STRONG EXPLOSION MODEL OF GAS DYNAMICS OF A ROCKET PLUME IN THE UPPER ATMOSPHERE

A.G. Molchanov, Yu.V. Platov

Typical value of combustion products pressure on a nozzle exit section of the rocketengine, operating in the upper atmosphere, makes ~ 0.005 MPa. As a pressure of an ambient gas on heights above 120 km is 10-2 Pa the underexpantion factor n= Pe /P , i.e. a ratio of gas pressure at a nozzle edge to an ambient gas pressure, may achieve a value ~105-107. Such a ratio of gas pressures should lead to the phenomena typical to a strong explosion in perpendicular to a rocket motion direction, namely, a formation of strong shock waves and gas expansion with the velocities up to 3-5 km/s.

The development of shock waves are conformed by numerous optical observations

L~50 km

L300 km

SC “Sirius”

“Minotaur”

L~ 30 km

“MOLNIJA”

“Spherical” gas-dust cloud produced after solid fuel rocket stages separation

in the upper atmosphere

Region (1) is nearest to the rocket region with a complex structure of the shock waves. Region (2) may be called a region of a cylindrically symmetric explosion. It is characterized by almost a free gas expansion in a transversal direction and may occupy from tens to hundreds kilometers. In region (3), the pressure of combustion products becomes comparable with the ambient pressure, PpP. This region may extend to some hundreds kilometers.

Solid fuel rocket, All Sky camera, time interval is 1 minute.

Development of gas dust rocket cloud. The expansion speed is ~ 3 km/s

Region (1) was studied in detail by Draper at al. In this work, we investigate a structure of a rocket plume in region (2). A radial expansion of a plume was described Earlier as the self-similar solutions for a cylindrically symmetric point-like explosion.

r = C1 t1/2 , V = C2 / t1/2, P = C3 / t

However that the self-similar solutions are not suitable for an accurate description of large central parts of a plume and large parts of the space where the ambient medium pressure is to be taken into account. We had to undertake the numerical calculations basing on 3T 1D gas dynamic equations in a cylindrically symmetric geometry in order to describe in detail a motion of combustion products.

A supersonic jet in a wake hypersound underexpanded flow may also be considered as a streamline flow of a body with the characteristic transversal R and longitudinal X dimensions,

R=re (Me/M) (e n/ ), X=R/θ, θ = {2/[e (e +1) Me + Sin2 e /2} 1/2

where ; re and e are the nozzle radius and the tilt angle of the exit gas velocity vector, respectively; e, , the exhaust specific heat ratio, and Me and M , the exit and ambient Mach numbers, respectively.

The velocity of a transversal plume expansion reach ~4 km/sec, during the first few seconds, and the motion itself is sufficiently accurately described by the self-similar approximation. After 25 seconds of an expansion, there starts a strong difference in thenumerical solution which takes into account an ambient gas pressure and a self-similar approximation.

Near the rocket trajectory there may be formed the gasdynamic holes, in which the gas concentration is less than the ambient gas concentration. Such regions should follow a rocket by forming a gasdynamic bubble whose cross-section increase with altitude. A total volume of such region may achieve 104-105 кm3.

Results

References[1] Draper J.S., Bien F., Huffman R.E., Paulsen D.E., Rocket Plumes in the Thermosphere AIAA J 1975;13: 825-827.[2] Draper J.S., Sutton E.A. Nomogram for High-Altitude Plume Structures J. Spacecraft 1973;10: 682-684.[3] Boynton F.P. Highly Underexpanded Jet Structure: Exact and Approximate Calculations, AIAA J 1967; 5: 1703-1704.[4] Ivlev L.S., Romanova V.I., Model of a Gas and Dust Cloud of a Rocket Exhaust at High Altitudes, Optics of Atmosphere fnd Ocean (in Russian) 1993; 6: 458-468.[5] Korobeynikov V.P. Problems of the Theory of Point Explosion (in Russian), Nauka, Moscow, 1985.[6] Khramov G.A., Chekmarev S.F., Efflux Similarity of Highly Underexpanded Gas Jet in Accompaying Hypersound Flow, Izvestiya Acad. Sci., ser. Mech. Jidk. Gas. (in Russian) 1982; 4: 113-120.[7] Wu BJC. Possible Water Vapor Condensation in Rocket Exhaust Plume. AIAA J 1975: 13(6): 797-802.[8] Allen C.W., Astrophysucal quantities, Unuversity of London, The Athlone Press, 1973.[9] Adushkin VV, Kozlov SI, Petrov AV. Ecological problems and risks of influence of space-rocket technique on environment.Handbook Ed., Russia, Moscow, 2000. [10] Karlov V.D., Kozlov S.I., Tkachev G.N. Large-scale disturbances in the ionosphere, occurring during the flight of rocket with the working engine, Kosmicheskie issledovanija (Russia) 1980; 18(2): 266-274.[11] Y.V. Platov, S.A. Chernouss, M.J. Kosch., Classification of Gas-Dust Formations from Rocket Exhaust in the Upper Atmosphere, Journal of Spacecraft and Rockets 2004; 41(4): 667-670.[12] Platov Yu.V. Condensation of combustion products in rocket engines exhaust in the upper atmosphere Recent Patents on Space Technology 2011; 1(1): 46-50.

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“Spherical” gas-dust cloud produced after solid fuel rocket stages separation in the upper atmosphere