Nonlinear standing waves in 2-D acoustic resonators

Area of Science:

• Acoustics
• Fluid Dynamics
• Computational Physics

Background:

• Finite-amplitude standing waves in acoustic resonators are complex phenomena.
• Understanding nonlinear acoustic behavior is crucial for resonator design and application.
• Previous models often simplified thermoviscous dissipation and nonlinear effects.

Purpose of the Study:

• To develop and numerically solve a 2-D model for finite-amplitude standing waves in rectangular acoustic resonators.
• To incorporate gas dynamic nonlinearities, thermoviscous dissipation, and external driving forces.
• To investigate the acoustic field patterns and shock-wave excitation.

Main Methods:

• Derivation of a closed set of three partial differential equations in conservative form from gas dynamics.
• Formulation of equations in Cartesian coordinates, including acoustic velocity components and density.
• Numerical solution in the time domain using a central semi-discrete difference scheme for convection-diffusion equations.
• Analytical formula for pressure calculation.

Main Results:

• Simulation of various acoustic field patterns in resonators driven by a vibrating piston.
• Observation of lateral shock-wave mode excitation when longitudinal and transversal resonance conditions are met.
• Demonstration of the model's capability to capture complex nonlinear acoustic phenomena.

Conclusions:

• The derived model accurately simulates finite-amplitude standing waves in rectangular acoustic resonators.
• Nonlinear effects and thermoviscous dissipation significantly influence acoustic field behavior.
• The study highlights the potential for shock-wave generation in resonant acoustic systems.