An analytical and numerical study on the start-up flow of slightly rarefied gases in a parallel-plate channel and a pipe

Авраменко, А. А.; Tyrinov, A. I.; Shevchuk, Igor V.

doi:10.1063/1.4916621

Cited by 26 publications

(22 citation statements)

References 22 publications

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“…It is worth mentioning some other investigations of the unsteady slip flows, Refs. [45][46][47][48][49], where the Navier's slip condition, Eq. (1), was used, including the case of the oscillatory flow studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

Start-up slip flow in a microchannel with a rectangular cross section

Авраменко

Tyrinov

Shevchuk³

2015

Theor. Comput. Fluid Dyn.

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The paper outlines results of the theoretical study of an incompressible fluid flow in a rectangular microchannel subject to a sudden time-dependent pressure drop. The momentum equation together with the independent and dependent variables was reduced to a self-similar form by means of the symmetry analysis. The problem was solved using two analytical approaches, the Fourier method and the method of eigenfunction decomposition, as well as numerically by means of the lattice Boltzmann method. The unsteady two-dimensional velocity profiles in the microchannel were predicted using the infinite series and validated against the numerical solution. As expected, the flow pattern asymptotically attains the fully developed state, which is reached more rapidly for smaller Knudsen numbers. The analytical solution yielded expressions for the calculation of the hydraulic resistance coefficient.

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Section: Introductionmentioning

confidence: 99%

Start-up slip flow in a microchannel with a rectangular cross section

Авраменко

Tyrinov

Shevchuk³

2015

Theor. Comput. Fluid Dyn.

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“…This equation (Eq. 45) is same as the expression obtained by Avramenko et al (2015), Eq. (87)) for the limiting value of skin-friction factor.…”

Section: Starting Flow: Temporal Variation Of Velocity Profiles Skinmentioning

confidence: 96%

“…Recently, Ray et al (2005) obtained the analytical solution for different types of pulsation by approximating the mass flow-rate by Fourier series. In the second category (Laplace transform approach (Das & Arakeri, 2000;Brereton, 2000;Muntges & Majdalani, 2002;Khaled & Vafai, 2004;Chen et al, 2008;Hayat et al, 2011;Avramenko et al, 2015), the pressure gradient is an unknown parameter and the additional condition to solve the governing equation is obtained from the time-varying mean volume flow-rate. Das and Arakeri (2000) successfully applied the second method to obtain the transient variation of the velocity profile and pressure gradient for different inflow configurations.…”

Section: I|ntroductionmentioning

confidence: 99%

“…In an interesting study Avramenko et al, 2015) obtained an analytical solution for starting flows with slip conditions for pipe and channel flows. To model the starting flow, Avramenko et al (2015) represented the pressure gradient term using a Heaviside function and solved using Cauchy's residue theorem in conjunction with the Laplace transform method. In this work we have considered three unsteady flows in a pipe with known inlet flowrate (Q (t)) variation than the pressure gradient variation which is considered in many other previous studies.…”

Section: I|ntroductionmentioning

confidence: 99%

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Analytical Solutions for Unsteady Pipe Flows with Slip Boundary Condition

Pillai

Manu

2020

JAFM

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In this paper analytical expressions for time-dependent velocity profiles and pressure gradient are obtained for fully-developed laminar flows with given volume flow-rate conditions in circular pipe flows with slip boundary conditions. The governing equations are solved analytically using the traditional Laplace transform method together with Mellin's inversion formula. The evolution of velocity profiles and pressure gradient for starting and pulsatile flow with slip boundary conditions are analyzed. New simplified expressions and perspectives on velocity and pressure gradient for no-slip and slip flows are obtained from the analytical results. New scalings in starting and pulsatile flows are proposed for pipe flows with no-slip and slip boundary conditions using nondimensional numbers. Special attention is paid to the effect of slip factor and pulsatile flow frequency on the time-dependent skin-friction factor. Finally, by using the starting and pulsating flow results, analytical expressions of velocity and pressure for arbitrary inflow are obtained by approximating the arbitrary volume flow-rate by a Fourier series

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“…The paper [9] presents results of an investigation of the response of an incompressible fluid in a circular micro pipe to a sudden time-independent pressure drop. Solutions of the problem were obtained analytically using the Laplace transform technique and numerically using the lattice Boltzmann method.…”

Section: Introductionmentioning

confidence: 99%

Measurement of the Liquid Level in the Fuel Tank of Rocket

Klyuev¹

2016

AJAE

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Abstract:In this paper we consider the problem of mathematical modeling of fluid flow in the vertical channel of fuel management system. The system has a vertical measuring channel with sensors inside the channel for fixing the free surface level of fluid in the channel. By lowering the level of fuel in the tank fuel level decreases in the channel. When the level of fuel in the channel reaches the sensor, the sensor activation occurs. Thus, the level of fuel in the channel determining fuel level in the tank.

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An analytical and numerical study on the start-up flow of slightly rarefied gases in a parallel-plate channel and a pipe

Cited by 26 publications

References 22 publications

Start-up slip flow in a microchannel with a rectangular cross section

Start-up slip flow in a microchannel with a rectangular cross section

Analytical Solutions for Unsteady Pipe Flows with Slip Boundary Condition

Measurement of the Liquid Level in the Fuel Tank of Rocket

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