I am new to rocket engines. I was looking at an image of RS-25 engine's MCC and found these acoustic cavities, and I want to know how they work. Can somebody please explain their working principle? Thank you.
They are provided to help damp out combustion instabilities.
The main injector uses cooled baffle elements, developed at Glenn in the 1960s to control pressure waves that could destroy the engine. Pressure waves in the space shuttle main engine combustion chamber are also controlled by acoustic cavities. Testing by Glenn engineers determined the most effective size and location of these cavities, which act somewhat like cavities in acoustic ceilings.
You can read more on the theory of how they work in this book Liquid Rocket Engine Combustion Instability starting at page 384.
It starts out
Acoustic cavities such as Helmholtz and quarter-wave resonators were successfully used as damping devices for the suppression of combustion oscillations. resonator consists of a small volume connected with the combustion chamber through an orifice. If the dimensions of the various resonator elements are small in comparison to the wavelength of the oscillation, the gas motion behavior in the resonator is analogous to a mass-spring-dashpot system.
Acoustic cavity design is also discussed in the NASA monograph Liquid Rocket Engine Combustion Stabilization Devices. It includes this figure showing some other applications.