This work characterizes the compressibility dynamics in turbulent fast flames for a range of turbulent flame speeds. These turbulent fast flames experience increased effects of compressibility through the formation of strong shocks and may develop a runaway acceleration combined with a pressure buildup that leads to turbulence induced deflagration-to-detonation transition (tDDT). Simultaneous high-speed particle image velocimetry, OH* chemiluminescence, schlieren, and pressure measurements are used to examine the reacting flow field and flame dynamics. We examine flames with turbulent flame speeds ranging from 100 to 600 m/s. At lower turbulent flame speeds, the flame is not able to produce favorable background conditions for deflagration-to-detonation transition (DDT) onset, and thus flame compressibility and turbulence amplification are less dominant, resulting in a weaker acoustic coupling between the flame and compressed region. As the turbulent burning velocities exceed the Chapman–Jouguet deflagration speed, favorable background conditions are produced, as we observe flame-generated shocks and flame-generated turbulence with higher turbulent velocities and larger turbulent scales. At this regime, the flame is categorized to be at the runaway transition regime that leads to tDDT.
Detonations are highly energetic modes of combustion that exhibit desired qualities, such as higher thermodynamic efficiencies, rapid heat release, and increased stagnation pressures.1 Detonations can be achieved through direct initiation or the deflagration-to-detonation transition (DDT), where a deflagration that propagates with velocities on the order of 0.1–10 m/s is accelerated to form a detonation propagating at ∼2000 m/s.2–4 The DDT process is highly stochastic and can occur through several mechanisms, such as the Zeldovich reactivity-gradient mechanism, where hot spots are created by Mach stem reflections, localized explosions, shock reflections, turbulent boundary layers, or turbulence.5–9 Thus, the timescale, location, and mechanism responsible for DDT cannot be generalized and depend on the specific experimental conditions. Many computational and experimental studies have been dedicated to understanding the physics and flow conditions responsible for DDT.
Early studies by Oppenheim and several collaborators observed flame acceleration and DDT in long smooth channels for hydrogen–oxygen mixtures.6,10–12 They observed a laminar flame, which accelerated, became turbulent, and ultimately resulted in DDT. They described the detonation onset as an explosion in an explosion, which starts out as a local event and spherically propagates into a shock-compressed medium. Several computational and theoretical analyses have also shown that DDT can successfully occur for a laminar flame without turbulence.8,13–16 Furthermore, Shelkin found that the presence of obstacles along the channel walls resulted in faster flame acceleration and significantly reduces the run-up distance required for DDT.17 These turbulence generating obstacles resulted in several hydrodynamic instabilities, such as Kelvin–Helmholtz, Rayleigh–Taylor (RT), and Richtmyer–Meshkov (RM), that can be driven by shear forces, flame–shock interactions, shock–shock interactions, and flame surface corrugations.18,19 As a propagating flame interacts with obstacles, these instabilities develop, the flame morphology changes, resulting in an increased flame surface area. It is well known that this process increases the effective turbulent burning velocity (ST) of the flame, generating pressure waves, which coalesce into a leading shock.1,4 This essentially results in a flame acceleration process driven by turbulence.
DDT is typically observed in confined systems where various sources of turbulence may arise due to shock–flame interactions in obstructed channels, boundary layers in channels without obstacles,20–22 and turbulent jets. DDT in tubes without obstacles has been observed to exhibit three stages in both computational and experimental studies: (1) Flame accelerates exponentially during a short time producing a shock far downstream of the flame, (2) the flame produces compression waves that steepen to a pseudo-shock directly adjacent to the flame front, (3) detonation onset or the actual transition.13,23,24 In this work, we are isolating the effect of turbulence on DDT. We generate a controlled turbulence using perforated plates and try to minimize boundary layer effects. Turbulent flame acceleration results in the formation of a compressed region, which is a typical process for turbulence-driven DDT (tDDT). Critical characteristics, such as the expansion factor that is the density ratio of reactants to products (α = ρr/ρp), CJ number (sometimes referred to as the flame Mach number) Mf = ST/SCJ, and the turbulent Mach number, MT = u′/cs,f, drive the formation of the compressed region. A similar region denoted as a preheat zone has been observed in previous experiments conducted by Kuznetsov et al. and simulations by Liberman et al., where their turbulence originated from boundary layers.20,22,24 Note that the preheat region they observed is not the same as a preheat zone of a laminar flamelet. They show that the preheat zone produces a temperature gradient, which may result in DDT depending on the width and temperature of the preheat zone.
An important parameter that influences DDT is the CJ deflagration speed. These next studies mentioned involve the term CJ deflagration speed. However, the way we define CJ deflagration speed vs what is mentioned in the subsequent discussion is different. The following authors define their CJ deflagration speed as the propagation speed where the flame is thermally choked, in the order of Cs,p. We define it as SCJ = cs,p/α (sometimes called CJ number), which is the maximum possible speed for a steady-state deflagration without shocks. The flame can be a CJ deflagration if ST ∼ SCJ, but is not known until ST is measured. From qualitative observations, one could say that a flame is a super-CJ deflagration because it generates shocks which propagate forward and support the leading shock, and, according to the tDDT theory, this indicates ST ∼ SCJ. Saif et al. experimentally investigated CJ deflagration speeds by decoupling a detonation into a shock-flame complex through a row of cylinders.26 They found that the necessary condition for DDT is the establishment of a quasi-steady flame propagating at the sound speed of the products.25 A computational study by Liu et al. also examined a CJ deflagration created by decoupling a CJ detonation wave, and they report similar findings for the CJ deflagration speed.27 Valiev et al. investigated the flame acceleration process with a large range of flame Mach numbers changing by three orders of magnitude.28 They show that the flame acceleration process undergoes three distinct stages: (1) an initial exponential acceleration in the quasi-isobaric regime; (2) linear increase in the flame velocity to supersonic speed with constant acceleration; and (3) saturation to high-speed deflagration velocity. However, these studies do not consider the coupling of turbulence and compressibility in the evolution from a slow deflagration to a shock-inducing fast deflagration.
Several numerical studies by Poludnenko et al. have highlighted the significance of intrinsically unstable turbulent fast flames.29–31 Turbulence was used instead of solid obstacles as the flame acceleration mechanism. For these high-speed flames, the interactions between flames, turbulence, and acoustics, including intermittent flame collisions, provide the favorable background conditions for flames to produce shocks and runaway toward DDT. It has been previously shown that non-reacting32 and reacting compressible turbulence tends to display an inverse energy cascade, where pressure pulsations generated by the flame tend to form stronger ones. The pressure pulsations within the turbulent flame brush also couple with the density gradient across the flame, which results in vorticity generation through baroclinicity.31 Baroclinicity drives the turbulence amplification process, known as flame-generated turbulence. Sosa et al. examined this flame-generated turbulence phenomena for a standing fast flame in a turbulent shock tube facility.33 For lower flame Mach numbers (Mf < 0.35), the turbulent Mach number remained nominally constant, but as Mf increased (0.35–0.45), there was a non-linear increase in turbulence. They showed that as the ST approaches SCJ, turbulence amplification occurs across the flame, i.e., flame-generated turbulence. As a result, flame-generated turbulence can lead to a self-continuous loop of a turbulent flame producing turbulence and also interacting with that newly generated turbulence, resulting in the unbounded growth of the turbulent flame speed and transition to a detonation. Poludnenko used the relationship of ST > SCJ as a necessary condition for tDDT.
In this paper, we further analyze the relationship between the turbulent flame speed (ST) and CJ deflagration speed (SCJ) defined by Eqs. (1) and (2) using high-speed optical diagnostics in a turbulent shock tube facility. We will (1) further validate and classify the turbulence-compressibility characteristics associated with fast flames that lead to detonation onset in a highly turbulent environment, (2) quantify local turbulent flame speeds, and (3) investigate the flow field conditions of flame modes related to the SCJ criteria, from fast deflagrations to shock-flame complexes. High-speed Schlieren, particle image velocimetry (PIV), chemiluminescence, and pressure measurements are used to characterize the spatiotemporal evolution.
II. EXPERIMENT AND DIAGNOSTICS
A. Experimental facility
Figure 1 shows the schematic of a specifically tuned turbulent shock tube (TST) facility used to explore flame regimes from slow deflagrations to detonations.33–36 The TST facility is guided by the DNS simulations from,29,37 which specifically target the conditions for fast propagating turbulent flames, tDDT, and detonations. The facility is open at one end, has a square cross section of 45 × 45 mm2, and includes a 145 mm long test section with full optical access for imaging and laser diagnostics. In this work, we use six perforated plates placed in series with the last perforated plate located in between the flanges just before the test section. This geometric configuration was the result of extensive experimental testing to achieve the desired flame-turbulence conditions.33–39 The six-plate configuration allows us to examine the largest range of flame regimes, from slow deflagrations to tDDT. A spark plug is mounted at the center axis of the channel at the closed end. The optical window is approximately 125 × 45 mm2, and the windows are 25 mm thick designed to sustain detonation pressures and temperatures. An open end is used to prevent the shocks from reflecting off the end wall and inducing detonations. This allows us to observe the flame evolution as it interacts with the turbulence generated by a moving normal shock.
B. Flow control and procedure
A timed control system was used to produce a nominally homogenous mixture of hydrogen and air before ignition. Premixed hydrogen and air are issued into the facility at low flow rates and atmospheric pressure to mitigate flow perturbations in the channel. The fuel and air mixture are controlled to attain the desired equivalence ratio Φ in the range of 0.79–1.1 ± 0.007. Air pressure is controlled using a 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 pressure regulator and a Dwyer VFA-3-BV flow meter. The desired span of equivalence ratios is achieved using flow rates in the range of 0.0162–0.0173 ± 0.000 52kg/s (28–30 ± 0.9 SCFH) for air and 0.000 46–0.000 52 ± 0.000 017 kg/s (2.85–3.25 ± 0.104 SCFH) for hydrogen. The hydrogen flow rate is corrected for use on an air calibrated flowmeter (CFHH2·0.26 = SCFHH2). The hydrogen and air lines merge to premix in one line, which is fed to the closed end of the facility. A BNC Model 575 Pulse/Delay Generator was used to trigger the valve and initiate the spark plug.
The facility operation begins by opening the hydrogen and air lines and setting the appropriate flow rates for the equivalence ratio of interest. After the flow rates are set, the facility is filled with the premixed mixture and seed through the feed line to the facility for 20 s. A TTL signal triggers the three-way solenoid valve to halt the channel filling process and exhaust the mixture after it fires. The mixture in the chamber settles for 2 s, and a 21 ms pulse width signal is sent to the supercoil. At the point of ignition, signals are sent to begin the acquisition procedure for cameras, lasers, and pressure transducers. The flame kernel expands to fill the cross-sectional area, and a flame front develops to propagate toward the open end of the channel. A series of six consecutive perforated plates having holes with 6.35 mm in diameter and 58% open area are positioned inside the facility close the spark plug to promote rapid flame acceleration. This generates a leading shock wave ahead of the flame, which then passes through a final perforated plate just before the test section. At this stage, a shock wave ranging from Mach 2 to 3, depending on the flow rate, interacts with this final perforated plate transmitting the leading shock into the test section and forming choked unreacted turbulent jets that produce high levels of isotropic turbulence behind this shock.33,40 The flame enters the test section through the perforated plate later forming burning turbulent jets that quickly coalesce into a fast, turbulent flame behind the leading shock. The turbulence intensity is controlled by the equivalence ratio of the initial mixture, which affects the flame acceleration in the turbulence generator section. Faster initial flame acceleration increases shock velocity and results in higher turbulence levels. The shock and flame behavior immediately after the last perforated plate are observed using the optical test section.
The diagnostics setup is shown in Fig. 1(b) and has been previously documented in Refs. 33, 34, 37, and 41. Schlieren was used to observe the general characteristics of the regime of interest within the test section domain. A standard folded Z formation is set up using two 150 mm diameter parabolic mirrors with focal lengths of 1.52 m. Photron Fastcam SA-Z cameras with 1024 × 1024-pixel focal plane arrays and a 12-bit range depth were used for all the schlieren, chemiluminescence, and PIV measurements. The schlieren camera was equipped with a 200 mm and f/2.8 Nikon lens resulting in a pixel resolution of 157 μm/px. This corresponds to a pixel-based velocity uncertainty of 8 m/s. The camera was operated with a 640 × 280-pixel field of view (FOV), which is the entire test section window, frame rate of 100 kHz, and 0.248 μs exposure.
High-speed PIV is used to acquire quantitative flow field information for the analysis of the turbulent flow field. An Nd:YAG Lee 300MQG Dual 532 nm Laser with a maximum power of 25 mJ is operated at 20 kHz. The laser beam travels through a 1000 mm focusing lens and −25.4 mm cylindrical lens to create a laser sheet that is under 1 mm thick verified using laser burn paper, which is a dominant challenge for general 2D planar measurements. The sheet forming optics is set to project the laser sheet in the center of the test section. The main flow is seeded with 0.2 μm aluminum oxide particles using a seeder designed with three levels of filtration for uniform seed density. The particle size has been chosen to ensure that it has minimal impact on the flow.42 Based on the range of flow conditions, the maximum Stokes number is ∼0.093. The particle imaging maintained a ratio of the particle image diameter dτ to pixel size dpix at approximately dτ/dpix ≈ 1.5. The pulse separation of 2 μs is targeted to resolve the mean convective velocity of the shock and post-shock reactants.42,43 The Photron Fastcam SAZ camera mounted with a 532 nm bandpass filter, Nikon 50 mm, and f/1.2 lens is used with a frame straddling method to achieve 20 kHz PIV. The PIV spatial resolution in the horizontal and vertical directions is 42 μm/px (measurement scale is based on 4-pixel overlap, λm = 168 μm, and 16-pixel scale results in λm= 672 μm) with a field of view of 44 × 22 mm2. This results in a spatial resolution that is half the laminar flame thickness (320 μm) and the ratio of the measurement scale to the approximate Kolmogorov scale λm/λk ∼ 20–100. The Kolmogorov scale estimates are based on the Peters correlation.44–46 The image sensor used for the flow imaging and diagnostics is a CMOS sensor with a sensitivity peak of ∼680 nm. The relative spectral response is 87% of peak value at 600 nm and 70% of peak value at 532 nm. The viewing test section is optically accessible on three walls, which are recessed and fitted with fused silica quartz glass. The glass allows for transmission over 250 − 700 nm at 95% transmittance required for the laser diagnostics. Theoretical light transmittance in the percentage, σ, of the optical system is calculated using σλ = 100 × ηglass × sλ, where ηglass is the relative amount of light transmitted by the optical component, and sλ is the image sensor relative sensitivity at a given wavelength. This results in 82.65 ± 4.1% transmittance at 600 nm and 66.5 ± 3.4% transmittance at 532 nm. The uncertainty was calculated using the manufacturer's reported uncertainty and the propagation of error approach. DaVis software is used for processing the PIV images with 30-step multi-pass method ending with a 16 × 16-pixel interrogation and a 75% overlap resulting in a peak velocity uncertainty that is less than 5 m/s (±0.026 ST/SCJ) using DaVis uncertainty quantification.
Simultaneous OH* radical is measured to capture the instantaneous images of the reaction front. The PIV and OH* cameras are set up opposing to each other from both sides of the test section, while the schlieren measurements were acquired separately. The flame profile is outlined and superimposed onto the PIV images to identify exact spatial flame and flow conditions. The chemiluminescence camera is equipped with a 50 mm f/1.2 Nikon lens and a 310 ± 5 nm filter (Edmund Optics, 34–980), producing a 156 μm/px spatial resolution with a 3 m/s pixel-based velocity uncertainty. The FOV spans the entire optical access window, 135 × 45 mm, with a frame rate of 40 kHz.
Pressure transducers are lined along the test section to capture pressure peaks, resolve shock strength, and velocity and acquire the pressure profiles for the turbulent flame regimes. Four PCB Model #113B26 transducers are positioned with intervals of 25 mm in the axial direction at the top plate of the test section, as shown in Fig. 1. The transducers have a sensitivity of 10 mV/psi and are operated at a frequency of 250 kHz to temporally resolve shock pressure rise and compressions. When considering the non-linearity and sensitivity variation, static pressure values result in an uncertainty of ±0.17 atm (±0.01 P/PCJ). The transducers are connected to a PCB signal conditioner 482C Series to amplify the voltage signals and then are routed to a National Instruments DAQ device coupled with LabVIEW control hardware and software. The pressure measurements are conducted simultaneously with high-speed particle image velocimetry (PIV) and OH* measurements.
D. Turbulent flow field calculations
The turbulent flow field information can be combined with the flame compressibility characteristics in order to understand the relationship between the turbulent burning velocity and turbulent velocity. Using Eq. (5), we can extract the local turbulent flame speed along the flame edge. Since there are 128 streamwise components in the PIV output grid, the resulting calculation will yield 128 ST values.42 An example of this procedure is shown in Fig. 2, where ST,0,1 and Ug,1 are the flame propagation speed and compressed region gas velocity in the first streamwise row, respectively.
III. RESULTS AND DISCUSSION
A. Flame propagation dynamics
In the exploration of fast turbulent compressible flames, we examine the relationship between the turbulent flame speed (ST) and Chapman–Jouguet deflagration speed (SCJ). This relationship can be characterized by observing four key flame regimes: shockless fast deflagrations, shock-inducing fast deflagrations (fast flames), shock-flame complexes, and detonations. These regimes have been illustrated and described in detail in previous papers;53 here, we briefly describe them for convenience. We typically differentiate these regimes based on the flame front propagation velocity in the laboratory reference frame (ST,0). The critical boundaries between these regimes, shown in Fig. 3, are the sonic velocity of the reactant mixture (cs,r), sonic velocity of the products (cs,p), and CJ detonation velocity (DCJ). These boundaries are driven by empirical correlations and are easily obtainable through experiments. The empirical boundaries are approximate and are not necessarily the only way to define these turbulent fast flame regimes. These parameters have been computed based on the initial quiescent state of the mixture at 1 atm and 297 K.
Figures 3(a) and 3(b) show a shockless deflagration and shock-inducing deflagration, respectively. The terms “shockless” and “shock-inducing” are not related to the leading shock transmitted through the perforated plate, but the ability of turbulent flames to generate new shocks. This secondary shock adjacent to the flame is denoted as the compressed region. The shock strength depends on the ratio of ST/SCJ. The flame produces weak shocks as its propagation speed passes cs,r, while ST/SCJ remains < 1. As the flame propagation speed nears cs,p (ST/SCJ ∼ 1), the secondary shocks strengthen and form the compressed region. When the flame reaches the product sonic velocity, the flow of products becomes choked resulting in a tight acoustic coupling of the flame and the compressed region. The compressed region becomes stronger as the flame accelerates, where ST,0 approaches cs,p, and ST nears SCJ.48,53 The compressed region that is tightly coupled with the flame catches up with the leading shock and merges as shown in Fig. 3(c). In this shock-flame complex regime, the shock and flame are coupled, propagating on the order of 1/2DCJ (upper detonation CJ speed), which is similar in magnitude to the combustion products sonic speed; this regime is caused by a sonic plane in the products, thus choking the flow. The shock-flame complex continues to accelerate, eventually transitioning to a detonation. The resulting detonation shown in Fig. 3(d) propagates with a velocity close to DCJ and is characterized by the presence of strong transverse waves, cellular structure, and a complete coupling between the shock and reaction front.
Figure 4(a) shows the ST vs SCJ scatter, classifying 3key regimes that are examined throughout this paper: (1) ST < SCJ, (2) ST ≈ SCJ, and (3) ST > SCJ. The data points in Fig. 4(a) are the same ones discussed in Fig. 3; however, the boundaries in Fig. 4(a) are differentiated based on the tDDT theory. These new theoretical boundaries are based on ST and SCJ, which are difficult to measure. In this work, we focus on ST and its relationship with SCJ in different turbulent fast flame regimes; thus, we focus more on Fig. 4(a) classification of regimes rather than Fig. 3. In Fig. 4(b), we show five pressure profiles as ST increases past SCJ; the pressure traces are shifted to the same location of the leading shock. For all cases except the SFC, two pressure peaks are evident, indicating the leading shock and compressed region. The ST < SCJ cases are typically shockless deflagrations (SD) with compressed region pressures on the order of, or less than the leading shock pressure. The SD and SID leading shocks typically propagate ∼Mach 2; thus, their leading shock pressures are similar in magnitude. As ST approaches SCJ, a shock-inducing fast flame forms, compressed region begins to form, and compressed region pressure will begin to exceed the leading shock pressure. The location of the flame brush shifts to right, indicating that the flame brush is catching up to the leading shock (flame acceleration). Once ST > SCJ, the shock-inducing fast flame will continually accelerate to form a shock-flame complex as shown at the higher ST cases in Fig. 3(c). The shock-flame complex pressure profile (in red) only shows one peak (∼17 atm) because the compressed region and leading shock have merged. The spread of the turbulent flame speed is also noticeably increased, ST ranges from 480 to 620 m/s. We have also previously shown that the flame brush generates pressure gain due to ST > SCJ, resulting in stronger flame-driven compression and overall stagnation pressure gain.53
B. Characterization of reacting turbulent flow field
We now examine the general flow field behavior at the flame brush location (upstream of the leading shock) for the three conditions: (1) ST < SCJ, (2) ST ≈ SCJ, and (3) ST > SCJ. Figure 5 shows instantaneous OH*, flow velocity, and vorticity fields overlaid with the flame edge for the three conditions.
These three cases serve as a representation of the velocities and vorticity magnitudes for each of the regimes. In general, as ST increases to SCJ and eventually surpasses it, the flow velocity in the compressed region ahead of the flame increases. The flame is thermally choked in this regime with the leading shock propagating on the order of 3.5–4. In this regime, there are cases where close coupling between the leading shock and compressed region occurs. The moving leading shock in addition to the compressed region both contribute to these large reactant velocities. Similarly, the vorticity magnitudes also increase with the formation of more vortices. Within this compressed region, the horizontal flow velocity and vorticity reach peak values of ∼700 m/s and ±50 000 s−1 for ST > SCJ, respectively. This prominent vorticity generation in the compressed region ahead of flame front indicates a stage where the fast flame is simultaneously producing compression waves and turbulence as it evolves closer to tDDT. Vorticity generation in the flame can be attributed to the dilatational and baroclinic terms from the vorticity transport equation. Since the density and pressure gradients are substantially large between the compressed region and flame, they contribute toward these vorticity generation terms. Higher vorticity levels and flow velocities are also observed within the flame products.
To illustrate the local characteristics of these turbulent flames at various levels of compressibility, probably density functions of the velocity fluctuations and vorticity are examined at various locations of interest in our flow field. Figure 6 shows a probability density function of u′ and v′ between the leading shock and compressed region. Since the u′ and v′ distributions are similar, we can denote this flow field as nominally isotropic. Figure 7 shows histograms and probability density functions (PDF) for the turbulent velocity and vorticity for both reactants and products in the compressed region for the same three cases and flow fields shown in Fig. 5. The top row [Figs. 7(a)–7(c)] compares the horizontal and vertical turbulent velocities, and bottom row [Figs. 7(d)–7(f)] compares vorticity between the compressed region reactants and products. As described in Sec. II B, a leading shock transmitted through the last perforated plate produces isotropic turbulence for the flame to interact with. For ST < SCJ, flame compressibility effects are low and nominally isotropic turbulence within the flame brush is observed [Fig. 7(a)]. There is no noticeable increase in vorticity from reactants to products shown in Fig. 7(d). The PDFs in Figs. 7(a) and 7(d) are typical distributions for a shockless deflagration. When ST ≈ SCJ, flame compressibility becomes more prominent and the vorticity distribution in the products begin to broaden [Fig. 7(e)], which indicates an increase in turbulence production as the material moves from the compressed region to the flame brush. Here, flame compressibility is the source, which generates further deviation from isotropic turbulence. This behavior continues as u′ and ω-product distributions become even more broader as ST surpasses SCJ. This behavior clearly shows flame generated turbulence as the flame accelerates from the shockless deflagration to the shock-inducing deflagration regime. Similar behavior has been shown in simulations of high-speed flames by Poludnenko.30 In those simulations, net production rates of the y- and z-components of vorticity inside the flame brush are significantly larger than turbulence upstream of the flame, which amplifies the velocity component transverse to ωy and ωz, i.e., the x-direction. Thus, there is amplification in all three directional components, but it is more dominant in the x-direction than the y- and z-direction.
For further illustration, the probability density functions of axial velocity fluctuation between the reactants and products for ST < SCJ, ST ≈ SCJ, and ST > SCJ are shown in Fig. 8. It was previously shown that turbulence behind the leading shock is nominally isotropic (Fig. 6). The axial velocity fluctuations undergo a slight increase in products for ST < SCJ [Fig. 8(a)]. As the global turbulent flame speed reaches the CJ deflagration regime (ST ≈ SCJ), the compressed region begins to form and there is moderate amplification of u′ through the products. This behavior continues to occur as the flame enters the super-CJ-flame regime [Fig. 8(c)]. The turbulence inside the flame brush also starts to become slightly anisotropic [Fig. 7(b)]. Based on previous simulations,30,37,55 in the super-CJ-flame regime, ST decouples from the turbulence behind the leading shock, which can no longer supply unreacted mixture sufficiently fast to sustain a high burning rate. This behavior is further illustrated by Poludnenko et al.30 for a flame interacting with highly subsonic, isotropic turbulence where the transverse velocity fluctuations undergo moderate amplification, while the axial velocity fluctuations experience significant anisotropic amplification.
It is important to note that the turbulence amplification experienced during flame acceleration is not an abrupt but a gradual change. This will certainly cause some overlap between cases where the global turbulent flame speed is transitioning from ≪ SCJ to ST/SCJ ∼1.
Several cases are now examined for each of the three global turbulent flame speed regimes. For reference, Table I shows the corresponding average (or global) turbulent flame speed, compressed region max pressure, and equivalence ratio for each of the cases discussed herein. For consistency, the color spectrum shown in Fig. 9 is used throughout the discussion for distinguishing the regimes: blue: ST < SCJ, green ST ≈ SCJ, and red: ST > SCJ. Figure 9 shows PDFs for several cases corresponding to Table I. We observe a significant shift in average turbulent flame speeds as Φ increases from 0.84 to 1.03. This behavior is due to our facility tuning and ability to produce shockless deflagrations or shock-flame complexes through control of the equivalence ratio.48 Depending on the case, the PDF shape may have a distinct peak or a broadened distribution due to the flame front structure and gas velocity distribution in the reactants. A flatter flame front will likely result in a PDF with a distinct peak as seen in Fig. 9 for cases 1, 8, 12, and 14. Flame fronts, which are highly biased [like Fig. 5(a)], will result in wider distributions. For example, case 6 has a local minimum and maximum ST at 75 and 600 m/s, respectively. However, the average ST ≈ 312 m/s that is on the order of SCJ for that particular case (SCJ,6 = 294.5 m/s). This behavior is similar for case 10, but here, ST > SCJ.
|Case .||ST,avg (m/s) .||SCJ (m/s) .||Pcomp (atm) .||Φ .|
|Case .||ST,avg (m/s) .||SCJ (m/s) .||Pcomp (atm) .||Φ .|
Cases 1–3 have the lowest ST (< SCJ) and are typically associated with shockless deflagrations as shown in Fig. 3(a). This is supported by the lower compressed region pressures, which range from 3 to 5 atm depending on the level of flame compressibility. Cases 4–8 have ST values on the order of, or greater than SCJ, and are typically shock-inducing fast deflagrations [Figs. 3(b) and 4(a)]. These flames propagate with velocities on the order of combustion products speed of sound and continuously accelerate until thermally choked. A thermally choked flame (where ST > SCJ) will continually produce strong pressure waves that reinforces the compressed region and strengthens it. This causes a larger difference between the leading shock pressure and compressed region pressure, resulting in a transition away from constant pressure combustion.53 Cases 9–14 are much greater than SCJ, and their flow field structure is typically stronger shock-inducing fast deflagrations or shock-flame complexes. These cases generate the highest pressures since the compressed region and leading shock are either neighboring each other or merged.
To further demonstrate the effect of increasing ST, we plot the turbulent flame speed as a function of normalized turbulence intensities in Fig. 10. Each of the points in the scatter is the respective value at each streamline along the flame edge (128 points per case). They are shown in a transparent color to highlight the local minimum and maximum values. The lines are length scale boundaries defined by Peters.44,45 In general, at higher turbulence intensities, we observe larger turbulent burning velocities. The cases where ST < SCJ, fall closer to length scale boundaries L11/lf = 10, where L11 is the integral length scale. These flames are beginning to experience moderate turbulence-compressibility effects as they are impacted by both large- and small-scale turbulence coupled with pressure waves generated by the flame. The large-scale turbulence interacts with the flame front, creating wrinkling and corrugations as seen in the OH* imaging in Fig. 5. These corrugations increase the flame surface area, which increases the effective burning rate and turbulent burning velocity. As the turbulent burning velocity increases to the order of SCJ, the turbulence intensities show local maxima of ∼170. The shock-flame complex cases (12–14) exhibit the highest turbulent burning velocities. This behavior is supported from previous studies showing that high turbulent burning velocities are a result of larger length scales and turbulent Reynolds numbers.45,56 Shock-inducing fast flames and shock-flame complexes are dominated by compressibility effects since ST > SCJ. The leading shock and compressed region both increase the density of the unburnt reactants, followed by a large decrease in density in the products. Thus, the flow field immediately ahead of the flame is influenced by compression rather than gas expansion due to these shocks generated when ST exceeds SCJ.
C. Characterization of compressible turbulence
At faster flame front propagation velocities (ST,0), we observe higher turbulent burning velocities (ST) and turbulence intensities. Flame acceleration causes the turbulent burning velocity to approach SCJ and flame propagation velocity to approach the combustion products speed of sound. Hence, we can quantify the compressibility dynamics using the instantaneous turbulent velocity scaled by the compressed region speed of sound (MT = u′/cs,f) and turbulent flame speed scaled by the CJ deflagration speed (CJ number = ST/SCJ). As shown in Fig. 11, the speed of sound is computed at the compressed region pressure and temperature conditions. We scale ST by SCJ on the bottom x axis and by cs,f on the top x axis to compare these two characteristic velocities in defining compressibility of the turbulent fast flame. We observe that for CJ number < 1, the turbulent Mach number has less scatter, with maxima reaching MT ∼0.32. It has been shown previously that in compressible turbulent flow fields, there is continual exchange of energy between the longitudinal and transverse turbulence components.32,40,57 At these lower turbulent Mach numbers, the nonlinear interactions between these two components are small,32 which likely supports the behavior of less scatter MT values for CJ number < 1.
When the CJ number > 1 (Mf > 0.49), there is a nonlinear increase in turbulent Mach numbers with local peaks reaching MT ∼0.56. From previous studies, this indicates that the interactions between the longitudinal and transverse turbulence components increase in this regime.32,57 In this regime, the turbulent Mach number shows more spread than for CJ number < 1. These local peaks of high ST and high u′ areas of the flow have been shown in DNS simulations to drive local conditions in the flame brush to promote DDT.30,31,37 Thus, it is interesting to note we see this behavior both in the simulations and experiments for higher turbulent flame speed regimes. Since the CJ number > 1, the turbulent flame can be classified as super-CJ globally. Note there is overlap of points for cases near CJ number ∼1. This behavior has been observed in DNS simulations by Towry et al.58,59 and Poludnenko et al.,29,30,55 and experimental findings for standing compressible flames by Sosa et al.33 As these turbulent Mach numbers increase past MT = 0.3, nonlinear compressibility will dominate the flow and local supersonic flows may develop giving rise to small-scale eddy shocklets. These compressible turbulent fluctuations coupled with baroclinic torque (due to the pressure and density gradient across the compressed region and flame front) results in flame-generated turbulence, which is a driving mechanism for tDDT. This flame generated turbulence in super-CJ flames is expected to continue until the flame transitions into a detonation. Thus, we can observe this runaway mechanism begins to occur even before shock-flame propagation velocities reach 1/2DCJ.
Further characterization of the local flame turbulence is examined using the classical Borghi diagram.60 This diagram classifies the reaction zone into several regimes based on the integral length scale (L11) normalized by the laminar flame thickness (lf) and turbulent velocity (u′) normalized by the laminar flame speed (SL). Figure 12 shows three Borghi diagrams corresponding to the three ST regimes relative to SCJ. Refer to Sec. III B on the calculation details for L11.47,50–52 Data points are turbulent intensities extracted ahead of the flame front, in the compressed region where turbulence–flame interactions occur. See Sec. III B and Ref. 47 for details on the turbulence calculations and extraction procedure. The ST < SCJ [Fig. 12(a)] cases have local minima in the corrugated flamelets regime where the local flame structure is minimally perturbed by turbulent fluctuations and remains quasi-steady. However, most of the points for all cases are classified within the thin reaction zone regime where the flame thickness is in the order of the Kolmogorov length scale (λk) (Klimov–Williams criterion) and u′ ≫ SL.
Within these thin reactions zones, the smallest eddies on the order of λk < lf can typically penetrate the preheat zone, increasing the reaction rate, and eliminating a steady flame structure. However, DNS simulations by Poludnenko and Oran61 found the evolution of a turbulent flame brush to be determined by scales λ > lf. This conclusion is supported from our experimental observations, where the turbulent fast flames have L11 ≫ lf and large turbulent velocities. Furthermore, these findings are supported with DNS simulations by Poludnenko et al.30,55 whose turbulence conditions are similar to the experiments. They allowed the flame to interact with high-speed turbulence to investigate how turbulence can drive the development of tDDT conditions. The u′ values from the DNS case exhibiting the runaway condition range from 12.5SL to 24SL, and those that transitioned to detonation within the time domain were at u′ = 39.2SL. We show that our u′ values fall in the similar ranges in Figs. 12(b) and 12(c) as ST increases. These higher turbulence intensities coupled with ST/SCJ > 1 dominate the flow field resulting in large turbulent burning velocities. As the flame self-compresses (creating the compressed region as ST nears SCJ), there will likely be larger density gradient between the highly compressed reactants and rapidly expanding products. This rapid expansion coupled with large turbulence intensities results in local maxima in the broken reactions zone regime. Turbulent flames in the broken reactions zone regime have been found to spontaneously DDT,30 which is supported through an evolution from a shock-inducing fast flame, to shock-flame complex, to a detonation (Fig. 3).
Taking into account the flame compressibility from Fig. 11, we can extend the Borghi diagram (Fig. 12) into a third dimension by adding the CJ number (ST/SCJ). Figure 13 shows a modified three-dimensional combustion regime diagram, which considers turbulent velocities, turbulent scales, and compressibility (ST/SCJ). Additional viewing orientations of Fig. 13 have been added in the supplemental material in Fig. S2. The addition of CJ number on the third axis helps us visualize how higher u′ values result in higher CJ numbers. Since we are able to control u′ by increasing Φ, we are able to observe flame regimes with faster turbulent burning velocities and thus larger CJ numbers. This clearly shows the turbulence flame compressibility relationship. Flames with lower turbulent burning velocities (CJ number < 0.4) are expected to have less pronounced compressibility effects, which will not significantly affect the turbulent scales and velocities. As the CJ number increases closer to unity, flame compressibility plays a dominant role in turbulence generation due to baroclinic torque. In these regimes, DNS simulations have shown turbulent premixed flames to be intrinsically unstable,30 which results in the larger burning velocities and turbulent scales. Once CJ number > 1, the flame has met the CJ deflagration criteria for runaway tDDT; thus, the flame acceleration will continuously occur until detonation given enough reactants and length.
This work presented the results of experimental studies of turbulent fast flames in hydrogen–air mixtures using a turbulent shock facility that allowed us to control the turbulence intensity u′ and thus the burning velocity ST, by varying the equivalence ratio. High-speed PIV, schlieren, OH* chemiluminescence, and pressure measurements were used to measure the turbulence, gas dynamic, flame front, and flow field behavior. We examined several cases and observed three regimes of turbulence burning that differ by the ratio of burning velocity ST to the CJ deflagration velocity SCJ: shockless deflagrations (ST < SCJ), shock-inducing deflagrations (ST ∼ SCJ), and strong shock-inducing deflagrations or shock-flame complexes (ST > SCJ).
For shockless deflagrations, ST is basically defined by the background turbulence generated in the experiment. The turbulent motions wrinkle the flame surface resulting in an increase in the flame surface area and thus an increased ST. As ST increases past SCJ, the compressibility effects begin to play an important role. The pressure in the flame brush increases, the flame begins to generate shocks and also produces more turbulence. This is in contrast to flames that are much lower than ST, which are diffusion driven. This results in a runaway flame acceleration that leads to the formation of strong shocks and detonations. Thus, the CJ number Mf = ST/SCJ serves as an indicator for the flame ability to self-accelerate and produce shocks and detonations. Turbulent deflagrations with an increasing CJ number > 1 can be considered as consecutive stages of a turbulence-induced DDT process.
The analysis of measured turbulent velocities using the Borghi diagram shows that most of the points for all observed turbulent burning regimes correspond to the thin reaction zone regimes on the diagram with local minima in the corrugated flamelet regime for Mf < 1, and local maxima in the broken reaction zone regime for Mf > 1. Furthermore, these high turbulent flame speed burning regimes may be beneficial for detonation-based engine devices. However, the ability of a supersonic flame to produce strong shocks and turbulence amplification may have a destructive effect on constant pressure combustion systems as seen in turbofans and turbojets. Thus, the complex nature of these supersonic flame regimes places them in a regime between constant volume and constant pressure combustion.
See the supplementary material for other pressure and velocity plots as a function of equivalence ratio to highlight repeatability. More viewing angles for Fig. 13 have been added.
The authors acknowledge the Air Force Office of Scientific Research support under Award No. 9RT0258/FA9550-19-0322 by Program Manager Dr. Chiping Li and the National Science Foundation under NSF Award No. 1914453. AYP was supported in part by the AFOSR Award No. FA9550-21-1–0012. This work has also been cleared for release to an external audience by the Lawrence Livermore National Laboratory Office of Classification and Export Control, IM Release No: LLNL-JRNL-830197.
Conflict of Interest
The authors have no conflicts to disclose.
Hardeo M. Chin: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Jessica Chambers: Data curation (equal); Formal analysis (equal); Investigation (equal); Visualization (equal). Alexei Y. Poludnenko: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Validation (equal). Vadim Gamezo: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (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 from the corresponding author upon reasonable request.