Effect of spatial inhomogeneities on detonation propagation with yielding confinement

The propagation of detonations in layers of reactive gas bounded by inert gas is simulated computationally in both homogeneous and inhomogeneous systems described by the two-dimensional Euler equations with the energy release governed by an Arrhenius rate equation. The thickness of the reactive layer is varied and the detonation velocity is recorded as the layer thickness approaches the critical value necessary for successful propagation. In homogeneous systems, as activation energy is increased, the detonation wave exhibits increasingly irregular cellular structure characteristic of the inherent multidimensional instability. The critical layer thickness necessary to observe successful propagation increases rapidly, by a factor of five, as the activation energy is increased from Ea/RT0=20–30; propagation could not be observed at higher activation energies due to computational limitations. For simulations of inhomogeneous systems, the source energy is concentrated into randomly positioned squares of reactive medium embedded in inert gas; this discretization is done in such a way that the average energy content and the theoretical Chapman–Jouguet (CJ) speed remain the same. In the limit of highly discrete systems with layer thicknesses much greater than critical, velocities greater than the CJ speed are obtained, consistent with our prior results in effectively infinite width systems. In the limit of highly discretized systems wherein energy is concentrated into pockets representing 10% or less of the area of the reactive layer, the detonation is able to propagate in layers much thinner (by an order of magnitude) than the equivalent homogeneous system. The critical layer thickness increases only gradually as the activation energy is increased from Ea/RT0=20−55, a behavior that is in sharp contrast to the homogeneous simulations. The dependence of the detonation velocity on layer thickness and the critical layer thickness is remarkably well described by a front curvature model derived from the classic, ZND-based model of Wood and Kirkwood. The results of discrete sources are discussed as a conceptual link to the behavior that is experimentally observed in cellular detonations with highly irregular cellular structure in which intense turbulent burning rapidly consumes detached pockets behind the main shock front. The fact that highly discrete systems are well described by classical, curvature-based mechanisms is offered as a possible explanation as to why curvature-based models are successful in describing heterogeneous, condensed-phase explosives

Numerical investigation of gaseous cellular detonation propagation in rough-walled channels

When a cellular detonation propagates in a tube with rough-wall boundary conditions, its propagating velocity becomes less than the ideal Chapman-Jouguet (CJ) value due to losses. In addition, the intrinsic cellular pattern of this quasi-detonation and its reacting flow fields can be strongly changed by the presence of wall roughness. This study aims to clarify the wall boundary effect by investigating the quasi-detonations under different degrees of wall roughness defined by various characteristic factors. A computational analysis is conducted using two-dimensional numerical simulations. The governing equations are given by the reactive Euler equations with a two-step Arrhenius induction-reaction kinetic model and solved numerically using a second order finite-volume scheme with Graphics Processing Unit (GPU) computing. A parametric study is reported by varying the channel width, obstacle size, obstacle spacing and chemical reaction parameters, to investigate perturbations created by the rough wall to the intrinsic cellular detonation instability and eventually the detonation failure or propagation limit. Apart from the numerical smoked foils to reveal the dynamic evolution and irregularity of cellular detonation patterns, the degree of instabilities caused by the roughness is analyzed by looking at the probability density function of the pressure and induction rate from the detonation flow fields

Computational study of gaseous cellular detonation diffraction and re-initiation by small obstacle induced perturbations

A gaseous detonation wave that emerges from a channel into an unconfined space is known as detonation diffraction. If the dimension of the channel exit is below some critical value, the incident detonation fails to re-initiate (i.e., transmit into a self-sustained detonation propagating) in the unconfined area. In a previous study, Xu et al. [“The role of cellular instability on the critical tube diameter problem for unstable gaseous detonations,” Proc. Combust. Inst. 37(3), 3545–3533 (2019)] experimentally demonstrated that, for an unstable detonable mixture (i.e., stoichiometric acetylene–oxygen), a small obstacle near the channel exit promotes the re-initiation capability for cases with a sub-critical channel size. In the current study, two-dimensional numerical simulations were performed to reveal this obstacle-triggered re-initiation process in greater detail. Parametric studies were carried out to examine the influence of obstacle position on the re-initiation capability. The results show that a collision between a triple-point wave complex at the diffracting shock front and the obstacle is required for a successful re-initiation. If an obstacle is placed too close or too far away from the channel exit, the diffracting detonation cannot be re-initiated. Since shot-to-shot variation in the cellular wave structure of the incident detonation results in different triple-point trajectories, for an obstacle at a fixed position, the occurrence of re-initiation is of a stochastic nature. The findings of this study highlight that flow instability generated by a local perturbation is effective in enhancing the re-initiation capability of a diffracting cellular detonation wave in an unstable mixture

Critical Tube Diameter for Quasi-Detonations

The critical tube diameter problem for quasi-detonations is studied via experiments and two-dimensional numerical simulations based on the reactive Euler equations. In the experiments, quasi-detonation in stoichiometric acetylene-oxygen mixtures is generated in rough-walled tubes with three different diameters, where the wall roughness is introduced by using spiral inserts with different wire diameters. Photodiodes are placed along the rough tubes to record the detonation time-of-arrival to deduce the velocity, and a high-speed schlieren system is used to observe the diffraction processes. Near the critical regime of detonation diffraction, the quasi-detonation emerging from the rough tube is again shown to first fail and subsequently re-initiate from a local explosion center in the spherical deflagration reaction zone. For quasi-detonations, stronger turbulence and instabilities produce stronger local hot spots, which balances the significant velocity deficit as much as approximately 15% in the rough tube, resulting in the critical pressure remaining relative constant. The cell sizes for quasi-detonation in rough tubes are directly measured, and the ratio of critical tube diameters (dc) to these determined cell sizes (λ) is used to quantify the critical criterion of detonation initiation. In rough tubes with coil springs, the previous criterion of dc/λ ≧ 13 for detonation re-initiation appears invalid, and the critical initiation regime for quasi-detonation in rough tubes is found approximately as dc/λ ≧ 8. Despite the cell enlargement and the lower propagation velocity for quasi-detonation, it is hypothesized that the increase in cell irregularities or instabilities can in turn benefit the transmission process. These unstable features of quasi-detonation are supported by the two-dimensional numerical simulations, also showing a higher degree of cell irregularities, a wider spectrum of induction rate, and the generation of shocked reactive pockets

Classical and reactive molecular dynamics: Principles and applications in combustion and energy systems

Molecular dynamics (MD) has evolved into a ubiquitous, versatile and powerful computational method for fundamental research in science branches such as biology, chemistry, biomedicine and physics over the past 60 years. Powered by rapidly advanced supercomputing technologies in recent decades, MD has entered the engineering domain as a first-principle predictive method for material properties, physicochemical processes, and even as a design tool. Such developments have far-reaching consequences, and are covered for the first time in the present paper, with a focus on MD for combustion and energy systems encompassing topics like gas/liquid/solid fuel oxidation, pyrolysis, catalytic combustion, heterogeneous combustion, electrochemistry, nanoparticle synthesis, heat transfer, phase change, and fluid mechanics. First, the theoretical framework of the MD methodology is described systemically, covering both classical and reactive MD. The emphasis is on the development of the reactive force field (ReaxFF) MD, which enables chemical reactions to be simulated within the MD framework, utilizing quantum chemistry calculations and/or experimental data for the force field training. Second, details of the numerical methods, boundary conditions, post-processing and computational costs of MD simulations are provided. This is followed by a critical review of selected applications of classical and reactive MD methods in combustion and energy systems. It is demonstrated that the ReaxFF MD has been successfully deployed to gain fundamental insights into pyrolysis and/or oxidation of gas/liquid/solid fuels, revealing detailed energy changes and chemical pathways. Moreover, the complex physico-chemical dynamic processes in catalytic reactions, soot formation, and flame synthesis of nanoparticles are made plainly visible from an atomistic perspective. Flow, heat transfer and phase change phenomena are also scrutinized by MD simulations. Unprecedented details of nanoscale processes such as droplet collision, fuel droplet evaporation, and CO2 capture and storage under subcritical and supercritical conditions are examined at the atomic level. Finally, the outlook for atomistic simulations of combustion and energy systems is discussed in the context of emerging computing platforms, machine learning and multiscale modelling

Impact of Particle Injection on Gas Flow at Elevated Pressure: A Numerical Study

Modeling of a turbulent two-phase gaseous-solid flow still faces challenges. The present study is devoted to two-phase flow in an annular pipe (hollow cylinder) operating at an elevated pressure of 15 bar and moderate Reynolds numbers of circa 6 x 103. The influence of the various factors – such as the particle loading, the interaction between the phases, and turbulent dispersion – on the flow dynamics is systematically studied by means of the computational simulation employing the ANSYS FLUENT commercial package. To be specific, particle loading with a volumetric fraction of 1.2 % is defined as high particle loading, while the flow with a volumetric fraction of 0.13 % is referred to as low particle loading. In particular, seven various cases for a gas-solid phase flow are investigated: 1) Pure gas flow; 2) Low particle loading two-phase flow with one-way coupling and with turbulence dispersion; 3) Low particle loading two-phase flow with two-way coupling but without turbulence dispersion; 4) Low particle loading two-phase flow with two-way coupling and with turbulence dispersion; 5) High particle loading two-phase flow with one-way coupling and with turbulence dispersion; 6) High particle loading two-phase flow with two-way coupling but without turbulence dispersion; 7) High particle loading two-phase flow with two-way coupling and with turbulence dispersion. The boundary layer was found to be growing without fluctuations of the turbulent kinetic energy (TKE) for Cases 1, 2, and 5 above. For Case 4, the TKE fluctuations have been identified though appeared not as substantial as in Cases 6 and 7. The author attributes such a difference in the fluctuations to the particle loading. In addition, the onset and development of the flow instability have been observed at a random axial distance in Cases 4, 6, and 7. Such instability is presumably attributed to the two-way coupling with turbulence dispersion in a flow. It is concluded that the particle loading, one-way, or two-way coupling between the phases, and the turbulence dispersion models significantly influence the flow dynamics. The present computational results inspire to perform experimental verification and validation of the simulations, so the simulation results can subsequently be used for the design analysis

Numerical Investigations of Combustion

This Special Issue will highlight the latest advances in numerical modeling of combustion-related applications. With the recent advancements in computational capacities and the widespread use of simulations in engineering problems, numerical methods are becoming increasingly important to improve existing models and develop new models that can help researchers to better understand the underlying mechanisms of combustion, their interaction with other physical phenomena, such as turbulence, and their impacts on the performance of related applications at both fundamental and practical levels

Validation Of The Kurganov-Tadmor/Kurganov-Noelle Petrova Scheme for Rotating Detonation Engine Simulations Using OpenFOAM

Detonation waves are a challenging field of study given the short time and length scales involved in the phenomenon. Such waves exhibit a complex structure consisting of a lead shock and shock waves travelling transversely to a detonation’s normal propagation direction. The interaction between the shocks and the rapid chemical reactions they trigger results in the emergence of a natural length scale, the detonation cell size. There are still no complete theory or model that can accurately predict the cell size or a detonation waves initiation, propagation and failure dynamics. The numerical simulation of detonation waves is also challenging, due to the rapid reaction rates encountered. The Open source Field Operation And Manipulation (OpenFOAM) framework, commonly referred to as OpenFOAM, Computational Fluid Mechanics (CFD) package is increasingly used and referenced. One drawback of the stock OpenFOAM package is that the only finite volume numerical scheme available for the solution of the Euler equations in conservative form is the Kuganov-Tadmor (KT)/Kuganov-Noelle-Petrova (KNP) numerical scheme. Moreover, combustion is not implemented, hence which needs to be modified to simulate detonation waves; a coupling of compressible flows and reaction. This particular scheme is 2nd order accurate in smooth region based on the idea behind the Lax-Friedrichs scheme and which does not involve the solution to a Riemann problem in order to evaluate the intercell fluxes. This is unlike the methods currently used in detonation research, which nearly always consist of Godunov-type schemes with an approximate Riemann Solver such as Harten-Lax-van Leer-Contact (HLLC). OpenFOAM, with the KNP scheme, was recently used to simulate the two-dimensional structure of detonation waves despite having not been fully validated for the detonation simulation. Efforts to get access to the codes used proved abortive. In this work, we create a custom solver named rhoCentralFoamreac which we used to evaluate (validate) the KNP scheme for detonation cases, by simulating a standard 1D detonation case that usually results in pulsating propagation with a single mode. Metrics for detailed comparison and convergence studies are the oscillation peak pressure and period. Using the KNP scheme, we then examine OpenFoam as a CFD tool for the simulation of a detonation based engine, where an initiated wave propagates circumferentially in a combustion chamber, commonly referred to as a rotating detonation engine. We study the effect of different ignition methods, and initiation flow fields (subsonic and supersonic) on the formation of these rotating detonation waves