Shape optimization of acoustic horns for improved directivity control and radiation efficiency based on the multimodal method

Abstract

The multimodal method is used to develop an approach for optimizing the shape of axisymmetric acoustic horns for both well-controlled directivity and high radiation efficiency over a wide frequency range. A horn with an arbitrary profile can be efficiently modeled with the multimodal method by projecting the wave field over transverse modes in connected short cylinders; the radii of the cylinders are used directly as design variables. Many design variables are employed in the optimization process to ensure design flexibility and computational accuracy. The relative weights for the design objectives of constant directivity, high radiation efficiency, and acceptable shape smoothness are adjusted by two coefficients in the objective function. The optimization problem is solved with a gradient-based algorithm, which takes advantage of algebraic gradient expressions. Numerical experiments demonstrate that the optimization procedure generates smooth horn contours that exhibit considerably improved performance over the target frequency band. Interestingly, a high-quality horn produced with moderate weight coefficients is similar in shape to constant-directivity horns invented earlier while having good low-frequency loading properties. The proposed method provides an attractive alternative to conventional horn design approaches.

Coupled-mode separation of multiply scattered wavefield components in two-dimensional waveguides

“…Linear relations between the corresponding coefficient column vectors appear with so-called impedance and admittance matrices, which are easy to relate to the reflection matrices; cf. [ 57 , eqn (13)]. Obviously, related recursions for impedance matrices could be used instead of the reflection-matrix recursions in §4.2, and the boundary conditions could be transported using impedance matrices.…”

“…Some texts, e.g. [ 57 ] for shape optimization of acoustic horns and [ 58 ] for acoustic simulation of the vocal tract, apply the impedance-matrix approach. Just as for the reflection matrices [ 7 ], differential equations of Riccati type appear in the continuous case without medium discretization.…”

Acoustic radiation from an engine intake using an admittance multimodal method

“…The current paper proposes an alternative and less computationally demanding multimodal approach. This method has already been used for computing the acoustic radiated field and has demonstrated high performance, making it suitable for optimization procedures [6,7,8]. However, like most multimodal methods, it is currently limited to cases without mean flow.…”