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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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
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)
Calculation of the flow on the leeward side using the Godunov method
General flow pattern
Velocity profile along the axis of symmetry
Longitudinal velocity and pressure distributions in the X = 39 section
Longitudinal velocity contours
Vertical velocity contours
The similar situation can occur in subsonic flow past a supersonic source
Reflection of a shock wave from the axis of symmetry in uniform, wake, and source flows
Formation of return flow zones on reflection of an incident shock from the axis of symmetry in a wake-type flow
2 – flame stabilizer
3 – thermal wake from combustion
4 – shock wave
5 –recirculation zone
Hydrogen burns behind a cylindrical stabilizer,G.Winterfeld,1968.
Low-pressure jetlet in a supersonic underexpanded jet shock from the axis of symmetry in a wake-type flow
4– recirculation zone
G. F. Glotov, 1994
B.J. Gribben, K.J. Badcock, B.E. Richards. shock from the axis of symmetry in a wake-type flow 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
Numerical experiment by M. Frey shock from the axis of symmetry in a wake-type flow
Our calculations of return flow zones in supersonic underexpanded jets (M = 3, n = 3.5)
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).
For testing the technique the wake-type flow experimentally studied by Glotov was numerically modeled.
Numerical calculation (streamlines)
Density c ontours for the above calculation studied by Glotov was numerically modeled.
The problem of supersonic spherical source flow in a cylindrical channel
Calculated flow pattern atgamma = 1.05
Source flow with nonuniform angular velocity distribution cylindrical channel(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.
THANK YOU result, the return flow zone enlarges.