- We want to understand the route from deflagration to detonation
- A useful abstraction is to treat the flame as a piston: as it propagates it pushes on the gas ahead of it
- If the flame accelerates, Riemann characteristics of the same family can converge, leading to shock formation
- This shock changes the thermodynamic state of the deflagration's inlet mixture through this process
- What are the critical conditions that lead to a detonation?
- To solve the piston problem, we adopt Lagrangian coordinates, i.e. we follow fluid parcels instead of spatial locations
- A key advantage with this approach is the formulation of the boundary condition, namely, move a boundary fluid parcel at a prescribed rate
- The governing equations are the three fluid conservation laws for mass, momentum, and energy. ** We keep things inviscid and non-reacting for now.
- We use classic viscous dissipation to handle shocks (following Richtmyer & Morton 1968)
- Heavy WIP: run
python piston_demo.pyfor the simplest case
- RD Richtmyer and KW Morton: Difference Methods for Initial-Value Problems, Interscience Publishers, New York, 1968.
- Zeldovich, Ya B., and Yu P. Raizer. Physics of shock waves and high-temperature hydrodynamic phenomena. 1965.