The resonator density measurement

At a glance
In the previous part (1) we learned about the basics of density measurement and the definition of density. This section is dedicated to the vibration method which is also used by density sensors for density measurement. This method also has some advantages and disadvantages, which are explained in detail.

Link to part 1 - Basics of density measurement

How does the resonator density easurement work?

With the resonator density measuring method, the density is measured indirectly by a frequency determination. The liquid to be measured is filled into a tube (resonator) which is set into resonance vibration. The resulting oscillation frequency, which depends on the density of the liquid and the rigidity of the resonator, now provides information on the density.

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The higher the vibration frequency, the lower the density of the liquid

Liquid density/vibration frequency dependence

The properties of the resonator (e.g. stiffness) depend on temperature and pressure. These dependencies are determined on the basis of calibration measurements
and compensated for by the measuring instrument.

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The only remaining variable that can be influenced is thus the density of the liquid

The following equation illustrates the relationship between density ρ of the liquid, the properties of the resonator (constants A and B) and the oscillation frequency ƒ:

Formula - Relationship between medium density ρ and vibration frequency f

Relationship between medium density ρ and vibration frequency ƒ

How the resonator measuring device works:

Resonator is firmly clamped at both ends.
Exciter causes the tube to vibrate.
Vibration sensors detect the vibration frequency.

The shape and materials of the resonator are not fixed. Thus, the resonator can be either a round tube or a square tube.

1. Vibration sensor, 2. Exiter, 3. Firmly clamped resonator

What are the advantages?

The straightforward handling which goes hand in hand with the low complexity of the testing techology, is one of the greatest advantages of the resonator density measurement. The density is measured after the medium has been added without any further adjustments having to be made. Reading errors can be excluded, as the density value is shown on a digital display. Temperature control of the medium is
not required; instead, the temperature is measured in situ. In addition, the extraction of an exact volume is not required.

The miniaturization of the technology that is possible means that only small sample quantities are needed for reliable density determination. This feature is particularly relevant for expensive media. The use of small sample quantities also makes it easier to determine the medium temperature for density measurement.

The measurement can be performed in a closed system and thus under pressure. This is particularly relevant for certain media such as alcohol-water mixtures or gases. Without the appropriate pressure, such media would volatilize, leading to incorrect measuring values.

Finally, the measuring results are available in an extremely short measuring time.

Resonator measuring instruments can also be used for a continual measurement with flow directly in the process.

What are critical factors (disadvantages)?

The method does not allow direct traceability, i.e. the measured density cannot be compared with the national standards (kg and m3) for this measured variable. The reason for this is that the density is calculated using a measured frequency. At least two reference media with known density are required for the calculation. Traceability is therefore only possible via these two reference media.

The measuring sensitivity is influenced by the nature of the measuring tube. The smaller the dead weight of the measuring tube, the lower its influence on the
frequency and the higher the measuring sensitivity. Conversely, measuring low medium masses with a simultaneously high dead weight of the measuring tube is problematic.

The mechanical properties of the resonator are changed by pressure and temperature influences. As a result, the frequency also changes. These dependencies can be compensated for by calibrations with different pressure and temperature points.

In addition, the frequency is also dependent on the viscosity of the measuring liquids. This can give rise to further measuring uncertainties.

Air bubbles in the measuring liquid can also lead to measuring errors. This is not the case if degassing is carried out before the measurement.

The measuring result can be falsified by contamination of the resonator. An indication that the resonator is clean is reading the correct air density when empty.

Where is the resonator density measurement
used?

Resonator density measuring methods are particularly suitable for measuring the density of liquids in industries with different accuracy requirements in the laboratory and process:

In the oil and gas industry, e.g. for determining calorific value, energy content or composition.
At filling stations for settlement of the correct value and determining foreign particles.
In transport for settlement of the correct value and to check the medium.
In aircraft refuelling for optimizing the filling quantity to the flight distance.
On engine test benches to test for constant fuel quality.
Etc.