MODELING AND SIMULATION OF EXPLOSIVELY DRIVEN ELECTROMECHANICAL - - PowerPoint PPT Presentation

MODELING AND SIMULATION OF EXPLOSIVELY DRIVEN ELECTROMECHANICAL DEVICES

Paul N. Demmie Computational Physics and Simulation Frameworks Department Sandia National Laboratories

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.

Topics in Presentation

• What is a Firing Set?
• Goal of Firing Set Modeling
• The EMMA Computer Code
• Elements of the EMMA Computational Models
• Calibration of the Models
• Verification Process
• Validation Process
• Parameter Studies
• Conclusions and Discussion

What is a firing set?

• A firing set is a device whose purpose is to remain in an

inactive state and initiate detonators in a safe and reliable manner only when intended.

• A slim-loop ferroelectric (SFE) firing set --

− Stores electrical energy in SFE material PBZT when a voltage is applied. − Releases this energy into circuits when the permittivity of the PBZT is explosively reduced.

Exploded View of an SFE Firing Set

SFE TRANSDUCER OUTPUT CABLES DIELECTRIC SWITCH ISOLATION PLATE TRACK COVER PLATE DETONATOR HOLDER CERAMIC BACKUP PLATE SFE CERAMIC STACK BUFFER PLATE EXPLOSIVE EXPLOSIVE LENS SPRING HOLD DOWN OUTPUT PLATE

Our goal is to create a

Comprehensive, Coupled 3D Electromechanical (EM), Age- Aware Model of an SFE Firing Set

− Comprehensive model - include:

• High fidelity physical description of every sub-component
• Start with accurate “age capable” materials models

− Comprehensive model - include effects of:

• aging of explosive dynamic model
• SFE aging on EM and “hydro” response
• Interface degradation or materials changes

− Coupled 3D electromechanical model:

• Use EMMA, a 3D computer code based on ALEGRA, which includes

electromagnetic field calculations and attached circuits.

ρ∂2xi/∂t2 = ∂Tij/∂xj + ρbi ∂/∂xi (εij ∂Φ/∂xj) = ∂Pi/∂xi Qi = Cij Φj + Si

EMMA EMMA

Continuum Model (Newton’s Laws)

+

Quasi-Static Approximation to Maxwell’s Equations Circuit Model (Kirchoff’s Laws)

+

. . .

EMMA’s algorithms solve coupled models for electromechanical phenomena

Principle Elements of Model

• Explosive
• Explosive Lens
• Buffer Plate
• Mylar layer and electrode interfaces
• Slim-Loop Ferroelectric (SFE) Ceramics
• Output Circuit
• Explosively Inert Regions (everything else)

Assembly Screw Holes (3) Explosive Fill Holes (6) Timing Tracks Shock Isolation Voids (2) Detonator Cavity Lens Attachment Through Holes (6) Fixture Alignment Holes (2)

Lexan Track Plate

Main Explosive Tracks Timing Track “Adjustment”

Calibration Features of the Models

• Known geometry and material properties.
• Explosive with density of 1490 kg/m3 from DV and rheology

block tests (programmed burn).

• SFE parameters determined from experiments.

− Equilibrium permittivity and electrostrictive coupling parameters for electromechanical model

• Measured resistance (R) and inductance (L) for output circuit

with attached wires.

• Included intrinsic R and L for firing set.

Verification Process

.

• Features expected for a correct representation of

the performance of an SFE firing set are

− A detonation propagates in the track plate, − detonates the explosive pellets in the output plate, − produces pressures waves that propagate through the buffer plate and into the SFE ceramic stack, − shatters the SFE ceramics and produces an electric field , and − produces currents in the circuits

. .

Validation Process

• Experiments used:

− 29 firings of device into test circuit

• peak current, width at half height, pulse length, and switch closure-

time differences

− blockage tests

• calculated fractions of peak currents differ from

data by less than 2%

− track-plate timing tests

• detonation arrival times at sensor locations
• detonation velocities (DV) between locations in track
• calculated arrival times and DVs differ from data by less than 1%

− VISAR (velocity interferometer system for any reflecting surface) measurements below SFE stack (pressures not available)

Calculated and Measured Currents

CURRENT TIME

Sensitivity Studies

• Used quarter-cell model

− include a quarter of a pellet and adjacent region

• Variations considered:

− Charging Voltage − Input parameters to SFE model − Circuit parameters (resistance and inductance) − Detonation velocity (unreacted explosive density) − Switch-closure initiation times

Some Results of Sensitivity Studies

Peak Current Versus Equilibrium Permittivity

900 950 1000 1050 1100 1150 1200 75 85 95 105 115 125 135 Equilibrium Permittivity (nF) Peak Current (A)

Peak Current Versus Charging Voltage

300 400 500 600 700 800 900 1000 1100 150 200 250 300 350 400 450 500 Charging Voltage (V) Peak Current (A)

Peak Current Versus Unreacted XTX Density (switch-closure time adjusted)

900 950 1000 1050 1100 1150 1200 1200 1300 1400 1500 1600 XTX Density (kg/m3) Peak Current (A)

Peak Current Versus Inductance of Test Circuit

850 1000 1150 1300 1450 1600 100 200 300 400 500 600 700 Inductance (nH) Peak Current (A)

Conclusions

• We developed a full-scale model whose results make sense and agree well

with experimental data.

• We developed a small-scale, fast-executing model to answer many

questions quickly.

• We used modeling and simulation synergistically with experimental results

to better understand the performance of an electromechanical SFE firing set. − Results indicate that device is robust and indicates that it will perform its intended function as it ages

• We can improve the model (present work).

− Higher fidelity model with Mylar layer and interfaces. − Electric-field dependence in SFE model.