Applications of Resonant Density Sensors The principle of density measurement using resonance

Introduction: This article mainly introduces a density measurement method that uses the resonance principle to measure, and analyzes in detail the advantages and disadvantages of this density measurement method.

1. Principle of density measurement using resonance

The measurement principle of the resonant density sensor is to indirectly measure the density of the liquid through the resonant frequency during resonance.

The density sensor fills the liquid to be measured into the resonant tube, causing the liquid to be measured to resonate with the resonator. According to the relationship between the density of the liquid and the resonant frequency, it can be seen that the oscillation frequency generated depends on the density of the liquid and the stiffness of the resonator. We can deduce the density of the gas based on the formula.

The properties of the resonator, such as stiffness, depend on temperature and pressure, and their dependence is determined by calibration measurements and compensated by the measuring instrument.

Therefore, the only remaining variable that can affect the resonant frequency is the density of the liquid. The following equation illustrates the relationship between the density of the liquid ρ, the characteristics of the resonator (constants A and B) and the oscillation frequency ƒ:

How resonance measurement equipment works:

(1) Clamp both ends of the resonator firmly.

(2) The exciter makes the tube vibrate.

(3) The vibration sensor detects the vibration frequency.

The shape and material of the resonator are not fixed. Therefore, the resonator can be a round or square tube.

Figure 1: Design of resonance measuring instrument "1. Vibration sensor, 2. Harmonic generator, 3. Fixed resonator"

2. Advantages of using the resonance principle for density measurement

(1) Direct processing combined with simple testing techniques is one of the greatest advantages of resonator density measurement, allowing the density to be measured after adding the medium without any further adjustments. Since the density value is displayed directly on the digital display, reading errors can be ruled out. No temperature control of the medium is required; instead, the temperature is measured in real time. Additionally, there is no need to extract exact volumes.

(2) Technology miniaturization requires only a small amount of sample to perform reliable density determination. This feature is particularly useful when measuring expensive fluid media. Using a small sample also makes it easier to determine the medium temperature for density measurements.

(3) The measurement can be performed at the corresponding pressure in a closed system. This is especially important for certain media such as alcohol-water mixtures or gases. Without appropriate ambient pressure, such media will evaporate, resulting in incorrect measurements.

(4) Finally, measurement results can be obtained in an extremely short measurement time. Resonant density recorders also enable continuous direct measurement of flow rates during processes.

3. Disadvantages of using the resonance principle for density measurement

(1) This method does not allow direct traceability, that is, it is impossible to compare the measured density with the national standards (kg and m3) for this measured variable. The reason for this is that density is calculated using measured frequencies, rather than the density value obtained by dividing mass (kg) by volume (m3). Calculating density from frequency requires at least two reference media with known densities. Traceability is therefore only possible via these two reference media.

(2) The measurement sensitivity is affected by the properties of the measuring tube. The smaller the self-weight of the measuring tube, the smaller the impact on the measured frequency, and the higher the sensitivity of the measurement. On the contrary, high self-weight measuring tubes cannot be used to measure low-density media.

(3) The mechanical properties of the resonator are changed by pressure and temperature. The result is a change in the measured frequency. These effects can be compensated for by calibration at different pressure and temperature points.

(4) Frequency is also affected by the viscosity of the measurement liquid, which may increase measurement uncertainty. At the same time, bubbles in the measurement liquid and contamination of the resonator will also cause measurement errors. The liquid to be measured must be degassed and the resonant cavity cleaned before measurement.

4. Purpose of resonant density measurement sensor

Resonant density sensors are particularly suitable for industries with different accuracy requirements for laboratories and processes:

(1) In the oil and gas industry, it can be used to determine its calorific value, energy content or composition.

(2) At the gas station, the correct value and the measurement of foreign particulate matter can be carried out.

(3) During transportation, the correct value can be measured and the medium checked.

(4) On the aircraft, monitor the fuel level and optimize the flight distance of the aircraft through refueling.

(5) Test constant fuel quality on engine test bench.

5. Some commercial resonant density meters:

(1) TrueDyne Sensors’ density sensor DLO-M1: MEMS density module

     Dimensions: 66 x 30 x 15 mm

(2) Density meter DIMF 2.1 from Bopp & Reuther: used for density measurement in process processes

     Dimensions: approx. 650 x 450 x 150 mm

(3) Anton Paar company’s density meter DMA 5000: high-precision general-purpose instrument (0.000005g/cm3)

     Dimensions: 482 x 340 x 231mm

(4) AMETEK company’s UGC-density meter: used for density measurement in process

   Dimensions: approx. 450 x 200 x 100 mm