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 CERAMIC BACKUP PLATE SFE CERAMIC STACK SFE TRANSDUCER BUFFER PLATE EXPLOSIVE OUTPUT CABLES OUTPUT PLATE DIELECTRIC SWITCH EXPLOSIVE LENS ISOLATION PLATE TRACK SPRING HOLD DOWN COVER PLATE DETONATOR HOLDER
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.
EMMA’s algorithms solve coupled models for electromechanical phenomena EMMA EMMA . . . Continuum Model Circuit Model Quasi-Static Approximation (Newton’s Laws) (Kirchoff’s Laws) to Maxwell’s Equations + + ρ∂ 2 x i / ∂ t 2 = ∂ T ij / ∂ x j + ρ b i ∂ / ∂ x i ( ε ij ∂Φ / ∂ x j ) = ∂ P i / ∂ x i Q i = C ij Φ j + S i
Principle Elements of Model • Explosive Fixture Lens Attachment Explosive Fill Holes (6) Alignment Shock Isolation Voids (2) Through Holes (6) Holes (2) Timing Tracks Lexan Track Plate Timing Track Main Explosive “Adjustment” Tracks Assembly Screw Holes (3) Detonator Cavity • Explosive Lens • Buffer Plate • Mylar layer and electrode interfaces • Slim-Loop Ferroelectric (SFE) Ceramics • Output Circuit • Explosively Inert Regions (everything else)
Calibration Features of the Models • Known geometry and material properties. • Explosive with density of 1490 kg/m 3 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 TIME CURRENT
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 Inductance of Test Circuit Peak Current Versus Equilibrium Permittivity 1200 1600 1150 Peak Current (A) Peak Current (A) 1450 1100 1300 1050 1150 1000 1000 950 850 900 100 200 300 400 500 600 700 75 85 95 105 115 125 135 Inductance (nH) Equilibrium Permittivity (nF) Peak Current Versus Charging Voltage Peak Current Versus Unreacted XTX Density (switch-closure time adjusted) 1100 1200 1000 900 Peak Current (A) 1150 Peak Current (A) 800 1100 700 1050 600 1000 500 950 400 300 900 150 200 250 300 350 400 450 500 1200 1300 1400 1500 1600 Charging Voltage (V) XTX Density (kg/m3)
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.
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