Nonlinear Dynamic Characteristics of Combustion Wave in SHS Process

Vol.17 No. 1Journal of Wuhan University of Technology - Mater. Sci. Ed.Mar. 2002Nonlinear Dynamic Characteristics of CombustionWave in SHS ProcessZOU Zheng-guang' ) FU Zheng-yi? ) YUAN Run-zhang2 ) MAI Li-qiang?))Guilin Institute of Technololgy ?)Wuhan University of Technology( Received :Dec.29 2000 )Abstract : The charcteristic of combustion uwaue and its change rwere analyzed by numerical value calcula-tion and computer simulaion ,based on the combustion dynamical model of SHS process. It is shorn that with thechange of condition parameters in SHS process various time- space order combustion waves appear. It is concludedfrom non-liner dynamical mechanism analysis that the strong coupling of 1too non- linear dynamical proesses is thedynamical mechanism causing the time- space order dissipation structures .Key words: SHS ; combustion ucue simulation ; disspation structure ; non-linear dynamics1 Introductionsion of substance are the two main aspects causing thechange of reactants concentration. The combustion chemi-Self-propagating High- temperature Synthesis( SHS )cal reaction decreases the reactant concentration and in-technology is a new method for synthesizing materi-creases product concentration in the reaction zone. Theals 1-31. SHS process is a complicated nonlinear one farconcentration change caused by a chemical reaction in afrom thermodynamic equilibriunt 4J. To control the processcombustion reaction process usually regarded to follow Ar-and obtain wanted high quality materials , it is necessaryrhenius form. Due to great the reaction rate and very nar-to study the nonlinear dynamical characteristics of com-row reaction zone , the effect of heat diffusion in a sub-bustion wave in SHS process in detail. In this paper thestance on concentration change in reaction zone is relativelower. Two factors cause the change of temperature in re-combustion reaction dynamical model of SHS process wafounded and the numerical value calculation and computeraction zone : exothermic combustion chemical reaction ;simulation were made on the model. The pattern thatheat conduction and heat loss. The great amount of heatcombustion wave characteristics change with parameterreleased by combustion chemical reaction in SHS processconditions was given .' The nonlinear dynamical mechanismincreases the temperature of the system. The heat conduc-of oscillatory combustion wave in SHS process wastion , heat radiation and heat convection make heat flowfrom high temperature zone to low temperature zone , andprobed.so decrease the temperature in reaction zone. Because theSHS process is a fast one , the effect of heat loss on tem-2 The Combustion Reaction Dynami-perature in reaction z2one is relatively smaller in a certaincal Model of SHS Processperiod.Consider a sample cylinder and assume that a com-Several main inreversible processes are involved inbustion reaction is from right to lef( Fig.1 ). In three di-SHS process : combustion chemical reaction , heat andmensional coordinate systen( X'1 X'2 X'3 ) ,the combus-substance transportation. The inreversible processes intion reaction dynamic characteristics of SHS process canSHS process are all controlled and effcted by reactantbe described by the basic equations :concentration and temperature change in the system.1,=-A'( T)F( Y )exp(-Dn )+Therefore the reactant concentration and temperature inJt~RT"the system are the main variables describing the state of中国煤化工2y(1)SHS system. Combustion chemical reaction and heat diffu-.MHCNMHG7=D'( T" )v2T"+ H'A'R( Y" )exp( -Rr )Z0U Zheng-guan(邹正光):Borm in 1962 ;Professor ;Ph.D ,Material Department Guilin Institute of Technology ,Guilin 541004 ,- K{ T"- T"o)- K{ T"4- T"f)(2)ChinaFunded by, the National Natural Science Foundation of Chi-Y'= Y"'o T"=T"o at X'3→_∞(3)ne( 5006200Y'=0 T'=T”at . X'3→+∞. (4)24Joumal of Wuhan University of Technology - Mater. Sci. Ed.Mar.2002In eguations( 1 H4 ),Y’is reactant concentra-Y_= 7Y2exp(-个)< 13)tion ,Y' is reactant concentration in raw mixture ,F( Y" )is a function of reactant concentration ,A' is a reactiont= Aot' T= T"/Tot' E=”。Do= D'o/A'rate constant ,T” is temperature ,T' is environment tem-AT dperature,Ea' is reaction activation energy ,Ed' is heatT=x+rrY2x(-只)-K(T*-1) (14)diffusion activation energy ,D' is cofficient of diffusion ,D' is cefficient of conduction temperature ,H' is reactionSubstitute above into equation(9H( 12):Y=YoT=1atX→-∞( 15)enthalpy ,K1 ,K2 are the coefficients of heat conductionY=0 T=TatX→+∞( 16)and heat radiation in air respectively ,R is a gas constant ,t' is time ,V2- is Laplacian.3 Calculation and Stimulation ResultsUsing different methods in a computer to resolve e-x"="[x"x')x'=S[tx'rx'zt) x"quations( 13 )- ( 16 )and stimulating the combustion wavein a computert 7 J ,we obtained the change of the tempera-ture and velocity of combustion wave under different pa-rameter conditions while the SHS process is proceeding.Reactant ZoneReaction Zone Prodluct ZontTo study the effect of parameter condition on SHSdynamical characteristics ，we investigated the changingFig. 1 Schematic representation of position relation of reactioncharacteristics of combustion wave ( stability and pulsatingzone in SHS processperiodic characteristics of combustion wave ) while changeDue to the high rate of SHS process , the effect ofone parameter with ofthers unchanged. When Do= 500 ,heat diffusion in a substance on concentration is veryd=8.4 ,K=0.22 E=20 ,H= 300 ,Yo=0.6 are fixedsmall and so is neglected generally. The heat loss by theand β is changed ,the change of combustion temperature Theat conduction of air also can be neglected because thein combustion synthesis process is presented in Fig. 2Atemperature in reaction zone is very high and heat radia-and Fig. 2B. Fig. 2A is the temperature distribution attion is the main factor causing heat loss. So equationsdifferent time along sample direction and Fig.2B is com-(1)H(4)can be witten as :bustion wave front temperature along sample direction .ay"=-A(T" )F( r" )ex(一R7) (5)Whenβ is changed from 0. 06 to 0.12.combustion waveJtfront temperature changes from steady( Fig.2A a )to pul-a Y'sating periodic characteristics( Fig. 2A b ) along sampleJt'= - D'( T" )v2T"' + H'A'F( Y')direction ;As β changes from 0.12 to 0.14 the pulsatingexp( -)- K( T4- rt)(6)frequency of combustion wave front temperature changesobviously ,that is ,the pulsating frequency decreases andY'= Y"o T"= T”。 atX'3→_∞(7)the pulsating period becomes longer( Fig.2A c);As β=Y'=0 T"=T" atX'3→+∞0.16 a clear bi-period pulsating combustion wave occursIn case of one dimension( along cylinder direction ),(Fig.2A d ). The change of β practically reflects theequations(5H(8)can be witten as :change of environment temperature and heat conductionY'_-A(T")R( yr)ex(_ E'a)cofficient . So lowering preheating ( environment ) temper-RT"ature or increasing heat conduction coefficient could causer__ axD'( T"成+ H'A'T"F( Y" )expcombustion wave change from steady flame to pulsatingflame or spinning flame .( - Rr)-KL T"4- r"t)( 10)The change of Yo also causes the change of combus-tion wave characteristics. At Do= 10 ,H=490 ,d=8.1 ,Y"'= Y'o T"= T"o atX'3-➢-∞(11 )β=0.2中国煤化工6 to0.3( Fig.3 )theY'=0 T"= T”atX'3→+∞( 12)flame ofCNMHGeS from stead(C a)toAccording to the basic relationship between chemicalperidic b ) bolpernodid c and cnaos flam( d ). The resultreaction and heat conductiorf56] ,adopt :is confirmed by experiments of combustion synthesis of Ti-D'( T)=D'dd' +pT") A'=AoT F( Y')= y2C-Fe systenf8].And introduce :The value of d has much effect on combustion waveβ= H'/r万市数据/TBAoD( T)=D{ d+βT)Y= Y'characteristics. At Yo=0.6 ,Do=500 β =0.252 ,the25Vol.17 No.1zou Zheng guang et al Nonlinear Dynamic Characteistics od..combustion wave changes from steady to unsteady flamesents the change of combustion wave velocity as d changeswith the increasingof d.( Fig.4a ford=7.92 Ab for dfrom 7.92 to 8.37.=8.1 Acfor d=8.3 Ad for d=8.37 ).Fig.5 repre-日slrendy flanea stcady flarmeb pndeating flameb pulsating flamepuleating flamed pubeating flaned buperied fanmFig.2 The numerical simulating result on conbustion wave temprature。stroaly fnmea sroly fameh palouling lunm山pulaing lame。liyorinl lam。biperinol laud tuepetiod flame小torprind far中国煤化工MYHCNMHGFig.4 The the numerical solving resul on combustion waveFig.3 The the mumerical solving reult on combustion wavetemperature26Joumal of Wuhan University of Technology - Mater. Sci. Ed.Mar. 2002constant and the combustion mode is a stable one. Whenthe parameters conditions change to some extent a smalla_ stendy fametemperature disturbance ,which can not be balanced byanother nonlinear reaction could cause combustion devel-/WWWwwwwwwwwwoping from stable to unstable. In a period one nonlinearb pulsating flamereaction plays a main role in the process . But this cannotMjMMWMWwMNcontinue limitlesly. W hen the process develops to certainstage ,another nonlinear reaction would play a main rolee bi-periodic flamneand make the process developing in another direction. Scthe strong coupling of the two nonlinear reactions causesvwMwwwwwWw.various period combustions .d tri-periodie flarne5 ConclusionFig.5 The numerical solving result on combustion wave veloci-tyBased on the of foundation of combustion dynamicalmodel combustion wave characteristics in SHS process4 Discussionwere stimulated. W hen the parameters of combustion syn-thesis change to some extent ,a stable combustion would. It is shown by the above stimulating results of com-change to periodic or chaos combustion. The two strong-bustion wave that the change of combustion wave is com-coupled nonlinear dynamical processes are the dynamicalplicated，regular and ordered. Under certain combustionmechanism causing nonlinear oscillation of combustion inconditions there could be pulsating flame , bipeoried flameSHS system.and triperiod flame. The ordered structures in SHS pro-cess are typical dissipation structures 9」. To study the de-Referencesveloping regularity of nonlinear dynamical behavior andobtain a theoretic understanding of SHS process it is nec-1 A G Merzhanov I P Borovinshaya. 'The New Class of the Com-essary to make a further study of the nonlinear dynamicalbustion Process . Combustion Sci. Tech. 1975 ,10 195mechanism that causes the complicated , regular and or-2 Wang Hao, Fu Zheng-yi ,Kostogorov E P，Yuan Run-zhang.dered behavior in SHS process .Effect of GTA on Gas Transporting SHS of TisSis. Joumal ofWuhan University of Technology-Mater. Sci. Ed. 2001 ,16( 1 ):In SHS process there are two main nonlinear pro-25-29cesses : one is that of combustion temperature and reactionrate , the other is that of heat losing rate and combustion3 Yuan Runzhang. Research on Progress in SHS Technology.Wuhan :1W uhan University of Technology Press ,1994temperature. The reaction rate increases with a rise in4 Zou Zhengguang Fu Zhengyi and Yuan Runzhang. The Dissipa-temperature and the reaction rate increase in turm resultstion Structure in SHS Materials and the Sense of the Sudy.in a temperature rise. There is a logarithm relationshipJournal of Wuhan University of Technology 1998 20( 1 )between them. On the other hand , there is another nonlin-5 Den Jingfa. Physical Chemistry. Beijing : Publishing House ofear relationship between the heat losing rate and sampleHigh Education , 1993temperature. The higher the temperature , the quicker the6 Yang Shimeng. Heat Transfer. Beijing : Publishing House of Highheat loss. Due to the strong coupling of the nonlinear re-Education , 19807 Gao Yingcai. Math-physical Equation and Its Numerical Valueactions , there are different combustion modes in SHS pro-Volving . Beijing :Publishing House of High Education ,1983cess at different parameters conditions. Under a certain8 Zou Zhengguang Fu Zhengyvi and Yuan Runzhang. The Effect ofparameter condition the two nonlinear reactions reach aComposition and Particle Size of Raw Materials on SHS ofTi- Cbalance ,that is , in reaction zone the production of heatFe system. Journal of Ilnorganic Materials ,12 2 ) ,1998and loss of heat are equal. In this case the temperature of9 Li Rusheno_ Non-ermrilihrium Thormndlynamics and Dissipationcombustion and the velocity of combustion wave remainStruc中国煤化工of Tsinghua University ,1986YHCNMHG