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Omid Ejtehadi Ehsan Roohi, Javad Abolfazli Esfahani
Transcript of Omid Ejtehadi Ehsan Roohi, Javad Abolfazli Esfahani
Omid Ejtehadi
Ehsan Roohi, Javad Abolfazli Esfahani
Department of Mechanical Engineering
Ferdowsi university of Mashhad, Iran
Overview
Micro/Nano Couette Flow
DSMC Algorithm
Code Validation
Entropy and Entropy Generation
Results
Compressibility Effects
Rarefaction Effects
Conclusion
Micro-Fluidic Systems
Micro-Channel
Micro-Pump Micro-Motor Micro-Nozzle Micro-Valve
Micro-Turbine
Micro-Fluidic Systems
Thermal ink-jet operation
Micro-Beam
Micro-Propulsion
System
Flow Regimes
Boltzmann Equation (BE) / DSMC Collisionless BE /
DSMC Molecular
Models
Continuum
Models
Euler Equations
Navier-Stokes Equations
Burnett Equations
Kn 0.001 0.01 0.1 1 10 0
MEMS NANO
Slip-Flow Regime
Transition
Regime Free Molecular Regime
Continuum
Regime
Knudsen
Number = Mean Free Path
System Length
Micro-Fluidics: Governing Equation
• Boltzmann Equation: temporal-spatial changes of number of molecules in a velocity class c
Local rate of change of
number of molecules
11
*
1
*
4
0
2 )()(.)(.)( dcdcffffnnfc
Fnfr
cnft
r
Binary Collision term Influx of molecules due to
external force
Influx of molecules due to
convection
Assumptions i) Dilute Gas: Binary Collision
ii) Molecular Chaos: colliding particles are uncorrelated
DSMC Algorithm
-Developed by Bird (1960’s)
Initialize system with particles
Loop over time steps
Create particles at open boundaries
Move all the particles
Cell size < λ, time step < 1/ν
Process any interactions of particle &
boundaries
Sort particles into cells
Sample statistical values
Select and execute random collisions
Slide taken from Alejandro L. Garcia, Department of Physics, San Jose State University
DSMC Applications
Hypersonic Flight at High Altitudes
Vacuum Technology
Micro/nano Scale Devices
Micro/Nano Couette Flow
Schematic of the Planar Couette flow
Micro-Bearing A Hard Disk Drive and its Schematic
Platter
Convergence Check
Problem is essentially 1-D, periodic BC’s on the sides
At least 300 particles per each cell
Heat transfer coefficient Temperature
Grid Independency Study
Code Validation
Current Gu-Emerson DSMC NS Analytical
Kn= 0.01
Mw= 0.16
Kn= 0.1
Mw= 0.16
Entropy
Tendency of a process to proceed in a particular
direction
Proceeding from order into disorder (randomness )
Boltzmann Relation
the number of possible microstates in the system
In DSMC:
Sorting particles to achieve velocity distribution function f
and integrating the resulting distribution
Entropy Generation
Irreversibilities
Quantifying Non-equilibrium
Optimum Design
Positive Definite
Naterer and Camberos
Equilibrium Based Definition
Myong Formula
Entropy: Compressibility Effects
Similar trends in entropy and temperature profiles
T depends on variance of velocity
In probability theory, the variance is a measure of how far a set of
numbers is spread out (Wikipedia)
Increase of Mach number results in increase of entropy (disorder) in
the domain
Mach Mach
Entropy Generation: Compressibility
effects
Similar trends in density and entropy generation shows this parameter can
be used for quantifying non-equilibrium
Increase of Mach number results in increase of entropy generation
Also as Mach increases entropy profiles become non-uniform
Entropy Generation: Different
Approaches
Role of Entropy Flux
Entropy Generation: Compressibility
Effects
Generation of entropy is mainly due to viscous dissipation
Viscous Thermal
Entropy: Rarefaction Effects
Similarities between entropy and temperature profiles
Entropy Generation: Rarefaction
effects
In a more rarefied flow less entropy is generated
Entropy Generation: Rarefaction
Effects
Generation of entropy is mainly due to viscous dissipation
Viscous Thermal
Concluding Remarks
Increase of wall Mach number results in non-uniform entropy
profiles
Entropy and temperature profiles are following an identical
trend
Increase of Knudsen number results in more uniform entropy
profiles
Entropy generation can be properly applied in quantifying
non-equilibrium phenomena
In the micro-Couette flow the generation of entropy is mainly
due to viscous dissipation term
Thanks