Model Formulation and Predictions for a Pyrotechnically ~ctuated Pin - PowerPoint PPT Presentation

Model Formulation and Predictions for a Pyrotechnically ~ctuated Pin Puller Founded 1842 Univer si ty of Notre Dame Keith A. Gonthier* and Joseph M. Powers** Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, Indiana 46556-5637 USA presented at the Fifth International Conference of the Groupe de Travail de Pyrotechnie Strasbourg, France * Ph.D. Candidate ** Assistant Professor June6-ll, 1993

Acknowledgment Support NASA Lewis Research Center Cleveland, Ohio, USA Contract Number: NAG-1335 Contract Monitor: Dr. Robert M. Stubbs

Pyrotechnically Actuated Pin Puller end expans10n chamber 1/4" 0.64cm stroke 9/16" 1.43 cm energy absorbing cup NASA Standard/ Initiator (NSI) assembly

Review Sources for guidance in model development: • Pin Puller tests: Bement, Schimmel, et al. • Pyrotechnics Chemistry: McLain, Conklin • NSI ignition study: Varghese • Multiphase combustion: Krier, Butler, Powers, Baer, Nunziato, etc. • Automobile airbags: Butler, Krier • Solid Propellants: Williams, Kuo, Strehlow, etc.

Engineering Problems • Operational failures. • Qualification after many tests. • Difficult to predict behavior of new formulations. • Difficult to quantify effects of modifications: - diffusive processes, - pin puller geometry, - friction.

Modeling Approaches • Full Scale Models: - time dependent, - 3-D spatial gradients, - multiple species, - fully resolved chemical kinetics, - compressibility, - turbulence, - real gas effects, - limited kinetic data available, - more complex than justified by data.

Modeling Approaches (continued) • Empirical Models: - experimentally-based correlations, - somewhat inflexible. • Simple Models - present approach: - analytically tractable, - introduction of ad hoc assumptions. • Stochastic Models: - estimates for uncertainty required, - could be coupled with simple model.

Model Assumptions Pin Fundamental Assumptions (g) Gas Phase Products Burn Surface • Well-stirred reactor: ( cp) Condensed Phase Products - no spatial variations, - time-dependent variables. • Total system modeled as three subsystems: solid pyrotechnic reactants, condensed phase products, gas phase products.

~ r-+-~-, L-~ ~' ~cp ~ Model Assumptions (continued) • • Vbut qn , system boundary • ( cp) condenseq ocp,g (g) gas phase p ase h .,.. products products 1J 1I I (s) solid pyrotechnic Mass and Heat Transfer • No mass exchange between total system and surroundings. • Mass exchange from reactants to products. • Heat and work exchange between gas phase subsystem and surroundings. · • Heat exchange between product subsystems. • No work exchange between subsystems.

Model Assumptions (continued) Combustion Process • Combustion products produced in ratios which minimize the Gibbs free energy: - constant mass fractions. • Ideal gas. • Gas has temperature dependent specific heat.

Model Assumptions (continued) Remaining Assumptions • Vessel's wall temperature is constant. • Solid pyrotechnic has constant density. • Condensed phase products have constant density. • Total kinetic energy of system is negligible. • Body forces are negligible .

Non-Dimensional Governing Equations mass evolution: d -[pV]--pr dt s s - s ' energy evolution: d -[p Ve]= -per dt s s s s s ' d[ ] ( ) . . . + - Ve =1- er+ -W df pg g g T]cp Ps s Qin Qcp ,g out• Newton's Law of Motion: 2 z = p ] - d F [ m,V,lj] I~' c '. dt' [ ,]

Scaling used in Non-Dimensionalization • Thermodynamic variables and time are 0( 1) quantities at completion of the combustion process. ,., ,., v =V T =T c ad' c so ' - ft =AP ,.., e =e c c ' p c so ' ,., ,., v b,.., p,., II ,., r = [=,., c Ar c c ' c p c

~ ~ ~ Geometrical and Constitutive Relations A. Geometry • Total Volume: V=V +V +V s g ( v%J z= -=-v • Pin Position: A p p B. Combustion Model N tv X -->:Lv X +:Lv X • Irreversible reaction: i=I s; s, i=I cp, cp; i=I Ki g, • Pyrotechnic burn rate:

Geometrical and Constitutive Relations (continued) p =pT C. Thermal Equation of State: g g g D. Caloric Equations of State: E. Constant Volume Specific Heats: d d [ ( )] N, c. (T) =:LY -[e (T )], c. T =:LY e T , N,, ( ) cp; dT S; dT i=I s i=I s '"" cp cp ; cp S; 1, s cp

Geometrical and Constitutive Relations (continued) F. Heat Transfer Models • Gas phase products - Condensed phase products: ) [ h t ]( ) . . ( T T = T - T = - A. r e cp.g c Qcp.g Qcp cp , g cp g Pc p c c • Gas phase products - surroundings:

Geometrical and Constitutive Relations (continued) G. Rate of work done by gas phase products in moving pin: F. Force acting on the pin: • F crit , critical force necessary for shear pin failure, • work done in shearing the pin is not accounted for.

Final Form of Model Equations dV [p v]. e v -= e mp r: ' dt dV = - r(V, V , _s V , T ), df ep s g dVep - n (~J r(V V V T ) d! - cp ' s ' cp ' 'I g ' Pep dTcp _ 11ep Ps r(V, Vs, Vep' rJ(eso -ecp(Tcp))-Qep,g(Tep'TJ dt- Pep Vep c,.cp (Tep) )+ Qep,g (Tep,Tg) + es 0 -eg (TJ (t(rJ- KPJV, Vs, Vep' Tg) V dT _ (l- 77ep) Ps r(V, Vs, Vep'TJ( 8 P 8 (V, Vs, Vep)(V-Vs -VCJc,,, (rJ dt- F (v, V, V ,T ). dV = d! ep P s g Initial Conditions: V(t = 0) = V (t = 0) = V (t = 0) = V V V o' s so' ep epo' T (t = 0) = T (t = 0) = V(t = 0) = T T 0. ep o ' g o '

Experimental • Tests conducted by Mr. Laurence J. Bement • NASA Langley Research Center, Hampton, Virginia, USA Apparatus Pressure Transducer NS! Assembly/

Results • NSI Driven Pin Puller • 10 cm 3 Closed Bomb Combustion of NSI • NSI Driven Dynamic Test Device Balanced Stoichiometric Equation: 3. 7735 Zr(s) + 2.6917 KC/0 4 (s) ~ 3.1563Zr(cp)+1.9246O(g)+1. 7031 KCl(g) +O. 9715 Cl(g) + 0.8590 K(g) + 0.6309 0 2 (g) +0.5178 Zr0 2 (g) + 0.1220 KO(g) + 0.0993 ZrO(g) +0.0106 C/O(g) +0.0022 K 1 C/ 2 (g) + 0.0016 K 1 (g) +0.0011 C/ 2 (g) + 0.0001 Zr(g) NSI Pyrotechnic Composition: • 114 mg of a Zr/KC/0 4 mixture: - 53.6 mg of Zr (s), - 60.4 mg of KC/0 4 (s)

p~p Parameters used in pyrotechnic combustion simulations. I I e.arameter value 0.64a, 2.0b, 5.01c cm2 AP 3.0 glcm3 P11 288.0 K Ts 1.5 glcm 1.25xl06 g/s3/K h 0.60 £ a 0.60 3.2xlolO g cm2ts3/K hcp,g 3.56xl07 dyne (80 lb/) Fcri1 b 0.004 dyne-0.69cmls n 0.69 (a - pin puller, b - closed bomb, c - Dynamic Test Device) Initial conditions used in pyrotechnic combustion simulations. I initial value : condition I 21.69a, 263.lSb, 32.59C Vo 1.0 Vso 8.56x10-5 Vcpo 5.66x10-2 To v_a 0.0 (a - pin puller, b - closed bomb, c - Dynamic Test Device)

~ Pin Puller Simulation Pressure Prediction Temperature Prediction t(ms) -t (ms) -0.07 0.03 0.13 0.23 0.33 0.43 -0.07 0.03 0.13 0.23 0.33 0.43 1 .2 -I-'-..._._ .................................................................................. ..._._ ........... ....._ 1.2 6000 1 8000 ,.-... 1 ,..-.._ C<j ~ c:: .8 0.8 0 · c;; 0.8 4000"""'31 6000 "'t:ll c:: en ,.-... c:: 0 Q.) E '6' E 0.6 ...... 0.6 c.., "Cl I c:: 4000-:::; I c:: 0 g 5 0.4 0.4 2000 ,_,... E-< 2000 predicted result 0.2 0.2 -t- experimental result 0 0 -5 0 5 1 0 15 20 25 30 -5 0 5 1 0 15 20 25 30 t (non-dimensional) t (non-dimensional) • Model correctly predicts time scales and pressure magnitudes.

p:'.:ro:'.du:cts~ ~ ~ ,-~as:J:!ph:=as:.!e Pin Puller Simulation (continued) Predicted Energy Distribution t(ms) -0.07 0.03 0.13 0.23 0.33 0.43 Kinetic Energy of Pin at completion of stroke: solid pyrotechnic >. 0.8 c:: 2000 §1 i:.il g (1) condensed phase products Predicted: 240 in-lb [27 J] 0.6 ~ '< ,...._ ;:;· '+-< - 0 § 0.4 OOO 2:: ...... 1 ...... Experimental: 200 in-lb [22.6 J] £ 0.2 -5 0 5 1 0 15 20 25 30 t (non-dimensional)

-1-1._._.i.-i.-.L-'-.i.r.i._._"-'-~-'-'-'- 10 cm 3 Closed Bomb Simulation Pressure Pressure Prediction Transducer t(ms) -0.12 0.18 0.48 0.78 1. 2 800 1 ,.-._ 10 cm 3 ~ c: ·- 0.8 0 Vessel <Zl c: Q) .§ 0.6 "O I c: 0 5 0.4 0... 200 - predicted result 0.2 -+- experimental result -5 0 5 10 15 20 25 30 35 40 t (non-dimensional) NSI Cartridge Port NASA Specification: • firing of an NSI into a 10 cm 3 bomb shall produce a peak pressure of 650 + 125 psi [4.48 + 0.86 MPa] within 5 ms.

~ 30~ Dynamic Test Device Simulation Pressure Prediction 1(ms) Pressure Transducer Sealing Ring -0.11 0.29 0.69 1.09 1.49 1 predicted result 5000 -+- experimental result ,..-... 0.8 c:: ·- 4000 0 en s c:: '"Ol o.6 ·- -· c;.., "O I '-' c:: g 0.4 2000 '-' 0.2 1000 Piston NSI Cartridge Port (1 inch diameter, 0 0 1 lbm) -50 100 250 400 550 700 t (non-dimensional) Average Kinetic Energy of the Piston during the stroke: • Predicted: 391 in. lbf [44.2 J] • Experimental: 258 in. lbf [29 .2 J]

Preliminary Sensitivity Analysis (Earlier Work) Objective: • Study sensitivity of the model to changes in model parameters. Methodology: • Model prediction for pin puller - base solution. • Independently change parameters and note the change in the predicted kinetic energy of pin at completion of stroke.