# Non-Destructive Evaluation Device for Monitoring Fluid Viscosity

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design and Fabrication

#### 2.1. Design

_{o}sin(wt+ϕ

_{o}) where V

_{o}is the applied voltage at a particular frequency (f = w/2π), and an initial phase angle ϕ

_{o}= 0. The actuator produces sound pressure waves that travel approximately 5 mm through the fluid medium to the sensor that then records a waveform with an amplitude, V

_{r}or received voltage, and a phase angle ϕ

_{r}, V

_{R}sin(wt+ϕ

_{r}). The proposed method is illustrated in Figure 1.

#### 2.2. Fabrication

#### 2.2.1. Materials

#### 2.2.2. Assembly

## 3. Experimental Setup

^{3}measured using a syringe. In this manner, only the tip of the probe is submerged in the liquid.

^{®}program records and controls a Hewlett Packard 4194A Impedance/Gain-Phase Analyser capable of measuring capacitance, impedance, gain, and phase angles. The analyzer scans frequencies and supply a sinusoidal wave to the actuator and monitor the signal received by the sensor. The applied signal is a sinusoidal wave with an amplitude of 0.5Volts at a range of frequencies between 100 Hz and 40 MHz. The measured gain and phase are the ratio of the amplitudes and the phase difference between the two signals. All measurements were performed in a custom-made Faraday cage to avoid interference in the high-frequency ranges. Figure 3 illustrates the experimental setup.

## 4. Modeling

^{®}.

_{x}= u

_{y}= u

_{z}= 0.

^{®}relase19R2). Using this software, eigenvalue frequencies (natural frequencies) for the piezoelectric viscosity probe can be calculated. However, if the probe is immersed in a fluid can have a significant effect on the calculation of natural frequencies and require additional tools [36]. A Fluid Solid Interaction module (FSI) that can couple the effects of the fluid and calculate the interactions is necessary. In this case, a harmonic acoustic analysis was performed for the probe and its surrounding fluid using a two-way Fluid Solid Interaction (FSI) method. This method is based on performing of a harmonic analysis for the actuator under the excitation voltage and then transferred effect of the acoustic wave due the excitation voltage to the sensor through the fluid medium using harmonic acoustic analysis. Then, an additional acoustic analysis is performed on the sensor to calculate the effect of the sound wave propagating in the fluid. In this case, the fluid is stationary and the fluid velocity is small and there is no need to solve for all the fluid dynamic parameters. Those effects are assumed negligible.

_{s}], [M

_{f}], [C

_{s}], [C

_{f}], [K

_{s}], [M

_{fs}], and [K

_{fs}] are the structural mass, the fluid mass, the structural damping, the fluid damping, the structural stiffness, the equivalent coupling “mass”, and the equivalent coupling “stiffness” matrices, respectively. In the same equation, {F

_{s}}, {u}, and {p} are the applied load vector, the nodal displacement, and the acoustic pressure, respectively.

_{0}] is the relative permittivity, [e] is the coupling (in C/m

^{2}), and [C] is the elasticity (in Pa) matrices, respectively. In this manner, the model predicts the phase shift for the sensor immersed in a viscous flow under the same excitation voltage and range of frequency that had been used in the experimental work.

## 5. Results

#### 5.1. Experimental Phase Shift Measurements

^{2}of 0.99, indicating that the data fits a profile of the form is defined as follows.

_{R}is the resonance frequency (MHz), f

_{0}, and a, and b are constants that could be related to damping and sound propagation. Though the R

^{2}is high the parameters may not be quite accurate (coefficients have a high standard error and high p-values). This type of equation is usually used for a Gaussian wave equation and maybe significant in calibrating and predicting viscosity values. The large standard errors indicate multi-cocolinearity which indicates more refinement of this equation is needed and more data is required for a more definite model. The purpose of Equation (5) is to illustrate the trends observed in the experiments.

#### 5.2. Numerical Simulation Results

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Model built in ANSYS: (

**a**) schematic of the built model and fluid level; (

**b**) the layers of the model; and (

**c**) the mesh configuration.

**Figure 5.**Peak phase shift vs. frequency as detected by the Gain-Phase Analyzer at different Glycerin concentrations (0 to 100%).

**Figure 8.**Variation of phase shift with frequency for both experimental and simulated at different concentration of glycerin and water.

Method | Viscometer Type | Typical Measurable Range (cP) | Price | Disposable |
---|---|---|---|---|

Displacement (1st type) | Capillary * | 0.2–200 | $$$ | No |

Rotating * | 0.3–320 M | $$$$$ | No | |

Vibration/mass (2nd type) | Vibration * | 0.3–100 k | $$$$ | No |

MEMS ** | variable | variable | No | |

Acoustic (3rd type) | Wave reflection *** | 1.005–1400 | variable | No |

Non-destructive | 1.005–1600 | $ | Yes |

**Table 2.**Mechanical properties for the viscosity probe [35].

Material | Piece # | Dimensions (mm) | Density (kg/m^{3}) | Modulus of Elasticity (N/m^{2}) |
---|---|---|---|---|

Hollow brass | 1 | 5 × 5 × 70 | 8500 | 96 × 10^{9} |

Copper | 2 | 6 × 0.1 × 25 | 8900 | 110 × 10^{9} |

PZT 5A | 2 | 5 × 0.1 × 23 | 7550 |

R | R^{2} | Adjusted R^{2} | Standard Error of Estimate | |
---|---|---|---|---|

0.9987 | 0.9975 | 0.9969 | 22.19 | |

Coefficient | Std. Error | t | P | |

a | 1341.292 | 342,891,640 | 3.91 × 10^{−6} | 1.00 |

b | 0.115 | 118,380 | 9.73 × 10^{−7} | 1.00 |

f_{0} | 7.365 | 213,305 | 3.687 × 10^{−5} | 1.00 |

Analysis of Variance | ||||

DF | SS | MS | ||

Regression | 3 | 1,812,696 | 604,232 | |

Residual | 8 | 3940 | 492 |

Fluid | Density (kg/m^{3}) | Speed of Sound (m/s) | Mode 1 | Mode 2 | Mode 3 |
---|---|---|---|---|---|

Air | 1.2 | 343 | 683.86 | 684.24 | 2358 |

Water | 1000 | 1484 | 499.88 | 533.88 | 1080.2 |

Glycerin | 1260 | 1920 | 468.53 | 501.72 | 625.45 |

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**MDPI and ACS Style**

Abdulkareem, A.; Erturun, U.; Mossi, K.
Non-Destructive Evaluation Device for Monitoring Fluid Viscosity. *Sensors* **2020**, *20*, 1657.
https://doi.org/10.3390/s20061657

**AMA Style**

Abdulkareem A, Erturun U, Mossi K.
Non-Destructive Evaluation Device for Monitoring Fluid Viscosity. *Sensors*. 2020; 20(6):1657.
https://doi.org/10.3390/s20061657

**Chicago/Turabian Style**

Abdulkareem, Ahmed, Ugur Erturun, and Karla Mossi.
2020. "Non-Destructive Evaluation Device for Monitoring Fluid Viscosity" *Sensors* 20, no. 6: 1657.
https://doi.org/10.3390/s20061657