Topic
Knudsen number
About: Knudsen number is a research topic. Over the lifetime, 5052 publications have been published within this topic receiving 104278 citations.
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TL;DR: In this paper, a phenomenological nonlinear coupled constitutive relation model was proposed to explain the origin behind the central temperature minimum and a heat transfer from the cold region to the hot region.
Abstract: The compressible Poiseuille gas flow driven by a uniform force is analytically investigated using a phenomenological nonlinear coupled constitutive relation model. A new fully analytical solution in compact tangent (or hyperbolic tangent in the case of diatomic gases) functional form explains the origin behind the central temperature minimum and a heat transfer from the cold region to the hot region. The solution is not only proven to satisfy the conservation laws exactly but also well-defined for all physical conditions (the Knudsen number and a force-related dimensionless parameter). It is also shown that the non-Fourier law associated with the coupling of force and viscous shear stress in the constitutive relation is responsible for the existence of the central temperature minimum, while a kinematic constraint on viscous shear and normal stresses identified in the velocity shear flow is the main source of the nonuniform pressure distribution. In addition, the convex pressure profile with a maximum at the center is theoretically predicted for diatomic gases. Finally, the existence of the Knudsen minimum in the mass flow rate is demonstrated by developing an exact analytical formula for the average temperature of the bulk flow.
41 citations
TL;DR: In this article, the authors examined the experimental data of Kuhlthau [A.R. Kuhlhau] on two concentric rotating cylinders with a low pressure gas in the gap and deduced the slip coefficient in the slip flow and transition flow regimes.
41 citations
TL;DR: In this article, numerical simulations have been performed on the pressure-driven rarefied flow through channels with a sudden contraction-expansion of 2:1:2 using isothermal two and three-dimensional lattice Boltzmann method (LBM).
Abstract: Numerical simulations have been performed on the pressure-driven rarefied flow through channels with a sudden contraction–expansion of 2:1:2 using isothermal two and three-dimensional lattice Boltzmann method (LBM). In the LBM, a Bosanquet-type effective viscosity and a modified second-order slip boundary condition are used to account for the rarefaction effect on gas viscosity to cover the slip and transition flow regimes, that is, a wider range of Knudsen number. Firstly, the in-house LBM code is verified by comparing the computed pressure distribution and flow pattern with experimental ones measured by others. The verified code is then used to study the effects of the outlet Knudsen number Kn
o
, driving pressure ratio P
i
/P
o
, and Reynolds number Re, respectively, varied in the ranges of 0.001–1.0, 1.15–5.0, and 0.02–120, on the pressure distributions and flow patterns as well as to document the differences between continuum and rarefied flows. Results are discussed in terms of the distributions of local pressure, Knudsen number, centerline velocity, and Mach number. The variations of flow patterns and vortex length with Kn
o
and Re are also documented. Moreover, a critical Knudsen number is identified to be Kn
oc
= 0.1 below and above which the behaviors of nonlinear pressure profile and velocity distribution and the variations of vortex length with Re upstream and downstream of constriction are different from those of continuum flows.
41 citations
01 Dec 1971
TL;DR: Theoretical equations for the pressure drop of high-porosity fibrous aerosol filters for low-speed Newtonian flow are summarized and the relations between them are discussed in this article.
Abstract: Theoretical equations for the pressure drop of high-porosity fibrous aerosol filters for low-speed Newtonian flow are summarized, and the relations between them are discussed. Using these equations the general character of the dependence of the pressure drop on the gas pressure (pressure characteristics) is analyzed over the whole range of Knudsen numbers. The dimensionless equations describing the reduction of the pressure drop with decreasing gas pressure are derived. Analyzing these equations, it is concluded that the pressure-drop reduction is dependent on three factors: the character of flow through a filter at normal pressure (continuum, slip, transient and free molecule flow), the dilution (reduction of the gas pressure), and porosity of the filter. The theory is checked against available experimental data.
41 citations
TL;DR: In this article, a simple analytical model with second-order slip boundary conditions for a normalized Poiseuille number is proposed, which can be applied to either rarefied gas flows or apparent liquid slip flows.
Abstract: This paper significantly extends previous studies to the transition regime by employing the second-order slip boundary conditions. A simple analytical model with second-order slip boundary conditions for a normalized Poiseuille number is proposed. The model can be applied to either rarefied gas flows or apparent liquid slip flows. The developed simple models can be used to predict the Poiseuille number, mass flow rate, tangential momentum accommodation coefficient, pressure distribution of gaseous flow in noncircular microchannels and nanochannels by the research community for the practical engineering design of microchannels and nanochannels. The developed second-order models are preferable since the difficulty and “investment” is negligible compared with the cost of alternative methods such as molecular simulations or solutions of Boltzmann equation. Navier–Stokes equations with second-order slip models can be used to predict quantities of engineering interest such as the Poiseuille number, tangential momentum accommodation coefficient, mass flow rate, pressure distribution, and pressure drop beyond its typically acknowledged limit of application. The appropriate or effective second-order slip coefficients include the contribution of the Knudsen layers in order to capture the complete solution of the Boltzmann equation for the Poiseuille number, mass flow rate, and pressure distribution. It could be reasonable that various researchers proposed different second-order slip coefficients because the values are naturally different in different Knudsen number regimes. It is analytically shown that the Knudsen’s minimum can be predicted with the second-order model and the Knudsen value of the occurrence of Knudsen’s minimum depends on inlet and outlet pressure ratio. The compressibility and rarefaction effects on mass flow rate and the curvature of the pressure distribution by employing first-order and second-order slip flow models are analyzed and compared. The condition of linear pressure distribution is given.
41 citations