# Applicability of Acoustic Concentration Measurements in Suspensions of Artificial and Natural Sediments Using an Acoustic Doppler Velocimeter

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## Abstract

**:**

## 1. Introduction

## 2. Acoustics of the ADV Probe

#### 2.1. Rayleigh Scattering and the Intensity of the Backscatter Signal

#### 2.2. Application of Sonar Theory

#### 2.3. How Particles Influence the SNR

## 3. Experimental Investigation

#### 3.1. Experimental Setup

#### 3.2. Suitability of the ADV Probe

#### 3.3. Acoustic Feedback: Based on Quartz Powder Measurements

## 4. Modeling the Signal-to-Noise Ratio

#### 4.1. Application of the Sonar Equation

^{®}Curve-Fitting-Tool. It can be seen that the fit function and the measurements are in good agreement. The unknown parameters were found as ${\Pi}_{1}$ = 1.712, ${\Pi}_{2}$ = 4.34, and ${C}_{ADV}$ = 42.08 dB. We mention that the analytical solution of the Urick-coefficient gave $U{r}_{analyt.}$ = 1.727 m${}^{2}$/kg, which deviated in comparison to $U{r}_{sonar}$ = ${\Pi}_{2}$ · $U{r}_{analyt.}$ = 7.43 m${}^{2}$/kg. Furthermore, we mention that ${\Pi}_{1}$ is a transformation coefficient of the SNR (see Equation (13)), which is expected to be close to 1.

#### 4.2. Evaluation of the Sonar Model for Different Sediments

## 5. Discussion

#### Practical Use and Reliability

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**The experimental setup is shown for calibrating the ADV’s SNR and the concentration. The sketch is showing the stirrer and the ADV probe in side view, and the photograph is showing the experiment in top view.

**Figure 3.**A box plot evaluation is shown of the SNR data for three repeated measurements in a low concentrated quartz powder suspension. Only negligible deviations of the median of each beam are recognizable.

**Figure 4.**The evaluation of the frequency of measured SNR data is described in histograms (Run 03). Histograms are given for each receiver (beam) with corresponding mean and standard deviation values.

**Figure 5.**SNR measurements are shown for two different measurement heights as a function of the quartz powder concentration. Measurement results of each receiver are summarized. For better interpretation, the curve is divided into three characteristic areas (I, II, III).

**Figure 6.**The measured SNR data are shown as a function of quartz powder concentration. The fit function is given for the evaluation of the sonar equation (Equation (14)). This model predicts a decreasing SNR in the high concentration regime and a log-linear development in the low concentration regime.

**Figure 7.**The measured SNR data are shown as a function of concentration for different artificial sediments: (

**upper left**) quartz powder; (

**upper right**) bentonite; (

**lower left**) metakaolin; (

**lower right**) Chinafill. The fit function is given for the evaluation of the sonar equation (Equation (14)). This model predicts a decreasing SNR in the high concentration regime and a log-linear development in the low concentration regime.

**Figure 8.**The measured SNR data are shown as a function of concentration for different artificial sediments: upper left: Lake Eixendorf: upper right: Lake Altmühl; lower left: Ems 2012; lower right: Ems 2015. The fit function is given for the evaluation of the sonar equation (Equation (14)). This model predicts a log-linear evolution in the low concentration regime and a decreasing SNR in the high concentration regime.

**Figure 9.**Artificial sediments have lower uniformity coefficients ${C}_{U}$ than natural sediments. This results in lower values of ${\alpha}_{p,fit}$/${\alpha}_{p,analyt.}$, which means that the agreement increases towards the formula of Urick.

**Figure 10.**Artificial sediments have lower uniformity coefficients ${C}_{U}$ than natural sediments. As a result, the sonar model predicts greater ${C}_{ADV}$ values.

Sediment/Location | ${\mathit{d}}_{50}$ ($\mathsf{\mu}$m) | ${\mathit{k}}_{\mathit{w}}\mathit{r}$$(-)$ |
---|---|---|

Quartz powder | 18 | 0.377 |

Bentonite | 7 | 0.147 |

Metakaolin | 9 | 0.189 |

Chinafill | 9 | 0.189 |

Ems 2012 | 10 | 0.209 |

Ems 2015 | 18 | 0.377 |

Lake Eixendorf | 20 | 0.419 |

Lake Altmühl | 12 | 0.251 |

**Table 2.**The different particle parameters used to calculate the Ur-coefficient and the material parameter A.

Sediment | r ($\mathsf{\mu}$m) | ${\mathit{\rho}}_{\mathit{s}}$ (kg/m${}^{3}$) | ${\mathit{C}}_{\mathit{U}}$ (-) | ${\mathit{Ur}}_{\mathit{analyt}.}$ (m${}^{2}$/kg) | $\mathrm{Y}$ (-) | A (m${}^{-1}$) |
---|---|---|---|---|---|---|

Quartz powder | 9 | 2650 | 3.806 | 1.727 | 0.129 | 0.329 |

Bentonite | 3.5 | 2600 | 3.90 | 4.066 | 0.129 | 0.019 |

Metakaolin | 4.5 | 2215 | 2.01 | 2.788 | 0.123 | 0.047 |

Chinafill | 4.5 | 2673 | 2.15 | 3.264 | 0.129 | 0.041 |

Ems 2012 | 5 | 2525 | 3.20 | 2.846 | 0.128 | 0.058 |

Ems 2015 | 9 | 2450 | 4.16 | 1.649 | 0.127 | 0.348 |

Lake Eixendorf | 10 | 2500 | 4.61 | 1.545 | 0.127 | 0.470 |

Lake Altmühl | 6 | 2463 | 6.49 | 2.357 | 0.127 | 0.103 |

**Table 3.**Fit parameter of the sonar model for different sediments. ${R}^{2}$ as a statistical parameter is the square of the correlation between the fitted and the measured values.

Material/Location | ${\mathsf{\Pi}}_{1}$ (-) | ${\mathsf{\Pi}}_{2}$ (-) | ${\mathit{C}}_{\mathit{ADV}}$ (dB) | ${\mathit{R}}^{2}$ (%) |
---|---|---|---|---|

Quartz powder | 1.712 | 4.34 | 42.08 | 96.34 |

Bentonite | 1.890 | 0.94 | 57.06 | 88.91 |

Metakaolin | 1.719 | 4.57 | 54.98 | 91.02 |

Chinafill | 1.887 | 3.08 | 55.54 | 92.99 |

Ems 2012 | 1.441 | 4.47 | 38.84 | 96.32 |

Ems 2015 | 1.253 | 7.40 | 20.62 | 95.69 |

Lake Eixendorf | 1.070 | 11.06 | 10.97 | 88.34 |

Lake Altmühl | 0.921 | 3.37 | 6.27 | 96.59 |

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**MDPI and ACS Style**

Chmiel, O.; Baselt, I.; Malcherek, A.
Applicability of Acoustic Concentration Measurements in Suspensions of Artificial and Natural Sediments Using an Acoustic Doppler Velocimeter. *Acoustics* **2019**, *1*, 59-77.
https://doi.org/10.3390/acoustics1010006

**AMA Style**

Chmiel O, Baselt I, Malcherek A.
Applicability of Acoustic Concentration Measurements in Suspensions of Artificial and Natural Sediments Using an Acoustic Doppler Velocimeter. *Acoustics*. 2019; 1(1):59-77.
https://doi.org/10.3390/acoustics1010006

**Chicago/Turabian Style**

Chmiel, Oliver, Ivo Baselt, and Andreas Malcherek.
2019. "Applicability of Acoustic Concentration Measurements in Suspensions of Artificial and Natural Sediments Using an Acoustic Doppler Velocimeter" *Acoustics* 1, no. 1: 59-77.
https://doi.org/10.3390/acoustics1010006