Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Snežana S. Milićev ◽  
Nevena D. Stevanović
Keyword(s):  
Mach Number ◽  
Friction Factor ◽  
Cross Section ◽  
Gas Flow ◽  
Variable Cross Section ◽  
Molecular Flow ◽  
Variable Cross ◽  
General Boundary Condition ◽  
Poiseuille Number ◽  
Isothermal Gas

Abstract The analytical solution for steady viscous pressure-driven compressible isothermal gas flow through micro- and nanochannels with variable cross section for all Knudsen and all Mach number values is presented in this paper. The continuum one-dimensional governing equations are solved using the friction factor that is established in a special way to provide solutions for mass flow rate, pressure, and velocity distribution through the microchannels and nanochannels in the entire rarefaction regime. The friction factor, defined by the general boundary condition and generalized diffusion coefficient proposed by Beskok and Karniadakis (1999, “A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales,” J. Microscale Thermophys. Eng., 3, pp. 43–77), spreads the solution application to all rarefaction regimes from continuum to free molecular flow. The correlation between the product of friction factor and Reynolds number (Poiseuille number) and Knudsen number is established explicitly in the paper. Moreover, the obtained solution includes the inertia effect, which allows the application of the solution to both subsonic and supersonic gas flows, which was not shown earlier. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging, and microchannels and nanochannels with constant cross section. The proposed solution is verified by comparison with experimental, analytical, and numerical results available in literature.

Simulation of Gas Flow in Channels with Variable Cross-Section at Different Flow Modes using Lattice Boltzmann Method (LBM)

2019 ◽  
pp. 105-115
Author(s):  
A.V. Burmistrov ◽  
S.I. Salikeev ◽  
A.A. Raykov
Keyword(s):  
Lattice Boltzmann Method ◽  
Cross Section ◽  
Lattice Boltzmann ◽  
Gas Flow ◽  
Stokes Equations ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Wide Range ◽  
Boltzmann Method ◽  
Contact Free

All contact-free vacuum pumps operate in a very wide pressure range. Therefore, the calculation of flows through the slot channels is associated with the need to take into account the laws of all three modes of gas flow: viscous, transitional and molecular. Most of channels of contact-free pumps are formed by curved walls, which are slits of variable cross-section in the direction of gas flow, having a minimum gap in some place. The paper considers the basic methods of calculating flows in channels of variable cross-section: the Monte Carlo method for molecular mode, the numerical solution of Navier --- Stokes equations for viscous mode and the Lattice Boltzmann method (LBM) for a wide range of pressures. The results of gas flow simulation calculated in COMSOL Multiphysics with LBM method are presented. The influence of the gas flow mode on the velocity profile in the channel is discussed. Based on the simulation results, the conductivity of channels of different geometries was calculated at various pressures at the inlet and outlet of the channel. The graphs of conductivity dependence on the Knudsen number for the method of angular coefficients, the model of lattice Boltzmann equations and experimental data are presented. It is shown that for slit channels of variable cross-section, the LBM model agrees well with the experiment under any gas flow modes.

Effects of processing parameters on the extrusion by continuous variable cross-section direct extrusion with 7A09 aluminium alloy

2016 ◽  
Vol 30 (06) ◽  
pp. 1650053 ◽  
Author(s):  
Feng Li ◽  
Hongbin Wu ◽  
Minghan Qin
Keyword(s):  
Aluminium Alloy ◽  
Friction Factor ◽  
Cross Section ◽  
Processing Parameters ◽  
Variable Cross Section ◽  
Continuous Variable ◽  
Variable Cross ◽  
Extrusion Speed ◽  
Direct Extrusion ◽  
Forming Temperature

In order to study the effects of processing parameters on the continuous variable cross-section direct extrusion (CVCDE), taking 7A09 aluminium alloy for example, the extrusion speed and forming temperature and the friction factor as key processing parameters are applied to research by finite element (FE) simulation. The research result showed that the extrusion speed had a significant influence on the maximum temperature of the billet, at the same time, both decreasing the friction factor and increasing forming temperature within a certain range were beneficial to reduce extrusion load. Both forming temperature and the extrusion speed were inversely linked to extrusion load, but the friction factor was directly proportional to extrusion load. Forming temperature had a far more important influence on extrusion load by comparison: when forming temperature increased from 380[Formula: see text] to 430[Formula: see text]C, the peak value of extrusion load decreased by 25.6% and the flow uniformity of extruded product got improved. The process window based on both the press limit and surface defects limit was established and the most reasonable forming temperature was 405[Formula: see text]C under this process condition, which provided theoretical basis for formulation process of 7A09 aluminium alloy on the CVCDE extrusion.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

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