Detonation. Joint Summer School on Fuel Cell and Hydrogen Technology September 18-22, 2011, Crete, Greece

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1 Joint Summe School on Fuel Cell and Hydogen Technology Septembe 8-, 0, Cete, Geece Detonation Gaby Ciccaelli Queen s Univesity Kingston, Ontaio Canada

2 Hydogen explosion in nuclea powe plants a majo concen

3 Detonation? Fuushima nuclea powe plant post hydogen explosion, 0 3

4 Content -D detonation - Chapman Jouguet model - Unsteady ZND model - Tansient model Real detonations - cellula stuctue - detonation initiation - deflagation-to-detonation tansition (DDT) 4

5 -D Detonation waves 5

6 6 -D Combustion Wave Analysis u u R,, T R,, T ) ( h u h u u u u u u Steady-state combustion occus within the contol volume and equilibium is achieved at state Fo pefect gas K T T T c h h RT o o p o f 0 whee ) ( and Enegy equation o f o h f h q T c u q T c u p p whee chemical enegy pe unit mass Have 5 unowns (,,T, u, u ) and only 4 equations

7 7 Combining consevation of mass and momentum yields the Rayleigh eqn u u Combining consevation of momentum and enegy yields the Hugoniot eqn ) ( ) ( ) ( q q T c T c p p If it is assumed that thee is no change in the specific heat ( = =): sensible enegy content initial enegy eleased chemical ) ( T c q q v whee q = 0 gives the shoc Hugoniot ) ( q

8 Hugoniot Cuves fo Combustion Waves ossible solutions CV q C The Hugoniot equation gives all possible end states fo given heat elease q including constant volume (CV) and pessue (C) 8

9 9 / (s -s )/c p q ln ln ln ln ln p p T T c R T T c s s Second Law equies that s -s 0, Entopy Change Acoss Combustion Wave / <, / > deflagation waves Fo q > 0 can have expansive and compessive combustion waves : / >, / < detonation waves Can only have compessive shoc (q=0) 0 q

10 Classical -D Detonation Wave Detonation pocess consists of shoc compession followed by enegy elease, equilibium achieved at the end of the eaction zone u u =D VonNeuman state Equilibium Hugoniot (q 0) Shoc Hugoniot (q = 0) Rayleigh line (slope popotional to D) ' ' 0

11 Classical -D detonation stuctue The Rayleigh line intesects the Hugoniot cuve at two points so thee ae two possible end states fo a given detonation velocity: Stong (ovediven) detonation wave (state ): - flow is subsonic elative to wave (u <c ) - solution is unstable because expansion waves catch up to the font and weaen the lead shoc wave u=0 D Wea detonation (state ): - flow is supesonic elative to wave (u >c ) - solution not possible because all of the enegy is eleased at state, also entopy dops fom state to violates nd Law

12 Classical -D detonation stuctue Unique solution coesponds to the point whee the Rayleigh Line is tangent to the Hugoniot cuve, the Chapman-Jouget (CJ) state CJ CJ state CJ

13 CJ Detonation State At the time of Chapman 899 it was believed that enegy elease in a detonation occued instantaneously, i.e., no eaction zone pesent Chapman stated that since the Rayleigh line going though the CJ state epesents the minimum velocity detonation it must be stable This was suppoted by the fact that the measued detonation velocity ageed vey well with the CJ theoy, i.e, the measued detonation velocity depends on the enegy eleased q and not the ate of chemical eaction. 3

14 4 The CJ state also epesents the downsteam state that has a minimum entopy ise acoss the wave. ln ln c s s p The minimum is detemined as follows: 0 / / / / / / d d d c s d p Diffeentiating the Hugoniot equation to get yields: / / d d / / min s Can use this to obtain jump elations acoss the detonation wave.

15 5 / / / / / / M u Fom the Rayleigh equation and u = u Substituting / / min s yields M = At the CJ state the flow is choed (u =c ) at the end of eaction zone Rayleigh Line is tangent to isentope as well as Hugoniot cuve D>c M = M< q (enegy equied to choe flow) Jouget (97) pointed out that because of this distubances fom behind cannot ente the eaction zone and thus this is a stable solution

16 6 Solve fo the density atio by equating the pessue atio in the Rayleigh and Hugoniot equations: M q M M Note fo a given font velocity M thee ae two possible solutions: (+) fo wea solution and ( ) fo stong solution q q q M M q M CJ CJ CJ 0 CJ Velocity c q q whee Unique solution obtained when squae oot tem is set to zeo (CJ state)

17 Again thee ae two solutions, (+) fo tangency at uppe detonation banch and (-) fo tangency at lowe deflagation banch. CJ det Detonation banch M > M = > > CJ defl Deflagation banch M < M = < < CJ det CJ defl 7

18 8 Appoximate CJ state elations s m q u q M M q M q M CJ CJ CJ CJ / Note, M CJ 8, q 80 so (/M CJ ) << Theefoe, the detonation velocity only depends on the specific enegy q Fo stong detonation / >>, / / min u u u CJ CJ CJ s (=., q=80)

19 Can calculate CJ detonation popeties using chemical equilibium codes such as STANJAN, GASEQ 9

20 ZND Detonation Model 940 s Zeldovich, vonneuman and Doing independently developed the idea that a detonation wave consists of a shoc wave followed by an inviscid eaction zone teminating at a sonic CJ plane (flow is steady) CJ-plane Reaction zone Shoc T CJ D T S S CJ M CJ = M D 6 M S < 0

21 Detonation Velocity Deficit Expeimentally measued detonation velocity is typically -3% below theoetical CJ value, the velocity deficit is invesely popotional to the initial pessue and the tube diamete Zeldovich poposed that the deficit is due to momentum and heat losses within the eaction zone d dx d dx u h u d u 0 dx w u R d q Q dx R c D R w fiction facto w : wall shea stess (= fu D ) q c : wall heat flux : eaction pogess vaiable Zeldovich theoy pedicts that velocity deficit should be popotional to the wall dag divided by the momentum flux: dag ~ D/R

22 osition of CJ lane Conside a simple eaction (R ): h= h(,,) also =RT whee is the eaction pogess d h d h d h dh,,, Combining with the consevation equations fo diveging channel h u h A d h d h d ln Can show that the denominato becomes zeo when but, denominato equals zeo when u= c (CJ condition), s d d u, c d d s

23 Fo the pessue gadient at the sonic plane (u=c) to be finite, the numeato must appoach zeo Theefoe, the CJ plane is located whee h h d d ln A Fo a constant aea duct d(lna)=0 the CJ plane is located whee this is the point whee chemical equilibium is eached dh 0 d Note, theoetically equilibium is appoached asymptotically so it is difficult to identify the CJ plane With flow divegence sonic plane eached befoe chemical equilibium so enegy deposited afte choing is lost since it can t feed into the eaction smalle q yields smalle D 3

24 -D Steady Detonation Wave Stuctue Hugoniot analysis assumes steady-state and pedicts detonation velocity and change in popeties fom initial state to the equilibium CJ state. No nowledge of the details of the chemisty is equied In ode to model the eaction zone details an additional equation fo the change in species with time is equied: d dt E RT exp is the eactant mass faction Knowing the post shoc state can integate the steady consevation and above equation get change in popeties though the eaction zone CJ-plane Shoc T CJ T S T 4

25 D Since the post shoc flow Mach numbe asymptotes to unity use point of maximum heat elease (induction length) to define the detonation eaction zone length, D. 5

26 Steady Detonation Reaction Zone Length Appoximation: assume constant volume combustion in eaction zone, don t need to conside consevation of momentum. Solve the tansient enegy equation with eaction equation to get tempeatue vs time and get t M coesponding to dt/dt max D= u sh t M Validity of this appoximation based on steepness of the Rayleigh Line CJ small 6

27 Flow behind steady detonation wave A detonation popagating fom the closed end of the tube is followed by an unsteady expansion wave (called the Taylo wave) whose ole is to bing the flow to est nea the closed end of the tube. The pessue, tempeatue, and flow velocity decease though the Taylo wave. 0.4

28 educed activation enegy (E a /RT ) Stability of D Detonation Wave Epenbec (960s) showed using petubation theoy that the steady ZND detonation wave stuctue is unstable to infinitesimal longitudinal petubations UNSTABLE STABLE Q/RT =50 and =. Degee of ovedive (f=d/d CJ ) 8

29 -D Tansient Detonation Wave Ficet and Woods (966) calculated the time-evolution of eaction zone using the tansient equations and a simple one-step eaction Detonation initiated by a piston poducing an ovediven detonation wave. f=(d/d CJ )=.6, Q/RT =50 and =. 9

30 -D Tansient Detonation Wave f=(d/d CJ )=.6, Q/RT =50 and =. Reaction 99% complete

31 Real detonation waves 3

32 Multi-dimensional Detonation Wave Stuctue White s (96) intefeogams showed that the detonation wave stuctue is tansient and multi-dimensional. Tansvese Shoc wave Cougated lead Shoc wave = atm H +O +0.9Xe =0.04 atm White DR. Tubulent stuctue of gaseous detonations. hys Fluids 96; 4(4) 3

33 Multi-dimensional Detonation Wave Stuctue Denisov and Toshin (96) used the soot foil technique to investigate the detonation font stuctue steamline Tansvese wave Incident wave Tiple-point tajectoy Mach stem Based on conveging and diveging lines they descibed the stuctue of the detonation wave as two tiple-point configuations ABK Denisov YN, Toshin YK. On the mechanism of detonative combustion. oc Combust Inst, 8, 96 33

34 Detonation Font Tiple-point Configuation 50% nitogen dilution no dilution 40% agon dilution H + ½O at 0. atm The highe the value E a /RT, T is the post shoc tempeatue, the moe iegula the cellula patten. T popotional to heat capacity of diluent R.A. Stehlow, The natue of tansvese waves in detonations, Astonautica Acta 4,969 34

35 Detonation Cellula Stuctue Stat of exothemic eaction 35

36 Detonation cell shoc dynamics l.6d CJ D CJ M tw. 0.6D CJ x/l C 36

37 l pecompessed detonation tajectoy M t L t 0.8 > t L t 0.8 RZ I x/l C

38 Multi-dimensional Reaction Zone aticle tajectoy Buned gas Austin JM, intgen F, Shephed JE. Reaction zones in highly unstable detonations. oc Combust Inst, 30,

39 Measued and edicted Detonation Cell Size (effect of tempeatue) Detonation cell size epesents the fundamental length-scale fo a detonation wave Hydogen-ai l= A D ZND 0 < A < 00 Ciccaelli et al., Comb. Sci. and Tech., 8,

40 Measued and edicted Detonation Cell Size (effect of HO) Ciccaelli et al., Comb. Sci. and Tech., 8,

41 Detonation initiation 4

42 Diect initiation A detonation can be initiated diectly if sufficient enegy is deposited at a point Subcitical Supecitical 4

43 Citical initiation condition Bach et al.,

44 Citical Detonation Enegy E c ~ l 3 Lee JHS. Dynamic paametes of gaseous detonations. Ann Rev Fluid Mech, 6,

45 Deflagation to detonation tansition in a smooth tube Nomalized un-up distance: = 0.4, K= 5.5, C= 0., SL= lamina flame thicness, d flame thicness, s density atio, a p = speed sound h =. and m=-.8 (empiical constants) Kuznetsov M, Aleseev V, Matsuov I, Doofeev S. DDT in a smooth tube filled with a hydogen oxygen mixtue. Shoc Waves 4(3), 005;4(3) 45

46 Deflagation to detonation tansition in a smooth tube Tubulent flame Shoc wave Utiew A, Oppenheim AK. Expeimental obsevation of the tansition to detonation in an explosive gas. oc of Roy Soc A, 95,

47 Deflagation to detonation tansition in a ough tube Initial Stage of Flame Acceleation Combustion oducts V flame Unbuned Gas V flame Inteaction with tubulent flow ahead of flame font flame folding Flame-shoc inteactions Final Stage of Flame Acceleation DDT 47

48 Flame acceleation (BR=0.6) Detonation Fast flame Slow flame Kuznetsov et al., Effect of obstacle geomety on behavio of tubulent flames, Repot No. FZKA-638, Foschungszentum Kalsuhe/epint No. IAE-637/

49 Steady combustion popagation egimes Detonation popagation limit: d > l Lee JHS. Dynamic paametes of gaseous detonations. Ann Rev Fluid Mech, 6,

50 Steamwise distance (cm) essue (atm) Flame acceleation in obstacle laden channel D Ion obe 708 m/s 648 m/s 598 m/s 386 m/s 37 m/s 58 m/s 9 m/s Time (ms)

51 Δt =.67 ms Flame acceleation, ealy stage Johansen and Ciccaelli, Combustion and Flame, 008 5

52 Δt = 0.67 ms Flame acceleation, ealy stage Johansen and Ciccaelli, Combustion and Flame, 008 5

53 Flame Velocity (m/s) Flame acceleation (LES model w/ flame) Expeiment Simulation 40 0 obstacle positions Distance (m) 53

54 Shea laye development (LES model no flame) 54

55 Shoc fomation 55

56 Flame acceleation, late stage

57 Shoc-flame inteaction 57