Microfluidics and Nanofluidics

, 21:18

DSMC investigation of rarefied gas flow through diverging micro- and nanochannels

Research Paper

Abstract

Direct simulation Monte Carlo (DSMC) method with simplified Bernoulli trials (SBT) collision scheme has been used to study the rarefied pressure-driven nitrogen flow through diverging micro- and nanochannels. The fluid behaviours flowing between two plates with different divergence angles ranging between 0° and 17° are described at different pressure ratios (1.5 ≤ Π ≤ 2.5) and Knudsen numbers (0.03 ≤ Kn ≤ 12.7). The primary flow field properties, including pressure, velocity, and temperature, are presented for divergent micro- and nanochannels and are compared with those of a micro- and nanochannel with a uniform cross section. The variations of the flow field properties in divergent micro- and nanochannels which are influenced by the area change, the channel pressure ratio, and the rarefication are discussed. The results show no flow separation in divergent micro- and nanochannels for all the range of simulation parameters studied in the present work. It has been found that a divergent channel can carry higher amounts of mass in comparison with an equivalent straight channel geometry. A correlation between the mass flow rate through micro- and nanochannels, the divergence angle, the pressure ratio, and the Knudsen number has been suggested. The present numerical findings prove the occurrence of Knudsen minimum phenomenon in micro- and nanochannels with non-uniform cross sections.

Keywords

Divergent micro/nanochannel Rarefied gas flow DSMC Simplified Bernoulli trials Knudsen minimum 

List of symbols

a

Constant [kg s−1]

DOFrot

Rotational degree of freedom

dp

Molecular diameter [m]

DSMC

Direct simulation Monte Carlo

H

Channel height [m]

Kn

Knudsen number

L

Channel length [m]

Ma

Mach number

\(\dot{M}\)

Mass flow rate [kg s−1]

mp

Molecular mass [kg]

n

Number density [m−3]

NTC

No time counter

P

Pressure [Pa]

PPC

Particle per cell

R

Specific gas constant [J kg−1 K−1]

RMSE

Root mean squared error

SBT

Simplified Bernoulli trials

T

Temperature [K]

VHS

Variable hard sphere

w

Channel depth [m]

x, y

Cartesian coordinates

Greek symbols

β

Divergence angle

κb

Boltzmann constant [m2 kg s−2 K−1]

λ

Molecular mean free path [m]

Π

Inlet-to-outlet pressure ratio

ρ

Density [kg m−3]

ω

Viscosity index

Subscripts

in

Inlet

m

Mean

n

Normalised

out

Outlet

slip

Slip

straight

Straight

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.High-Performance Computing (HPC) Laboratory, Department of Mechanical Engineering, Faculty of EngineeringFerdowsi University of MashhadMashhadIran
  2. 2.Department of Materials Science and EngineeringDelft University of TechnologyDelftThe Netherlands

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