Motor Stability. Plateau and Mesa Burning
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1 Mtr Stability Recall mass cservati fr steady erati ( =cstat) m eit m b b r b s r m icr m eit Is this cditi (it) stable? ly if rmally use.3<<.7 m m icr m eit m icr m icr m eit m icr m eit m icr Slid Mtr Stability Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi Plateau ad Mesa Burig Plateau burig regi f weak deedece () f bur rate Mesa burig lcally egative (<) l r Payff ehace stability regi ca kee cstat eve with chages i ( b ) rmal mesa lateau l Slid Mtr Stability 2 Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi
2 Temerature Sesitivity What haes if the iitial (strage) temerature f the rellat chages? (sia) =T Bur rate ad ressure icrease shrter durati bur, m similar ttal imulse 26 t (sec) Slid Mtr Stability 3 Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi Temerature Sesitivity Sesitivity f burig rate t T l r r T r T with St. Rbert s Law emirically (e.g., strad/ Crawfrd burer tests) a T T T T, T emirical cstats (at secific ) a a T ls have r sesitivity t T at fied r l T a a T wat high T r get small rage f usable T tyically O( ) T =25r/r~few % t 25% Slid Mtr Stability 4 Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi 2
3 Temerature Sesitivity Sesitivity f ressure t T (at secific ) l T T * with St. Rbert s Law a s c a T a mre sesitive tha r t T If chages ather reas t kee small (<.8) usually measure i mtr tests additially, T ca flw/ slum ; T (+ cyclig) crackig ( b, ht gas at isulati/casig); frm (VI.5) Slid Mtr Stability 5 Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi If r t lw Cmbusti Limits d t get stable cmbusti after igiti, rellat s sts burig (r) m t t high ssibility f erratic, uredictable burig (usually > 5 si) Slid Mtr Stability 6 Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi 3
4 ial Variatis S far eglected variable gas rerties alg bre Okay if lw Mach umber (M) i rt, cc >> t Iitially, hwever, cc ~ O( t ) M smewhere i rt Leads t ) ersive burig 2) aial ressure distributi Head Ed cc ft r Nzzle Ed t Slid Mtr Stability 7 Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi Ersive Burig Cmact ietic Eergy Missile HTPB/P rellat Large ehacemet i, r esecially durig begiig f bur Iteral Ballistics mdel based burig rate data fr rellat Frm B. McDald PhD Thesis, T (24) Slid Mtr Stability 8 Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi 4
5 Ersive Burig - Cause Head Ed Variati i heat feedback t rellat surface alg bre leads t variatis i r M,u~ Higher M (r u ) thier budary layers (T), ad higher turbulece mre heat trasfer q t surface haes mre at aft ed (M, u icrease dwstream due t mass additi) ad durig early times ( cc / t ear ) still mst f q t surface is frm heat release f ear surface flame cc q ft/nzzle Ed M,u large t Ca get similar ersive burig if flw accelerated by vehicle accelerati r si Slid Mtr Stability 9 Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi r/r Ersive Burig - Scalig Fast bur rellat Ca arimate effect with additial term t burig rate r r r e Here 5-8% r icrease with ersive burig Reduced effect fr higher r (cataylzed) rellat less deedet u (m/s) additial heat fer Frm Sutt Slid Mtr Stability Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi 5
6 Ersive Burig: Emirical Mdels ree (954) r r r e.8 rs e e. 2 Leir-Rbillard mdel (957) r D mass flu m u S D rt hydraulic diam. 4 S, emirical cstats e.g., ~ 5 55 m c kg m s r r k e ~.288 s c s RT s Pr T T s 3 kg m Ts T k cstat Slid Mtr Stability Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi Ersive Burig: Emirical Mdels (c t) riedler (964) re r k.485 Eetial Law r r k M e k cstat These mdels quasi-redictive (cstats may chage with rellat ad mtr) Must kw hw r M vary alg rt kem re r k e cstat Slid Mtr Stability 2 Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi 6
7 ial Variatis Eve withut ersive burig, we ca eect rerty variatis alg rt (i.e., aial siti) Csider effect f mass additi () Mmetum equati (iviscid) Slid Mtr Stability 3 d udm mdu Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. mass additi flw area sice mass flw rate ad velcity bth geerally icrease (RHS+) ressure must dr dwstream but small variati usually d mu d dmu, u, +d, u+du, +d E645 Rcket Prulsi Itegrate Cstat rea Eamle ssume rt area aially uifrm must lik () t (t) due t b (t) ad chked thrttle cstrait 2 d mu mu s rsd RT s S a Recall, erimeter d assumig little chage i T ecet very clse t surface m assumig V chage takes lger tha flw residece time m Slid Mtr Stability 4 Cyright 27, 2, 22 by Jerry M. Seitzma. ll rights reserved. E645 Rcket Prulsi 7
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