Biomedical subjects

M Willatzen

Publications and source records attributed to M Willatzen.

15 recordsLinked to original sources

PubMed2005

Flow acoustics in periodic structures.

A recent paper [A.A. Krokhin, J. Arriaga, L.N. Gumen, Speed of sound in periodic elastic composites, Phys. Rev. Lett. 91 (2004) 264302-1-4] addresses the speed of sound in periodic elastic composites (phononic crystals) with particular emphasis to the case where air bubbles are present in water and arranged periodically. In such periodically arranged mixtures, the well-known phenomena of the drop of the speed of sound may occur and applications related to, e.g., sound-beam focusing and acoustic surgery are possible [F. Cervera, L. Sanchez, J.V. Sanchez-Perez, R. Martinez-Sala, C. Rubio, F. Meseguer, C. Lopez, D. Caballero, J. Sanchez-Dehesa, Phys. Rev. Lett. 88 (2002) 023902]. In this paper, the analysis is extended theoretically to include cases where a background flow in a periodic structure is maintained. Calculations of dispersion relations and group velocities are presented in cases with one- and two-dimensional material periodicity for background flow values in the range: 0-1m/s. Materials considered in the calculations are periodic water-air mixtures. It is shown that acoustic waves couple to the group velocities only if the (acoustic) wave vector has a component along the background flow velocity direction.

Acoustics↗

PubMed2004

Flow acoustics modelling and implications for ultrasonic flow measurement based on the transit-time method.

A comparison between three mathematical models frequently used in flow acoustics is presented and discussed with respect to ultrasonic flow-meter performance based on the transit-time method. The flow-meter spoolpiece geometry is assumed to be a cylindrical pipe. Semi-analytical calculations employing the Frobenius power series expansion method are shown for the cases of a constant-, linear-, parabolic-, and cubic-flow profiles although the Frobenius method presented can be applied to any smooth flow profile. It is shown that the so-called deviation of measurement, often used as a measure of the flow-meter accuracy, is strongly dependent on the acoustic mode excited and the flow profile. Furthermore, differences with respect to deviation of measurement results exist among the three mathematical models analyzed.

Journal Article↗

PubMed2004

Ultrasonic flow measurement and wall acoustic impedance effects.

An examination of the influence of wall acoustic impedance effects on sound propagation in flowing liquids confined by cylindrical walls is presented. Special focus is given to the importance of the wall acoustic impedance value for ultrasonic flow meter performance. The mathematical model presented allows any radially-dependent axial flow profile to be examined in the linear flow acoustics regime where fluid flow speed is much smaller than the fluid sound speed everywhere in the fluid medium.

Acoustic Impedance Tests↗

PubMed2004

Acoustic cavity modes in lens-shaped structures.

A method for solving exactly the Helmholtz equation in parabolic rotational coordinates is presented using separability of the eigenfunctions and the Frobenius power series expansion technique. Two examples of interest in acoustics are considered and analyzed quasianalytically: The acoustic pressure in a cavity defined by two paraboloids (forming a lens-shaped structure) with (I) rigid wall boundary conditions and (II) pressure-release boundaries. The rigid-wall (pressure-release) acoustic enclosure problem is a Neumann (Dirichlet) boundary condition problem. In both cases, eigenfunctions and eigenmodes are calculated and the shape dependence of the eigenvalue for the ground state is examined.

Journal Article↗

PubMed2004

Eigenmodes of triaxial ellipsoidal acoustical cavities with mixed boundary conditions.

The linear acoustics problem of resonant vibrational modes in a triaxial ellipsoidal acoustic cavity with walls of arbitrary acoustic impedance has been quasi-analytically solved using the Frobenius power-series expansion method. Eigenmode results are presented for the lowest two eigenmodes in cases with pressure-release, rigid-wall, and lossy-wall boundary conditions. A mode crossing is obtained as a function of the specific acoustic impedance of the wall; the degeneracy is not symmetry related. Furthermore, the damping of the wave is found to be maximal near the crossing.

Journal Article↗

PubMed2003

Ultrasonic flowmeters: temperature gradients and transducer geometry effects.

Ultrasonic flowmeter performance is addressed for the case of cylindrically shaped flowmeters employing two reciprocal ultrasonic transducers A and B so as to measure time-of-flight differences between signals transmitted from transducer A towards B followed by an equivalent signal transmitted from transducer B towards A. In the case where a liquid flows through the flowmeter's measuring section ("spoolpiece"), the arrival times of the two signals differ by an amount related to the flow passing between the two transducers. Firstly, a detailed study of flow measurement errors with mean flow in the laminar flow regime is carried out as a function of the mode index and the transducer diameter/cylinder diameter ratio in the case where no temperature gradients are present in the flowmeter sensor. It is shown that all modes except the fundamental mode overestimate the mean flow by a factor of 33.33% while excitation of the fundamental mode solely give error-free measurements. The immediate consequences are that the flowmeter error decreases as the transducer diameter/cylinder diameter ratio approaches 1 from 0 reflecting the fact that the excitation level of the fundamental mode increases from almost 0 to 1 as this ratio approaches 1 from 0. Secondly, the effect on flowmeter performance due to flow-induced temperature gradients is examined. It is shown that the presence of temperature gradients leads to flowmeter errors at the higher-flow values even in the case where the fundamental mode is the only mode excited. It is also deduced that flowmeter errors in general depend on the distance between transducers A and B whether temperature gradients exist or not. This conclusion is not reflected in the usual definition of flowmeter errors given by the so-called mode-dependent deviation of measurement introduced in earlier works.

Journal Article↗

PubMed2001

Ultrasound transducer modeling--general theory and applications to ultrasound reciprocal systems.

A tutorial presentation on the theory of reciprocal ultrasound systems is given, and a complete set of modeling equations for one-dimensional multi-layer ultrasound transducers is derived from first principles. The model includes dielectric losses and mechanical losses in the transducer material layers as well as sound absorption in the transmission medium. First, the so-called constitutive relations of a piezoelectric body are derived based on general thermodynamic considerations, assuming that transducer operation takes place under almost isentropic conditions. Second, full attention is given to transducers oscillating in the thickness mode, discarding all other vibration modes. Dynamic transducer equations are determined using Newton's Second Law, Poisson's equation, and the definition of strain applied to a piezoelectric transducer with one or more non-piezoelectric layers on the front surface (multilayer transducer). Boundary conditions include continuity of normal velocity and stress across material interfaces as well as a subsidiary electrical condition over the piezoceramic electrodes. Sound transmission is assumed to take place in a water bath such that the Rayleigh equation can be used to obtain the incoming pressure at the receiver aperture from the acceleration of the opposing transmitter. This allows, e.g., a detailed treatment of receiver signal variations as the receiver moves from the near-field zone to the far-field zone of the transmitter. In the remaining part of the paper, receiver voltage and current signals are obtained by solving the full set of dynamic equations numerically. Special attention is given to transducers consisting of a) a pure piezoceramic layer only, b) a piezoceramic layer and a quarter-wavelength matching layer of polyphenylensulphide (PPS), c) a piezoceramic layer and a half-wavelength matching layer of stainless steel, and d) a piezoceramic layer and a half-wavelength matching layer of stainless steel tuned to resonance by a parallel inductance. Results are also given for receiver incoming pressure and receiver voltage signals when sound reception takes place in the near-field and far-field zones of the transmitter.

Journal Article↗

PubMed2001

Perturbation theory applied to sound propagation in flowing media confined by a cylindrical waveguide.

First-order perturbation theory is employed to examine sound propagation in flowing media confined by a cylindrical waveguide. The use of perturbation theory allows examination of mode phase-speed changes due to any radially dependent flow w(r) as long as the flow magnitude is sufficiently small. The condition to be fulfilled is satisfied in the flow range: 0-0.3 m/s for the specific values of cylinder radius, ultrasound frequency, and sound speed analyzed in the present work [in the general case, however, the condition in Eq. (1) of the present work must be fulfilled]. This freedom of choice, i.e., the possibility to handle any radial flow profile, is used to analyze two flow profile cases: (1) where w(r) is a linear combination of a laminar flow profile and a flat profile corresponding to turbulent flow, and (2) where w(r) is a linear combination of a laminar flow profile and a more realistic logarithmic-dependent turbulent flow profile. In both cases, it is shown that large errors may result in ultrasound flow measurements if several modes are excited by the transmitting transducer, and that a logarithmic flow profile in the turbulent regime leads to somewhat larger measurement errors at high flow values as compared to assuming a simple flat profile in the turbulent regime.

Acoustics↗

PubMed2000