Study of subsonic–supersonic gas flow through micro/nanoscale nozzles using unstructured DSMC solver Authors Masoud Darbandi Center of Excellence in Aerospace Systems, Department of Aerospace Engineering Sharif University of Technology Ehsan Roohi Center of Excellence in Aerospace Systems, Department of Aerospace Engineering Sharif University of Technology Research Paper

First Online: 28 July 2010 Received: 10 March 2010 Accepted: 28 June 2010 DOI :
10.1007/s10404-010-0671-7

Cite this article as: Darbandi, M. & Roohi, E. Microfluid Nanofluid (2011) 10: 321. doi:10.1007/s10404-010-0671-7
Abstract We use an extended direct simulation Monte Carlo (DSMC) method, applicable to unstructured meshes, to numerically simulate a wide range of rarefaction regimes from subsonic to supersonic flows through micro/nanoscale converging–diverging nozzles. Our unstructured DSMC method considers a uniform distribution of particles, employs proper subcell geometry, and follows an appropriate particle tracking algorithm. Using the unstructured DSMC, we study the effects of back pressure, gas/surface interactions (diffuse/specular reflections), and Knudsen number on the flow field in micro/nanoscale nozzles. If we apply the back pressure at the nozzle outlet, a boundary layer separation occurs before the outlet and a region with reverse flow appears inside the boundary layer. Meanwhile, the core region of inviscid flow experiences multiple shock-expansion waves. In order to accurately simulate the outflow, we extend a buffer zone at the nozzle outlet. We show that a high viscous force creation in the wall boundary layer prevents any supersonic flow formation in the divergent part of the nozzle if the Knudsen number exceeds a moderate magnitude. We also show that the wall boundary layer prevents forming any normal shock in the divergent part. In reality, Mach cores would appear at the nozzle center followed by bow shocks and expansion region. We compare the current DSMC results with the solution of the Navier–Stokes equations subject to the velocity slip and temperature jump boundary conditions. We use OpenFOAM as a compressible flow solver to treat the Navier–Stokes equations.

Keywords Micro/nanoscale nozzles Rarefied flow Subsonic regime Supersonic regime DSMC Unstructured mesh Navier–Stokes Slip boundary condition OpenFOAM

References Agrawal A, Prabhu SV (2008) A survey on measurement of tangential momentum accommodation coefficient. J Vac Sci Technol A 26:634–645

CrossRef Agrawal A, Djenidi L, Antonia RA (2005) Simulation of gas flow in microchannels with a sudden expansion or contraction. J Fluid Mech 530:135–144

MATH CrossRef Alexeenko AA, Levin DA, Gimelshein SF, Collins RJ, Reed BD (2002) Numerical modeling of axisymmetric and three-dimensional flows in microelectromechanical systems nozzles. AIAA J 40(5):897–904

CrossRef Alexeenko A, Fedosov DA, Gimelshein SF, Levin DA, Collins RJ (2006) Transient heat transfer and gas flow in a MEMS-based thruster. J Microelectromech Syst 15(1):181–194

CrossRef Bird GA (1994) Molecular gas dynamics and the direct simulation of gas flows. Clarendon Press, Oxford

Bird G (2007) Sophisticated DSMC. Notes prepared for a short course at the DSMC07 meeting, Santa Fe, USA

Cai C, Boyd ID, Fan J, Candler GV (2000) Direct simulation methods for low-speed microchannel flows. J Thermophys Heat Transf 14(3):368–378

CrossRef Darbandi M, Schneider GE (2000) Performance of an analogy-based all speed procedure without any explicit damping. Comput Mech 26:459–469

MATH CrossRef Darbandi M, Vakilipour S (2007) Developing consistent inlet boundary conditions to study the entrance zone in microchannels. J Thermophys Heat Transf 21(3):596–607

CrossRef Darbandi M, Vakilipour S (2009) Solution of thermally developing zone in short micro/nano scale channels. J Heat Transf 131:044501

CrossRef Darbandi M, Roohi E, Mokarizadeh V (2008) Conceptual linearization of Euler governing equations to solve high speed compressible flow using a pressure-based method. Numer Methods Partial Differ Equ 24:583–604

MATH CrossRef MathSciNet Le M, Hassan I, Esmail N (2006) DSMC simulation of subsonic flows in parallel and series microchannels. J Fluids Eng 128:1153–1163

CrossRef Lin CX, Gadepalli V (2009) A computational study of gas flow in a De-Laval micronozzle at different throat diameters. Int J Numer Methods Fluids 59:1203–1216

MATH CrossRef MathSciNet Liu M, Zhang X, Zhang G, Chen Y (2006) Study on micronozzle flow and propulsion performance using DSMC and continuum methods. Acta Mech Sin 22:409–416

MATH CrossRef Louisos WF, Hitt DL (2005) Optimal expander angle for viscous supersonic flow in 2D micro-nozzles. AIAA paper 2005-5032

Louisos WF, Alexeenko AA, Hitt DL, Zilić A (2008) Design considerations for supersonic micronozzles. Int J Manuf Res 3(1):80–113

CrossRef O’Hare L, Lockerby DA, Reese JM, Emerson DR (2007) Near-wall effects in rarefied gas micro-flows: some modern hydrodynamic approaches. Int J Heat Fluid Flow 28:37–43

CrossRef OpenFOAM (2009) The Open Source CFD toolbox, user guide, version 1.6

Roohi E, Darbandi M (2009) Extending the Navier–Stokes solutions to transition regime in two-dimensional micro-/nanochannel flows using information preservation scheme. Phys Fluids 21:082001

CrossRef Roohi E, Darbandi M, Mirjalili V (2009) DSMC solution of subsonic flow through micro-nano scale channels. J Heat Transf 131:092402

CrossRef San O, Bayraktar I, Bayraktar T (2009) Size and expansion ratio analysis of micro nozzle gas flow. Int Commun Heat Mass Transf 36(5):402–411

CrossRef Shen C, Fan J, Xie C (2003) Statistical simulation of rarefied gas flows in micro channels. J Comput Phys 189:512–526

MATH CrossRef Sun ZX, Li ZY, He YL, Tao WQ (2009) Coupled solid (FVM)–fluid (DSMC) simulation of micro-nozzle with unstructured-grid. J Microfluid Nanofluid 7(5):621–631

CrossRef Titove EV, Levin DA (2007) Extension of DSMC method to high pressure flows. Int J Comput Fluid Dyn 21(9–10):351–368

CrossRef MathSciNet Uribe FJ, Garcia AL (1999) Burnett description for plane poiseuille flow. Phys Rev E 60(4):4063–4078

CrossRef Vakilipour S, Darbandi M (2009) Advancement in numerical study of gas flow and heat transfer in microchannels. J Thermophys Heat Transf 23(1):205–208

CrossRef Wang M, Li Z (2004) Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method. Int J Heat Fluid Flow 25:975–985

CrossRef Xie C (2007) Characteristics of micronozzle gas flows. Phys Fluids 19:037102

CrossRef Xu J, Zhao C (2007) Two-dimensional numerical simulations of shock waves in micro convergent–divergent nozzles. Int J Heat Mass Transf 50:2434–2438

MATH CrossRef Xue H, Ji HM, Shu C (2003) Prediction of flow and heat transfer characteristics in micro-Couette flow. Nanoscale Microscale Thermophys Eng 7:51–68

CrossRef Yang J, Ye J, Zheng J, Wong I, Ma Y, Lam C, Link S (2009) Improving DSMC with new pressure boundary conditions for heat and mass transfer of microchannel flows. Nanoscale Microscale Thermophys Eng 13:165–183

CrossRef Zhou Q, Leschziner MA (1999) An improved particle-locating algorithm for Eulerian–Lagrangian computations of two-phase flows in general coordinates. Int J Multiph Flow 25:813–825

MATH CrossRef