Session HL: Acoustics I

Scattering of an entropy disturbance into sound by a symmetric thin body

The interaction of a convecting entropy disturbance, such as generated by a gas turbine combustor, with a solid object is known to generate sound. The sound generation is due to (i) the acceleration of the convected disturbance by the mean flow and (ii) satisfaction of the wall-boundary condition on the object. This process, which leads to the so-called indirect combustion noise, is known to be present in modern gas turbine engines but its specific details are not known, including its overall contribution to the acoustic signature of the engine and its influence on the combustor. Computational and analytical results are presented to examine the sound field created by a localized entropy disturbance convecting in the vicinity of a symmetric thin body. Unsteady calculations of the compressible Euler equations are used to directly compute the radiated sound. Rapid distortion theory is used, when combined with a low frequency Green's function, to estimate the dominant radiated field. It is found that the source structure is dominated by a streamwise-oriented dipole, with the most important interactions occurring near the stagnation points.   

Interaction of sound with an elastic plate in a duct

The interaction of sound with a cavity backed elastic plate in a duct is studied using analytical and numerical methods. The problem consists of an incoming plane wave in an infinite duct with a finite elastic plate mounted flush on one of the walls of the duct. The analytic solution is found by series expansion of pressure in the cavity, duct and velocity of the plate using cosine and sine modes that satisfy the boundary conditions. Two separate boundary conditions for the plate are considered, simply-supported and clamped. The response of the plate is quantified by $V_{rms}$, the square root of integral average of velocity square of plate. A corresponding numerical simulation, based on first principles, of the same problem further illustrates the sound-plate interaction. Variation of $V_{rms}$ of the plate with forcing frequency shows that the acoustic-structure interaction modifies the frequency of peak response from that of the natural frequency of the plate.   

The sound of boundary-layer flow over a roughness patch

The sound radiation by a turbulent boundary layer over an array of 4 (spanwise) by 10 (streamwise) hemispherical roughness elements is studied using large-eddy simulation and Lighthill's theory. The roughness height is $12.7\%$ of the boundary layer thickness and $17\%$ of the spacing between neighboring elements in both directions. The momentum-thickness based Reynolds number is 2984. The acoustically compact roughness elements and their images in the wall radiate primarily as acoustic dipoles in the plane of the wall. Similar to previous findings with a pair of roughness elements, the dipole sources are mainly generated by the interaction of roughness elements with incoming turbulent eddies and horseshoe vortices. Spanwise dipoles are stronger than streamwise dipoles in the low and intermediate frequency range, and wake turbulence enhances sound radiation from downstream elements. It is found that the leading row of roughness elements produces the weakest sound. After a small overshoot by the second row, the rows further downstream generate sound of comparable intensity, which is stronger than that of the first row. The correlations between dipole sources associated with neighboring roughness elements are weak, suggesting that the roughness elements radiate as essentially independent sources.   

Acoustic source mechanisms for boundary-layer flow over small steps

The aeroacoustics of low-Mach-number boundary-layer flow over small backward and forward facing steps is studied using large-eddy simulation and Lighthill's theory with a low frequency (compact step height) Green's function. The Reynolds number based on the step height and free-stream velocity ranges from 328 to 21000 as the step height varies from $0.83\%$ to $53\%$ of the boundary layer thickness. The steps act primarily as acoustic dipole sources aligned in the streamwise direction. Consistent with previous experimental measurements, the forward step is louder than the backward step, because it generates stronger sources in regions closer to the step corner, which is heavily weighted by the Green's function. A detailed analysis of flow field and Green's function weighted sources reveals that the backward step generates sound mainly through diffraction of the boundary-layer source field which is not much affected by the step in the acoustically important region, whereas the forward step generates sound through a combination of diffraction and turbulence modification by the step. As the step height decreases, the difference in sound level between forward and backward steps is much reduced as turbulence modification becomes less significant.   

Accurate calculation of high-frequency sound generated by interaction of low Mach number flows and rigid bodies

According to N. Curle, the interaction of turbulent flow and rigid bodies is an efficient mechanism of sound generation at low Mach number regimes. A popular approach to compute the sound due to this interaction is to use an approximation of Curle's solution to Lighthill's equation. In this approximation, pressure on rigid surfaces is replaced by the hydrodynamic pressure which can be easily obtained from the solution of incompressible Navier-Stokes equation; however, this approximation is known to be valid only at low frequencies and under-predict the sound at high frequencies. The objective of the present study is to improve this approximation for the high frequency range. In this work we construct the high frequency sound by formally decomposing the surface pressure into contributions from hydrodynamics and acoustics. The acoustic pressure on the surface is obtained by splitting the acoustic Green's function and solving a boundary integral equation. The projection of surface acoustic pressure to the farfield compensates for the missing portion of sound at high frequencies. This method is applied to the problem of sound generated by turbulent vortex shedding of a cylinder at Re=10,000.   

Acoustic chambers for sonofusion experiments - sensitivity on geometry and materials

Sonofusion (SF) relies on the perfect realization of a symmetrically imploding vapor bubble in a compressing acoustic field, so that the center of the singularity yields extreme energy densities, potentially allowing for thermonuclear fusion to occur. An assembly of a cylindrical acoustic chamber with longitudinal wave reflectors allows excitation of the fundamental mode of the liquid body. Our finite-element simulations of such a vibrating glass chamber filled with liquid attempt to answer questions that have arisen since the claimed successful SF experiments of Taleyarkhan. In particular, we show that the sensitivity to geometry and materials of the acoustic chamber may be the reason why SF is apparently difficult to reproduce. This could be a reason why completely independent confirmation of SF is still lacking. A 2-D axisymmetric forced harmonic analysis in ANSYS, is presented and compared to own measurements of pressure amplitude and wall displacement.   

Molecular simulation of sound propagation

Numerical simulation of molecular dynamics of sound propagation in a gas is carried out to clarify the propagation property of sound waves with large amplitude and very high frequency. Assuming the Lennard--Jones inter-molecular potential, we calculate the motions of hundreds of thousand of monatomic molecules excited by an oscillating plate in a gas phase. The result is compared with corresponding numerical solutions of model Boltzmann equation and Navier--Stokes equations.   

A Formulation of Compressing Process and Aeroacoustics

We study the general theoretical formulation of compressing (longitudinal) process and aeroacoustics. A maximum Helmholtz decomposition (MaxHD) principle is proposed as the basic criterion of the formulation, which is applied at two levels. At the fundamental level, the MaxHD leads to a convective wave equation for dilatation as the counterpart of the diffusion equation for vorticity in the shearing (transverse) process. This is the fundamental governing equation for the compressing, equivalent to, among others, Lilley's (1973) 3rd-order equation for logarithmic pressure and, for inviscid flow, Howe's (1975) total-enthalpy equation. Phillips' (1960) 2nd-order equation is disqualified by MaxHD. At the operational level, the MaxHD further isolates the compressing variables from the others by decomposing the velocity itself. This yields a 4th-order convective wave equation for the velocity potential. Unlike equations of Lilley, Howe, and other equivalents, the source terms do not contain compressible velocity potential, and the vortical velocity appears only in source terms and operator coefficients. Thus, its linearized version should be the rational basis for problems of sound wave in various shear flows.