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

SLIDE 1

Founded 1842 Universi ty of Notre Dame

Model Formulation and Predictions for a Pyrotechnically ~ctuated Pin Puller

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

June6-ll, 1993

* Ph.D. Candidate

** Assistant Professor

SLIDE 2

Acknowledgment

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

SLIDE 3

1/4"

0.64cm

Pyrotechnically Actuated Pin Puller

expans10n chamber stroke 9/16" 1.43 cm

NASA Standard/

Initiator (NSI) assembly end energy absorbing

cup

SLIDE 4

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.

SLIDE 5

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.

SLIDE 6

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.

SLIDE 7

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.

SLIDE 8

Model Assumptions

Fundamental Assumptions

• Well-stirred reactor:
• no spatial variations,
• time-dependent variables.
• Total system modeled as three subsystems:

solid pyrotechnic reactants, condensed phase products, gas phase products.

(g) Gas Phase Products ( cp) Condensed Phase

Products Pin Burn Surface

SLIDE 9

Model Assumptions (continued)

• Vbut

qn

~

system boundary r-+-~-,

,

• (

cp) condenseq

• cp,g

h (g) gas phase p ase .,..

~

products products

1I

~cp

1J

~'

Mass and Heat Transfer

(s) solid pyrotechnic

I

L-~

• 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.

SLIDE 10

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.

SLIDE 11

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 .

SLIDE 12

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

• ut•

Newton's Law of Motion:

• z =

c

F d

2 [

p ]

dt' [ ,] m,V,lj] I~'

'.

SLIDE 13

Scaling used in Non-Dimensionalization

• Thermodynamic variables and time are 0(

1) quantities at

completion of the combustion process.

,., ,.,

v =V

c so '

T =T

c

ad'

• ,..,

e =e

c so '

ft =AP

c p c '

,.,

,.,

b,.., p,., II

r =

c c '

,.,

v

[=,., c

c

Ar

p

c

SLIDE 14

Geometrical and Constitutive Relations

• A. Geometry
• Total Volume:
• Pin Position:
• B. Combustion Model
• Irreversible reaction:
• Pyrotechnic burn rate:

V=V +V +V

s

~

g

(v%J

z= -=-v

p

A

p

N ~

~

tv X -->:Lv X +:Lv X

i=I

s;

s, i=I cp, cp; i=I

Ki

g,

SLIDE 15

Geometrical and Constitutive Relations (continued)

• C. Thermal Equation of State:

p =pT

g g g

• D. Caloric Equations of State:
• E. Constant Volume Specific Heats:

N,

d

• c. (T) =:LY -[e (T )],

1,

s

i=I

S; dT S;

s

( )

N,,

d [ ( )]

• c. T =:LY

e T ,

'""

cp

i=I

cp; dT cp; cp

s

cp

SLIDE 16

Geometrical and Constitutive Relations (continued)

• F. Heat Transfer Models
• Gas phase products - Condensed phase products:

. . ( ) [ h t ](

)

=

T T =

cp.g c

T - T

Qcp.g

Qcp

cp , g

• A. r

e

cp g

Pc

p c c

• Gas phase products - surroundings:

SLIDE 17

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.

SLIDE 18

Final Form of Model Equations

• =

e e v

dV [p v]. dt

mp r:

'

dV

_s =

• r(V, V ,

V , T ), df

s

ep

g

dVep - n (~J

r(V V V T ) d! -

'I cp

' s ' cp '

g '

Pep

dTcp _ 11ep Ps r(V, Vs, Vep' rJ(eso -ecp(Tcp))-Qep,g(Tep'TJ

dt-

Pep Vep c,.cp (Tep)

dT

8 _ (l- 77ep) Ps r(V, Vs, Vep'TJ(

es0 -eg (TJ

)+ Qep,g (Tep,Tg) +

(t(rJ- KPJV, Vs, Vep' Tg) V

dt-

P8 (V, Vs, Vep)(V-Vs -VCJc,,, (rJ dV =

F (v, V, V ,T ).

d!

P s

ep

g

Initial Conditions:

V(t =

0) =

V V (t =

0) =

V V (t =

0) =

V

• '

s

so'

ep

epo'

T (t = 0) = T T (t = 0) = T

V(t =

0) = 0.

ep

• '

g

• '

SLIDE 19

Experimental

• Tests conducted by Mr. Laurence J. Bement
• NASA Langley Research Center, Hampton, Virginia, USA

Apparatus

NS! Assembly/ Pressure Transducer

SLIDE 20

Results

• NSI Driven Pin Puller
• 10 cm3 Closed Bomb Combustion of NSI
• NSI Driven Dynamic Test Device

Balanced Stoichiometric Equation:

• 3. 7735 Zr(s) + 2.6917 KC/04 (s) ~

3.1563Zr(cp)+1.9246O(g)+1. 7031 KCl(g)

NSI Pyrotechnic Composition:

+O. 9715 Cl(g) + 0.8590 K(g) + 0.6309 0 2 (g) +0.5178 Zr02 (g) + 0.1220 KO(g) + 0.0993 ZrO(g) +0.0106 C/O(g) +0.0022 K 1C/2 (g) + 0.0016 K 1 (g) +0.0011 C/2 (g) + 0.0001 Zr(g)

• 114 mg of a Zr/KC/04 mixture:
• 53.6 mg of Zr (s),
• 60.4 mg of

KC/04 (s)

SLIDE 21

Parameters used in pyrotechnic combustion simulations.

I

e.arameter value

I

AP 0.64a, 2.0b, 5.01c cm2

P11

3.0 glcm3

Ts

288.0 K

p~p

1.5 glcm h 1.25xl06 g/s3/K

£

0.60

a

0.60

hcp,g

3.2xlolO g cm2ts3/K

Fcri1

3.56xl07 dyne (80 lb/)

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.

: condition

I initial

value

I

Vo 21.69a, 263.lSb, 32.59C Vso

1.0

Vcpo

8.56x10-5

To

5.66x10-2

v_a

0.0

(a - pin puller, b - closed bomb, c - Dynamic Test Device)

SLIDE 22

Pin Puller Simulation

Pressure Prediction

• t (ms)
• 0.07

0.03 0.13 0.23 0.33 0.43

1 .2 -I-'-..._._

.................................................................................. ..._._ ...........

....._

1

,..-.._

C<j

.8 0.8

en

c::

Q.)

E 0.6

......

"Cl

I

c::

g

0.4

,_,...

0.2

predicted result

• t-

experimental result

8000 6000 "'t:ll

'6'

c..,

4000-:::; 2000

• 5

5 1 15 20 25 30 t (non-dimensional)

Temperature Prediction

t(ms)

• 0.07

0.03 0.13 0.23 0.33 0.43

1.2

,.-...

1

~ c::

·c;; 0.8

c::

E

~

0.6

I

c::

5 0.4

E-<

0.2

• 5

5 1 15 20 25 30

t (non-dimensional)

• Model correctly predicts time scales and pressure magnitudes.

6000 4000"""'31

,.-...

2000

SLIDE 23

Pin Puller Simulation (continued)

Kinetic Energy of Pin at completion

• f stroke:

Predicted: 240 in-lb [27 J] Experimental: 200 in-lb [22.6 J] Predicted Energy Distribution

t(ms)

• 0.07

0.03 0.13 0.23 0.33 0.43

>.

~ 0.8

c::

i:.il

g

~

0.6

'+-<

§ 0.4

......

......

£

0.2

solid pyrotechnic

2000 §1

(1)

condensed phase products ~ '<

,...._

;:;·

• ,-~as:J:!ph:=as:.!e

p:'.:ro:'.du:cts~

1

OOO 2::

• 5

5 1 15 20 25 30 t (non-dimensional)

SLIDE 24

10 cm3 Closed Bomb Simulation

Pressure Transducer

• 0.12

Pressure Prediction

t(ms)

0.18 0.48 0.78 1. 2

• 1-1._._.i.-i.-.L-'-.i.r.i._._"-'-~-'-'-'-

800

10 cm 3 Vessel NSI Cartridge Port

1

,.-._

~ c:

0.8

·-

<Zl

c:

Q)

.§ 0.6

"O

I

c:

5 0.4

0...

0.2

• predicted result
• +-

experimental result

• 5

5 10 15 20 25 30 35 40

t (non-dimensional)

NASA Specification:

• firing of an NSI into a 10 cm3 bomb shall produce a peak

pressure of 650 + 125 psi [4.48 + 0.86 MPa] within 5 ms.

200

SLIDE 25

Dynamic Test Device Simulation

Pressure Transducer Sealing Ring Piston

Pressure Prediction

1(ms)

• 0.11

0.29 0.69 1.09 1.49

1

,..-...

~

0.8

c::

·-

en

c::

s

• .6

·-

"O

I

c::

g 0.4

'-'

0.2

predicted result

• +-

experimental result

5000 4000

'"Ol 30~

c;..,

• ·

'-'

2000 1000

NSI Cartridge Port (1 inch diameter, 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]

SLIDE 26

Objective:

Preliminary Sensitivity Analysis

(Earlier Work)

• 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.

SLIDE 27

0.1

>-.

::::::

e.'l .s 0.08

<U .......

::::::

u ~

~

.~

~

0.06

.......

4-<

<U

.s

>-.

~

e.'l 0.04

.s

~

0-t

~

0.02

Burn Rate Parameters

r =Pn

g

0.1

::::::

>. 0

0.08

O> ·.o ......

u

Q)

~

c:

<U

~ ~

0.06

1D

c

>-. ~

e.'l 0.04

.!::

~ 0... ~

0.02

• -~

............................... --...-............ ..,._,._.......,.._.........,...,.........-

0--............

• ~-.-.-i

1x10-5 1x10-4 1x1o-3 1x10-2 1x10-1 1x10°

f"'

• 69

Bum Rate Parameter, o (dyne ·

cm/ sec) 0.25 0.5 0.75

Burn Index, n 1

Two distinct regions are identified:

• slow burning (burn rate ,...., heat transfer to surroundings)
• fast burning (burn rate > heat transfer to surroundings)

SLIDE 28

Heat Transfer Parameters . [ ri v

2 ' 3 t J

[ av

2 ' 3 t 4 J

=

c c A T -T + c c A aT

4

• cT

4

Q,"

• Are

.( • .)

• Are .(
• .)

Pc

p c c

Pc

p c c

0.12-r-----------------.

0.1

i::

e> .g 0.08

a>

u c

ro

w ~

(.)

'+-< 0.06

""fil c

>. S2

OJ)

c

a:> 0.04

a:

i::

l:il

0.02

O-+-............

.....-..........,,,..,,.,...

...........

.....,__........._,...........,..,.,.,.,,,........,..............i

10x103 1x105 1x106 1x107 1x108 1x109 1x1o10

Convective Heat Transfer Coefficient, h (gl

sec3

I K)

0.1-

............. D<....

>. §

e> ·;::: 0.08 -

a> g

c

(])

w

~

.g

'+-< 0.06-

Q)

c

>. S2

e,'J

c

(]) 0.04-<

a: &5

0.02-<

O-t--ir--T""-,-,,-,.-..,......,.-,r--T""-,-,-T........,......,.-...-.-T..,.....,--,--1

0.2 0.4 0.6 0.8

1

Absorptivity, ac:::. Emissivity, E

SLIDE 29

Heat Transfer Parameters (continued)

>. i::

C> .9 0.08

~

.....

Cl>

(.)

c

ro

~ ~

0.06

·.;:::; 4-< Q)

c

S2 >. c

e.n 0.04

0::: ~

i:il

0.02

. [ h t

](

)

=

cp,g c

T -T

Qcp.g

• A. r e

cp g

~c

p c c

0-+-,,_..,..,"'""'"'"""'"T'""l"..,.,.,...,.,

............

..,...,...,.....,.-.,....,......,.,.,..,,..---.-...,..,.,.,.,.,f

1x106 1x107 1x108 1x109 1x1o10 1x1011

CP-GP Heat Transfer Parameter,

'h (cm2 glsec3tK) cp,g

SLIDE 30

Conclusions

Model correctly predicts experimentally observed features:

• peak pressures,
• velocity of pin at completion of the stroke.

Model correctly predicts the time scales of events:

• time to peak pressure,
• time to complete the stroke.

SLIDE 31

Conclusions (Sen.sitivity Study)

Sensitivity analysis suggests increased model potential:

• may not need detailed empirical data,
• predicted solution is insensitive to variations in burn rate for

fast burning rates. For peak performance:

• fast burning rate,
• low convective heat transfer rate,
• high heat rate from condensed phase to gas phase products.

SLIDE 32

Future Work

• Perform analytical studies:
• examine simplest possible case (constant volume,

adiabatic, constant specific heats, etc.)

• study predicted solution near equilibrium states.
• Better justify choice of model parameters:
• burn rate,
• heat transfer.
• Continue sensitivity studies:
• model parameters,
• initial conditions.
• Include frictional effects.
• Include grain size effects.
• Study other pyrotechnic formulations.
• Study other geometries.