Gas Rarefaction Research Articles

Conductive heat transfer in a rarefied polyatomic gas confined between coaxial cylinders

The conductive heat transfer through rarefied gases composed by rigid rotators and confined between coaxially placed cylinders maintained at different temperatures is investigated on the basis of the Holway and Rykov kinetic models as well as on the Boltzmann equation via the DSMC scheme supplemented by the Borgnakke–Larsen collision model. The translational and rotational parts as well as the total temperature and heat flux distributions are computed and their behavior in terms of the gas rarefaction, the temperature difference between the cylinders and the ratio of the radii is investigated. The two kinetic models and the DSMC method provide results which are in good agreement for HS and VHS molecules. Furthermore, very good agreement with available experimental data for polyatomic gases has been observed at small and large temperature differences validating the implemented modeling. Qualitatively the behavior of the dimensionless total macroscopic quantities is similar to that of the monatomic ones. Quantitatively however, the heat fluxes of polyatomic gases are significantly higher than the corresponding monatomic ones. Also, as the amount of the elastic compared to the inelastic collisions is increased, the translational heat fluxes are increased and they tend to the monatomic ones, while always the rotational heat fluxes are about 50% and 75% of the translational ones for linear and non-linear rigid rotators, respectively. It is clearly demonstrated that heat transfer simulations through rarefied polyatomic gases in MEMS and other devices cannot rely on typical monatomic modeling. On the contrary, reliable kinetic modeling for polyatomic gases must be implemented.

Test Equipment for SHS processes: Safety and standardization

The test equipment for main operations of self-propagating high-temperature synthesis (SHS) processes (charge mixture, compaction, and synthesis) is considered. A description of its structural components, which are most responsible for the safety and efficiency of operation with powders and their mixtures associated with fire and explosion hazard, is given. For example, a pressure-sealing valve of original design by means of which the protective gas atmosphere and rarefaction or excess pressure can be created in the mill is applied in the crushing cylinder for ball mills. The mold for preliminary compaction uses a teflon insert, which completely excludes the probability for powder intrusion between sliding surfaces of a punch and a body, thereby preventing the possibility for powder ignition from friction sparks. A reaction mold with the filling of the charge mixture by a layer of quartz sand, one destination of which is the removal of flue gases for the prevention of the mold rupture, is designed for SHS with compaction. Safety of the SHS reactor operation is built into all stages of their life cycle from design to operation. In this regard a system of measures and rules described in the corresponding technical documentation, the references to which are given in the article, is developed. Synthesis in the SHS mode is nonhazardous with the fulfillment of necessary strict measures and the adherence of rules.

Pressure driven flows of rarefied gases through long channels with double trapezoidal cross-sections

Steady flows of rarefied single gases through long channels with double trapezoidal cross-section shapes are investigated numerically. The flow is between two large reservoirs having the gas at different pressures. The channels have constant cross-sections along the axial direction. The gas is modeled by the linearized Bhatnagar–Gross–Krook kinetic equation. The diffuse reflection boundary condition is used at the channel walls. The solution of the problem is divided into two stages. At a particular cross-section, the flow is driven by the local pressure gradient. First, the local problem for an arbitrary driving term is solved by using the discrete velocity method. This solution yields the dimensionless flow rate and the velocity profile for a wide range of the gaseous rarefaction. Second, the global flow behavior, i.e. the flow rate and the distribution of the pressure, is deduced for global pressure driven flows on the basis of the conservation of mass. The numerical solution of the kinetic equation is based on the discretization of the spatial and velocity spaces. The spatial space is represented on a rectangular grid. The walls of the channels are aligned parallel to the grid lines or along the diagonal of the grid. Such a choice provides a straightforward calculation of the spatial derivatives. In the interior part of the domain and near the channel walls, second- and first-order finite difference forms are used, respectively. The velocity space is represented by a Gauss–Legendre quadrature. The resulting discrete equations are solved in an iterative manner. The dimensionless flow rates are calculated and tabulated for particular cross-sections in a wide range of the gaseous rarefaction. The flow rate function exhibits the Knudsen minimum. The results are compared to the corresponding ones with other cross-sections. Typical velocity profiles are also shown. Finally, representative results are delivered for global pressure driven flows.

Numerical study of unsteady rarefied gas flow through an orifice

Transient flow of rarefied gas through an orifice caused by various pressure ratios between the reservoirs is investigated for a wide range of the gas rarefaction, varying from the free molecular to continuum regime. The problem is studied on the basis of the numerical solution of unsteady S-model kinetic equation. It is found that the mass flow rate takes from 2.35 to 30.37 characteristic times, which is defined by orifice radius over the most probable molecular speed, to reach its steady state value. The time of steady flow establishment and the steady state distribution of the flow parameters are compared with previously reported data obtained by the Direct Simulation Monte Carlo (DSMC) method. A simple fitting expression is proposed for the approximation of the mass flow rate evolution in time.

Oscillatory rarefied gas flow inside rectangular cavities

AbstractTwo-dimensional oscillatory lid-driven cavity flow of a rarefied gas at arbitrary oscillation frequency is investigated using the linearized Boltzmann equation. An analytical solution at high oscillation frequencies is obtained, and detailed numerical results for a wide range of gas rarefaction are presented. The influence of both the aspect ratio of the cavity and the oscillating frequency on the damping force exerted on the moving lid is studied. Surprisingly, it is found that, over a certain frequency range, the damping is smaller than that in an oscillatory Couette flow. This reduction in damping is due to the anti-resonance of the rarefied gas. A scaling law between the anti-resonant frequency and the aspect ratio is established, which would enable the control of the damping through choosing an appropriate cavity geometry.

Investigation of ionized metal flux in enhanced high power impulse magnetron sputtering discharges

The metal ionized flux fraction and production of double charged metal ions Me2+ of different materials (Al, Cu, Fe, Ti) by High Power Impulse Magnetron Sputtering (HiPIMS) operated with and without a pre-ionization assistance is compared in the paper. The Electron Cyclotron Wave Resonance (ECWR) discharge was employed as the pre-ionization agent providing a seed of charge in the idle time of HiPIMS pulses. A modified grid-free biased quartz crystal microbalance was used to estimate the metal ionized flux fraction ξ. The energy-resolved mass spectrometry served as a complementary method to distinguish particular ion contributions to the total ionized flux onto the substrate. The ratio between densities of doubly Me2+ and singly Me+ charged metal ions was determined. It is shown that ECWR assistance enhances Me2+ production with respect of absorbed rf-power. The ECWR discharge also increases the metal ionized flux fraction of about 30% especially in the region of lower pressures. Further, the suppression of the gas rarefaction effect due to enhanced secondary electron emission of Me2+ was observed.

Kinetic modeling of a tapered Holweck pump

The Holweck pump is a device widely used in many pumping systems. It can be a self-standing device or part of a multi-stage system, usually combined with a turbo-molecular pump (TMP). In the present work, an existing methodology [Sharipov et al., 2006] for the simulation of a Holweck pump with channels of constant cross sections, is extended and becomes more general by including pumps with tapered channels. The implemented procedure is based on the kinetic approach, is applicable in the whole range of the Knudsen number and is divided into two steps. First the flow through a tapered channel of a T-shape cross section is decomposed in four simple two-dimensional flows and a database for the dimensionless flow rate in terms of the reference gas rarefaction and the channel geometrical data is built based on linear kinetic theory. Then, using the mass conservation principal and the kinetic database, an ordinary differential equation is solved to yield the pressure evolution along the pump and the pump characteristic quantities of practical interest. Comparison of simulation results with existing experimental data has shown good agreement, proving the validity of the method and its capability of simulating the flow in a Holweck pump with small computational effort. In addition, the great advantage of the method for fast and easy-to-go parametric and sensitivity analysis concerning various operational and geometrical characteristics of the pump is demonstrated.

Ab initio simulation of rarefied gas flow through a thin orifice

A rarefied gas flow through a thin orifice is calculated for the three noble gases, helium, argon and krypton, applying the direct simulation Monte Carlo method based on the ab initio potential. The calculations have been carried out over the whole range of the gas rarefaction and for several values of the pressure ratio with the numerical error less than 0.5%. A comparative analysis showed that the relative difference of the flow rate based on the ab initio potential from that obtained for the hard sphere molecular model depends on many factors, namely, gas species, pressure ratio, gas rarefaction and gas temperature. Among the gases considered here, the difference for helium is smallest and does not exceed 0.7%. The deviation for krypton is largest and reaches 1.4%. A relative deviation of the flow rate due to the temperature variation is within 0.9%. A comparison of the axial distributions of density, temperature and bulk velocity shows that the Mach discs for the ab initio potential are stronger than those for the hard sphere model.

On the road to self-sputtering in high power impulse magnetron sputtering: particle balance and discharge characteristics

The onset and development of self-sputtering (SS) in a high power impulse magnetron sputtering (HiPIMS) discharge have been studied using a plasma chemical model and a set of experimental data, taken with an aluminum target and argon gas. The model is tailored to duplicate the discharge in which the data are taken. The pulses are long enough to include both an initial transient and a following steady state. The model is used to unravel how the internal discharge physics evolves with pulse power and time, and how it is related to features in the discharge current–voltage–time characteristics such as current densities, maxima, kinks and slopes. The connection between the self-sputter process and the discharge characteristics is quantified and discussed in terms of three parameters: a critical target current density Jcrit based on the maximum refill rate of process (argon) gas above the target, an SS recycling factor ΠSS-recycle, and an approximation of the probabilities of ionization of species that come from the target (both sputtered metal and embedded argon atoms). For low power pulses, discharge voltages UD ⩽ 380 V with peak current densities below ≈ 0.2 A cm−2, the discharge is found to be dominated by process gas sputtering. In these pulses there is an initial current peak in time, associated with partial gas rarefaction, which is followed by a steady-state-like plateau in all parameters similar to direct current magnetron sputtering. In contrast, high power pulses, with UD ⩾ 500 V and peak current densities above JD ≈ 1.6 A cm−2, make a transition to a discharge mode where SS dominates. The transition is found not to be driven by process gas rarefaction which is only about 10% at this time. Maximum gas rarefaction is found later in time and always after the initial peak in the discharge current. With increasing voltage, and pulse power, the discharge can be described as following a route where the role of SS increases in four steps: process gas sputtering, gas-sustained SS, self-sustained SS and SS runaway. At the highest voltage, 1000 V, the discharge is very close to, but does not go into, the SS runaway mode. This absence of runaway is proposed to be connected to an unexpected finding: that twice ionized ions of the target species play almost no role in this discharge, not even at the highest powers. This reduces ionization by secondary-emitted energetic electrons almost to zero in the highest power range of the discharge.

Stable and high-quality Al-doped ZnO films with ICP-assisted facing targets sputtering at low temperature

FTS (facing targets sputtering) has been studied intensively for high-quality TCO films in low-temperature processes. In this study, we designed ICP-assisted FTS process for high-quality Al-doped ZnO film synthesis in a low temperature process. A one-turn ICP coil was installed a few cm above the upper target edge through which hydrogen was introduced and fully dissociated to the atomic radicals. The increase of ICP power caused heating and rarefaction of Ar gas and generated abundant hydrogen atoms and hydrogenated molecules. In FESEM analysis, the films synthesized with high ICP power showed high crystallinity. XPS was used to analyze the film structure. In O1s spectra, the low binding energy component located at ∼530.3 ± 0.4 eV corresponding to O2− ions on the wurtzite structure of the hexagonal Zn2+ ion array increased with the ICP power, indicating good crystal quality. With increasing ICP power fixing while fixing the RF power at the cathode, the resistivity was observed to decrease to 5 × 10−4 Ω-cm. For thermal reliability tests, films were stored in an air-based chamber at 200 °C. The films synthesized without ICP showed rapid degradation in the electrical properties, while the films synthesized with high ICP power showed good stabilities with little change in the electrical properties after 30 h of storage in an oven. By adding hydrogen, the carrier concentration of the films increased, while the mobility did not change much. From these results, it is expected that hydrogen was incorporated into the film as a stable n-dopant by using an auxiliary ICP plasma source.

On the damping effect of gas rarefaction on propagation of acoustic waves in a microchannel

We consider the response of a gas in a microchannel to instantaneous (small-amplitude) non-periodic motion of its boundaries in the normal direction. The problem is formulated for an ideal monatomic gas using the Bhatnagar, Gross, and Krook (BGK) kinetic model, and solved for the entire range of Knudsen (Kn) numbers. Analysis combines analytical (collisionless and continuum-limit) solutions with numerical (low-variance Monte Carlo and linearized BGK) calculations. Gas flow, driven by motion of the boundaries, consists of a sequence of propagating and reflected pressure waves, decaying in time towards a final equilibrium state. Gas rarefaction is shown to have a “damping effect” on equilibration process, with the time required for equilibrium shortening with increasing Kn. Oscillations in hydrodynamic quantities, characterizing gas response in the continuum limit, vanish in collisionless conditions. The effect of having two moving boundaries, compared to only one considered in previous studies of time-periodic systems, is investigated. Comparison between analytical and numerical solutions indicates that the collisionless description predicts the system behavior exceptionally well for all systems of the size of the mean free path and somewhat larger, in cases where boundary actuation acts along times shorter than the ballistic time scale. The continuum-limit solution, however, should be considered with care at early times near the location of acoustic wavefronts, where relatively sharp flow-field variations result in effective increase in the value of local Knudsen number.

The characteristic shape of emission profiles of plasma spokes in HiPIMS: the role of secondary electrons

A time-resolved analysis of the emission of high power impulse magnetron sputtering (HiPIMS) plasmas reveals inhomogeneities in the form of rotating spokes. The shape of these spokes is very characteristic depending on the target material. The localized enhanced light emission has been correlated with the ion production. Based on these data, the peculiar shape of the emission profiles can be explained by the localized generation of secondary electrons, resulting in an enhanced outward diffusion. This general picture is able to explain the observed emission profile for different target materials including gas rarefaction and second ionization potential of the sputtered elements.

An Efficient Hybrid DSMC/MD Algorithm for Accurate Modeling of Micro Gas Flows

AbstractAiming at simulating micro gas flows with accurate boundary conditions, an efficient hybrid algorithm is developed by combining the molecular dynamics (MD) method with the direct simulation Monte Carlo (DSMC) method. The efficiency comes from the fact that the MD method is applied only within the gas-wall interaction layer, characterized by the cut-off distance of the gas-solid interaction potential, to resolve accurately the gas-wall interaction process, while the DSMC method is employed in the remaining portion of the flow field to efficiently simulate rarefied gas transport outside the gas-wall interaction layer. A unique feature about the present scheme is that the coupling between the two methods is realized by matching the molecular velocity distribution function at the DSMC/MD interface, hence there is no need for one-to-one mapping between a MD gas molecule and a DSMC simulation particle. Further improvement in efficiency is achieved by taking advantage of gas rarefaction inside the gas-wall interaction layer and by employing the “smart-wall model” proposed by Barisiket al.The developed hybrid algorithm is validated on two classical benchmarks namely 1-D Fourier thermal problem and Couette shear flow problem. Both the accuracy and efficiency of the hybrid algorithm are discussed. As an application, the hybrid algorithm is employed to simulate thermal transpiration coefficient in the free-molecule regime for a system with atomically smooth surface. Result is utilized to validate the coefficients calculated from the pure DSMC simulation with Maxwell and Cercignani-Lampis gas-wall interaction models.

Ab initio simulation of heat transfer through a mixture of rarefied gases

The heat flux problem for a binary gaseous mixture confined between two parallel plates with different temperatures is studied on the basis of the direct simulation Monte Carlo method with an implementation of ab initio potential. The calculations were carried for a wide range of the gas rarefaction, for several values of the mole fraction and for two values of the temperature difference. The smaller value of the difference corresponds to the limit when the nonlinear terms are negligible, while the larger value describes a nonlinear heat transfer. The heat flux, temperature, and mole fraction distributions are presented. To study the influence of the intermolecular potential, the same simulations are carried out for the hard sphere molecular model. A relative deviation of the results based on this model from those based on the ab initio potential is analyzed. It is pointed out that the difference between the heat flux of the two potentials is about 8% and 5% for the small and large temperature differences, respectively. The temperature distribution between plates is weakly affected by the molecular potential, while the chemical composition variation is the most sensitive quantity for the considered problem. The reported results can be used as benchmark data to test model kinetic equations for gaseous mixtures.

Experimental study of a rarefied plume impinging on a cylinder-plate configuration

An experimental analysis of the interaction of a rarefied jet plume with a cylinder-plate system is presented. The main goal is to show that the gas rarefaction can change the distribution of pressure between the two bodies quite unpredictably. The geometrical configuration has been proposed as test case to investigate the development of plume that are typically present in complex structures on spatial satellite. The results are qualitatively in a good agreement with analogous experiments and numerical simulations.

Brownian coagulation in dense systems: Thermal non-equilibrium effects

Non-equilibrium effects in Brownian coagulation at particle number densities that are large in comparison to that of the background gas are analysed theoretically and through computer experiments. With increasing rarefaction of the suspending gas there is a point, when the particle relaxation time becomes longer than the characteristic coagulation time. At that point the average velocity of particles will decrease due to mutual inelastic collisions and will fall below the value predicted by the energy equipartition theorem for there is insufficient time between the collisions to restore the thermal equilibrium. This reduced particle velocity results in a lower coagulation rate than predicted by the classical coagulation theory and this effect is shown through first principle computer experiments using the Langevin dynamics methodology developed in our previous studies on the particle crowding effects, as well as through the novel application of the kinetic Monte Carlo method with the majorant kernel proposed in this work. A theoretical model quantifying the effect of the coagulation rate suppression is formulated by introducing the concept of a thermalization number, which is defined as the reduced mean kinetic energy of particle motion. An expression for this quantity is derived and used to extend the classical coagulation theory to this new non-equilibrium regime of coagulation by following, and extending further, the methodology that we proposed previously to describe the concentration enhancement effects in coagulation. A closed-form, analytical formula for the coagulation kernel is obtained and shown to be applicable for all particle sizes and a wide range of concentrations. Close agreement is demonstrated between the predictions from this formula and the results from first principle simulations in the monodisperse case and this agreement can be improved further still, as well as extended to the polydisperse case, if a single model parameter is allowed to be adjusted from its theoretically derived value.

Time-resolved measurement of film growth during reactive high power pulsed magnetron sputtering (HIPIMS) of titanium nitride

The growth rate during reactive high power pulsed magnetron sputtering (HIPIMS) of titanium nitride is an inherent time-dependent process. By using a rotating shutter setup it is possible to gain an insight into its variation with a temporal resolution of up to 25 µs. In this apparatus a 200 µm slit is rotated in front of the substrate synchronous with the HIPIMS pulses. This ensures that the incoming growth flux is laterally distributed over the substrate. By measuring the resulting deposition profile with profilometry and x-ray photoelectron spectroscopy, the temporal variation of the titanium and nitrogen growth flux per pulse is deduced. The analysis reveals that film growth occurs mainly during an HIPIMS pulse, with the growth rate following the HIPIMS phases ignition, current rise, gas rarefaction, plateau and afterglow. The growth fluxes of titanium and nitrogen follow slightly different behaviours with titanium dominating at the beginning of the HIPIMS pulse and nitrogen at the end of the pulse. This is explained by the gas rarefaction effect resulting in a dense initial metal plasma and metal films which are subsequently nitrified.

Gas flow through microtubes with different internal surface coatings

An experimental setup based on the constant volume technique is developed to measure the mass flow rate through microtubes under isothermal stationary flow conditions. Four different working gases (helium, nitrogen, argon, and carbon dioxide), and two surface materials (stainless steel and Sulfinert) are considered. The Knudsen number calculated for the experimental conditions varies from ∼10−4 (hydrodynamic regime) to ∼ 5 (transitional regime). In the reduced range (10−4−0.1) corresponding to the hydrodynamic and slip regimes, an approach based on the analytical solution of the Stokes equation subjected to a first order velocity slip boundary condition is used. The velocity slip coefficient and the tangential momentum accommodation coefficient are extracted from the experimental data of the mass flow rate using their analytical expressions. The results are summarized in the tables representing the accommodation coefficients for the corresponding gas-surface material combinations. The influence of the molecular mass on the tangential momentum accommodation coefficient is discussed. In addition, an original technique is proposed to extract the accommodation coefficient in the whole experimentally available range (10−4−5) of the gas rarefaction. The accommodation coefficients obtained using this technique are close to those found in the slip regime.

Analysis of Pressure Distribution on Head Disk Air Bearing Slider Involved Van der Waals Force

This paper focuses on the pressure distribution on the surface of slider in hard disk drive when its flying height is in nanoscale. The gas rarefaction effect and van der Waals force are involved in the analysis process. Here the air bearing force model is based on F-K model and we establish the equation of van der Waals force between the head and disk. Using the finite element method, the modified Reynolds equation and the van der Waals force were obtained. The air bearing force on slider before and after the van der Waals force involved were compared. The results illustrate that the effect of van der Waals force on the air bearing force is different according to the slider shapes and flying heights. As a result, van der Waals force plays an important role when the flying height of slider is below 10 nm.

Modeling and Analysis of Micro Hybrid Gas Spiral-Grooved Thrust Bearing for Microengine

The micro hybrid spiral-grooved thrust bearing is a promising candidate to support the rotating elements in power MEMS devices such as micro gas turbine engines. However, the realization of hybrid thrust bearings has encountered a number of technical challenges due to the very high rotating speed and DN number (the product of the inner diameter and the rotational speed of the bearing, mm · rpm) to achieve high power density, the super thin gas film between rotors and thrust pad, and the relative large fabrication uncertainties according to the imperfection of the fabrication technology. In this paper, the configuration of a micro hybrid spiral-grooved thrust bearing for power MEMS is designed, and the steady and dynamic characteristics of this kind of bearing are then analyzed comprehensively, with the consideration of both the rarefaction effects and the influence of potential microfabrication defects. The nonlinear equations of molecular gas-film lubrication describing the gas rarefaction effects in a micro hybrid bearing are discretized by the finite volume method and solved by the Newton–Raphson techniques. The small perturbation technique is employed to study the dynamic behavior of a micro hybrid bearing. The results show that the micro hybrid thrust bearing exhibits better steady-state and dynamic performance than the existing micro hydrodynamic and hydrostatic bearings and that the hybrid bearings are likelier to be stable than their hydrodynamic counterparts, especially when the frequency number is high. The load capacity of the micro hybrid bearing increases slightly with the number of orifices and gradually with the diameter ratio of the orifice. The microfabrication defects of clogged orifices could lessen the load capacity and the dynamic coefficients of the hybrid thrust bearing. The model developed in this paper can serve as a useful tool to provide insight into micro hybrid gas thrust bearing-rotor systems.