flow on the leeward side of a supersonic source in a supersonic stream
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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. - PowerPoint PPT PresentationTRANSCRIPT
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
M. G. LEBEDEV
• 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
Calculation using the Babenko—Rusanov method (1980)
Calculation of supersonic flow past a supersonic source (windward side)
Formulation of the problem in the tail flow region
Streamlines General flow pattern
Velocity profile along the axis of symmetry
.
Calculation of the flow on the leeward side using the Godunov method
Longitudinal velocity and pressure distributions in the X = 39 section
Calculated results
Density contours Pressure contours
Longitudinal velocity contoursVertical velocity contours
Another (time-dependent) formulation of the same problem with the formation of the return-flow zones
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
11 – nozzle– nozzle; ; 2 2 – flame stabilizer– flame stabilizer3 3 – thermal wake – thermal wake from combustionfrom combustion4 4 – shock wave– shock wave5 5 –recirculation –recirculation zonezone
Hydrogen burns behind a cylindrical stabilizer, G.Winterfeld,1968.
Formation of return flow zones on reflection of an incident Formation of return flow zones on reflection of an incident shock from the axis of symmetry in a wake-type flowshock from the axis of symmetry in a wake-type flow
1 1 –– nozzle; nozzle; 22 – – jetlet; jetlet; 33 – – shock;shock;44 –– recirculation recirculation zonezone
G. F. Glotov, 1994
Low-pressure jetlet in a supersonic Low-pressure jetlet in a supersonic underexpanded jetunderexpanded jet
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
Shock reflection in imperfectly expanded jets
Numerical experiment by M. Frey
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)Glotov’s experiment
Density c ontours for the above calculation
The problem of supersonic spherical source flow in a cylindrical channel
Calculated flow pattern at gamma = 1.4
Calculated flow pattern atgamma = 1.05
Calculations by the AAV method
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.
In this case the velocity on the axis is minimum. As a result, the return flow zone enlarges.
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