1. Converging detonation in
a expanding radially
symmetric flow
A. Kasimov and S. Korneev

2. fresh mixture
reaction zone
products
adiabatic expansion

3. Reactive Euler equations with one step chemistry

4. In this case the Reactive Euler equations can be written:
Point is singular
For solution existence, the numerator
and denominator should vanish
Point is saddle point
start integration from the sonic point

6. Hydrogen-Oxygen mixture with 90% argon dilution

7. Starting with the
steady-state solution
The solution is unstable
and average radius of the detonation
increase
Increase heat release
cell size decrease
Pressure field

8. sonic curve
obstaclesreflected shock waves

10. With obstacles Without obstacles

11. Pressure Temperature
Density Velocity magnitude

12. Converging detonation was considered
in a radially symmetric expanding flow
The average radius of the detonation
increase in time
The detonation exist for a reasonable
flow parameters
Obstacles behind the detonation may
keep it inside bounded area