Impact of a Variable Blockage Ratio on the Detonation Transition in a Pre-Detonator

Abstract

The deflagration-to-detonation transition (DDT) is a critical process for achieving reliable ignition in detonation-based propulsion systems, such as Rotating Detonation Engines (RDEs). This study experimentally investigates the effect of spatial variations in blockage ratio (BR) on flame acceleration and detonation onset within a modular pre-detonator. Three DDT device configurations (converging, constant, and diverging) were designed to have an identical average BR of 0.5 and were tested over equivalence ratios ranging from 0.64 to 1.6. High-speed imaging, pressure transducers, and schlieren visualization were employed to characterize flame propagation velocity, pressure evolution, and exit wave structures. The converging configuration consistently promoted earlier detonation onset and higher success rates, especially under fuel-rich conditions (ϕ = 1.6), while the diverging configuration failed to initiate detonation in all cases. Enhanced flame compression in the converging layout led to strong coupling between the shock and reaction fronts, facilitating robust detonation formation. These findings indicate that the spatial distribution of BR, rather than average BR alone, plays a decisive role in DDT performance. This work offers validated design insights for optimizing pre-detonator in RDE applications.

1. Introduction

Detonative propulsion has emerged as a next-generation high-efficiency thrust mechanism due to its ability to generate high pressure and release energy rapidly, outperforming conventional deflagrative systems in thermodynamic efficiency [1,2]. Unlike constant-pressure combustion in Brayton cycle engines, detonation-based combustion not only reduces energy losses but also enables compact engine designs with high thrust density [3,4].

Among various detonative propulsion concepts, the Rotating Detonation Engine (RDE) is particularly promising, as it maintains a self-sustained rotating detonation wave following a single ignition. This enables continuous thrust generation, high-frequency operation, and simplified combustor design [5,6,7]. Experimental studies have demonstrated the feasibility of RDE operation with various fuels and configurations, highlighting its potential in aerospace propulsion systems [8]. More recently, RDEs have been tested on ground-based thrust stands and have also been demonstrated in scaled UAV prototypes, confirming their applicability under realistic operating conditions [5,6,8].

However, one of the most critical challenges in RDE development is achieving reliable detonation initiation. Conventional spark-based ignition methods often suffer from low repeatability and limited robustness under varying chamber conditions. In contrast, pre-detonator-assisted ignition, where a detonation wave is first formed in a confined chamber and then injected into the main combustor, has been shown to achieve ignition success rates exceeding 90% [4].

The performance of pre-detonators is highly sensitive to several parameters, including fuel composition, initial pressure, channel geometry, and internal obstacle configuration. In particular, the deflagration-to-detonation transition (DDT) process is strongly governed by flame acceleration, turbulence generation, and unburned gas compression, all of which are affected by the distribution of blockage ratio (BR) and the flow structures induced by internal obstacles [9,10,11].

Recent numerical studies have examined the effects of variable BR and flow area gradients on the success of DDT. However, most of these efforts have focused on simplified PDE models or closed-channel simulations. Experimental validation of such effects in modular pre-detonator geometries remains limited, underscoring the need for targeted research in this area.

DDT is a fundamental phenomenon relevant to both combustion safety and detonation-based propulsion systems. Numerous studies [12,13,14,15,16,17] have investigated how structural configurations influence this transition process. Ciccarelli and Dorofeev [12] presented a comprehensive review of DDT in obstructed flows, emphasizing the roles of flame acceleration, shock-flame interaction, and the SWACER (Shock Wave Amplification by Coherent Energy Release) mechanism. They also discussed the effects of duct curvature, turbulence intensity, and ignition location on DDT behavior. Sorin et al. [13] experimentally examined various BR configurations and demonstrated that placing high BR obstacles near the leading edge promotes flame acceleration and reduces the DDT run-up distance, suggesting a correlation between BR and detonation cell size. Mehr and Ciccarelli [14] developed a predictive framework for estimating the DDT run-up distance in ducts equipped with orifice plates. They modeled flame acceleration as a conical front periodically perturbed by obstacle-induced shock reflections and highlighted the importance of flame–shock–obstacle interactions, particularly under high BR conditions where galloping detonation modes and strong induction effects become prominent. Han et al. [15] numerically investigated the complete DDT process in both micro- and macro-channels, showing that viscous boundary effects, turbulence, and flame instabilities play distinct roles in accelerating the flame and detonation onset. Roy et al. [16] reviewed the key challenges in pulse detonation propulsion and emphasized the importance of robust ignition systems incorporating pre-detonators and DDT-promoting structures, further underscoring the critical impact of obstacle design and BR distribution. Lastly, Dounia’s group [17] investigated the sensitivity of DDT predictions to chemical kinetics. By comparing one-step and detailed reaction mechanisms, they demonstrated that ignition delay and detonation strength strongly depend on the fidelity of the chemical model employed.

Pre-detonators play a critical role in detonation-based propulsion systems such as RDEs and PDEs by enabling rapid and reliable initiation of detonation waves in the main combustor. Both experimental and numerical approaches have been employed to investigate how pre-detonator design and operating conditions influence detonation transition. Lei et al. [18] experimentally demonstrated that sustaining an overdriven detonation at the pre-detonator exit is essential for achieving supercritical or critical transition modes in a flat combustion chamber. By varying pre-detonator length and nitrogen dilution ratios, they mapped the transition probability and identified a narrowing “transition canyon” under high dilution conditions, where a higher degree of overdrive is required for successful transition.

Shi et al. [19] numerically analyzed the re-initiation of diffracted detonation waves using obstacles placed immediately downstream of the pre-detonator. Using OpenFOAM’s DCRFoam solver, they showed that detonation re-initiation is highly sensitive to the geometric relationship between obstacle height (h) and distance (w) and identified a bounded design space within which detonation re-initiation can occur.

Xia et al. [20] numerically studied the influence of pre-detonator configuration and ignition parameters on RDE ignition performance. They analyzed how variations in tube length, diameter, and ignition energy affect ignition delay and detonation initiation under realistic engine conditions, providing practical design guidelines for compact and effective pre-detonators.

Spatial variations in BR significantly affect turbulence generation, flame acceleration, and hot spot formation, all of which are key factors that govern DDT conditions. Feng and Huang [21] numerically demonstrated that variable BR configurations, such as converging layouts, shorten the DDT distance compared to constant BR cases, even when the average BR is held constant. This was attributed to earlier flame compression and hot spot formation facilitated by downstream-increasing BR profiles. Ahumada et al. [22] experimentally investigated hydrogen detonation onset in tubes containing two obstacles with unequal BRs. They found that BR-increasing configurations (e.g., 40–60%, 40–80%) resulted in significantly faster DDT onset than constant BR cases (e.g., 40–40%). The results confirmed that BR had a greater impact on detonation initiation time than obstacle geometry or opening size. Ni et al. [23] numerically studied the effects of arc-shaped obstacles on hydrogen–air detonation characteristics and identified that an optimal BR of 0.7 minimized the DDT distance while enhancing propagation velocity. Their results also showed that both excessively low and high BR values inhibited detonation initiation, with distinct flame structures and initiation mechanisms observed across BR regimes. Saeid et al. [24] conducted numerical simulations with a fixed BR of 0.6 to evaluate the influence of obstacle shape and thickness. Their findings indicated that rectangular obstacles induced stronger flame acceleration and turbulence compared to semicircular ones, implying that geometrical effects can significantly affect transition behavior even when the BR is kept constant.

Previous research on deflagration-to-detonation transition (DDT) has extensively investigated the effects of obstacle geometry, ignition conditions, and blockage ratio (BR) on flame acceleration and transition distance using both numerical and experimental approaches. In particular, numerous studies have demonstrated that a variable BR arrangement—where the average BR remains fixed, but the distribution varies—can significantly affect DDT performance.

However, most of these studies have been conducted in simplified experimental setups such as straight tubes or pulse detonation engine (PDE) configurations. Experimental investigations applying variable BR concepts to pre-detonator geometries representative of RDEs remain extremely limited.

Prior work on pre-detonators has predominantly focused on single-tube configurations with fixed BR values or devices employing Shchelkin spirals to promote flame acceleration. Intentional manipulation of BR distribution within a modular pre-detonator and direct experimental comparison of its effects on DDT characteristics has rarely been attempted. Furthermore, many of these earlier studies rely on qualitative assessments of pressure trends or transition distance without providing reproducible, quantitatively validated metrics that could inform structural design criteria.

To address these limitations, the present study extends the variable BR methodology, previously applied in PDE studies, to a pre-detonator scaled for RDE operation. Three configurations—converging, constant, and diverging—were designed to maintain the same average BR while varying the spatial distribution of BR through obstacle arrangement. Flame acceleration behavior, shock–flame coupling, and detonation onset position were quantitatively evaluated through high-speed imaging and pressure diagnostics. These results enable systematic assessment of how BR distribution influences DDT performance in RDE-relevant geometries.

In contrast to previous work confined to idealized test sections, this study experimentally implements and analyzes a modular pre-detonator that is directly applicable to RDE systems. The results demonstrate that variable BR distribution acts as a structural design parameter that significantly enhances ignition reliability.

Accordingly, this work offers both academic and practical value by experimentally validating the feasibility and impact of structurally optimized DDT configurations for robust and repeatable RDE ignition.

2. Experimental Setup

To investigate the influence of the DDT device configuration on detonation onset within the pre-detonator, the experimental combustor illustrated in Figure 1 was designed and employed. Port 1 serves as the purge gas inlet, through which nitrogen (N₂) is supplied before and after each experiment to minimize potential variations in mixture composition caused by residual combustion products or atmospheric air ingress. Ports 2 and 3 are designated for the oxidizer and fuel supply, respectively. The two reactants are premixed in the chamber labeled 4 before entering the combustion channel. The combustion channel has a square cross-section with a length of 250 mm and side dimensions of 10 mm. The premixed propellants are ignited by a spark plug located at position 5. The ignited flame then propagates through the DDT device positioned at location 6, which is designed to promote flame acceleration and induce turbulence. To characterize the propagation of the detonation and shock waves, four piezoelectric pressure transducers were installed at position 7 along the combustor wall at distances of 80 mm, 130 mm, 180 mm, and 230 mm from the channel inlet. Based on these signals, the average propagation velocities in each section were calculated and denoted as V₁, V₂, and V₃, respectively. The geometry of the combustor was modularized at location 8, allowing the DDT section to be replaced with one of three configurations: converging, constant, or diverging, thereby enabling a comparative assessment of their effects on detonation onset. In addition, one side of the combustor wall was fabricated from polycarbonate to enable optical access for visualizing flame propagation inside the chamber using high-speed imaging.

To investigate the combustion characteristics influenced by the geometry of the DDT device, three different configurations were constructed, as illustrated in Figure 2. Figure 2a–c correspond to the converging, constant, and diverging configurations, respectively. The shape of each DDT device was varied by adjusting the blockage ratio (BR) of individual obstacles. The BR is defined by Equation (1) as the ratio of the blocked area to the total cross-sectional area of the channel, representing the degree of flow area reduction caused by the obstacles. All configurations employed five obstacles placed at equal intervals, with the average BR maintained at 0.5 for consistency. The selection of blockage ratios was based on two key considerations. First, following Feng et al. [21], we employed variable BR distributions to investigate the effect of spatial trends on DDT performance while maintaining a constant average BR. Second, Saeid et al. [24] reported that BRs above 0.7 tend to reduce detonation velocity and induce instability. To avoid such adverse effects, we linearly distributed the BR values within a practical range of 0.3 to 0.7, resulting in an average BR of 0.5. In the converging configuration, the first obstacle was set to a BR of 0.3, with each subsequent obstacle increasing by 0.1, resulting in a final BR of 0.7. Conversely, the diverging configuration started with a BR of 0.7 and decreased by 0.1 for each obstacle, ending at 0.3. In the constant configuration, all obstacles were designed with a fixed BR of 0.5 and served as a baseline for comparison. The BR of each obstacle are explicitly detailed in

Table 1. Blockage ratio (BR) distribution for each DDT configuration.

	BR 1	BR 2	BR 3	BR 4	BR 5
Converging	0.3	0.4	0.5	0.6	0.7
Constant	0.5	0.5	0.5	0.5	0.5
Diverging	0.7	0.6	0.5	0.4	0.3

.

$$BR={\displaystyle \frac{A_{closed}}{A_{total}}}$$

(1)

In this study, CH₄ and O₂ were used as the fuel and oxidizer, respectively, and experiments were conducted over a range of equivalence ratios from 0.6 to 1.6. The equivalence ratio for CH₄/O₂ mixture was calculated using Equation (2). The specific mass flow rates and equivalence ratio conditions are summarized in

Table 2. Experimental conditions for different equivalence ratios.

Oxidizer	MFRox [g/s]	Fuel	MFRfuel [g/s]	Φ
O2	0.25	CH4	0.040	0.64
			0.050	0.80
			0.065	1.04
			0.080	1.28
			0.100	1.60

. The flow rates of the propellants were controlled using mass flow controllers (MFCs). Oxygen was regulated using a mini CORI-FLOW M15 model from Bronkhorst, while CH₄ was supplied via an FMA-2607A-I model from OMEGA. In each experiment, the fuel and oxidizer valves were opened for approximately 5 s to allow complete filling of the combustion chamber with premixed gases. The chamber was confirmed to be at room temperature and atmospheric pressure prior to ignition. Immediately after closing the valves, a spark plug was activated for 0.5 s to initiate ignition. Following combustion, a purge process was conducted to evacuate residual combustion products from the chamber.

$$\mathsf{\Phi }={\displaystyle \frac{{F/O}_{actual}}{{F/O}_{stoic}}}=4.0\times {\displaystyle \frac{{\dot{m}}_{fuel}}{{\dot{m}}_{ox}}}$$

(2)

To analyze the combustion characteristics of detonation waves generated within the combustion chamber, pressure transducers, high-speed imaging inside the chamber, and schlieren imaging at the exit were employed. The measurement systems and conditions used are described as follows. Pressure measurements were conducted using PCB piezoelectric transducers (models 113A24 and 111A24). Considering the detonation wave propagation speed on the order of several thousand meters per second, a sampling rate of 1 M sample/s was used. This sampling rate was determined by the maximum acquisition capability of the oscilloscope and was sufficient to resolve the steep pressure gradients and microsecond-scale transients characteristic of detonation events. Flame propagation inside the combustion chamber was visualized using a high-speed camera (Phantom VEO710L) equipped with a 50 mm f/1.4 Nikon prime lens. High-speed images were recorded at a resolution of 1024 × 56 pixels, a frame rate of 120,000 fps, and an exposure time of 1 μs, resulting in a pixel resolution of approximately 0.29 mm/pixel. To visualize shock waves and combustion products at the combustor exit, a Z-type schlieren optical system was constructed. Illumination was provided by a Thorlabs MNWHL4 LED, and light was reflected using a 6-inch diameter, 36-inch focal length parabolic mirror from Edmund Optics. Schlieren images were captured using the same Phantom VEO710L camera and the 50 mm f/1.4 Nikon lens. The imaging was performed at a resolution of 256 × 192 pixels, a frame rate of 100,000 fps, and an exposure time of 1 μs, with an effective pixel resolution of approximately 0.33 mm/pixel. The raw images obtained from both visualization methods were post-processed using MATLAB(R2025a)to enable quantitative analysis. It is noted that pressure measurements and schlieren imaging were conducted using a back plate with ports for transducer installation, while high-speed imaging inside the chamber was performed using a flat back plate without sensor ports. This structural difference in the setup may introduce a degree of systemic error in flame propagation characteristics under otherwise identical test conditions.

3. Result and Discussion

3.1. Flame Transition in the Combustion Chamber

To analyze the flame and wave propagation characteristics inside the combustion chamber, high-speed imaging and pressure transducer measurements were utilized. High-speed images qualitatively revealed the flame structure and luminosity variations, while post-processed image data enabled quantitative evaluation of the flame front propagation velocity. Pressure transducers, installed at four locations along the combustion chamber, provided pressure histories that were used to calculate average propagation velocities between sensor pairs, thereby capturing both flame propagation and detonation transition behavior.

Figure 3 presents a sequence of high-speed images captured inside the combustor equipped with a diverging-type DDT device at an equivalence ratio of 1.04. The image set consists of 15 consecutive frames, with a time interval (Δt) of approximately 8 μs between each frame. The flame propagation behavior can be divided into two distinct regions, separated by the dashed line: a developing region on the left and a fully developed region on the right. In the developing region, the flame front exhibits a highly wrinkled structure and relatively low luminosity. This flame morphology is attributed to the transition from laminar to turbulent combustion, driven by flow disturbances and increased turbulence intensity generated by the DDT device. The disorganized flame shape and weak self-luminosity indicate that the combustion remains in a deflagration phase, with incomplete coupling between the flame front and any leading shock wave. In this study, a “fully developed detonation transition” is defined based on three observable criteria: (1) a rapid and sustained increase in flame luminosity, (2) the emergence of a planar detonation front, and (3) the sustained propagation of this front at an approximately constant velocity downstream of the transition region. These characteristics indicate that strong coupling between the reaction zone and the leading shock has been established. During the DDT process, a rapid increase in flame luminosity is observed, followed by the formation of a planar detonation front, indicating the onset of a fully developed detonation wave. The presence of a stabilized planar front implies strong coupling between the reaction zone and the leading shock. This transition mechanism has been reported in several previous studies [12,25,26,27], and the present results confirm that a similar DDT process occurred in this experiment. Except for the case at an equivalence ratio of 1.6, all other tested conditions exhibited detonation onset through a transition sequence similar to that shown in Figure 3.

To quantitatively analyze the captured high-speed images, flame front and detonation wave propagation velocities were extracted through image post-processing using MATLAB(R2025a). For each test condition, three to five repeated experiments were conducted. Figure 4 shows the propagation velocity profiles along the axial locations inside the combustion chamber. Individual data points from repeated experiments are shown to preserve the flame acceleration and transition behavior unique to each case.

Except for the fuel-rich condition at an equivalence ratio of 1.6, all other cases exhibited a trend in which the propagation velocity gradually converged toward the theoretical Chapman–Jouguet (C–J) detonation velocity. Relatively larger random errors were observed at equivalence ratios of 0.64 and 1.6 compared to the stoichiometric condition (ϕ = 1.0), which reflects greater variability among the repeated trials. In particular, under the condition of ϕ = 1.6, the occurrence of detonation transition was found to be significantly affected by the DDT device configuration. For the constant and diverging configurations, the measured flame propagation velocities remained below 1000 m/s in all cases, indicating that the flame remained in a deflagration regime without transitioning to detonation. In contrast, for the converging configuration, two out of five tests showed propagation velocities exceeding the theoretical C–J velocity, two cases exhibited deflagration-like behavior, and one case displayed flame acceleration without full detonation transition before reaching the chamber exit.

These results demonstrate that the propagation velocity varies with equivalence ratio in accordance with theoretical expectations, and that the effect of DDT configuration on detonation onset becomes more pronounced as the mixture deviates from stoichiometric conditions. A detailed discussion of this behavior is provided in Section 3.3.

To investigate the pressure variations during detonation wave propagation inside the combustion chamber, four piezoelectric pressure transducers were installed along the axial direction at 80 mm, 130 mm, 180 mm, and 230 mm. Figure 5 displays the pressure data recorded at each sensor, where (a) corresponds to an equivalence ratio of 0.64, and (b) corresponds to an equivalence ratio of 1.04. A low-pass FFT filter was applied to suppress high-frequency noise, and signals below 200 kHz were extracted for analysis.

A comparison between Figure 5a,b reveals distinct differences in pressure response patterns. In case (a), pressure at the first sensor (80 mm) increases gradually, while sudden pressure rises are observed at the second through fourth sensor. Notably, the fourth sensor exhibits a von Neumann spike, characterized by a sharp pressure rise at the detonation front and subsequent decay across the induction zone. In contrast, the pressure profiles at the second and third sensors show milder increases without the steep rise associated with a fully developed von Neumann spike. These observations suggest the presence of an incident shock and subsequent compression of unreacted gas rather than a complete transition to detonation.

In case (b), a steep pressure rise is observed even at the first sensor, likely due to an early formed incident shock in the chamber. Furthermore, well-defined von Neumann spikes appear at all subsequent sensors, with the second sensor recording the highest peak pressure, indicating an overdriven detonation wave immediately after transition. Beyond this point, peak pressures gradually decrease downstream, suggesting wave stabilization.

These pressure data correlate well with the flame propagation velocities presented in Figure 4. For the case with an equivalence ratio of 0.64, the flame begins accelerating around 125 mm and transitions to detonation near 200 mm. This trend is consistent with the pressure history: the first sensor (80 mm) does not capture any abrupt pressure rise typically associated with the shock passage, while second and third sensors, located in the acceleration zone, show moderate pressure increases consistent with an incident shock. A fully developed von Neumann spike appears only at the fourth sensor, aligning with the detonation transition point.

In contrast, for ϕ = 1.04 case, flame acceleration begins near 110 mm with detonation onset around 130 mm, as indicated by the second sensor’s strong overdriven peak pressure. The subsequent sensors show decreasing pressure peaks and propagation velocities, confirming downstream stabilization of the detonation wave.

In addition, average flame propagation velocities across different segments of the combustion chamber were calculated from the pressure data, as presented in Figure 6. The velocity was determined by identifying the wave arrival time, defined as the point at which pressure began to rise at each transducer, and dividing the distance between transducers by the corresponding time difference. The chamber was divided into three axial segments from the inlet, designated V1, V2, and V3.

In the V1 region, where the flame remains in the deflagration regime, propagation velocities were below 2000 m/s for all test conditions. In the V2 region, detonation transition occurred in all cases except at equivalence ratios of 0.64 and 1.6, as indicated by velocities converging to within 10% of the theoretical C–J velocity. In the V3 region, detonation transition was confirmed even at ϕ = 0.64. Regarding DDT configurations, the converging design showed detonation under all tested conditions. In contrast, the constant configuration yielded two cases of deflagration-like propagation, one case with a deviation of approximately 15% from the C–J velocity, and one with flame acceleration but no complete transition to detonation. The diverging configuration exhibited only deflagration propagation across all conditions. These results further support the conclusion that the converging configuration effectively promotes detonation transition.

However, some discrepancies were observed between pressure-based transition behavior, and that results from high-speed imaging in Figure 4. This discrepancy may be attributed to structural differences in experimental setup. As discussed in the Experimental Setup Section, high-speed imaging was conducted using a flat back plate without pressure transducer ports to ensure optical clarity, whereas pressure and schlieren measurements used a back plate equipped with four pressure transducers. Small gaps or surface roughness around the ports may have unintentionally acted as DDT-promoting features, potentially triggering detonation in cases where no transition was observed in the images. While the back plate with ports may introduce minor turbulence or local perturbations that could assist detonation onset, all configurations were subjected to the same measurement structure and port layout, ensuring that comparative trends across different geometries remain valid. Moreover, no significant hot spot localization near port locations was observed in schlieren images, supporting the assumption that such effects are negligible for relative analysis.

3.2. Wave Propagation at the Combustion Exit

In evaluating pre-detonator performance, the discharge characteristics of the detonation and shock waves at the combustor exit are considered critical indicators of ignition success in Rotating Detonation Engines (RDEs). Schlieren imaging was employed to visualize high-density-gradient phenomena, such as shock waves and combustion fronts, at the chamber exit. Figure 7, Figure 8 and Figure 9 present schlieren images of the combustor exit for the converging, constant, and diverging DDT configurations, respectively, at an equivalence ratio of 1.6. For equivalence ratios ranging from 0.64 to 1.28, detonation transitions were observed in all cases, yielding similar structures to those observed in Figure 7; therefore, only the representative case of ϕ = 1.6 is presented.

In the converging configuration (Figure 7), a fully developed detonation wave was observed inside the combustor, consistent with earlier pressure data. The schlieren images reveal coupled propagation of the incident shock and combustion products, with the shock appearing as a sharp black front and the combustion products trailing behind as a wrinkled structure. This behavior, along with the hemispherical expansion pattern, is consistent with observations reported in previous studies [28,29].

After approximately 30 μs, decoupling begins to occur between the incident shock and the combustion products, with the separation gap gradually increasing over time. This behavior is likely attributed to reduced reactivity outside the combustor, where the burned gases mix with ambient air, thereby suppressing sustained combustion and weakening the coupling between the shock and flame front.

Figure 8 shows schlieren images of the constant DDT configuration at ϕ = 1.6. Based on the earlier pressure data, this condition resulted in one case of detonation, one of flame acceleration, and two of deflagration. Figure 8a corresponds to the detonation and flame acceleration case, whereas Figure 8b represents the deflagration case. In Figure 8a, the propagation behavior closely resembles that observed in Figure 7, with an initially coupled structure that eventually decouples. In contrast, Figure 8b displays a decoupled structure from the outset, where the shock wave and combustion products separate immediately upon exiting the combustor. The shock wave in this case also propagates qualitatively more slowly than in Figure 8a.

Similar deflagration characteristics are observed in the diverging configuration shown in Figure 9. In this case, the shock wave and combustion products remain decoupled throughout the propagation, and the shock structure resembles that of a traditional shock tube, as reported in the prior studies [30,31,32,33].

Overall, the schlieren images indicate that, in detonation cases, the incident shock and combustion products initially propagate in a coupled manner before gradually decoupling outside the combustor. In contrast, for deflagration cases, the two flow structures are separated from the point of exit, with the shock exhibiting behavior similar to that of a shock tube-generated wave.

3.3. Effect of DDT Device

As demonstrated by the previous experimental results, the configuration of the DDT device plays a significant role in facilitating detonation transition. This section examines how variations in DDT geometry influence flame acceleration, unburned gas compression, and, ultimately, the onset of detonation. Figure 10 shows the pressure traces recorded by a pressure transducer located 80 mm downstream of the DDT device, for three configurations: (a) converging, (b) constant, and (c) diverging, at an equivalence ratio of 1.04.

Although none of the cases exhibited a distinct von Neumann spike, a sharp pressure rise was observed in all configurations, interpreted as the passage of an incident shock generated by flame propagation. The magnitude of this pressure rise varied with the DDT geometry, with the peak pressure of approximately 18 bar for the converging case, 15 bar for the constant case, and 12 bar for the diverging case. These results suggest that unburned gas behind the incident shock was more strongly compressed in the converging configuration.

This trend can be interpreted using the flame piston model [34,35], in which the propagating flame front acts like a piston, compressing the unburned gas ahead of it. This compression increases turbulence intensity and promotes flame wrinkling, thereby enlarging the effective flame surface area and elevating the local heat release rate. This strengthened combustion feedback intensifies the leading pressure wave and further amplifies gas compression, forming a positive feedback loop that can ultimately lead to detonation transition. Once the acceleration exceeds a critical threshold, a transition to detonation occurs.

The extent of flame acceleration is strongly influenced by the geometry of the DDT device. In the converging configuration, where the BR increases along the propagation direction, the narrowing cross-sectional area enhances both the unburned gas compression and flame acceleration. In contrast, although the diverging configuration also produces flame piston effects, the expanding cross-section diminishes the effectiveness of these mechanisms. Moreover, under fuel-rich conditions (e.g., Φ = 1.6), the inherent reduction in detonability further suppresses flame acceleration in the diverging case, ultimately preventing detonation transition.

These differences in gas compression are qualitatively reflected in the peak pressure values in Figure 10, where the relative strength of unburned gas compression follows the order: converging > constant > diverging.

4. Conclusions

This study demonstrated that the geometry of the deflagration-to-detonation transition (DDT) device has a decisive influence on detonation onset behavior within a pre-detonator, even when the average blockage ratio (BR = 0.5) is held constant. Through a series of controlled experiments using three geometric configurations (converging, constant, and diverging) across a range of equivalence ratios (ϕ = 0.64 to 1.6), distinct differences were observed in flame acceleration, pressure response, and wave propagation characteristics. High-speed imaging, pressure diagnostics, and schlieren visualization collectively confirmed that subtle geometric variations strongly affect the success and structure of detonation transition.

Under fuel-rich conditions (ϕ = 1.6), the effect of DDT configuration on wave propagation was especially pronounced. In the converging case, rapid flame compression and increased luminosity led to the formation of a planar detonation wave. In contrast, the diverging configuration retained a wrinkled deflagration structure and exhibited consistently lower propagation velocities.

Velocity profiles derived from high-speed flame visualization showed that propagation velocity is primarily governed by the equivalence ratio. As ϕ increased, flame speeds approached the theoretical C–J velocity, a trend corroborated by pressure transducer data. These results suggest that while the equivalence ratio primarily determines flame speed, the DDT configuration plays a secondary but essential role in determining whether detonation transition occurs.

Notably, the converging configuration exhibited structural features favorable for detonation onset, including enhanced rearward gas compression, as predicted by the flame piston model. This led to higher transition success rates and more frequent overdriven conditions. Schlieren images at the combustor exit further revealed that in the converging case, the incident shock and combustion products remained coupled, whereas decoupling or isolated shock propagation were observed for the constant and diverging cases.

These findings not only highlight the critical impact of obstacle arrangement and BR gradient on detonation transition success, even when the average BR is fixed, but also emphasize the importance of DDT device designs with strategically placed flame compression zones and turbulence-generating features to achieve robust and repeatable detonation initiation.

In conclusion, this study presents one of the few experimental investigations into variable BR DDT configurations within a pre-detonator, providing practical guidelines for improving ignition reliability in RDEs and for structurally optimizing pre-detonator design. Future work may further build on these findings by exploring variations in propellant compositions, ignition location, and channel geometries to refine strategies for robust detonation transition.

Although the experimental setup involved different back plate configurations for high-speed imaging and pressure measurements, the consistent layout across all DDT configurations and the absence of localized detonation triggering near sensor ports suggest that the comparative conclusions drawn from pressure data remain valid. Nevertheless, this structural distinction should be considered in future studies when attempting quantitative matching between optical and pressure diagnostics.