Abstract
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.
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