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Co-Author:
Allie Yuxin Lin
Marketing Writer II
A few years ago, I lived in a small suburban neighborhood in Portland, Oregon. More than once, as I was driving at a leisurely pace of 30 mph down a local road, someone would whiz by me at an outrageously high speed. While they probably weren’t going at 100 mph (as I would passionately claim to my passenger), it certainly felt like it.
Today, I work at a company that deals with modeling combustion, and that experience is how I taught myself the concept of the deflagration to detonation transition (DDT). If, in some dystopic universe, my reality and the speedster’s reality were merged into one, that new car would be going steady at 30 mph and then suddenly accelerating to 100 mph in under a second, theoretically experiencing DDT.
DDT is defined as the process where a slow-moving flame (i.e., my car) rapidly accelerates to a supersonic detonation wave (i.e., the speedster’s car). The microseconds leading up to DDT are known as flame acceleration (FA), and these phenomena are typically studied together. Conventionally, FA and DDT are studied in large-scale settings such as supernova explosions, large shock tubes, or coal mine passages. However, emissions regulations and the rising demand for more compact energy systems have also motivated their study in much smaller settings such as microchannels. These devices offer enhanced heat and mass transfer with lower manufacturing costs and are used in a variety of applications, including electronics cooling, biological systems, and HVAC devices. However, combustible fuel mixtures are more prone to detonating when passing through the highly confined passageways of microchannels, which are similar in size to the diameter of a single strand of hair. Studying FA and the ensuing DDT in microchannels can increase our understanding of the conditions that trigger detonation and enable better control and mitigation strategies in high-pressure systems.
Much of the existing literature on explosion safety has centered on investigating the effect of thermal wall boundary conditions, which play a significant role in flame propagation by affecting heat loss, flame stability, and ignition behavior. Another factor that can influence flame propagation and detonation is heterogeneous chemistry, in particular, surface reactions at catalytic walls. In micro-reactors, reactive catalytic wall coatings can alter and induce chemical exchange at the wall, affecting the FA and DDT process. Catalytic walls provide a surface on which fuel/air mixtures can react; this heterogeneous combustion takes place on the catalyst surface, rather than in the gas phase. The bulk of the catalytic combustion literature has focused on catalytic combustion over noble metals such as platinum or rhodium. By contrast, transition metals like nickel have only been studied for chemical reforming, a process that alters the molecular structure of hydrocarbons to produce other chemicals. In this study, Suryanarayan (Surya) Ramachandran, a Ph.D. candidate at the University of Minnesota Twin Cities, teamed up with Professor Suo Yang and research engineers at ExxonMobil Technology. They examined hydrogen ignition and flame propagation in a microchannel with catalytic nickel walls, where the highly confined environment of the microchannel prompted additional concerns of FA and DDT.1 I’ll hand it over to Surya to tell us about his research!
Co-Author:
Suryanarayan Ramachandran
Ph.D Candidate,
University of Minnesota
In an ideal hydrogen combustion system, the fuel/oxidizer mixture would consist of hydrogen, with oxygen and nitrogen coming from the air. In industrial settings, some combustion products, such as water, may make their way back into the fuel/oxidizer mix. As a result, the mixture becomes highly vitiated with H2O. To mimic a realistic combustion scenario, we simulated combustion with the mixture of hydrogen, oxygen, nitrogen, and water. This mixture, which is named case C1, showed no detonation.
This didn’t really answer any of our questions, since our research group set out to understand DDT. The C1 case didn’t show any detonation, so we wanted to figure out why it didn’t explode and if there would be another mixture that would actually show some kind of detonation. So, I thought, why not remove the water? The water isn’t really contributing to combustion or heat release; rather, it’s acting as a diluent. Plus, it has a high specific heat capacity, which means it pretty much acts like an energy sink by sucking away the heat release and reducing the overall flame temperature. By removing the water, we were left with a mixture of pure hydrogen and dry air, which we called C1d. C1d has nitrogen acting as the diluent in the mixture, but no vitiation (i.e., no water vapor). To evaluate other interactions and gather some comparison data, we also tested a H2/O2 mixture; this final variation was called C1p.
Since we wanted to study the influence of both gas-phase (homogeneous) and surface (heterogeneous) chemistry on the FA & DDT process, we decided to use CONVERGE for the CFD part of this study. The kind of detonation problems that we are studying require highly resolved meshes and Adaptive Mesh Refinement (AMR) to capture the flame front. In that sense, CONVERGE was the ideal choice, since it has the high-quality meshing capabilities we needed, as well as the option to include coupled homogeneous and heterogeneous surface chemistry.
To begin, we used CONVERGE to solve the governing multi-component reacting Navier-Stokes equations, accomplished through a collocated finite volume method (FVM), which conserves mass, momentum, total energy, and the species’ mass-fractions on a discretized mesh consisting of many cells. The velocities at the cell faces were obtained using a blended central and upwind scheme (i.e., the flux-blending scheme), where cell-face velocities represent weighted sums of upwinded (i.e., first-order accurate) and cell-averaged (i.e., second-order accurate) velocities. The Pressure Implicit with Splitting of Operators (PISO) scheme was employed to capture pressure-velocity coupling, while the Rhie-Chow interpolation scheme was used to avoid potential “checkerboarding” issues with the collocated grid.2 CONVERGE’s biconjugate gradient stabilized (BiCGSTAB) linear solver was used for the pressure Poisson equation, a reformulation of the Navier-Stokes equations that allowed us to directly calculate pressure by decoupling pressure from the velocity field. Additionally, we used the SAGE detailed chemical kinetics solver to solve the gas-phase and surface combustion reactions. SAGE solved the surface coverages and gas-phase mass fractions, enabling coupled gas-phase/surface reactions at the wall.
CONVERGE’s AMR helped us refine the mesh in areas of greater computational complexity and coarsen the mesh in others. We chose not to use AMR in Case C1, due to the large flame thickness (δf= 700μm). For the purposes of this study, cells were refined according to the local cell temperature. To ensure finer meshes on the accelerating flame front, we only employed AMR when the cell temperature fell in the range of 800-1900 K. For Case C1d, we applied AMR on top of the base mesh resolution to ensure six cells spanned the small flame thickness (δf= 27μm). The final mixture, Case C1p, had an even smaller flame thickness of δf = 20 μm, so we further refined the mesh to achieve 16 points across the flame thickness, ensuring adequate resolution of the flame structure.
Next, we performed several validation studies for CONVERGE’s gas-phase and surface chemistry mechanisms to enhance confidence in our simulation results. For example, CONVERGE’s gas-phase SAGE detailed chemistry solver and its hydrodynamic coupling was compared with results from the PeleC solver, an open-source CFD code used for combustion applications. Validation results are shown in Figure 1.
CONVERGE’s surface chemistry module was validated against Chen et al.3, a well-cited paper that simulates a catalytic micro-tube with gas-phase and surface reactions for premixed H2/air mixtures. This publication described a simple catalytic combustion study focusing on flame stabilization, rather than FA/DDT. CONVERGE’s results matched well with those of the paper.1
In Case C1, the flame did not exhibit acceleration, nor did it become a detonating flame. Rather, it simply propagated with a constant flamespeed. However, compared to the traditionally observed parabolic-like flame front profile, the flame inverted whenever surface chemistry was active (i.e., when the chemical reactions at the surface were explicitly modeled and accounted for), as seen in Figure 2. This reflects the preferential propagation of the flame along the walls due to catalytic surface chemistry.
However, when surface chemistry was disabled, the flame returned to the traditional parabolic shape, as shown in Figure 3.
After finding a strong production of the intermediate radicals OH and O along the wall surface, we concluded that catalytic surface reactions promote preferential propagation of the flame via the production of reactive intermediates that directly promote gas-phase combustion. In other words, the flame propagates along the catalytic walls due to the surface reactions from the fuel/oxidizer mixture and the intermediate radicals. We also found the temperature distribution for the C1 cases run with surface chemistry were higher than the ones run with gas-phase chemistry only. This is likely due to the fact that surface chemistry calculations take into account additional heat generated by surface reactions.
In all C1 cases, the flame did not exhibit acceleration. This is attributed to the presence of diluents and vitiation in the mixture, which lowers the flamespeed and inhibits FA/DDT.4 Therefore, the same simulation and analysis procedure was carried out for the C1d mixture. In this case, removing water from the mixture led to higher flamespeeds and FA, but not DDT. In contrast with the vitiated cases (C1), the flame inversion occurred only for the case where surface chemistry is enabled without gas-phase chemistry. In cases with gas-phase reactions, the flame became parabolic. The flame in all C1d cases accelerated to high speeds (i.e., around Mach 0.1). Unlike case C1, there was no flame propagation along the wall since the short residence time (i.e., the time available for surface chemistry to couple with gas-phase chemistry) reduced the effect of catalytic walls. The C1d cases exhibited rapid FA, but did not reach DDT. We believe this is due to the long DDT run-up distance (i.e., the distance required for the flame to undergo the DDT process). On the other hand, the C1p cases exhibited rapid DDT after forming a tulip-like flame front in the initial stages. Both flame branches propagated preferentially along the wall before eventually uniting, forming a detonation front, as shown in Figure 4.
Thanks, Surya! To recap, Surya and his team, along with researchers from ExxonMobil Technology, used CONVERGE to simulate the propagation and acceleration of H2/O2 and H2/air flames for three different fuel mixtures over catalytic nickel walls. Each mixture responded differently to the interplay between surface and gas-phase chemistry, resulting in varying outcomes in terms of FA and DDT. Read more about Surya’s research in his paper!
Overall, this study was the first in the field to consider coupled gas-phase and surface reactions in catalytic nickel microchannels for assessing DDT. These findings have the potential to drive more specific studies tailored to industrial scenarios to improve explosion safety.
[1] Ramachandran, S., et al. “Flame Acceleration and Deflagration to Detonation Transition in a Microchannel with Catalytic Nickel Walls.” Physics of Fluids, 36(11), 2024, 116-143. https://doi.org/10.1063/5.0235540
[2] Zhang, S., Zhao, X., and Bayyuk, S., “Generalized Formulations for the Rhie–Chow Interpolation.” Journal of Computational Physics, 258, 2014, 880–914. https://doi.org/10.1016/j.jcp.2013.11.006
[3] Chen, G.-B., et al. “Effects of Catalytic Walls on Hydrogen/Air Combustion inside a Micro-Tube.” Applied Catalysis A: General, 332(1), 2007, 89–97 https://doi.org/10.1016/j.apcata.2007.08.011 [4] Ramachandran, S., Srinivasan, N., Wang, Z., Behkish, A. and Yang, S., “A Numerical Investigation of Deflagration Propagation and Transition to Detonation in a Microchannel With Detailed Chemistry: Effects of Thermal Boundary Conditions and Vitiation.” Physics of Fluids, 35(7), 2023, https://doi.org/10.1063/5.0155645
