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

^{*}

## 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

- Nezu, I.; Nakagawa, H. Turbulence in Open-Channel Flows. J. Fluid Mech.
**1994**, 269, 373–374. [Google Scholar] [CrossRef] - Schrottke, K. Dynamik fluider Schlicke im Weser und Ems-Ästuar—Untersuchung und Analysen zum Prozessverständnis; BAW/BfG Kolloqium: Karlsruhe, Germany, 2006. [Google Scholar]
- Cellino, M. Experimental Study of Suspension Flow in Open Channels. Ph.D. Thesis, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland, 1998. [Google Scholar]
- Pope, S.B. Turbulent Flows; Cambridge University Press: Cambridge, UK, 2001. [Google Scholar]
- Salehi, M.; Strom, K. Using Velocimeter Signal to Noise Ratio as a Surrogate Measure of Suspended Mud Concentration. Cont. Shelf Res.
**2011**, 31, 1020–1032. [Google Scholar] [CrossRef] - Fugate, D.C.; Friedrichs, C.T. Determining concentration and fall velocity of estuarine particle populations using ADV, OBS and LISST. Cont. Shelf Res.
**2002**, 22, 1867–1886. [Google Scholar] [CrossRef] - Urick, R. The absorption of sound in suspensions of irregular particles. J. Acoust. Soc. Am.
**1948**, 20, 283–289. [Google Scholar] [CrossRef] - Lohrmann, A.; Cabrera, R.; Kraus, N.C. Acoustic-Doppler Velocimeter (ADV) for Laboratory Use. In Proceedings of the Fundamental and Advancements in Hydraulic Measurements and Experimentation, Buffalo, NY, USA, 1–5 August 1994; pp. 351–365. [Google Scholar]
- Thorne, P.D.; Hanes, D.M. A review of acoustic measurement of small-scale sediment processes. Cont. Shelf Res.
**2002**, 22, 603–632. [Google Scholar] [CrossRef][Green Version] - Jay, D.A.; Orton, P.; Kay, D.J.; Fain, A.; Baptista, A.M. Acoustic determination of sediment concentrations, settling velocities, horizontal transports and vertical fluxes in estuaries. In Proceedings of the IEEE Sixth Working Conference on Current Measurement, San Diego, CA, USA, 13 March 1999; pp. 258–263. [Google Scholar]
- Hoitink, A.; Hoekstra, P. Observations of Suspended Sediment from ADCP and OBS Measurements in a Mud-dominated Environment. Coast. Eng.
**2005**, 52, 103–118. [Google Scholar] [CrossRef] - Ha, H.; Hsu, W.Y.; Maa, J.Y.; Shao, Y.; Holland, C. Using ADV backscatter strength for measuring suspended cohesive sediment concentration. Cont. Shelf Res.
**2009**, 29, 1310–1316. [Google Scholar] [CrossRef] - Decrop, B.; De Mulder, T.; Toorman, E.; Sas, M. New methods for ADV measurements of turbulent sediment fluxes–application to a fine sediment plume. J. Hydraul. Res.
**2015**, 53, 317–331. [Google Scholar] [CrossRef] - Best, J.; Bennet, S.; Bridge, J.; Leeder, M. Turbulence Modulation and Particle Velocities over Flat Sand Beds at Low Transport Rates. J. Hydraul. Eng.
**1997**, 123, 1118–1129. [Google Scholar] [CrossRef] - Cellino, M. Ultrasonic Measurements of Instantaneous Velocity and Suspended Concentration in Open-Channel Flow. In Proceedings of the Third International Symposium on Ultrasonic Doppler Methods for Fluid Mechanics and Fluid Engineering Co-organized by EPFL and PSI, Lausanne, Switzerland, 9–11 September 2002. [Google Scholar]
- Hurther, D.; Thorne, P.D.; Bricault, M.; Lemmin, U.; Barnoud, J.M. A multi-frequency Acoustic Concentration and Velocity Profiler (ACVP) for boundary layer measurements of fine-scale flow and sediment transport processes. Coast. Eng.
**2011**, 58, 594–605. [Google Scholar] [CrossRef] - Revil-Baudard, T.; Chauchat, J.; Hurther, D.; Barraud, P.A. Investigation of sheet-flow processes based on novel acoustic high-resolution velocity and concentration measurements. J. Fluid Mech.
**2015**, 767, 1–30. [Google Scholar] [CrossRef][Green Version] - McAnally, W.H.; Friedrichs, C.; Hamilton, D.; Hayter, E.; Shrestha, P.; Rodriguez, H.; Sheremet, A.; Teeter, A. Management of Fluid Mud in Estuaries, Bays, and Lakes. I: Present State of Understanding on Character and Behavior. J. Hydraul. Eng.
**2007**, 133, 9–22. [Google Scholar] [CrossRef] - Becker, M.; Maushake, C.; Winter, C. Observations of Mud-Induced Periodic Stratification in a Hyperturbid Estuary. Geophys. Res. Lett.
**2018**, 45, 5461–5469. [Google Scholar] [CrossRef] - Craig, R.G.; Loadman, C.; Clement, B.; Rusello, P.J.; Siegel, E. Characterization and testing of a new bistatic profiling acoustic Doppler velocimeter: The vectrino-II. In Proceedings of the 2011 IEEE/OES 10th Current, Waves and Turbulence Measurements (CWTM), Monterey, CA, USA, 20–23 March 2011; pp. 246–252. [Google Scholar]
- Thomas, R.; Schindfessel, L.; McLelland, S.; Creëlle, S.; De Mulder, T. Bias in mean velocities and noise in variances and covariances measured using a multistatic acoustic profiler: The Nortek Vectrino Profiler. Meas. Sci. Technol.
**2017**, 28, 075302. [Google Scholar] [CrossRef] - Bruens, A. Communications on Hydraulic and Geotechnical Engineering—Entraining Mud Suspensions; Report No. 03-1; Delft University of Technology: Delft, The Netherlands, 2003. [Google Scholar]
- Mietta, F.; Chassagne, C.; Winterwerp, J. Shear-induced flocculation of a suspension of kaolinite as function of pH and salt concentration. J. Colloid Interface Sci.
**2009**, 336, 134–141. [Google Scholar] [CrossRef] [PubMed] - Medwin, H.; Clay, C.S. Fundamentals of Acoustical Oceanography; Academic Press: Cambridge, MA, USA, 1997. [Google Scholar]
- Lerch, R.; Sessler, G.; Wolf, D. Technische Akustik: Grundlagen und Anwendungen; Springer: Berlin/Heidelberg, Germany, 2009. [Google Scholar]
- Lohrmann, A. Monitoring Sediment Concentration with Acoustic Backscattering Instruments; Nortek Technical Note; Nortek: Bologna, Italy, 2001; p. 9. [Google Scholar]
- Guerrero, M.; Szupiany, R.N.; Latosinski, F. Multi-frequency acoustics for suspended sediment studies: An application in the Parana River. J. Hydraul. Res.
**2013**, 51, 696–707. [Google Scholar] [CrossRef] - AS Nortek. VECTRINO Velocimeter User Guide (Rev. C); AS Nortek: Carlsbad, CA, USA, 2004. [Google Scholar]
- Dyer, K.; Manning, A. Observation of the size, settling velocity and effective density of flocs, and their fractal dimensions. J. Sea Res.
**1999**, 41, 87–95. [Google Scholar] [CrossRef] - Groposo, V.; Mosquera, R.L.; Pedocchi, F.; Vinzón, S.B.; Gallo, M. Mud Density Prospection Using a Tuning Fork. J. Waterw. Port Coast. Ocean Eng.
**2015**, 141, 04014047. [Google Scholar] [CrossRef] - Ali, A.; Lemckert, C.J. A traversing system to measure bottom boundary layer hydraulic properties. Estuar. Coast. Shelf Sci.
**2009**, 83, 425–433. [Google Scholar] [CrossRef][Green Version]

**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 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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