces plays a vital role in many advanced technologies. In this study, the scattering behavior of helium on graphene surfaces was investigated, including the thermal accommodation coefficient (TAC), outgoing zenith angle of helium, bounce number, and interaction time. First, we performed molecular dynamics simulations to describe the incident angle-resolved behaviors, and showed that the scattering is highly dependent on the zenith angle of incident helium but insensitive to the azimuthal angle. The contribution of the normal velocity component of the incident helium dominated the energy transfer. The nonlinear relationship of the parameters to the zenith angle of the incident helium could be suppressed by increasing the graphene temperature or decreasing the speed of the incident helium. Subsequently, the scattering performance considering all gas molecules in the hemispherical space was evaluated using the Monte Carlo method with angle-resolved results. The result showed that the TAC, its nominal components, and the zenith angle of the scattered helium increased with higher speeds of incident helium and lower temperatures of graphene. This study should provide a fundamental understanding of energy transfer between gas and two-dimensional materials and guidelines to tune the scattering behavior between them.

Direct simulation Monte Carlo of the gas-adsorption of particles in gas–particle flows

The acceleration and heating of particles in gas–particle flows represents a general question in fluid mechanics and has been widely studied since the 1920s. However, studies on the gas adsorption–desorption process of a particle in a gas–particle flow are still lacking. In this paper, we aim to introduce a framework with which to explain the gas adsorption–desorption kinetic equilibrium of a spherical particle in a gas–particle flow. We also explore the potential influences of gas adsorption and desorption on the heating and acceleration of a particle in such a flow. We study the gas adsorption–desorption process using the Langmuir adsorption model and the flow method presented by Brancher in a Direct Simulation Monte Carlo simulation. We develop a new model to consider the gas adsorption–desorption kinetic equilibrium on the surfaces of spherical particles in the calculation of the Thermal Accommodation Coefficient. We observe from the simulations that the trend of gas adsorption is opposite to that of the particle surface temperature. We also find that the efficiency of the convective heat transfer and acceleration of a particle is higher for a particle with a higher adsorption probability on its surface. This paper provides a new framework with which to study the gas adsorption–desorption processes of particles in gas–particle flows. It also inspires for future work on the potential applications of the particle gas adsorption–desorption model in astrophysics.