A vibrating-rod densimeter

Torsional and bending mode vibrations of a hollow cylinder shall be used for combined measurement of density and viscosity of a fluid. The employment of two different vibration modes has the advantage that modes with good sensitivity for either density or viscosity measurements can be used. For a detailed discussion of the dependencies of the sensitivity, a description of the fluid forces and a model of the sensor are required. Analytical solutions for the fluid forces acting on an oscillating cylindrical structure usually consider a two-dimensional situation. FEM simulations are performed in order to investigate the suitability of such solutions in order to describe fluid forces in a three-dimensional situation and for different bending modes. For the case at hand, an analytical relationship between the resonance frequency and the density of the liquid can be formulated. This analytical relationship forms a valuable basis for further investigations.

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“…= P e iϕ (5) in which P , ϕ are magnitude and phase of the ratio k 4 /k 4 0 and are introduced for convenience.…”

Section: Analytical Model For Fluid-loaded Resonatormentioning

confidence: 99%

“…It must be noted, that both density and viscosity could be measured solely with one mode of operation (forced or free decay), but either the viscosity or density obtained this way would be less accurate. An application of the presented theory is given in Bett et al [5].…”

Section: Introductionmentioning

confidence: 99%

On modeling two-mode vibration sensors for combined density and viscosity measurements

Wattinger

Zartmann

Dual

2011

WIT Transactions on the Built Environment

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“…This problem was studied for a single fluid surrounding a rod by Retsina, Richardson & Wakeham (1986). A device based on a vibrating rod has been used for single-phase density measurement (see Bett et al 1989), and the analysis given in Retsina et al (1986) was used directly and in detail to help design the meter. Our objective in the present paper is somewhat different.…”

Section: A Model Problemmentioning

confidence: 99%

Modelling the response of a vibrating-element density meter in a two-phase mixture

Billingham

1997

J. Fluid Mech.

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A vibrating-element density meter is a mechanical oscillator with known properties, for example a tuning fork or a simple rod, driven to vibrate at a known frequency. The oscillator is immersed in a fluid and the resonant frequency measured. The density of the fluid can then be inferred. We consider an idealized meter immersed in two-phase flows of various types, and investigate whether a simple single-phase interpretation allows us to deduce the density of the mixture. We find that, when the density contrast between the two fluids is not great, the simple interpretation gives good results, for example in oil/water flows. However, when the density contrast is significant, for example in gas/liquid flows, the simple interpretation is highly inaccurate.

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“…A similar phenomenon occurs in transversally vibrating rod densimeter, where the fluid perturb the oscillations of the rod. [6][7][8] Transverse waves ͑shear waves͒ are also emitted in our geometry. They produce additional damping of the oscillations of the sensor.…”

Section: Introductionmentioning

confidence: 98%

An acoustic sensor for simultaneous density and viscosity measurements in liquids

Lévêque

Ferrandis

Est

et al. 2000

Review of Scientific Instruments

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Articles you may be interested inSimultaneous determination of density and viscosity of liquids based on quartz-crystal resonators covered with nanoporous alumina J. Appl. Phys. 98, 014305 (2005); 10.1063/1.1942646 Simultaneous liquid viscosity and density determination with piezoelectric unimorph cantilevers Simultaneous measurement of liquid density and viscosity using remote query magnetoelastic sensors Rev. Sci. Instrum. 71, 3822 (2000)We studied theoretically the properties of a vibrating sensor, constituted of a cylindrical tip partly immersed in a liquid. The tip is driven axially by a stepped horn and by a piezoelectric element. Equations of the fluid flow around the tip are solved and show that longitudinal and transverse waves are emitted in the fluid. This allows the device to be sensitive to the density and viscosity of the fluid. It is shown that the properties of the fluid can be deduced by measuring the frequency shift at resonance and the corresponding electric impedance. The precision of the actual device is still low for several reasons, which are discussed. Then our apparatus seems to be more convenient to in situ reaction monitoring rather than for rheological precise measurements.

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A vibrating-rod densimeter

Cited by 15 publications

References 11 publications

On modeling two-mode vibration sensors for combined density and viscosity measurements

On modeling two-mode vibration sensors for combined density and viscosity measurements

Modelling the response of a vibrating-element density meter in a two-phase mixture

An acoustic sensor for simultaneous density and viscosity measurements in liquids

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