To evaluate the condition of the oil in an engine or other lubricant, the fluid's viscosity is one of the most important indicators. In many cases, direct sampling is not an option, and process-integrated sensors are often required. This chapter discusses resonant sensors, which allow for process integration and the measurement of the viscosity of a fluid without sampling. A key aspect of this measurement method is the interaction of the sensor with the fluid. We discuss different modeling methods to describe the fluid–structure interaction of the resonant sensor with the surrounding fluid using a weak coupling. The benefit of weak coupling is that it allows for different approaches when modeling the fluid and structural domains. Within the structural domain, the resonator is described either by a single degree of freedom, multiple degrees of freedom, or as a continuous resonator. The fluid interaction with the resonator is described by two parameters within the structural domain, one for mass loading and the other for damping. These parameters are derived from the flow field surrounding the resonator. We discuss how to derive these parameters and how to compute the flow field. Methods for solving the flow field around simple geometries, such as a flat plate or a cylinder, are discussed. For more complex structures, a numerical approach is presented. In the final section, we describe a method of coupling different structural models and analytical fluid models to describe the fluid–structure interaction of a torsional resonator.

This paper discusses a state-of-the-art inline tubular sensor that can measure the viscosity–density (ρη) of a passing fluid. In this study, experiments and numerical modelling were performed to develop a deeper understanding of the tubular sensor. Experimental results were compared with an analytical model of the torsional resonator. Good agreement was found at low viscosities, although the numerical model deviated slightly at higher viscosities. The sensor was used to measure viscosities in the range of 0.3–1000 mPa·s at a density of 1000 kg/m3. Above 50 mPa·s, numerical models predicted viscosity within ±5% of actual measurement. However, for lower viscosities, there was a higher deviation between model and experimental results up to a maximum of ±21% deviation at 0.3 mPa·s. The sensor was tested in a flow loop to determine the impact of both laminar and turbulent flow conditions. No significant deviations from the static case were found in either of the flow regimes. The numerical model developed for the tubular torsional sensor was shown to predict the sensor behavior over a wide range, enabling model-based design scaling.

The formation of Faraday waves in a liquid inside a cylindrical vessel under the influence of vertical vibration is studied. The stability thresholds and its mode decomposition are obtained using a linear stability analysis. The stability model is validated with a vibration experiment in a vertical vibration table. The Faraday instability threshold is found for accelerations ranging from 0.1 to 1.0 times the gravitational acceleration. The confinement effect by the vessel introduces cut-off the low frequency modes and the allowed frequencies are discretized. The resulting acceleration stability threshold is high at low frequencies and it is the lowest at medium frequencies, , where the discretization of the mode -momenta introduces low stability regions delimited by more stable frequency ranges. The relevance of these characteristics for the agitation of liquids will be discussed.

This paper discusses numerical methodologies to simulate micro vibrations on a nontrivial torsionally oscillating structure. The torsional structure is the tip of a viscosity-density sensor using micro vibrations to measure the fluid properties. A 2D transient simulation of the fluid domain surrounding the tip of the sensor has been conducted in ANSYS CFX and COMSOL Multiphysics software. ANSYS CFX uses a frame of reference to induce the micro vibration whereas a moving wall approach is used in COMSOL Multiphysics for the full Navier-Stokes equation as well as their linearized form. The shear rate and pressure amplitude have been compared between the different numerical approaches. The obtained results show good agreement for both pressure and shear rate amplitudes in all models.

High purity copper, suitable for electrical applications, can only be obtained by electro-winning. The hallmark of this process is its self-induced natural convection through density variations of the electrolyte at both anode and cathode. In order to do this, first the full dynamic complexity of the process needs to be understood. Thus an OpenFoam®-based 2D model of the process has been created. This finite-volume multiphysics approach solves the laminar momentum and copper-ion species conservation equations, as well as local copper-ion conversion kinetics. It uses a Boussinesq approximation to simulate the species-momentum coupling, namely natural draft forces induced by variations of the spatial copper concentration within the fluid. The model shows good agreement with benchmark-cases of real-life electrochemical cells found in literature. An additional flow was imposed at the bottom of a small scale electrochemical cell in order to increase the ionic transport and thereby increase the overall performance of the cell. In a small scale electrochemical cell in strictly laminar flow, the overall performance could be increased and stratification decreased.