Numerical study on leading-edge receptivity of acoustic waves in subsonic flow utilizing compressible linearized Navier–Stokes method

The investigation of leading-edge receptivity to freestream acoustic waves in subsonic flow employs compressible linearized Navier–Stokes (CLNS) equations. These are solved in harmonic form without supplementary assumptions, enabling analysis of receptivity and spatial development of linear stable and unstable perturbations at moderate computational costs. This study first addresses the feasibility and benefits of the CLNS method for a canonical problem, followed by a review of Tollmien–Schlichting wave extraction methods from multimodal solutions. The CLNS results were validated, showing excellent agreement with linear stability theory. Furthermore, various freestream acoustic wave formulations were evaluated. A theoretically rigorous model based on the Euler equations was established for comparison with three simplified models, including the infinite-wavelength assumption commonly adopted in subsonic receptivity studies. An assessment of the acoustic models revealed that the simplified formulations generated contaminated disturbance fields. Notably, even when an infinite-wavelength disturbance is imposed, a finite-wavelength disturbance field develops within the domain, implying that the requirement for phase relations is disregarded under the infinite acoustic wavelength assumption. This study demonstrates that accurate receptivity prediction requires a physically complete acoustic wave model based on Euler relations, even at low Mach numbers where infinite acoustic wavelength assumptions are often made.