Theory and Detonation Products Equations of State for a New Generation of Combined Effects Explosives. Dr. Ernest L. Baker
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1 Theory and Detonation Products Equations of State for a New Generation of Combined Effects Explosives Dr. Ernest L. Baker W. Balas, L.I. Stiel, C. Capellos and J. Pincay 16 OCT 2007
2 Outline Combined Effects Explosives Eigenvalue Detonation Detonation Velocities Cylinder Velocities Equations of State Conclusions
3 Combined Effects Explosive High Energy Explosive High nitramine content High early work output (before 7V/V0) High Blast Explosive Typically aluminum and additional oxidizer Later work output (after 7V/V0) Combined Effects Explosive Nitramine with fine aluminum: micron & submicron Aluminum reaction occurs very early and contributes to early work PAX-29: 77/15 Cl-20/Al PAX-30: 77/15 HMX/Al PAX-42 77/15 RDX/Al
4 Combined Effects Explosives PAX-30 (HMX, 15%Al) C-J Det Velocity, Km/s Experiment ρ 0 = g/cm 3 JAGUAR Aluminum Percent Reaction, % C-J Detonation velocity decreases with extent of Al reaction Experiments: Detonation velocity agrees with 0% Al reaction Cylinder velocity agrees with 100% Al 7V/V0 0%: 1.69Km/s, 100%: 1.90Km/s, Experiment: 1.88Km/s
5 ZND Model Rayleigh line (momentum) 2 2 R = ρ0 D P/( V 0 V) = 0 smaller D larger D Unreacted Hugoniot Reacted Hugoniot Rayleigh line Pressure Chapman-Jouguet State Hugoniot (energy) Η = E E0 1/2P( V0 V) = 0 Specific Volume ZND construction
6 ZND Model Unreacted Hugoniot Reacted Hugoniot Rayleigh line Pressure Von Neumann Spike Chapman-Jouguet State Principal Isentrope (products expansion) Specific Volume ZND construction
7 ZND Model Final CJ state Reaction Zone von Neumann point λ (reaction fraction) Hugoniot Curves Pressure Following flow - Taylor wave D (v 0, p 0 ) Pressure von Neumann point D CJ Chapman- Jouguet state (v 0, p 0 ) Distance Specific Volume (1/ρ)
8 Eigenvalue Detonation p 0 λ (reaction fraction) 1.0 What if the reacted Hugoniot lay below the unreacted Hugoniot? (opposite of normal) v=1/ρ
9 Eigenvalue Detonation larger D smaller D Unreacted Hugoniot (energy) Reacted Hugoniot (energy) Rayleigh line (momentum) Pressure 100% reaction CJ State Specific Volume Eigenvalue State W-point (weak point) Fickett 1979 Tarver 2003
10 Eigenvalue Detonation Unreacted Hugoniot (energy) Reacted Hugoniot (energy) Rayleigh line (momentum) Eigenvalue State Pressure W-point W-point Isentrope (products expansion) Specific Volume
11 p Eigenvalue Detonation Aluminized Explosive Al Reaction Zone Organic Reaction Zone von Neumann point Final W state Eigenvalue point D Following flow - Taylor wave (v 0, p 0 )
12 Eigenvalue Detonation Aluminized Explosive Von Neumann Spike Unreacted Hugoniot (energy) Inert Al Hugoniot (energy) Reacted Al Hugoniot (energy) Rayleigh line (momentum) Pressure Eigenvalue State W-point W-point Isentrope (products expansion) Specific Volume
13 Eigenvalue Detonation Combined Effects Explosive 40 JAGUAR Calculations PAX-29 (CL-20, 15%Al) Eigenvalue State Pressure, GPa Rayleigh Line 0% Al Reaction 50% Al Reaction 100% Reaction ρ 0 = g/cm 3 W-point: 50% Al reaction W-point: 100% Al reaction Relative Specific Volume Aluminum reaction produces lower Hugoniots
14 Eigenvalue Detonation Combined Effects Explosive JAGUAR Calculations PAX-30 (HMX, 15%AL) Eigen State P, kbar % AL REACTION 100% AL REACTION RAYLEIGH LINE W-point VOLUME cc/gm Detonation velocity controlled by 0% AL reaction Hugoniot!
15 Detonation Velocity Aluminized Explosives Data JAGUAR Calculations Experiment Inert Al Reacting Al EXPLOSIVE Al% ρ 0 (gm/cc) D (Km/s) D (Km/s) D (Km/s) HMX HMX HMX BTNEN BTNEN NG TNT TNT TNT PAX PAX PAX PAX AVERAGE ERROR % Detonation velocities agree with little or no aluminum reaction
16 Cylinder Velocity Analytic Cylinder Model JWLB Equation of State: λ R * = A C 1 ( + 1) i λe λ P V ω i e V * i RiV * V * ω Gruneisen Parameter: λ λ ( Ai λ V * + Bi λ ) e R iv * + ω Analytic Model: i Reference Frame at Detonation Velocity Isentropic Products Expansion Constant Properties Along Spherical Surfaces New: Modified for Eigen Detonation W-point Provides excellent agreement with hydrocodes!
17 Cylinder Test Results PAX-3 (HMX, 18%AL - large) Vcyl, km/s EXPERIMENTAL 0%AL REACTION 100%AL REACTION AREA EXPANSIONS HMX with large particle size Aluminum: AL reacts late!
18 Cylinder Test Results PAX-30 (HMX, 15%AL - small) Vcyl, km/s % Al REACTION 100%Al REACTION W-POINT EXPERIMENTAL AREA EXPANSIONS HMX with small particle size aluminum: AL reacts early!
19 Cylinder Test Results PAX-29 (CL-20, 15%AL - small) Vcyl, km/s % Al REACTION 100% Al REACTION W-POINT EXPERIMENTAL AREA EXPANSIONS CL-20 with small particle size Aluminum: AL reacts early!
20 JWLB Equations of State PAX-3 (Al INERT) PAX-29 PAX-30 PAX-42 ρ0 (g/cc) E0 (Mbar) D (cm/μs) P (Mbar) A1 (Mbar) A2 (Mbar) A3 (Mbar) A4 (Mbar) R R R R C (Mbar) ω D and P are from W-Point (not C-J values)
21 JWL Equations of State LX14 PAX-2A PAX-29 PAX-30 PAX-42 ρ0 (g/cc) E0 (Mbar) D (cm/μs) P (Mbar) A1 (Mbar) A2 (Mbar) R R C (Mbar) ω Combined effects explosives: note large blast energies!
22 Conclusions New combined effects explosives produce both high metal pushing (early) and high blast (late) work output. Detonation velocities agree with little or no Al reaction even with sub-micron particles However, with small particles, complete Al reaction is indicated during early products expansion Eigen detonation theory used for EOS development
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