CLTORC

Motivation

• 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?

Numerical Method

• 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)

Use Cases

• Heavy WIP: run python piston_demo.py for the simplest case

References

• 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.