Abstract
Numerical investigations of high-speed rarefied gas outflow into a vacuum through channels with a forward- or backward-facing step have been conducted using the direct simulation Monte Carlo method. Calculations have been performed for various free-stream Mach numbers, covering transonic, supersonic, and hypersonic flow regimes, and over a wide range of gas rarefaction from free molecular to near hydrodynamic conditions. Mass flow rates through the channel and the gas flow field have been accurately calculated both inside the channel and in the regions upstream and downstream. It has been established that channel geometry, the free-stream velocity, and gas rarefaction strongly influence the gas flow. In the flow field, in front of the channel, a phenomenon known as a detached shock occurs, while inside the channel, a gas recirculation zone may form.
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The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.
References
Aristov VV, Rovenskaya OI (2015) Kinetic description of the turbulence in the supersonic compressible flow over a backward/forward-facing step. Comput Fluids 111:150–158
Armaly BF, Durst F, Pereira JCF, Schönung B (1983) Experimental and theoretical investigation of backward-facing step flow. J Fluid Mech 127:473–496
Bird GA (1994) Molecular gas dynamics and the direct simulation of gas flow. Oxford University Press
Chaudhuri A, Guha C, Dutta TK (2007) Finite volume simulation of supersonic to hypersonic gas flow and heat transfer through microchannels. Chemical Engineering Technology 30(1):41–45
Chen L, Asai K, Nonomura T, Xi G, Liu T (2018) A review of backward-facing step (BFS) flow mechanisms, heat transfer and control. Thermal Science and Engineering Progress 6:194–216
Chen L, Yang C, Xiao Y, Yan X, Hu L, Eggersdorfer M, Ye F (2021) Millifluidics, microfluidics, and nanofluidics: manipulating fluids at varying length scales. Materials Today Nano 16:100136
Ching T, Toh YC, Hashimoto M (2022) Design and fabrication of micro/nanofluidics devices and systems. Prog Mol Biol Transl Sci 186(1):15–58
Darbandi M, Mosayebi G 2016. The simulations of flow and heat over microscale sensors in supersonic rarefied gas flows using DSMC. In International conference on micro/nanoscale heat transfer Vol. 49668, p. V002T15A003. American Society of Mechanical Engineers.
Gatsonis NA, Al-Kouz WG, Chamberlin RE (2010) Investigation of rarefied supersonic flows into rectangular nanochannels using a three-dimensional direct simulation Monte Carlo method. Phys Fluids 22(3):032001
Ivanov MS, Rogasinsky SV (1988) Analysis of numerical techniques of the direct simulation monte carlo method in the rarefied gas dynamics. Russ J Numer Anal Math Model 3(6):453–466
Joneidipour MM, Kamali R 2011. DSMC simulation of supersonic gas flow in microchannel. In International conference on nanochannels, microchannels, and minichannels Vol. 44632, pp. 359–367.
Kherbeet AS, Safaei MR, Mohammed HA, Salman BH, Ahmed HE, Alawi OA, Al-Asadi MT (2016) Heat transfer and fluid flow over microscale backward and forward facing step: a review. Int Commun Heat Mass Transfer 76:237–244
Le M, Hassan I, Esmail N (2007) The effects of outlet boundary conditions on simulating supersonic microchannel flows using DSMC. Appl Therm Eng 27(1):21–30
Leite PH, Santos WF 2009. Direct simulation calculations of the rarefied hypersonic flow past a backward-facing step. In 20th International congress of mechanical engineering.
Li XJ, Yang C, Li PC (eds) (2021) Multidisciplinary Microfluidic and Nanofluidic Lab-on-a-chip. Principles and Applications, Newnes
Murugan JN, Govardhan RN (2016) Shock wave–boundary layer interaction in supersonic flow over a forward-facing step. J Fluid Mech 807:258–302
Nabapure D 2020. DSMC simulation of rarefied gas flow over a 2D backward-facing step in the transitional flow regime: effect of mach number and wall temperature. Proceedings of the institution of mechanical engineers, Part G: Journal of Aerospace Engineering, 0954410020959872.
Nabapure D (2021) DSMC investigation of rarefied gas flow over a 2D forward-facing step: effect of knudsen number. Acta Astronaut 178:89–109
Nabapure D, Sanwal J, Rajesh S, Murthy KRC 2019. Investigation of Subsonic and hypersonic rarefied gas flow over a backward facing step. In Journal of Physics: Conference Series Vol. 1276, No. 1, p. 012007 IOP Publishing.
Nabapure D, Guha P, Murthy KRC 2019. DSMC simulation of rarefied gas flow over a backward-facing step: effect of expansion ratio. Proceedings of the 25th national and 3rd international ISHMT-ASTFE heat and mass transfer conference IHMTC-2019 Dec 28–31, 2019, IIT Roorkee, Roorkee, India.
Qing-Hu Z, Shi-He Y, Yang-Zhu Z, Zhi C, Yu W (2013) The effect of micro-ramps on supersonic flow over a forward-facing step. Chin Phys Lett 30(4):044701
Salman S, Talib AA, Saadon S, Sultan MH (2020) Hybrid nanofluid flow and heat transfer over backward and forward steps: A review. Powder Technol 363:448–472
Sattari S, Jahani M, Gorji BM (2015) Numerical simulation of the supersonic flow over forward-facing step in micro couette flow using direct simulation monte carlo method. Int J Advanced Design and Manufacturing Technology 8(3):49–57
Sazhin O (2008) Gas flow through a slit into a vacuum in a wide range of rarefaction. J Exp Theor Phys 107(1):162–169
Sazhin O (2021) Gas outflow into vacuum over a forward-and backward-facing step in a wide range of rarefaction. Int J Heat Mass Transf 179:121666
Sazhin O (2023) Gas Dynamics of micro-and nanofluidic systems. Fluids 8(1):24
Venkattraman A, Alexeenko AA, Gallis MA, Ivanov MS 2012. A comparative study of no-time-counter and majorant collision frequency numerical schemes in DSMC. In AIP Conference Proceedings Vol. 1501, No. 1, pp. 489–495. American Institute of Physics.
Wu Y, Ren H (2013) On the impacts of coarse-scale models of realistic roughness on a forward-facing step turbulent flow. Int J Heat Fluid Flow 40:15–31
Yarin AL (2020) Novel nanofluidic and microfluidic devices and their applications. Curr Opin Chem Eng 29:17–25
Zhu Y, Yi S, Gang D, He L (2015) Visualisation on supersonic flow over backward-facing step with or without roughness. J Turbul 16(7):633–649
Acknowledgements
This research was supported by the Russian Science Foundation and Government of Sverdlovsk region, Joint Grant No 22-21-20121, https://rscf.ru/en/project/22-21-20121/.
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O.S. wrote the main manuscript text and A.S. prepared figures. All authors reviewed the manuscript.
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Sazhin, O., Sazhin, A. Transonic, supersonic, and hypersonic flow of rarefied gas into vacuum through channels with a forward- or backward-facing step. Microfluid Nanofluid 28, 32 (2024). https://doi.org/10.1007/s10404-024-02727-x
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DOI: https://doi.org/10.1007/s10404-024-02727-x