Design, Modelling, and Experimental Validation of a Glass U-Tube Mass Sensing Cantilever for Particulate Direct-on-Line Emissions Measurement

Abstract

The requirement to monitor and control industrial processes has increased over recent years, therefore innovative techniques are required to meet the demand for alternative methods of particulate measurement. Resonant mass sensors are now strong candidates for accurate mass measurement and are frequently used in many diverse fields of science and engineering. This paper presents the design, modelling, and optimal geometry selection for sensitivity improvement of a U-shaped glass tube as a resonant mass sensing cantilever with a view to becoming a component of particulate measurement equipment. Finite Element Analysis (FEA) was used to develop the system which was validated experimentally using a physical model. This paper focuses on both the proof of concept and the geometry selection of the sensor using analysis of the system sensitivity for best selection. Modal and harmonic analysis were undertaken across a range of commercially available glass tube sizes from 6 mm to 10 mm diameter, to determine the optimal geometry selection, validated with practical experimental data. Results show a consistent difference of 3–5% between the simulation and experimental results, showing strong correlation. This research provides a methodology on the development of using a U-shaped glass tube for accurate mass measurement with a view to exploring the design as a component of particulate emissions equipment. The experimental and simulation results confirm that the highest sensitivity is achieved when the geometry dimensions, and therefore the vacant mass of the tube, is reduced. The 6 mm diameter tube with the smallest bend radius was the most suitable design to meet the design criteria. The calibration curve was plotted to allow an unknown mass to be calculated, which gave an R² value of 0.9984. All experimental work was repeated three times with results giving an average of 0.44% between the minimum and maximum showing strong linearity and suggesting the potential for implementation of the methodology in its intended application. The design provides possible solutions to some of the issues currently seen with particulate measurement from stationary sources.

1. Introduction

When a U-shaped glass tube cantilever is set to resonance at its natural frequency, the frequency of the tube will vary depending upon the characteristics and properties of the tube [1]. The natural frequency is inversely proportional to the combined mass of the body of the tube and any additional unknown mass [2]. General considerations that can affect the resonant frequency are shape, size, elasticity of the tube’s material, induced stress, mass, mass distribution inside the body, and damping. A good system design is critical to achieving repeatable and reliable results. The vibrating U-tube design is based on the principal that a measured change in resonant frequency can be used to determine an unknown mass applied to the vibrating tube. The resonant frequency will have the greatest change when the mass is at the antinode point, meaning that the effect of the mass will have a different effect on the frequency depending upon its position in the glass tube [3,4].

The focus of this research is to simulate a U-tube glass resonator for accurate mass measurement, analysing a range of geometry selections to achieve the greatest sensitivity, with results confirmed through experimental validation. A range of glass tubes have been chosen for analysis in this research from 6 mm to 10 mm in external diameter. The tube is manufactured from a straight glass tube bent into a U-shape and is made from borosilicate glass with a density of 2.23 g/cm³ and Young’s modulus of 63 GPa. The glass tube is a component that forms part of a wider system, which, in its most basic form, includes supports for the glass tube, counter mass, exciter, frequency sensor, temperature control, and process control. Anton Paar use this principal for the measurement of density in lab-based instruments [5,6]. This paper details the design of a U-tube glass sensor, specifically for mass measurement, with the potential to measure particulate emissions from industrial processes and overcome some issues associated with the Standard Reference Method (SRM) procedure detailed in BS EN 13284-1 [7].

The requirement to accurately measure particulate emissions is imperative to the understanding, and, therefore, the control and reduction in particulate emissions [8]. There are serious health and economic effects of particulate emissions, as detailed in a study completed by Zhang [9]. Nicklin and Darabkhani [10] explain the issues surrounding particulate emissions measurement, in particular the calibration of Continuous Emissions Monitoring Systems (CEMS) with the SRM. Innovative research to develop the SRM procedure is required for the accurate calibration of CEMS [11]. The representativeness of continuous particulate measurement is dependent upon accurate calibration using a repeatable and reliable calibration procedure [12]. Measurement with the SRM according to BS EN 13284-1 [7] is difficult at mass concentration levels of <10 mg/m³ and the methodology is only validated for processes >5 mg/m³ [13]. This research, therefore, seeks to develop a system and propose methods to improve the process of particulate mass concentration measurement through the development of a component which forms part of the wider equipment. There are currently nine commercially available techniques used to measure particulate from stationary sources [10]. Amaral [14] lists the techniques to measure particulate emissions as gravimetric, optical, microbalance, and Yan [15] adds electrostatic sensing. There is currently no particulate measurement technology available to measure the mass concentration of particulate directly on-line to give real time measurements. All continuous emissions monitoring equipment requires application calibration, which, should the process conditions change, render the calibration factor inaccurate [12]. This research seeks to address some of these issues.

2. Theory

The idealised mechanical system model that is commonly used to describe the system behaviour of the proposed design is a spring mass system, oscillating under a forced displacement [16,17] as detailed in Figure 1.

The total mass of a vibrating glass U-tube system consists of a combination of the tube and any additional unknown masses. The resonant frequency of a vibrating sensor is determined by [18,19,20,21]:

$$f=\frac{1}{2\pi }\sqrt{\left(\frac{k}{ms}\right)}$$

(1)

where:

• f = resonant frequency,
• ms = effective mass of the sensor,
• k = spring constant of the sensor.

The resonant frequency of a vibrating sensor is inversely proportional to the effective mass of the sensor. Any mass added to the tube increases the effective mass of the sensor (ms), resulting in a measurable reduction in the resonant frequency of the U-tube. The use of this principal is currently used in resonating cantilevers to measure the density of fluids [22,23,24]. In this research, the concept was developed for the measurement of mass concentration of particulates from industrial processes.

In work conducted by Ansari [25], which investigates deflection, frequency, and stress characteristics in microcantilevers, sensitivity is increased when the deflection and resonant frequency are increased. Reducing the moment of inertia reduces the bending stiffness, which in turn results in higher deflection; where the moment of inertia is the structure’s ability to resist bending, and the bending stiffness (K) is a function of the Young’s modulus, the moment of inertia, the cross-sectional area, and the length of the beam.

The moment of inertia (I) of a round structure can be determined by

$$I=\left(\pi {(r}^4\right))/4$$

(2)

where:

• $I$ = moment of inertia,
• $r$ = radius of geometry.

The bending stiffness (K) can be determined by

$$K=3EI/\left(L^3\right)$$

(3)

where:

• $K$ = bending stiffness,
• $E$ = elastic modulus,
• $I$ = moment of inertia,
• $L$ = length of tube.

Therefore, to achieve the desired effect of an increase in deflection, a longer glass tube with the smallest radius would be the most suitable option. A tube with a smaller radius has a lower moment of inertia, and a smaller moment of inertia results in a smaller bending stiffness, but a longer tube also has a smaller bending stiffness.

The design objective of this research is to achieve the greatest measured change in resonant frequency for the smallest change in additional mass to achieve the highest sensitivity. Where the smallest change in additional point load mass gives the greatest change in resonant frequency, the highest sensitivity will be observed. Therefore, the highest sensitivity will be seen when the ratio between the additional point load mass and the change in resonant frequency is smallest.

The fundamental resonant frequency of a cantilever beam can be calculated by

$$f=\frac{1}{2\pi }\sqrt{\frac{EIg}{w{l}^4}}$$

(4)

where:

• $f$ = resonant frequency,
• $E$ = elastic modulus,
• $I$ = moment of inertia,
• $l$ = beam length,
• $w$ = uniform load per unit length,
• $g$ = gravitational constant.

As stated by Sanmamed [26], the spring constant of a hollow mass sensor can be determined by

$$k=\frac{3E}{L^3}\frac{\pi }{4}\left(r_e^4-r_i^4\right)$$

(5)

where:

• $k$ = spring constant,
• $E$ = Young’s modulus of sensor tube material,
• $L$ = total length of sensor tube,
• $r_e$ = external radius of sensor tube,
• $r_i$ = internal radius of sensor tube.

To achieve the desired effect of increasing resonant frequency, a shorter length glass tube with a larger radius would be the most suitable option. The reduction in length increases resonant frequency and a higher moment of inertia also increases resonant frequency caused by an increase in the tube’s radius. Therefore, when designing a system to increase the resonant frequency and the deflection of the glass tube, several design conflicts are observed. DesignXplorer of Ansys Workbench [27,28] was used to determine the optimal geometry sizes for a glass tube resonant mass sensor, which was designed for the greatest change in resonant frequency for the smallest addition of mass. This research has a particular industrial application focus and is, therefore, influenced by commercially available components and manufactures tolerances when considering component selection. The expected effects of damping are present during oscillation but, in a well-designed system, the effects are minimised [29]. The system is excited via forced vibration and the exciter will operate to keep the system, for any change in additional mass (ms), at its resonant frequency, overcoming damping effects as seen in work undertaken by Hermiyanty [30]. As explained by Rechberger [23], glass flexural resonators are established as being one of the standard methods for the measurement of density of liquids in a laboratory. The core component of the system is the U-shaped glass tube measuring cell detailed in Figure 2a, whose oscillator’s resonance frequency changes with the mass of the fluid within the tube. The displacement of the tube is detailed in Figure 2b, where the hotter, red colours indicate areas of higher displacement, and the cooler, blue colours indicate areas of lower displacement. During the initial analysis of the geometry, the end faces of the tube were used as a fixed support, it is therefore expected that the highest displacement is seen at the opposing end of the cantilever. The mass of the tube support should ideally be infinitely higher than the mass of the tube to avoid interference from external sources [30,31]. This assumption is made throughout the initial analysis by applying an infinite fixed support to the tube to allow sensitivity analysis to be carried out on the size and geometry of the tube with external influence. In practise this is not possible but good design should make considerations for the best tube supports.

3. Methodology

3.1. Development Methodology

The requirement to measure the mass of particulates in an emissions gas stream from stationary sources, both online and directly, was identified by Nicklin and Darabkhani [10]. Generally, CEMS measure a characteristic of particulates, which could include the diameter, size distribution, colour, shape, and chemical composition. These CEMS measure particulate characteristics as a function of the mass concentration and give an output in mg/m³ for emissions reporting purposes after applying a calibration factor. The issue surrounding the use of CEMS is that the SRM used for calibration is difficult <10 mg/m³. The accuracy is also questionable due to the influence of errors in the process [32], and the process is labour intensive and therefore costly. Anton Parr [5] have developed lab-based equipment capable of measuring the density of fluids using the vibrating glass tube method. When a glass U-tube is free to move as a cantilever and forced to vibrate at its natural frequency, a measured change in frequency is proportional to a change in density of the fluid inside the tube [33]. This principal is adapted through this research as a method to accurately measure an unknown mass with the potential to measure particulate emissions from an industrial process, online, and in real time.

Preliminary geometry designs of a glass U-tube, similar to those used in commercially available lab-based densitometers [34,35], were drawn for initial development. Ansys Mechanical software was chosen as the tool for simulating the system [36] as successfully used in similar research [37,38,39]. The measurement system requirements included the capability to support the glass U-tube, mechanically excite the tube, and accurately measure any changes to the tubes resonant frequency as a result of the addition of any mass. Conditions for simulation through Ansys Mechanical included a fixed ambient temperature of 22 °C, borosilicate glass tubing with a density of 2.23 g/cm³ and Young’s modulus of 63 GPa, and point loads of 130 mg and 260 mg in addition to the vacant tube. Two input design parameters for the glass tube were defined as the straight length of the two shafts of the U-tube, and the radius of the U-bend in the tube. The limits of the manufacturing process were taken into consideration through the development process and only the minimum and maximum tolerances were used for simulation. As external diameters of the tube increase, the minimum limit of parameter P2 also increases due to manufacturing limits. Tube geometries with an external diameter of 6 mm–10 mm were chosen for testing to determine the effect of tube sizes on the sensitivity of the design. The full support system was designed to hold the glass tube and comprises of two adjustable tube supports to allow for testing of all tube variations as detailed in Figure 3, taking influence from previously published work [17,19,34,35]. Support inserts were designed to house the piezo chips which are used for the forced excitation and measurement of the tube’s frequency. The inserts are size specific to suit the external diameter of the tubes. The piezo chips are held in place up to, and along the surface of the tube, with the connecting wires for termination passing through the body of the support.

Ansys DesignXplorer was used to analyse the system geometry to maximise sensitivity, giving the greatest change in frequency for the smallest addition of mass for optimum performance. DesignXplorer is a post-processing tool [27], allowing the realisation of how the output parameters are driven by input parameters, and how changes to model geometry affects performance to meet the design deliverables. The optimisation process was undertaken for each tube diameter from 6 mm to 10 mm, with the minimum and maximum bend radius, and tube length determined by the manufacturing tolerances. Following the optimisation analysis, the three most sensitive designs for each tube were selected for further evaluation and experimental validation, as detailed in

Table 1. Ansys DesignXplorer optimised geometry results.

Tube Size, External Diameter (mm)	P1—Length (mm)	P2—Radius (mm)	Resonant Frequency (Hz)
10	50.01	13.00	1921.62
	61.35	22.88	993.42
	78.48	22.40	740.35
9	50.01	9.00	2037.13
	61.38	18.85	1004.87
	78.46	18.72	732.52
8	50.01	7.00	1972.42
	61.38	16.88	945.45
	78.64	16.21	687.52
7	50.01	7.00	1710.11
	61.31	17.00	816.05
	78.57	16.41	591.96
6	50.01	6.00	1513.31
	61.38	15.88	725.27
	78.31	15.16	543.85

. Variations in the manufactured components resulted in differences between the required optimised geometry sizes and the actual measured sizes. To allow for accurate validation of the results, the measured values were used for harmonic analysis which was undertaken to determine the natural response of the system, as successfully used to determine the response of systems in previous research [40,41,42].

3.2. Experimental Methodology

Experimental work was undertaken for validation purposes to determine the degree to which the simulation is an accurate representation of the real-world physical model, and to confirm the measurement concept. Advances in FEA has improved the accuracy of simulation work, as seen in research by Mullen [43]; whilst the percentage difference between simulation and experimental work is reducing, differences are still noted. Geometry optimisation for highest sensitivity is the design objective through modal analysis, design optimisation, harmonic analysis, and result validation. Using the optimised geometry results detailed in Table 1, the 15 tubes were manufactured from borosilicate glass tubing with a density of 2.23 g/cm³, and Young’s modulus of 63 GPa. Each of the 15 tube geometries were tested at no load (0 mg), 130 mg, and 260 mg, resulting in a total of 45 combinations. For reliability of results, all combinations were repeated three times and tested at a constant temperature of 22 °C in a similar manner to research undertaken by Rechberger [23] which was monitored by a climatic chamber, as shown in the system schematic in Figure 4 and equipment setup in Figure 5. LabVIEW software was used on a laptop to measure and control the system, as implemented in similar studies [19,44,45,46,47]. A National Instruments USB X Series Data Acquisition Device [48] was used as the interface between the physical model and the laptop. The tube was excited to its resonant frequency by a piezo chip located in the tube insert, adjacent to the face of the tube at the end of the support. The resonant frequency was measured using a piezo transducer located in the same manner as the piezo exciter, allowing accurate measurement and feedback control for the system. A feedback control loop was developed in LabVIEW to excite the glass U-tube at its resonant frequency using a similar methodology to that developed by Ruff [46]. The approach automated the process of tracking and plotting the tubes frequency, whilst maintaining a resonant state. The temperature of the climatic chamber was controlled through the LabVIEW software and monitored via a thermocouple connected directly to the Data Acquisition Device. The vibrating tube system was left in the climatic chamber for 15 min to stabilise before the experimental work commenced. During each test, the following information was recorded:

• The measured internal and external radius of the glass tubes;
• The measured bend radius;
• The climatic chamber temperature;
• The resonant frequency;
• The mass of the tube.

Figure 4 details the experimental schematic diagram and connectivity of the setup, and Figure 5 is a photograph of the system during testing.

3.3. Application Methodology

The development of an accurate mass measurement device in this research has an industrial application focus to accurately measure particulate emissions from stationary sources. The design objective is to optimise the geometry for the highest sensitivity and to prove the concept through a measured change in resonant frequency as a result of the addition of mass to the tube. The physical properties of the system components and the fluid contained in the system will be affected by changes in temperature; in commercial densitometers, this is commonly controlled using Peltier elements. During simulation and experimental testing, a constant temperature of 22 °C was used. In application, consideration for the moisture content in stationary source emissions must be made. Moisture content in the emissions could negatively affect the accuracy of the measurement system developed in this research. Careful control and consideration using Peltier elements can reduce the negative effects of moisture within the sample by maintaining the measurement cell above the dew point of the emissions.

The general principal of measurement using the SRM is to sample a known volume of flue gas through a filter. The sampling must be undertaken isokinetically, where the suction at the nozzle is at the same velocity as the flue gasses in the duct or stack. By weighing the filter before and after sampling, the total particulate per volume of gas can be determined [13]. To take an online, direct, mass concentration measurement from a stationary source, there is a requirement to measure the mass of particulate directly in a gas flow [10]. When a particle flows through a glass U-tube sensor as detailed in this paper, the resonant frequency of the tube is dependent upon the position of the particulate. The greatest change in frequency will be seen when the particle is at the anti-nodal point. For an isolated mass travelling through the tube, the mass can be calculated accurately following a calibration and set-up procedure of the tube by measuring the resonant frequency change when the mass is greatest in the tube. For the intended application of industrial stationary source emissions measurement, particulate will not be in isolation; will be of different colour, shape, and concentration. The proposed solution uses a filter fitted at the anti-nodal point in the U-tube shown in Figure 6 to measure the accumulated mass concentration. In the intended application, a measured volume of particulate laden gas from a stationary source is to be passed through the glass U-tube from the inlet to the outlet with the filter capturing the particulate. The mass of the filter will subsequently increase due to the mass of the captured particulate reducing the resonant frequency and, therefore, allowing the glass U-tube to be used to accurately measure the accumulation of particulate. By measuring the volume of gas passed through the glass tube and the mass of particulate captured on the filter in the tube, a mass concentration in mg/m3 can be given. This method has the potential to address issues associated with the handling and processing of filters during the SRM measurement process, reduces the time required to undertake a full test procedure, reduces high costs associated with annual surveillance testing, increases accuracy, and provides the potential to achieve stack profiling to determine optimum positioning for continuous monitoring. It should be noted that in its current form the U-tube sensor is a mass measurement instrument, therefore consideration of how to extract a representative sample and pass this sample through the tube must be made.

3.4. Analysis and Validation Methodology

The three sets of data from the experimental work were compared to determine the consistency of results and the reliability of each of the experimental setups. These three sets of experimental data were taken for the purposes of validating the mass measurement instrument, which can be described as the extent to which repeated measurements yield consistent results [49]. For each test set, the tube and support system were disassembled and reassembled for accurate analysis of the system. The procedure then included an analysis of the standard deviation [50], between the datasets with a visual representation to aid evaluation and to determine patterns in the consistency of results.

A visual aid was used as an initial comparison of the simulation and experimental data to verify the results and, therefore, the design principal and was also used to show the percentage difference between the sets of data [51,52]. To determine if the two sets of data follow the same distribution, a Kolmogorov–Smirnov test [53,54] was undertaken. This test statistically determines if the sets of data follow the same pattern by quantifying the distance between the distributions of the two samples. The effects of the bend radius, length, tube mass, and size of tube on the change in frequency was analysed by calculating the Pearson correlation coefficient which can be used to measure the strength of the relationship between the two variables [55]. Using the value calculated for r (correlation coefficient), the correlation strength can be assessed to determine the influence of parameters on the change in frequency and, therefore, the sensitivity of the tube.

A linearity check was undertaken on the measured resonant frequency for the tube showing greatest sensitivity by using the linear calibration curve and the linear regression equation. Using the linear regression equation, any unknown mass can be calculated from any measured resonant frequency [56]. The R² value was used to determine the linearity of the measured results.

4. Results and Discussion

Emissions monitoring is a technically challenging field. The measurement of particulate emissions from stationary sources is difficult due to the high level of accuracy required and the harsh environment in which equipment operates. Techniques currently available for continuous particulate monitoring rely on the measurement of the characteristics of particulate and not the mass directly. The method presented in this work seeks to overcome many of the parameter-driven measurement issues by measuring mass directly online, with the potential to give real time mass concentration measurements. The research process involved initial geometry design of the U-tube sensor, modal analysis, system design, geometry optimization, component manufacture, system assembly, experimental testing, and harmonic analysis. Throughout this structured process, a system capable of mass measurement using a vibrating glass U-tube was designed and developed. There are currently many issues surrounding the use of the SRM procedure, as detailed in BS EN 13284-1 [7]. This paper seeks to detail the optimum geometry selection of the proposed method with the potential to overcome some relevant industry issues. In a study completed by Nicklin and Darabkhani [32], significant errors are introduced when following the SRM procedure. The methodology detailed in this paper seeks to overcome some of these issues, including difficulties in the rinse and clean procedure, external influences affecting results (where high levels of ambient particulate is present), and the handling and processing of delicate filters. The development of an online direct mass measurement system with the ability to give accurate mass concentration values of particulate from stationary sources would see a significant improvement on current methods. There is also the possibility to introduce new applications to the emissions measurement industry, which could include providing a stack profile to determine the optimum location for continuous particulate monitoring. This is a process undertaken when installing gas emissions monitors, but with current technologies, is not available for particulate monitoring. Through the development of optimal geometry selection, this paper seeks to provide an alternative, improved measurement technique.

The experimental setup was assembled to be representative of the system design which was developed through the optimisation process in Ansys. A comparative analysis of the experimental data was undertaken through the standard deviation of results. The analysis was carried out across the three sets of data, for each tube diameter, at each optimised geometry, with the mass remaining constant for direct comparison and validation of the instrument to confirm its capacity for consistent measurement. The standard deviation for each tube size is visually displayed in Figure 7 on the same axis bounds for clarity of comparison. In ideal conditions, all results would be identical with no deviation in results. Small inconsistencies with the experimental setup results in differences between the sets of results. The Pearson correlation coefficient was calculated to determine the effect of the tube diameter on the standard deviation of results, which was undertaken to determine the reliability of each tube diameters setup on the consistency of results. The Pearson correlation coefficient gave an r-value of −0.4007 which is a negative and weak correlation. This is not strong enough to determine any reliable correlation in this study. The series of tests for each tube diameter were carried out consecutively, meaning that the setup process for each tube was undertaken for each test. The result from each test includes the internal and external diameter of the glass tubes, length of the tube (parameter P1), radius of the bend (parameter P2), measured radius, point load mass, measured frequency, temperature, measured external and internal diameter of the glass tubes, and the simulated resonant frequency. The simulation results are obtained through harmonic analysis using Ansys Mechanical software. The geometry values and boundary conditions used for harmonic analysis were the measured values taken from the physical model to allow for accurate comparison of simulation and experimental results.

Although no strong correlation between the tube diameters and standard deviation of the three test sets can be determined, Figure 8 details the maximum percentage difference between the results for each test set. All results have <1% difference between the minimum and maximum measured resonant frequency with an average of 0.44%. The deviation can be attributed to the manual process required for the setup of the tube into the support. In practical applications, the slight differences would be accounted for in a calibration factor applied specifically to the tube, as installed in the support system. Therefore, the difference in results is due to the inconsistency of the setup process and is not a measure of accuracy of the measurement system.

The design process of this research was undertaken through simulation in Ansys Mechanical software. The results were used for the development of a physical model to undertake experimental validation. A bar chart was used for a visual comparison of the simulation and experimental results, with a line graph showing the maximum percentage difference between the two sets of results, as detailed in Figure 9. It can be noted for all tests that the measured resonant frequency is always lower than the simulated resonant frequency and in all cases is between 3% and 5% difference. As expected, as the tube length increases the resonant frequency decreases, as the point load mass increases the resonant frequency decreases, and as the tube diameter decreases the resonant frequency decreases. A Kolmogorov–Smirnov test was undertaken on the two sets of data, with a significance level of 5% to determine if they follow the same distribution. The cumulative distributions are visually detailed showing similar distributions in Figure 10. The Kolmogorov–Smirnov d-value is 0.133 and the p-value is 0.825. The d-value denotes the maximum absolute difference between the two distributions with the low value indicating that the datasets closely follow the same distribution. A high p-value suggests that a small deviation has a high probability value and, therefore, we can conclude that the datasets follow the same distribution, and we cannot reject the null hypothesis, which is that the samples follow the same distribution. The consistently small differences between the simulation and experimental data show a slightly lower result for the measured values in each test and can be attributed to tolerances in material specification, manufacturing processes, and the assembly setup process.

Analysis was undertaken on the effects of each of the design parameters including the bend radius, tube length, tube mass, and diameter of the tube on the percentage change in resonant frequency for both 130 mg and 260 mg point load mass. This analysis was undertaken to determine the importance of each of the parameters on the sensitivity of the tube to establish the most appropriate design for the relevant application. The Pearson correlation coefficient was used to determine the strength of relationship between the parameters and the change in resonant frequency. All results were actual measured values that were experimentally tested and not data collected through simulation. The four comparisons are detailed in Figure 11, Figure 12, Figure 13 and Figure 14.

The relationship between the bend radius and the percentage change is detailed in Figure 11. The analysis using the Pearson correlation coefficient returns an r-value of −0.7917 for the 130 mg test, and −0.7924 for the 260 mg test. This shows a strong and negative correlation and confirms that the relative effect on the frequency is consistent with the changing load, concluding that a larger bend radius results in a smaller change to the measured resonant frequency.

The relationship between the tube length and the percentage change in resonant frequency is detailed in Figure 12. The analysis using the Pearson correlation coefficient returns an r-value of −0.6071 for the 130 mg test, and −0.5926 for the 260 mg test. This shows a moderate negative correlation and confirms that the relative effect on the frequency is consistent with the changing load, concluding that a longer tube results in a smaller change to the measured resonant frequency.

The relationship between the tube diameter and percentage change in resonant frequency is detailed in Figure 13. The analysis using the Pearson correlation coefficient returns an r-value of −0.61 for the 130 mg test, and −0.6234 for the 260 mg test. This again shows a moderate negative correlation and confirms that the relative effect on the frequency is consistent with the changing load, concluding that a larger diameter tube results in a smaller change to the measured resonant frequency.

The relationship between the tube mass and the percentage change in resonant frequency is detailed in Figure 14. The analysis using the Pearson correlation coefficient returns an r-value of −0.8996 for the 130 mg test, and −0.9048 for the 260 mg test. This shows strong negative correlation and confirms that the relative effect on the frequency is consistent with the changing load, concluding that the heavier the tube, the lower the change to the measured resonant frequency.

This paper focuses on the development of using a U-shaped glass tube for accurate mass measurement with a view to exploring the design for highest sensitivity. By using a known point load mass across the design geometry selections, the highest percentage change in resonant frequency will show the tube with the highest sensitivity. All analysis of the effects of geometry parameters on the percentage change in resonant frequency show that reducing the size and weight of the glass tube increases the measured change in resonant frequency when a load is applied to the tube. The U-tube measurement system was designed through simulation and experimentally tested at known masses, the first being a vacant empty tube, the second at 130 mg, and the third at 260 mg. The objective of this paper is to apply an unknown mass in the form of particulate extracted from a stationary source to give an accurate representative measurement. The measurement concept was tested using the measured resonant frequency at a known mass of 130 mg and 260 mg and calculating the expected resonant frequency for the respective mass. The calculated value can then be compared to the measured value to determine the error in the system and to prove the concept of the measurement of the unknown mass in the tube. The percentage error of the measured and calculated resonant frequency values were calculated. The average percentage error for the measurement system is 3.8%, showing strong potential of the proposed design for the measurement of an unknown mass. There are a small number of samples with a higher percentage error than the average suggesting inconsistencies with the measurement process, which can be attributed to the manual setup. In application these errors could be reduced as manual interference required for experimental testing would be reduced and, once calibrated, would not affect results.

This paper also focuses on the geometry and system development of a method of measurement of mass for the highest sensitivity. The greatest change in measured resonant frequency is noted for the 6 mm diameter tube at 50 mm length with 6 mm bend radius, suggesting that this tube is most sensitive for mass measurement. The sensitivity of the 6 mm tube is given by

$$Sensitivity=\frac{\Delta frequency}{\Delta point load mass}$$

(6)

where:

• $\Delta frequency$ = change in measured resonant frequency (Hz),
• $\Delta point load mass$ = change in additional point load mass (mg).

This results in a measurement sensitivity of 0.53 Hz/mg. A limit of detection (LOD) of 2.74 mg was calculated using data collected using the validated simulation model developed through this project. The 6 mm geometry response was analysed for a point load mass from 0 mg to 260 mg at 5 mg intervals for calculation of the LOD. Further experimental work would allow for additional data to be collected for analysis to realise the full potential and capabilities of the vibrating glass tube as a mass measurement system. The LOD was determined using the methodology taken from “Guidance for Industry, Validation of Analytical Procedures, Methodology” document, produced by ICH [57].

The linear calibration curve has been visually plotted against the measured data for the optimised geometry 1, for the 6 mm tube detailed in Figure 15. The linear regression equation used to plot the calibration curve can be used to calculate the unknown mass applied to the tube from the resonant frequency and is shown in Figure 15. The R² value is 0.9984. This high value shows that the measured data follows the linear calibration curve and, therefore, indicates strong linearity in the measurements.

The difficulties with the calibration of CEMS equipment can be overcome by improving the SRM procedure [12]. Automating the filter measurement process to produce an online, real-time measurement would be a significant improvement on current methods available. Currently the SRM procedure is a labour-intensive process where many measurement errors can be introduced. The interference of ambient particulate would not affect the accuracy of results with the proposed method due to the extractive system being sealed up to the filter location. The losses associated with handling the filter, not only during the removal of the filter from the isokinetic sampling equipment on site but also during the laboratory process, could be eliminated due to the filter not requiring any human interaction to achieve measurements. There are issues associated with the representativeness of an extracted sample with regards to the rinse procedure during the SRM process [32]. Although not developed through this project, the ability to perform an automated rinse procedure is now a possibility with the proposed method. Further research has the potential to develop this possibility. This would help to reduce issues with particulate captured in the sample train, where in some cases 100% of particulates can be caught within this equipment. The importance of a direct mass measurement instrument is fundamental to the particulate emissions measurement industry. Continuous particulate monitoring equipment requires application calibration against the SRM. The SRM suffers from measurement errors introduced through particulates captured within the sampling equipment, and by human interaction with the filter, rinse equipment, and laboratory testing. In addition to the potential to overcome some of the current issues faced within the particulate measurement industry, the proposed methodology opens further application opportunities. The ability to perform stack profiling is now a possibility. This is a process that is currently undertaken to determine the most suitable location for CEMS and is currently not feasible with particulate measurement equipment currently available. The ability to take a stack profile from a stationary source would allow better placement of CEMS and would improve the representativeness of the measurements currently being taken.

5. Conclusions and Further Works

The purpose of this research is to design, simulate, and validate experimentally, a glass U-tube mass sensor designed for highest sensitivity. The intended application of the methodology is to measure the mass concentration of particulate emissions from stationary sources with a view to using the methodology to overcome some known issues associated with the SRM method detailed in BS EN 13284-1 [7]. Analysis was undertaken on glass tubes with external diameters of 6 mm–10 mm. Geometry optimisation was undertaken to develop a measurement system for the highest sensitivity. The data collected through simulation and experimental work suggests that the most sensitive system is designed when the tube mass is smallest by reducing the length, bend radius, and external diameter. The 6 mm tube with smallest length and smallest bend radius gives the greatest percentage change in resonant frequency for the smallest addition of mass, with a measurement sensitivity of 0.53 Hz/mg. The distribution of the simulation and experimental data shows a strong correlation, resulting in a maximum difference of between 3% and 5%. The strong linearity shown in a high R² value of the linear regression equation confirms that the natural resonant frequency is inversely proportional to the combined mass of the body of the tube and any additional unknown mass. The average percentage error for the measurement system is 3.8%, showing a strong potential of the proposed design for the measurement of an unknown mass. All experimental results have <1% difference between the minimum and maximum measured resonant frequency with an average of 0.44%.

This paper delivers the development of the most suitable geometry for highest sensitivity mass measurement and details the process to aid selection of the most appropriate tube geometry. The proposed application for the glass U-tube developed in this research is for the measurement of the mass concentration of particulate emissions from stationary sources. Whilst this research has detailed the geometry, system design, and evidence of the measurement concept, it is suggested that further research should be undertaken to develop this measurement technique to measure particulate emissions. It is suggested that this should include the integration of the measurement system with existing extractive techniques, address the issues associated with the harsh environment where equipment operates (including temperature regulation), and integrate the measurement technique with the measurement of gas volume to generate mass/volume concentration measurements (required for emission measurement reporting).