Nonlinear behavior of Helmholtz resonator with a compliant wall for low frequency, broadband noise control

Low frequency sound attenuation is often pursued using Helmholtz resonators (HRs). The introduction of a compliant wall around the acoustic cavity results in a two-degree-of-freedom (2DOF) system capable of more broadband sound absorption. In this study, we report the amplitude-dependent dynamic response of a compliant walled HR and investigate the effectiveness of wall compliance to improve the absorption of sound in linear and nonlinear regimes. The acoustic-structure interactions between the conventional Helmholtz resonator and the compliant wall result in non-intuitive responses when acted on by nonlinear amplitudes of excitation pressure. This paper formulates and studies a reduced order model to characterize the nonlinear dynamic response of the 2DOF HR with a compliant wall compared to that of a conventional rigid HR. Validated by experimental evidence, the modeling framework facilitates an investigation of strategies to achieve broadband sound attenuation, including by selection of wall material, wall thickness, geometry of the HR, and other parameters readily tuned by system design. The results open up new avenues for the development of efficient acoustic resonators exploiting the deflection of a compliant wall for suppression of extreme noise amplitudes.

Modal analysis of a viscous fluid falling over a compliantwall

We study the modal instability of a three-dimensional Newtonian viscous fluid falling over a compliant wall under the framework of coupled evolution equations for normal velocity and normal vorticity, respectively. The Chebyshev spectral collocation numerical technique is applied in exploring unstable modes for the three-dimensional disturbances. The unstable zones pertaining to surface mode, wall mode and shear mode reduce as long as the spanwise wavenumber amplifies and corroborates the stabilizing influence of spanwise wavenumber. However, the onset of instability for the wall mode decays as long as the capillary number amplifies and ensures the destabilizing influence of the capillary number. Furthermore, the critical Reynolds number corresponding to surface mode found in the long-wave zone shifts towards the finite wavelength zone with increasing spanwise wavenumber and confirms the extinction of long-wave instability. But the inertialess instability created due to the wall mode disappears with increasing spanwise wavenumber. Moreover, the shear mode emerges in the high Reynolds number zone and is stabilized in the presence of spanwise wavenumber. In addition, the analytical derivation of Squire’s theorem is provided in appendix B for the flow over a compliant wall.

Experiments and Modeling of a Compliant Wall Response to a Turbulent Boundary Layer with Dynamic Roughness Forcing

The response of a compliant surface in a turbulent boundary layer forced by a dynamic roughness is studied using experiments and resolvent analysis. Water tunnel experiments are carried out at a friction Reynolds number of Reτ≈410, with flow and surface measurements taken with 2D particle image velocimetry (PIV) and stereo digital image correlation (DIC). The narrow band dynamic roughness forcing enables analysis of the flow and surface responses coherent with the forcing frequency, and the corresponding Fourier modes are extracted and compared with resolvent modes. The resolvent modes capture the structures of the experimental Fourier modes and the resolvent with eddy viscosity improves the matching. The comparison of smooth and compliant wall resolvent modes predicts a virtual wall feature in the wall normal velocity of the compliant wall case. The virtual wall is revealed in experimental data using a conditional average informed by the resolvent prediction. Finally, the change to the resolvent modes due to the influence of wall compliance is studied by modeling the compliant wall boundary condition as a deterministic forcing to the smooth wall resolvent framework.

Effects of (MHD) and wall properties oscillatory flow for williamson fluid with constant viscosity through porous channel

In this research, the williamson flow with heat transfer through the tube of compliant wall properties with slip at boundaries is analyzed analytically. An approximated theoretical model is constructed of springbacked flexible compliant walls pipe, chosen to move as sinusoidal wave

Engineering Applications of Peristaltic Fluid Flow with Hall Current, Thermal Deposition and Convective Conditions

This article addresses the peristaltic flow in a compliant wall channel. Analysis has been carried out in the presence of a Hall current and chemical reaction. Convective conditions in terms of both heat and mass transfer are employed. Mathematical modeling is developed for an incompressible Carreau fluid. Thermal deposition effect and convection at the channel walls are considered. Series solutions are obtained for small Weissenberg number We. Solution expressions of velocity, temperature, concentration and stream function are obtained. These physical quantities are displayed and analyzed. Heat transfer coefficient and trapping are explored in detail.