scholarly journals Analytical solution to the problem of diffusion of the light component of the binary gas mixture in a plane channel

2021 ◽  
Vol 2056 (1) ◽  
pp. 012004
Author(s):  
V N Popov ◽  
I V Popov
Keyword(s):  
Analytical Solution ◽  
Flow Rate ◽  
Diffuse Reflection ◽  
Plane Channel ◽  
Boltzmann Kinetic Equation ◽  
Heavy Component ◽  
Light Component ◽  
Reflection Model ◽  
Binary Gas Mixture ◽  
Gas Component

Abstract Within the framework of the kinetic approach, an analytical solution to the problem of diffusion of the light component of a binary mixture in a flat channel with infinite parallel walls is constructed. It is assumed that the mass of light component molecules and their concentration is much less than the mass of molecules and the concentration of heavy components. The flow rate of the heavy component is assumed to be zero. The change in the state of a light gas component is described on the basis of the BGK (Bhatnagar, Gross, Kruk) model of the Boltzmann kinetic equation. The diffuse reflection model is used as a boundary condition on the channel walls. The mass velocity profile of the light gas component is constructed. The flow rate of the light gas component per unit channel width is calculated. A comparison with similar results presented in open sources was done.

scholarly journals A collocation method for the Williams equation with Chebyshev polynomials

2021 ◽  
Vol 2056 (1) ◽  
pp. 012005
Author(s):  
O V Germider ◽  
V N Popov
Keyword(s):  
Collocation Method ◽  
Chebyshev Polynomials ◽  
Basic Equation ◽  
Gas Flow ◽  
Diffuse Reflection ◽  
Constant Pressure ◽  
Plane Channel ◽  
Reflection Model ◽  
Linearized Problem ◽  
The Given

Abstract The linearized problem of gas flow in plane channel with infinite walls has been solved in the kinetic approximation. The flow in the channel is caused by a constant pressure gradient parallel to the walls of the channel. The Williams equation has been used as a basic equation, and the boundary condition has been set in terms of the diffuse reflection model. The collocation method for Chebyshev polynomials has been applied to construct the solution of the equation of Williams with the given boundary conditions. The mass flux of the gas in the channel has been calculated.

scholarly journals Неизотермическое течение газа в эллиптическом канале с внутренним круговым цилиндрическим элементом в свободномолекулярном режиме

2019 ◽  
Vol 89 (1) ◽  
pp. 27
Author(s):  
О.В. Гермидер ◽  
В.Н. Попов
Keyword(s):  
Mass Flow ◽  
Basic Equation ◽  
Gas Flow ◽  
Diffuse Reflection ◽  
Boltzmann Kinetic Equation ◽  
Molecular Gas ◽  
Pressure Drops ◽  
Reflection Model ◽  
Linearized Problem ◽  
Temperature And Pressure

AbstractThe linearized problem of free-molecular gas flow in a long elliptic channel with a circular cylindrical element inside has been solved in the kinetic approximation. The flow in the channel is caused by temperature and pressure drops between its ends. The Boltzmann kinetic equation for collisionless gas has been used as a basic equation, and the boundary condition has been set in terms of the diffuse reflection model. The distribution of the mass velocity of the gas over the cross section of the channel has been obtained. The mass flow rate of the gas in the channel versus the temperature and pressure drops between its ends has been calculated. It has been found that the mass flow of the gas substantially depends on the radius of the inner cylinder.

scholarly journals Simulation of a two-dimensional binary gas mixture outflow into vacuum through a thin slit on the basis of direct solution of the Boltzmann kinetic equation

2021 ◽  
Vol 2056 (1) ◽  
pp. 012007
Author(s):  
S S Sitnikov ◽  
F G Tcheremissine ◽  
T A Sazykina
Keyword(s):  
Kinetic Equation ◽  
Boltzmann Kinetic Equation ◽  
Gas Mixture ◽  
Two Dimensional ◽  
Direct Solution ◽  
Steady State Regime ◽  
Collision Integrals ◽  
Flow Formation ◽  
Binary Gas Mixture ◽  
State Regime

Abstract Two-dimensional binary gas mixture outflow from a vessel into vacuum through a thin slit is studied on the basis of direct solution of the Boltzmann kinetic equation. For evaluation of collision integrals in the Boltzmann equation a conservative projection method is used. Numerical simulation of a two-dimensional argon-neon gas mixture outflow from a vessel into vacuum was performed. Graphs of mixture components flow rate dependence on time during the flow formation, as well as fields of molecular density and temperature for steady-state regime, were obtained.

The Effect of Slip on the Discharge From Partially Filled Circular and Fully Filled Lens and Figure 8 Shaped Pipes

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Samuel Irvine ◽  
Luke Fullard
Keyword(s):  
Free Surface ◽  
Analytical Solution ◽  
Flow Rate ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Symmetry Plane ◽  
Volumetric Flow Rate ◽  
Wall Slip ◽  
Circular Pipe ◽  
Gravity Driven Flow

In this work, we examine the effect of wall slip for a gravity-driven flow of a Newtonian fluid in a partially filled circular pipe. An analytical solution is available for the no-slip case, while a numerical method is used for the case of flow with wall slip. We note that the partially filled circular pipe flow contains a free surface. The solution to the Navier–Stokes equations in such a case is a symmetry of a pipe flow (with no free surface) with the free surface as the symmetry plane. Therefore, we note that the analytical solution for the partially filled case is also the exact solution for fully filled lens and figure 8 shaped pipes, depending on the fill level. We find that the presence of wall slip increases the optimal fill height for maximum volumetric flow rate, brings the “velocity dip” closer to the free surface, and increases the overall flow rate for any fill. The applications of the work are twofold; the analytical solution may be used to verify numerical schemes for flows with a free surface in partially filled circular pipes, or for pipe flows in lens and figure 8 shaped pipes. Second, the work suggests that flows in pipes, particularly shallow filled pipes, can be greatly enhanced in the presence of wall slip, and optimal fill levels must account for the slip phenomenon when present.

scholarly journals An analytical solution for critical withdrawal of layered fluid through a line sink in a porous medium

1997 ◽  
Vol 39 (2) ◽  
pp. 271-279 ◽  
Author(s):  
H. Zhang ◽  
G. C. Hocking ◽  
D. A. Barry
Keyword(s):  
Porous Medium ◽  
Analytical Solution ◽  
Flow Rate ◽  
Close Agreement ◽  
Critical Flow ◽  
Hodograph Method ◽  
Critical Flow Rate ◽  
Line Sink ◽  
Surface Profiles ◽  
Layered Fluid

AbstractFluid withdrawn through a line sink from a layered fluid in a vertically confined porous medium is considered. A hodograph method is used to obtain the shape of the interface for a given sink position at the critical flow rate. The analytical solution is compared with a more general numerical solution developed in earlier work. It was found that the surface profiles obtained by the two methods are in close agreement. However, the present work has the advantage that it gives a fully explicit solution.

The Thermocapillary Convection in Locally Heated Laminar Liquid Film Flow Caused by a Co-Current Gas Flow in Narrow Channel

2003 ◽  
Author(s):  
E. Y. Gatapova ◽  
Y. V. Lyulin ◽  
I. V. Marchuk ◽  
O. A. Kabov ◽  
J.-C. Legros
Keyword(s):  
Free Surface ◽  
Analytical Solution ◽  
Liquid Film ◽  
Gas Flow ◽  
Surface Deformation ◽  
Plane Channel ◽  
Film Surface ◽  
Local Heat ◽  
Narrow Channel ◽  
Liquid Film Flow

A two-dimensional model of a steady laminar flow of liquid film and co-current gas flow in a plane channel is considered. It is supposed that the height of a channel is much less than its width. There is a local heat source on the bottom wall of the channel. An analytical solution for the temperature distribution problem in locally heated liquid film is obtained, when the velocity profile is linear. An analytical solution of the linearized equation for thermocapillary film surface deformation is found. A liquid bump caused by the thermocapillary effect in the region where thermal boundary layer reaches the film surface is obtained. Damped oscillations of the free surface may exist before the bump. This is obtained according to the solution of the problem in an inclined channel. It depends on the forces balance in the film. The defining criterion is found for this effect. The oscillations of free surface do not exist for horizontally located channel.

scholarly journals Analytical Solution for Transient Hydraulic Head, Flow Rate and Volumetric Exchange in an Aquifer Under Recharge Condition

2009 ◽  
Vol 57 (2) ◽  
pp. 113-120 ◽  
Author(s):  
Rajeev Bansal ◽  
Samir Das
Keyword(s):  
Analytical Solution ◽  
Flow Rate ◽  
Stream Water ◽  
Closed Form Solution ◽  
Hydraulic Head ◽  
Flow Equation ◽  
Form Solution ◽  
Positive Zero ◽  
Rain Infiltration ◽  
Analytical Result

Analytical Solution for Transient Hydraulic Head, Flow Rate and Volumetric Exchange in an Aquifer Under Recharge ConditionThis paper presents closed form solution for unsteady flow equation corresponding to the transient hydraulic head, flow rate and volumetric exchange of a confined aquifer which is in contact with a constant piezometric head at one end and a stream whose water level is rising at a constant rate at the other end. The aquifer is also subjected to receive constant inflow due to rain infiltration. The unsteady groundwater flow equation is solved using Laplace transform to get analytical expressions for the transient hydraulic head and flow rate at the left and right interfaces and the net volumetric exchange of water at the aquifer-stream interface. The analytical results presented here show the effect of recharge due to rain infiltration on the net volumetric exchange and reveal the conditions for which net inflow in the aquifer could be positive, negative or zero. The results obtained have the capability to determine transient hydraulic head for two extreme scenarios: (i) very slow rise and (ii) very fast rise in the stream water. Analytical result show that the net volumetric exchange could be positive, zero or negative depending on the surface infiltration and stream water rise rate.

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