Thermal Accommodation Coefficient Research Articles

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.

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.

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.

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.

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.

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.

Investigation into the thermal effect of the LIPS-200 ion thruster plume

The distribution of the thermal effects of the ion thruster plume are essential for estimating the influence of the thruster plume, improving the layout of the spacecraft, and for the thermal shielding of critical sensitive components. In order to obtain the heat flow distribution in the plume of the LIPS-200 xenon ion thruster, an experimental study of the thermal effects of the plume has been conducted in this work, with a total heat flow sensor and a radiant heat flow sensor over an axial distance of 0.5–0.9 m and a thruster angle of 0°–60°. Combined with a Faraday probe and a retarding potential analyzer, the thermal accommodation coefficient of the sensor surface in the plume is available. The results of the experiment show that the xenon ion thruster plume heat flow is mainly concentrated within a range of 15°. The total and radial heat flow of the plume downstream of the thruster gradually decreases along the axial and radial directions, with the corresponding values of 11.78 kW m−2 and 0.3 kW m−2 for the axial 0.5 m position, respectively. At the same position, the radiation heat flow accounts for a very small part of the total heat flow, approximately 3%–5%. The thermal accommodation factor is 0.72–0.99 over the measured region. Furthermore, the PIC and DSMC methods based on the Maxwell thermal accommodation coefficient model (EX-PWS) show a maximum error of 28.6% between simulation and experiment for LIPS-200 ion thruster plume heat flow, which, on the one hand, provides an experimental basis for studying the interaction between the ion thruster and the spacecraft, and on the other hand provides optimization of the ion thruster plume simulation model.

A robust trivariate approach for characterizing the primary particle size distribution of soot aggregates using time-resolved laser-induced incandescence

This study proposes a new trivariate retrieval method based on a moderate-fluence laser-induced incandescence (LII) model. By changing the undesirable mathematical properties present in our previous work, this upgraded new method is able to obtain robust estimates of the two primary particle size distribution parameters and one assembled parameter, and still maintains the advantage of not requiring prior knowledge of thermal accommodation coefficient and aggregate structure. The robustness of the upgraded method is verified on a large number of numerical results, as evidenced by significantly improved retrieval accuracy and substantially reduced estimation uncertainty. The generality of the upgrade method is demonstrated over a large range of three variables. Furthermore, the influence of several key factors (the number of shots used for averaging noisy LII signal, the intensity ratio of the measurement termination, and the sublimation sub-model error) on the retrieval results of the upgraded method is investigated numerically.

Methodical selection of thermal conductivity models for porous silica-based media with variation of gas type and pressure

If the effective thermal conductivity of a silica powder in any gas atmosphere is to be calculated analytically, one is faced with a whole series of decisions. There are a lot of different models for the gas thermal conductivity in the pores, the thermal accommodation coefficient or the effective thermal conductivity itself in the literature. Furthermore, it has to be decided which input parameters should be used. This paper gives an overview and recommendations as to which calculation methods are best suited for the material classes of precipitated silica, fumed silica, silica gel and glass spheres. All combinations of the described methods result in a total of 2800 calculation models which are compared with pressure-dependent thermal conductivity measurements of 15 powdery materials with 7 different gases using Matlab computations. The results show that with a model based on a spherical unit cell, which considers local Knudsen numbers, the measuring points of all powder-gas combinations can be determined best with an average variance of about 18.5%. If the material class is known beforehand, the result can be predicted with an average accuracy of about 10% with the correspondingly determined methods.

Thermal Conductivity Decomposition and Accommodation Coefficient Extraction for Thermal Insulation Materials

Thermal Conductivity Decomposition and Accommodation Coefficient Extraction for Thermal Insulation Materials

Measurement of soot primary particle size in co-flow laminar diffusion flames of n-heptane at elevated pressures

To comprehensively understand soot formation in flames of liquid fuel, the soot primary particle size (PPS) in n-heptane\\air diffusion flame at pressures up to 5 bar was investigated in this work. A series of experiments were conducted in a high-pressure laminar flame burner system, and the spatial distributions of soot primary particle size in the flames at atmospheric and elevated pressures were evaluated by two-dimensional Time-Resolved Laser-Induced Incandescence (TiRe-LII). The results indicated a tendency that the conunt mean diameter (Dp,mean) of soot primary particle increased with enhancing laser fluence, which might be attributed to inaccuracy of the thermal accommodation coefficient at the increasing laser fluences. The spatial distribution of Dp,mean varied with pressures. Further, the evolution of Dp,mean along the centerline and the radial distribution of Dp,mean at the pressures of 1.0–3.0 bar were also presented. The zone of the maximum Dp,mean moved from the flame centerline to the flame edge as the pressure increases. The spatial distribution of Dp,mean at 3.5–5.0 bar showed the area of maximum Dp,mean located at the annular wing region in flames and being floated as the pressure increased. This study complemented the existing theoretical knowledge of spatial primary particle size distribution (PPSD) in n-heptane laminar diffusion flames.

Determination of thermal accommodation coefficients on [formula omitted] and [formula omitted] using molecular dynamics and experiments

The thermal accommodation coefficient α has been assumed, although lacking any experimental proof, to be near unity for most gases so far, which denotes no influence. However, it plays a contributing role in the field of the effective thermal conductivity of highly porous insulation materials based on SiO2 or CaSiO3 as it is shown in this work. Besides, this work investigates a possible influence on α for Ar,N2,He within parameters like temperature, roughness and contamination as this has not been examined on such materials so far. More importantly, it answers the question whether the assumption of α = 1 is valid. By using a parallel plates device, very similar to the guarded-hot-plate, following EN 12667 it was possible to determine α on a dense CaSiO3. It occured that the assumptions α = 1 (for Ar,N2) and α = 0.3 (for He) are valid for measurements near room temperature. Further, physical adsorption was found to increase α. The determination of the influence of roughness has been started showing an interesting effect, but it still remains an open topic. In a collaborative study molecular dynamics (MD) simulations were performed showing a strong equivalence of α between SiO2 and CaSiO3. These results can be considered a lower limit of α as neither roughness nor adsorption processes have been included in the simulation. Therefore, any deviations between experiments and MD could be considered as an apperance of physical adsorption.

Experimental measurements of thermal and tangential momentum accommodation coefficients on solid surfaces: Water vapor in comparison with noble gases

In the high Knudsen number flows, like micro gaseous flows and flows in vacuum, the gas-surface interaction plays an important role. Among many gas species, water is a common and useful fluid in wide area of engineering applications, and it is one of the main residual gas components in the high vacuum environment. However, experimental measurements on the gas-surface interaction of water molecules are still limited. In this study, we focus on the accommodation coefficient, which represents the mean behavior of gas molecules on the scattering process from a surface. We measure the thermal accommodation coefficient (TAC) and the tangential momentum accommodation coefficient (TMAC) of water molecules. TAC is measured from the heat flux between two surfaces with different temperatures in vacuum. TMAC is derived through the viscous slip coefficient from the measurement of the mass flow rate through a microtube. To investigate the characteristics of water molecules clearly, the measured accommodation coefficients are compared with those of noble gases, helium, neon, and argon, measured with the same apparatus and procedures. For the accommodation coefficients of noble gases, TAC increases with increasing the molecular weight, while TMAC decreases, which are in good agreement with the previous studies. The TAC and TMAC of water are slightly larger than those estimated from the corresponding molecular weight of noble gases.

Numerical study of supersonic boundary-layer modal stability for a slightly rarefied gas using Navier—Stokes approach

In this paper, a systematic study on the supersonic boundary-layer modal stability for a slightly rarefied gas is conducted by considering velocity slip and temperature jump effects in the Navier–Stokes (NS) equations. The effects of slip boundary on the first- and second-mode instability at different conditions are presented in detail. The laminar flow is obtained by solving the NS equations along with no-slip and slip boundary conditions, which shows that the slip boundary causes the boundary layer becoming thinner and the supersonic region near the wall becoming narrower. The perturbation slip boundary conditions at the wall and their influence on the stability are carefully discussed. The tangential momentum accommodation coefficient and the thermal accommodation coefficient are set equal or unequal for a broad range to study the combined or leading effects of velocity slip and temperature jump, respectively. It is found that velocity slip significantly stabilizes the second-mode disturbances while largely destabilizes the first-mode perturbations. On the contrary, the temperature jump apparently enhances the second-mode instability, while it has little influence on the first mode. When velocity slip and temperature jump are both present, the first mode is more destabilized, while a competitive effect acts on the second mode. Additional results show that the neutral stability curves for the second and third modes as well as the synchronization between fast and slow modes are delayed further downstream due to velocity slip. These findings are shown consistently regardless of the wall cooling for both supersonic and hypersonic flows.