Omid Ejtehadi Ehsan Roohi, Javad Abolfazli Esfahani. Department of Mechanical Engineering Ferdowsi university of Mashhad, Iran

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1 Omid Ejtehadi Ehsan Roohi, Javad Abolfazli Esfahani Department of Mechanical Engineering Ferdowsi university of Mashhad, Iran

2 Overview Micro/Nano Couette Flow DSMC Algorithm Code Validation Entropy and Entropy Generation Results Compressibility Effects Rarefaction Effects Conclusion

3 Micro-Fluidic Systems Micro-Channel Micro-Turbine Micro-Pump Micro-Motor Micro-Nozzle Micro-Valve

4 Micro-Fluidic Systems Thermal ink-jet operation Micro-Propulsion System Micro-Beam

5 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 Kn MEMS NANO Continuum Regime Slip-Flow Regime Transition Regime Free Molecular Regime

6 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

7 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

8 DSMC Applications Hypersonic Flight at High Altitudes Vacuum Technology Micro/nano Scale Devices

9 Micro/Nano Couette Flow Platter Micro-Bearing A Hard Disk Drive and its Schematic Schematic of the Planar Couette flow

10 Convergence Check Problem is essentially 1-D, periodic BC s on the sides At least 300 particles per each cell Heat transfer coefficient Temperature

11 Grid Independency Study

12 Code Validation Kn= 0.01 Mw= 0.16 Kn= 0.1 Mw= 0.16 Current Gu-Emerson DSMC NS Analytical

13 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

14 Entropy Generation Irreversibilities Quantifying Non-equilibrium Optimum Design Positive Definite Naterer and Camberos Equilibrium Based Definition Myong Formula

15 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

16 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

17 Entropy Generation: Different Approaches

18 Role of Entropy Flux

19 Entropy Generation: Compressibility Effects Viscous Thermal Generation of entropy is mainly due to viscous dissipation

20 Entropy: Rarefaction Effects Similarities between entropy and temperature profiles

21 Entropy Generation: Rarefaction effects In a more rarefied flow less entropy is generated

22 Entropy Generation: Rarefaction Effects Viscous Thermal Generation of entropy is mainly due to viscous dissipation

23 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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