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Kinetic simulation of near field of plume exhausting from a plane micronozzle

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Abstract

Numerical simulations of near field of a plume exhausting from a plane wedge-like micronozzle into vacuum are performed using two different kinetic approaches: one of the model kinetic equations (ellipsoidal statistical model) and direct simulation Monte Carlo method. Adequacy and accuracy of the model kinetic equation as applied to such strongly non-equilibrium flows are studied by comparing the results with the data of DSMC simulations.

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References

  • Adamyak BY, Stepanov AE, Makarov KN, Sen VI, Pichugin VV (2010) A plasma scalpel based on a plasma microjet for soft tissue and bone surgery. Perspektivnye Materialy 8:119–124

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Aniskin VM, Bountin DA, Maslov AA, Mironov SG, Tsyryulnikov IS (2012) Stability of a subsonic gas microjet. Tech Phys 57(2):174–180

    Article  Google Scholar 

  • Bayt R, Breuer KS (2001) Fabrication and testing of micron-sized cold gas thrusters in micropropulsion of small spacecraft. Adv Aeronaut Astronaut 187:381–397

    Google Scholar 

  • Beijerinck HCW, Verster NF (1981) Absolute intensities and perpendicular temperatures of supersonic beams of polyatomic gases. Physica 111C:327–352

    Google Scholar 

  • Bejhed J (2006) Fluid microsystems for micropropulsion applications in space. Dissertation, Uppsala University

  • Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev 94:511–525

    Article  MATH  Google Scholar 

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

    Google Scholar 

  • Dettleff G (1991) Plume flow and plume impingement in space technology. Prog Aerospace Sci 28:1–71

    Article  Google Scholar 

  • Dulov VG, Lukyanov GA (1984) Gas dynamics of exhaust processes. Nauka, Novosibirsk (in Russian)

    Google Scholar 

  • Giordano D, Ivanov MS, Kashkovsky A, Markelov G, Tumino G, Koppenwallner G (1997) Application of DSMC to the study of satellite thruster plumes. AIAA Paper No. 97–2538

  • Gorbachev YE, Zakharov W, Lukianov GA (1999) Direct Monte Carlo simulation of monoatomic and diatomic non-equilibrium gas jet outflow in vacuum. Math Model 11(9):38–44 (in Russian)

    MATH  Google Scholar 

  • Habets AHM (1977) Supersonic expansion of argon into vacuum. Dissertation, Eindhoven University of Technology

  • Hamel BB, Willis RD (1966) Kinetic theory of source flow expansion with application to the free jet. Phys Fluids 9(5):829–841

    Article  MathSciNet  Google Scholar 

  • Hao P-F, Ding Y-T, Yao Z-H, He F, Zhu K-Q (2005) Size effect on gas flow in micro nozzles. J Micromech Microeng 15:2069–2073

    Article  Google Scholar 

  • Hastings D, Garrett H (1996) Spacecraft-environment interactions. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Holway LH Jr (1963) Approximation procedures for kinetic theory. Dissertation, Harvard University

  • Holway LH Jr (1966) New statistical models for kinetic theory: methods of construction. Phys Fluids 9:1658–1673

    Article  Google Scholar 

  • Ivanov MS, Gimelshein SF (1998) Computational hypersonic rarefied flows. Ann Rev Fluid Mech 30:469–505

    Article  MathSciNet  Google Scholar 

  • Ivanov MS, Markelov GN, Ketsdever A, Wadsworth DC (1999) Numerical study of cold gas micronozzle flow. AIAA Paper No. 99–0166, 11 p

  • Ivanov MS, Markelov GN (2000) Numerical study of thruster nozzle plume. AIAA Paper No. 2000–0468

  • Ivanov MS, Markelov GN, Bondar Y (2000) Numerical simulation of thruster plumes in cryogenic vacuum facility. AIAA Paper No. 2000–2502

  • Ketsdever A, Wadsworth DC, Wapner PHG, Ivanov MS, Markelov GN (1999) Fabrication and predicted performance of conical DeLavale micronozzles. AIAA Paper No. 99–2724. 12 p

  • Kogan MN (1969) Rarefied gas dynamics. Plenum, New York

    Book  Google Scholar 

  • Kudryavtsev AN, Shershnev AA (2013) A numerical method for simulation of microflows by solving directly kinetic equations with WENO schemes. J Sci Comput 57(1):42–73

    Article  MATH  MathSciNet  Google Scholar 

  • Kumar R, Titov EV, Levin DA, Gimelshein NE, Gimelshein SF (2010) Assessment of bhatnagar-gross-krook approaches for near continuum regime nozzle flows. AIAA J 48(7):1531–1541

    Article  Google Scholar 

  • Ladyzhenskii MD (1962) On the efflux of a viscous gas into a vacuum. J Appl Math Mech 26(4):965–974

    Article  Google Scholar 

  • Lekholm V, Palmer K, Thornell G (2012) Schlieren imaging of microthruster exhausts for qualitative and quantitative analysis. Meas Sci Technol 23(8):085403

    Article  Google Scholar 

  • Liaw G-S (1992) Numerical investigations in the backflow region of a vacuum plume. NAG8-201, 31 p

  • Louisos WF, Hitt DL (2007) Heat transfer and viscous effects in 2D & 3D micro-nozzles. AIAA Paper No. 2007–3987

  • Louwerse MC (2009) Cold gas micro propulsion. University of Twente, 176 p

  • Lutfurakhmanov A, Loken G, Schulz DL, Akhatov IS (2010) Capillary-based liquid microdroplet deposition. Appl Phys Lett 97:124107

    Article  Google Scholar 

  • Micci MM, Ketsdever AD (2000) Micropropulsion for small spacecraft. Progress in Astronautics and Astronautics Series, p 187

  • Mieussens L (2000) Discrete velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries. J Comput Phys 162:429–466

    Article  MATH  MathSciNet  Google Scholar 

  • Phalnikar KA, Kumar R, Alvi FS (2008) Experiments on free and impinging supersonic microjets. Exp Fluids 44(5):819–830

    Article  Google Scholar 

  • Rae WJ (1971) Some numerical results on viscous low-density nozzle flows in the slender-channel approximation. AIAA J 9(5):811–820

    Article  Google Scholar 

  • Rothe DE (1971) Electron-beam studies of viscous flow in supersonic nozzles. AIAA J 9(5):804–811

    Article  Google Scholar 

  • Sanna G, Tomassetti G (2005) Molecular beams gas dynamics. Imperial College Press, London

    Book  Google Scholar 

  • Scroggs SD, Settles GS (1996) An experimental study of supersonic microjets. Exp Fluids 2(6):4O1–4O9

    Google Scholar 

  • Shakhov EM (1968) Generalization of the Krook kinetic relaxation equation. Fluid Dyn 3:95–96

    Article  Google Scholar 

  • Sone Y, Sugimoto H (1993) Kinetic theory analysis of steady evaporating flows from a spherical condensed phase into a vacuum. Phys Fluids A 5:1491–1511

    Article  MATH  Google Scholar 

  • Sone Y, Sugimoto H (1995) Evaporation of a rarefied gas from a cylindrical condensed phase into a vacuum. Phys Fluids 7:2072–2085

    Article  MATH  Google Scholar 

  • Sone Y (2007) Molecular gas dynamics: theory, techniques, and applications. Birkhäuser, Boston

    Book  Google Scholar 

  • Struchtrup H (2005) Macroscopic transport equations for rarefied gas flows. Springer, Berlin

    MATH  Google Scholar 

  • Sutherland GS, Maes ME (1966) A review of microrocket technology: \(10^{-6}\) to 1 lbf thrust. J Spacecr Rockets 3(8):1153–1165

    Article  Google Scholar 

  • Titarev VA (2007) Conservative numerical methods for model kinetic equations. Comput Fluids 36(9):1446–1459

    Article  MATH  MathSciNet  Google Scholar 

  • Welander P (1954) On the temperature jump in a rarefied gas. Ark Fys 7:507–553

    MATH  MathSciNet  Google Scholar 

  • Whitfield DL, Lewis CH (1970) Boundary-layer analysis of low-density nozzles. J Spacecr Rockets 7(4):462–468

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Yang JY, Huang JC (1995) Rarefied flow computations using nonlinear model Boltzmann equations. J Comput Phys 120:323–339

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the Grant of the Government of the Russian Federation (Agreement No. 14.Z50.31.0019) for supporting research supervised by leading scientists and by the Russian Foundation for Basic Research (RFBR Project No. 12-01-00776-a).

We are deeply grateful to our colleague Dr. Alexander Kashkovsky for his consultations on the SMILE software system and numerous fruitful discussions.

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Correspondence to Anton Shershnev.

Tabulated data

Tabulated data

In this section we present tabulated data from the ESBGK computation for the centerline and angular non-dimensional distributions of gasdynamic quantities. As previously, the subscript h denotes quantities in the nozzle throat.

Table 2 Centerline non-dimensional distributions of main gasdynamic quantities in plume, ESBGK computation
Table 3 Angular non-dimensional distributions of gasdynamic quantities in plume at \(x/H = 21.8\) distance from nozzle exit, ESBGK computation

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Shershnev, A., Kudryavtsev, A. Kinetic simulation of near field of plume exhausting from a plane micronozzle. Microfluid Nanofluid 19, 105–115 (2015). https://doi.org/10.1007/s10404-015-1553-9

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