# Numerical and experimental comparison of H2/air flame-shock interaction

Emilie Yhuel, Anthony Roque Ccacya, Guillaume Ribert, Pascale Domingo, Nabiha Chaumeix

► To cite this version:

Emilie Yhuel, Anthony Roque Ccacya, Guillaume Ribert, Pascale Domingo, Nabiha Chaumeix. Numerical and experimental comparison of H2/air flame-shock interaction. Proceedings of the Combustion Institute, 2025, 41, pp.105847. 10.1016/j.proci.2025.105847. hal-05326697

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# Numerical and experimental comparison of H₂/air flame-shock interaction

Emilie Yhuel<sup>a ID</sup>, Anthony Roque Ccacya<sup>b ID</sup>, Guillaume Ribert<sup>a ID,*</sup>, Pascale Domingo<sup>a ID</sup>, Nabiha Chaumeix<sup>b ID</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

**Keywords:**

Hydrogen combustion

Supersonic

LES

Experimental schlieren

## ABSTRACT

A high-fidelity three-dimensional numerical simulation is performed to replicate the experimental shock tube setup of the ICARE laboratory, where a hydrogen-air flame-shock interaction (FSI) is studied. Following the experimental procedure, a lean flame ($\phi = 0.8$) is ignited at the closed end of a rectangular channel before a shock wave, traveling at a Mach number of $M_s = 1.9$, is triggered from the opposite side. The FSI occurs when the shock wave encounters the laminar flame in the visualization window, where experimental schlieren images have been captured. To reproduce this experiment, the fully compressible Navier-Stokes equations are solved using the San Diego mechanism, which includes nine reacting species (excluding nitrogen oxides) and 23 kinetic reactions. Species diffusion is modeled using the Hirschfelder-Curtiss model combined with thermal diffusion (Soret effect). Additionally, gravity is accounted for in the simulation.

The three major observations of the experiment were well captured by the numerical simulations through a comparison of experimental and numerical schlieren images: the laminar flame propagation and its interaction with adjacent walls; the first FSI, which leads to the formation of Richtmyer-Meshkov instabilities (RMI); and finally, the second FSI, occurring when the reflected shock wave travels back towards the entrance, generating reactive boundary layers and multiple shock interactions within the funnel of fresh gases produced by the RMI.

## 1. Introduction

Advancing our understanding of hydrogen combustion is essential for ensuring the safe use of future systems involving hydrogen production, transport or transformation. Indeed, hydrogen ($H_2$) is very diffusive, i.e., prone to leak, very reactive in air, and capable of rapidly transitioning from deflagration to detonation (DDT) under favorable conditions. To address the risks associated with DDT, lab-scale experimental studies are conducted to analyze the characteristics of $H_2$ flames propagating in confined environments [1,2], as well as their interactions with obstacles [3] and shock waves [4-6]. Experimental data play a crucial role in validating numerical simulations, which can then be used with greater confidence during the pre-design phase of combustion chambers, given the significant safety challenges posed by DDT. For instance, the centimeter-scale flame-shock interaction (FSI) experiment of Thomas et al. [7] has been used to validate the direct numerical simulations of Zhu et al. [8], just as the experiments of Yang and Radulescu [4,5] have been simulated by Xiao et al. [9].

Numerically predicting these complex phenomena presents significant challenges from both multi-physics and multi-scale perspectives [10]. Moreover, computations can quickly become extremely

expensive when the computational domain is large or when high resolution is required to capture all relevant phenomena. Tang et al. [11] have explored very small 2D domains (2 mm in height) which allows to maintain adequate resolution. While keeping in check the CPU-cost, Gamezo et al. [12,13] simulated flame-shock-wall interactions in 3D using symmetry assumptions and adaptive meshing to refine specific regions, highlighting the crucial role of sidewalls and reactive boundary layers. Bambauer et al. [14] investigated flame-shock interactions (FSI) without walls, focusing on Richtmyer-Meshkov instabilities at the center of the domain. Other studies [15-17] examined FSI with walls using simplified chemistry or boundary conditions to facilitate the analysis. Finally, recent works [4,5,18] have tackled a particularly challenging configuration in which an incoming shock wave interacts with a laminar flame in a semi-closed channel, reflects off the back wall, and generates a second FSI as the reflected shock wave propagates back towards the inlet before exiting the domain.

These studies have highlighted the difficulty of simulating a realistic flame-shock interaction while maintaining a reasonable computational cost. Having a reliable 3D digital twin enables a deeper understanding

<footnote><sup>a</sup> CORIA-CNRS, Normandie University, INSA de Rouen Normandie, Rouen, 76000, France</footnote>

<footnote><sup>b</sup> CNRS-INSIS, I.C.A.R.E., Orléans, 45071, France</footnote>

<footnote>* Corresponding author.
E-mail address: guillaume.ribert@insa-rouen.fr (G. Ribert).</footnote>
of the physics behind experimental observations, which can be challenging to interpret using only 2D representations. This study aims to achieve this mutual enrichment between experiment and simulation by describing the flame-shock interaction in a semi-closed channel from a recent laboratory-scale experiment.

## 2. Target configuration and numerical setup

The target experiment is the ICARE laboratory shock tube [19,20], which consists of a high-pressure chamber separated from the observation area, set to $P = 0.2$ bar and $T \approx 295 \pm 10$ K, by a diaphragm. Once the diaphragm is ruptured, a shock wave propagates at a Mach number $M_s \approx 1.9 \pm 0.05$ towards the close end of a rectangular channel ($4.5 \times 2.1 \text{ cm}^2$) where a lean H$_2$/air flame (equivalence ratio $\phi \approx 0.8 \pm 0.05$) has been ignited by a spark. The resulting flame-shock interaction is visualized with the schlieren technique, and the shock propagation is detected by wall pressure sensors. The experimental observation window measures $L_{Exp} = 14$ cm long from the right wall.

Such a configuration is simulated with the numerical code SiTCom-B [21,22], already used in [18] for 2D simulations of a model shock tube inspired by ICARE's setup. SiTCom-B is a fully compressible structured code working with cartesian grids based on an explicit Finite Volume scheme. The code has a fourth-order centered skew-symmetric-like scheme for the convective terms [23] and a fourth-order centered scheme for the diffusive terms. An explicit formulation is employed for the integration of finite-rate chemical kinetics. A fourth-order Runge-Kutta method is applied for the time integration. Besides, second and fourth-order artificial dissipation terms of Swanson et al. [24] are implemented to overcome spurious oscillations and damp high-frequency modes.

In agreement with the experiment, a hydrogen-air flame ($\phi = 0.8$) moves from the closed end of the channel to the open part, from which a shock wave propagates at a Mach number $M_s = 1.9$. The sketch of the setup is given in Fig. 1 (left). The dimensions of the ICARE experiment simulated with SiTCom-B are also detailed along with the mesh resolution and the boundary conditions.

To mimic the experiment, isothermal no-slip walls are set to 300 K (as in [25]). The fully compressible Navier-Stokes equations are then solved, plus nine equations for the transport of the reactive species thanks to the San Diego mechanism in its most recent version [26]. An explicit formulation is employed for the integration of finite-rate chemical kinetics. The Hirschfelder and Curtiss model [27] is combined with thermal diffusion (Soret effect), applied only for light species having a molecular weight less than $5 \text{ g mol}^{-1}$ [28]. The gravity force is activated in the $-\bar{y}$ direction.

Following the recommendations given in [18], the mesh resolution is fixed to $\Delta x_i = 62.5 \text{ µm}$, on the distance $L_{Exp}$. The influence of the mesh resolution can be found in [18]. The mesh is then coarsened up to 625 µm in the left part of the domain to reduce the computational cost over a length of about 10 cm from the left inlet/outlet of the domain sketched in Fig. 1. A mesh refinement up to 15 µm is applied at the walls to capture the main features of the resulting reactive boundary layers (RBL) along with the Richtmyer-Meshkov instability that will impact the right wall once the incoming shock is reflected [18]. As such refinement is still insufficient to describe the boundary layer [11], the Smagorinsky model is then activated near the wall on a thickness of 312.5 µm in the areas where the boundary layer could be under-resolved. Indeed, there is no wall-damping function specifically developed for the present high-speed flow. If activated, the model constant is set to $C_s = 0.15$, and the Prandtl and Schmidt turbulent numbers are fixed to $Pr_t = 0.7$ and $Sc_t = 0.7$, respectively. This model is disabled in the rest of the domain, to avoid the thickening of the shock waves, which would then be accompanied by a poor estimation of their propagation speed. Once Richtmyer-Meshkov instabilities affect the right wall in a similar way to an impinging jet, turbulent structures will form. It may then be necessary to activate the

<figure><img src="image_4.png" /><figcaption>Fig. 1. Sketch of the numerical configuration mimicking ICARE's shock tube (left) and first stages of the flame propagation from the closed end of the channel.</figcaption></figure>

Smagorinsky model across the entire domain. The turbulent-to-laminar viscosity ratio ($v_{turb}/v_{lam}$) is presented in the appendix for an instant that is representative of the second FSI. Except on the walls, this ratio remains low (below 10), only taking on significant values at shock wave locations. As these discontinuities are already handled by the shock-capturing approach, adding subgrid viscosity would be redundant (see Merlin et al. [29]). Therefore, the LES model is only activated near the wall throughout the entire simulation. In other words, MiLES (implicit LES without additional subgrid-scale modeling) is employed except in a very thin layer close to the wall where additional viscosity is added. The advantage of this approach is that it minimizes the addition of numerical viscosity, ensuring close agreement with instantaneous experimental results and preventing the blurring of small structures.

## 3. Laminar flame propagation

The lean H$_2$-air mixture is ignited on the right wall. The spark ignition is represented in the simulations by a 1D premixed flame profile interpolated in a half-sphere of radius 5 mm at the center of the right wall. The flame thus propagates from right to left in the channel, and the half-sphere transforms into a glove finger flame, as depicted in Fig. 1 (right). Extinction zones appear when the flame touches the cold walls, especially in the shock tube corners where the flame is very stretched, as observed already by Xiao et al. [30] in a square section channel. This 3D flame is compared to the experimental schlieren in Fig. 2, for the same position of the flame front on the axis of symmetry.

Both the numerical and experimental flames are very similar. However, the numerical flame propagates slightly faster than the experimental flame, taking less time to reach the same position. The observed difference remains small (5% at $t = 2.4$ ms, and 6.7% at $t = 4.1$ ms), and it can be attributed to the uncertainty of the equivalence ratio set in the experiment ($\phi \approx 0.8 \pm 0.05$) or, more probably, to the imposed temperature ($T \approx 295 \pm 10$ K), which differs from the numerical value, $T = 300$ K. The estimation of the difference in shape between these two flames is carried out by recording the position of points A, B, A', B' and O over time in order to form the angles $\theta_1 = \bar{A}'OB'$ and $\theta_2 = \bar{A}OB$ (see Fig. 3). O is on the symmetry axis, A' and B' (A and B) are 5 mm (10 mm) from the upper and lower walls, respectively, to maximize the flame curvature effects.

The relative differences between the angles $\theta_1^{Exp}$ and $\theta_1^{Simu}$ (same for $\theta_2$), are calculated as

$$E_{R_n} = 100 \times \frac{\theta_n^{Exp} - \theta_n^{Simu}}{\theta_n^{Exp}}, \quad n = 1 \text{ or } 2, \qquad (1)$$

and the results are reported in Fig. 3 for five specific experimental times. A very good comparison is observed with a maximum deviation
<figure><img src="image_5.png" /><figcaption>Fig. 2. Schlieren of flame propagation in the plane of symmetry. Simulation at the top. Experiment at the bottom. Graduation in cm. Time in ms.</figcaption></figure>

of 10% between the numerical and experimental results found for $\theta_1$, i.e. where the flame is more stretched. The angles recorded on the experimental schlieren are always larger than in the simulation because the propagation speed is slightly lower in the experiment compared to the simulation. Indeed, the higher the speed, the smaller the angle and the more the flame is stretched.

## 4. Flame-shock interaction

A pressure-temperature discontinuity is introduced in the domain (see Fig. 1) at 14.9 cm from the right wall, and corresponding to a Mach number $M_s = 1.9$. The post-shock pressure and temperature conditions of the shocked fresh gases, calculated using the Rankine-Hugoniot relations, are set to $P_s = 0.8$ bar and $T_s = 483$ K, respectively. As already observed in [18], the incoming shock wave will interact with the flame front (FSI 1) before reflecting on the right wall, leading to a reflected shock that will interact with the distorted flame front (FSI 2).

For the shock to interact with a flame having the same shape in the experiment and the simulation, the numerical flame at $t = 4.9$ ms ($E_{R2} = 2.5\%$ in Fig. 3) is kept for the FSI, because it has a smaller relative deviation than the flame at the same position at $t = 4.7$ ms ($E_{R2} = 4.65\%$). However, this flame has a longer burnt gas length of 8.94 mm ($\approx 6\%$), which will influence the second FSI after the shock reflection on the right wall of the channel. The tip of the flame front is located at 14.55 cm from the right wall (wall: $x = 0$ cm).

Comparisons are made using experimental 2D schlieren and integrated 3D numerical images, the latter being based on density gradients ($\nabla\rho$) [31],

$$S(x, y, z) = \beta \exp \left( - \frac{\kappa |\nabla \rho|}{\max(\nabla \rho)} \right), \quad (2)$$

with $\beta = 0.8$ and $\kappa = 15$, and integrated along the depth $z$ such that

$$S(x, y) = \frac{1}{N_z} \sum_{k=1}^{N_z} S(x, y, z). \quad (3)$$

$N_z$ is the number of cells following $z$.

### 4.1. First interaction (FSI 1)

In order to compare the simulation with the experiment, the initial time $t_{ISI} = 0$ µs (incident shock interaction) corresponds to the beginning of the interaction between the shock and the flame front.

In Fig. 4, the numerical (left) and experimental (right) schlieren are visible at several instants and depict the first flame-shock interaction (FSI 1) until the incident shock reaches the right wall.

<figure><img src="image_6.png" /><figcaption>Fig. 3. Study of the laminar flame curvature, through the position of five characteristic points (A, B, A', B' and O) forming the angles $\theta_1 = \bar{A}'\bar{O}B'$ and $\theta_2 = \bar{A}\bar{O}B'$.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Temporal evolution of the first flame-shock interaction (FSI 1). Left: simulation; Right: experiment.</figcaption></figure>

The 3D simulation describes the experimentally observed flame-shock interaction very well. The flame front is flattened, pushed towards the right wall by the incoming shock to finally be the site of Richtmyer-Meshkov instabilities (RMI). The incident shock wave slightly curves when propagating in the burnt gases. The flow structure is thus well captured by simulation, as shown in Fig. 5, where a zoom is provided on the FSI and the subsequent RMI formation, between $t_{ISI} + 16$ µs and $t_{ISI} + 76$ µs.

The FSI (Fig. 5(a)) leads to a flattened flame front (FF) and a transmitted shock wave (TS) propagating faster in the burnt gases than the part of the incident shock (IS) still present in the fresh gases. Reflected waves (RW) from the FSI and propagating in the opposite direction of the incident shock are visible in the fresh gases. Two flame fronts are visible in the center of the domain (Fig. 5(b)): the central RMI forming an elongated mushroom and the much less stretched flame front at the side walls of the channel (FFW) due to the low flow velocity in the boundary layer. The flame front at the wall is however less visible on the numerical schlieren, due to the integration along $z$, which dampens the weaker gradients. It is nevertheless very present when
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Zoom on schlieren images for the FSI 1. Down: simulation; Up: experiment.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Two views of the flame front defined by the progress variable $c = 0.5$ and colored by temperature $T \in [300; 1700]$ K (orange). The isosurface of $\nabla P$ is given in transparent white. The white and black isolines are located in the mid-plane of the channel. $t = t_{ISI} + 56$ µs.</figcaption></figure>

looking at the 3D flame front (see Fig. 6). The small instabilities (I) attached to the RMI in Fig. 5(c) are also visible with a 3D surface, while they are attenuated on the integrated schlieren. A folded flame front (FFF) is visible in the experiment and the simulation (Fig. 5(d)). Since the flow velocity at the wall is lower than at the center, the flame front is, therefore, strongly folded near the wall. Similarly, two shock fronts are visible in the burnt gases (TS and TSW). The first front (TS) is ahead of the other (TSW) due to the higher velocity at the center of the domain and lower at the walls. It leads to a shock bending along $z$.

From $t_{ISI} + 76$ µs, the flame front appears wrinkled (I in Figs. 5 and 6) in experimental schlierens, but it is much less visible in simulations (Fig. 6) because the mesh resolution is certainly not fine enough to capture the small structures present in the flame front. Indeed, such structures have already been observed in a similar configuration [18]

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Wall pressure in the mid-plane of the channel (c/2), on the lower wall. The right wall is at $x = 0$ cm.</figcaption></figure>

with a regular mesh of 31.25 µm. Nevertheless, $\Delta x_i = 62.5$ µm is sufficient to capture the flame behavior interacting with shocks or in the boundary layers. The wall pressure is plotted in Fig. 7 in the mid-plane of the channel (c/2), on the lower wall.

When the incident shock crosses the flame front, a pressure peak twice as high as the initial post-shock pressure appears, corresponding to an overpressure located between the lower wall and the flame front (see Fig. 5(b)). At $t_{ISI} + 56.4$ µs, two pressure peaks can be distinguished. The one on the right corresponds to the shock wave propagating towards the bottom of the channel. The second corresponds to the overpressure previously observed. At $t_{ISI} + 76.4$ µs, only the first peak remains visible, the burnt gases having dissipated the second one. Finally, the pressure profiles at $t_{ISI} + 96.4$ µs and 116.4 µs correspond to the transmitted shock wave propagating in the burnt gases, with a constant maximum close to 1.6 bar.

## 4.2. Second interaction (FSI 2)

Since the initial length of the burnt gases is larger in the simulation than in the experiment, a time lag appears as soon as the incident shock wave reflects off the right wall. Accordingly, a new initial time is defined when the reflected shock starts to interact with the flame, $t_{RSI} = 0$ µs (Reflected Shock Interaction), and numerical and experimental schlierens can, therefore, be compared, as shown in Fig. 8.

The overall dynamic of the experimental FSI 2 is still very well represented by the simulation. The RMI interacts with the reflected shock, altering its shape before crashing against the right wall. The reflected shock is also affected by its interaction with the RMI, bending towards the center of the channel in the fresh gases since its propagation speed is faster in the burnt gases than in the fresh gases. A complex set of reflecting compression waves appears in the center of the channel, located in the fresh gases. Near the wall, the flame succeeds in attaching to the shock crossing it, allowing the development of a reactive boundary layer as in [12,18].

A zoom on the FSI 2 and the formation of the shock bifurcation is given in Fig. 9.

Before the start of the FSI 2 (Fig. 9(a)), the RMI appears very stretched, and thin boundary layers (TBL) of burnt gases are attached to the walls. The reflected shock (RS) is not bent anymore after reflecting off the right wall (see Fig. 4), and the head of the flame exhibits a curvature that is similar in both numerical and experimental approaches. Once the reflected shock crosses the head of the RMI, a folded flame front (FFF) appears before impacting the right wall like an impinging jet [32,33]. A turbulent flame (TFF) also develops and intensifies once the reflected shock crosses it, increasing local instabilities. Once the shock has crossed the flame front, two lines can be observed on the schlieren images, which correspond to shock waves in the mid-plane
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Temporal evolution of the second flame–shock interaction (FSI 2). Left: simulation; Right: experiment.</figcaption></figure>

and near the wall, as for the FSI 1. Such a fluid dynamic is highlighted in Fig. 10, where the FSI 2 is detailed from simulation for five specific times.

At $t_{RSI} - 6.4$ µs and $t_{RSI} + 3.6$ µs, the flow structure is composed of an RMI, forming a funnel of fresh gases, and a reflected shock coming from the right wall. Once the reflected shock penetrates inside the funnel, multiple wave interactions occur while the reflected shock still in the burnt gases progresses much faster towards the entrance, on the left ($t_{RSI} = 23.6$ µs and $t_{RSI} + 43.6$ µs). Two oblique shocks develop ($t_{RSI} = 83.6$ µs), both connected by a plane shock in the center. At this stage, a highly turbulent flame becomes visible, in contrast to the integrated numerical schlieren, the adjustment of which erases the flame surface wrinkling. A portion of the flame front remains trapped in the boundary layer along the walls due to the nearly zero velocity at the no-slip walls and in the channel corners. Following the FSI 2, multiple wave reflections occur, leading to a pressure increase in the domain, especially when the RMI impacts the rear wall at $t_{RSI} + 43.6$ µs (light blue on walls). Such wall pressure is recorded (Fig. 11) in the center of the bottom and right end walls. At $t_{RSI} - 6.4$ µs, the reflected shock is identified by the peak of pressure around 1.75 bar at the bottom wall.

When the shock leaves the thin boundary layer of burnt gases at $t_{RSI} + 53.6$ µs, the maximum value decreased to 1.25 bar. Then, the pressure behind the oblique shock increases progressively during the propagation of the RBL. A higher pressure near the right wall (2.5 bar) is observed than at the foot of the oblique shock (1.5 bar). Focusing on the pressure along y (Fig. 11(b)), a sudden increase in the center of the wall approaching 3 bar appears when the RMI hits the right end wall at $t_{RSI} + 33.6$ µs. Between $t_{RSI} + 43.6$ µs and $t_{RSI} + 73.6$ µs, the RMI then spreads all over the wall surface, decreasing the pressure at the center but increasing it on sides up to 2 bar. Then, as the reactive boundary layer develops, the pressure at the right end wall gradually increases until it exceeds 3 bar at the center and 2 bar on the sides.

<figure><img src="image_12.png" /></figure>

**TFF:** Turbulent Flame Front

**FFF:** Folded Flame Front

**RS:** Reflected Shock

**RW:** Reflected Wave

**RMI:** Richtmyer-Meshkov Inst.

**TBL:** Thin Boundary Layer

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Temporal evolution of the FSI 2 from simulation. The flame front is defined by the progress variable $c = 0.5$ and colored by temperature (black-orange). The isosurface of $\nabla P$ is given in transparent white. The white and black isolines are located in the mid-plane of the channel. The wall pressure field is given in blue-yellow.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 11.** Temporal evolution of the pressure profile recorded (a) at the bottom wall (x; y = -2.25 cm; z = 0 cm), and (b) at the right wall (x = 0 cm; y; z = 0 cm).</figcaption></figure>

## 5. Conclusion

The use of hydrogen as an energy carrier presents both scientific and technological challenges. Its low density and high propensity for explosion make its application in engineering systems complex and potentially hazardous. Therefore, validated numerical tools are crucial for accurately predicting dangerous scenarios, such as the transition from low-speed combustion to high-speed detonation.

A numerical simulation has been conducted to replicate an experimental shock tube at the ICARE lab, focusing on a hydrogen-air flame interacting with a shock wave in a semi-closed channel. The numerical framework is based on the compressible Navier-Stokes equations to model fluid dynamics, coupled with a detailed reaction mechanism to accurately capture various flame interactions and thermodynamic variations. Species diffusion is modeled using complex transport properties following the Hirschfelder-Curtiss approach, combined with thermal diffusion (Soret effect), due to the low Lewis number of hydrogen. Additionally, gravity is included in the simulation, as it may break the symmetry of the laminar flame. A LES model is activated near the wall since the laminar boundary layer is not resolved. Nevertheless, even if a good agreement with the experimental results is achieved, this coarse approach to the under-resolved thermal boundary layer needs to be improved in future work. Furthermore, if an adiabatic wall condition is used, there is no need to artificially thicken the boundary layers and no subgrid modeling is required.

There is good agreement between the experimental schlieren images and the integrated schlieren images from the 3D numerical simulations, despite the fact that the simulations were performed prior to the experiment and did not undergo any numerical fine tuning. Even if experimental uncertainties in the equivalence ratio and temperature are present, the key flow characteristics — such as laminar flame propagation, flame-shock interactions, and the formation of Richtmyer-Meshkov instabilities — are very well captured.

Finally, since the numerical simulations give access to information in three dimensions, they provide a clearer interpretation of the experimental results, particularly in distinguishing shocks that appear at the center of the domain from those occurring near the walls.

## Novelty and significance statement

The novelty of this research is the advanced comparison between a complex experiment featuring flame-shock interactions and a highly refined simulation of the same setup, including state-of-the-art physics. Validated numerical methods, including the necessary physics, are critical for accurately predicting hazardous scenarios, such as the transition from low-speed combustion to high-speed detonation.

## CRediT authorship contribution statement

**Emilie Yhuel:** Writing (first draft), Simulation, Validation, Visualization, Methodology, Investigation. **Anthony Roque Ccaya:** Experiment, Visualization, Methodology, Investigation. **Guillaume Ribert:** Writing (review and editing), Conceptualization, Methodology, Supervision. **Pascale Domingo:** Writing (review and editing), Conceptualization, Methodology, Supervision, Funding acquisition, Project administration. **Nabiha Chaumeix:** Conceptualization, Methodology, Supervision, Funding acquisition, Project administration.

## Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Emilie Yhuel and Anthony Roque Ccaya report financial support was provided by French National Research Agency. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

Emilie Yhuel is founded by the Agence Nationale de la Recherche, France (ANR-20-CE05-0014 - PHYSSA). This work was performed using HPC resources from GENCI-IDRIS (Grant 2021-A0112B00152) and from CRIANN (Centre Régional Informatique et d'Applications Numériques de Normandie).

## Appendix

The turbulent to laminar viscosity ratio is given in Fig. 12 in the x-y mid-plane and on the right wall in the case of a 3D FSI at $M_s = 1.9$ when the Smagorinsky model is activated throughout the domain. At $t_{RSI} + 193.6$ µs, the reflected shock is nearly exiting the channel on the left while the RMI spreads along the rear wall.

A maximum viscosity ratio of $v_{turb}/v_{lam} = 50$ is observed on the right wall of the channel, where the impact of the RMI induces a behavior similar to that of a jet impinging on a wall [32]. A second viscosity extremum, with a ratio of $v_{turb}/v_{lam} = 10$, is found at the reflected shock wave. The shock bifurcations exhibit a ratio of approximately 4, comparable to that of secondary shock waves in fresh gases. At the flame front, a ratio lower than 1 is observed, indicating that the reactive boundary layer remains unaffected by the LES model. Since $v_{turb}/v_{lam}$ remains below 10 outside the walls, activating the LES model in these regions is unnecessary, as recommended in [32].
<figure><img src="image_15.png" /><figcaption>Fig. 12. Turbulent to laminar viscosity ratio in the x-y mid-plane (left) and on the right wall (right). 3D FSI with $M_s = 1.9$ at $t_{RSI} + 193.6$ µs. The Smagorinsky model is activated throughout the domain.</figcaption></figure>

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