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Journal articles on the topic 'High Knudsen Number Flow'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

GU, XIAO-JUN, and DAVID R. EMERSON. "A high-order moment approach for capturing non-equilibrium phenomena in the transition regime." Journal of Fluid Mechanics 636 (September 25, 2009): 177–216. http://dx.doi.org/10.1017/s002211200900768x.

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The method of moments is employed to extend the validity of continuum-hydrodynamic models into the transition-flow regime. An evaluation of the regularized 13 moment equations for two confined flow problems, planar Couette and Poiseuille flows, indicates some important limitations. For planar Couette flow at a Knudsen number of 0.25, they fail to reproduce the Knudsen-layer velocity profile observed using a direct simulation Monte Carlo approach, and the higher-order moments are not captured particularly well. Moreover, for Poiseuille flow, this system of equations creates a large slip velocity leading to significant overprediction of the mass flow rate for Knudsen numbers above 0.4. To overcome some of these difficulties, the theory of regularized moment equations is extended to 26 moment equations. This new set of equations highlights the importance of both gradient and non-gradient transport mechanisms and is shown to overcome many of the limitations observed in the regularized 13 moment equations. In particular, for planar Couette flow, they can successfully capture the observed Knudsen-layer velocity profile well into the transition regime. Moreover, this new set of equations can correctly predict the Knudsen layer, the velocity profile and the mass flow rate of pressure-driven Poiseuille flow for Knudsen numbers up to 1.0 and captures the bimodal temperature profile in force-driven Poiseuille flow. Above this value, the 26 moment equations are not able to accurately capture the velocity profile in the centre of the channel. However, they are able to capture the basic trends and successfully predict a Knudsen minimum at the correct value of the Knudsen number.

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2

TAMAGUCHI, Hiroki, Yu MATSUDA, and Tomohide NIIMI. "W052001 Micro Gaseous Flow as a High Knudsen Number Flow." Proceedings of Mechanical Engineering Congress, Japan 2013 (2013): _W052001–1—_W052001–2. http://dx.doi.org/10.1299/jsmemecj.2013._w052001-1.

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3

Niimi, Tomohide, Hideo Mori, Hiroki Yamaguchi, and Yu Matsuda. "Experimental Analyses of High Knudsen Number Flows." International Journal of Emerging Multidisciplinary Fluid Sciences 1, no. 3 (September 2009): 213–27. http://dx.doi.org/10.1260/175683109789686691.

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4

Venugopal, Vishnu, and Sharath S. Girimaji. "Unified Gas Kinetic Scheme and Direct Simulation Monte Carlo Computations of High-Speed Lid-Driven Microcavity Flows." Communications in Computational Physics 17, no. 5 (May 2015): 1127–50. http://dx.doi.org/10.4208/cicp.2014.m391.

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AbstractAccurate simulations of high-speed rarefied flows present many physical and computational challenges. Toward this end, the present work extends the Unified Gas Kinetic Scheme (UGKS) to a wider range of Mach and Knudsen numbers by implementing WENO (Weighted Essentially Non-Oscillatory) interpolation. Then the UGKS is employed to simulate the canonical problem of lid-driven cavity flow at high speeds. Direct Simulation Monte Carlo (DSMC) computations are also performed when appropriate for comparison. The effect of aspect ratio, Knudsen number and Mach number on cavity flow physics is examined leading to important insight.

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5

Fukui, S., and R. Kaneko. "Experimental Investigation of Externally Pressurized Bearings Under High Knudsen Number Conditions." Journal of Tribology 110, no. 1 (January 1, 1988): 144–47. http://dx.doi.org/10.1115/1.3261554.

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The characteristics of the externally pressurized bearings under high Knudsen number conditions were investigated experimentally by the use of surface restriction bearings in a medium vacuum on the order of 0.1 kPa (10−3 atm.). The experimental results agreed well with the numerical results calculated from a generalized lubrication equation based on the Boltzmann equation. Therefore, it would appear that this generalized lubrication equation is valid even when flows are categorized into transition flow or free molecular flow.

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6

Fukui, S., and R. Kaneko. "Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized Boltzmann Equation: First Report—Derivation of a Generalized Lubrication Equation Including Thermal Creep Flow." Journal of Tribology 110, no. 2 (April 1, 1988): 253–61. http://dx.doi.org/10.1115/1.3261594.

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A generalized Reynolds-type lubrication equation valid for arbitrary Knudsen numbers, defined as the ratio of the molecular mean free path to the film thickness, is derived from a linearized Boltzmann equation by semi-numerically calculating the flow rates of fundamental flows in the lubrication film: Poiseuille flow, Couette flow, and thermal creep flow. Numerical analysis of the equation for high Knudsen numbers reveals three principal results. First, Burgdorfer’s modified Reynolds equation featuring the first-order velocity slip boundary condition overestimates load carrying capacities, while the approximation equation including both the first- and second-order velocity slip boundary condition underestimates them. Second, since the flow rate of the Couette flow, which is independent of Knudsen numbers, becomes dominant as the bearing number increases, all the lubrication equation results tend toward the same asymptotic value for an infinite bearing number. Third, a new kind of load carrying capacity caused by thermal creep flow occurs if temperature gradients at the boundaries exist in the flow direction.

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7

Oh, C. K., E. S. Oran, and R. S. Sinkovits. "Computations of High-Speed, High Knudsen Number Microchannel Flows." Journal of Thermophysics and Heat Transfer 11, no. 4 (October 1997): 497–505. http://dx.doi.org/10.2514/2.6289.

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8

Lu, Qingzheng, Lynn A. Melton, C. K. Oh, E. S. Oran, and R. S. Sinkovits. "Computations of high-speed, high Knudsen number microchannel flows." Journal of Thermophysics and Heat Transfer 11 (January 1997): 497–505. http://dx.doi.org/10.2514/3.927.

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9

KUMARAN, V. "Granular flow of rough particles in the high-Knudsen-number limit." Journal of Fluid Mechanics 561 (August 2006): 43. http://dx.doi.org/10.1017/s0022112006000127.

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10

Malhotra, Chetan P., Roop L. Mahajan, and W. S. Sampath. "High Knudsen Number Physical Vapor Deposition: Predicting Deposition Rates and Uniformity." Journal of Heat Transfer 129, no. 11 (July 21, 2006): 1546–53. http://dx.doi.org/10.1115/1.2712855.

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The problem of predicting deposition rates and film thickness variation is relevant to many high-vacuum physical vapor deposition (PVD) processes. Analytical methods for modeling the molecular flow fail when the geometry is more complicated than simple tubular or planar sources. Monte Carlo methods, which have traditionally been used for modeling PVD processes in more complicated geometries, being probabilistic in nature, entail long computation times, and thus render geometry optimization for deposition uniformity a difficult task. Free molecular flow is governed by the same line-of-sight considerations as thermal radiation. Though the existence of an analogy between the two was recognized by Knudsen (1909, Ann. Phys., 4(28), pp. 75–130) during his early experiments, it has not been exploited toward mainstream analysis of deposition processes. With the availability of commercial finite element software having advanced geometry modelers and built-in cavity radiation solvers, the analysis of diffuse thermal radiation problems has become considerably simplified. Hence, it is proposed to use the geometry modeling and radiation analysis capabilities of commercial finite element software toward analyzing and optimizing high-vacuum deposition processes by applying the radiation-molecular flow analogy. In this paper, we lay down this analogy and use the commercial finite element software ABAQUS for predicting radiation flux profiles from planar as well as tube sources. These profiles are compared to corresponding deposition profiles presented in thin-film literature. In order to test the ability of the analogy in predicting absolute values of molecular flow rates, ABAQUS was also employed for calculating the radiative flux through a long tube. The predictions are compared to Knudsen’s analytical formula for free molecular flow through long tubes. Finally, in order to see the efficacy of using the analogy in modeling the film thickness variation in a complex source-substrate configuration, an experiment was conducted where chromium films were deposited on an asymmetric arrangement of glass slides in a high-vacuum PVD chamber. The thickness of the deposited films was measured and the source-substrate configuration was simulated in ABAQUS. The variation of radiation fluxes from the simulation was compared to variation of the measured film thicknesses across the slides. The close agreement between the predictions and experimental data establishes the feasibility of using commercial finite element software for analyzing high vacuum deposition processes.

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11

Cai, Zhenning, Ruo Li, and Yanli Wang. "Numerical Regularized Moment Method For High Mach Number Flow." Communications in Computational Physics 11, no. 5 (May 2012): 1415–38. http://dx.doi.org/10.4208/cicp.050111.140711a.

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AbstractThis paper is a continuation of our earlier work [SIAM J. Sci. Comput., 32(2010), pp. 2875-2907] in which a numerical moment method with arbitrary order of moments was presented. However, the computation may break down during the calculation of the structure of a shock wave with Mach number M0≥ 3. In this paper, we concentrate on the regularization of the moment systems. First, we apply the Maxwell iteration to the infinite moment system and determine the magnitude of each moment with respect to the Knudsen number. After that, we obtain the approximation of high order moments and close the moment systems by dropping some high-order terms. Linearization is then performed to obtain a very simple regularization term, thus it is very convenient for numerical implementation. To validate the new regularization, the shock structures of low order systems are computed with different shock Mach numbers.

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12

Zhu, Yajun, Chengwen Zhong, and Kun Xu. "GKS and UGKS for High-Speed Flows." Aerospace 8, no. 5 (May 19, 2021): 141. http://dx.doi.org/10.3390/aerospace8050141.

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The gas-kinetic scheme (GKS) and the unified gas-kinetic scheme (UGKS) are numerical methods based on the gas-kinetic theory, which have been widely used in the numerical simulations of high-speed and non-equilibrium flows. Both methods employ a multiscale flux function constructed from the integral solutions of kinetic equations to describe the local evolution process of particles’ free transport and collision. The accumulating effect of particles’ collision during transport process within a time step is used in the construction of the schemes, and the intrinsic simulating flow physics in the schemes depends on the ratio of the particle collision time and the time step, i.e., the so-called cell’s Knudsen number. With the initial distribution function reconstructed from the Chapman–Enskog expansion, the GKS can recover the Navier–Stokes solutions in the continuum regime at a small Knudsen number, and gain multi-dimensional properties by taking into account both normal and tangential flow variations in the flux function. By employing a discrete velocity distribution function, the UGKS can capture highly non-equilibrium physics, and is capable of simulating continuum and rarefied flow in all Knudsen number regimes. For high-speed non-equilibrium flow simulation, the real gas effects should be considered, and the computational efficiency and robustness of the schemes are the great challenges. Therefore, many efforts have been made to improve the validity and reliability of the GKS and UGKS in both the physical modeling and numerical techniques. In this paper, we give a review of the development of the GKS and UGKS in the past decades, such as physical modeling of a diatomic gas with molecular rotation and vibration at high temperature, plasma physics, computational techniques including implicit and multigrid acceleration, memory reduction methods, and wave–particle adaptation.

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13

Hayashi, T., S. Fukui, T. Ohkubo, and R. Kaneko. "Dynamic Characteristics of Gas-Lubricated Slider Bearings Under High Knudsen Number Conditions." Journal of Tribology 112, no. 1 (January 1, 1990): 111–18. http://dx.doi.org/10.1115/1.2920214.

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This paper presents numerical analyses of the dynamic characteristics of gas-lubricated slider bearings under high Knudsen number conditions using a generalized lubrication equation based on the the Boltzmann equation. These analyses are compared with those of the slip flow approximation equations and the differences are clarified. The present analysis is applied to the dynamic response of flying head sliders for magnetic disk storage devices. For a small slider with ultra-thin spacing, the deviations of the slip flow approximation equations are remarkable in regard to steady flying characteristics, but insignificant in regard to dynamic characteristics.

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14

Fukui, S., and R. Kaneko. "A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems." Journal of Tribology 112, no. 1 (January 1, 1990): 78–83. http://dx.doi.org/10.1115/1.2920234.

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This paper proposes the use of a Poiseuille flow rate database for rapid calculation of a generalized lubrication equation for high Knudsen number gas films. The database is created by numerical calculations based on the linearized Boltzmann equation. The proposed interpolation method is verified to reduce calculation time to several tenths of that required to perform rigorous calculations with the same accuracy.

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15

Cheng, Chin-Hsiang, and Feng-Liang Liao. "DSMC Analysis of Rarefied Gas Flow Over a Rectangular Cylinder at All Knudsen Numbers." Journal of Fluids Engineering 122, no. 4 (July 13, 2000): 720–29. http://dx.doi.org/10.1115/1.1315301.

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The present study is concerned with the flow behavior of the rarefied gas over a rectangular square cylinder. Attention has been focused on the transition regime between the continuous flow (at low Knudsen number) and the molecular flow (at high Knudsen number). The direct simulation Monte Carlo method (DSMC) is employed for predicting the distributions of density, velocity, and temperature for the external cross-flow. Meanwhile the pressure, skin friction, and net heat transfer coefficients on the surfaces of the cylinder are also evaluated. The length (l) and width (h) of the cross-section of the cylinder are both fixed at 0.06 m. The Mach number (Ma) ranges from 0.85 to 8, and the Knudsen number (Kn) is in the range 0.01⩽Kn⩽1.0. Results for various parameter combinations are presented. For some special cases, the numerical predictions are compared with existing information, and close agreement has been found. [S0098-2202(00)01404-8]

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16

Avramenko, A. A., N. P. Dmitrenko, Yu Yu Kovetska, and E. A. Kondratieva. "FEATURES OF HEAT TRANSFER IN A FLAT POROUS MICROCHANNEL." Thermophysics and Thermal Power Engineering 42, no. 1 (April 12, 2020): 12–18. http://dx.doi.org/10.31472/ttpe.1.2020.1.

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A steady heat transfer process of mixed convection in a flat vertical porous microchannel is considered. The results of simulation showed that Knudsen number effects are more significant in the neighborhood of the wall where growth of Knudsen numbers is accompanied with the velocity and temperature jumps on wall. With increasing parameter of porosity M (decreasing permeability), the flow velocity decreases and the velocity jump decrease as well. For all combinations of the criteria Ra, Kn and M increasing Knudsen number reduces heat transfer intensity. This can be attributed to increasing temperature jump on wall which causes deterioration of thermal interaction between the fluid and the wall. For low Rayleigh numbers increasing parameter M leads to increasing heat transfer since the temperature jump decrease on walls. For large Rayleigh numbers the trend becomes reversed, since for larger parameters M, the near-wall velocity decreases. For low Rayleigh numbers increasing the Knudsen number leads to decreasing hydraulic resistance coefficient, but with increasing parameter M leads to increasing this coefficient. At high Ra numbers increasing Knudsen number leads to growth of hydraulic resistance, which is due to increasing velocity gradient on the wall.

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17

Watvisave, D. S., U. V. Bhandarkar, and B. P. Puranik. "Investigation of Wall Effects on Flow Characteristics of a High Knudsen Number Nozzle." Nanoscale and Microscale Thermophysical Engineering 17, no. 2 (May 2013): 124–40. http://dx.doi.org/10.1080/15567265.2012.760694.

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18

Roseman, Christopher A., and Brian M. Argrow. "Low-Speed DSMC Simulations of Hotwire Anemometers at High-Altitude Conditions." Fluids 6, no. 1 (January 2, 2021): 20. http://dx.doi.org/10.3390/fluids6010020.

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Numerical simulations of hotwire anemometers in low-speed, high-altitude conditions have been carried out using the direct simulation Monte Carlo (DSMC) method. Hotwire instruments are commonly used for in-situ turbulence measurements because of their ability to obtain high spatial and temporal resolution data. Fast time responses are achieved by the wires having small diameters (1–5 μm). Hotwire instruments are currently being used to make in-situ measurements of high-altitude turbulence (20–40 km). At these altitudes, hotwires experience Knudsen number values that lie in the transition-regime between slip-flow and free-molecular flow. This article expands the current knowledge of hotwire anemometers by investigating their behavior in the transition-regime. Challenges involved with simulating hotwires at high Knudsen number and low Reynolds number conditions are discussed. The ability of the DSMC method to simulate hotwires from the free-molecular to slip-flow regimes is demonstrated. Dependence of heat transfer on surface accommodation coefficient is explored and discussed. Simulation results of Nusselt number dependence on Reynolds number show good agreement with experimental data. Magnitude discrepancies are attributed to differences between simulation and experimental conditions, while discrepancies in trend are attributed to finite simulation domain size.

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19

Isfahani, A. H. Meghdadi, A. Soleimani, and A. Homayoon. "Simulation of High Knudsen Number Gas Flows in Nanochannels via the Lattice Boltzmann Method." Advanced Materials Research 403-408 (November 2011): 5318–23. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.5318.

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Using a modified Lattice Boltzmann Method (LBM), pressure driven flow through micro and nano channels has been modeled. Based on the improving of the dynamic viscosity, an effective relaxation time formulation is proposed which is able to simulate wide range of Knudsen number, Kn, covering the slip, transition and to some extend the free molecular regimes. The results agree very well with exiting empirical and numerical data.

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20

Cai, Chunpei, and Chun Zou. "Gaskinetic Solutions for High Knudsen Number Planar Jet Impingement Flows." Communications in Computational Physics 14, no. 4 (October 2013): 960–78. http://dx.doi.org/10.4208/cicp.040812.281112a.

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AbstractThis paper presents a gaskinetic study and analytical results on high speed rarefied gas flows from a planar exit. The beginning of this paper reviews the results for planar free jet expanding into a vacuum, followed by an investigation of jet impingement on normally set plates with either a diffuse or a specular surface. Presented results include exact solutions for flowfield and surface properties. Numerical simulations with the direct simulation Monte Carlo method were performed to validate these analytical results, and good agreement with this is obtained for flows at high Knudsen numbers. These highly rarefied jet and jet impingement results can provide references for real jet and jet impingement flows.

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21

NIIMI, Tomohide. "High Knudsen Number Flows (Focusing on Experiments for Gaseous Microflows)." TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B 77, no. 777 (2011): 1168–77. http://dx.doi.org/10.1299/kikaib.77.1168.

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22

Karakitsiou, Stamatina, Bodil Holst, and Alex Christian Hoffmann. "Pressure-Driven Gas Flow through Nano-Channels at High Knudsen Numbers." Journal of Nano Research 50 (November 2017): 116–27. http://dx.doi.org/10.4028/www.scientific.net/jnanor.50.116.

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Flow through nano-channels is important in several fields, ranging from natural porous media to microfluidics. It is therefore important to study the flow under controlled conditions. While quite a lot of work has been done on the flow of liquids through nano-channels, comparatively little systematic work has been done on gas flow. Here we present a study of the flow of argon through nano-channels. We study samples with 2000 parallel nano-channels, with quadratic cross section. Each side is 100nm. The total length is 20 m. The nano-channels are made by patterning a Si<110> wafer usingelectron beam lithography (EBL) followed by reactive ion etching and with subsequent anodic bonding between silicon and a borosilicate glass as a top plate. The samples were investigated using a home-built apparatus which allows us to measure flow at high Knudsen numbers (from around 10 to 550). We compare our results with a range of theoretical flow models. As innovation this work provides measurements of gas transport from the home-built apparatus. The system records the pressure profile of each sample and the mass flow rate is calculated numerically from the pressure data.

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23

Harley, John C., Yufeng Huang, Haim H. Bau, and Jay N. Zemel. "Gas flow in micro-channels." Journal of Fluid Mechanics 284 (February 10, 1995): 257–74. http://dx.doi.org/10.1017/s0022112095000358.

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An experimental and theoretical investigation of low Reynolds number, high subsonic Mach number, compressible gas flow in channels is presented. Nitrogen, helium, and argon gases were used. The channels were microfabricated on silicon wafers and were typically 100 μm wide, 104 μm long, and ranged in depth from 0.5 to 20 μm. The Knudsen number ranged from 10-3 to 0.4. The measured friction factor was in good agreement with theoretical predictions assuming isothermal, locally fully developed, first-order, slip flow.

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24

YAMAGUCHI, Hiroki, Yu MATSUDA, Hideo MORI, and Tomohide NIIMI. "1310 Discussion on Application of Pressure Sensitive Paint in High Knudsen Number Flow(2)." Proceedings of the Fluids engineering conference 2007 (2007): _1310–1_—_1310–4_. http://dx.doi.org/10.1299/jsmefed.2007._1310-1_.

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25

YAMAGUCHI, Hiroki, Yu MATSUDA, Hideo MORI, and Tomohide NIIMI. "1310 Discussion on Application of Pressure Sensitive Paint in High Knudsen Number Flow(1)." Proceedings of the Fluids engineering conference 2007 (2007): _1310—a_. http://dx.doi.org/10.1299/jsmefed.2007._1310-a_.

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26

TATSUNO, Yusuke, Hiroki YAMAGUCHI, Yu MATSUDA, and Tomohide NIIMI. "Measurement of heat transfer on a gas-solid interface in high Knudsen number flow." Proceedings of Mechanical Engineering Congress, Japan 2016 (2016): J0540505. http://dx.doi.org/10.1299/jsmemecj.2016.j0540505.

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27

Chadha, S., R. Jefferson-Loveday, and T. Hussain. "Modelling Knudsen number effects in suspension high velocity oxy fuel thermal spray." International Journal of Heat and Mass Transfer 152 (May 2020): 119454. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2020.119454.

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28

Taamneh, Yazan, and Reyad Omari. "Slip-Flow and Heat Transfer in a Porous Microchannel Saturated with Power-Law Fluid." Journal of Fluids 2013 (November 14, 2013): 1–9. http://dx.doi.org/10.1155/2013/604893.

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This study aims to numerically examine the fluid flow and heat transfer in a porous microchannel saturated with power-law fluid. The governing momentum and energy equations are solved by using the finite difference technique. The present study focuses on the slip flow regime, and the flow in porous media is modeled using the modified Darcy-Brinkman-Forchheimer model for power-law fluids. Parametric studies are conducted to examine the effects of Knudsen number, Darcy number, power law index, and inertia parameter. Results are given in terms of skin friction and Nusselt number. It is found that when the Knudsen number and the power law index decrease, the skin friction on the walls decreases. This effect is reduced slowly while the Darcy number decreases until it reaches the Darcy regime. Consequently, with a very low permeability the effect of power law index vanishes. The numerical results indicated also that when the power law index decreases the fully-developed Nusselt number increases considerably especially, in the limit of high permeability, that is, nonDarcy regime. As far as Darcy regime is concerned the effects of the Knudsen number and the power law index of the fully-developed Nusselt number is very little.

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29

Alkhalidi, Ammar, Suhil Kiwan, Wael Al-Kouz, Aiman Alshare, and Ma’en Sari. "Rarefaction and scale effects on heat transfer characteristics for enclosed rectangular cavities heated from below." Thermal Science 23, no. 3 Part B (2019): 1791–800. http://dx.doi.org/10.2298/tsci170621234a.

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The fluid-flow and heat transfer in a buoyancy-driven microcavity heated from below are numerically investigated. In spite of the fact that microcavities are widely used in microelectro- mechanical systems, now a day, more interest in the evacuated cavity on Eqn. solar collectors are very common to reduce heat loss from the system. This paper provides a useful information for engineers to estimate heat transfer in low pressure cavities. The finite volume technique was used to solve the governing equations along with temperature jump and slip flow boundary conditions.The simulations are carried out for various cavity aspect ratios (H/L) and different Rayleigh number for both macroand micro-fluids. The effect of Knudsen number in the rarefied flow regime (microfluidic) has also been investigated. It is shown that for both cases the effect of aspect ratios on heat transfer becomes significant at high Rayleigh numbers and when the aspect ratio is below 5. It was also found that increasing Knudsen number reduces the heat transfer. The interaction between Nusselt, Rayleigh, Knudsen numbers, and the aspect ratio was investigated using the design of experiments, results show that no interaction between these parameters. To help engineers to estimate heat transfer in low pressure cavities, widely used in solar energy applications, a correlation for convection heat transfer coefficient is introduced.

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30

Yang, Hailing, and Yi Xia. "Hydrodynamic instability of nanofluids in round jet for small Stokes number." Modern Physics Letters B 33, no. 33 (November 30, 2019): 1950419. http://dx.doi.org/10.1142/s0217984919504190.

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The flow instability of particle-laden jet has been widely studied for large Stokes numbers. However, there is little attention on the case with small Stoke number, which often occurs in practical applications with nanoparticle-laden fluid. In this paper, the instability of nanofluids in round jet is studied numerically for [Formula: see text]. The results show that the law of nanofluids instability is quite similar to regular particle instability for axisymmetric azimuthal mode [Formula: see text]. However, for asymmetric azimuthal mode [Formula: see text], the regular pattern of instability is quite complex and different compared to common particle instability. The variations of wave amplification with wave number for different jet parameter [Formula: see text], Reynolds number Re, particle mass loading [Formula: see text], Knudsen number Kn, Stokes number St and the azimuthal modes [Formula: see text] are given. The flow usually gets more unstable as Knudsen number Kn increases, but the varying law gets inverse at high Reynolds number and at [Formula: see text]. The flow gets more unstable as Stokes number St increases at [Formula: see text] but gets more stable at [Formula: see text]. The decreases in wave number stimulate the flow instability at [Formula: see text] which shows distinct difference for the case at [Formula: see text]. Some unusual results of the effect of B, Re, Z on the flow instability are also discussed.

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31

Nguyen, Thuong X., Choong K. Oh, Robert S. Sinkovits, John D. Anderson, and Elaine S. Oran. "Simulations of High Knudsen Number Flows in a Channel-Wedge Configuration." AIAA Journal 35, no. 9 (September 1997): 1486–92. http://dx.doi.org/10.2514/2.272.

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32

Lopez, P., and Y. Bayazitoglu. "High Knudsen Number Thermal Flows with the D2Q13 Lattice Boltzmann Model." Numerical Heat Transfer, Part A: Applications 64, no. 2 (July 15, 2013): 93–106. http://dx.doi.org/10.1080/10407782.2013.773794.

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33

Nguyen, Thuong X., Choong K. Oh, Robert S. Sinkovits, John D. Anderson, and Elaine S. Oran. "Simulations of high Knudsen number flows in a channel-wedge configuration." AIAA Journal 35 (January 1997): 1486–92. http://dx.doi.org/10.2514/3.13695.

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34

Myong, R. S. "Thermodynamically consistent hydrodynamic computational models for high-Knudsen-number gas flows." Physics of Fluids 11, no. 9 (September 1999): 2788–802. http://dx.doi.org/10.1063/1.870137.

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35

Dongari, Nishanth, and Amit Agrawal. "Modeling of Navier–Stokes equations for high Knudsen number gas flows." International Journal of Heat and Mass Transfer 55, no. 15-16 (July 2012): 4352–58. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.04.002.

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36

Fissell, William H., A. T. Conlisk, Subhra Datta, Jeffrey M. Magistrelli, Jeffrey T. Glass, Aaron J. Fleischman, and Shuvo Roy. "High Knudsen number fluid flow at near-standard temperature and pressure conditions using precision nanochannels." Microfluidics and Nanofluidics 10, no. 2 (August 26, 2010): 425–33. http://dx.doi.org/10.1007/s10404-010-0682-4.

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Mitsuya, Y., and T. Ohkubo. "High Knudsen Number Molecular Rarefaction Effects in Gas-Lubricated Slider Bearings for Computer Flying Heads." Journal of Tribology 109, no. 2 (April 1, 1987): 276–82. http://dx.doi.org/10.1115/1.3261351.

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This paper presents a study into the gas lubrication capability of an ultra-thin 0.025 μm film (converted value for ambient air film). The experimental results obtained using subambient helium as the lubricating film are compared with the calculated results using the modified Reynolds equation considering flow slippage due to the molecular mean free path effects. This comparison confirms that the slip flow model holds true within the range of the present experiments, and that the modified Reynolds equation is applicable for designing the computer flying heads operating at such thin spacing. The reason for the excellent agreement is discussed considering the locality of rarefaction effects on the lubricating surfaces and the anisotropy of these effects between the film thickness and the slider width.

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She, Wen Xu, Jun Bin Chen, Jie Zhang, Bo Wei, Han Qing Wang, and Rui Bai. "The Calculation of Apparent Permeability for Shale Gas Considering Adsorption and Flow Patterns." Advanced Materials Research 1073-1076 (December 2014): 2305–9. http://dx.doi.org/10.4028/www.scientific.net/amr.1073-1076.2305.

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The flow pattern is unique in a certain range of pore size divided by the Knudsen number. In order to characterize permeability of nanopore in shale gas reservoir more accurately, the formulas of nanopore permeability are put forward considering the influence of adsorption gas and flow patterns. After the calculated results were compared and analyzed, the conclusions are obtained as follows: (1) Pore size is the main factor to determine the flow pattern; (2) There are three main flow pattern in the nanopore of Longmaxi formation shale reservoirs, slip flow, Fick diffusion and transition diffusion, meanwhile Darcy percolation and Knudsen diffusion do not exist; (3) Flow pattern has great influence on apparent permeability and adsorption has a greater impact in a high pressure condition (greater than 20MPa).

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Corson, James, G. W. Mulholland, and M. R. Zachariah. "Hydrodynamic interactions between aerosol particles in the transition regime." Journal of Fluid Mechanics 855 (September 19, 2018): 535–53. http://dx.doi.org/10.1017/jfm.2018.632.

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We present a method for calculating the hydrodynamic interactions between particles in the kinetic (or transition regime), characterized by non-negligible particle Knudsen numbers. Such particles are often present in aerosol systems. The method is based on our extended Kirkwood–Riseman theory (Corson et al., Phys. Rev. E, vol. 95 (1), 2017c, 013103), which accounts for interactions between spheres using the velocity field around a translating sphere as a function of Knudsen number. Results for the two-sphere problem at small Knudsen numbers are in good agreement with those obtained using Felderhof’s interaction actions for mixed slip-stick boundary conditions, which are accurate to order $r^{-7}$ (Felderhof, Physica A, vol. 89 (2), 1977, pp. 373–384). The strength of the interactions decreases with increasing Knudsen number. Results for two fractal aggregates demonstrate that one can apply a point force approach for interactions between particles in the transition regime; the interaction tensor is similar to the Oseen tensor for continuum flow. Using this point force approach, we present an analysis for the settling of an unbounded cloud of particles. Our analysis shows that for sufficiently high volume fractions and cloud radii, the cloud behaves as a gas droplet in continuum flow even when the individual particles are small relative to the mean free path of the gas. The method presented here can be applied in a Brownian dynamics simulation analogous to Stokesian dynamics to study the behaviour of a dense aerosol system.

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NIIMI, Tomohide. "K05200 High Knudsen Number Flows : To Micro-gas Flows from Rarefied Gas Flows." Proceedings of Mechanical Engineering Congress, Japan 2014 (2014): _K05200–1_—_K05200–2_. http://dx.doi.org/10.1299/jsmemecj.2014._k05200-1_.

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Le, Nam Tuan Phuong, Ngoc Anh Vu, Le Tan Loc, and Tran Ngoc Thoai. "New temperature jump boundary condition in high-speed rarefied gas flow simulations." Vietnam Journal of Mechanics 39, no. 2 (June 21, 2017): 165–76. http://dx.doi.org/10.15625/0866-7136/8760.

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The effect of the sliding friction has been important in calculating the heat flux of gas flow from the surface since there is some slip over the surface. There has not been any the temperature jump condition including the sliding friction part so far. In this paper, we will propose a new temperature jump condition that includes the sliding friction. Our new temperature jump condition will be evaluated for NACA0012 micro-airfoil in high-speed rarefied gas flow simulations using the CFD method, which solves the Navier-Stokes equations within the OpenFOAM framework with working gas as air. The airfoil case is simulated with various Knudsen numbers from 0.026 to 0.26, and the angles-of-attack (AOAs) from 0-deg to 20-deg. The surface gas temperatures predicting by our new temperature jump condition give good agreements with the DSMC data, especially the NACA0012 micro-airfoil cases with the high Knudsen numbers, Kn = 0.1, and Kn = 0.26 with AOA = 20-deg. for the lower surface.

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Isfahani, A. H. Meghdadi, and A. Soleimani. "Numerical Study of Flow and Heat Transfer of High Knudsen Number Flow Regimes in Nanochannels Filled with Porous Media." Advanced Materials Research 403-408 (November 2011): 5324–29. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.5324.

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Considering the dependency of viscosity on Kn, a unified flow model for all flow regimes with different Kn was obtained. Applying the Dary Brinkman – Forchheimer flow model with the slip boundary condition, finite difference solutions for fully developed velocity distribution in a nanochannel of circular cross section, filled with porous media was presented. Convection heat transfer of the system, reflected in Nu was analyzed using the temperature jump boundary condition. It is shown that despite of the fact that in most of previous researches, Kn was assumed constant along the channel, the variations of Kn due to the pressure variations, have considerable effects on heat transfer and temperature distribution across the channel cross section.

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NIIMI, Tomohide. "Application of Laser and Image Sensing Techniques to High Knudsen Number Flows." Proceedings of the Thermal Engineering Conference 2003 (2003): 241–44. http://dx.doi.org/10.1299/jsmeted.2003.241.

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Ganeshan, Karthik, and David M. Williams. "An implicit discontinuous Galerkin finite element discrete Boltzmann method for high Knudsen number flows." Physics of Fluids 33, no. 3 (March 2021): 032019. http://dx.doi.org/10.1063/5.0041636.

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Singh, Narendra, and Thomas E. Schwartzentruber. "Aerothermodynamic correlations for high-speed flow." Journal of Fluid Mechanics 821 (May 25, 2017): 421–39. http://dx.doi.org/10.1017/jfm.2017.195.

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Heat flux and drag correlations are developed for high-speed flow over spherical geometries that are accurate for any Knudsen number ranging from continuum to free-molecular conditions. A stagnation point heat flux correlation is derived as a correction to the continuum (Fourier model) heat flux and also reproduces the correct heat flux in the free-molecular limit by use of a bridging function. In this manner, the correlation can be combined with existing continuum correlations based on computational fluid dynamics simulations, yet it can now be used accurately in the transitional and free-molecular regimes. The functional form of the stagnation point heat flux correlation is physics based, and was derived via the Burnett and super-Burnett equations in a recent article, Singh & Schwartzentruber (J. Fluid Mech., vol. 792, 2016, pp. 981–996). In addition, correlation parameters from the literature are used to construct simple expressions for the local heat flux around the sphere as well as the integrated drag coefficient. A large number of direct simulation Monte Carlo calculations are performed over a wide range of conditions. The computed heat flux and drag data are used to validate the correlations and also to fit the correlation parameters. Compared to existing continuum-based correlations, the new correlations will enable engineering analysis of flight conditions at higher altitudes and/or smaller geometry radii, useful for a variety of applications including blunt body planetary entry, sharp leading edges, low orbiting satellites, meteorites and space debris.

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Obi, Shinnosuke, and Huiying Jin. "2612 Measurement of slip velocity in annular Couette flow at high Knudsen numbers." Proceedings of the JSME annual meeting 2006.2 (2006): 285–86. http://dx.doi.org/10.1299/jsmemecjo.2006.2.0_285.

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Wang, Ziyan, Moran Wang, and Shiyi Chen. "Coupling of high Knudsen number and non-ideal gas effects in microporous media." Journal of Fluid Mechanics 840 (February 6, 2018): 56–73. http://dx.doi.org/10.1017/jfm.2018.46.

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High Knudsen number non-ideal gas flows in porous media are important and fundamental in various applications including shale gas exploitation and carbon dioxide sequestration. Because of the small pore size in tight rocks, the Knudsen number (Kn) may be high (i.e. much higher than 0.01) even though the gas is really dense. In fact, due to the high pressure and temperature underground, the gas usually manifests a strong non-ideal gas effect. Understanding the coupling mechanism of the high Kn effect and non-ideal gas effect is a premise to accurately model deep-seated underground gas exploitation or carbon dioxide sequestration. In this work, we theoretically analyse the high Kn non-ideal gas flows in microporous media. Based on the relative importance of the non-ideal gas effect and high Kn effect, the coupling is divided into four types. The analysis is subsequently validated by multiscale numerical simulations, in which the four types of coupling are clearly demonstrated. After applying the analysis to laboratory measurements, we propose a characteristic pressure model to calculate the gas permeability of tight rocks with better precision. The new model incorporates the non-ideal gas effect with the high Kn effect accurately and better bridges the laboratory measurements with the reservoir engineering.

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Song, Cheng Qian, Xie Yuan Yin, and Feng Hua Qin. "Analytic Solution for Microscale Poiseuille Flow Based on Super-Burnett Equations." Advanced Materials Research 705 (June 2013): 609–15. http://dx.doi.org/10.4028/www.scientific.net/amr.705.609.

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The previous studies show that the transverse distribution of pressure and temperature in microscale Poiseuille flow cannot be predicted by Navier-Stokes equation with the slip boundary condition. In this paper, we analyzed the planar microchannel force-driven Poiseuille flow by high order continuum model. The super-Burnett constitutive relations were used and the nonlinear ordinary differential Equations of higher-orders were obtained by the hypothesis of parallel flow. With a perturbations theory, we linearized the equations and obtained the analytic solutions. The results show that the solutions can capture the temperature dip which is the same as the DSMC result. However, we also find that the temperature profile near the wall does always not match with the DSMC result. Especially, the difference in the qualitative exists when the Knudsen number is large enough. The non-equilibrium effect near the wall such as Knudsen layer can not be described entirely by continuous model even with high order constitutive relations and this confines the extension of the continuous model such as super-Burnett one.

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Yan, Fang, and Bakhtier Farouk. "Computations of Low Pressure Fluid Flow and Heat Transfer in Ducts Using the Direct Simulation Monte Carlo Method." Journal of Heat Transfer 124, no. 4 (July 16, 2002): 609–16. http://dx.doi.org/10.1115/1.1458018.

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High Knudsen number (Kn) gas flows are found in vacuum and micro-scale systems. Such flows are usually in the slip or transition regimes. In this paper, the direct simulation Monte Carlo (DSMC) method has been applied to compute low pressure, high Kn flow fields in partially heated channels. Computations were carried out for nitrogen, argon, hydrogen, oxygen and noble gas mixtures. Variation of the Kn is obtained by reducing the pressure while keeping the channel width constant. Nonlinear pressure profiles along the channel centerline are observed. Heat transfer from the channel walls is also calculated and compared with the classical Graetz solution. The effects of varying pressure, inlet flow and gas transport properties (Kn, Reynolds number, Re and the Prandtl number, Pr respectively) on the wall heat transfer (Nusselt number, Nu) were examined. A simplified correlation for predicting Nu¯ as a function of the Peclet number, Pe¯ and Kn¯ is presented.

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SZALMÁS, LAJOS. "LATTICE BOLTZMANN METHOD WITH OPTIMIZED BOUNDARY LAYER AT FINITE KNUDSEN NUMBERS." International Journal of Modern Physics C 19, no. 02 (February 2008): 249–57. http://dx.doi.org/10.1142/s0129183108012078.

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We present an optimization procedure in high-order lattice Boltzmann models in order to fine-tune the method for micro-channel flows in the transition region. Both the first and second slip coefficients are tunable, and the hydrodynamic and Knudsen layer solutions can be tailored. Very good results are obtained in comparison with the continuous solution for hard sphere molecules. For the first time, we provide an accurate description of Poiseuille flow in the transition region.

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