Numerical Analysis of Rarefied Gas Flow through a System of Short Channels

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Abstract

The S-model kinetic equation is used to study the rarefied gas flow from a high-pressure tank to a low-pressure one through a flat membrane with a finite number of pores. The kinetic equation is solved numerically using a second-order accurate implicit conservative method implemented in the in-house code Nesvetay. For transitional and continuum flow regimes, numerical solutions of the compressible Navier–Stokes equations are obtained. The gas flow rate through the system of pores and the forces acting on the membrane bars are investigated as functions of the Knudsen number (Kn) at a pressure ratio of 2 : 1 in the tanks. The features of the flow field near the membrane and away from it are described.

About the authors

I. V. Voronich

Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences

Email: i.voronich@frccsc.ru
119333, Moscow, Russia

V. A. Titarev

Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333

Author for correspondence.
Email: vladimir.titarev@frccsc.ru
119333, Moscow, Russia

References

  1. Sharipov F., Seleznev V. Data on internal rarefied gas flows // J. Phys. Chem. Ref. Data. 1997. V. 27. № 3. P. 657–706.
  2. Sharipov F., Seleznev V. Flows of rarefied gases in channels and microchannels. Russian Academy of Science, Ural Branch, Institute of Thermal Physics, 2008. in Russian.
  3. Titarev V.A., Shakhov E.M. Nonisothermal gas flow in a long channel analyzed on the basis of the kinetic S‑model // Comput. Math. and Math. Phys. 2010. V. 50. № 12. P. 2131–2144.
  4. Pantazis S., Valougeorgis D. Rarefied gas flow through a cylindrical tube due to a small pressure difference // Eu-rop. J. Mech. / B Fluids. 2013. V. 38. P. 114–127.
  5. Valougeorgis D., Vasileiadis N., Titarev V. Validity range of linear kinetic modeling in rarefied pressure driven single gas flows through circular capillaries // Europ. J. Mech. / B Fluids, Special Issue on Non-equilibrium Gas Flows. 2017. V. 64. P. 2–7.
  6. Varoutis S., Valougeorgis D., Sharipov F. Simulation of gas flow through tubes of finite length over the whole range of rarefaction for various pressure drop ratios // J. Vac. Sci. Technol. A. 2009. V. 27. № 6. P. 1377–1391.
  7. Aristov V.V., Frolova A.A., Zabelok S.A., Arslanbekov R.R., Kolobov V.I. Simulations of pressure-driven flows through channels and pipes with unified flow solver // Vacuum, Special Issue “Vacuum Gas Dynamics: Theory, experiments and practical applications”. 2012. V. 86. № 11. P. 1717–1724.
  8. Varoutis S., Day C., Sharipov F. Rarefied gas flow through channels of finite length at various pressure ratios // Vacuum. 2012. V. 86. № 12. P. 1952–1959.
  9. Titarev V.A., Shakhov E.M. Computational study of a rarefied gas flow through a long circular pipe into vacuum // Vacuum, Special Issue “Vacuum Gas Dynamics: Theory, experiments and practical applications”. 2012. V. 86. № 11. P. 1709–1716.
  10. Shoev G.V., Bondar Y.A., Khotyanovsky D.V., Kudryavtsev A.N., Ivanov M.S., Maruta K. Numerical study of shock wave entry and propagation in a microchannel // Thermophys. Aeromech. 2012. V. 19. № 1. P. 17–32.
  11. Titarev V.A. Rarefied gas flow in a circular pipe of finite length // Vacuum. 2013. V. 94. P. 92–103.
  12. Titarev V.A., Shakhov E.M. Rarefied gas flow into vacuum through a pipe composed of two circular sections of different radii // Vacuum. SI “Advances in Vacuum Gas Dynamics”. 2014. V. 109. P. 236–245.
  13. Dou H., Xu Mi, Wang B., Zhang Z., Wen G., Zheng Y., Luo D., Zhao L., Yu A, Zhang L., Jiang Z., Chen Z. Microporous framework membranes for precise molecule/ion separations // Chemic. Soc. Rev. 2021. V. 50. P. 986–1029.
  14. Taassob A., Bordbar A., Kheirandish S., Zarnaghsh A., Kamali R., Rana A.S. A review of rarefied gas flow in irregular micro/nanochannels // J. Micromechan. and Microengineer. 2021. V. 31. P. 113002.
  15. Wu L., Ho M., Germanou L., Gu X., Liu C., Xu K., Zhang Y. On the apparent permeability of porous media in rarefied gas flows // J. Fluid Mech. 2017. V. 822. P. 398–417.
  16. Popov S.P., Tcheremissine F.G. Subsonic rarefied gas flow over a rack of flat transverse plates // J. Appl. Mech. and Tech. Phys. 2008. V. 49. № 1. P. 46–52.
  17. Plotnikov M.Yu. Hydrogen dissociation in rarefied gas flow through a wire obstacle // J. Appl. Mech. and Tech. Phys. 2018. V. 59. № 5. P. 794–800.
  18. Shakhov E.M. Approximate kinetic equations in rarefied gas theory // Fluid Dynamic. 1968. V. 3. № 1. P. 112–115.
  19. Shakhov E.M. Generalization of the Krook kinetic relaxation equation // Fluid Dynamic. 1968. V. 3. № 5. P. 95–96.
  20. Titarev V.A. Computer package Nesvetay-3D for modelling three-dimensional flows of monatomic rarefied gases // Science & Education. Scientifical periodic of the Bauman MSTU. 2014. № 6. P. 124–154.
  21. Konopel’ko N.A., Titarev V.A., Shakhov E.M. Unsteady rarefied gas flow in a microchannel driven by a pressure difference // Comput. Math. and Math. Phys. 2016. V. 56. № 3. P. 470–482.
  22. Titarev V.A. Implicit numerical method for computing three-dimensional rarefied gas flows using unstructured meshes // Comput. Math. and Math. Phys. 2010. V. 50. № 10. P. 1719–1733.
  23. Titarev V.A. Application of model kinetic equations to hypersonic rarefied gas flows // Computers and Fluids, Special issue “Nonlinear flow and transport”. 2018. V. 169. P. 62–70.
  24. Titarev V.A. Application of the Nesvetay node for solving three-dimensional high-altitude aerodynamics problems // Comput. Math. and Math. Phys. 2020. V. 60. № 4. P. 737–748.
  25. Titarev V.A., Morozov A.A. Arbitrary Lagrangian-Eulerian discrete velocity method with application to laser-induced plume expansion // Appl. Math. and Comput. 2022. V. 429. P. 127241.
  26. Колган В.П. Применение принципа минимальных значений производной к построению конечно-разностных схем для расчета разрывных течений газовой динамики // Уч. зап. ЦАГИ. 1972. Т. 3. № 6. С. 68–77.
  27. Kolgan V.P. Application of the principle of minimizing the derivative to the construction of finite-difference schemes for computing discontinuous solutions of gas dynamics // J. Comput. Phys. 2011. V. 230. № 7. P. 2384–2390.
  28. van Leer B. Towards the ultimate conservative difference scheme V: a second order sequel to Godunov’s method // J. Comput. Phys. 1979. V. 32. P. 101–136.
  29. Titarev V.A. Conservative numerical methods for model kinetic equations // Computers and Fluids. 2007. V. 36. № 9. P. 1446 – 1459.
  30. Bhatnagar P.L., Gross E.P., Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems // Phys. Rev. 1954. V. 94. № 511. P. 1144–1161.
  31. Mieussens L. Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries // J. Comput. Phys. 2002. V. 162. № 2. P. 429–466.
  32. Gusarov A.V., Smurov I. Gas-dynamic boundary conditions of evaporation and condensation: numerical analysis of the Knudsen layer // Phys. Fluids. 2002. V. 14. № 12. P. 4242–4255.
  33. Yoon S., Jameson A. Lower-upper symmetric-gauss-seidel method for the Euler and Navier Stokes equations // AIAA J. 1988. V. 26. № 9. P. 1025–1026.
  34. Men’shov I.S., Nakamura Y. An implicit advection upwind splitting scheme for hypersonic air flows in thermochemical nonequilibrium // A Collection of Technical Papers of 6th Int. Symp. on CFD. V. 2. P. 815. Lake Tahoe, Nevada, 1995.
  35. Titarev V.A., Dumbser M., Utyuzhnikov S.V. Construction and comparison of parallel implicit kinetic solvers in three spatial dimensions // J. Comput. Phys. 2014. V. 256. P. 17–33.
  36. Titarev V.A., Utyuzhnikov S.V., Chikitkin A.V. OpenMP + MPI parallel implementation of a numerical method for solving a kinetic equation // Comput. Math. and Math. Phys. 2016. V. 56. № 11. P. 1919–1928.
  37. Gorobets A.V. Parallel Algorithm of the NOISEtte Code for CFD and CAA Simulations // Lobachevskii J. Math. 2018. V. 39. № 4. P. 524–532.
  38. Gorobets A.V., Duben A.P. Technology for supercomputer simulation of turbulent flows in the good new days of exascale computing // Supercomputing Frontiers and Innovation. 2021. V. 8. № 4. P. 4–10.
  39. Alvarez-Farre X., Gorobets A., Trias F.X. A hierarchical parallel implementation for heterogeneous computing. Application to algebra-based CFD simulations on hybrid supercomputers // Comput. and Fluid. 2021. V. 214. P. 104768.
  40. Titarev V.A., Utyuzhnikov S.V., Shakhov E.M. Rarefied gas flow through a pipe of variable square cross section into vacuum // Comput. Math. and Math. Phys. 2013. V. 53. № 8. P. 1221–1230.
  41. Titarev V.A., Shakhov E.M. Unsteady rarefied gas flow with shock wave in a channe // Fluid Dynamic. 2018. V. 53. № 1. P. 143–151.
  42. Titarev V.A., Frolova A.A., Rykov V.A., Vashchenkov P.V., Shevyrin A.A., Bondar Ye.A. Comparison of the Shakhov kinetic equation and DSMC method as applied to space vehicle aerothermodynamics // J. Comput. Appl. Math. 2020. V. 364. P. 1–12.
  43. Titarev V.A., Shakhov E.M. A hybrid method for the computation of a rarefied gas jet efflux through a very long channel into vacuum // Comput. Math. and Math. Phys. 2020. V. 60. № 11. P. 1936–1949.
  44. Ansys CFX – Solver Theory Guide. Release 2021R2. Ansys, Inc. 2021.
  45. Barth T., Jespersen D.C. The design and application of upwind schemes on unstructured meshes // AIAA paper 89-0366. 1989.
  46. Rao S.S. The Finite Element Method in Engineering. 6th ed. Elsevier, 2018.
  47. Ansys ICEM CFD Help Manual, version 2021 R2. 2021.
  48. Frolova A.A. Analysis of the boundary conditions for rarefied molecular gases with partial accommodation coefficients and energy exchange // Comput. Math. and Math. Phys. 2021. V. 61. № 10. P. 1672–1681.
  49. Koshamarov Yu.A., Ryzhov Yu.A. Applied Rarefied Gas Dynamics. Moscow, Mashinostroenie, 1977. in Russian.

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Copyright (c) 2023 И.В. Воронич, В.А. Титарев

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