Overall Assessment of Heat Transfer for a Rarefied Flow in a Microchannel with Obstacles Using Lattice Boltzmann Method

The objective of this investigation is to assess the effect of obstacles on numerical heat transfer and fluid flow momentum in a rectangular microchannel(MC).Two distinct configurations were studied:one without obstacles and the other with alternating obstacles placed on the upper and lower walls.The research utilized the thermal lattice Boltzmann method(LBM),which solves the energy and momentum equations of fluids with the BGK approximation,implemented in a Python coding environment.Temperature jump and slip velocity conditions were utilized in the simulation for the MC and extended to all obstacle boundaries.The study aims to analyze the rarefaction effect,with Knudsen numbers(Kn)of 0.012,0.02,and 0.05.The outcomes indicate that rarefaction has a significant impact on the velocity and temperature distribution.The presence of nine obstacles led to slower fluid movement inside the microchannel MC,resulting in faster cooling at the outlet.In MCs with obstacles,the rarefaction effect plays a crucial role in decreasing the Nusselt number(Nu)and skin friction coefficient(Cf).Furthermore,the study demonstrated that the obstacles played a crucial role in boosting fluid flow and heat transfer in the MC.The findings suggest that the examined configurations could have potential applications as cooling technologies in micro-electro-mechanical systems and microdevice applications.

Transmission effects of high energy nanosecond lasers in laser-induced air plasma under different pressures

When a high energy nanosecond(ns)laser induces breakdown in the air,the plasma density generated in the rarefied atmosphere is much smaller than that at normal pressure.It is associated with a relatively lower absorption coefficient and reduces energy loss of the laser beam at low pressure.In this paper,the general transmission characterizations of a Joule level 10 ns 1064 nm focused laser beam are investigated both theoretically and experimentally under different pressures.The evolution of the electron density(n_(e)),the changes in electron temperature(T_(e))and the variation of laser intensity(I)are employed for numerical analyses in the simulation model.For experiments,four optical image transfer systems with focal length(f)of 200 mm are placed in a chamber and employed to focus the laser beam and produce plasmas at the focus.The results suggest that the transmittance increases obviously with the decreasing pressure and the plasma channels on the transmission path can be observed by the self-illumination.The simulation results agree well with the experimental data.The numerical model presents that the maximum n_e at the focus can reach 10^(19)cm^(-3),which is far below the critical density(n_(c)).As a result,the laser beam is not completely shielded by the plasmas.

Analysis of Rarefied Effects of a Nano-scale Magnetic Head/Disk

When the decrease in the space between magnetic head and disk arrived at 10 nm or less, which is much lower than the mean free path of gas molecules, the gas flow presents distinctive features against the macro features because of the rarefied effects. The modified Reynolds equation considering rarefied gas effect is used to calculate the rarefied region of a negative pressure magnetic head working in the distance of 10 nm. Inverse Knudsen number was adopted to calculating the ratio of the rarefied area. According to the numerical resuks, discussions and analyses are then presented to reveal the rarefied effect on the working performances of a magnetic head. The results show that the magnetic head works in the slip-flow and transition regions and moves to the transition region with the increase in velocity. Furthermore, the maximum rarefied effects occur at the side edges where the flying height is thinner and pressure is lower, rather than in the minimum flying height on the rear. The results also show that with considering the rarefied effects, the load-carrying capacity of the magnetic head and the maximum pressure decrease significantly, but the minimum pressure slightly changes.

The effect of surface roughness on rarefied gas flows by lattice Boltzmann method

This paper studies the roughness effect combining with effects of rarefaction and compressibility by a lattice Boltzmann model for rarefied gas flows at high Knudsen numbers. By discussing the effect of the tangential momentum accommodation coefficient on the rough boundary condition, the lattice Boltzmann simulations of nitrogen and helium flows are performed in a two-dimensional microchannel with rough boundaries. The surface roughness effects in the microchannel on the velocity field, the mass flow rate and the friction coefficient are studied and analysed. Numerical results for the two gases in micro scale show different characteristics from macroscopic flows and demonstrate the feasibility of the lattice Boltzmann model in rarefied gas dynamics.

Rarefied planar jets into vacuum

This paper presents a fundamental gaskinetic study on high speed rarefied jets expanding into vacuum from a cluster of planar exits.Based on the corresponding exact expressions for one planar jet,this paper straightforwardly derives the combined multiple jet flowfield solutions of density and velocity components,however,for the combined temperature and pressure solutions,extra attention shall be practiced.Several direct simulation Monte Carlo simulation results are provided and they validate these analytical solutions of rarefied planar jet flows.

Ballistic Principle of the Property Balance in Space and Its Application to Modeling of Fluid Dynamics Problems

A newly discovered Ballistic Principle of the Property Balance in the Space (BPPBS) occupied by the gas is introduced to simplify and reduce computations in applications dealing with modeling of fluid dynamics problems. The integro-differential balance equations for mass, momentum, and energy, which were formulated by applying the BPPBS, are derived. The integro-differential balance equations for mass and momentum were further approximated for the collision-dominated flow regime. Then they were reduced to the corresponding vector differential equations by the method of vector differentiation with subsequent elimination of the terms belonging to the original equation. It was shown that in the collision-dominated flow regime, the derived vector differential equations of mass and momentum balance are identical to the corresponding Navier-Stokes equations. This finding validates the BPPBS and suggests that, in the collision-dominated flow regime, the formulated integro-differential forms of the balance are exact implicit solutions for corresponding Navier-Stokes equations. Six additional tests demonstrating the feasibility of the proposed method and validity of the BPPBS are presented here. The BPPBS and the methodology discussed here will be highly useful not only as the basis to solve the fluid dynamics problems, but also to model any dynamic system composed of presumably chaotically moving particles/elements, each carrying a specific amount of property/information.

Planar collisionless jet impingement on a specular reflective plate

This paper presents a fundamental gas-kinetic study on a high speed planar rarefied jet impinging on a flat plate of specular reflections. Based on previous collisionless planar free jet results, it is straightforward to obtain jet impingement flowfield solutions, and jet impingement for specular reflective plate surface properties. Several direct simulation Monte Carlo simulation results are provided and they validate these analytical solutions of rarefied planar jet flows. The results can find applications in many disciplines, such as materials processing, molecular beams, and space engineering.

Effect of Ballistic Bouncing of Gas Particles across a Microchannel on Rarefied Gas Flows

This paper proposes a novel computationally efficient method of modeling rarefied gas flow in microchannels based on the newly discovered and mathematically proven Ballistic Principle of the Property Balance in Space (BPPBS). The mechanism of influence of the effect of rarefication on the gas flow is specifically investigated. Also, a differential form of the momentum balance equation governing gas flow in the channel between two parallel plates due to the pressure gradient along the channel and its exact implicit solution in the form of an integral equation have been derived. The theory does not use the generalized concept of viscosity based on the variable mean free path (MFP) in the Knudsen layer (KL). Comparing the normalized flow rate as a function of the inverse Knudsen number according to the current theory and the experimental data shows good agreement in the range of the inverse Knudsen number from 0.01 to about 40. The correlation factor is found to be about 0.995. The results show that our approach based on the BPPBS offers substantial and practical advantages in modeling and simulation of rarefied gases. The validity of the widely disseminated claim of the geometry-dependent MFP in the KL was analyzed.

Computer Modelling of Aerothermodynamic Characteristics for Hypersonic Vehicles

The purpose of this work is to describe the suitable methods for aerodynamic characteristics calculation of hypersonic vehicles in free molecular flow and the transitional regimes. Moving of the hypersonic vehicles at high altitude, it is necessary to know the behavior of its aerodynamic characteristics for all flow regimes. Nowadays, various engineering approaches have been developed for modelling of aerodynamics of aircraft vehicle designs at initial state. The engineering method that described in this paper provides good results for the aerodynamic characteristics of various geometry designs of hypersonic vehicles in the transitional regime. In this paper present the calculation results of aerodynamic characteristics of various hypersonic vehicles in all range of regimes by using engineering method.

Flow characteristics of supersonic gas passing through a circular micro-channel under different inflow conditions

Gas flow in a micro-channel usually has a high Knudsen number. The predominant predictive tool for such a microflow is the direct simulation Monte Carlo(DSMC) method, which is used in this paper to investigate primary flow properties of supersonic gas in a circular micro-channel for different inflow conditions, such as free stream at different altitudes, with different incoming Mach numbers, and with different angles of attack. Simulation results indicate that the altitude and free stream incoming Mach number have a significant effect on the whole micro-channel flow field, whereas the angle of attack mainly affects the entrance part of micro-channel flow field. The fundamental mechanism behind the simulation results is also presented. With the increase of altitude, thr free stream would be partly prevented from entering into micro-channel.Meanwhile, the gas flow in micro-channel is decelerated, and the increase in the angle of attack also decelerates the gas flow. In contrast, gas flow in micro-channel is accelerated as free stream incoming Mach number increases. A noteworthy finding is that the rarefaction effects can become very dominant when the free stream incoming Mach number is low. In other words, a free stream with a larger incoming velocity is able to reduce the influence of the rarefaction effects on gas flow in the micro-channel.

Efficient molecular model for squeeze-film damping in rarefied air

Based on the energy transfer model(ETM) proposed by Bao et al.and the Monte Carlo(MC) model proposed by Hutcherson and Ye, this paper proposes an efficient molecular model(MC-S) for squeeze-film damping(SQFD) in rarefied air by releasing the assumption of constant molecular velocity in the gap.Compared with the experiment data, the MC-S model is more efficient than the MC model and more accurate than ETM.Besides, by using the MC-S model, the feasibility of the empirical model proposed by Sumali for SQFD of different plate sizes is discussed.It is proved that, for various plate sizes, the accuracy of the empirical model is relatively high.At last, the SQFD of various vibration frequencies is discussed, and it shows that, for low vibration frequency, the MC-S model is reduced to ETM.

DIRECT NUMERICAL TEST OF THE B-G-K MODEL EQUATION BY THE DSMC METHOD

In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.

Simulation of Vapor Flows Between Two Closed Surfaces of Evaporation and Condensation at High Vacuum

The steady multi component vapor flows between two closed surfaces of evaporation and condensation are investigated numerically by the nonlinear Bhatnagar Gross Krook equation. The mathematical model will make it possible to determine the profiles of the process variables between two surfaces of evaporation and condensation if the conditions of evaporation and condensation surfaces are taken into consideration. It is used to simulate the vapor behaviors of the pure dibutylphthalate and the ethylhexyl phthalate ethylhexyl sebacate mixture. The effects of the liquid composition of the evaporation surface, the evaporation temperature, the condensation temperature and the distance between evaporation and condensation surfaces on the evaporation efficiency and separation factor are discussed.

Spacecraft aerodynamics and trajectory simulation during aerobraking

This paper uses a direct simulation Monte Carlo （DSMC） approach to simulate rarefied aerodynamic characteristics during the aerobraking process of the NASA Mars Global Surveyor （MGS） spacecraft. The research focuses on the flowfield and aerodynamic characteristics distribution under various free stream densities. The vari- ation regularity of aerodynamic coefficients is analyzed. The paper also develops an aerodynamics-aeroheating-trajectory integrative simulation model to preliminarily calculate the aerobraking orbit transfer by combining the DSMC technique and the classical kinematics theory. The results show that the effect of the planetary atmospheric density, the spacecraft yaw, and the pitch attitudes on the spacecraft aerodynamics is significant. The numerical results are in good agreement with the existing results reported in the literature. The aerodynamics-aeroheating-trajectory integrative simulation model can simulate the orbit transfer in the complete aerobraking mission. The current results of the spacecraft trajectory show that the aerobraking maneuvers have good performance of attitude control.

An Empirical Method for Prediction of Hypersonic Rarefied Flow-Field Structure

Numerical simulations are presented about the effects of gas rarefaction on hypersonic flow field.Due to the extremely difficult experiment,limited wind-tunnel conditions and high cost,most problems in rarefied flow regime are investigated through numerical methods,in which the direct simulation Monte-Carlo(DSMC)method is widely adopted.And the unstructured DSMC method is employed here.Flows around a vertical plate at a given velocity 7 500 m/s are simulated.For gas rarefaction is judged by the free-stream Knudsen number(Kn),two vital factors are considered:molecular number density and the plate′s length.Cases in which Kn varies from 0.035 to13.36 are simulated.Flow characters in the whole rarefied regime are described,and flow-field structure affected by Knis analyzed.Then,the dimensionless position D*of a certain velocity in the stagnation line is chosen as the marker of flow field to measure its variation.Through flow-field tracing and least-square numerical method analyzing,it is proved that hypersonic rarefied flow field expands outward linearly with the increase of 1/2Kn.An empirical method is proposed,which can be used for the prediction of the hypersonic flow-field structure at a given inflow velocity,especially the shock wave position.

Flows of a Rarefied Gas between Coaxial Circular Cylinders with Nonuniform Surface Properties

Flows of a rarefied gas between coaxial circular cylinders with nonuniform surface properties are studied on the basis of kinetic theory. It is assumed that the outer cylinder is a diffuse reflection boundary and the inner cylinder is a Maxwell-type boundary whose accommodation coefficient varies in the circumferential direction. Three fundamental flows are studied: 1) a flow caused by the rotation of the outer cylinder (Couette flow), 2) a flow induced between the cylinders at rest kept at different temperatures (heat transfer problem), and 3) a flow induced by the circumferential temperature distribution along the cylindrical surfaces (thermal creep flow). The linearized ES-BGK model of the Boltzmann equation is numerically analyzed using a finite difference method. The time-independent behavior of the gas is studied over a wide range of the gas rarefaction degree, the radii ratio, and a parameter characterizing the distribution of the accommodation coefficient. Due to an effect of nonuniform surface properties, a local heat transfer occurs between the gas and the cylindrical surfaces in Couette flow;a local tangential stress arises in the heat transfer problem. However, the total heat transfer between the two cylinders in Couette flow and the total torque acting on the inner cylinder in the heat transfer problem vanish irrespective of the flow parameters. Two nondegenerate reciprocity relations arise due to the effect of nonuniform surface properties. The reciprocity relations among the above-mentioned three flows are numerically confirmed over a wide range of the flow parameters. The force on the inner cylinder, which also arises due to the effect of nonuniform surface properties in Couette flow and the heat transfer problems, is studied.

3D DSMC Simulation of Rarefied Gas Flows around a Space Crew Capsule Using OpenFOAM

An open source Direct Simulation Monte Carlo (DSMC) code, called as dsmcFoam in OpenFOAM, is used to study a blunt body with the shape of a space crew capsule return vehicle. The rarefied gas has the Knudsen number with 0.03. The flow with a Mach number 4.35 over the capsule was simulated by DSMC. The distributions of velocity field and temperature around the capsule were calculated. This study may provide some useful information for the reentry of the return vehicle.

Thermal Electromagnetic Radiation of Rarefied Gas

The Boltzmann kinetic equation for rarefied radiating gas is found. It is shown, that process of radiation is defined by excitation of atoms at their collision, and also spontaneous radiation of quantums at transition of electrons to the basic power level and the compelled radiation of quantums at collision of the excited atoms. It is shown, that distributions on velocities of the excited and not excited atoms submit to various laws. Distinctions in laws of distribution of the excited and not excited atoms define power parameters of radiating gas, and also a share of radiating molecules in gas.

A Closed-Form Solution of a Kinetic Integral Equation for Rarefied Gas Flow in a Cylindrical Duct

A spectral method based on Hermite cubic splines expansions combined with a collocation scheme is used to develop a solution for the vector form integral S-model kinetic equation describing rarefied gas flows in cylindrical geometry. Some manipulations are made to facilitate the computational treatment of the singularities inherent to the kernel. Numerical results for the simulation of flows generated by pressure and thermal gradients, Poiseuille and thermal-creep problems, are presented.

稀薄气体效应对高超声速边界层稳定性的影响

临近空间高超声速飞行器在跨越大气层飞行时可能经历从连续到稀薄流域.本文基于Navier-Stokes(NS)方程和NS改进模型研究了稀薄气体效应对高超声速边界层稳定性的影响.首先在传统线性稳定性理论(linear stability theory,LST)中引入壁面滑移条件和非线性输运模型,发展了适用于稀薄剪切流的拓展稳定性分析方法.然后重点分析了马赫数10、飞行高度55 km的尖平板绕流,研究了稀薄气体效应(包括壁面滑移效应和剪切非平衡效应)对边界层稳定性的影响机理.结果表明,对于基本流,稀薄气体效应使得边界层变薄,边界层剖面的广义拐点向壁面靠近.对于稳定性,稀薄气体效应通过影响基本流使第二模态更稳定,而通过修正稳定性方程使第二模态更不稳定,综合效应使得第二模态更稳定.然而,对于第一模态,稀薄气体效应始终起不稳定效果.这些结果从宏观角度揭示了近连续流域高超声速平板边界层的稳定性特征.