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FLOW ON THE LEEWARD SIDE OF A SUPERSONIC SOURCE IN A SUPERSONIC STREAM

International Space Science Institute Team Meeting “Modeling Cometary Environments in the Context of the Heritage of the Giotto Mission to Comet Halley” 19—24 November, 2012. FLOW ON THE LEEWARD SIDE OF A SUPERSONIC SOURCE IN A SUPERSONIC STREAM. M. G. LEBEDEV.

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FLOW ON THE LEEWARD SIDE OF A SUPERSONIC SOURCE IN A SUPERSONIC STREAM

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  1. International Space Science Institute Team Meeting “Modeling Cometary Environments in the Context of the Heritage of the Giotto Mission to Comet Halley” 19—24 November, 2012 FLOW ON THE LEEWARD SIDE OF A SUPERSONIC SOURCE IN A SUPERSONIC STREAM M. G. LEBEDEV

  2. Unexpected and interesting phenomena can occur on the leeward (night) side of a comet in the solar wind flow. One of these phenomena can be the formation of return (circulatory) flow zones. • The results of Dr. Benna’s simulation hint at this possibility

  3. Calculation of supersonic flow past a supersonic source (windward side) Formulation of the problem in the tail flow region Calculation using the Babenko—Rusanov method (1980)

  4. Calculation of the flow on the leeward side using the Godunov method . General flow pattern Streamlines Velocity profile along the axis of symmetry Longitudinal velocity and pressure distributions in the X = 39 section

  5. Calculated results Density contours Pressure contours Longitudinal velocity contours Vertical velocity contours

  6. Another (time-dependent) formulation of the same problem with the formation of the return-flow zones

  7. The similar situation can occur in subsonic flow past a supersonic source

  8. Reflection of a shock wave from the axis of symmetry in uniform, wake, and source flows

  9. Formation of return flow zones on reflection of an incident shock from the axis of symmetry in a wake-type flow 1– nozzle; 2 – flame stabilizer 3 – thermal wake from combustion 4 – shock wave 5 –recirculation zone Hydrogen burns behind a cylindrical stabilizer,G.Winterfeld,1968.

  10. Low-pressure jetlet in a supersonic underexpanded jet 1 –nozzle; 2 –jetlet; 3 –shock; 4– recirculation zone G. F. Glotov, 1994

  11. B.J. Gribben, K.J. Badcock, B.E. Richards. Numerical study of shock-reflection hysteresis in an underexpanded jet // AIAA Journal. 2000. V. 38. N. 2. P. 275—283.M. Frey. Behandlung von Strömungsproblem in Racketendüsen bei Überexpansion // Inst. für Aerodynamik und Gasdynamik, Univ. Stuttgart. Dr.-Ing. Diss. 2001. (http://elib.uni-stuttgart.de/opus/volltexte/2001/800/pdf/diss_frey.pdf)В.А. Горяйнов. О возможности реверса течения в свободных сверхзвуковых струях // Мат. моделирование. 2003. Т. 15. № 7. С. 86—92.О.В. Бочарова, М.Г. Лебедев, А.В. Савин, Е.И. Соколов. Стационарные циркуляционные зоны в сверхзвуковых неравномерных потоках // XXI Школа-семинар ЦАГИ «Аэродинамика летательных аппаратов». Тезисы докладов М.: Изд. ЦАГИ. 2010. С. ??--??. The existence of these experimentally observed structures was confirmed in numerical calculations. So far, in the case of the source-type nonuniformity analogous structures were obtained only in numerical experiments

  12. Shock reflection in imperfectly expanded jets

  13. Numerical experiment by M. Frey

  14. Our calculations of return flow zones in supersonic underexpanded jets (M = 3, n = 3.5)

  15. To confirm these results, recently we calculated some flows with the formation of circulation, or return, or reverse, zones The following numerical methods were employed 1. Godunov method (first order) 2. Method of adaptive artificial viscosity (second order of accuracy, on irregular, triangular grids) developed by I.V. Popov and I.V. Fryazinov in Keldysh Institute of Applied Mathematics. 3. Babenko—Rusanov method (shock-fitting technique of the second order of accuracy).

  16. For testing the technique the wake-type flow experimentally studied by Glotov was numerically modeled. Numerical calculation (streamlines) Glotov’s experiment

  17. Density c ontours for the above calculation

  18. The problem of supersonic spherical source flow in a cylindrical channel

  19. Calculated flow pattern at gamma = 1.4 Calculated flow pattern atgamma = 1.05

  20. Calculations by the AAV method

  21. Source flow with nonuniform angular velocity distribution (a maximum velocity is reached at the channel axis). The initial data correspond to the case of “uniform” source (gamma = 1.1). The return flow zone disappears.

  22. In this case the velocity on the axis is minimum. As a result, the return flow zone enlarges.

  23. THANK YOU

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