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-Turbine Micro-Pump Micro-Motor Micro-Nozzle Micro-Valve
Micro-Fluidic Systems Thermal ink-jet operation Micro-Propulsion System Micro-Beam
Flow Regimes Knudsen Number = Mean Free Path System Length Molecular Models Boltzmann Equation (BE) / DSMC Collisionless BE / DSMC Continuum Models Euler Equations Navier-Stokes Equations Burnett Equations 0 0.001 0.01 0.1 1 10 Kn MEMS NANO Continuum Regime Slip-Flow Regime Transition Regime Free Molecular Regime
Micro-Fluidics: Governing Equation Boltzmann Equation: temporal-spatial changes of number of molecules in a velocity class c t Local rate of change of number of molecules 4 2 * * ( nf ) c. ( nf ) F. ( nf ) n ( f f1 ff1) cr d dc1 r c 0 Influx of molecules due to Influx of molecules due to external force Binary Collision term 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 Platter Micro-Bearing A Hard Disk Drive and its Schematic Schematic of the Planar Couette flow
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 Kn= 0.01 Mw= 0.16 Kn= 0.1 Mw= 0.16 Current Gu-Emerson DSMC NS Analytical
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 Mach Mach 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
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 Viscous Thermal Generation of entropy is mainly due to viscous dissipation
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 Viscous Thermal Generation of entropy is mainly due to viscous dissipation
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
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