Measurement procedure for acoustic absorption and bulk viscosity of liquids
Section snippets
Motivation
The analysis and description of fluid dynamic processes are among the most challenging tasks in modern mathematics and engineering. While the fundamental formalism, the Navier-Stokes equations, is well established, its solutions are a matter of ongoing research. For mathematical analysis as well as for application in computational fluid dynamics (CFD), the parameters of these equations need to be known. The shear and bulk viscosity occur as thermodynamic state properties in the
Signal processing
Signal attenuation can experimentally be determined by comparing the peak values and of the signal at different spatial positions and . It is common practice to anticipate an exponential decay of a wave’s amplitude, resulting in the classical expression for acoustic absorption Evaluating the bulk viscosity by comparing Eqs. (3), (5) requires the acoustic signal’s angular frequency to be known. The signal’s mean frequency can be used as an estimate
Analysis of systematic measurement deviations
In contrast to the effects of the transducer’s frequency response and the electrical signal transmission that can be accounted for by the methods presented above, systematic measurement deviations caused by diffraction and imperfect reflections need to be corrected with other approaches. The approach presented here is based on literature data for bulk viscosity and acoustic absorption as a reference to derive a correcting procedure using a number of reference measurements. A prerequisite for
Modification of the measurement setup
On the basis of the present simulation results, a modification of the two-chamber pulse-echo measurement setup is proposed, aiming to reduce the systematic measurement deviation. The original setup (Fig. 1) aims at precision measurements of the sound velocity of liquids. It is designed with a single-sided, conically shaped transducer mounting, having a circular opening facing the longer chamber and thus giving rise to asymmetric emission characteristics. The quartz crystal is placed on the
Correction procedure for systematic measurement deviations
The simulation study in Section 3 shows that the systematic measurement deviation due to the acoustic wave propagation in the measurement system is expected to be continuous and dependent on the properties of the fluid. Further, the deviation appears to be additively superimposed to the loss in the fluid. However, as the simulation model does not account for all effects that occur in the physical measurement setup, the results of the simulations cannot directly be used to correct the systematic
Results and discussion
The proposed modifications of the two-chamber pulse-echo measurement setup significantly reduce the systematic measurement deviation of acoustic absorption measurements. The subsequently applied signal processing in combination with the correction accounts for the remaining deviations between the measured loss and the proper thermo-viscous loss .
However, verification is only partially possible, as values for the measured quantities for some of the fluids have not been published
Conclusions
A measurement procedure based on the pulse-echo technique is proposed for the determination of the acoustic absorption and consequently the bulk viscosity of pure liquids over a wide range of thermodynamic states. Systematic measurement deviations that are present in the raw measurement data and depend on the properties of the fluid are reduced twofoldedly. First, modifications of the measurement setup are made and, second, signal processing in combination with a correction approach for
CRediT authorship contribution statement
Leander Claes: Conceptualization, Methodology, Software, Investigation, Data curation, Writing - original draft, Visualization. René Spencer Chatwell: Methodology, Software, Validation, Writing - original draft, Writing - review & editing. Elmar Baumhögger: Methodology, Resources. Tim Hetkämper: Methodology. Henning Zeipert: Methodology. Jadran Vrabec: Writing - review & editing, Supervision, Project administration. Bernd Henning: Writing - review & editing, Supervision, Project administration.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The authors would like to thank the staff at Paderborn Center for Parallel Computing (PC2) for providing computing resources.
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