Slip Flow in Rectangular and Annular Ducts

1965 ◽  
Vol 87 (4) ◽  
pp. 1018-1024 ◽  
Author(s):  
W. A. Ebert ◽  
E. M. Sparrow
Keyword(s):  
Pressure Drop ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Velocity Slip ◽  
Density Level ◽  
Axial Pressure ◽  
Slip Regime ◽  
Rarefied Gas Flows ◽  
Axial Pressure Gradient ◽  
Viscous Shear

An analysis has been performed to determine the velocity and pressure-drop characteristics of moderately rarefied gas flows in rectangular and annular ducts. The density level is such that a velocity slip may occur at the duct walls. In general, it is found that the effect of slip is to flatten the velocity distribution relative to that for a continuum flow; furthermore, the axial pressure gradient is diminished under slip-flow conditions. The conditions characterizing the onset of the slip regime have been determined on the basis of a 2 percent reduction in friction factor relative to the continuum value. For all the geometries studied here, the onset of slip occurred at a Knudsen number of 0.003. The effect of compressibility on the axial pressure drop was also investigated. It was found that compressibility increases the pressure drop primarily through an increase in viscous shear rather than through an increase in momentum flux.

Is the Lattice Boltzmann Method Applicable to Rarefied Gas Flows? Comprehensive Evaluation of the Higher-Order Models

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Minoru Watari
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Higher Order ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Slip Flow Regime ◽  
Boltzmann Method ◽  
Higher Order Models

Lattice Boltzmann method (LBM) whose equilibrium distribution function contains higher-order terms is called higher-order LBM. It is expected that nonequilibrium physics beyond the Navier–Stokes can be accurately captured using the higher-order LBM. Relationship between the level of higher-order and the simulation accuracy of rarefied gas flows is studied. Theoretical basis for constructing higher-order LBM is presented. On this basis, specific higher-order models are constructed. To confirm that the models have been correctly constructed, verification simulations are performed focusing on the continuum regime: sound wave and supersonic flow in Laval nozzle. With applications to microelectromechanical systems (MEMS) in mind, low Mach number flows are studied. Shear flow and heat conduction between parallel walls in the slip flow regime are investigated to confirm the relaxation process in the Knudsen layer. Problems between concentric cylinders are investigated from the slip flow regime to the free molecule regime to confirm the effect of boundary curvature. The accuracy is discussed comparing the simulation results with pioneers' studies. Models of the fourth-order give sufficient accuracy even for highly rarefied gas flows. Increase of the particle directions is necessary as the Knudsen number increases.

Slip Flow with Axial Pressure Gradient

1962 ◽  
Vol 29 (11) ◽  
pp. 1393-1394 ◽  
Author(s):  
A. Pozzi ◽  
P. Renno
Keyword(s):  
Pressure Gradient ◽  
Slip Flow ◽  
Axial Pressure ◽  
Axial Pressure Gradient

Effects of Axial Corrugated Roughness on Low Reynolds Number Slip Flow and Continuum Flow in Microtubes

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Zhipeng Duan ◽  
Y. S. Muzychka
Keyword(s):  
Pressure Drop ◽  
Slip Flow ◽  
Velocity Slip ◽  
Analytical Models ◽  
Axial Distance ◽  
Microchannel Flow ◽  
Compressibility Effect ◽  
Continuum Flow ◽  
Experimental Pressure ◽  
The Stokes Equation

The effect of axial corrugated surface roughness on fully developed laminar flow in microtubes is investigated. The radius of a microtube varies with the axial distance due to corrugated roughness. The Stokes equation is solved using a perturbation method with slip at the boundary. Analytical models are developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow. The developed model proposes an explanation on the observed phenomenon that some experimental pressure drop results for microchannel flow have shown a significant increase due to roughness. The developed model for slip flow illustrates the coupled effects between velocity slip and small corrugated roughness. Compressibility effect has also been examined and simple models are proposed to predict the pressure distribution and mass flow rate for slip flow in corrugated rough microtubes.

scholarly journals Velocity Measurements in Channel Gas Flows in the Slip Regime by means of Molecular Tagging Velocimetry

Micromachines ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 374 ◽  
Author(s):  
Dominique Fratantonio ◽  
Marcos Rojas-Cárdenas ◽  
Christine Barrot ◽  
Lucien Baldas ◽  
Stéphane Colin
Keyword(s):  
Slip Velocity ◽  
Rarefied Gas ◽  
Numerical Models ◽  
Slip Flow ◽  
Diagnostic Methods ◽  
Gas Flows ◽  
Reconstruction Method ◽  
Molecular Tagging Velocimetry ◽  
Molecular Tagging ◽  
Slip Regime

Direct measurements of the slip velocity in rarefied gas flows produced by local thermodynamic non-equilibrium at the wall represent crucial information for the validation of existing theoretical and numerical models. In this work, molecular tagging velocimetry (MTV) by direct phosphorescence is applied to argon and helium flows at low pressures in a 1-mm deep channel. MTV has provided accurate measurements of the molecular displacement of the gas at average pressures of the order of 1 kPa. To the best of our knowledge, this work reports the very first flow visualizations of a gas in a confined domain and in the slip flow regime, with Knudsen numbers up to 0.014. MTV is cross-validated with mass flowrate measurements by the constant volume technique. The two diagnostic methods are applied simultaneously, and the measurements in terms of average velocity at the test section are in good agreement. Moreover, preliminary results of the slip velocity at the wall are computed from the MTV data by means of a reconstruction method.

Rarefied Gas Flow Analysis of a Suborbital Shuttle With the Academic CFD Code Galatea

2017 ◽  
Author(s):  
Angelos G. Klothakis ◽  
Georgios N. Lygidakis ◽  
Ioannis K. Nikolos
Keyword(s):  
Gas Flow ◽  
Microelectromechanical Systems ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Flow Analysis ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rarefied Gas Flows ◽  
Wide Range

During the past decade considerable efforts have been exerted for the simulation of rarefied gas flows in a wide range of applications, like the flow over suborbital vehicles, in microelectromechanical systems, etc. Such flows appear to be significantly different from those at the continuum regime, making the Navier-Stokes equations to fail without further amendment. In this study an in-house academic CFD solver, named Galatea, is modified appropriately to account for rarefied gases. The no-slip condition on solid walls is no longer valid, hence, velocity slip and temperature jump boundary conditions are applied instead. Additionally, a second-order accurate slip model has been incorporated, namely, this of Beskok and Karniadakis, increasing the accuracy in the same area but avoiding simultaneously the numerical difficulties, entailed by the computation of the second derivative of slip velocity when complex geometries and unstructured grids are coupled. The proposed solver is validated against rarefied laminar flow over a suborbital shuttle, designed by the Azim’UTBM team. The obtained results are compared with those extracted with the parallel open-source kernel SPARTA, which is based on the DSMC method. A satisfactory agreement is reported between the two methodologies, demonstrating the potential of the modified solver to simulate effectively such flows.

scholarly journals Pressure Drop of Microchannel Plate Fin Heat Sinks

Micromachines ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 80 ◽  
Author(s):  
Zhipeng Duan ◽  
Hao Ma ◽  
Boshu He ◽  
Liangbin Su ◽  
Xin Zhang
Keyword(s):  
Fluid Dynamics ◽  
Pressure Drop ◽  
Slip Flow ◽  
Numerical Data ◽  
Velocity Slip ◽  
Fundamental Solutions ◽  
Momentum Equation ◽  
Channel Length ◽  
Microchannel Plate ◽  
Heat Sinks

The entrance region constitutes a considerable fraction of the channel length in miniaturized devices. Laminar slip flow in microchannel plate fin heat sinks under hydrodynamically developing conditions is investigated semi-analytically and numerically in this paper. The semi-analytical model for the pressure drop of microchannel plate fin heat sinks is obtained by solving the momentum equation with the first-order velocity slip boundary conditions at the channel walls. The simple pressure drop model utilizes fundamental solutions from fluid dynamics to predict its constitutive components. The accuracy of the model is examined using computational fluid dynamics (CFD) simulations and the experimental and numerical data available in the literature. The model can be applied to either apparent liquid slip over hydrophobic and superhydrophobic surfaces or gas slip flow in microchannel heat sinks. The developed model has an accuracy of 92 percent for slip flow in microchannel plate fin heat sinks. The developed model may be used to predict the pressure drop of slip flow in microchannel plate fin heat sinks for minimizing the effort and expense of experiments, especially in the design and optimization of microchannel plate fin heat sinks.

scholarly journals Modeling viscous effects on boundary layer of rarefied gas flows inside micronozzles in the slip regime condition

2018 ◽  
Vol 148 ◽  
pp. 838-845 ◽  
Author(s):  
Maria Grazia De Giorgi ◽  
Donato Fontanarosa ◽  
Antonio Ficarella
Keyword(s):  
Boundary Layer ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Viscous Effects ◽  
Slip Regime ◽  
Rarefied Gas Flows

Modeling and Preliminary Experiment for Rarefied Gas Flows in Constricted Microchannels

2008 ◽  
Author(s):  
Xiaohui Guo ◽  
Chihyung Huang ◽  
Alina Alexeenko ◽  
John P. Sullivan
Keyword(s):  
Rarefied Gas ◽  
Numerical Models ◽  
Pressure Ratio ◽  
Frictional Resistance ◽  
Manufacturing Defects ◽  
Slip Regime ◽  
Rarefied Gas Flows ◽  
Mass Flowrate ◽  
Accommodation Coefficients ◽  
Slip Flows

Gaseous slip flows in 3D rectangular microchannels with constrictions have been study numerically, and the experiment using pressure-sensitive-paints (PSP) for polymer microchannel pressure measurements are proposed. Constrictions inside microchannels, either being manufacturing defects or functional design features such as micro-orifices or micro-nozzles, will change the flow pattern because of additional frictional resistance and flow separation. In current research, mass-flowrate reduction due to constrictions has been investigated numerically for air flows in the slip regime, where Knudsen number ranges from 0.003 to 0.07. The results have been compared with both straight microchannels and with 3D analytical solutions. Similar to nozzle cases at macroscale, chocked flows has been observed at the critical pressure ratio of about 1.89. A numerical model including finite inlet and outlet chambers has been used in simulations to evaluate effects of reflection waves. Slip effects have been studied for different accommodation coefficients in presence of constrictions. By implementing multi-species numerical models, thermal induced mass transport has also been studied. Preliminary experiment based on PSP measurement for polymer microchannels has able to generate high spatial resolution pressure data, which are comparable with numerical simulations. Finally, further improvement of experimental setup is discussed.

Low-Speed Slip Flow Over a Wedge

1970 ◽  
Vol 37 (2) ◽  
pp. 454-460 ◽  
Author(s):  
K. E. Kasza ◽  
W. L. Chow
Keyword(s):  
Boundary Layer ◽  
Free Path ◽  
Asymptotic Method ◽  
Slip Velocity ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Velocity Slip ◽  
Mean Free Path ◽  
Low Speed ◽  
Boundary Layer Equations

The problem of low-speed slip flow of a rarefied gas over a wedge has been solved using Meksyn’s asymptotic method of integrating the boundary-layer equations. Detailed results are given for slip velocity and developing velocity profiles for various wedge angles. The solution tends far downstream asymptotically to the Falkner and Skan profiles of conventional nonslip flow. In addition, the first correction to the skin friction due to velocity slip is found to be of the order of the first power of the molecular mean free path of the gas.

scholarly journals Numerical Simulation of Rarefied Gas Flows with Specified Heat Flux Boundary Conditions

2015 ◽  
Vol 17 (5) ◽  
pp. 1185-1200 ◽  
Author(s):  
Jianping Meng ◽  
Yonghao Zhang ◽  
Jason M. Reese
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
High Speed ◽  
Rarefied Gas ◽  
Flow Behavior ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Rarefied Gas Flows ◽  
Flux Boundary Conditions

AbstractWe investigate unidirectional rarefied flows confined between two infinite parallel plates with specified heat flux boundary conditions. Both Couette and force-driven Poiseuille flows are considered. The flow behaviors are analyzed numerically by solving the Shakhov model of the Boltzmann equation. We find that a zero-heat-flux wall can significantly influence the flow behavior, including the velocity slip and temperature jump at the wall, especially for high-speed flows. The predicted bimodal-like temperature profile for force-driven flows cannot even be qualitatively captured by the Navier-Stokes-Fourier equations.

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