Effect of Plasma on the Deflagration to Detonation Transition

ABSTRACT

Numerical results of plasma supported deflagration to detonation transition have been presented. The mathematical model includes Reynolds averaged Navier-Stokes equations for the compressible medium, enthalpy equation, the standard k-$\omega$ turbulence model, transport equations for the progress variable and flame wrinkling factor. Non-equilibrium plasma was modeled as a source of radicals. Initial concentrations of radicals were taken from the detailed plasma simulation using a three-temperature plasma model. To model equilibrium plasma we used a Joule heating source with the conductivity depending on the energy deposition time. Simulations showed that the injection of radicals was more efficient than a thermal effect of plasma in the deflagration to detonation transition time and distance. We observed changes in the detonation cell size and improvement of the detonation structure stability with the plasma addition. Because the oxygen atoms injection primarily controls the phenomenon, the detonation cell size depends on the oxygen atoms concentration and on the orientation of the plasma energy spot with respect to the detonation wave.

KEYWORDS:

• Deflagration to detonation transition
• non-equilibrium plasma
• numerical simulation
• detonation cell

Nomenclature

c	=	Progress variable
$d$	=	Cell size, mm
E	=	Electric field, V/m
$h$	=	Mixture enthalpy, J
k	=	Turbulent kinetic energy, m2/s2
K	=	Kinetic energy of the mixture, m2/s2
N	=	Number density, 1/m3
p	=	Pressure, Pa
$\dot{Q}$	=	Reaction heat source, J/s
Sl	=	Laminar flame speed, m/s
St	=	Turbulent burning speed, m/s
$T$	=	Temperature, K

Symbols
$\hat{\tau }$	=	Reynolds stress tensor
Θ	=	Flame wrinkling factor
$vk$	=	Diffusion velocity, m/s
${\sigma }_{\hspace{0.17em}}$	=	Electric conductivity, (Ohm m)−1
$\mathrm{\Phi }$	=	Equivalence ratio

Sub scripts
b	=	Burned mixture
e	=	Electron
L	=	Laminar
t	=	Turbulent
u	=	Unburned mixture