# Experimental Analysis of the Effect of End-gas Temperature on Spontaneous Detonation Development Mechanisms for a Hydrogen/N-decane Fuel Mixture

Roseline Ezekwesili, Camille Strozzi, Marc Bellenoue, Myles Bohon

► To cite this version:

Roseline Ezekwesili, Camille Strozzi, Marc Bellenoue, Myles Bohon. Experimental Analysis of the Effect of End-gas Temperature on Spontaneous Detonation Development Mechanisms for a Hydrogen/N-decane Fuel Mixture. Flow, Turbulence and Combustion, 2025, 116 (1), pp.21. 10.1007/s10494-025-00699-8. hal-05428703

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# Experimental Analysis of the Effect of End-gas Temperature on Spontaneous Detonation Development Mechanisms for a Hydrogen/N-decane Fuel Mixture

Roseline Ezekwesili¹,²,⁴ · Camille Strozzi¹,³,² · Marc Bellenoue¹,²,³ · Myles Bohon⁴

Received: 31 March 2025 / Accepted: 8 November 2025
© The Author(s) 2025

## Abstract

In Constant Volume Combustion (CVC) and wider combustion applications, unwanted transitions to detonation can occur in highly reactive end-gas with a reactivity gradient present. The objective of this present study was to identify variables encountered in practical applications which influence detonation transition behavior. Different temperature gradients were imposed on stoichiometric H₂/C₁₀H₂₂/O₂/Ar mixtures with a 5% H₂ fuel mass percentage in a closed optical vessel through varying the temperature of heating cartridges placed at the top, middle and bottom of the chamber. In Part 1 of this study, ultra-high-speed schlieren records were analyzed to identify the exact mechanism by which detonation transition occurred for a mixture initially at 3 bar with top, middle and bottom heating cartridge temperatures of 453 K, 455 K and 441 K respectively. At this reference temperature gradient, both a vertically and laterally propagating autoignition wave would form. Zones with a reactivity high enough to transition to detonation would form at the intersection of the two waves as well as at the end wall due to the effects of reflecting pressure waves. Part 2 of this study analysed the effects of varying temperature gradient. A stronger temperature gradient resulted in end-gas with insufficient reactivity to transition to detonation. A weaker temperature gradient resulted in the development of more zones with sufficient reactivity to transition to detonation when compared to the reference temperature gradient. Although temperature gradient was the ultimate determinant of detonation transition behavior, it was found that changing chamber geometry could work towards suppressing detonations in borderline cases.

**Keywords** Autoignition · Detonation · Transition

<footnote>Camille Strozzi, Marc Bellenoue and Myles Bohon contributed equally to this work.</footnote>

<footnote>Extended author information available on the last page of the article</footnote>
# 1 Introduction

In Constant Volume Combustion (CVC) applications and in combustion applications with high compression ratios, end-gas can become very reactive and unwanted transitions to detonations can occur from hotspot autoignition (Campbell and Gear 1995; Gao et al. 2019; Pan et al. 2019). Hotspots are spots of increased reactivity in the fuel-oxidizer pre-mixture which arise due to inhomogeneities in the premixture. If the end-gas is reactive enough, these hotspots autoignite ahead of the propagating deflagration. This premature hotspot autoignition is considered to be responsible for knock in Spark-ignition (SI) engines (Wang et al. 2017; Pan et al. 2014; Bradley et al. 1996; Heywood 1988). If there is a reactivity gradient across the hotspot, the sequential autoignition of neighbouring pockets of gas can produce an autoignition wave. This autoignition wave can transition to detonation through the Deflagration-Autoignition-Detonation-Transition mechanism (DAIDT). The DAIDT mechanism is explained by the Shockwave Amplification by Coherent Energy Release (SWACER) model proposed by Lee et al. (1978). In this model, autoignition in a confined space induces pressure waves which propagate ahead into the unburnt gas. If the heat release from the autoignition wave is in phase with these leading pressure waves, the heat release will feed into the pressure waves, reinforce them and lead to a transition to detonation. The SWACER mechanism is one of the phenomena responsible for super-knock in SI engines (Pan et al. 2019; Luong et al. 2021; Rönn et al. 2023; Shahanaghi et al. 2022).

According to Zeldovich et al. (1980), the autoignition wave speed can be described by Eq. 1 where $u_a$ is the autoignition wave speed, $\tau_i$ is the ignition delay time (IDT), $x$ is the spatial variable, $T$ is temperature and $t$ is the time variable.

$$u_a = \left( \frac{dx}{d\tau_i} \right) = \left( 1 \middle/ \frac{dT}{dx} \right) \left( 1 \middle/ \frac{d\tau_i}{dT} \right) \quad (1)$$

The term $(d\tau_i/dT)$ represents the IDT temperature sensitivity. It is consistent with Eq. 1 that both a lower IDT temperature sensitivity $(d\tau_i/dT)$ and a weaker spatial temperature gradient $(dT/dx)$ result in a higher autoignition wave speed. In (Gu et al. 2005), through numerical investigation, it was found that varying the temperature gradient and initial conditions for H₂/air and H₂/CO/air hotspots led to 5 different combustion regimes including thermal explosion, supersonic autoignition, developing detonation, a slow autoignition and a propagating deflagration.

Another factor which has been found to influence the resulting combustion regime is fuel Negative Temperature Coefficient (NTC) behavior (Griffiths et al. 2002). Large hydrocarbons experience 2-stage ignition and NTC behavior (Liang and Law 2018). In (Peng et al. 2017) when investigating dimethyl ether/air hotspots, with temperatures below, within and above the NTC region, additional detonation transition modes were identified including detonation transitions originating from cold spots. Moreover, at the boundaries of the NTC region, the IDT temperature sensitivity is a minimum, therefore temperatures near the NTC region boundary have low IDT temperature sensitivities which will influence the resulting combustion regimes.

Another phenomenon has been observed experimentally where, in certain conditions, autoignition first occurs at the end-wall as opposed to the unburnt gas just ahead of the propagating deflagration where the temperature is slightly higher (Heywood 1988). The

<figure><img src="image_3.png" /></figure>
authors have hypothesized that this phenomenon could be due to the NTC behavior. How-
ever, in a study of end-gas in a Rapid Compression Machine (RCM), another mode of
detonation development called Shockwave Reflection Induced Detonation (SWRID) was
identified (Wang et al. 2016). In this mechanism, shockwaves reflecting from the cham-
ber walls coupled with the heat release from local autoignition and this coupling led to a
detonation developing. When numerically studying the combustion modes resulting from a
deflagration propagating in a closed chamber, it was found that if the unburnt gas was on the
verge of autoigniting, the reflection of a pressure wave at the end wall could locally raise the
temperature enough to cause autoignition at the end wall (Yu and Cheng 2015). Therefore,
alongside the temperature gradient and end-gas reactivity, the NTC behavior and reflecting
pressure waves can also have an influence on whether a transition to detonation occurs and
the mechanism by which it occurs.

N-decane is one of the main components of kerosene and is representative of kerosene's behavior but with a much simpler chemistry (Gascoin and Gillard 2010; Alekseev et al. 2017). N-decane is also a large hydrocarbon which undergoes 2-stage ignition within certain temperature ranges (Borghesi and Mastorakos 2016). Hydrogen is an attractive fuel for the future because of its zero-carbon emissions. However, pure hydrogen is challenging to implement in propulsion applications (Juste and Benavides 2008). A first feasible step towards decarbonization is mixing hydrogen with jet fuels. The effects of mixing hydrogen with large hydrocarbons has already been the focus of numerous studies (Xu et al. 2022; Hui et al. 2014; Liu et al. 2014). However, the DAIDT behavior of hydrogen when mixed with hydrocarbons, specifically kerosene surrogates such as n-decane, is a field which as of yet has not been explored.

Unwanted transitions to detonation can have disastrous consequences in CVC and other
SI applications and must be suppressed. As a first step towards deriving strategies to sup-
press detonations, the variables which contribute towards detonation transition must be
understood. Therefore, the objective of this present study is to identify variables encoun-
tered in practical applications which influence detonation transition behavior for a stoichio-
metric hydrogen/n-decane/air mixture. The work will be split into 2 parts. Part 1 will use
ultra-high-speed schlieren images to identify the exact mechanism of detonation transition
and the factors which influence detonation transition behavior for a mixture at a reference
temperature gradient. Part 2 will explore how changing temperature gradient affects the
influence of the factors identified in Part 1.

**2 Methods and Tools**

The Modular Deflagration Autoignition Detonation (MDAID) combustion chamber used in the present work is shown in Fig. 1a.). Moreover, the structure and function of the thermo-couples used to monitor wall temperature are shown in Fig. 1b.).

The combustion chamber in the MDAID configuration has dimensions of 40 × 40 × 172 mm. Heating cartridges are placed at the top, middle and bottom of the chamber. Each set of heating cartridges are controlled by 3-zone PID regulators. The wall temperature is monitored by thermocouples mechanically fastened into the chamber walls. By setting the PID-regulators to different set-points, a temperature gradient and therefore a reactivity gradient is imposed on the gas within the chamber. The PID-regulators controlled
<figure><img src="image_4.png" /><figcaption>Fig. 1 a.) Experimental MDAID chamber used in present study. b.) Diagram demonstrating the placement and function of the thermocouples and heating cartridges used in MDAID chamber</figcaption></figure>

the wall temperatures. To find the corresponding temperature of the gas within the chamber, initially a cap attached to a K-thermocouple with a 7.6 µm wire diameter mounted to it was placed at the top of the chamber. The K-thermocouple is similar to that described in detail in (Ossman et al. 2023). The chamber was heated to the experimental heating configuration, the temperature was taken every 5 mm on a vertical axis between the end wall and 130 mm above the end wall. The acquisition frequency was set to 10 Hz, each vertical position was measured for a duration of 5 minutes and the mean temperature at each height was recorded. The standard deviation in temperature for each vertical height was around 0.7 K largely due to measurement noise which was considered acceptable. The cap was removed and the spark plug and its top plug coil igniter were mounted at the top wall of the chamber delivering an energy discharge of approximately 30 millijoules. For an experimental procedure, the chamber is initially filled with the fuel-air premixture. Spark ignition initiates a deflagration which propagates downwards in the chamber. In many applications, including the present study, a propagating deflagration eventually develops an inverted flame front (Ponizy et al. 2014) called a tulip flame and an example of such is shown in Fig. 2.

The unburnt gas within the tulip flame pocket is considered to experience conditions comparable to adiabatic compression (Quintens et al. 2020). Therefore, it is due to tulip flame formation and the corresponding compression that the unburnt gas in the MDAID chamber within the tulip flame pocket is brought to conditions reactive enough to autoignite. The origins of a tulip flame are not as yet completely understood however, possible explanations include pressure waves, hydrodynamic instabilities and the formation of vortexes in the burnt gas (Gu'enoche. 1964; Matalon and McGreevy 1994; Matalon and Metzener 1997).

There was a piezo electric pressure sensor (Kistler 6152CU20) mounted at the bottom wall of the chamber (henceforth referred to as the end wall) with a flame guard. This monitored the pressure evolution of the chamber with a cut-off frequency of 70 kHz. The subsequent combustion regimes are observed through 40 × 60 mm UV quartz windows located at
<figure><img src="image_5.png" /><figcaption>**Fig. 2** a.) Example of a tulip flame formation in a 120 mm chamber (Quintens et al. 2019). The top of the image corresponds to the upper chamber wall, b.) A schematic drawing of tulip flame structure (Quintens et al. 2019), c.) A schlieren image of a tulip flame in MDAID chamber for a stoichiometric $C_{10}H_{22}/O_2/Ar$ mixture initially at 3 bar and the heating configuration of $T_h=453$ K, $T_m=455$ K and $T_b=441$ K. in d.), the bottom of the image corresponds to the end wall</figcaption></figure>

the bottom of the chamber. A Photron SAZ high-speed camera with a frequency of 80 kHz and an exposure time of 159 ns was used to capture schlieren images of the resulting DAIDT processes. The camera captured approximately the bottom 45 mm of the chamber which is the region in which the DAIDT processes occur. The optical schlieren system is similar to that described by Quintens et al. (2019, 2020). A higher capture speed was required to capture the detonation transition process. For these schlieren images, an ultra-high-speed camera (Shimadzu HPVX2) running at frequencies ranging between 0.5 and 2 MHz was used. This ultra-high-speed camera was mounted perpendicular to the high-speed camera and a cube beam-splitter is used so that both cameras simultaneously record images of the ensuing combustion regimes. Due to the perpendicular placement, camera images taken from the ultra-high-speed camera are in a reverse horizontal sense to those taken by the high-speed camera. The ultra-high-speed camera could only record 256 frames, therefore acquisition had to be well synchronized to capture the desired regimes.

## 2.1 Mixture Preparation

In this present work, stoichiometric 5%H₂/C₁₀H₂₂/O₂/Ar mixtures were investigated. The 5% H₂ refers to the mass percentage in the fuel mixture. The focus of this study is the specific mechanisms by which an autoignition wave transitions to detonation. A 5% H₂ fuel mass percentage mixture was chosen for this present work because when exploring the DAIDT behavior of stoichiometric n-decane/hydrogen/air mixtures with different H₂ fuel mass percentages in (Ezekwesili et al. 2025), it was found that a 5% H₂ mixture resulted in 100% transition whilst at higher H₂ percentages, the instances of detonation transition were less than 100% (Ezekwesili et al. 2025): the chosen mixture is close to the 100% transition limit. It is worth noting that both the autoignition wave and detonation transition initiated early enough in the chamber for their properties to be analyzed. Moreover, a 5% H₂ fuel
mass percentage corresponds to a 78.8% H₂ molar fuel percentage. As the molar composition determines the chemical behavior of a mixture, this mixture provides a good insight into the effects of mixing hydrogen with n-decane. The premixture composition is shown in Table 1. Synthetic air with the composition shown in Table 1 was also used. Argon was chosen for the synthetic air because compared to nitrogen, it is a monotonic gas and therefore has a higher specific heat ratio (γ). As a result, a higher temperature is attained for the same compression and an autoignitable temperature is achieved more easily.

Mixture composition was controlled through the partial pressure method. The H₂/O₂/Ar components of the mixture were prepared in gaseous form in a pressurized bottle. Liquid n-decane was injected via a syringe into the heated chamber which had been placed under vacuum beforehand. The n-decane immediately vaporized upon injection and the increase in the partial pressure was measured by a heated capacitive pressure sensor (MKS baratron 631) with a sensitivity range of 0–1300 mbar and a precision of 0.1 mbar. Before adding the gaseous mixture to the chamber, the gaseous mixture bottle was rotated to ensure mixing homogeneity between the low-density hydrogen and synthetic air. The gaseous mixture was then added slowly to the heated chamber to avoid re-condensation of the vaporized n-decane. During the gaseous mixture addition, the overall chamber pressure was measured by a 0–13000 mbar capacitive pressure sensor (MKS baratron 870). The heated chamber containing the complete premixture was left for 10 minutes to homogenize. At least 10 experiments were performed for each temperature gradient condition.

## 2.2 Varying Temperature Gradient 5%H₂/C₁₀H₂₂/O₂/Ar

The effect of changing temperature gradient is the principle focus of part 2 of the present study. In all tests, the 5%H₂/C₁₀H₂₂/O₂/Ar mixtures were initially at 3 bar. The top (T₁) and middle (T₂) heating cartridge temperatures were set to 453 K and 455 K respectively. The temperature gradient was varied through changing the temperature of the bottom heating cartridge (T₃). T₃ temperatures of 433 K, 441 K, and 443 K were examined in this present work. The resulting temperature gradient conditions will be referred to as strong, standard and weak temperature gradients henceforth. Figure 3 shows the initial temperature and temperature gradient profiles at each of the different temperature gradient conditions. In all experiments, the tulip flame had already progressed far in the chamber by the time the autoignition processes began. Therefore, it is the temperature profile at the bottom part of the chamber (highlighted in Fig. 3) which is significant in the detonation transition behavior and in analyzing the effects of temperature gradient.

## 2.3 Numerical Tools

A variable volume reactor (Quintens et al. 2017), which will henceforth be referred to as the 0-D compressor, was used to simulate autoignition under adiabatic and variable volume conditions. The experimental pressure data was input into the 0-D compressor and the latter simulated an adiabatic compression following the same pressure evolution. The thermodynamic properties were updated at each time step. The temperature of the points in the

<table><caption>**Table 1** Mixture compositions of fluids used in present study</caption><tr><td>Fuel-Oxidizer premixture</td><td>3.71 H<sub>2</sub> + C<sub>10</sub>H<sub>22</sub> + 17.36 O<sub>2</sub> + 65.26 Ar (molar)</td></tr><tr><td>Synthetic air composition</td><td>0.21 O<sub>2</sub> + 0.79 Ar (molar)</td></tr></table>
<figure><img src="image_6.png" /><figcaption>Fig. 3 a.) Initial temperature profile, b.) Initial temperature gradient profile for stoichiometric 5%H₂/C₁₀H₂₂/O₂/Ar mixtures initially at 3 bar and the different initial temperature gradient conditions</figcaption></figure>

compressed temperature profile was found by compressing each point in the initial tempera-
ture profile to the compressed pressure (this compressed pressure is defined in Sect. 3.1).
The compressed height of each point in the compressed temperature profile was deduced
by assuming a 1-D compression hypothesis such as that used by Quintens et al. (2020) and
also used in (Ezekwesili et al. 2025). More information on the methods used to derive the
compressed temperature profile can be found in the supplementary materials. To simulate
IDT values, a 0-D adiabatic constant volume reactor was also used. All the numerical tools
were built using the Cantera library and the mechanism selected was the n-decane Polimi
mechanism (Ranzi et al. 2014).

2.4 Verifying a Detonation Transition

In this present study a detonation transition was identified by four criteria.

1. When a kernel was observed in the schlieren images.

2. When the propagating speed of this kernel in the region of unburnt gas was found to attain the Chapman-Jouguet (CJ) velocity.

3. When strong pressure fluctuations were observed in the pressure file.

4. When strong reflected shockwaves were observed in the burnt gas after the suspected detonation kernel hit the end wall.

Criterion 2 could only be evaluated if ultra-high-speed images were available. If these
images were not available, the satisfaction of criteria 1, 3 and 4 were sufficient for the com-
bustion event to be considered as a transition to detonation.
# 3 Results and Discussion

This first part of the results and discussion section aims to analyze the detonation transition mechanisms at the standard temperature gradient condition and identify the variables which influence detonation transition behavior. This will act as the reference case.

## 3.1 Detonation Transition at the Standard Heating Configuration

Figure 4 shows the schlieren images of the combustion regime for a stoichiometric 5%H₂/C₁₀H₂₂/O₂/Ar mixture initially at 3 bar and the reference heating configuration. For each image within which the cool flame was propagating, subtracted images were created by subtracting the previous image from that image. These subtracted images highlight the transient changes which occur in the time interval between the two images, therefore through these images, the propagating disturbance representing the cool flame could be identified. Moreover, to better visualize the cool flame, a median blur filter was applied with a size ranging between 15 and 21 pixels depending on the strength of the cool flame. Quintens et al. (Quintens et al. 2020) identified different stages in the DAIDT combustion regime preceding detonation transition. These stages are shown in Fig. 4 for the MDAID chamber used in the present work. At each stage, the gas in the chamber will have different properties (temperature, pressure and composition).

As observed in Fig. 4, after ignition, the deflagration propagating down the chamber eventually forms a tulip flame which compresses the unburnt gas to a temperature high enough to autoignite. N-decane is a long hydrocarbon which experiences 2-stage ignition

<figure><img src="image_7.png" /><figcaption>**Fig. 4** Schlieren images demonstrating the different stages in a combustion regime for a stoichiometric 5%H₂/C₁₀H₂₂/O₂/Ar mixture in the MDAID chamber initially at 3 bar and the standard heating configuration (T<sub>b</sub>=441 K). Row three shows subtracted consecutive schlieren images, contrasted and blurred to better visualize the cool flame propagating into the state II gas</figcaption></figure>

<figure><img src="image_8.png" /></figure>
at low and intermediate temperatures. The 1st stage ignition along the temperature gradient results in a cool flame as shown in Fig. 4. This has also been shown by Quintens et al. (2020) in a similar DAID chamber with pure n-decane as a fuel, by using simultaneous chemiluminescence and schlieren imaging.

Comparing the experimental delays between 1st and 2nd stage ignition with values simulated in the 0-D reactor confirmed that the observed phenomenon was a cool flame. State II is the compressed state of the gas just before the passage of the cool flame. The unburnt gas autoignites from compressed conditions, therefore, it is the state II rather than the state 0 properties which determine the properties of the resulting autoignition wave. In the conditions studied in this present work, the low heat release associated with 1st stage ignition is assumed to not be substantial enough to result in a transition to detonation by the DAIDT mechanism. The more powerful 2nd stage ignition along the temperature gradient produces the main heat release (MHR) wave which has a high enough heat release to transition to detonation. State III represents the state of the gas just after the passage of the cool flame and before the passage of the MHR wave. It represents the state of the gas which the MHR autoignition wave is propagating into. How the gas conditions at each state are determined is detailed in (Ezekwesili et al. 2025) and additionally in the supplementary materials. The cool flame and MHR autoignition wave speeds were found through tracking the vertical position of the peak of the autoignition wave at each time step. Because the temperature profile is varied along a vertical axis, only the vertical component of the velocity was calculated. Table 2 summarizes the description and relevance of each of the states. Figure 5a shows a schematic demonstrating the occurrence of each state and Fig. 5b shows a schematic summarizing how the conditions at each state were calculated. More information about the process obtained to gain the state properties can be found in the supplementary materials.

As seen in Fig. 4, shockwaves are observed in the burnt gas at t+4787.5 µs indicating that a transition to detonation has occurred between t+4775.0 µs and t+4.7875 µs. However, at this capture frequency (80 kHz), the mechanism by which the detonation transition occurs cannot be determined.

Fig. 6a shows the simulated State II compressed temperature profile and corresponding temperature gradient profile for a representative experiment from the standard heating configuration group and Fig. 6b shows the corresponding simulated compressed State II $d\tau_i/dT$ profile.

These compressed temperature profile properties are estimated using the methods detailed in (Ezekwesili et al. 2025) and in the supplementary materials. The MHR wave propagates into state III gas. Therefore, the simulated state III speed of sound (determined using the methods detailed in (Ezekwesili et al. 2025) and in the supplementary materials) was used in combination with the experimental wave speed to determine the MHR wave Mach number. Figure 6c shows the average experimental MHR speed against domain posi-

<table><caption>**Table 2** Summary of all the states referred to in this present work</caption><tr><td>State 0</td><td>The initial mixture conditions</td></tr><tr><td>State I</td><td>The mixture when the spark plug ignited (identical conditions to state 0)</td></tr><tr><td>State II</td><td>The compressed state of the gas just before the onset of the cool flame</td></tr><tr><td>State III</td><td>The state of the gas before the onset of the MHR flame</td></tr></table>
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 5** a.) Schematic demonstrating the occurrence of each state, b.) Schematic demonstrating the temperature and pressure evolution as a gas passes through the different states as well as the method by which the different states properties were determined</figcaption></figure>

tion averaged across all experiments at this heating configuration and Fig. 6d shows the corresponding experimental Mach number. Due to the limitations of the 0-D tools used to simulate the compressed temperature profile, the chamber positions of certain MHR wave behaviours in Figs. 6c and 6d will not perfectly match the chamber position in the simulated compressed temperature profile properties in Figs. 6a and 6b. However, the simulated compressed temperature profile characteristics can still be used to provide a qualitative explanation of the observed MHR wave speed behaviours. Domain positions of interest are labelled by numbers in Fig. 6a and 6b and the corresponding domain positions are labelled by the same number but with a prime symbol in Figs. 6c and 6d.

Between the time when the MHR wave first appeared and the time just before the MHR wave transitioned to detonation, the simulated speed of sound in the unburnt gas was found to vary only by a maximum of 6 m/s within the limitations of the 0-D analysis. Therefore, it is assumed that the main contributor to the change in Mach number is the variations in the MHR wave speed (which is shown in Fig. 6c). It is recalled from Eq. 1 that lower $dT/dx$ and lower $d\tau_i/dT$ values lead to a faster autoignition wave speed. As shown in Fig. 6b, although the $d\tau_i/dT$ value increases as the end wall is approached, the effects of the change in $dT/dx$
<figure><img src="image_11.png" /><figcaption>**Fig. 6** For the 5%H₂/C₁₀H₂₂/O₂/Ar mixtures initially at 3 bar and the standard heating configuration (T_b=441 K): **a.)** State II compressed temperature and temperature gradient profile for a representative experiment, **b.)** State II compressed dτᵢ/dT profile for a representative experiment, **c.)** Averaged experimental MHR wave speed, **d.)** Averaged experimental MHR wave Mach number against domain position. In **c.)** and **d.)**, dashed lines represent the speed and Mach number standard deviation at each chamber position</figcaption></figure>

were more significant and therefore dominated over dτᵢ/dT characteristics in determining the autoignition wave speed behavior.

The region of increasing dT/dx between positions 1 and 2 in Fig. 6a corresponds to a region of decreasing speed and Mach number between domain positions 1' and 2' in Figs. 6c and 6d. The region of decreasing dT/dx between domain positions 2 and 3 in Fig. 6a corresponds to a region of MHR acceleration between domain positions 2' and 3' in Figs. 6c and 6d. Shortly after the acceleration period between domain positions 2' and 3', a transition to detonation occurs. Acceleration preceding the detonation transition is consistent with the SWACER mechanism, however the detonation transition occurs, on average, at an MHR Mach number between 0.25 and 0.3 which is relatively low.

For ten of the experiments performed at this heating configuration, Fig. 7 shows the subtraction of two consecutive schlieren images of the chamber in the frames just before the detonation consumes all of the unburnt gas. Points of interest are labelled by numbers.

In the subtracted images, the lower boundary of the light region, indicated by point 2, represents the MHR autoignition front location at the present time step and the top of the light boundary, indicated by point 1, represents the location of the MHR autoignition front in the previous time step. The thicker this boundary, the larger the distance moved by the front in one timestep and therefore the faster the autoigniting front. Several observations can be made in this figure: Firstly, at point 4, alongside the vertically propagating MHR wave (henceforth referred to as the primary MHR wave), there is a laterally propagating MHR wave. This laterally propagating MHR wave is observed in experiments 3,4,5,6,7,9 and 10. At point 3, a kernel, can actually be observed originating from the intersection between the primary and laterally propagating MHR wave. This kernel is assumed to be a developing detonation kernel. At point 5, there is an autoignition event occurring at the end wall whilst the primary MHR wave is propagating. This end wall autoignition event is also observed in
<figure><img src="image_12.png" /><figcaption>**Fig. 7** Subtracted and contrasted consecutive schlieren images of the two consecutive frames before the detonation kernel consumes all of the unburnt gas, recorded by the high-speed camera at a frequency of 80 kHz for 5%H₂/C₁₀H₂₂/O₂/Ar mixtures initially at 3 bar and the standard heating configuration (T_b=441 K)</figcaption></figure>

experiments 1,2,5,6 and 8. At point 6, kernels can be seen appearing at the end wall beneath the primary MHR waves, these are assumed to be detonation kernels. The assumptions of the nature of the observed kernels will be defended in section 3.1.3. To explain these observed events, ultra-high speed schlieren images were taken of the combustion regimes with higher frame rates ranging from 0.5 MHz to 1 MHz. Due to the experimental set-up, these images are in a reverse horizontal direction to those taken by the high-speed camera. Different experiments at the standard heating configuration are considered, see Figs. 8 and 9.

In Fig. 8, at time t, a kernel (K1) starts to form at the intersection between the primary MHR wave and the lateral autoignition wave. This kernel continues to propagate outwards until it meets the end wall and reflects. This reflected kernel (K2) goes on to consume the rest of the unburnt gas. This mixture had a simulated state III mean temperature and pressure of 19 bar and 981 K. Using the Cantera shock and detonation toolbox (Browne and Ziegler 2004), these state III conditions corresponded to a CJ speed of 1754 m/s. The CJ speed will only be attained in unburnt gas. Moreover, the detonation propagates out spherically and will attain different speeds at different radial positions. The K1 kernel speed ranged between approximately 1375 and 1750 m/s. The K2 speed ranged between 1350 m/s and 1930 m/s. Therefore, it is hypothesized that kernel K1 is a developing detonation kernel which has not yet attained the CJ speed and K2 is a detonation kernel. Figure 9 shows the ultra-high speed schlieren images taken for another experiment at this heating configuration at a frequency of 1 MHz.

As seen in Fig. 9, a kernel (K1) forms at the intersection of the primary MHR wave and the laterally propagating autoignition wave, similarly to the experiment in Fig. 8. This kernel continues to propagate outwards, however, at t + 4 µs, kernels (such as kernel K2 in Fig. 9) start propagating at the end wall at the same time that K1 is propagating. Using the CJ speed comparison method discussed earlier, both kernels K1 and K2 attained the detonation velocity. Therefore, K1 and K2 are hypothesized to be detonation kernels.

Therefore, in this transition mechanism, detonation kernels originated from both the intersection of the primary MHR and lateral autoignition wave and also from the end wall. In all experiments at this heating configuration captured by the ultra-high-speed camera,
<figure><img src="image_13.png" /><figcaption>**Fig. 8** Ultra-high-speed schlieren images of the combustion regime for a stoichiometric 5%H₂/C₁₀H₂₂/O₂/ Ar mixture initially at 3 bar and the standard heating configuration (T_b=441 K) taken at a frequency of 0.5 MHz. The subtracted images are of consecutive frames</figcaption></figure>

every detonation kernel originating from the primary MHR wave originated from the inter-section between the primary MHR wave and lateral autoignition wave.

In order to identify the variables that influence the detonation transition behavior, the underlying phenomenon behind the observed detonation transition behavior in Figs. 7, 8 and 9 must be explained. To explain this behaviour, the concept of the time to ignition, the effects of pressure waves and the origins of the laterally propagating autoignition wave need to be understood.

### 3.1.1 Time to Ignition and The Role of Pressure Waves

At a given instant, a pocket of gas will have a time to ignition which will be denoted by the symbol $\tau_i^*$. This is the time it would take that pocket of gas to autoignite from the conditions at that instant. The $\tau_i^*$ value is a measure of how close the gas is to autoigniting and is therefore a measure of reactivity. A $\tau_i^*$ value of 0 means that the gas is autoigniting. Figure 10 shows a schematic of the propagation of an MHR wave. The relative $\tau_i^*$ values of the unburnt gas are represented by color intensity.

The pockets of gas undergoing 2^nd^ stage ignition as part of the primary MHR wave will induce powerful pressure waves which will propagate spherically and reflect at reflective surfaces. The propagating tulip flame will also induce weak pressure waves. Due to
<figure><img src="image_14.png" /><figcaption>**Fig. 9** Schlieren images of the combustion regime for a stoichiometric 5%H₂/C₁₀H₂₂/O₂/Ar mixture initially at 3 bar and the standard heating configuration (T_b = 441 K) at a capture speed of 1 MHz. The subtracted images are of consecutive frames</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 10** Schematic illustrating the change in $\tau_i^*$ values during the propagation of an MHR wave</figcaption></figure>
the spherical propagation of the pressure waves, the further a point from the source of the incident or reflected pressure wave, the weaker the amplitude of the pressure experienced. Therefore, as shown in Fig. 10, the zone of unburnt gas which will have the lowest $τ_i^*$ values at a given instant is the gas beneath the propagating MHR wave. This is not only because this gas is next in line to autoignite but also because this gas experiences the strongest pressure waves from the propagating MHR wave. Other zones with decreased $τ_i^*$ values are at the reflective surfaces in the unburnt gas due to the effects of reflected pressure waves and additionally in the conduction region ahead of the tulip flame front where the temperature is slightly elevated. However, it should be noted that this conduction region is likely very thin.

The propagating MHR wave will compress the unburnt gas beneath it increasing both the temperature and pressure and decreasing the overall $τ_i^*$ values as demonstrated by the color evolution of the unburnt gas with time in the schematic in Fig. 10. It is hypothesized that eventually there will reach a point where the $τ_i^*$ values in the reactive zones can become so low that the passage of an induced or reflected pressure wave, instead of reducing the $τ_i^*$ value further, will actually trigger instant autoignition of the gas. At this point, the heat release from autoignition and the pressure wave are coupled, leading to a developing detonation. Moreover, the passage of reflected pressure waves at reflective surfaces such as the end wall can lead to premature autoignition of the unburnt gas there. Such a phenomenon has been observed in (Yu and Cheng 2015). This can lead to the gas at the end wall autoigniting at the same time that a pocket of gas higher up in the chamber autoignites as part of the primary MHR wave. The $τ_i^*$ distribution of the unburnt gas is largely a function of initial temperature gradient.

### 3.1.2 Origins of the Laterally Propagating Autoignition Wave

It was observed in Figs. 7, 8 and 9 that the hypothesized detonation kernels always originated from the intersection between the lateral autoignition wave and the primary MHR wave. Figure 11 shows the high-speed schlieren images for an experiment at the standard heating configuration. In Fig. 11a, the reactive regions with lower $τ_i^*$ values (identified in Sect. 3.1.1) are highlighted.

<figure><img src="image_16.png" /><figcaption>Fig. 11 Schlieren images before detonation transition for a stoichiometric 5%H₂/C₁₀H₂₂/O₂/Ar mixture initially at 3 bar and the standard heating configuration (T_b = 441 K) taken at a frequency of 80 kHz. The subtracted images are of consecutive frames</figcaption></figure>
Region 1 is the gas beneath the propagating MHR wave. Region 2 is the reflective sur-
face in the unburnt gas closest to the primary MHR wave which in this experiment is the end
wall directly underneath the primary MHR wave. Region 3 is the conduction region ahead
of the tulip flame front. Region 4 is where regions 1 and 3 intersect in a plane perpendicular
to the schlieren images and therefore this region experiences two phenomena which lead to
lower τᵢ* values. As observed in Fig. 11b, it is approximately at this region 4 position that
the lateral autoignition wave initiates.

The heat release from the autoignition at region 4 combined with the lateral components
of the imposed temperature gradient drive the propagation of this lateral autoignition wave.
At a time of t+75 µs, in the frame just before detonation transition, the lateral autoignition
wave and primary MHR wave have met and formed an intersection. Figure 12 shows the
high-speed schlieren images for another experiment at the standard heating configuration.

As shown in Fig. 12a, because of the way the tulip flame distributes itself, instead of the end wall, region 4 is the reflective surface in the unburnt gas closest to the primary MHR wave. Region 3 is the conduction zone ahead of the tulip flame. This introduces Region 6 which is an overlap of these two zones and therefore experiences two phenomena leading to lower τᵢ* values. As observed in Fig. 12b, the lateral autoignition wave first initiates from region 6. This lateral autoignition wave propagates until, as seen at time t+50 µs, it meets the primary autoignition wave. The light regions in the subtracted images representing the lateral autoignition wave are much thicker when compared to the lateral autoignition wave in Fig. 11. This indicates that the lateral autoignition wave is propagating at a faster speed when compared to the experiment in Fig. 11. The properties of the lateral autoignition wave largely depend on when and where the lateral autoignition wave initiates. When and where the lateral autoignition wave initiates is dependent on the position of the highlighted zones of premature autoignition which depend on how the deflagration/tulip flame distributes itself. Therefore, how the deflagration/tulip flame distributes itself has an impact on the properties of the lateral autoignition wave.

<figure><img src="image_17.png" /><figcaption>**Fig. 12** Schlieren images before detonation transition for a stoichiometric 5%H<sub>2</sub>/C<sub>10</sub>H<sub>22</sub>/O<sub>2</sub>/Ar mixture initially at 3 bar and the standard heating configuration (T<sub>b</sub> = 441 K) taken at a frequency of 80 kHz. The subtracted images are of consecutive frames</figcaption></figure>
### 3.1.3 Hypothesis of Detonation Transition Mechanism

Using the analysis from the previous paragraphs, the following hypothesis is proposed to explain the observed detonation transition behaviour: In Figs. 8 and 9, the developing detonation kernels always originate from the intersection between the lateral propagating and primary MHR wave. At this intersection, the pressure waves generated by the heat release from both reactive fronts creates a region of higher pressure, this will decrease the IDT of the gas ahead of the autoignition front and therefore locally accelerate the autoignition wave. As both waves continue to propagate, the reactivity at the intersection of the 2 waves will increase, until there reaches a point where the $τ_i*$ values ahead of the propagating autoignition wave have locally decreased to values low enough to couple with an induced pressure wave and transition to detonation by the SWACER mechanism. This explains why in Figs. 11 and 12, in the frames just before detonation transition, the lateral autoignition wave and primary autoignition wave had always met. This hypothesis is compatible with the assumption that point 3 in Fig. 7 and the kernels in Figs. 8 and 9 are developing detonation kernels. This also explains why the transition to detonation occurred at such a low Mach number in Fig. 6d. The Mach number represented in Fig. 6d is the Mach number of the primary MHR wave. However, the Mach number of the autoignition wave at the intersection of the lateral and primary autoignition wave is the real Mach number at detonation transition and is likely much higher. The faster the MHR wave and lateral autoignition wave, the sooner the reactivity at the intersection builds up to a reactivity where detonation transition can occur. This analysis is consistent with the numerical work of Taleb et al. (Taileb et al. 2023), as the group of authors showed that an angle between two propagating autoignition fronts favors the transition to detonation and the more acute the angle, the more this effect is favored.

Depending on the how fast the lateral autoignition wave and primary MHR wave intersect and transition to detonation, autoignition at a reflective surface can occur before the primary MHR wave has transitioned to detonation. It is hypothesized that at this initial temperature gradient condition, incident and reflected pressure waves originating from the deflagration, cool flame and MHR wave are enough to reduce the $τ_i*$ values of the unburnt gas at the reflective surface to values low enough for a reflected pressure wave to trigger instant autoignition. Moreover, it is hypothesized that the $dτ_i*/dx$ values of the pockets of gas near the reflective surfaces are low enough that the passage of a reflected pressure wave not only triggers instant autoignition of the unburnt gas at the reflective surface but also triggers autoignition in the neighbouring pockets of gas as it passes through them. This leads to a coupling of the pressure wave and heat release zone which leads to a developing detonation kernel in a mechanism comparable to the SWACER mechanism. The main difference from the SWACER mechanism is that in the SWACER mechanism, an autoignition wave precedes detonation transition, whilst in this mechanism the coupling of the pressure wave and heat release zone occurs instantly without a preceding autoignition wave. This would explain the end wall autoignition kernels observed in Figs. 9 and 7. There are many possible explanations as to why the $τ_i*$ values are low enough for this end wall detonation mechanism to occur. Firstly, these low $τ_i*$ values could be due to the initial temperature gradient and the proximity of the compressed temperatures to the NTC region. Another reason could be that the MHR wave and the corresponding induced pressure waves are sufficiently close to the reflective surfaces for the reflected pressure waves to be strong enough to trigger
detonation transition. Lastly, it was found in (Wu and Schießl 2025) and (Tokи and Bellan 2022) that due to the Soret effect - thermophoresis - in boundary layers, if the free stream temperature is higher than the wall temperature, species migrated away from the cold wall. In the heating configuration used in the present work, the temperature was a minimum at the end wall, therefore it is possible that the low-density hydrogen could have migrated to the warmer core of the chamber. Simulations found that for mixtures with the same initial conditions and the same molar amounts of n-decane and oxygen, as the amount of hydrogen decreases, the IDT decreases. Therefore, the lower $\tau_i^*$ values near the end wall could also be a consequence of the migration of hydrogen due to the Soret effect.

Therefore, it is the formation of zones of locally increased reactivity which influence the mechanism by which a detonation transition occurs. As discussed, how the deflagration distributes itself influences if a lateral autoignition wave forms and the speed of said wave. Therefore, how the deflagration/tulip flame distributes itself has an indirect influence on the detonation transition mechanism. Moreover, if there were a longer chamber and the pressure waves had further to travel to reach the reflective surfaces, perhaps the incident and reflected pressure waves would not be strong enough to trigger detonation transition at the reflective surfaces. Therefore, the chamber geometry also has an indirect influence on the detonation transition mechanism.

## 3.2 Effects of Changing Temperature Gradient

In sect. 3.1, a hypothesis was proposed on the exact mechanism by which detonation development occurred at the standard heating configuration and the variables which can influence detonation transition behavior. This 2nd part of the results and discussion section will analyse how changing temperature gradient affects the influence of the factors identified in sect. 3.1.

### 3.2.1 Compressed Gas State

As previously discussed, the autoignition properties depend on the compressed state II conditions. Table 3 summarizes the mean state II properties and the observed detonation transition behavior at each temperature gradient condition.

As shown in Table 3, the mean state 0 chamber temperature does not vary significantly between the different temperature gradient conditions. The mean initial chamber temperature influences the initial deflagration speed; therefore, it is assumed that the deflagration speed and resulting compression rate does not vary significantly between the different temperature gradient conditions. This assumption was confirmed through comparison of the pressure evolution files between each of the temperature gradient conditions and it was found that the rate of compression was comparable between all temperature gradient conditions. As seen in Table 3, the mean state II chamber pressure decreases as $T_b$ increases. This

<table><caption>**Table 3** Percentage of cases transitioning to detonation for stoichiometric 5%H₂/C₁₀H₂₂/O₂/Ar mixtures initially at 3 bar and a heating configuration of $T_h = 453$ K, $T_m = 455$ K. At least 10 experiments were performed for each condition</caption><thead><tr><th>Temperature gradient condition</th><th>Mean state 0 temperature (K)</th><th>Mean state II pressure (bar)</th><th>Percentage transitioning to detonation (%)</th></tr></thead><tbody><tr><td>$T_b = 433$ K (strong)</td><td>451</td><td>17.99</td><td>0</td></tr><tr><td>$T_b = 441$ K (standard)</td><td>452</td><td>17.29</td><td>100</td></tr><tr><td>$T_b = 443$ K (weak)</td><td>453</td><td>17.25</td><td>100</td></tr></tbody></table>
is because the small increase in the state 0 mean temperature with increasing T<sub>b</sub> does not greatly affect the deflagration speed but does lead to a slightly earlier autoignition onset. An earlier autoignition means that the unburnt gas is subjected to less deflagration compression time before the autoignition processes begin. The autoignition processes therefore begin at a lower pressure. From the standard to the strong temperature gradient conditions, the percentage of cases transitioning to detonation decreased from 100% to 0%. Whilst Fig. 3 shows the initial temperature profile conditions, Figs. 13a and 13b shows the state II compressed temperature and temperature gradient profiles in the bottom 25 mm of the chamber where the autoignition processes were observed to occur for representative experiments from each temperature gradient condition group.

As shown in Fig. 13a, the state II temperatures are higher for the strong temperature gra-
dient condition due to the greater degree of deflagration compression as a result of the later
autoignition onset. The strong temperature gradient condition has higher temperatures but
also has higher compressed dT/dx values. The standard and weak temperature gradient con-
ditions have very similar temperature profiles until approximately the bottom 10 mm where
the weak temperature gradient condition has higher temperatures and lower dT/dx values.
The IDT values from the mean state II pressures were simulated in the 0-D reactor for a
range of temperatures. For all temperature gradient conditions, the NTC region began at a
temperature of approximately 790 K. Therefore, the compressed temperatures are relatively
close to the NTC boundary but also do not cross it.

Before presenting the schlieren images of the observed combustion regimes, the relative $\tau_i^*$ values of the unburnt gas beneath the propagating MHR waves at the different temperature gradient conditions are approximated. To do this, the IDT from state II conditions, relative to the IDT of a pocket of gas 15 mm from the end wall, was found for each point in the compressed temperature profile. This was supposed to provide an estimate of the time to ignition of the unburnt gas beneath the MHR wave at a time the MHR wave has travelled to a distance of 15 mm from the end wall. This estimate of $\tau_i^*$ does not take compression

<figure><img src="image_18.png" /><figcaption>**Fig. 13 a.** State II temperature profile, **b.** State II temperature gradient profile for representative experiments from each temperature gradient condition for stoichiometric 5%H<sub>2</sub>/C<sub>10</sub>H<sub>22</sub>/O<sub>2</sub>/Ar mixtures initially at 3 bar and different temperature gradient conditions</figcaption></figure>
history into consideration and therefore is distinct from the real value and will therefore be referred to as the TTI value. These estimates act to offer some insight into the behavior of the real $τ_i^*$ values. A distance of 15 mm was chosen as this was the approximate chamber position at which detonation transition was observed across the experiments with detonation transition in this present study

Figure 14a shows the simulated TTI profile and Fig. 14b also shows the average experimental MHR autoignition Mach number against domain position averaged across all experiments in each temperature gradient condition. These figures will be used to aid in the explanation of the observed combustion regimes.

### 3.2.2 Strong Temperature Gradient Case ($T_b = 433$ K)

Figure 15 shows the schlieren images of the combustion regime for a representative experiment from the strong temperature gradient heating configuration. As seen in Fig. 15, the MHR wave propagates and compresses the unburnt gas beneath it, a lateral autoignition wave begins to form at a time of $t+12.5 \ \mu s$ and by a time of $t+50 \ \mu s$, the lateral autoignition wave intersects with the primary MHR wave. However, a detonation kernel does not form at the intersection of the two waves and the MHR wave continues to propagate until it hits the end wall. This combustion regime can be explained as follows: In Fig. 13b, it is seen that the strong temperature gradient has higher compressed $dT/dx$ values. Despite the higher compressed gas temperatures when compared to the other temperature gradient conditions, these high $dT/dx$ values lead to higher TTI values of the gas beneath the MHR wave as shown in Fig. 14a. These higher approximated TTI values indicate that the real $τ_i^*$ values are higher at this temperature gradient when compared to the other temperature gradients indicating that the gas ahead of the MHR wave is further from autoignition and less reactive. Moreover, as seen in Fig. 14b, the MHR wave speed is much slower, which means that the overall com-

<figure><img src="image_19.png" /><figcaption>**Fig. 14 a.)** Simulated TTI values from state II conditions relative to the IDT of a pocket of gas at a distance of 15 mm from the end wall **b.)** Averaged experimental MHR autoignition wave Mach number against domain position for each temperature gradient condition. The mixtures are stoichiometric 5%H₂/C₁₀H₂₂/O₂/Ar mixtures at an initial pressure of 3 bar and different temperature gradient conditions. Dashed lines represent the Mach number standard deviation at each chamber position</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Fig. 15** Schlieren images of the combustion regime for a stoichiometric 5%H₂/C₁₀H₂₂/O₂/Ar mixture initially at 3 bar and the strong temperature gradient condition taken at a frequency of 80 kHz. Subtracted schlieren images are of consecutive frames</figcaption></figure>

pression by the MHR wave is weaker meaning even lower $\tau_i^*$ values would be required for a coupling with a pressure wave and a transition to detonation to occur. Therefore, it can be inferred that due to a combination of the higher $\tau_i^*$ values and the weaker pressure waves induced from the propagating reaction fronts, no zones with $\tau_i^*$ values low enough to couple with a pressure wave occur before the MHR wave hits the end wall. This is the case even at the intersection of the two autoignition waves where there is a local build up in reactivity.

### 3.2.3 Weak Temperature Gradient Case ($T_b = 443$ K)

Figure 16 shows the subtracted consecutive schlieren images of the chamber in the frames just before the detonation kernel consumes all of the unburnt gas. Points of interest are labelled by numbers. As observed in Fig. 16, a laterally propagating autoignition wave can be observed at point 1. Point 2 shows detonation kernels forming at the end wall before the primary MHR has transitioned to detonation. Point 4 shows a detonation kernel which appears to have originated from the intersection between the lateral autoignition wave and the primary autoignition wave. These combustion regime behaviors are similar to those observed at the standard temperature gradient condition. Point 3 however, shows a develop-
<figure><img src="image_21.png" /><figcaption>**Fig. 16** Subtracted and contrasted consecutive schlieren images in the frames before the detonation kernel consumed all of the unburnt gas, recorded by the high-speed camera at a frequency of 80kHz for 5%H₂/C₁₀H₂₂/O₂/Ar mixtures initially at 3 bar and the weak heating configuration ($T_b$=443 K)</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Fig. 17** Subtracted and contrasted consecutive ultra-high-speed schlieren images during detonation transition for 5%H₂/C₁₀H₂₂/O₂/Ar mixtures initially at 3 bar and the weak temperature gradient condition taken at frequencies ranging between 0.5–2 MHz</figcaption></figure>

ing detonation kernel which appears to originate from the bottom corner of the chamber. This is also the case in experiment 8. This was not seen at the standard heating configuration.

To better understand the transition mechanisms, Fig. 17 shows subtracted and contrasted ultra-high-speed images during detonation transitions for 4 experiments at the weak temperature gradient condition.

As shown in Fig. 17, in experiments 1, 3 and 4, detonation kernels develop at the end wall. In experiment 1, detonation kernels develop at the end wall before the primary MHR wave begins the transition to detonation. Moreover, in experiment 2, the detonation kernel develops from a location on the lateral autoignition wave below the primary MHR wave.

The following hypothesis is proposed to explain the observed detonation transition behaviour: As shown in Fig. 13b, above 10 mm from the end wall, the compressed temperature gradient does not vary significantly when compared to the standard temperature gradient condition. As a result, as shown in Fig. 14b, the primary MHR wave has a similar speed profile to that at the standard heating configuration. The main difference in behaviour is that, as shown in Fig. 14a, the weak temperature gradient condition has much lower TTI values at the bottom of the chamber which implies that in reality, compared to the standard temperature gradient condition, at the point when the MHR wave has progressed to 15 mm from the end wall, the unburnt gas has lower $\tau_i^*$ values and is therefore more reactive. This higher reactivity has many consequences. Firstly, the unburnt gas at the chamber reflective surfaces
is closer to autoignition, the lateral autoignition wave initiates sooner, propagates faster and resultingly meets the primary MHR wave faster. The propagating lateral autoignition wave also reaches the end wall faster. When this lateral autoignition wave reaches the end wall, it is hypothesized that the combination of the incident pressure waves induced from the lateral autoignition wave and the corresponding reflected pressure waves creates an additional zone of higher pressure in portions of the end wall closest to the lateral autoignition wave leading to local τᵢ* values low enough for a detonation transition to occur. This could explain the developing detonation kernel originating from the bottom corner of the chamber observed in Fig. 16. Moreover, due to the faster lateral autoignition wave speed and therefore the stronger pressure waves ahead of the lateral autoignition wave at this temperature gradient condition combined with the overall lower τᵢ* values, it can happen that a point ahead of the lateral autoignition wave is reactive enough to couple with an induced pressure wave and transition to detonation via the SWACER mechanism. Therefore, imposing a stronger temperature gradient successfully suppressed a detonation and imposing a weaker temperature gradient introduced new zones reactive enough to transition to detonation.

Temperature gradients were also explored where the sign of the gradient changed near the end wall leading to an autoignition wave propagating upwards from the end wall. However, having a higher temperature at the bottom of the chamber in this case led to more complex and less controlled gradients which are less appropriate for this fundamental analysis, therefore, these experiments were not included in the present article.

# 4 Conclusion

This study analyzed the combustion processes of 5%H₂/C₁₀H₂₂/O₂/Ar premixtures in a constant volume chamber. In particular, it aimed to identify variables encountered in practical applications which influence autoignition to detonation transition behavior and analyze the importance of these variables when the temperature gradient changed.

It was found that the determinant as to whether detonation transition occurred was the development of zones of increased reactivity under the propagating primary MHR wave with the necessary reactivity to transition to detonation. At the standard heating configuration, these zones were located at the intersection between the lateral autoignition wave and the primary MHR wave and at the end wall. At the intersection between the lateral autoignition wave and the primary MHR wave, the transition was favored by the interactions of the pressure waves issued from these two autoignition fronts, locally increasing mixture reactivity and locally accelerating the autoignition wave to a point where detonation transition by the SWACER mechanism could occur. It was also hypothesized that the end wall detonation kernels were due to the pairing between the local end wall autoignition and reflected pressure waves in a mechanism comparable to the SWACER mechanism. At the strong temperature gradient condition, the MHR front was slower. The MHR wave was so slow and the τᵢ* values of the unburnt gas between the propagating reaction fronts were so much larger when compared to the other temperature gradient conditions that no zones of - pressure wave induced - increased reactivity could attain τᵢ* values low enough to couple with a pressure wave and transition to detonation. At a weaker temperature gradient condition, due to the faster MHR wave speed and lower τᵢ* values, additional reactive zones formed,
when compared to the standard heating configuration, where the gas was reactive enough to
transition to detonation.

These results show that in this experimental configuration, the gas reactivity at the bot-
tom of the chamber and its gradient, which is contingent on the initial temperature gradient,
are key variables in determining whether a detonation transition occurs or not. However,
in a borderline condition where the system is on the verge of transitioning to detonation,
changing how the deflagration distributes itself and the strength of the incident and reflected
pressure waves at reflective surfaces can work towards suppressing detonations. These
changes can be achieved through chamber geometry. Assuming a relatively simple and sim-
ilar geometry with a premixture, it is hypothesized that a longer chamber would promote
autoignition over deflagration, which may favor the transition to detonation. However, a
shorter chamber could aid in mitigating detonation transition by promoting deflagration
over autoignition, it would also make the tulip flame appear later, or it could even suppress
it.

Finally, in the conditions for which the MHR wave propagates, an appropriate geometry
design could attenuate pressure wave reflections or avoid focusing pressure wave reflections
which would work towards suppressing detonation transition mechanisms at reflective sur-
faces triggered by reflected pressure waves. However, this large topic lies beyond the scope
of this present work and deserves a specific study of its own.

**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1007/s10494-025-00699-8.

**Acknowledgements** The authors are grateful to the Region Nouvelle Aquitaine and Europe for financial support from the CPER-FEDER, Transport and Aerotrans programs. This work pertains to the French government program "Investissements d'Avenir" (EUR INTREE, reference ANR-18-EURE-0010). Alain Claverie is acknowledged for his assistance with optical diagnostics. Sylvia Romeo and Suryadeb Malik are acknowledged for contributing to preliminary works and to the implementation of the MDAID set up.

**Author Contributions** R.E. wrote the main manuscript text. All authors reviewed the manuscript.

**Funding** Open Access funding enabled and organized by Projekt DEAL. This project received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowsk-Curie grant agreement No 956803.

**Data Availability** No datasets were generated or analysed during the current study.

**Declarations**

**Competing Interests** The authors declare no competing interests.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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## Authors and Affiliations

Roseline Ezekwesili<fnref n="1" />,<fnref n="2" />,<fnref n="4" /> · Camille Strozzi<fnref n="1" />,<fnref n="3" />,<fnref n="2" /> · Marc Bellenoue<fnref n="1" />,<fnref n="2" />,<fnref n="3" /> · Myles Bohon<fnref n="4" />

<figure><img src="image_23.png" /></figure>

Roseline Ezekwesili

r.ezekwesili@tu-berlin.de

Camille Strozzi

camille.strozzi@ensma.fr

Marc Bellenoue

marc.bellenoue@ensma.fr

Myles Bohon

m.bohon@tu-berlin.de

<footnote n="1">¹ Institut Pprime CNRS, Poitiers, France</footnote>

<footnote n="2">² ISAE-ENSMA, Poitiers, France</footnote>

<footnote n="3">³ Poitiers University, Poitiers, France</footnote>

<footnote n="4">⁴ Technical University Berlin, Berlin, Germany</footnote>