Elsevier

Measurement

Volume 184, November 2021, 109919
Measurement

Measurement procedure for acoustic absorption and bulk viscosity of liquids

https://doi.org/10.1016/j.measurement.2021.109919Get rights and content

Highlights

  • Pulse-echo-based measurement procedure for acoustic absorption and bulk viscosity.

  • Absorption determined by evaluating the signal spectrum’s raw moments.

  • Acoustic field simulations to investigate systematic measurement deviations.

  • Method to identify and correct systematic measurement deviations.

  • Results for methanol, n-hexane, n-octane, and n-decane.

Abstract

A measurement procedure using a modified two-chamber pulse-echo experimental setup is presented, enabling acoustic absorption and bulk viscosity (volume viscosity) measurements in liquids up to high temperature and pressure. Acoustic absorption measurements are particularly challenging, since other dissipative effects, such as diffraction at the acoustic source and at acoustic reflectors, are typically superimposed to the measurement effect. Acoustic field simulations are performed, allowing to investigate acoustic wave propagation qualitatively. The absorption coefficient is determined by evaluating the signal spectrum’s raw moments and applying a method to identify and correct systematic measurement deviations. Measurement uncertainties are estimated by a Monte Carlo method. In order to validate the present measurement procedure, the acoustic absorption in liquid methanol, n-hexane, n-octane, and n-decane is determined experimentally and compared to literature data. The measurement results for methanol are additionally validated by comparison to bulk viscosity data sampled with molecular dynamics simulation.

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 μs and bulk viscosity μb occur as thermodynamic state properties in the

Signal processing

Signal attenuation can experimentally be determined by comparing the peak values uˆ(z1) and uˆ(z2) of the signal at different spatial positions z1 and z2. It is common practice to anticipate an exponential decay of a wave’s amplitude, resulting in the classical expression for acoustic absorption α α=1z2z1lnuˆ(z1)uˆ(z2).Evaluating the bulk viscosity by comparing Eqs. (3), (5) requires the acoustic signal’s angular frequency ω 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 μmeas and the proper thermo-viscous loss μfluid.

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.

References (48)

  • BetheH.A.

    On the theory of shock waves for an arbitrary equation of state

  • BahmaniF. et al.

    Suppression of shock-induced separation in fluids having large bulk viscosities

    J. Fluid Mech.

    (2014)
  • RudenkoO.V. et al.
  • BuckinghamM.J.

    Causality, Stokes’ wave equation, and acoustic pulse propagation in a viscous fluid

    Phys. Rev. E

    (2005)
  • PinkertonJ.M.M.

    A pulse method for the measurement of ultrasonic absorption in liquids: Results for water

    Nature

    (1947)
  • LitovitzT.A. et al.

    Effect of pressure on sound propagation in water

    J. Appl. Phys.

    (1955)
  • Johnson Jr.W.H. et al.

    Analysis of ultrasonic absorption measurements in liquids at high pressure

    Rev. Sci. Instrum.

    (1968)
  • HolmesM. et al.

    Temperature dependence of bulk viscosity in water using acoustic spectroscopy

    J. Phys. Conf. Ser.

    (2011)
  • DubberkeF.H. et al.

    Apparatus for the measurement of the speed of sound of ammonia up to high temperatures and pressures

    Rev. Sci. Instrum.

    (2014)
  • JavedM.A. et al.

    Thermodynamic speed of sound data for liquid and supercritical alcohols

    J. Chem. Eng. Data

    (2019)
  • CarnevaleE.H. et al.

    Pressure dependence of sound propagation in the primary alcohols

    J. Acoust. Soc. Am.

    (1955)
  • ClaesL.

    Messverfahren für die Akustische Absorption in Reinen Fluiden Zur Bestimmung Der Volumenviskosität (Measurement Procedure for Acoustic Absorption in Pure Fluids to Determine Bulk Viscosity)

    (2021)
  • QuanY. et al.

    Seismic attenuation tomography using the frequency shift method

    Geophysics

    (1997)
  • ClaesL. et al.

    A spectral approach to acoustic absorption measurement

  • View full text