We use advanced experimental techniques to explore turbulence-induced deflagration-to-detonation transition (tDDT) in hydrogen–air mixtures. We analyze the full sequence of turbulent flame evolution from fast deflagration-to-detonation using simultaneous direct measurements of pressure, turbulence, and flame, shock, and flow velocities. We show that fast turbulent flames that accelerate and develop shocks are characterized by turbulent flame speeds that exceed the Chapman–Jouguet deflagration speed in agreement with the tDDT theory and direct numerical simulation (DNS) results. Velocity and pressure evolutions are provided to detail the governing mechanisms that drive turbulent flame acceleration. Turbulent flame speeds and fluctuations are examined to reveal flow field characteristics of the tDDT process. This work contributes to the understanding of fundamental mechanisms responsible for spontaneous initiation of detonations by fast turbulent flames.
Detonations occur as a unique form of pressure gain combustion (PGC) that augments flow momentum and produces significant rises in stagnation pressure.1 The process can result in increased specific impulse and higher thermodynamic efficiencies beneficial to enhancing the performance of current and future engine technologies.2–4 Alternatively, when uncontrolled, detonations can result in unprecedented destruction to industrial and transport facilities, cities, and coal mines.5 Additionally, detonations are theorized to occur during thermonuclear supernova explosions.6 The multifaceted potential of detonations affirms the importance of fundamentally understanding the formation and sustainability of detonations.
Detonations are driven by shock-induced reactions and can either be initiated directly by strong shocks or developed through the deflagration to detonation transition (DDT) mechanism. DDT is a complex process that usually involves three stages: (1) preconditioning stage that provides the turbulent conditions required for rapid flame acceleration and formation of strong shocks, (2) detonation initiation that usually occurs in a local pocket behind the leading shock, and (3) detonation survival when the detonation spreads into large areas of the unburned material.7–11 A detailed overview of the physical characteristics witnessed in these stages can be seen in Fig. 1. The first stage is dependent on initial turbulence and system geometry.12 The second stage is more universal and can involve a few known mechanisms but occurs on short time and length scales making observations difficult.13
There has been significant progress numerically in defining physical mechanisms that drive DDT in confined chemical systems.14–16 Experimental results, however, have focused on the preconditioning stage, exploring the conditions for flame acceleration leading to a detonation.17,18 While the detonation initiation process has been witnessed in experimental work, the experimental data often do not provide enough detail to deduce the mechanisms responsible for detonation formation.18 The current fundamental understanding of DDT is mostly based on theoretical models and numerical results.19–24
In particular, the gradient mechanism that allows detonations to arise from spontaneous reaction waves is often considered to be responsible for the second stage of DDT in confined systems.25 Numerical results show that temperature gradients required by this mechanism can form in hot spots that appear and ignite behind strong shocks produced by accelerating flames. Though the actual structure of such naturally produced hot spots and details of their ignition has not been previously resolved in experiments, the detonation development is consistent with the gradient mechanism observed in experiments, where reactivity gradients were artificially created using electrical discharges.26
Another mechanism of detonation formation, referred to as turbulence-induced DDT (tDDT), was discovered using direct numerical simulations (DNS).27 The numerically explored process occurs when the turbulent flame speed (ST) eventually reaches the Chapman–Jouguet (CJ) deflagration velocity (SCJ), where the flame begins to generate shocks that quickly amplify and accelerate the burning, which further amplifies the shocks. This runaway process eventually ignites a local detonation on the leading edge of a turbulent flame.27,28 Theoretical analysis showed that this process is universal and is consistent with the fact that CJ deflagration is the fastest possible steady-state burning regime without a shock. As ST exceeds SCJ, the burning can transition to a faster steady-state regime, which is known as a CJ detonation and can also be considered as a CJ deflagration coupled with a shock. This mechanism does not depend on chemistry or flame structure, does not require confinement, and is independent of turbulence.29 It can also be observed in idealized one-dimensional flames if the laminar flame speed is artificially increased above SCJ.30
Though the turbulence-induced DDT (tDDT) mechanism has a theoretical foundation supported by robust numerical results, it requires substantial experimental validation. Existing experimental observations of detonations arising from turbulent flames do not provide enough detail to understand exactly where and how the detonation forms. The objective of this experimental work is to fill the diagnostic gap by using multiple techniques to study the evolution of highly turbulent fast flames leading to the detonation onset with minimal confinement effects. This allows the exploration of the dynamics of fast turbulent flames in sufficient detail to validate and explore the tDDT mechanism.
The formation of the compressed reactants region ahead of the flame front during the fast deflagration stage is a key characteristic of the dynamics leading to the transition to detonation.28,31 Compression waves ahead of the flame have been experimentally captured but not yet completely understood in the context of detonation initiation.32 The conditions in this region depend on the initial reactant conditions, flame turbulence levels, and flame propagation velocity. Numerical simulations capture a pressure buildup at the flame front when the turbulent flame speed, ST, approaches SCJ.27 These conditions that are suggested to guarantee a tDDT occurrence have been partially analyzed in previous experimental studies.33,34 The work presented in this paper elaborates on previous DNS and experimental investigations into the governing physics of flame acceleration and the tDDT process.3,27,28,31,35 Objectively, this study aims to (1) validate theoretical relations and numerical simulations with experimental data to fill the diagnostic gap in understanding the global tDDT process, (2) explore a local hot spot as a detonation initiation mechanism in the tDDT process, and (3) investigate flame–turbulence interactions after the flame has exceeded the CJ deflagration speed to experimentally validate the runaway mechanism proposed by Poludnenko et al.29 The turbulent shock tube (TST) enables the detailed investigation of critical conditions required to initiate a detonation transition using controlled shock-driven turbulence. Advanced laser optical diagnostic techniques including high-speed simultaneous particle image velocimetry PIV and OH* coupled with pressure and temperature measurements are used to explore the reactant flow and investigate the flame runaway mechanism. The results show that once the turbulent flame speed, ST, surpasses the CJ deflagration velocity, SCJ, the runaway mechanism is initiated, and tDDT will occur.
A. Experimental facility
The experiment is conducted in a 1.5 m long semi-confined stainless-steel channel, known as the Turbulent Shock Tube (TST).3,29,33,34 As shown in Fig. 2, the facility was used to provide the conditions for a turbulent deflagration-to-detonation transition to occur. The TST has a 45 mm square cross section, referred to as the characteristic height (H), with three sets of 101 × 45 mm quartz windows with a thickness of 25.7 mm for optical access designed for advanced laser diagnostics. To initiate the mixture, a weak ignition source is placed on the center axis of the closed end. Following the initiator, a series of six perforated plates with a 58% blockage ratio make up a turbulence generator. In this configuration, the first perforated plate is 200 mm downstream of the closed end. The subsequent four plates are then spaced 50 mm apart over the next 200 mm. The final perforated plate is 750 mm downstream of the closed end or 350 mm after the fifth plate. The final plate is used to break up any boundary layer growth and ensure isotropic turbulence ahead of the flame front.
B. Flow control equipment
A timed control system was used to produce a homogenous mixture of hydrogen and air before ignition. To achieve the stoichiometric equivalence ratio (Φ = 1.03), air is introduced into the system at 28 ± 0.9 SCFH, while fuel flows in at 9 ± 0.4 SCFH. Air is directed through an SMC Pneumatics AW20-N02E-CZ pressure regulator and then flows into a Dwyer VFA-6-BV flowmeter. Compressed hydrogen gas is regulated and controlled using a Specialty Gases Southeast Inc. #HP-702-125-000-A regulator and a Dwyer VFA-3-BV flow meter. The premixed fuel–air mixture is fed through a MAC 226b-111BAAA solenoid valve into the closed end of the facility for the reactant fill stage. A BNC Model 575 Pulse/Delay Generator is used to trigger the valve and initiate the spark plug. The spark plug is powered through a 12-V power supply and ACCEL Supercoil 140001. The ignition system results in a 118 mJ spark energy at the beginning of each test.
C. Experimental procedure
To initiate the facility operation, fuel and air lines are opened and set to the desired flow rates based on the equivalence ratio of interest. The fuel and air flows merge 0.15 m downstream of the flow meters, and the reactants then mix while traveling through a 0.5 m tube with an inner diameter (ID) of 9.5 mm. The reactants then split into two 6.3 mm ID tubes and continue branching every 0.15 m until the flow has split into eight lines. A detailed overview of this process is shown in Fig. 3. The pre-mixed reactants then enter the facility through eight inlets perpendicular to the spark plug, with two inlets on each side of the square facility, to ensure an initially uniform flow distribution around the spark. The mixture fills through these inlets for 20 s, and a TTL signal then triggers the three-way solenoid valve to redirect the inflow of reactants to the exhaust after a 3 s wait time that allows the mixture to settle before a final flow control signal is sent to the coil and spark plug. The spark-ignited flame near the closed end propagates through a series of perforated plates, accelerates, and generates a shock wave that travels ahead of the flame. This shock passes through the last plate and enters the test section. A closely coupled flame follows and propagates through the first window. The shock–flame complex then enters the second window, transitions to a detonation, and continues as a sustained detonation wave in the third window.
Schlieren diagnostics are used to quantify the shock and flame velocity and to observe the universal characteristics of the phenomenon within the test section domain. A standard Schlieren Z formation is set up using two parabolic mirrors with focal lengths of 120 in. The schlieren is powered through a Newport Corporation 300 W Xenon Arc Lamp. A Photron Fastcam SAZ camera operating at 100 kHz records the evolution at a spatial resolution of 640 × 280 pixels with a 12-bit range. A Nikon lens with the focal length of 200 mm and aperture of f/2.8 is mounted on the camera resulting in an image resolution of 175 μm/pix and a pixel-based shock velocity uncertainty of 5.6 m/s. To investigate hotspot formation, schlieren imaging is repeated using a Hadland Shimadzu HPVX-2 camera. The images are collected at a rate of 5 MHz with a 50 ns exposure and 400 × 250-pixel resolution. A Nikon lens with a 500 mm focal length and a maximum aperture of f/5.6 is mounted on the Shimadzu camera, providing a resolution of 162.5 μm/pix. To capture the pressure profile, 12 PCB Model #113B24 dynamic pressure transducers are placed along the test section at intervals of 25 mm. The transducers with a sensitivity of 10 mV/psi are operated at a frequency of 500 kHz to resolve the entirety of the DDT evolution. A PCB signal conditioner 482C Series amplifies the signal for the NI DAQ and LabVIEW.
Simultaneous high-speed frame-straddled PIV and OH* chemiluminescence are set up to investigate the local flow field characteristics in the first window. An Nd: YAG Lee Laser LDP Dual Laser (532 nm, 25 mJ) is operated at 20 kHz. The 1 mm laser sheet is set at the center of the test section. Additional analysis has been conducted to show agreement of the flow velocities at varying planes in the test section.36 The premixed flow is seeded with 0.2 μm Al2O3 particles. The particle size has been selected to ensure a low Stokes' number and has been numerically validated to trace accurate flow measurements in high-speed reacting flows, such as detonations.37 A Photron Fastcam SAZ camera equipped with a Nikon 50 mm and f/1.2 is used for the 20 kHz PIV. The PIV resolution is 42 μm/pix (measurement scale is λm = 168 μm) with a field of view of 44 × 22 mm2. The imaging maintained a ratio of the particle image diameter dτ to pixel size dpix at approximately dτ/dpix ≈ 1.5. This results in a spatial resolution that is half the laminar flame thickness and measurement scale relative to the approximate Kolmogorov scale λm/λk ≈ 20–100. LaVision DaVis software is used for processing the PIV images with the two-step multi-pass method resulting in a 16 × 16-pixel interrogation and a 75% overlap for a peak velocity uncertainty of less than 3 m/s. The PIV case discussed in the results was repeated 31 times and showed consistent streamwise velocities within a range of ±68 m/s or less than 15% of the average flow velocity.
Simultaneous OH* signal is also acquired using a Photron Fastcam SAZ camera with a 50 mm f/1.2 Nikon lens and a 384 nm narrow bandpass filter. The camera operates at 40 kHz providing a spatial resolution of 156 μm/pix. An unprocessed OH* chemiluminescence and simultaneous OH* and PIV image are shown in Fig. 4. Figure 4(a) depicts an OH* chemiluminescence image of a lean hydrogen-air flame in an unseeded flow. Figure 4(b) also displays the OH* chemiluminescence image of a lean hydrogen-air flame; however, the flow in this image is seeded for PIV and is captured while the laser is firing at 20 kHz. This figure validates similarity in flame shape and structure along with consistent intensities emitted from the flame front and products when the flow is illuminated via a 1 mm laser sheet. Additionally, Fig. 4 confirms that the resulting flow remains unperturbed by the 20 nm seed particles.
For data processing, the schlieren is processed and discussed separately while examining similar cases to give qualitative insight. The schlieren imaging shown in the results was collected separately from the PIV and chemiluminescence but at the same test conditions. For PIV and OH* chemiluminescence, the diagnostics are synchronized during the experimental process through the timing box. During post processing, calibration images from each diagnostic are compared and correspondingly altered (straightened, translated, or expanded) to ensure accurate measurements.
III. RESULTS AND DISCUSSION
The results provide detailed schlieren imaging and direct flow field measurements for the turbulence-induced deflagration-to-detonation transition process. The presented work is a portion of an ongoing study to fully characterize the DDT process from various aspects.28,29,34 The experimental data and DNS simulations provide evidence of the spontaneous transition of subsonic flames to supersonic detonation waves.27,29 This transition occurs when a turbulent fast flame interacts with intense turbulence and undergoes a runaway acceleration leading to tDDT. The dynamic transition process is captured experimentally and compared to the DNS results. The wave speeds, pressures, and turbulence conditions are quantified.
A. Turbulence-induced deflagration-to-detonation transition
A series of schlieren images showing the flame evolution and tDDT in a stoichiometric hydrogen–air mixture are presented in Fig. 5. This is documenting experimental evidence of a full spontaneous transition from a fast deflagration to the onset of a detonation over 200 μs. The results show the intense flame–turbulence interactions that lead to a global transition. The process of turbulence-induced DDT begins when a preconditioned flame interacts with intense subsonic turbulence as shown in the first 60 μs of Fig. 5(a). The process continues in a feedback loop of pressure build-up and flame acceleration until a global transition to detonation is observed between 90 and 100 μs in Fig. 5(a). Finally, the initially overdriven detonation relaxes to a self-sustained detonation for the remaining 110 μs. The propagating self-sustained detonation confirms the completion of the DDT process.
During the time period shown in Fig. 5(a) between 90 and 100 μs, the flow field conditions become favorable for detonation onset to occur. The flame is propagating at or above the CJ deflagration speed (ST = SCJ) and has formed a highly compressed region between the closely coupled shock and flame. The transition to a detonation ultimately occurs as a result of hot spot formation in a highly compressed region immediately ahead of the flame. Figure 5(b) shows the production of compression waves emanating from the flame front providing qualitative evidence of a distinctly compressed area generated by the flame. Section III B will analyze the same mechanism quantitatively.
In this frame, the flame is separated from the leading shock by a small band of compressed gas with multiple shocks generated by the flame. Three microseconds later, a small disturbance occurs near the wall, at x = 7 mm. Corresponding chemiluminescence data show that this disturbance is auto-ignition at the wall. Less than a microsecond later (t0 + 3.8 μs), the new flame ignition kernel generates a visible shockwave and expands 2 mm in the vertical direction. By t0 + 7.2 μs, the expanding hotspot has formed a bulge at the leading shock and continues to expand spherically into the flow. At t0 + 12 μs, the burning hotspot has transitioned to a local detonation that continues propagating into the unburned gas. While the hotspot ignition for the case presented in Fig. 6 begins near the wall, this process is repeatable and has been witnessed at various locations in the turbulent shock tube (TST). However, the boundary layer near the wall often provides a preferable location for hotspot formation due to the increased friction and pressure gradients in this region. A further investigation of detonation initiation in experimental data will be detailed in future work.
Figure 6 provides experimental evidence of the hotspot formation presumed to occur in Fig. 5(a). The images in Fig. 5(a) detail an overview of the entirety of the deflagration-to- detonation transition process recorded at 100 kHz, whereas Fig. 6 identifies hotspot formation and evolution that becomes evident when recording in the megahertz range. At t0 in Fig. 6, a shock–flame complex enters the field of view.
The DNS results shown in Fig. 5(c) present a similar tDDT process.28,29 The computational domain with a 1.328 × 1.328 cm cross section contains the stoichiometric methane–air mixture with a laminar flame speed of 38 cm/s and an initial laminar flame thickness of 0.04 cm. The first sequence of images in Fig. 5(c) shows the transient process of a turbulent flame interacting with nominally isotropic turbulent reactants. The compressible flame then transitions to a detonation through the tDDT process, first revealed by Poludnenko et al.29 The evolution of the pressure field for this transition process is also shown in Fig. 5(c). The theoretical CJ detonation pressure for this mixture is 17.12 atm. The front begins to approach this value in the first three frames and largely exceeds the theoretical CJ pressure in the fourth image. During the initial transition phase, the detonation is overdriven and first experiences peak pressures up to 40 atm. The DNS results are consistent with experimental line-of-sight imaging and provide insight into the three-dimensionality of the turbulent flame front through the fuel mass fraction (left column). Additionally, the DNS reveals the pressure distribution across the reaction front, detailing several triple points, common features witnessed in unstable detonations. The pressure evolution in the DNS results is similar to the trends found in experimental data.
B. Quantification of tDDT process
The observed wave speed of the tDDT process is quantified. From the experimental measurements presented in Fig. 5(a), the shock propagation velocity and the distance between the shock and the flame are extracted and shown in Fig. 7 as functions of the distance x from the beginning of the first window scaled by the characteristic height of the facility (H = 45 mm). The flame front location is extracted from the mean axial location on the flame front brush. The values plotted in Fig. 7 correspond to the frames in Fig. 5(a). Since each test section is 2H long, the first five data points fall within the first optical window domain, followed by the next four measurement points from the second optical window, and finally, the last four are extracted from data in the third optical window.
The velocity in Fig. 7(a) is normalized by the theoretical CJ detonation velocity of 1965 m/s, DCJ. Initially, a shock–flame complex enters the interrogation window propagating with a velocity around 65% DCJ that remains constant through the first five points. The following two points, which correspond to the second window, mark the onset of DDT causing the front velocity to more than double in 1.5x/H distance. This value represents the overdriven detonation that relaxes over the following three points to a steady detonation propagating at DCJ.
The distance between the shock and the flame is shown in Fig. 7(b). The measurements extracted from the data in Fig. 5(a) track the leading shock and the flame front at the centerline. As the shock–flame complex enters the data collection region, the shock and flame remain equidistant for some period. As a hot bright region forms on the flame front, the shock accelerates, appearing to temporarily increase the distance between the shock and flame around 2x/H. The distance at x/H ≈ 2.5 correlates with the overdriven portion defined in Fig. 7(a).
The disparity between the overdriven shock speed and a significant (10 mm) shock-flame separation at the x/H 2.5 appears because the separation is still computed for the original flame. While the hotspot ignition is temporarily contributing to a shock propagating above UCJ, the original flame front still remains detached. This apparent disparity disappears when the shock and flame fully couple at x/H ≈ 3. Shortly after, the global mechanism of DDT is completed causing the flame to accelerate and further decrease the gap between the shock and flame. Finally, the shock and reaction merge and continue to propagate as a detonation for the remainder of the experimental length.
As we seek to quantify various components of a highly volatile process, it is imperative to ensure that repeatable evidence supports the observed values. Through gathering various datasets, results can be repeated and confirmed further supporting the full experimental evolution of DDT. In Fig. 8, multiple datasets at a stoichiometric equivalence ratio are explored. The pressure evolution shown in Fig. 8 is collected across a series of twelve pressure transducers 25 mm apart, starting at the beginning of the first window. The points shown in Fig. 8 correspond to the peak pressures recorded by each transducer. The figure shows that the pressure wave consistently enters the test section with a peak pressure below the theoretical CJ detonation pressure of 15.65 atm. Once the runaway process initiates, the peak pressure increases and consistently reaches the maximum between 2 and 4x/H. After the shock and flame couple, the pressure begins to settle to the theoretical CJ pressure validating that the detonation consistently enters a steady propagation mode. While there is variance present between the datasets, the overall process is the same. In this figure, case B represents the evolution explored in Figs. 5(a) and 7.
C. Flame-flow turbulence conditions
The turbulent flame and flow conditions resulting in this tDDT process are characterized through further measurements extracted from simultaneous advanced PIV and OH* chemiluminescence diagnostics. These measurements offered insight into the turbulent field behavior and characterized the turbulent nature of the flame that leads to tDDT. The results of these diagnostics are presented in Fig. 9. The image displayed in Fig. 9(a), depicts a horizontal velocity (u) flow field in m/s with a flame front trace extracted from OH*. The flame front values were determined using MATLAB Canny Edge detection feature after the images were binarized with a thresholding progress variable value and processed through a three-pixel disk-shaped morphological structuring element.
Figures 9(b) and 9(c) show the distribution of the turbulent flame speed and turbulent flow velocity using the probability density function (PDF). In Fig. 9(b), a PDF of the turbulent flame speed along the flame front is shown measured at 1.15x/H, immediately preceding the detonation onset location shown in Fig. 7(a). The ST value is computed by subtracting the average convective velocity ahead of the flame from the flame front velocity known via OH* measurements. The local flame front velocity is calculated from a forward time step for y/H between −0.25 and 0.25. By relationships defined by Poludnenko et al.,27 the runaway to DDT begins when the turbulent flame speed exceeds the CJ deflagration speed, SCJ = cs,p/α, where cs,p is the speed of sound in hot products and α is the ratio of densities of fuel and combustion products.28 For stochiometric hydrogen–air mixtures, the CJ deflagration speed in the compressed region ahead of the flame is calculated to be 292 m/s. In Fig. 9(b), the average turbulent flame speed is 502 m/s. Therefore, this validates that the ST = SCJ criterion has been surpassed, and the flame is experiencing a runaway acceleration and will complete the DDT process downstream.
Figure 10 also examines the turbulent flame speeds of the three different datasets, first explored in Fig. 8. The average ST values measured for these three flame fronts are 425, 500, and 675 m/s. These measurements were extracted from highly turbulent flame fronts between approximately 1.15 and 1.85x/H show that the criterion ST = SCJ for the runaway process is repeatedly exceeded. This provides repeatable evidence that the flame acceleration and DDT observed in our experiments agree with the tDDT theory.
This work presents the experimental evidence of the turbulence-induced deflagration-to-detonation transition process that includes direct measurements of pressure, flame, flow, and turbulent velocities through high-speed schlieren, and simultaneous OH* and PIV. The study validated the CJ deflagration runaway mechanism proposed by Poludnenko et al.,27 presented a detailed global and local detonation initiation process to suggest hot spot formation as the primary method of transition, and used flame–turbulence interactions to gain further insight into flow field conditions leading to tDDT. Additionally, the experiment revealed coupled shock speed and shock–flame separation measurements to provide details into the flow parameters witnessed when a shock and flame couple for detonation formation.
More specifically, the study implemented high-speed pressure and velocity measurements and schlieren to visualize the global event and reveal the full transition from a shock flame complex to a sustained detonation. Ultra-high-speed schlieren was then used to locally examine the shock–flame complex transition to a detonation over 12 μs. These images depicted an evident hot spot initiated on the flame brush in the highly compressed region. Previous work has theorized that his highly compressed region forms due to the runaway process causing strong compression between the shock and flame. The turbulence measurements were used to quantify the flame–turbulence interactions leading up to this regime. The turbulent flame speed measurements are presented to verify the runaway mechanism and contribute to the understanding of how deflagrations develop the conditions for detonation transition. The measurements provided offer detailed insight into a novel understanding of the fundamental governing mechanisms of flame acceleration. The study presented explored the process of turbulence-driven DDT in detail in an effort to reduce the gap between numerical and experimental data. The work validated theoretical relationships while contributing new experimental evidence of hot spot initiation in the turbulent deflagration-to-detonation transition process. Future work will seek to further explore and deduce the driving mechanisms of turbulent flame acceleration as it contributes to the DDT process.
The authors would like to acknowledge the sponsorship of this work by the Air Force Office of Scientific Research (Nos. FA9550-19-1-0322, and FA9550-21-1-0012 by Program Manager Dr. Chiping Li) and the National Science Foundations (NSF Award No. 1914453).
Conflict of Interest
The authors have no conflicts to disclose.
Rachel Hytovick: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Jessica Chambers: Data curation (equal); Investigation (equal). Hardeo M. Chin: Data curation (equal); Formal analysis (equal); Investigation (equal). Vadim Gamezo: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Alexei Y. Poludnenko: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal). Kareem Ahmed: Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal).
The data that support the findings of this study are available within the article and its supplementary material.