Mass Production Rate. Solid Propellant Burning Rate

Transcription

1 Mass Prductin Rate Prpellant cnverted t gas at rate given by m r (VI.) s b (Surface) Regressin Rate r r dx smetimes r b standard mdel (Burning Rate Law r St. Rbert s Law, als Vielle s Law) n (VI.2) r ap with a=f (T, ) after M. de Saint-Rbert n als, r c bp etc. flame Burning rea, b s m r q x Slid Mtr Burning Rate Slid Prpellant Burning Rate r ap n ln r ln a nln p Frm Suttn Slid Mtr Burning Rate 2

2 Measuring Burning Rate Blast Shield Vent Explding Diaphragm Ignitin Wire 8 Sample Pre-pressurize (e.g., up t 2500 psi) Ignite tp f prpellant Measure regressin rate (ptically, embedded wires, ) Slid Mtr Burning Rate 3 N 2 Pressurizatin Sides cated with inhibitr Mtr Internal Ballistics What gverns mtr internal cnditins? Examine mass cnservatin dm CV 0 u nˆ d d V V m exit m b 0 CV d dv V dp b r RT 2 p 2 RT rs b t m b m exit ssuming: ) unifrm gas prp s. in CV 2) TPG, CPG 3) T =cnstant (e.g., T ad ) 4) p, b, r given at time t Slid Mtr Burning Rate 4 2

3 Internal Ballistics (cn t) Slve fr rate f pressure change 2 V dp rb s p t RT RT Fr steady (neutral) burning / c dp b 0 p * r s c (VI.4) t using standard burning rate law (VI.3) p n b ap c * p ak t Fr steady burning (if a, n, T,, and t cnstant) then b must be cnstant s * n c s p b ~ K K t n * ~ s in many cases (VI.5) Slid Mtr Burning Rate 5 Pressure Histries Mtr designer can adjust pressure prfile ( histry ) f a slid mtr by arranging hw burning area changes with time (grain gemetry) Thrust given by p t c s thrust histry f mtr essentially fllws mtr s pressure histry Characterize pressure/thrust histries as generally prgressive: increase with time neutral: cnstant with time regressive: decrease with time cmbinatins Slid Mtr Burning Rate 6 3

4 Grain Gemetries and Thrust Histry r bst sustain Frm Hill and Petersn Slid Mtr Burning Rate 7 Many Slid Mtr Grain Gemetries high thrust ( b ) web designs develped befre high burn rate prpellants (r>8 mm/s) Enhanced structural prperties analytic (2-d) expressins available fr b Hartfield et al., I Slid Mtr Burning Rate 8 Frm Suttn 4

5 Cmputatinal Ballistic Mdeling Unifrm and 2-d appraches unifrm axial cnditins Mre generally need t cnsider evlutin f grain ND cupling t the flwfield in the prt(s) In bth cases, can cuple t nzzle slver Can ften use partially-cupled apprach flwfield develps at different (faster) time scale then grain gemetry (burning area) regressin rate O(-0 mm/s) flw velcity O(0 s m/s) Slid Mtr Burning Rate 9 Cmputatinal Ballistic Mdeling Must handle determinatin f burning surface evlutin surface usually assumed t burn nedimensinally (regressin is nrmal t surface) ppraches discretize surface n cmputatinal grid elabrate schemes t define surface nrmals level-set methds handles cmplex curved surfaces (with tplgy change) n fixed Cartesian (CFD) grid withut having t parameterize bjects, but cnvergence prblems signed minimum distance functins (Rcgrain frm UIUC) Slid Mtr Burning Rate 0 5

6 Other ppraches t Thrust Cntrl Cast multiple prpellants, e.g., biprpellant star cnfiguratin Functinally graded prpellants prpellants whse prperties can be varied gradually as a Frm NS SP-8076 functin f depth int grain e.g., 50% variatin in r example: reduce burning rate with depth in therwise prgressive web design requires advanced manufacturing appraches Slid Mtr Burning Rate 6