The evaporation process of unsymmetric dimethylhydrazine drops at their movement to the Earth's surface after seal failure of fuel tanks of launch rockets at heights up to 50 km has been simulated

Dolotov, A. E.

Kuznetsov, Geny Vladimirovich

Nemova, T. N.

Electronic archive of Tomsk Polytechnic University

Losses are also conditioned by decrease of burningsite size d at reaching the concentration limit, as1/d~S/V, where S is the site surface; V is its volume.Slight decrease of burning temperature results in drop ofheat flow from burning site but it is not capable of compensating completely the increasing losses owing todrop of velocity un and size d. This tendency, finally, results in the lowest possible temperature Tb*(σ±) and burning rate unmin(Tb*)=unmin(σ±).Power engineering45REFERENCES1. Marshal V. The main hazards of chemical industries: Translationfrom English. – Moscow: Mir, 1989. – 672 p.2. Lewis B., Elbe G. Burning, flame and explosions in gases: Translation from English. – Moscow: Mir, 1968. – 592 p.3. Williams F.A. Theory of burning: Translation from English. – Moscow: Nauka, 1971. – 615 p.4. Klimov A.M. Laminar flame in turbulent flow // Zhurnal PrikladnoyMekhaniki i Tekhnicheskoy Fiziki. – 1963. – № 3. – P. 49–58.5. Zeldovich Ya.B. Chemical physics and hydrodynamics: IzbrannyeTrudy. – Moscow: Nauka, 1984. – 347 p.6. Landau L.D., Livshits E.M. Theoretical physics. V. VI. Hydrodynamics. – Moscow: Nauka, 1986. – 733 p.7. Netleton M. Detonation in gases: Translation from English. – Moscow: Mir, 1989. – 280 p.Received on 7.12.2006Introduction The problem of air pollution with unsymmetric dimethylhydrazine (NDMG) being in tanks of liquid engines of launch rockets [1, 2] after first steps work out, isstill urgent. It is conditioned to a large scale, by the factthat a concrete mechanism of appearing this pollutanton the Earth’s surface is not determined so far. On theone side there are no direct evidences of appearing thissubstance in soil or phytocoenosis structure. On theother side, in the regions of separation of launch rocketsfirst stage (for example, Gorny Altai [3]) there areexamples of abnormal development of some biologicalsystems while there are no other negative influencingfactors on these systems. The known results of modelingthe processes of «evolution» of liquid NDMG cloud[4, 5] after seal failure of fuel tanks at heights do not allow forming the definite answer to the question ofNDGM phase state in atmosphere.The aim of this work is the numerical simulation ofevaporation process of NDMG drop at its motion to theEarth’s surface subject to inhomogeneous temperaturefield of a drop, the conditions of heat exchange with theenvironment changing in time and resistance force.Statement of a problem At problem set the assumption that NDMG drop isnot deformed at its motion and remains of spherical formduring the whole flying till the evaporation process stopwas accepted. The convective heat exchange of NDMGwith the environment the parameters of which (temperature, pressure and density) were considered to be variable in height according to distributions introduced in [6]was taken into account. Radiation heat exchange with theenvironment was not taken into account. Calculating thedrop rate of motion υ it was accepted that gravity and resistance forces of gaseous medium influence it. The convective heat exchange αNDMG with air was computedsubject to the dependence α on density ρ and rate of motion of NDMG drop υ.The special feature of the problem is a shift of thedrop external boundary because of NDMG evaporationwith time variable velocity w. Magnitude w depends ondrop surface temperature which changes nonlinearly byits motion to the Earth’s surface. The problem in suchstatement is reduced to solution of the following differential equation system with proper boundary and initial conditions.UDC 504.3.054:629NUMERICAL MODELING OF THE EVAPORATION PROCESS OF UNSYMMETRIC DIMETHYLHYDRAZINE DROPS IN THE EARTH’S ATMOSPHEREA.E. Dolotov, G.V. Kuznetsov, T.N. Nemova*Tomsk Polytechnic University*Tomsk state architecturalconstruction universityEmail: elf@tpu.ruThe evaporation process of unsymmetric dimethylhydrazine drops at their movement to the Earth’s surface after seal failure of fuel tanksof launch rockets at heights up to 50 km has been simulated.Temperature distribution at initial condition t=0,T=T0 is described by the equation of heat conductivityfor a drop in spherical form:where C(T), ρ(T), λ(T) are the temperature dependences of NDMG for heat capacity, density, heat conductivity; r is the reference radius; T is the temperature ofNDMG on radius r; t is the time.Boundary conditions:where R is the drop outer radius; α is the heat transfercoefficient; TB is the air temperature; wисп, θисп are the rate and heat of NDMG evaporation.The evaporation rate is calculated for current timevalue by the following formula:where TS is the temperature of NDMG saturation.For calculation the heat transfer coefficient with theinitial conditions υ=0, t=0 the equation of sphericaldrop motion:where g is the gravity acceleration; CD is the resistancecoefficient; ρВ, υВ are the air density and rate, was solved.The following assumptions were accepted at problem statement. The drop has spherical form and is notdeformed when flying. At fixed radius all drop pointshave one and the same temperature. The heat ofNDMG evaporation θисп is taken constant and equal theevaporation heat at initial conditions. Air rate υВ equalszero. Functions C(T), ρ(T), λ(T) are obtained by extrapolation of tabulated values [7]. Air pressure and temperature at a certain height are determined as functions ofheight obtained by interpolation of standard table datain the latitude of 45° [6]. Possible chemical interactionsof NDMG with air and water vapors were not examined.Results and discussionThe problem is solved for drops of 5 and 1 mm in diameter at their initial temperature 290 K. The change ofdrop characteristic dimensions, as it follows from thecarried analysis, should not influence significantly theNDMG phase state. It is seen how rapidly the drops of5 mm (Table 1) and 1 mm (Table 2) in diameter evaporate by the obtained dependences of drop evaporationtime on initial height.It was determined that if the seal failure occurs atheights from 50,0 to 40,7 km then NDMG evaporatesfully for drops of all sizes. From the height lower than40,7 km the drops of NDMG move to the Earth’s surface without evaporation. The stated regularities areconditioned by thermodynamics of NDMG phase transformations [7] and changes of air temperature andpressure at change of distance to the Earth’s surface [6].The numerical analysis showed that temperature difference between the drop surface and gaseous medium atd=5 mm is always higher than the same temperature difference at d=1 mm (Table 3), while the motion rate of adrop with a larger diameter exceeds the rate of the dropwith smaller diameter (Fig. 3).Table 1. Dependence of evaporation time tи of NDMG on initial height at drop diameter of 5 mmTable 2. Dependence of NDMG evaporation time tи on the initial height at drop diameter of 1 mmTable 3. Dependence of temperature difference between thedrop surface and gaseous medium on height, KThe obtained results may be explained if the dependence of heat exchange coefficient of drops with differentdiameter on the movement rate is analyzed (Fig. 4). It wasestablished that the heat exchange coefficient for a drop atd=5 mm is less than at d=1 mm. In the rang of heightchange 0<H<40 km subject to the change of rate of dropswith different diameter at height (Fig. 3), the dependences of α on movement rate were computed (Fig. 4).The dependences of temperature difference andmovement rate of NDMG drop on height (Table 3 andFig. 3) confirm the necessity of accounting temperatureradius distribution inhomogeneity at the initial movement area. The more the drop the more time is requiredfor its full warming up or cooling down.It should be noted as well that NDMG drops cannot achieve the Earth’s surface not only owing to theirHeight H, kmDrop diameter d, mm5 139,980 17,9 4,739,957 13,9 1,639,926 11,1 0,439,646 4,7 0,430,081…0,106 1,4 0,4Height H, km Drop evaporation time tи, ms50,00 0,141,60 0,240,90 0,340,75 0,440,70 0,540,00… 0,00 –Height H, km Drop evaporation time tи, ms50,00 1043,90 2041,45 2940,95 4040,75 5040,70 7040,00…0,00 –23 ( ) ,8D ÂÂCd gdt Rρυ υ υρ⋅ ⋅= − ⋅ −⋅ ⋅( ) ,Â SèñïèñïT Tw α θ⋅ −=0, 0;, ( ) ( ) ,Â èñï èñïTrrTr R T T w Trα θ λ∂= =∂∂= ⋅ − − ⋅ = ⋅ ∂222( ) ( ) ( ) ( ) ,T T TC T T Tt r rrρ λ∂ ∂ ∂⋅ ⋅ = ⋅ + ⋅∂ ∂∂Bulletin of the Томsк Pоlytеchnic University. 2007. V. 311. № 446evaporation but due to air resistance. So, the less thedrop diameter, the longer it can move to the Earth’s surface (Fig. 5).Fig. 3. Dependence of NDMG drop movement rate on theheight at drop diameter, mm: 1) 5; 2) 1Fig. 4. Dependences of heat exchange coefficients of dropswith different diameter on movement rate at drop diameter, mm: 1) 5; 2) 1The stated dependence (Fig. 5) shows that NDMGmay be distributed over rather long distances being inliquid state. So, for example, a drop of a starting diameter 1 mm at rather moderate wind velocity at heights10 m/s may shift to the distance to 50 km from the place of fuel tank seal failure. The drops with smaller diameters stay longer in the air and, therefore, shifted by airmass to the longer distances.The theoretical results obtained in this work showthat the mechanism of NDMG transformations at itsmotion to the Earth’s surface is rather complex. Phasestates of this substance depend on many factors and further analysis of the most probabilistic scenarios of physicochemical drop transformation of the liquid NDMGdrops at the movement in the air is appropriate. Account of all features of NDMG drop warming up andevaporation may increase considerably the accuracy ofprediction of air pollution in the area of separation ofthe launch rocket first stages.Fig. 5. Dependence of drop height over the Earth’s surface ontime at drop diameter, mm: 1) 5; 2) 1Conclusion It was shown that unsymmetric dimethylhydrazineevaporates fully at seal failure of launch rocket fuel tanksat heights from 50,0 to 40,7 km at its initial temperature 290 К. Starting from height about 40 km the NDMGstops evaporating and moves to the Earth’s surface inliquidphase state. NDMG phase state depends to thelarge extent on seal failure height and initial temperature. Drop evaporation rate depends on its diameter. According to the calculation results the evaporation timefor a drop of a diameter 5mm is two orders higher thanfor a drop of diameter 1mm. The time of achieving theEarth’s surface by drops of diameter 1 mm exceeds twice the respective time for drops of diameter 5 mm.The work was fulfilled at financial support of the RFBR (projectcode №060800873а).Power engineering47REFERENCES1. Ecological problems and risks of the influence of spacerocketequipment on the environment: Reference book / Ed. by V.V. Aldushin, S.I. Kozlov, A.V. Petrov. – Moscow: ANKIL, 2000. – 600 p.2. Arkhipov V.A., Berezikov A.P., Kozlov E.A. et al. Technogenic pollution modeling at separation of launch rocket stages // Izvestiya Vuzov. Fizika. – 2005. – № 11. – P. 5–9.3. Streltsova T.A., Ushakova G.V., Cherdantseva O.I. et al. Modelingthe NDMG influence on domestic plants // Fundamental problemsof environment conservation and ecology of natural territorial complexes in western Siberia: Materials of scientific conference. – GornoAltaisk, 2000. – P. 123–125.4. Arkhipov V.A., Berezikov A.P., Kozlov E.A. et al. Modeling the formation and evolution processes of liquiddrop cloud at seal failure ofrocket fuel tanks in atmosphere // Fundamental problems of environment conservation and ecology of natural territorial complexes inwestern Siberia: Materials of scientific conference. – GornoAltaisk.– 2000. – P. 78–79.5. Nemova T.N., Kuznetsov G.V., Mamontov T.Ya., Bulba E.E. Numerical simulation of dimethylhydrazine drop state at motion from upper air to the Earth’s surface // Izvestiya Vuzov. Fizika. – 2006. –№ 6. – P. 112–115.6. GOST 2463181 State standard of SSR union. Reference atmosphere. Parameters. State standards committee of the USSR. Moscow.7. Bolshakov G.F. Chemistry and technology of liquid fuel components. – Leningrad: Khimiya, 1983. – 320 p., ill.Received on 15.10.2007

Numerical modeling of the evaporation process of unsymmetric dimethylhydrazine drops in the Earth's atmosphere

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