Combined Numerical and Experimental Study of a Slit Resonator Under Grazing Flow

Abstract

This study compares two numerical methods based on the Linearized Navier-Stokes equations (LNSE) for the simulation of a resonator in presence of a cold mean flow: a time domain Runge-Kutta Discontinuous Galerkin (RKDG) code and a frequency-domain high-order continuous Finite Element Method (pFEM). The results are compared to experimental data from a dedicated experimental campaign on a slit resonator. It was shown that the simulations predict the correct trends, but some discrepancies have been observed. The origin of these differences has to be investigated further. Different impedance measurement techniques are applied to the numerical and experimental data to obtain the acoustic impedance of the slit resonator. Within their respective range of validity, reasonable agreement is found between the different techniques. Nomenclature B Width of the duct, [m] Z Acoustic impedance, [Rayl] c Speed of sound, [m/s] z Specific impedance, [-] f Frequency, [Hz] z i Location of microphone i, [m] k Acoustic wave number, [m −1 ] δ Flow boundary layer thickness, [m] H Back cavity depth, [m] δ ij Kronecker delta function, [-] L Length of the test section, [m] Acoustic monopole source amplitude, [P a] M Mach number, [-] κ Thermal conductivity, [W/(m.K)] p Pressure, [P a] λ Acoustic wavelength, [m] R +/− Reflection coefficient of scatter matrix, [-] µ Dynamic viscosity, [kg/(m.s)] S Cross section of the channel, [m 2 ] ν Kinematic viscosity, [m 2 /s] S c Surface of perforation, [m 2 ] τ Viscous stress tensor, [P a] T Absolute temperature, [K] Φ Dissipation function, [W/m 3 ] T +/− Transmission coefficient of the scatter matrix, [-] ρ Density, [kg/m 3 ] u Velocity vector, [m/s] ω Angular frequency, [rad/s] x Vector of the cartesian coordinate position, [m]

Linearized Euler Equations for the Determination of Scattering Matrices for Orifice and Perforated Plate Configurations in the High Mach Number Regime

“…It has been shown that the unidirectional coupling from the mean flow to the acoustics provides an adequate description of relevant interaction effects in acoustic problems using frequency transformed fields equations (see [20,29]), but time domain field equations are also very capable (see [34][35][36][37][38]) and references therein. The generation and interaction of vorticity and entropy fluctuations are especially well captured due to the incorporation of gradients of the mean flow quantities.…”

Determination of Acoustic Impedance for Helmholtz Resonators Through Incompressible Unsteady Flow Simulations

“…In this case, the impedance is independent of the sound amplitude, and the resonator or orifice behaves like a linear system. Numerical methods based on linearized equations, like the linearized Navier-Stokes equations, allow for an efficient treatment of this linear regime with limited computational costs [1]. By increasing the excitation amplitudes, nonlinear effects appear and become progressively dominant.…”