Inversion of the transverse force on a spinning sphere moving in a rarefied gas

The flow around a spinning sphere moving in a rarefied gas is considered in the following situation: (i) the translational velocity of the sphere is small (i.e. the Mach number is small); (ii) the Knudsen number, the ratio of the molecular mean free path to the sphere radius, is of the order of unity (the case with small Knudsen numbers is also discussed); and (iii) the ratio between the equatorial surface velocity and the translational velocity of the sphere is of the order of unity. The behaviour of the gas, particularly the transverse force acting on the sphere, is investigated through an asymptotic analysis of the Boltzmann equation for small Mach numbers. It is shown that the transverse force is expressed as $\boldsymbol{F}_L = {\rm \pi}\rho a^3 (\boldsymbol{\varOmega} \times \boldsymbol{v}) \bar{h}_L$ , where $\rho$ is the density of the surrounding gas, a is the radius of the sphere, $\boldsymbol {\varOmega }$ is its angular velocity, $\boldsymbol {v}$ is its velocity and $\bar {h}_L$ is a numerical factor that depends on the Knudsen number. Then, $\bar {h}_L$ is obtained numerically based on the Bhatnagar–Gross–Krook model of the Boltzmann equation for a wide range of Knudsen number. It is shown that $\bar {h}_L$ varies with the Knudsen number monotonically from 1 (the continuum limit) to $-\tfrac {2}{3}$ (the free molecular limit), vanishing at an intermediate Knudsen number. The present analysis is intended to clarify the transition of the transverse force, which is previously known to have different signs in the continuum and the free molecular limits.

Investigation of rarefied flow over backward-facing step in different rarefaction regimes using direct simulation Monte Carlo

Hypersonic aerothermodynamics for a re-entry vehicle approaching the earth’s atmosphere is critical in the exploration of space. These vehicles often encounter various flow regimes due to the density variations and have surface abnormalities. The backward-facing step (BFS) is one such simplified configuration for modeling anomalies around such space vehicles. The present work examines rarefied hypersonic flow over a BFS using the direct simulation Monte Carlo (DSMC) method. The purpose of this research is focused on exploring the various loads encountered by a re-entry vehicle passing through different altitudes covering different rarefaction regimes. The fluid considered was non-reacting air, with the free-stream Mach number as 25, and the Knudsen number considered ranged from 0.05-21.10. The influence of the Knudsen number on flow characteristics has been elucidated graphically in various streamwise directions. The normalised flow properties such as velocity, pressure, temperature and density showed an increasing trend with the Knudsen number due to compressibility and viscous heating effects. In all flow regimes, there was an appearance of flow recirculation. With rarefaction, the recirculation lengths decreased, whereas the boundary layer thickness showed an increase. The aerodynamic surface properties such as pressure coefficient, skin friction, and heat transfer coefficient, by and large, showed an increase with the Knudsen number. When the chemical reactions were accounted for and compared against the non-reacting flows, the velocity, pressure, and density field showed no marked variation; however, considerable variations were observed in the temperature field. Furthermore, the present study also depicts the compressibility factor contour, showing the flow regions that diverge from the ideal gas behaviour.

Theoretical and numerical study of nanoporous evaporation with receded liquid surface: effect of Knudsen number

The liquid evaporation from nanoscale pores has attracted much attention from researchers due to its importance in water treatment and device cooling related applications. It is crucial to investigate the receded liquid case as the vapour flow resistance in a nanopore has high impacts on the evaporation rate. This paper proposed a semi-empirical analysis on nanoporous evaporation with a receded liquid surface under the influence of the Knudsen number. The vapour flow dynamics in a nanopore was examined considering the multiple reflections of vapour molecules. We calculated the value of pore transmissivity based on transitional gas flow correlation which incorporated the effect of the Knudsen number. Direct simulation Monte Carlo method was employed to provide validation for the present model. The vapour density jump near the liquid surface and the pressure ratio between the far field and saturation value were predicted by our model with good precision. It was shown that the vapour flow resistance in the nanopore accounted for more than 90 % of the total resistance in present cases. With increasing Knudsen number, the pressure ratio gradually drops and reaches an asymptotic level. This suggested a relatively higher evaporation resistance in free molecular regimes. The present work revealed the importance of the Knudsen number in nanoporous evaporation with receded liquids, providing insights into the governing factors under various Knudsen regimes.

Flow and thermal field investigation of rarefied gas in a trapezoidal micro/nano-cavity using DSMC

The impetus of the this study is to investigate flow and thermal field in rarefied gas flows inside a trapezoidal micro/nano-cavity using the direct simulation Monte Carlo (DSMC) technique. The investigation covers the hydrodynamic properties and thermal behavior of the flow. The selected Knudsen numbers for this study are arranged in the slip and transition regimes. The results show the center of the vortex location moves by variation in the Knudsen numbers. Also, as the Knudsen number increases, the non-dimensional shear stress increases, but the distribution deviates from a symmetrical profile. The cold to hot transfer, which is in contrast with the conventional Fourier law, is observed. We show that the heat transfer is affected by the second derivative of the velocity. By increasing the Knudsen number, the transferred heat through the walls decreases, but the contraction/expansion effects on the temperature in the corner of the cavity become higher.

Numerical Simulation of Plasma Jet Characteristics under Very Low-Pressure Plasma Spray Conditions

Plasma spray-physical vapor deposition (PS-PVD) is an emerging technology for the deposition of uniform and large area coatings. As the characteristics of plasma jet are difficult to measure in the whole chamber, computational fluid dynamics (CFD) simulations could predict the plasma jet temperature, velocity and pressure fields. However, as PS-PVD is generally operated at pressures below 500 Pa, a question rises about the validity of the CFD predictions that are based on the continuum assumption. This study dealt with CFD simulations for a PS-PVD system operated either with an argon-hydrogen plasma jet at low-power (<50 kW) or with an argon-helium plasma jet at high-power (≥50 kW). The effect of the net arc power and chamber pressure on the plasma jet characteristics and local gradient Knudsen number (Kn) was systematically investigated. The Kn was found to be lower than 0.2, except in the region corresponding to the first expansion shock wave. The peak value in this region decreased rapidly with an increase in the arc net power and the width of this region decreased with an increase in the deposition chamber pressure. Based on the results of the study, the local Knudsen number was introduced for detecting conditions where the continuum approach is valid under PS-PVD conditions for the first time and the CFD simulations could be reasonably used to determine a process parameter window under the conditions of this study.

A Study of Wall Temperature Jump Using UGKS Simulation With Diffuse-Specular Maxwell-Type Boundary

As the Maxwell-type boundary treatment can automatically capture temperature jump on boundary, it is widely used in gas flow simulation like Lattice Boltzmann method and Direct simulation Monte Carlo method. In present study, diffuse-specular Maxwell-type boundary with a diffusive fraction (a), which decides the mechanism of interaction between gas molecules and boundary, is realized in UGKS simulation. This diffuse-specular boundary can recover diffuse Maxwell boundary when a = 1.0, which proves the reliability of present boundary treatment. The influence of diffusive fraction on wall temperature jump under Knudsen number ranging from 0.001 to 1.0 is tested. The test cases are steady and unsteady state conditions of heat conduction and Couette flow between two infinite plates setting at specified temperatures. It is found that: 1) for cases of Knudsen number ranging from 0.01 to 1.0, owing to the loss of influence from equilibrium part on evolution of boundary gas distribution, the relative temperature jump increases when diffusive fraction varies from 1.0 to 0.25, this phenomenon is especially obvious on extreme point part in unsteady state cases; 2) for cases of Knudsen number equaling to 0.001, diffusive fraction has no significance influence on temperature jump as the temperature jump is less noticeable for such condition. Present study will help the further researches of heat transfer in rarefied gas.