Torbjörn Löfqvist

PSpice simulation of ultrasonic systems

The usage of electrical analogies for the simulation of wave generation and propagation in ultrasound transducers is well established. In this paper a PSpice approach that includes the temperature and frequency dependency of the transducer performance is proposed. The analogy between acoustic wave propagation and wave propagation in an electric transmission line is given. Further ways to deduce temperature and frequency dependencies are discussed. The simulation approach is applied to a pulse-echo setup for the determination of speed of sound and attenuation in liquids and solids. Experiments and simulations are made for three temperatures and in the frequency range 1-12 MHz using water, glycerine, and polymers (PMMA and PEEK) as test samples. Comparison shows a good agreement between simulation and experiments. Results for glycerine indicates that the available attenuation models for high viscosity liquids is inappropriate.

Transient flow towards a well in an aquifer including the effect of fluid inertia

Transient propagation of weak pressure perturbations in a homogeneous, isotropic, fluid saturated aquifer has been studied. A damped wave equation for the pressure in the aquifer is derived using the macroscopic, volume averaged, mass conservation and momentum equations. The equation is applied to the case of a well in a closed aquifer and analytical solutions are obtained to two different flow cases. It is shown that the radius of influence propagates with a finite velocity. The results show that the effect of fluid inertia could be of importance where transient flow in porous media is studied.

Material property estimates from ultrasound attenuation in fibre suspensions

An investigation of a new method for measuring fibre material properties from ultrasonic attenuation in a dilute suspension of synthetic fibres of uniform geometry is presented. The method is based on inversely solving an ultrasound scattering and absorption model of suspended fibres in water for the material properties of the fibres. Experimental results were obtained from three suspensions of nylon 66 fibres each with different fibre diameters. A forward solution to the model with reference material values is compared to experimental data to verify the models behaviour. Estimates of the shear and Youngs modulus, the compressional wave velocity, Poissons ratio and loss tangent from nylon 66 fibres are compared to data available from other sources. Experimental data confirms that the model successfully predicts that the resonance features in the frequency response of the attenuation are a function of diameter. Consistent estimated values for the compressional wave velocity and the Poissons ratio were found to be difficult to obtain but in combination gave values of shear modulus within previously reported values and with low sensitivity to noise. Youngs modulus was underestimated by 54% but was consistent and had low sensitivity to noise. The underestimation is believed to be caused by the assumption of isotropic material used in the model. Additional tests on isotropic fibre would confirm this. Further analysis of the model sensitivity and the reasons for the resonance features are required.

Lateral light scattering in fibrous media

Lateral light scattering in fibrous media is investigated by computing the modulation transfer function (MTF) of 22 paper samples using a Monte Carlo model. The simulation tool uses phase functions from infinitely long homogenous cylinders and the directional inhomogeneity of paper is achieved by aligning the cylinders in the plane. The inverse frequency at half maximum of the MTF is compared to both measurements and previous simulations with isotropic and strongly forward single scattering phase functions. It is found that the conical scattering by cylinders enhances the lateral scattering and therefore predicts a larger extent of lateral light scattering than models using rotationally invariant single scattering phase functions. However, it does not fully reach the levels of lateral scattering observed in measurements. It is argued that the hollow lumen of a wood fiber or dependent scattering effects must be considered for a complete description of lateral light scattering in paper.

Pulp consistency determined by a combination of optical and acoustical measurement techniques

In this study, methods based on ultrasonic attenuation and optical time-of-flight measurements are used simultaneously in determining both the fibres and fines mass fractions, respectively, of a cellulose pulp fibre suspension. The optical measurements are done by a laser radar and the acoustical measurements are based on ultrasonic attenuation measurements in a pulse-echo set-up. Two kinds of long-fibre fractions are studied, thermo-mechanical pulp and chemical softwood pulp. Fibre and fines mass fraction ranges are 0.25–1.0% and 0–0.75%, respectively. The results show that the fibres are the predominant source for absorption and scattering of ultrasonic waves and are thus mainly contributing to the attenuation of ultrasound in the pulp. It is also found that the fines are the predominant source for optical scattering and fines are thus mainly contributing to the propagation delay of the light pulse in the laser radar set-up. By combining the ultrasonic attenuation and the optical time-of-flight measurements, it is shown that the mass fraction of fines and the mass fraction of fibres in a pulp sample could be determined, respectively.

Ultrasonic measurements and modelling of attenuation and phase velocity in pulp suspensions

In the manufacturing process of paper the mass fraction and material properties of the fibres in the pulp suspen- sion are important for the quality of the finished product. This study presents two different methods of pulp characterisation. The first is based on phase velocity, which we use to investigate the composition of the pulp. Here a method is presented where the optimal number of circular shifts within the sampling window of the signal is determined which gives, in a weakly dispersive medium, a continuous phase spectrum and minimizes the likelihood of discontinuities within the bandwidth. Hence, the ambiguity in phase unwrapping is avoided. The results from phase velocity measurements show that the phase velocity weakly increases with increasing amount of fines in the suspension. The dispersion is caused by the fibres and it correlates with fibre mass fraction. The second method is based on attenuation and is used to characterise the wood fibres. The results of the attenuation experiments show that it is possible to inversely calculate wood fibre properties by fitting the model to the experimental data, if the fibre diameter distribution is known. However, the accuracy of these calculation is difficult to determined and more work in this area is required. In the manufacturing process of paper the mass fraction and material properties of the fibres in the pulp suspension are important for the quality of the finished product. When using recycled paper, fibres with unknown and varying material properties enter the process. Therefore, there is an increasing demand for methods of on-line characterisation of the pulp suspension as well as the fibres in suspension. This study presents two different methods of pulp charac- terisation. The first is based on phase velocity, which we use to investigate the composition of the pulp. The second is based on attenuation and is used to characterise the wood fibres. In the first method, we investigate how the phase velocity changes with different mass fractions of fibres and fines. To determine the phase velocity, a method is proposed based on a method by (1), where the an echo is circularly shifted an optimal number of samples. In the second method, to be able to characterise the wood fibres, we use an analytical model which relates the material properties of saturated fibres to the attenuation. We then aim to solve the inverse problem of identifying which values result in the best fit of the model to the attenuation values calculated from experiments. II. PHASE VELOCITY A. Theory and experiments When determining the phase velocity from pulse-echo measurements, one encounters the problem of performing a correct phase unwrapping. The problem is well known and has been addressed in earlier investigations, for instance (2). The problem arises when the phase velocity is calculated from the phase spectra of a the Fourier transform of each of the two echoes. In this study, we propose a method, termed Minimum Phase Angle (MPA), that determines an optimal number of circular shifts to the windowed signal which results in a continuous phase spectrum and minimizes the likelihood of discontinuities within the bandwidth. Therefore the ambiguity in the phase unwrapping is avoided. To experimentally test the method experiments were performed in pulp fibre suspensions, which are weakly dispersive. The experiments were carried out using the pulse-echo technique in a custom designed test cell. A schematical view of the measurement cell used in this study is shown in Fig. 1.

Estimating suspended fibre material properties by modelling ultrasound attenuation

An analytical model for use in the inverse problem of estimating material properties of suspended fibres from ultrasonic attenuation has been developed. The ultrasound attenuation is derived theore ...

Estimating material properties of solid and hollow fibers in suspension using ultrasonic attenuation

Estimates of the material properties of hollow fibers suspended in a fluid using ultrasound measurements and a simple, computationally efficient analytical model are made. The industrial application is to evaluate the properties of wood fibers in paper pulp. The necessity of using a layered cylindrical model (LCM) as opposed to a solid cylindrical model (SCM) for modeling ultrasound attenuation in a suspension of hollow fibers is evaluated. The two models are described and used to solve the inverse problem of estimating material properties from attenuation in suspensions of solid and hollow polyester fibers. The results show that the measured attenuation of hollow fibers differs from that of solid fibers. Elastic properties estimates using LCM with hollow-fiber suspension measurements are similar to those using SCM with solid-fiber suspension measurements and compare well to block polyester values for elastic moduli. However, using the SCM with the hollow-fiber suspension did not produce realistic estimations. In conclusion, the LCM gives reasonable estimations of hollow fiber properties and the SCM is not sufficiently complex to model hollow fibers. The results also indicate that the use of a distributed radius in the model is important in estimating material properties from fiber suspensions.

On laser-induced ultrasound generated in a thin semi-transparent layered polymer structure

We investigate laser-induced ultrasound generated in a plane semi-transparent layered polymer structure. The scope is to study relations between generated ultrasound, as e.g. amplitude, and centre frequency and bandwidth of its frequency spectrum, and properties of the polymer layers, like thickness and absorption. This knowledge can then be used when designing polymer film based, semi-transparent ultrasonic devices specifically for photoacoustic applications. The experimental study is set-up as a factorial experiment with a completely randomised design. In the experiments, the light source is a pulsed Nd:YAG laser. As absorber, a semi-transparent, non-conductive polymer film in a plane layered structure of one or more layers on a glass substrate is used. The frequency spectra of the generated ultrasound spans 2 to 20 MHz, which is recorded by a broadband PVDF ultrasonic transducer. The results show that an increased thickness of the polymer layer structure relate to a lower center frequency and a lower bandwidth, and that an increased optical absorption and a decreased layer structure thickness is related to a higher ultrasound amplitude.

Analytical one-dimensional model for laser-induced ultrasound in planar optically absorbing layer

Ultrasound generated by means of laser-based photoacoustic principles are in common use today and applications can be found both in biomedical diagnostics, non-destructive testing and materials characterisation. For certain measurement applications it could be beneficial to shape the generated ultrasound regarding spectral properties and temporal profile. To address this, we studied the generation and propagation of laser-induced ultrasound in a planar, layered structure. We derived an analytical expression for the induced pressure wave, including different physical and optical properties of each layer. A Laplace transform approach was employed in analytically solving the resulting set of photoacoustic wave equations. The results correspond to simulations and were compared to experimental results. To enable the comparison between recorded voltage from the experiments and the calculated pressure we employed a system identification procedure based on physical properties of the ultrasonic transducer to convert the calculated acoustic pressure to voltages. We found reasonable agreement between experimentally obtained voltages and the voltages determined from the calculated acoustic pressure, for the samples studied. The system identification procedure was found to be unstable, however, possibly from violations of material isotropy assumptions by film adhesives and coatings in the experiment. The presented analytical model can serve as a basis when addressing the inverse problem of shaping an acoustic pulse from absorption of a laser pulse in a planar layered structure of elastic materials.