Design and Implementation of a Cylindrical Microwave Sensor to Measure the Water Content of Brake Fluid

The braking system is one of the most vital components of a vehicle, as it directly ensures the safety of both drivers and passengers. Brake fluid plays a crucial role in this system by acting as a medium that converts the force exerted on the brake pedal into the force necessary to activate the wheel braking mechanisms. However, over time, brake fluid deteriorates due to water absorption, leading to a reduced braking effect and an increased risk of system failure [1].

Modern braking systems rely on brake fluid as a fundamental hydraulic medium to transfer force from the brake pedal to the braking mechanism. However, brake fluid is highly hygroscopic, meaning it absorbs moisture from the environment. This moisture uptake significantly lowers the boiling point of the fluid, increasing the risk of vapor lock formation and accelerating the corrosion of system components. Consequently, the performance of the braking system deteriorates, reducing its reliability, particularly during emergency braking or high-temperature conditions, which compromises overall vehicle safety [2].

Several factors contribute to brake fluid degradation, including weather conditions, fluctuations in temperature and speed, and the use of incorrect hydraulic brake fluid. At high temperatures, a higher water content in the brake fluid lowers its boiling point, which, while preventing vapor bubble formation in the brake system, also indicates the level of water contamination in the fluid. Maintaining an optimal boiling point is crucial for minimizing the risk of brake failure due to overheating. Additionally, the lifespan of brake fluid serves as a key indicator for monitoring fluid condition and determining when replacement is necessary [3, 4].

Given the importance of maintaining brake fluid quality, developing an effective, economical, and reliable method for measuring its water content has become essential. Traditionally, this has required either frequent inspections or expensive sensors, which placed a financial burden on vehicle owners [5, 6].

Recently, microwave technology seems to have become a valid way to determine the amount of water contained in brake fluid Microwaves are very sensitive to changes in the electrical properties of liquids due to the presence of an aqueous phase, so this application is well suited for this technique [7, 8]. The purpose of this research is to develop and apply a cylindrical microwave sensor that is very sensitive to water content in the measurement of brake fluids. As such, the device aims to provide a means of creating water content in a given brake fluid at a relatively low cost in an easy-to-use form to promote safer cars and therefore safer roads. Thus, providing a way to continuously and accurately measure humidity levels of this instrument can significantly reduce the likelihood of costly repairs due to internal corrosion breakage from high humidity volume.

Yang et al. [9] have previously proposed a new approach using microwave resonance cavity sensor and demonstrated accuracies within 0.01 of water content ratios of 30% to 100% (optimal at 50%), and flow rates of 3 and 7 m³/h. We propose a model of the boundaries related to the new boundary field factor of electromagnetic interference compensated with considerable output enhancement.

In a second work, Abdul Sattar introduced a fractal geometry-based microwave sensor which detects the changes of radio wave reflection from crude oil samples used S parameters for high-accuracy measurement of water concentration. This method offers an efficient means of keeping track of the quality of crude oil [10]. Andria et al. [11] developed a microwave sensor for in situ and real-time fuel quality monitoring considering water contamination. It is a compact, low-cost sensor that can be operated continuously during engine operation. Teng et al. [12] recent years, a microwave sensor application was proposed, which was relatively non-invasive to measure the water hardness in the heat exchangers with a 2.5 GHz cavity resonator, the application takes microwave technology on the side of industrial equip maintenance. These studies show that the electrical property of liquids, which includes electrical permittivity and conductivity, affects the nature of the liquid and the nature of the components. These insulating constants vary with different liquids, and therefore microwave techniques can be used to distinguish them correctly [13, 14].

Water measurement in brake fluid demands strict monitoring but the available conventional techniques have major performance restrictions. The current measurement methods involving phase separation as well as chemical analyses prove insufficient for real-time practical applications because they use invasive methods or take too long or are not precise enough for practical use. Studies conducted during the recent period reveal positive findings about microwave sensory technology within this field. Multiple current prototypes face difficulties during implementation because of their complex setup procedures and high construction expenses and their inability to achieve precision standards [15].

The current research work develops a new cylindrical microwave sensor system to enhance water fluid dynamics monitoring precision. The proposed sensor performs real-time fluid characteristic observation through resonance frequency changes while monitoring the S-parameter in a non-invasive horizontal assessment routine at minimal operational cost [16]. The advanced design method delivers precise and trustworthy performance along with superior accuracy through non-destroying testing frameworks. Rapid fluid quality examinations that ultimately maintain vehicular security and operational reliability are achieved by the findings of this research during urgent braking situations.

Analyzing the findings of the literature of previous studies, the research’s significance is boiled down to two pillars. The first point is a breakthrough in constructing a simple, non-invasive procedure for detecting water content in brake fluid to improve vehicle safety and the brake system. Secondly, it addresses actual issue of vehicle operation bringing down repair costs and increased brake system reliability. The current study also seeks to present a new cylindrical microwave sensor that has high operational efficiency and ease-of-use. It possesses a copper resonant cavity along the horizon flowing direction, and has better estimation than the other technologies. This study also provides a novel view on the applicability of microwave sensors in the 3-4 GHz range. The HFSS simulation program supported the experimental outcome to make this research more authoritative, and it was possible to carry out further experiment in other fields of study.

After preparing the sample and selecting the dimensions based on previous studies, the experimental setup was designed with a cylindrical cavity based on the diameters of the tubes under study. The diameters (4) cm were chosen for horizontal flow testing in the Ministry of Science and Technology / Department of Industrial Research and Development laboratory.

The sample preparation consists of a horizontal cylindrical cavity made of brass containing variable diameters according to the tube diameter used in the study. It also includes a pump to pump the mixture (Water and PEG) that controls the Water mechanism through a valve, as shown in Figure 3. Sample tubes are utilised to introduce substances into the cavity for examination. The cavity sensor apparatus is linked to an Agilent network analyser functioning within the 3-4 GHz range. The analyser device is linked to Port 1 (P1) and Port 2 (P2) by precision cables and appropriate adapters.

The microwave operates by reflecting electromagnetic waves perfectly through a polished copper cylinder. It measures the water content in a liquid mixture with different proportions of water by passing waves through a transparent acrylic tube. The idea lies in how to change the resonant frequencies according to the electrical properties of the materials. The cylindrical vacuum resonant body was designed from a copper alloy, and a lathe machine was used to carve the vacuum resonant body and also to produce the vacuum. Likewise, the cover's hole comes in different diameters, which align with the diameter of the tubing used for the flow as Figure 4.

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Figure 3. (a) The experimental rig (b) Schematic diagram of the experimental

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Figure 4. Fabricated cylindrical cavity resonator

For the part, the cylinder is drilled from the top with a 4 cm hole to pass an acrylic rod, and from the side, it is drilled with a diameter of 10 cm on two opposite sides for mounting a Waveguide adapter with a dipole antenna as Figure 5.

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Figure 5. Hole in fabricated cylindrical cavity resonator (a) Side view and (b) Top view

This experiment utilises three acrylic pipes of varying diameters (4cm) and a length of 50 cm. These pipes are interconnected through a manifold area for Water and PEG for different (mixture) supplies, and the opposite end empties into the mixing tank.

The complete tool setup for performance an illustration of the tests is shown in Figure 3. The tests were conducted using the VNA tool at the Ministry of Science and Technology / Department of Industrial Research and Development laboratory. The data was then shown on the VNA and the screen, as seen in Figure 6. The hollow can be filled with several substances, including Water, PEG, and a combination of Water and PEG.

The brake fluid (PEG) system with water yielded phase ratio readings at Mix.1, Mix.2, Mix.3, pure water and PEG, for illustrated in Table 1 utilising a benign and non-intrusive microwave cavity-based sensor that scans the entire sample. It was contingent upon the S22 measurements that estimate the extent to which microwave radiation infiltrates the combination.

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Figure 6. Show data in VNA and screen

Table 1. Composition and types of water-PEG mixtures

SNR: Signal–to–Noise Ratio.

Return Loss, Impedance, Admittance: R+jX, G+jB

specific description of the incident power wave at any given port is:

$a=\frac{1}{2} \frac{\left(V+Z_0 I\right)}{\sqrt{\left|R\left\{Z_0\right\}\right|}}$       (3)

The wave of reflected power throughout any port can be characterized as:

$b=\frac{1}{2} \frac{\left(V+Z_0^* I\right)}{\sqrt{\left|R\left\{Z_0\right\}\right|}}$      (4)

The S-parameter matrix specifies the powers of the reflected and incident waves.

$b=\mathrm{S} a$               (5)

The elements of S are a $N \times N$ matrix.

Efficient power networks: Electrical power dissipation within the network does not lead to any reduction or loss [24].

$\mathrm{S}_{22}=\frac{{ Reflected }}{{ Incident }}=\left.\frac{b_2}{a_2}\right|_{a_{1=0}}$      (6)

A comprehensive flow diagram of power waves is presented. The load matches the characteristic impedance of the testing system. The variables of network analysis and signal processing are also incorporated.

$S_{22}$: Represents the reflection ratio of the reflected signal at $Z=0$.

$a$: Symbolizes the reflected signal from the incident signal at $Z=0$.

$b$: Represents the transmitted signal from the reflected signal at $Z=0$.

7.1 Characteristics of S-parameter

Reasons for developing S-parameters:

They are easily obtainable at high frequencies.

A vector network analyzer (VNA) can measure voltage-traveling waves.

Bypass or short connections are crucial, as failure may lead to device oscillation and potential self-destruction.

These measurements include gain, loss, reflection coefficients, and other parameters.

S-parameters from cascaded devices facilitate system performance evaluation.

S-parameter measurement files can be easily shared and integrated into the HFSS simulation package.

7.2 The relationship between S-parameters and the permittivity of a mixture

This study concentrates on the reflected S-parameters. Our investigations revealed that the resonant frequencies are distinctly pronounced and highly responsive to alterations within the 3-4 GHz region for the reflected S22 parameters. The gathered experimental data quantifies both the reflected and transmitted characteristics. The permittivity of the mixture can be inferred from the reflected S-parameter, S22, as determined in reference [25].

$S_{22}=\frac{\left(\frac{1}{R}-R\right)\left(e^{\gamma d}-e^{-\gamma d}\right)}{D}$         (7)

The ratio of characteristic impedance with and without the test material is shown as R. The diameter of the material sample being tested is denoted by d, D represents the denominator quantity, and γ signifies the propagation constant.

Where $\gamma$ and $R$ can be found depending on frequency and cut-off frequency as follows,

$R=\sqrt{\frac{1-\left(\frac{f_c}{f}\right)^2}{\varepsilon_{M R}^{\prime}-I \varepsilon_{M R}^{\prime}-\left(\frac{f_c}{f}\right)^2}}$            (8)

$\gamma=i \frac{\omega}{c} \sqrt{\varepsilon_{m r}^{\prime}-i \varepsilon_{m r}^{\prime \prime}-\left(\frac{f_c}{f}\right)^2}$        (9)

where, $f_c, \omega, \varepsilon_{m r}^{\prime}, \varepsilon_{m r}^{\prime \prime}$, i and c represent the cut-off frequency, angular frequency, real, imaginary parts of mixture relative permittivity, $\sqrt{-1}$ and light speed $\left(3 \times 10^8 \mathrm{~ms}^{-1}\right)$ respectively.

7.3 Mixture permittivity

The determination of water-PEG (brake fluid) permittivity remains essential for microwave sensing applications together with dielectric analysis requirements. Multiple mathematical models serve to determine effective permittivity measurements of these mixture types. The models have different applicable scenarios with distinct assumptions about their behavior. The following section provides an analysis of available models together with justification for choosing the optimal model for water-PEG systems for Table 2.

Table 2. Comparison of mathematical models for mixture permittivity calculation

The mixture's relative permittivity of water-PEG is determined using several mathematical formulae. A well-known approximation is the power law [26].

$\varepsilon_{\mathrm{r}, \mathrm{eff}}^\beta=\mathrm{f}_1 \varepsilon_{\mathrm{r}, \mathrm{w}}^\beta+\mathrm{f}_2 \varepsilon_{\mathrm{r}, \mathrm{EPG}}^\beta+\left(1-\mathrm{f}_1-\mathrm{f}_2\right) \varepsilon_{\mathrm{r}, \mathrm{g}}^\beta$       (10)

where, $\varepsilon_{\mathrm{reff}}$ represents the relative effective permittivity of the mixture. $\varepsilon_{\mathrm{r}, \mathrm{w}}, \varepsilon_{\mathrm{r}, \mathrm{EPG}} \& \varepsilon_{\mathrm{r}, \mathrm{g}}$ represent the relative permittivity of water, EPG, and gas, respectively. $\mathrm{f}_1$ represents the volume fraction of water, $f_2$ represents the volume fraction of PEG (brake fluid), and β is the power parameter, if applicable.

When $\beta=\frac{1}{3}$, the following equation will provide the Looyenga formula.

7.4 Looyenga model

The Looyenga usage in studying water-PEG mixtures is advantageous because the model incorporates nonlinear water-PEG molecule interactions that exist in homogeneous liquid-liquid systems.

$\begin{gathered}\varepsilon_{r, e f f}=\varepsilon_{r, w}+ {\left[3 f_2 \varepsilon_{r, w}^{\frac{2}{3}}\left(\varepsilon_{r, E P G}^{\frac{1}{3}}-\varepsilon_{r, w}^{\frac{1}{3}}\right)+3 f_2^{\frac{2}{2}} \varepsilon_{r, w}^{\frac{2}{3}}\left(\varepsilon_{r, E P G}^{\frac{1}{3}}-\varepsilon_{r, w}^{\frac{1}{3}}\right)^2\right]} \\ +\left[3 f_3 \varepsilon_{r, w}^{\frac{2}{3}}\left(\varepsilon_{r, a}^{\frac{1}{3}}-\varepsilon_{r, w}^{\frac{1}{3}}\right)++3 f_3^2 \varepsilon_{r, w}^{\frac{2}{3}}\left(\varepsilon_{r, a}^{\frac{1}{3}}-\varepsilon_{r, w}^{\frac{1}{3}}\right)^2\right.\end{gathered}$        (11)

To obtain a more diverse method for determining the effective refractive index of a mixture, please consult references [27].

7.5 Analysis of water permittivity

Relative permittivity is a mathematical notion consisting of two components: the real part, termed the dielectric constant, and the imaginary part, designated as the dielectric loss. It regulates the reflection of electromagnetic waves at any interface and the attenuation of wave energy within materials [28]. To ascertain the relative permittivity of a composite material, it is essential to know the permittivity of its constituent constituents. The permittivity of water is delineated.

$\varepsilon_{r, w}=\varepsilon_r^{\prime}-i \varepsilon_r^{\prime \prime}$    (12)

The dielectric constant, which is the real component, is defined as the stored energy originating from an electric field.

$\varepsilon_{\mathrm{r}}^{\prime}=\frac{\varepsilon_{\mathrm{s}}-\varepsilon_{\infty}}{1+\omega^2 \tau^2}+\varepsilon_{\infty}$       (13)

where, $\varepsilon_s$ and $\varepsilon_{\infty}$ denote static and infinite permittivity’s, respectively, while $\omega$ and $\tau$ signify angular frequency ($2 \pi f$)  in radians per second and relaxation time in seconds, respectively.

Brief explanation of the need to involve the subject in the further discussion of the measurement of the water content in the brake fluid with the help of a microwave device. The investigation of properties of various fluids is deem necessary in many an aspect of engineering and sciences. In this case, a cylindrical microwave device was employed for the assessment of the water content in the brake fluid with a 4 cm diameter of acrylic tube inserted passing through it. Varying experiments were carried out using a solution of water with the proportions of 30%, 50%, and 70% and the goal of identifying the changes of the properties of the examined fluid.

Consequently, this work can be considered as making a further contribution to understanding the variations in material properties of the fluid, particularly where concentration of water is a major factor, along with thermal conductivity and viscosity of the fluid, which are deemed significant in the context of numerous applications in industry. From the results obtained from the experiments, it is possible to determine the impacts of water concentration on the fluid properties to design systems that enhance the proper-ties of the fluid. Our subsequent analysis will focus on the results produced by the experiments and discus the concentrations of water and their effects on the efficacy of density and viscosity measuring for fluids with similar physical characteristics.

9.1 Results extracted from VNA measurements: Determining water content in peg (brake fluid)

This study conducted VNA measurements to ascertain the water content of brake fluid (PEG). This investigation was conducted within a frequency range of 3 to 4 GHz, utilizing the S22 parameter to assess the reflection characteristics of the fluid. The study's conclusions indicated alterations in the observed signal level that signify fluctuations in water concentration within the fluid. The fluctuations are crucial for characterizing the dielectric constant of PEG, as its water content determines its electromagnetic response. Understanding the correlation between signal response and water content in the samples, we developed a method to quantify moisture concentration in stop fluids by the analysis of S22 data. This method enhances moisture detection accuracy and is beneficial in various fluid-based industrial processes where such information is crucial (refer to Figures 14-18).

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Figure 14. Results extracted from VNA measurements pure water

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Figure 15. Results extracted from VNA measurements Mix.1

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Figure 16. Results extracted from VNA measurements Mix.2

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Figure 17. Results extracted from VNA measurements Mix.2

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Figure 18. Results extracted from VNA measurements PEG

9.2 Simulation of electromagnetic properties of S22 parameter using HFSS: A study on PEG effects

S-parameter measurements, particularly S22, play a crucial role in evaluating system performance at high frequencies. This study investigates the behavior of S22 within the 3 GHz to 4 GHz frequency range, considering mixtures of water stoppers at 30%, 50%, and 70%, as well as pure water solvent and pure stopping fluid. The simulations were conducted using HFSS, a software well-suited for analyzing the electromagnetic properties of materials under various conditions.

The study of effect of water addition in the brake fluid (PEG) inside 4 cm diameter tube was a main topic for both electrical engineering and materials science. Experimental results reveal that the permittivity and conductivity of the resultant mixture changes considerably when introducing water, leading to significant alterations in reflection coefficients for frequencies between 3–4 GHz Such changes can be attributed to the intricate water and PEG interactions referred as a plasticizing agent, since it increases the ability of absorbing energy from mixture due to high carbon dioxide generation recently reported by the study [34]. But it is worth noting that increasing the water content in the brake fluid can slow down its effects of by degrading brake efficiency on systems used for various applications.

Characterization of properties but its physical property is changing when the water was adding, it can be seen in Figures 14-22. This behaviour is identified as one in which the reflection coefficient increases with water content, accompanied by a higher energy loss, the influence of permittivity is illustrated at different frequencies through which we can judge how it would become difficult to convey energy on account of water increasing its volume. The figures conductance versus water content shows the changing behaviour in response to hot components within a mixture.

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Figure 19. Results of S-parameter (S22) study in the HFSS simulation for PEG flow with pure water

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Figure 20. Results of S-parameter (S22) study in the HFSS simulation for PEG flow with 70% water

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Figure 21. Results of S-parameter (S22) study in the HFSS simulation for PEG flow with 50% water

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Figure 22. Results of S-parameter (S22) study in the HFSS simulation for PEG flow with 30% water

The net results of this analysis suggest that for water, the level of absorption is higher in comparison to others components (in a mixture), since energy reflected from port 2 has more losses. The ratio of moisture between the constituents is directly proportional to an increased auditory frequency loss coefficient enhancing water effectivity on overall performances. This highlights the need-to-know physical dynamics of individual particles to help design electronic systems [35]. Here it is extremely important to tweak up the water content if needed and be sure about balancing between having an effective brake fluid and inefficient [35].

This can help in understanding how the water as well as PEG affect the system for example by determining resonance ratios of a mixture components via information’s about their permittivity and conductivity. We use these results to identify the moisture amount in stopping fluid, thus assisting with offline endeavors like fabrication engineering and electronic system design.

9.3 Comparison between experimental and theoretical results for the reflection coefficient of water (4 cm)

The Curve Comparison with respect to the various calculated and experimental results of different frequencies from 3 GHz to 4 GHZ for water reflection coefficient. From the previous commentary, it is easily discernable that negative reflection coefficient values mean water absorbs electromagnetic energy but not in a reflecting manner. For example, it can be seen in the figures that at −26.10 and −27.94 dB there are critical points on a chart, these represent highlights how the variation of chemical elements transformation leads to changes its behavior as well through reflection coefficients significantly reduced.

In this case, it is possible to trust the program that was used for calculations which then showed their coincidence of experimental and theoretical results in determining percentage amount of water on the stopping fluid. This reliance is due to the precision of it leading all results converge and hence by using this program, we can confidently rely on its output for determining the water content in other mixtures. Hence, application of such computational tools can play a significant role for better understanding the material interactions with EM waves and their applications in different fields as shown Figure 23.

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Figure 23. Comparison between experimental and theoretical results for the reflection coefficient of water (4 cm)

9.4 Analysing the reflection coefficient of mixtures theoretically at frequencies ranging from 3 to 4 (GHz)

The reflection coefficient for various combinations of water and different concentrations of PEG has been theoretically calculated within the 3–4 GHz frequency range, as shown in Figure 24. In the chart, the x-axis represents frequency (GHz), while the y-axis represents the reflection coefficient (dB). The color-coded lines indicate different materials: red for water, green for Mix.1, blue for Mix.2, purple for Mix.3, and black for PEG.

The negative reflection coefficient values are primarily due to energy absorption rather than reflection, significantly influencing the electrical properties of the materials. This effect is particularly evident in the reflectivity curve. Notably, the graph and system frequency response do not align as expected, mainly because material reflection coefficients vary significantly across different frequencies and chemical compositions, affecting their overall behavior.

This analysis is crucial for the design of electronic systems, as it helps evaluate the response of materials to electromagnetic waves. Key factors such as reflection properties, electrical conductivity, and specific energy absorption rates for each mixture can be assessed, allowing for the determination of optimal water content proportions in the development of advanced components.

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Figure 24. Analysis of reflection coefficient for a series of mixtures at 3 to 4 GHz