Detonation Diffraction

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1 Detonation Diffraction E. Schultz, J. Shepherd Detonation Physics Laboratory Pasadena, CA MURI Mid-Year Pulse Detonation Engine Review Meeting February 10-11, 2000

$Diffraction$ Shadowgraphs

2 Super-critical Detonation Diffraction Laser Shadowgraphs Chemiluminescence Digital Image

$Diffraction$ Shadowgraphs

3 Sub-critical Detonation Diffraction Laser Shadowgraphs Chemiluminescence Digital Image

$Diffraction$ Shadowgraphs

5 Critical Detonation Diffraction Laser Shadowgraphs Chemiluminescence Digital Image

6 Motivation Diverging area from initiator tube to combustion chamber Converging and/or diverging nozzle Converging and/or diverging areas in combustion chamber Diverging area from nozzle into atmosphere Diverging area Possible detonation failure Converging area Overdriven detonation Possible wave failure

7 Diffracting Detonation Schematic Undisturbed detonation described by ZND model with reaction length ( and time (τ scale Locus of disturbance interaction points with detonation front r d V CJ z t 2 t 3 t c t 0 t 1 T Temperature evolution for particles crossing through interaction point at various times t 1 t 2 t 3 t

8 Critical Diffraction Model Consider the spherical reactive Euler equations: Dρ u ρ + --ρu = 0 Dt r r Du Dt + 1 ρ -- P = 0 r De Dt P Dρ ρ = 0 Dt Specializing to a system of ideal gases, shock-fixed reference frame, one-step irreversible reaction described by a first order Arrhenius kinetic rate law with linear depletion, and constant specific heats: c p ( 1 M 2 DT = h 0 k( 1 z ( 1 γm 2 exp Dt 2 R w 2 du x U s w 1 ( w w w s dt t ρ -- P + + t E R g T + Evaluating post-shock (s and imposing DT s /Dt = 0 critical criterion: DT s Dt T s τθ c R -- w 2 du s dw s 1 dp s = + s ( Us w s + w s w dt s = 0 dt p ( 1 M s ρ sdt Using perfect gas strong shock jump conditions, the Sedov similarity solution for spherical blast wave decay, and geometric relationships we arrive at an expression for the critical diameter: 10γ + 26 d c = VCJ τθtanα = γ γ θtanα γ 1

9 Parameters for Critical Diffraction Model Detonation Reaction Time (µs (O (O 2 φc (O Activation Energy Parameter θ=e/rt v N (O 2 φc (O 2 + 5(O Reaction Time ZND calculations with validated reaction mechanism (Konnov 1998 Activation Energy CV calculations with validated reaction mechanism (Konnov 1998 Disturbance Angle ( vn max Detonation Velocity V CJ (m/s (O 2 φc (O 2 + 5(O Disturbance Trajectory Skews (1967 shock diffraction signaling extended to detonations 1000 Detonation Velocity STANJAN (Reynolds 1986 chemical equilibrium calculations

10 Critical Diameter Results Critical Diameter D c (mm Critical Diameter D c (mm (O 2 + 3(O 2 + 5(O 2 φh (O 2 + 3(O 2 + 5(O Equivalence ratio: fuel-oxygen Equivalence ratio: fuel-air Critical Diameter D c (mm 10 1 H 2 C 2 C 3 H 2 C 2 C Initial Pressure (kpa Critical Diameter D c (mm H 2 C 2 C 3 H 2 C 2 C Nitrogen Dilution % vol Initial pressure: fuel-oxygen N 2 dilution: fuel-oxygen-nitrogen

11 Two-Mixture Detonation Diffraction Fuel-oxygen diffraction tube mixture Fuel-oxygen-nitrogen test section mixture Gate valve opening time < 400 ms Diffraction limits for one mixture experiments Mixture Critical β 2H 2 +(O 2 + βn C 2 +3(O 2 + βn C 3 +5(O 2 + βn Diffraction limits for two mixture experiments Diffraction Tube Mixture Test Section Mixture Critical β 2H 2 +O 2 2H 2 +(O 2 + βn C 2 +3O 2 C 2 +3(O 2 + βn C 3 +5O 2 C 3 +5(O 2 + βn

An analytical model for direct initiation of gaseous detonations

Issw21 An analytical model for direct initiation of gaseous detonations C.A. Eckett, J.J. Quirk, J.E. Shepherd Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena CA 91125,