External flow modulation in computational fluid dynamics

In many applications of current interest, one wishes to determine the acoustic response of a fluid system. This process requires the specification of acoustical and fluid mechanical conditions at the system input. We deal here with some of the problems encountered in formulating such conditions. One first considers the response of one-dimensional fluid systems to a velocity modulation specified at the inlet boundary. For a harmonic input velocity modulation, the response is a complex waveform including an oscillation at the modulation frequency combined with oscillations at the eigenfrequencies of the system. This is explained by noting that there is a mismatch between the initial state of the system and the state corresponding to an infinite time harmonic modulation. The system eigenmodes are excited at the initial instant and their amplitude remains finite if the numerical method is weakly dissipative. This explanation is supported by an analytical study of the system response. It is then shown that the development of the unwanted oscillations may be avoided by progressively increasing the amplitude of the modulation. The modulation may also be applied on ingoing acoustic waves, allowing outgoing waves to escape through the input boundary. The inlet now behaves like a nonreflecting boundary. This technique is applied to the case of interactions between acoustics and combustion. Numerical simulations are in good agreement with experiments.