Rarefied Conditions Research Articles

Numerical investigation of rarefied vortex loop formation due to shock wave diffraction with the use of rorticity

When compressed gas is ejected from a nozzle into a low-pressure environment, the shock wave diffracts around the nozzle lip and a vortex loop will form. The phenomenon has been widely investigated in the continuum flow regime, but how the shock diffraction and vortex behave under rarefied flow conditions has not received as much attention. It is necessary to understand this transient flow in rarefied environments to improve thrust vector control and avoid potential contamination and erosion of spacecraft surfaces. This work provides numerical results of the vortex loop formation caused by shock wave diffraction around a 90° corner using the direct simulation Monte Carlo method and the compressible Navier–Stokes equations with the appropriate Maxwell velocity slip and the von Smoluchowski temperature jump boundary conditions. The Mach number and rarefaction effects on the formation and evolution of the vortex loop are discussed. A study of the transient structures of vortex loops has been performed using the rorticity concept. A relationship of mutual transformation between the rorticity and shear vectors has been discovered, demonstrating that the application of this concept is useful to understand vortex flow phenomena.

Molecular dynamics study on scattering characteristics of nitrogen molecules from platinum surface by molecular beam method

Rarefied gas flow has received wide attention due to the booming of micro/nano-electromechanical systems and aerospace engineering. Under such rarefied conditions, the frequency of intermolecular collisions is sharply reduced, so the impacts of interactions between gas molecules and the wall surface on flow states become non-negligible. Owing to the complexity of theoretical research and the poor reproducibility of experimentation, molecular dynamics simulation has developed into an effective method to study the interplay between gases and solid surfaces. In this study, molecular dynamics simulations on the scattering process of nitrogen molecules from a platinum surface are conducted in a three-dimensional system. The dependences of scattering angle distributions and momentum/energy variations on the incident velocity, angles, and surface roughness are obtained. The results of this paper are not only an attempt to reveal the mechanisms of gas–surface interactions but can also be used as necessary reference data for the development of appropriate gas–surface interaction models.

Incident angle dependence of reflected particles in low-energy xenon-ion impacts on metal surfaces

Ion-wall reflection characteristics are of great importance in the design of ground test facilities for electric propulsion because these characteristics determine the rarefied flow conditions inside the vacuum chambers. In this study, the reflection characteristics of 300 eV xenon incident on aluminum and titanium metal targets were calculated by molecular dynamics (MD) simulations. The resultant characteristics show the angular dependence of the reflected particles. The trajectories of the reflected particles show that the dominant reflection mechanism is different depending on the incident angle. A practical model that can be used to reproduce the calculated reflection characteristics is presented. Three parameters required for the model are obtained by fitting the model to the MD calculation results of the polar probability and energy distributions of the reflected xenon particles. The three-dimensional distributions reproduced by applying the three parameters to the model show good agreement with the MD simulation results.

Analysis of Standby Losses and Charging Cycles in Flywheel Energy Storage Systems

Aerodynamic drag and bearing friction are the main sources of standby losses in the flywheel rotor part of a flywheel energy storage system (FESS). Although these losses are typically small in a well-designed system, the energy losses can become significant due to the continuous operation of the flywheel over time. For aerodynamic drag, commonly known as windage, there is scarcity of information available for loss estimation since most of the publications do not cover the partial vacuum conditions as required in the design of low loss energy storage flywheels. These conditions cause the flow regime to fall between continuum and molecular flow. Bearings may be of mechanical or magnetic type and in this paper the former is considered, typically hybridized with a passive magnetic thrust bearing. Mechanical bearing loss calculations have been extensively addressed in the open literature, including technical information from manufacturers but this has not previously been presented clearly and simply with reference to this application. The purpose of this paper is therefore to provide a loss assessment methodology for flywheel windage losses and bearing friction losses using the latest available information. An assessment of windage losses based on various flow regimes is presented with two different methods for calculation of windage losses in FESS under rarefied vacuum conditions discussed and compared. The findings of the research show that both methods closely correlate with each other for vacuum conditions typically required for flywheels. The effect of the air gap between the flywheel rotor and containment is also considered and justified for both calculation methods. Estimation of the bearing losses and considerations for selection of a low maintenance, soft mounted, bearing system is also discussed and analysed for a flywheel of realistic dimensions. The effect of the number of charging cycles on the relative importance of flywheel standby losses has also been investigated and the system total losses and efficiency have been calculated accordingly.

Numerical study of heat transfer in Rayleigh-Bénard convection under rarefied gas conditions.

The focus of this research is to delineate the thermal behavior of a rarefied monatomic gas confined between horizontal hot and cold walls, physically known as rarefied Rayleigh-Bénard (RB) convection. Convection in a rarefied gas appears only for high temperature differences between the horizontal boundaries, where nonlinear distributions of temperature and density make it different from the classical RB problem. Numerical simulations adopting the direct simulation Monte Carlo approach are performed to study the rarefied RB problem for a cold to hot wall temperature ratio equal to r=0.1 and different rarefaction conditions. Rarefaction is quantified by the Knudsen number, Kn. To investigate the long-time thermal behavior of the system two ways are followed to measure the heat transfer: (i) measurements of macroscopic hydrodynamic variables in the bulk of the flow and (ii) measurements at the microscopic scale based on the molecular evaluation of the energy exchange between the isothermal wall and the fluid. The measurements based on the bulk and molecular scales agreed well. Hence, both approaches are considered in evaluations of the heat transfer in terms of the Nusselt number, Nu. To characterize the flow properly, a modified Rayleigh number (Ra_{m}) is defined to take into account the nonlinear temperature and density distributions at the pure conduction state. Then the limits of instability, indicating the transition of the conduction state into a convection state, at the low and large Froude asymptotes are determined based on Ra_{m}. At the large Froude asymptote, simulations following the onset of convection showed a relatively small range for the critical Rayleigh (Ra_{m}=1770±15) that flow instability occurs at each investigated rarefaction degree. Moreover, we measured the maximum Nusselt values Nu_{max} at each investigated Kn. It was observed that for Kn≥0.02,Nu_{max} decreases linearly until the transition to conduction at Kn≈0.03, known as the rarefaction limit for r=0.1, occurs. At the low Froude (parametric) asymptote, the emergence of a highly stratified flow is the prime suspect of the transition to conduction. The critical Ra_{m} in which this transition occurs is then determined at each Kn. The comparison of this critical Rayleigh versus Kn also shows a linear decrease from Ra_{m}≈7400 at Kn=0.02 to Ra_{m}≈1770 at Kn≈0.03.

A modal discontinuous Galerkin method for simulating dusty and granular gas flows in thermal non-equilibrium in the Eulerian framework

A modal discontinuous Galerkin method was developed for computing compressible rarefied gaseous flows interacting with rigid particles and granular medium. In contrast to previous particle-based models that were developed to handle rarefied flows or solid phase particles, the present computational method employs full continuum-based models. This work is one of the first attempts to apply the modal discontinuous Galerkin method to a two-fluid model framework, which covers a wide range of gas and solid phase regimes, from a continuum to non-equilibrium gas, and from dusty to collisional regimes. The rarefaction effects were taken into account by applying the second-order Boltzmann-Curtiss-based constitutive relationship in a two-fluid system of equations. For the dust phase, computational models were developed based on the kinetic theory of the granular flows. Due to the orthogonal property of the basis functions in the method, no specific treatment of the source terms, commonly necessary in the conventional finite volume method, was required. Moreover, a high-fidelity approach was selected to treat the non-strictly hyperbolic equations of a dusty gas. This allows the same inviscid numerical flux functions to be applied to both the gaseous Euler and solid pressureless-Euler system of equations. Further, we observed that, for the discretization of the viscous fluxes in multiphase cases, the local discontinuous Galerkin is superior to the first method by Bassi and Rebay. After a verification and validation study, the new computational model was used to simulate the impingement of an underexpanded jet on a dusty surface in a rarefied condition. A surface erosion model based on viscous erosion associated with aerodynamic entrainment was implemented at a solid surface. Simulation cases in the near-field of the nozzle flow were tested to evaluate the capabilities of the present computational model in handling the challenging problems of multi-scale multiphase flows.

Development of MEMS gas actuator for analyzing a gas mixture

In this study, a computational technique is used to investigate the ability of a new MEMS gas actuator (MIKRA) for detection and sensation of the gas mixture. In this actuator, the temperature difference of two arms inside a rectangular domain at rarefied condition induces a Knudsen force which is relative to physical properties of the gas. Both 2d and 3D approaches are applied for the simulation of the flow inside the model. In order to define the flow feature of a low-pressure gas inside the micro gas actuator, a high order equation of Boltzmann should be solved to attain reliable results. Since the domain of this micro gas is non-equilibrium, Direct Simulation Monte Carlo (DSMC) method is applied for the simulation of the model. According to obtained results, a three-dimensional model presents more reliable results and the effect of a gap for three-dimensional model clearly demonstrates the impact of this parameter on the effective Knudsen force

Shear-driven micro/nano flows simulation using Fokker Planck approach: Investigating accuracy and efficiency

A detailed study on the performance and accuracy of the Fokker Planck (FP) approach in treating shear driven flows over a wide range of Knudsen numbers and Mach numbers at subsonic and supersonic regimes is considered. One-dimensional Couette flow and the two-dimensional cavity problem are considered. The FP method is evaluated in the Couette flow at a subsonic Mach number of 0.16 (Uw = 50 m/s) and at the supersonic Mach number of 3.1 (Uw = 1000 m/s), where Knudsen numbers range from 0.005 to 1. Correspondingly, the cavity flow is investigated at a wall Mach number of 0.31 (Uw = 100 m/s) and wall Mach number of 0.93 (Uw = 300 m/s) at Knudsen numbers ranging from 0.05 to 20. Interestingly, the results show that by increasing the wall velocity and Knudsen numbers, the accuracy of the FP approach increases in treating the cavity flow. In addition to the standard Knudsen number, we show that gradient length Knudsen number, KnGL, should be considered to determine the range of accuracy of the FP scheme. The latter depends on the strength of the center vortex of the cavity diminishing at higher rarefied conditions. The results demonstrate that the computational efficiency of the FP approach enhances at higher lid velocity.

Gas permeability in rarefied flow conditions for characterization of mineral membrane support

Abstract Gas Permeability Measurement Technique (GPMT) has the advantage of being a non-destructive method, which is efficient in characterizing filtration membranes. Ceramic filtration membranes consist of successive layers of micro (support) to nano size (skin) pores. When gas flows through such a small scale structure, the molecular mean free path becomes comparable to the pore size. The Slip flow model, validated to describe the gas transport properties under rarefied flow conditions in a microchannel, is extended to porous media. The porous structure is modeled as a cluster of several identical cylindrical channels. By measuring the pressure drop Δ P at several different mean pressures, the pore radius and the porosity on square tortuosity ratio ϵ ∕ τ 2 of the porous model structure that have the same flow property were estimated.

Relationship between flame thickness and velocity based on thermodynamic three kernels in a constant volume combustion chamber

The aim of this study is to analyze the relationship between the flame thicknesses and velocity based on thermodynamic three kernels, including spark, arc and jet plasma discharges in a constant volume combustion chamber (CVCC). As the research method, a CVCC designed to ensure 400 cm3 of internal volume were developed by the authors to analyze the combustion characteristics. The compositions of combustion system include the spark plugs (conventional spark, arc and jet types), pressure sensor, temperature sensor, oxygen sensor, control circuit, hardware and high-speed camera. A pressure sensor for measuring the progressive combustion uses a type of Kistler 601CBA00250. It is verified that the discharge level of a jet plasma model is higher by about 3.8 kV then an arc plasma model and the combustion time is also faster than other plasma types. Moreover, in the signal analysis, the charging time in a jet plasma model starts to detect the signal from −0.11 ms to 0 ms and the charging voltage height is raised up to 40 kV due to being affected by stored energy of a capacitor. Consequently, the combustion performances of the arc and jet plasma discharges are noticeable in that flame thickness and velocity characteristics could be affected by ionized kernels in a CVCC. As the air-C3H8 equivalence rates, the progressive combustion and reaction by the arc and jet plasma discharges are more improved than the conventional spark discharge in a rarefied condition.

Measurement of low-pressure Knudsen force with deflection approximation for gas detection

In this paper, experimental examinations are done to evaluate the thermal Knudsen force in Knudsen gauge at low-pressure condition. This work has focused on the simple technique to visibly observe the induced Knudsen force as main parameter which could be used in the micro sensor for gas detection in rarefied condition. In order to do this, the simple micro channel with presence of copper wire as hot element with a flexible element is prepared to observe the effect of the Knudsen force on the change of the degree of the flexible arm. This study investigates the effect of the pressure and temperature difference of element on the variation of the Knudsen force in the low-pressure condition. DSMC simulations are also done to confirm and evaluate the obtained results. Our findings show that proposed technique presents reasonable results and clearly demonstrates the effect of the Knudsen thermal force in the rarefied gas.

Predicting the rarefied gas flow through circular nano/micro short tubes: A semi-empirical model

A new explicit semi-empirical model was proposed for predicting the steady state gas flow rate through short tubes under rarefied condition. The experimental data produced by Fujimoto and Usami and the DSMC data provided by Varoutis et al. were utilized to obtain the model coefficients. The model was further validated by the published experimental data. The proposed model was capable to make predictions while meeting all the criteria of the rarefied gas flow in the following ranges of the variables: 0<Pr < 0.7, 0<δ < 4000 and 0<ω < 13. The model was capable to predict the reduced flow rate of rarefied systems, not only in the free molecular region and the hydrodynamic region, but also in the transition region, hence covering all the Knudsen number domain within the utilized data. It was also found that by increasing the pressure ratio and decreasing the length to diameter ratio, the transition region shifted to the higher values of the rarefaction parameter. The proposed model is useful in the vacuum gas community for engineering purposes by offering a practical closed form expression for the DSMC data to predict the rarefied gas flow rate.

The rarefied (non-continuum) conditions of tracer particle transport in soils, with implications for assessing the intensity and depth dependence of mixing from geochronology

Abstract. We formulate tracer particle transport and mixing in soils due to disturbance-driven particle motions in terms of the Fokker–Planck equation. The probabilistic basis of the formulation is suitable for rarefied particle conditions, and for parsing the mixing behavior of extensive and intensive properties belonging to the particles rather than to the bulk soil. The significance of the formulation is illustrated with the examples of vertical profiles of expected beryllium-10 (10Be) concentrations and optically stimulated luminescence (OSL) particle ages for the benchmark situation involving a one-dimensional mean upward soil motion with nominally steady surface erosion in the presence of either uniform or depth-dependent particle mixing, and varying mixing intensity. The analysis, together with Eulerian–Lagrangian numerical simulations of tracer particle motions, highlights the significance of calculating ensemble-expected values of extensive and intensive particle properties, including higher moments of particle OSL ages, rather than assuming de facto a continuum-like mixing behavior. The analysis and results offer guidance for field sampling and for describing the mixing behavior of other particle and soil properties. Profiles of expected 10Be concentrations and OSL ages systematically vary with mixing intensity as measured by a Péclet number involving the speed at which particles enter the soil, the soil thickness, and the particle diffusivity. Profiles associated with uniform mixing versus a linear decrease in mixing with depth are distinct for moderate mixing, but they become similar with either weak mixing or strong mixing; uniform profiles do not necessarily imply uniform mixing.

Chemical kinetics study in rarefied Martian atmosphere using quantum kinetics model

An open-source chemistry model based on Quantum-Kinetics (QK) is presented for the direct simulation Monte Carlo method. Chemistry modeling for the Martian atmosphere under rarefied re-entry conditions is analyzed in this study. An eight-species (CO2, N2, CO, O2, NO, C, N, and O) chemistry model is used to simulate the chemical reactions in the Martian environment. The QK model is based on the vibrational relaxation process of the molecule. A vibrational relaxation procedure for more than one vibrational mode is implemented to simulate various reactions in polyatomic molecules such as CO2. The reaction rates are validated with previous data based on the total collision energy model of Boyd and Arrhenius rates, as well as with the experimental data. The reaction rates obtained in this work are found to be in very good agreement with the previous results for near-equilibrium and non-equilibrium conditions.

Analysis of velocity slipping at wall boundary under rarefied gas condition based on the effect of viscosity

PurposeVelocity slipping model, based on the stratification theory (the film in inflatable support area of aerostatic guide way was divided into near wall layer, thin layer and continuous flow layer in the direction of height), was established, and the model was combined with viscosity changes in each layer.Design/methodology/approachSimulated and analyzed by LAMMPS and two-dimensional molecular dynamics method, some relevant conclusions were drawn.FindingsAt a high temperature, viscosity is low, velocity slipping is large and velocity gaps in near-wall layer and thin layer are large. When the temperature is constant, the dimensionless slipping length and Kn number are linear.Research limitations/implicationsThe effect of the equivalent viscosity on gas slipping model is proposed. viscosity is smaller, gas velocity slipping is greater, temperature is higher, gas velocity slipping is greater, velocity gap of near wall layer and thin layer is larger. When the temperature is constant, the dimensionless slipping length ls and Kn number are linear.Originality/valueThe global model of lubricating film velocity slipping between plates was established, and mathematical expression of slipping model in each layer, based on the stratification theory, was presented.

Heat transfer in rough microchannels under rarefied flow conditions

A hybrid solver dynamically coupling the kinetic solution computed in local rarefied areas and the Navier–Stokes solution in the rest of the flow is used for the investigation of heat transfer in microchannels with rough wall surfaces. Roughness is modeled as a series of triangular obstructions with a relative roughness height from 0 up to 5% of the channel height. A nearly incompressible gas flow (low Mach number) for a range of Knudsen numbers from 0.01 up to 0.1 is considered. The competition between roughness, rarefaction and heat transfer effects is discussed in terms of average Nusselt and Poiseuille numbers and mass flow rate. The discrepancy between the full Navier–Stokes and hybrid solutions is analyzed, assessing the range of applicability of the first order slip boundary condition for rough geometries in the presence of heat transfer.

Dissociation cross section for high energy O2-O2 collisions.

Collision-induced dissociation cross section database for high energy O2-O2 collisions (up to 30 eV) is generated and published using the quasiclassical trajectory method on the singlet, triplet, and quintet spin ground state O4 potential energy surfaces. At equilibrium conditions, these cross sections predict reaction rate coefficients that match those obtained experimentally. The main advantage of the cross section database based on ab initio computations is in the study of complex flows with high degree of non-equilibrium. Direct simulation Monte Carlo simulations using the reactive cross section databases are carried out for high enthalpy hypersonic oxygen flow over a cylinder at rarefied ambient conditions. A comparative study with the phenomenological total collision energy chemical model is also undertaken to point out the difference and advantage of the reported ab initio reaction model.

Multi-plume flow simulation of small bipropellant thrusters using parallel DSMC method

As a plume gas exhausted from a bipropellant thruster contains several kinds of chemical compositions, it has been identified as a critical source of heating and contamination on surfaces and components outside a satellite because it can degrade optical properties and performance gradually. Thus, accurate evaluations of the plume gas behaviors from the bipropellant thrusters and their influences on a satellite are necessary from an initial development phase of a satellite through a numerical simulation. In this regard, the present study intended to investigate multiple plume gas behaviors of the bipropellant thrusters with several kinds of gas compositions simultaneously and then to evaluate its influence on a solar panel of a geosynchronous (GEO) satellite numerically. To simulate complex multiple plume flow regimes efficiently, a combined approach of computational fluid dynamics (CFD) and parallelized Direct Simulation Monte Carlo (DSMC) was adopted to consider a continuum flow and a rarefied flow condition, respectively. Throughout the present numerical analysis results, multiple plume gas influences from three different bipropellant thrusters were evaluated on a three-dimensional satellite configuration with a large solar panel.

Numerical study of nonequilibrium gas flow in a microchannel with a ratchet surface.

The nonequilibrium gas flow in a two-dimensional microchannel with a ratchet surface and a moving wall is investigated numerically with a kinetic method [Guo et al., Phys. Rev. E 91, 033313 (2015)]PLEEE81539-375510.1103/PhysRevE.91.033313. The presence of periodic asymmetrical ratchet structures on the bottom wall of the channel and the temperature difference between the walls of the channel result in a thermally induced flow, and hence a tangential propelling force on the wall. Such thermally induced propelling mechanism can be utilized as a model heat engine. In this article, the relations between the propelling force and the top wall moving velocity are obtained by solving the Boltzmann equation with the Shakhov model deterministically in a wide range of Knudsen numbers. The flow fields at both the static wall state and the critical state at which the thermally induced force cancels the drag force due to the active motion of the top wall are analyzed. A counterintuitive relation between the flow direction and the shear force is observed in the highly rarefied condition. The output power and thermal efficiency of the system working as a model heat engine are analyzed based on the momentum and energy transfer between the walls. The effects of Knudsen number, temperature difference, and geometric configurations are investigated. Guidance for improving the mechanical performance is discussed.

A New Gaskinetic Model to Analyze Background Flow Effects on Weak Gaseous Jet Flows from Electric Propulsion Devices

Recent work on studying rarefied background and jet flow interactions is reported. A new gaskinetic method is developed to investigate two closely related problems. The first problem is how a collisionless background flow can affect a highly rarefied jet flow. The rarefied jet and background flow conditions are assumed available and described with seven parameters. Gaskinetic theories are applied and formulas are obtained for the mixture properties. Simulations are performed to validate these expressions, and excellent agreement is obtained. The second problem is to recover the collisionless background and jet flow parameters with limited measurements. A group of linearized equations are derived for the flowfield properties. The solving process includes initial estimations on the seven parameters, followed with iterations. Numerical tests are performed and the results indicate the procedure is accurate and efficient. The new method and expressions can reduce the amount of experimental work and numerical simulations to analyze facility effects. Parameter studies with particle simulations may require several months; however, the new methods may require minutes. These methods can be used to quantify and predict jet performance, vacuum chamber designs and optimization. Applications may be for many societies using vacuum conditions.