Calculation of duct acoustics with the parabolized stability equations

Area of Science:

• Computational Aeroacoustics
• Fluid Dynamics
• Acoustic Wave Propagation

Background:

• Accurate prediction of sound propagation in ducts is crucial for noise reduction in applications like turbofan engines.
• Existing methods often face computational limitations in complex flow scenarios.

Purpose of the Study:

• To explore and validate the application of Parabolized Stability Equations (PSEs) for computational duct acoustics.
• To assess the efficiency and accuracy of PSEs compared to traditional numerical methods.

Main Methods:

• Formulation of PSEs in a general duct-fitted coordinate system.
• Validation against test cases including uniform flow, temperature gradients, and laminar/turbulent flows.
• Comparison with Linearized Euler Equations (LEE) for fan noise propagation.

Main Results:

• PSEs demonstrated close agreement with existing literature and validated test cases.
• Significant computational efficiency: 75.8% reduction in computation time and 98.2% reduction in memory usage compared to LEE.
• PSEs showed superior performance over finite element and parabolic approximation methods, especially with viscous shear flow effects.

Conclusions:

• PSEs offer a computationally efficient and accurate method for predicting sound propagation in complex duct acoustics.
• The method is well-suited for applications involving boundary layer shielding and liner-boundary layer interactions.
• PSEs present a promising approach for future acoustic research and practical engineering applications.