About an opportunity of use of the catastrophe theory for definition of influence of microgravitation on burning in space systems

Paper number

IAC-08.C4.2.14

Author

Mr. Konstantin Prisniakov, Institute of Geotechnical Mechanics, National Academy of Sciences, Ukraine

Coauthor

Prof. Vladimir Prisniakov, Academy of Sciences of Ukraine, Ukraine

Year

2008

Abstract

Burning in space-rocket systems is used basically in chemical rocket engines, and in conditions of essential overloads that does not result in any problems. But at microgravitation the starting of rocket engines is a challenge which demands knowledge of laws of burning at weak gravitational fields. Similar tasks arise and at calculations of processes of burning on a spacecraft. Burning and gasification represent spasmodic transition of a liquid phase or of a solid  phase in gaseous one. The theoretical description of process of burning (and of gasifications) is connected to the big difficulties. Specific speed of interaction of a solid or liquid phase j with the oxidizing environment depends basically on temperature T, from speed of a gas flow w (which determines the factor of the heat and  mass transfer ? between liquid or solid phases with surrounding gas), and from pressure p. In conditions of microgravitation the heat and  mass transfer is determined by number Grasgophe which depends on overloads in a power1/4. Paper is demonstrated, that dependence j = j (T, ?(w), p) corresponds in mathematical to expression to catastrophe of type cusp at influence of speed of a flow:
(j+?w?T2)(1/?T–?)=cww
Consideration of the determining influence of two competing factors (of speed of a flow of firm particles or drops and temperatures or pressure and temperatures) for specific speed of burning has allowed to show by means of catastrophe of type of cusp of the degeneration of a minimum and a maximum, that in the corresponding experiments was not observed in general. Parameters of the critical point being the center of an existent for assembly are determined: jc= ?w,p/(27?2); ?Tc =1/3?; wc= 8?/(27?cw); pc= 8?/(27?cp)..
Here a under critical values of variables are understood in not thermodynamic sense, and in mathematical one as the center of assembly. Use of analytical expressions for definition of speed of burning allows to find critical values of parameters at which there is a reduction of speed of burning, i.e. to control by the process of the burning with taking into account of size of a pressure of a gravitational field.  The presence of a maximum and a minimum on a curve j=j(T, w) opens opportunities for maintenance of steady or unstable burning (at the consideration, for example, of a fire on a spacecraft)  by change of speed of a flow moreover. 
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Abstract document

IAC-08.C4.2.14.pdf

Manuscript document

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