DETONATION DIFFRACTION, DEAD ZONES AND THE IGNITION-AND-GROWTH MODEL

Transcription

1 DETONATION DIFFRACTION, DEAD ZONES AND THE IGNITION-AND-GROWTH MODEL G. DeOliveira, A. Kapila and D. W. Schwendeman Rensselaer Polytechnic Institute J. B. Bdzil Los Alamos National Laboratory W. D. Henshaw and C. M. Tarver Lawrence Livermore National Laboratory 13TH DETONATION SYMPOSIUM JULY NORFOLK, VIRGINIA

2 Motivation Experiments appear to exhibit sustained regions of zero or partial reaction (dead zones) in corner turning experiments, such as in the hockey-puck geometry. Dead zone Detonation front Souers et al 04 Ignition-and-growth (I&G) reactive-flow model has long provided a framework for simulating a broad class of experiments. Although it captures breakout times well, it does not reproduce dead zones (Tarver 05). Is explicit accounting of desensitization the missing ingredient?

3 Outline A description of the standard I&G model. A proposed enhancement of the I&G model to include desensitization. 1-D shock-initiation results for the standard and enhanced I&G models. Hockey-puck corner-turning results for the standard and enhanced I&G models.

4 The I&G Model Proposed by Lee and Tarver (1980), refined in later studies. Calibrated for a variety of explosives including PBX 9501, PBX 9502, LX 17,.... Model particulars... - Explosive is a homogeneous mixture of two constituents (reactant and product). - Separate, JWL equations of state for each constituent. - Mixture energy and volume are weighted sums. - Closure conditions: pressure and temperature equilibrium. - Mixture variables satisfy reactive Euler equations. - A single progress variable (product fraction) measures reaction progress. - Single reaction rate with multiple terms (ignition and growth), switched on and off, calibrated to experiments, mimics hot-spot formation and growth. - Used to simulate a variety of experiments. - Parameters may need adjusting, depending upon the experiment.

5 Governing Equations U t + f(u) x + g(u) y = h(u) U = ρ ρu ρw ρe ρλ, f = ρu ρu 2 + p ρuw u(ρe + p) ρuλ, g = ρw ρwu ρw 2 + p w(ρe + p) ρwλ, h = ρr, E = e (u2 + w 2 ) EOS: Mechanical e s v s0 = p sv s ω s F s (v s /v s0 ) + F s (1), e g v s0 = p gv g ω g F g (v g /v s0 ) Q EOS: Thermal p s = ω s v s [C s T s +G s (v s /v s0 )+F s (v s /v s0 )], Mixture Rules p g = ω g v g [C g T g +G g (v g /v s0 )+F g (v g /v s0 )] Closure Rules e = (1 λ)e s + λe g, v = (1 λ)v s + λv g p s = p g, T s = T g

6 EOS Data Set (LX-17) ( V F i (V ) = A i 1 ) exp( R 1i V ) ω i R 1i +B i ( V ω i 1 R 2i ) exp( R 2i V ) G i (V ) = A i R 1i exp( R 1i V ) + B i R 2i exp( R 2i V ) i = s, g JWL parameters Unreacted Products A (Pa) 778.1e e11 B (Pa) e e11 R R ω Q (Pa-cc/cc) 0.069e11 C (Pa/K) 2.487e6 1.0e6 v s0 (m 3 /kg) 1/1905

7 Rate Law R = R I + R G1 + R G2 R I = I(1 λ) b (v s0 /v 1 a) x H(v s0 /v 1 a)h(λ igmax λ) R G1 = G 1 (1 λ) c λ d p y H(λ G1max λ) R G2 = G 1 (1 λ) e λ g p z H(λ λ G2min ) density threshold for ignition first growth shut off ignition shut off second growth switch Parameter Value I, (s 1 ) 4.0e12 b a 0.22 x 7.0 G 1, (10 11 P a) y s 1 ) 4500e6 c d 1 y 3 G 2, (10 11 P a) z s 1 ) 30e6 e g z 1 λ igmax 0.02 λ G1 max 0.8 λ G2 min 0.8 Tarver 05, LX-17 detonation set First growth term does not have an activation delay. Once ignition begins, first growth term switches on immediately and reaction must go to completion in due course as long as p > 0. No explicit accounting of desensitization due to weak shocks. Need for an enhanced model.

8 Ingredients of an Enhanced I&G Model A desensitization variable to measure the degree of compaction caused by the desensitizing shock. A dependence of the density threshold for ignition on the desensitization variable. A reaction extinction mechanism controlled by the desensitization variable. A negligible effect of desensitization on the propensity to initiate when the stimulus is sufficiently strong.

9 Proposed Enhancement of I&G Introduce desensitization parameter φ, and the associated evolution equation and rate law. (ρφ) t + (ρuφ) x + (ρwφ) y = ρs S = Ap(1 φ)(φ + ɛ) - A and ɛ are positive parameters, and any positive pressure drives φ from (no desensitization) to 1 (full desensitization). 0 Modify the reaction rate in two aspects. - Allow density threshold for ignition to be a function of φ. a(φ) = a 0 (1 φ) + a 1 φ, a 1 > a 0 - Introduce a delay λ G1min (φ). R G1 = G 1 (1 λ) c λ d p y H(λ λ G1min(φ) )H(λ G1max λ), λ G1min = λ c φ a 0 = 0.22, a 1 = 0.50, A = 1000, ɛ = 0.001, λ c = delay in activating first growth term

10 Numerical Method Godunov-type, shock-capturing scheme on a domain discretized using composite overlapping grids (overset grids). Riemann problems handled using Roe and HLL approximate solvers (extended to the mixture JWL equation of state). Reaction source term handled using an Runge-Kutta error-control scheme. AMR used to resolve fine-scale structures.

11 1D Initiation by a Weak Shock (12.54 GPa) 1 + a(φ) Standard model: successful initiation. Augmented model: desensitization prevents successful initiation. Ignition begins, but is shut off by the density threshold for ignition, rising above the post-shock density. Growth begins, but is shut off by the first-growth delay rising above the available λ. 1 + a(φ),

12 1D Initiation by a Strong Shock (14.97 GPa) ignition deactivated 1 + a(φ) Successful initiation with standard model (dashed line), augmented model (full line). Ignition begins, and is shut off by 1 + a(φ) rising above the post-shock density, as for the weak shock case. But the growth term is no longer deactivated, as the available λ exceeds the delay λ G1min. Thus desensitization is unable to prevent initiation to detonation.

13 Display of Axisymmetric Results pressure progress schlieren lead shock dead zone lead shock dead zone Typical post-corner-turning result. Numerical schlieren image carries more information, and will be the display mode of choice in the movie.

14 Hockey-puck Computations for LX-17 Reaction product at GPa Unreacted explosive t = 0 t = 1.6 dimensions in mm, time in microsec Show movie.

15 No desensitization t = 2.6 Desensitization phi

16 No desensitization t = 2.8 Desensitization phi

17 No desensitization t = 3.0 Desensitization phi

18 No desensitization t = 3.2 Desensitization phi

19 No desensitization t = 3.4 Desensitization phi

20 No desensitization t = 3.6 Desensitization phi

21 No desensitization t = 3.8 Desensitization phi

22 No desensitization t = 4.0 Desensitization phi