DSMC Simulation: Validation and Application to Low Speed Gas Flows in Microchannels

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
T. Ewart ◽  
J. L. Firpo ◽  
I. A. Graur ◽  
P. Perrier ◽  
J. G. Méolans
Keyword(s):  
Flow Regime ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Streamwise Velocity ◽  
Accommodation Coefficient ◽  
Transitional Flow ◽  
Linearized Boltzmann Equation

A direct simulation Monte Carlo method (DSMC) solver, adapted to the subsonic microflow, is developed under the object-conception language (C++). Some technical details critical in these DSMC computations are provided. The numerical simulations of gas flow in a microchannel are carried out using the developed DSMC solver. Streamwise velocity distributions in the slip flow regime are compared with the analytical solution based on the Navier–Stokes equations with the velocity slip boundary condition. Satisfactory agreements have been achieved. Furthermore, the domain of the validity of this continuum approach is discussed. Simulations are then extended to the transitional flow regime. Streamwise velocity distributions are also compared with the results of the numerical solutions of the linearized Boltzmann equation. We emphasize the influence of the accommodation coefficient on the velocity profiles and on the mass flow rate. The simulation results on the mass flow rate are compared with the experimental data, which allow us to validate the “experimental” technique of the determination of the accommodation coefficient.

DSMC Simalation of the Pressure and Temperature Driven Flows: Comparison With the Measurements

2009 ◽  
Author(s):  
Timothe´e Ewart ◽  
Irina A. Graur ◽  
Jean-Luc Firpo ◽  
Alexey Polikarpov ◽  
Pierre Perrier ◽  
...  
Keyword(s):  
Flow Regime ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Streamwise Velocity ◽  
Accommodation Coefficient ◽  
Transitional Flow ◽  
Linearized Boltzmann Equation

A DSMC solver, adapted to the subsonic micro flow, is developed under the object-conception language (C++). Some technical details critical in these DSMC computations are provided. The numerical simulations of gas flow in micro channel are carried out using developed DSMC solver. Streamwise velocity distributions in the slip flow regime are compared with the analytical solution based on the Navier-Stokes equations with the velocity slip boundary condition. Satisfactory agreements have been achieved. Furthermore, the domain of the validity of this continuum approach is discussed. Simulations are then extended to transitional flow regime. Streamwise velocity distributions are also compared with the results of the numerical solutions of the linearized Boltzmann equation. We emphasize the influence of the accommodation coefficient on the velocity profiles and on the mass flow rate. The simulation results on the mass flow rate are compared with the experimental data, that allow us to validate the “experimental” technique of the determination of the accommodation coefficient.

scholarly journals Non-equilibrium dynamics of dense gas under tight confinement

2016 ◽  
Vol 794 ◽  
pp. 252-266 ◽  
Author(s):  
Lei Wu ◽  
Haihu Liu ◽  
Jason M. Reese ◽  
Yonghao Zhang
Keyword(s):  
Boltzmann Equation ◽  
Flow Regime ◽  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Transitional Flow ◽  
Molecular Flow ◽  
Parallel Plates ◽  
The Boltzmann Equation

The force-driven Poiseuille flow of dense gases between two parallel plates is investigated through the numerical solution of the generalized Enskog equation for two-dimensional hard discs. We focus on the competing effects of the mean free path ${\it\lambda}$, the channel width $L$ and the disc diameter ${\it\sigma}$. For elastic collisions between hard discs, the normalized mass flow rate in the hydrodynamic limit increases with $L/{\it\sigma}$ for a fixed Knudsen number (defined as $Kn={\it\lambda}/L$), but is always smaller than that predicted by the Boltzmann equation. Also, for a fixed $L/{\it\sigma}$, the mass flow rate in the hydrodynamic flow regime is not a monotonically decreasing function of $Kn$ but has a maximum when the solid fraction is approximately 0.3. Under ultra-tight confinement, the famous Knudsen minimum disappears, and the mass flow rate increases with $Kn$, and is larger than that predicted by the Boltzmann equation in the free-molecular flow regime; for a fixed $Kn$, the smaller $L/{\it\sigma}$ is, the larger the mass flow rate. In the transitional flow regime, however, the variation of the mass flow rate with $L/{\it\sigma}$ is not monotonic for a fixed $Kn$: the minimum mass flow rate occurs at $L/{\it\sigma}\approx 2{-}3$. For inelastic collisions, the energy dissipation between the hard discs always enhances the mass flow rate. Anomalous slip velocity is also found, which decreases with increasing Knudsen number. The mechanism for these exotic behaviours is analysed.

Mass Flow Rate Measurements Through Metallic Microtubes in the Slip and Transition Regimes

2015 ◽  
Author(s):  
Ernane Silva ◽  
Cesar J. Deschamps ◽  
Marcos Rojas-Cárdenas
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Rarefied Gas ◽  
Mean Free Path ◽  
Accommodation Coefficient ◽  
Transitional Flow ◽  
Gas Flows ◽  
Slip Regime ◽  
Non Equilibrium

The exchange of momentum and energy in gas flows through microchannels is significantly influenced by the gas-surface interaction. At this scale often the gas is rarefied and therefore non-equilibrium effects in the fluid flow can arise in a layer which extends for a distance equivalent to the mean free path from the walls. Typical examples of non-equilibrium phenomena for rarefied gas flows are slip at the wall, thermal transpiration and temperature jump at the wall. The aim of the present study is to experimentally investigate the non-equilibrium effects present in an isothermal pressure induced flow for a large range of rarefaction conditions. The isothermal slip at the wall is usually characterized by the tangential momentum accommodation coefficient (TMAC). This coefficient depends on the molecular nature of the gas and on the physical characteristics of the surface, such as material and roughness. In particular this paper explores the influence of the surface material on the TMAC through measurements of the mass flow rate in capillaries for the special case of nitrogen. Commercially available microtubes of three different metallic materials — stainless steel, copper, and brass — were considered in the analysis. Measurements were performed with a dynamic measurement technique based on the constant volume method and comprehend the transitional flow regime and most part of the slip regime. Theoretical results obtained from the solution of the Boltzmann equation via the BGK kinetic model, which is a simplified approximation for the collisional term, were compared to the experimental results.

scholarly journals Development of Hybrid Airlift-Jet Pump with Its Performance Analysis

2018 ◽  
Vol 8 (9) ◽  
pp. 1413 ◽  
Author(s):  
Dan Yao ◽  
Kwongi Lee ◽  
Minho Ha ◽  
Cheolung Cheong ◽  
Inhiug Lee
Keyword(s):  
Boundary Conditions ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Jet Pump ◽  
Two Phase

A new pump, called the hybrid airlift-jet pump, is developed by reinforcing the advantages and minimizing the demerits of airlift and jet pumps. First, a basic design of the hybrid airlift-jet pump is schematically presented. Subsequently, its performance characteristics are numerically investigated by varying the operating conditions of the airlift and jet parts in the hybrid pump. The compressible unsteady Reynolds-averaged Navier-Stokes equations, combined with the homogeneous mixture model for multiphase flow, are used as the governing equations for the two-phase flow in the hybrid pump. The pressure-based methods combined with the Pressure-Implicit with Splitting of Operators (PISO) algorithm are used as the computational fluid dynamics techniques. The validity of the present numerical methods is confirmed by comparing the predicted mass flow rate with the measured ones. In total, 18 simulation cases that are designed to represent the various operating conditions of the hybrid pump are investigated: eight of these cases belong to the operating conditions of only the jet part with different air and water inlet boundary conditions, and the remaining ten cases belong to the operating conditions of both the airlift and jet parts with different air and water inlet boundary conditions. The mass flow rate and the efficiency are compared for each case. For further investigation into the detailed flow characteristics, the pressure and velocity distributions of the mixture in a primary pipe are compared. Furthermore, a periodic fluctuation of the water flow in the mass flow rate is found and analyzed. Our results show that the performance of the jet or airlift pump can be enhanced by combining the operating principles of two pumps into the hybrid airlift-jet pump, newly proposed in the present study.

scholarly journals Performance investigation of a volute porous tongue of a turbocharger turbine

2020 ◽  
Vol 40 (1) ◽  
pp. 59-66
Author(s):  
Abderrahmane Chachoua ◽  
Mohamed Kamal Hamidou ◽  
Mohammed Hamel
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Gas Turbines ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Recirculation Flow ◽  
Recirculating Flow ◽  
Show Evidence ◽  
The Right

The design for better performance of the spiral housing volute used commonly in radial and mixed inflow gas turbines is of prime importance as it affects the machine stage at both design and off design conditions. The tongue of the scroll divides the flow into two streams, and represents a severe source of disturbances, in terms of thermodynamic parameter uniformity, maximum kinetic energy, the right angle of attack to the rotor and minimum losses. Besides, the volute suffers an undesirable effect due to the recirculating mass flow rate in near bottom vicinity of the tongue. The present project is an attempt to design a tongue fitted with cylindrical holes traversing normal to the stream wise direction, where on account of the large pressure difference between the top and the bottom sides of the tongue will force the recirculating flow to go through the rotor inlet. This possibility with its limitations has not yet been explored. A numerical simulation is performed which might provide our suitable objectives. To achieve this goal the ANSYS code is used to build the geometry, generate the mesh, and to simulate the flow by solving numerically the averaged Navier Stokes equations. Apparently, the numerical results show evidence of favorable impact in using porous tongue. The realization of a contact between the main and recirculation flow by drilled holes on the tongue surface leads to a flow field uniformity, a reduction in the magnitude of the loss coefficient, and a 20 % reduction in the recirculating mass flow rate.

Mass Flow Rate Measurements in Microchannels

2009 ◽  
Author(s):  
Irina A. Graur ◽  
Pierre Perrier ◽  
J. G. Me´olans
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Accommodation Coefficient ◽  
Steady Flows ◽  
Molecular Weights ◽  
Slip Boundary ◽  
Accommodation Coefficients ◽  
Accommodation Process ◽  
Wall Interaction

Mass flow rate measurements in a single silicon micro channel were carried out for various gases in isothermal steady flows. The results obtained from hydrodynamic to near free molecular regime by using a powerful experimental platform, allowed us to deduce interesting information, notably about the reflection/accommodation process at the wall. In the 0 – 0.3 Knudsen range, a continuum analytic approach was derived from NS equations, associated to first or second order slip boundary conditions. Identifying the experimental mass flow rate curves to the theoretical ones the tangential momentum accommodation coefficient (TMAC) of various gases was extracted. Over all the Knudsen range [0 – 50] the experimental results were compared with theoretical values calculated from the kinetic approaches: using variable accommodation coefficient values as fitting parameter, the theoretical curves were fitted to the experimental ones. Whatever the Knudsen range and whatever the theoretical approach, the TMAC values are found decreasing when the molecular weights of the gas increase (as long as the different gases are compared using the same approach). Moreover, the values of the various accommodation coefficients are rather close one to other but sufficiently smaller than unity to conclude that the full accommodation modelling is not satisfactory to describe the gas/wall interaction.

Mass Flow Rate Measurements: From Hydrodynamic to Free Molecular Regime

2008 ◽  
Author(s):  
Timothe´e Ewart ◽  
Irina A. Graour ◽  
Pierre Perrier ◽  
J. Gilbert Me´olans
Keyword(s):  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Stationary Flow ◽  
Small Mass ◽  
Accommodation Coefficient ◽  
Navier Stokes ◽  
Number Range ◽  
Free Molecular Regime

An experimental investigation in a single silica microtube in isothermal stationary flow for various gases is made from the hydrodynamic to the near free molecular regime to study the reflection/accommodation process at the wall. This kind of investigation requires, more than other Micro-Electro-Mechanical-Systems (MEMS) experiments, a powerful experimental platform to measure very small mass flow rate. A global analytic expression, based on the Navier-Stokes (NS) equations with second order boundary conditions, is used to yield the Tangential Momentum Accommodation Coefficient (TMAC) in 0.003–0.3 Knudsen number range. Otherwise, the experimental results of the mass flow rate is compared with theoretical values calculated from kinetic approaches using variable TMAC as fitting parameter over the 0.3–30 Knudsen number range. Finally, whatever the theoretical approach the TMAC values obtained from the different gas-surface pairs are rather close one to other, but the TMAC values seem decreasing when the molecular mass increases.

Drainage flow of a viscous compressible fluid from a small capillary with a sealed end

2018 ◽  
Vol 839 ◽  
pp. 621-643 ◽  
Author(s):  
Kang Ping Chen ◽  
Di Shen
Keyword(s):  
Diffusion Coefficient ◽  
Acoustic Wave ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Compressible Fluid ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Viscous Compressible Fluid ◽  
Drainage Flow

Volumetric expansion driven drainage flow of a viscous compressible fluid from a small capillary with a sealed end is studied in the low Mach number limit using the linearized compressible Navier–Stokes equations with no-slip condition. Density relaxation, oscillation and decay as well as the velocity field are investigated in detail. It is shown that fluid drainage is controlled by the slow decay of the standing acoustic wave inside the capillary; and the acoustic wave retards the density diffusion by reducing the diffusion coefficient of the density envelope equation by one half. Remarkably the no-slip flow exhibits a slip-like mass flow rate. The period-averaged mass flow rate at the exit (drainage rate) is found proportional to the fluid’s kinematic viscosity via the density diffusion coefficient and the average drainage speed is independent of the capillary radius. These findings are valid for arbitrarily small capillaries as long as the continuum assumption holds and they are in stark contrast to the classical lubrication based theory. Generalization to a capillary with a sound absorbing end is achieved by a simple model. The reported results offer new insights to the nature of slow viscous compressible flows in very small capillaries.

Mass Flow Rate Measurement Through Rectangular Microchannels for Large Knudsen Number Range

2011 ◽  
Author(s):  
M. Hadj Nacer ◽  
Pierre Perrier ◽  
Irina Graur
Keyword(s):  
Boundary Condition ◽  
Mass Flow Rate ◽  
Knudsen Number ◽  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Rectangular Cross Section ◽  
Velocity Slip ◽  
Bgk Model ◽  
Number Range

The mass flow rate through microchannels with rectangular cross section is measured for the wide Knudsen number range (0.0025–26.2) in isothermal steady conditions. The experimental technique called ‘Constant Volume Method’ is used for the measurements. This method consists of measuring the small pressure variations in the tanks upstream and downstream of the microchannel. The measurements of the mass flow rate are carried out for three gases (Helium, Nitrogen and Argon). The microchannel internal surfaces are covered with a thin layer of gold with mean roughness Ra = 0.87nm (RMS). The continuum approach (Navier-Stokes equations) with first order velocity slip boundary condition was used in the slip regime (Knudsen number varies from 0.0025 to 0.1) to obtain the experimental velocity slip and accommodation coefficients associated to the Maxwell kinetic boundary condition. In the transitional and near free molecular regimes the linearized kinetic BGK model was used to calculate numerically the mass flow rate. From the comparison of the numerical and measured values of the mass flow rate the accommodation coefficient was also deduced.

Gas Mass Flow Rate Measurement in T-Shaped Microchannels in Slip Flow Regime

2011 ◽  
Author(s):  
Yongli Li ◽  
Christine Barrot ◽  
Lucien Baldas ◽  
Ste´phane Colin ◽  
Ju¨rgen J. Brandner ◽  
...  
Keyword(s):  
Flow Regime ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Slip Flow ◽  
Rate Measurement ◽  
Gas Mixing ◽  
Flow Rate Measurement ◽  
Slip Flow Regime ◽  
Good Agreement

A new setup was developed for gas mixing analysis in T-shaped microchannels. The principle of the flow rate measurement was based on the Constant Volume (CV) method [1]. The mass flow rate measurements of two gases N2 / CO2 mixing in a T mixer were carried out in the slip flow regime and followed by a simulation work for comparison. The mass flow rate has a magnitude of 10−8 or 10−7 kg/s and has good agreement with simulation for the lowest inlet over outlet pressures ratios and moderate agreement for the highest inlet over outlet pressures ratios.

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