Physical Waves In Reacting Flows

Many of these instabilities are linked hydrodynamic instabilities can create vortices in combustion chambers these vortices contain fuel and oxidizer and can burn after a certain delay, providing the source of excitation for the acoustic mode, this acoustic mode then can trigger new vortices [297]. 

Like in classical acoustics in cold flows [304], wave equations can also be derived for reacting flows but they are much more complex [270 340]. Af- 

These two methods are similar to what is found in the study of hydrodynamic instability where LES is replaced most often by DNS and Helmholtz solvers by Orr Sommerfeld solvers. Both methods have already been used and shown to be efficient more examples will be provided in Chapter 9. They were also compared in a few cases [350 321[. LES is much more expensive and cannot work if all boundary conditions are not known precisely. This means that impedances of all inlets and outlets for example are required. Helmholtz formulations also need impedances but since they run faster and can provide all modes (and not only the most excited), they are easier to use when impedances are not known precisely. 

A useful quantity to study combustion instabilities is the acoustic energy defined by [340]  

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