Study of Intra-Chamber Processes in Solid Rocket Motors by Fiber Optic Sensors

In this study, an experimental study of the burning rate of solid fuel in a model solid propellant rocket motor (SRM) E-5-0 was conducted using a non-invasive control method with fiber-optic sensors (FOSs). Three sensors based on the Mach–Zehnder interferometer (MZI), fixed on the SRM E-5-0, recorded the vibration signal during the entire cycle of solid fuel burning. The results showed that, when using MZI sensors, the non-invasive control of solid fuel burnout is made possible both by recording the time of arrival of the combustion front to the sensor and by analyzing the peaks on the spectrogram of the recorded FOS signal. The main mode of acoustic vibrations of the chamber of the model SRM is longitudinal, and it changes with time, depending on the chamber length. Longitudinal modes of the combustion chamber were detected by MZI only after the combustion front passed its fixing point, and the microphone was unable to register them at all. The results showed that the combustion rate was practically constant after the first second, which was confirmed by the graph of the pressure versus time at the nozzle exit.


Introduction
In modern engines and, particularly, in a solid propellant rocket motor (SRM), energy conversion processes are characterized by extreme temperatures and released power. For example, the thermodynamic temperature is around 3600 K in the combustion chamber of the Ariane-V launch vehicle's accelerator, EAP P241, which produces a thrust of 7.08 MN [1]. Under such conditions, the SRM operation parameters change frequently due to rates of the main intra-chamber processes-for example, fuel combustion. Therefore, we can describe the working process parameters in SRM as fast-flowing. They include vibrations, pressure in the combustion chamber, and acousto-optical and electrophysical characteristics [2,3].
There are various ways to monitor these parameters. Some methods include rather complex installations using, for example, X-ray analysis [4][5][6] for intra-chamber process control. This method allows for the observation of the fuel mass combustion patterns through the walls of the housing [7]. However, the sampling frequency is low, and the complexity of the setup makes this method inaccessible for common usage. There are also methods for the invasive monitoring of such processes, for example, by inserting thermocouples into test holes. This is simpler, but violates the integrity of the engine and probably changes the operation's parameters. Additionally, the connection wires require a lot of space, add mass to the setup, and can produce sparks. If we place thermocouples on the motor casing in a non-invasive way, the measurement obtained will be incorrect

Theory
Pressure, temperature, deformation, and vibration constitute the most important parameters of the working process in a model SRM chamber. Currently, only a limited number of FOSs are able detect these values [28,40,41]. The available data suggests the following requirement: an expected total measurement time of less than 10 seconds; typical oscillation frequencies of intra-chamber processes starting from tens of Hz, increasing to hundreds of kHz. In this case, optical time-domain reflectometry (OTDR) systems and devices based on FBG are insufficient due to the low sampling frequency of 30 kHz for phi-OTDR [42][43][44] and 10 kHz for FBG in configurations where there are a few sensors in one line [45][46][47]. In turn, the small SRM length and the requirement of less sensing points allows for the application of sensors based on the MZI. A phase-unwrapping technique was used for dynamic range improvement, based on the 3 × 3 output splitter providing phase-shifted signals.
A fiber MZI registers a phase difference between two arms, one of which is a reference and the other a sensing arm, as shown in Figure 1. No load is applied to the reference arm during the experiment. The sensing arm is fixed on the controlled object, and its length changes depending on the object's deformation. This leads to a signal intensity fluctuation, which is proportional to the cosine function of deformation. A 3 × 3 output splitter produces a 2π/3 phase shift between neighboring fibers. Thus, the recorded intensity on each photoreceiver can be determined by the following expression [48]: where I 1 , I 2 are the intensities from the reference and sensing arms, respectively; λ is the wavelength of laser radiation, m; ∆(t) is the optical path difference between the MZI arms, m and ϕ 0 is the initial phase difference, rad. A fiber MZI registers a phase difference between two arms, one of which is a reference and the other a sensing arm, as shown in Figure 1. No load is applied to the reference arm during the experiment. The sensing arm is fixed on the controlled object, and its length changes depending on the object's deformation. This leads to a signal intensity fluctuation, which is proportional to the cosine function of deformation. A 3 × 3 output splitter produces a 2π/3 phase shift between neighboring fibers. Thus, the recorded intensity on each photoreceiver can be determined by the following expression [48]: where I1, I2 are the intensities from the reference and sensing arms, respectively; λ is the wavelength of laser radiation, m; Δ(t) is the optical path difference between the MZI arms, m and φ0 is the initial phase difference, rad. The presence of two or more signals with a 2π/3 phase shift allows for the restoration of the phase φ of the deformation without uncertainty caused by a cosine function. We implemented a scheme with two photoreceivers for each MZI, reduced the number of photoreceivers, and simplified the measurement scheme. The deformation phase change Δϕ was obtained by the algorithm described in [49]. In this case, at each time t, it was calculated by the formula: where ( ) = ( ) − ( ), ( ) = ( ) + ( ).
The phase change depends on the deformation of the fiber, which was influenced by thermal, mechanical, and acoustic effects. In the experiment, the fiber was coiled in certain places on the outer surface of a model SRM, as shown in Figures 1 and 3. The total sensitive fiber length was Lsens = Nπd, where d = 19 mm is the initial outer diameter of the SRM housing and N = 10 is the number of turns. The SRM diameter increase, and phase change are linked through the fluctuations of the sensing arm length ΔLsens by the formula: where n is the effective refractive index of the fiber core, and consequently, The presence of two or more signals with a 2π/3 phase shift allows for the restoration of the phase ϕ of the deformation without uncertainty caused by a cosine function. We implemented a scheme with two photoreceivers for each MZI, reduced the number of photoreceivers, and simplified the measurement scheme. The deformation phase change ∆φ was obtained by the algorithm described in [49]. In this case, at each time t, it was calculated by the formula: where S 1 (t) = I PD1 (t) − I PD2 (t), S 2 (t) = I PD1 (t) + I PD2 (t).
The phase change depends on the deformation of the fiber, which was influenced by thermal, mechanical, and acoustic effects. In the experiment, the fiber was coiled in certain places on the outer surface of a model SRM, as shown in Figures 1 and 3. The total sensitive fiber length was L sens = Nπd, where d = 19 mm is the initial outer diameter of the SRM housing and N = 10 is the number of turns. The SRM diameter increase, and phase change are linked through the fluctuations of the sensing arm length ∆L sens by the formula: where n is the effective refractive index of the fiber core, and consequently, A frequency analysis of the phase change provides additional information about the combustion process. The SRM chamber's acoustic vibration modes depend on its size. The main types are the first longitudinal f lon , tangential f tan , and radial f rad , determined by the formula [50][51][52]: where a is the speed of sound, m/s, and l(t) is the combustion chamber length, m, at time t, s, as shown in Figure 2. Length l(t) varied from 8 to 109 mm during the experiments; d i = 15 mm is the chamber internal diameter. A frequency analysis of the phase change provides additional information about the combustion process. The SRM chamber's acoustic vibration modes depend on its size.
The main types are the first longitudinal flon, tangential ftan, and radial frad, determined by the formula [50][51][52]: where a is the speed of sound, m/s, and l(t) is the combustion chamber length, m, at time t, s, as shown in Figure 2. Length l(t) varied from 8 to 109 mm during the experiments; di = 15 mm is the chamber internal diameter. These frequencies contribute to phase change fluctuations and can be observed in the spectra. This observation method can precisely determine the chamber length.

Description of the Experimental Setup and Methods for Recording the Characteristics of Intra-Chamber Processes
In this study, a model SRM E-5-0 is the research object. It operates via a black powder [53], that was pressed into a cylindrical body made of cardboard. A graphite nozzle block was installed on the bottom with a critical section diameter of 3.4 mm. Fuel ignition was performed using a 0.5 g black powder sample via a combustible wire. The model SRM characteristics are shown in Table 1. Figure 3 shows the SRM photograph (a), a diagram with dimensions between the main components and the MZIs (b), and a section of the SRM after the study was conducted (c). The experimental setup included three MZIs; its scheme is shown in Figure 4. The MZI sensing arms were fixed equidistantly along the entire fuel length.  These frequencies contribute to phase change fluctuations and can be observed in the spectra. This observation method can precisely determine the chamber length.

Description of the Experimental Setup and Methods for Recording the Characteristics of Intra-Chamber Processes
In this study, a model SRM E-5-0 is the research object. It operates via a black powder [53], that was pressed into a cylindrical body made of cardboard. A graphite nozzle block was installed on the bottom with a critical section diameter of 3.4 mm. Fuel ignition was performed using a 0.5 g black powder sample via a combustible wire. The model SRM characteristics are shown in Table 1. Figure 3 shows the SRM photograph (a), a diagram with dimensions between the main components and the MZIs (b), and a section of the SRM after the study was conducted (c). The experimental setup included three MZIs; its scheme is shown in Figure 4. The MZI sensing arms were fixed equidistantly along the entire fuel length.   A narrow-band NKT BASIK MIKRO fiber laser with a central wavelength of 1550 nm and a bandwidth of less than 0.1 kHz was used. Its radiation emitted through a 3 × 3 splitter to three independent equal-arm MZIs. The supporting arms were at rest, and the sensing arms were coiled on the SRM housing (see Figure 1). The measuring arm of each  A narrow-band NKT BASIK MIKRO fiber laser with a central wavelength of 1550 nm and a bandwidth of less than 0.1 kHz was used. Its radiation emitted through a 3 × 3 splitter to three independent equal-arm MZIs. The supporting arms were at rest, and the sensing arms were coiled on the SRM housing (see Figure 1). The measuring arm of each A narrow-band NKT BASIK MIKRO fiber laser with a central wavelength of 1550 nm and a bandwidth of less than 0.1 kHz was used. Its radiation emitted through a 3 × 3 splitter to three independent equal-arm MZIs. The supporting arms were at rest, and the sensing arms were coiled on the SRM housing (see Figure 1). The measuring arm of each MZI consisted of L sens = Nπd = 10·π·19 mm ≈ 0.6 m of SMF-28. We glued this fiber loop-to-loop using one layer of double-sided tape. This method of construction increased the MZI sensitivity to fluctuations of housing diameter [54]. The SRM was fixed on the metal table by clamps. Such mounting proved adequate to complete the measurements; the motor shifted slightly at the start as a result of the highest pressure, and the sensing fiber remained connected to the housing at all times. The process was recorded, and is provided in the attached Video S1. Two fibers of each MZI 3 × 3 splitter outputs were transferred to photodiodes (PD). The signals were digitized on an ADC with a sampling rate of 2.5 MHz. This value determined the maximum detectable vibration frequency (1.25 MHz), according to the Nyquist theorem. An image of a laboratory setup with the measurement and registration systems is shown in Figure 5. Before the experiment, we checked the setup's integrity and its ability of deformation registration.
Sensors 2021, 21, x FOR PEER REVIEW MZI consisted of Lsens = Nπd = 10·π·19 mm ≈ 0.6 m of SMF-28. We glued thi loop-to-loop using one layer of double-sided tape. This method of construction inc the MZI sensitivity to fluctuations of housing diameter [54]. The SRM was fixed metal table by clamps. Such mounting proved adequate to complete the measure the motor shifted slightly at the start as a result of the highest pressure, and the s fiber remained connected to the housing at all times. The process was recorded, provided in the attached Video S1. Two fibers of each MZI 3 × 3 splitter output transferred to photodiodes (PD). The signals were digitized on an ADC with a sam rate of 2.5 MHz. This value determined the maximum detectable vibration freq (1.25 MHz), according to the Nyquist theorem. An image of a laboratory setup w measurement and registration systems is shown in Figure 5. Before the experime checked the setup's integrity and its ability of deformation registration.

Analysis of the Investigation Results
Images of the SRM stages are shown in Figure 6, including start-up (a,b), ope in nominal mode (c,d), and shutdown (e,f). It is worth noting that the tracks of th densed phase particles flowed out of the engine nozzle, which is common for the bustion products of powder and metal-containing fuels. The total operating tim about 5.5 s, during which the optical fiber did not undergo any damage or changes the effect of high-temperature combustion products.

Analysis of the Investigation Results
Images of the SRM stages are shown in Figure 6, including start-up (a,b), operation in nominal mode (c,d), and shutdown (e,f). It is worth noting that the tracks of the condensed phase particles flowed out of the engine nozzle, which is common for the combustion products of powder and metal-containing fuels. The total operating time was about 5.5 s, during which the optical fiber did not undergo any damage or changes due to the effect of high-temperature combustion products. MZI consisted of Lsens = Nπd = 10·π·19 mm ≈ 0.6 m of SMF-28. We glued this fiber loop-to-loop using one layer of double-sided tape. This method of construction increased the MZI sensitivity to fluctuations of housing diameter [54]. The SRM was fixed on the metal table by clamps. Such mounting proved adequate to complete the measurements; the motor shifted slightly at the start as a result of the highest pressure, and the sensing fiber remained connected to the housing at all times. The process was recorded, and is provided in the attached Video S1. Two fibers of each MZI 3 × 3 splitter outputs were transferred to photodiodes (PD). The signals were digitized on an ADC with a sampling rate of 2.5 MHz. This value determined the maximum detectable vibration frequency (1.25 MHz), according to the Nyquist theorem. An image of a laboratory setup with the measurement and registration systems is shown in Figure 5. Before the experiment, we checked the setup's integrity and its ability of deformation registration.

Analysis of the Investigation Results
Images of the SRM stages are shown in Figure 6, including start-up (a,b), operation in nominal mode (c,d), and shutdown (e,f). It is worth noting that the tracks of the condensed phase particles flowed out of the engine nozzle, which is common for the combustion products of powder and metal-containing fuels. The total operating time was about 5.5 s, during which the optical fiber did not undergo any damage or changes due to the effect of high-temperature combustion products. The recorded data from each MZI were processed in the time and frequency domains. The data ranges from 2 seconds before fuel ignition through the combustion process to around 2 seconds after its completion. Until the engine was turned on, the signal  The recorded data from each MZI were processed in the time and frequency domains. The data ranges from 2 seconds before fuel ignition through the combustion process to around 2 seconds after its completion. Until the engine was turned on, the signal at each PD changed with a small amplitude. The high-frequency component occurred due to the PD and the laser phase noise, and the low-frequency fluctuation was a result of the installation temperature drift and the laser wavelength drift. At launch, the amplitude increased in signal oscillations on all PDs. An example of the initial data from one channel of each MZI is presented in Figure 7-the oscillation amplitude increased on all interferometers from the moment the engine was launched, but it only reached the maximum contrast when the combustion surface of the solid fuel reached the MZI sensing arm on the SRM housing.
The recorded data from each MZI were processed in the time and freque mains. The data ranges from 2 seconds before fuel ignition through the combusti cess to around 2 seconds after its completion. Until the engine was turned on, th at each PD changed with a small amplitude. The high-frequency component o due to the PD and the laser phase noise, and the low-frequency fluctuation was a r the installation temperature drift and the laser wavelength drift. At launch, the tude increased in signal oscillations on all PDs. An example of the initial data fr channel of each MZI is presented in Figure 7-the oscillation amplitude increase interferometers from the moment the engine was launched, but it only reac maximum contrast when the combustion surface of the solid fuel reached the M ing arm on the SRM housing. For each sensor, the phase-unwrapping procedure was carried out accor Formula (2). An absolute value of the optical signal phase change, from the init (before the engine launch), was obtained and was found to be proportional to the of the fiber length on the model SRM according to Equation (3). The results highli the closer the MZI to the nozzle, the more changes it experienced. The plots housing diameter increase are presented in Figure 8. For each sensor, the phase-unwrapping procedure was carried out according to Formula (2). An absolute value of the optical signal phase change, from the initial state (before the engine launch), was obtained and was found to be proportional to the change of the fiber length on the model SRM according to Equation (3). The results highlight that the closer the MZI to the nozzle, the more changes it experienced. The plots for the housing diameter increase are presented in Figure 8. The derivatives of the housing diameter expansion graphs were calculated with a 60 ms window, allowing for the exclusion of high-frequency oscillations and their influence on the derivative stability. All of the sensors had a moment of initial expansion at the engine start, after which the diameter value became relatively stable, without a noticeable trend of expansion. Graphs illustrating the derivatives from each sensor are shown in Figure 9. A sharp increase in the derivative was observed when the combustion The derivatives of the housing diameter expansion graphs were calculated with a 60 ms window, allowing for the exclusion of high-frequency oscillations and their influence on the derivative stability. All of the sensors had a moment of initial expansion at the engine start, after which the diameter value became relatively stable, without a noticeable trend of expansion. Graphs illustrating the derivatives from each sensor are shown in Figure 9. A sharp increase in the derivative was observed when the combustion surface coordinate reached the sensor fixing point. These points are marked with circles in Figure 9. The derivatives of the housing diameter expansion graphs were calculated 60 ms window, allowing for the exclusion of high-frequency oscillations and thei ence on the derivative stability. All of the sensors had a moment of initial expan the engine start, after which the diameter value became relatively stable, withou ticeable trend of expansion. Graphs illustrating the derivatives from each sen shown in Figure 9. A sharp increase in the derivative was observed when the com surface coordinate reached the sensor fixing point. These points are marked with in Figure 9. The coordinates of the combustion-front propagation were determined by t of derivative sharp growth for the sensors, and are shown in Table 2. Based o values, we graphed the combustion surface movement, as presented in Figure 10.  The coordinates of the combustion-front propagation were determined by the time of derivative sharp growth for the sensors, and are shown in Table 2. Based on these values, we graphed the combustion surface movement, as presented in Figure 10.  The burning rate is non-linear in the first and smaller section of the graph due to the uneven combustion front, caused by the presence of a groove at the end of the solid fuel, as well as the combustion of the igniter sample, also made of black powder. After the end of the ignition period, the time dependence of the combustion surface movement was found to be close to linear with an average linear displacement velocity of 0.0193 m/s. This dependence (nonlinear during the ~1 second and then linear) is consistent with the results of a similar SRM test, showing that the pressure in the combustion chamber after around 1 second, following the engine start, became almost constant, as shown in Figure 11. The pressure in the combustion chamber during the experiment was measured using a special setup. The SRM was installed in a stainless steel external chamber with a pressure sensor. This setup was the only method by which to fix the pressure sensor to The burning rate is non-linear in the first and smaller section of the graph due to the uneven combustion front, caused by the presence of a groove at the end of the solid fuel, as well as the combustion of the igniter sample, also made of black powder. After the end of the ignition period, the time dependence of the combustion surface movement was found to be close to linear with an average linear displacement velocity of 0.0193 m/s. This dependence (nonlinear during the~1 second and then linear) is consistent with the results of a similar SRM test, showing that the pressure in the combustion chamber after around 1 second, following the engine start, became almost constant, as shown in Figure 11. The pressure in the combustion chamber during the experiment was measured using a special setup. The SRM was installed in a stainless steel external chamber with a pressure sensor. This setup was the only method by which to fix the pressure sensor to SRM. The described modification slightly increased the combustion time to 6.5 s. However, in general, the pressure change during the investigation remained unchanged for all SRMs of such a model. The fuel and housing construction provide a constant combustion surface area for when the fuel burns, therefore, a constant pressure in the chamber after~1 second after start becomes apparent even in the presence of deviations in the initial temperature, solid fuel composition, critical section diameter, etc.
The burning rate is non-linear in the first and smaller section of the graph due to the uneven combustion front, caused by the presence of a groove at the end of the solid fuel, as well as the combustion of the igniter sample, also made of black powder. After the end of the ignition period, the time dependence of the combustion surface movement was found to be close to linear with an average linear displacement velocity of 0.0193 m/s. This dependence (nonlinear during the ~1 second and then linear) is consistent with the results of a similar SRM test, showing that the pressure in the combustion chamber after around 1 second, following the engine start, became almost constant, as shown in Figure 11. The pressure in the combustion chamber during the experiment was measured using a special setup. The SRM was installed in a stainless steel external chamber with a pressure sensor. This setup was the only method by which to fix the pressure sensor to SRM. The described modification slightly increased the combustion time to 6.5 s. However, in general, the pressure change during the investigation remained unchanged for all SRMs of such a model. The fuel and housing construction provide a constant combustion surface area for when the fuel burns, therefore, a constant pressure in the chamber after ~1 second after start becomes apparent even in the presence of deviations in the initial temperature, solid fuel composition, critical section diameter, etc. Spectrograms of the unwrapped signal were calculated for each sensor to complete the frequency analysis. They are shown in Figure 12. Some peaks in the characteristic frequencies can be expected. The values of the first longitudinal f lon , tangential f tan, and radial f rad modes of chamber sound vibrations, according to Equation (4), are as follows:   f lon = from 45 kHz at SRM start to 3.30 kHz at finish f tan = 28.13 kHz f rad = 58.56 kHz A shifting peak, in the range from 3 to 20 kHz, and its harmonics are visible in the spectrograms, and have been caused by the changing longitudinal modes. They have a lower frequency in comparison to tangential and radial modes, so longitudinal modes were the most probable. It is possible to calculate the speed of sound, which is determined by the used fuel. Based on the boundary conditions-the minimum frequency of the longitudinal mode in Figure 12a is 3.3 kHz, and the length of the combustion chamber, which was 109 mm-the following results are found using Equation (4): The spectrograms in Figure 12 show that the peak of longitudinal oscillations only appeared in the interferometer signal when the burning front reached the MZI fixing point. We also analyzed the spectrogram of the audio signal, which was recorded by a microphone during the experiment, and is presented in Figure 13. This plot did not reveal any changing peaks during the burning process. This highlights the advantage provided by the FOS, which was able to detect vibrations that have been generated via sound longitudinal modes. Thus, the fiber MZI worked as a small, light, fire-safe, and easily installed sensor for SRM monitoring.
We plotted the graphs of the ideal longitudinal vibration modes with a known speed of sound and the length of the combustion chamber, calculated according to Equation (4). They are shown in Figure 12b,d,f and are in good agreement with the experimental data. The length changes of the combustion chamber account for two aspects. The first is a meniscus of the burning front, among other factors, caused by a deepening in the solid fuel, as shown in Figure 2. The second is a partial burnout of the plug with the nozzle, from 9 to 5 mm in the center, as shown in Figure 2b. It should be noted that the frequencies of the peaks on the MZI1 and MZI2 spectrograms coincide during their occurrence.
The graphs obtained allow us to conclude that the rate of fuel burnout in the model SRM was almost constant, since the burning front reached the coordinate of the MZI1 after 1 s following initiation.
veal any changing peaks during the burning process. This highlights the advantage provided by the FOS, which was able to detect vibrations that have been generated via sound longitudinal modes. Thus, the fiber MZI worked as a small, light, fire-safe, and easily installed sensor for SRM monitoring.
We plotted the graphs of the ideal longitudinal vibration modes with a known speed of sound and the length of the combustion chamber, calculated according to Equation (4). They are shown in Figure 12b,d,f and are in good agreement with the experimental data. The length changes of the combustion chamber account for two aspects. The first is a meniscus of the burning front, among other factors, caused by a deepening in the solid fuel, as shown in Figure 2. The second is a partial burnout of the plug with the nozzle, from 9 to 5 mm in the center, as shown in Figure 2b. It should be noted that the frequencies of the peaks on the MZI1 and MZI2 spectrograms coincide during their occurrence.  (e) (f)  The graphs obtained allow us to conclude that the rate of fuel burnout in the model SRM was almost constant, since the burning front reached the coordinate of the MZI1 after 1 s following initiation.

Discussion
A non-invasive diagnostic technique using fiber-optic MZIs as sensors has been developed. This technique makes it possible to determine the characteristics of intra-chamber processes-particularly the burning rate of solid fuel and the length of the combustion chamber-at a given time. The calculations aim to determine when the burning front passes through the MZI fixation points. For each MZI, this can be determined by the derivative growth. Additionally, the resonance frequencies of the acoustic vibration longitudinal modes in the combustion chamber can be determined via the shifting peaks in the spectrogram. As a result, the calculation of the combustion chamber length and the burning rate of solid fuel during the overall SRM worktime can be performed.
For the tested SRM, an uneven combustion of the fuel was detected during the first phase of the work due to deepening occurring at the point at which combustion begins.

Discussion
A non-invasive diagnostic technique using fiber-optic MZIs as sensors has been developed. This technique makes it possible to determine the characteristics of intra-chamber processes-particularly the burning rate of solid fuel and the length of the combustion chamber-at a given time. The calculations aim to determine when the burning front passes through the MZI fixation points. For each MZI, this can be determined by the derivative growth. Additionally, the resonance frequencies of the acoustic vibration longitudinal modes in the combustion chamber can be determined via the shifting peaks in the spectrogram. As a result, the calculation of the combustion chamber length and the burning rate of solid fuel during the overall SRM worktime can be performed.
For the tested SRM, an uneven combustion of the fuel was detected during the first phase of the work due to deepening occurring at the point at which combustion begins. Then, the burnout rate became almost constant; for our experimental conditions, the burnout rate was approximately 0.0193 m/s.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.