Gas-Laden Liquid Density Measurement Using Multi-Mode Vibration
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Solution Overview
Problem
Existing methods for determining the mass flow rate and density of gas-laden liquids face cross-sensitivities to the speed of sound and compressibility, which are not adequately compensated, leading to inaccuracies in measurements, especially with increasing gas loading.
Innovation Solution
A method using a sensor with a measuring tube that excites flexural vibrations of different modes to determine natural frequencies, allowing for the calculation of provisional density values and correction terms based on the speed of sound, which are used to derive corrected density and mass flow values, thereby compensating for cross-sensitivities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If single-mode vibration measurement is used, then device complexity is reduced, but measurement precision deteriorates due to cross-sensitivities to speed of sound and compressibility
Solution Approach 1:
The measurement process is segmented into multiple independent vibration mode measurements (f1 mode and f3 mode), where each mode provides separate density information. This segmentation allows the system to obtain multiple measurement data points without requiring complex simultaneous multi-mode sensing, thereby improving measurement precision while keeping the device relatively simple.
Solution Approach 2:
The invention changes the vibration frequency parameter by utilizing different natural frequencies (f1 and f3 modes) of the measuring tube. By measuring at these different frequency parameters, the system can determine separate provisional density values that are then used to calculate speed of sound and compressibility correction factors, thereby compensating for measurement inaccuracies.
2Measurement precision
If multiple vibration modes are measured, then measurement precision improves through cross-sensitivity compensation, but device complexity increases
Solution Approach 1:
The invention extracts the speed of sound and compressibility information from the vibration measurements themselves, rather than requiring separate sensors or complex measurement systems. By taking out these physical parameters from the vibration data and using them as correction factors, the system achieves high measurement precision without adding device complexity.
Solution Approach 2:
The system uses feedback by calculating correction terms based on the measured provisional density values and speed of sound, then applying these corrections to obtain accurate density and mass flow measurements. This feedback mechanism allows the system to automatically compensate for cross-sensitivities using the measurement data already collected.
3Ease of operation
If conventional single-frequency measurement is used, then ease of operation is maintained, but measurement precision deteriorates due to uncorrected cross-sensitivities
Solution Approach 1:
The invention performs preliminary measurements at different vibration modes (f1 and f3) to obtain provisional density values before final correction. This preliminary action allows the system to calculate speed of sound and compressibility factors in advance, which are then used to correct the final measurements, thereby maintaining ease of operation while improving precision.
Solution Approach 2:
The measuring tube itself serves multiple functions: it acts as both the flow conduit and the vibration sensor. The tube's natural vibrations provide the measurement data needed to determine density, speed of sound, and compressibility, eliminating the need for separate sensing devices and maintaining operational simplicity.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach provides a more robust and simpler method for compensating cross-sensitivities, improving the accuracy of mass flow and density measurements by accounting for the influence of oscillating gas-laden liquids and reducing errors associated with speed of sound and compressibility.
Implementation Method 1
the measuring tube can be excited between the two fixing devices to flexural vibrations of different modes with different natural frequencies
Implementation Method 2
the resonant frequency of the oscillating gas-laden liquid is usually above the natural frequency of the measuring tubes, the influence on the f3 bending vibration mode is greater than the influence on the f1 bending vibration mode
Implementation Method 3
determining a value for the speed of sound of the gas-laden liquid guided in the measuring tube
Data Source
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AI summary
The invention relates to a method for determining a physical parameter of a liquid charged with gas in the form of suspended bubbles, using a sensing element comprising a measuring tube for conducting the medium, which tube can be excited to vibrate in flexural vibration modes of differing resonant frequencies. The method comprises the following steps: determining the resonant frequency of the f1 mode and the f3 mode (110); determining previous density values (120) for the liquid charged with gas and conducted in the measuring tube, on the basis of the resonant frequencies of the f1 mode and the f3 mode; and determining a value for the sound velocity of the liquid charged with gas and conducted in the measuring tube and/or at least one correction term (130) and/or density error, which is dependent on the sound velocity and the resonant frequency of a mode, for the previous density value that was determined on the basis of the resonant frequency of the mode, in order to define a corrected density measurement value (140); or determining a correction term for a previous mass flow rate value in order to define a corrected mass flow rate measurement value on the basis of the first previous density value, the second previous density value, the resonant frequency of the f1 mode and the resonant frequency of the f3 mode.