Anton Krynkin

Scattering by coupled resonating elements in air

Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of these scatterers in air has been investigated analytically and through laboratory experiments. The composite scatterer forms a system of coupled resonators and gives rise to multiple low-frequency resonances. The corresponding analytical model employs polar angle dependent boundary conditions on the surface of the N-slit cylinder. The solution inside the slits assumes plane waves. It is shown also that in the low-frequency range the N-slit rigid cylinder can be replaced by an equivalent fluid layer. Further approximations suggest a simple square root dependence of the resonant frequencies on the number of slits and this is confirmed by data. The observed resonant phenomena are associated with Helmholtz-like behaviour of the resonator for which the radius and width of the openings are much smaller than the wavelength. The problem of scattering by a finite periodic array of such coupled resonators in air is solved using multiple scattering techniques. The resulting model predicts band-gap effects resulting from the resonances of the individual composite scatterers below the first Bragg frequency. Predictions and data confirm that use of coupled resonators results in substantial insertion loss peaks related to the resonances within the concentric configuration. In addition, for both scattering problems experimental data, predictions of the analytical approach and predictions of the equivalent fluid layer approximations are compared in the low-frequency interval.

Frequency-wavenumber spectrum of the free surface of shallow turbulent flows over a rough boundary

Data on the frequency-wavenumber spectra and dispersion relation of the dynamic water surface in an open channel flow are very scarce. In this work, new data on the frequency-wavenumber spectra were obtained in a rectangular laboratory flume with a rough bottom boundary, over a range of subcritical Froude numbers. These data were used to study the dispersion relation of the surface waves in such shallow turbulent water flows. The results show a complex pattern of surface waves, with a range of scales and velocities. When the mean surface velocity is faster than the minimum phase velocity of gravity-capillary waves, the wave pattern is dominated by stationary waves that interact with the static rough bed. There is a coherent three-dimensional pattern of radially propagating waves with the wavelength approximately equal to the wavelength of the stationary waves. Alongside these waves, there are freely propagating gravity-capillary waves that propagate mainly parallel to the mean flow, both upstream and downstream. In the flow conditions where the mean surface velocity is slower than the minimum phase velocity of gravity-capillary waves, patterns of non-dispersive waves are observed. It is suggested that these waves are forced by turbulence. The results demonstrate that the free surface carries information about the underlying turbulent flow. The knowledge obtained in this study paves the way for the development of novel airborne methods of non-invasive flow monitoring.

A non-invasive acoustical method to measure the mean roughness height of the free surface of a turbulent shallow water flow

In this paper, the directivity of the airborne sound field scattered by a dynamically rough free flow surface in a flume is used to determine the mean roughness height for six hydraulic conditions in which the uniform depth of the turbulent flow. The nonlinear curve fitting method is used to minimize the error between the predicted directivity and directivity data. The data fitting algorithm is based on the averaged solution for the scattered sound pressure as a function of angle which is derived through the Kirchhoff integral and its approximations. This solution takes into account the directivity of the acoustic source. For the adopted source and receiver geometry and acoustic frequency it is shown that the contribution from the stationary phase point (single specular point on the rough surface) yields similar results to those which can be obtained through the full Kirchhoffs integral. The accuracy in the inverted mean roughness height is comparable to that achieved with an array of conductive wave probes. This method enables non-invasive estimation of the flow Reynolds number and uniform flow depth.

Approximations to wave propagation through a lattice of Dirichlet scatterers

A scheme of matched asymptotic expansions is used to obtain approximations to the dispersion relation when waves, governed by the Helmholtz equation, propagate through a two-dimensional lattice of scatterers on each of which a homogeneous Dirichlet boundary condition is imposed. The scatterers must be identical, but can be of any shape as long as each is small relative to the wavelength and the lattice periodicity. The results differ from those obtained using homogenisation in that there is no requirement that the wavelength be much longer than the lattice periodicity, and hence it is possible to describe band gaps.

Physicomechanical properties of ultrahigh temperature heteromodulus ceramics based on group 4 transition metal carbides

Abstract Abstract Highly densified TiC, ZrC and HfC based ultrahigh temperature heteromodulus ceramics (HMC), containing 10-50 vol.-% of low modulus phase in the form of particulate graphite, were prepared by hot pressing at 2700°C and 12 MPa in argon atmosphere. The microstructure, elastic characteristics, flexural and compressive static strength, fracture toughness, impact resistance, hardness and thermal expansion were investigated and compared with those available in earlier works for clear understanding the composition-property correlations and anisotropy of this type of HMC composites. Different thermal shock resistant parameters for the HMC were calculated on the basis of obtained experimental data. A new principle of optimum materials design for the compositions in the refractory carbide-graphite systems is exemplified by the TiC-C HMC materials.

Analytical approximations for low frequency band gaps in periodic arrays of elastic shells

This paper presents and compares three analytical methods for calculating low frequency band gap boundaries in doubly periodic arrays of resonating thin elastic shells. It is shown that both Foldy-type equations (derived with lattice sum expansions in the vicinity of its poles) and a self-consistent scheme could be used to predict boundaries of low-frequency (below the first Bragg band gap) band gaps due to axisymmetric (n=0) and dipolar (n=1) shell resonances. The accuracy of the former method is limited to low filling fraction arrays, however, as the filling fraction increases the application of the matched asymptotic expansions could significantly improve approximations of the upper boundary of band gap related to axisymmetric resonance. The self-consistent scheme is shown to be very robust and gives reliable results even for dense arrays with filling fractions around 70%. The estimates of band gap boundaries can be used in analyzing the performance of periodic arrays (in terms of the band gap width) without using full semi-analytical and numerical models. The results are used to predict the dependence of the position and width of the low frequency band gap on the properties of shells and their periodic arrays.

Acoustic imaging in application to reconstruction of rough rigid surface with airborne ultrasound waves

Accurate reconstruction of the surface roughness is of high importance to various areas of science and engineering. One important application of this technology is for remote monitoring of open channel flows through observing its dynamic surface roughness. In this paper a novel airborne acoustic method of roughness reconstruction is proposed and tested with a static rigid rough surface. This method is based on the acoustic holography principle and Kirchhoff approximation which make use of acoustic pressure data collected at multiple receiver points spread along an arch. The Tikhonov regularisation and generalised cross validation technique are used to solve the underdetermined system of equations for the acoustic pressures. The experimental data are collected above a roughness created with a 3D printer. For the given surface, it is shown that the proposed method works well with the various number of receiver positions. In this paper, the tested ratios between the number of surface points at which the surface elevation can be reconstructed and number of receiver positions are 2.5, 5, and 7.5. It is shown that, in a region comparable with the projected size of the main directivity lobe, the method is able to reconstruct the spatial spectrum density of the actual surface elevation with the accuracy of 20%.

Doppler spectra of airborne ultrasound forward scattered by the rough surface of open channel turbulent water flows

Experimental data are presented on the Doppler spectra of airborne ultrasound forward scattered by the rough dynamic surface of an open channel turbulent flow. The data are numerically interpreted based on a Kirchhoff approximation for a stationary random water surface roughness. The results show a clear link between the Doppler spectra and the characteristic spatial and temporal scales of the water surface. The decay of the Doppler spectra is proportional to the velocity of the flow near the surface. At higher Doppler frequencies the measurements show a less steep decrease of the Doppler spectra with the frequency compared to the numerical simulations. A semi-empirical equation for the spectrum of the surface elevation in open channel turbulent flows over a rough bed is provided. The results of this study suggest that the dynamic surface of open channel turbulent flows can be characterized remotely based on the Doppler spectra of forward scattered airborne ultrasound. The method does not require any equipment to be submerged in the flow and works remotely with a very high signal to noise ratio.

An eigenvalue correction due to scattering by a rough wall of an acoustic waveguide

In this paper a derivation of the attenuation factor in a waveguide with stochastic walls is presented. The perturbation method and Fourier analysis are employed to derive asymptotically consistent boundary-value problems at each asymptotic order. The derived approximation predicts the attenuation of the propagating mode in a rough waveguide through a correction to the eigenvalue corresponding to smooth walls. The proposed approach can be used to derive results that are consistent with those obtained by Bass et al. [IEEE Trans. Antennas Propag. 22, 278-288 (1974)]. The novelty of the method is that it does not involve the integral Dyson-type equation and, as a result, the large number of statistical moments included in the equation in the form of the mass operator of the volume scattering theory. The derived eigenvalue correction is described by the correlation function of the randomly rough surface. The averaged solution in the plane wave regime is approximated by the exponential function dependent on the derived eigenvalue correction. The approximations are compared with numerical results obtained using the finite element method (FEM). An approach to retrieve the correct deviation in roughness height and correlation length from multiple numerical realizations of the stochastic surface is proposed to account for the oversampling of the rough surface occurring in the FEM meshing procedure.

Doppler spectra of airborne sound backscattered by the free surface of a shallow turbulent water flow

Measurements of the Doppler spectra of airborne ultrasound backscattered by the rough dynamic surface of a shallow turbulent flow are presented in this paper. The interpretation of the observed acoustic signal behavior is provided by means of a Monte Carlo simulation based on the Kirchhoff approximation and on a linear random-phase model of the water surface elevation. Results suggest that the main scattering mechanism is from capillary waves with small amplitude. Waves that travel at the same velocity of the flow, as well as dispersive waves that travel at a range of velocities, are detected, studied, and used in the acoustic Doppler analysis. The dispersive surface waves are not observed when the flow velocity is slow compared to their characteristic velocity. Relatively wide peaks in the experimental spectra also suggest the existence of nonlinear modulations of the short capillary waves, or their propagation in a wide range of directions. The variability of the Doppler spectra with the conditions of the flow can affect the accuracy of the flow velocity estimations based on backscattering Doppler. A set of different methods to estimate this velocity accurately and remotely at different ranges of flow conditions is suggested.