Session Q03: Reacting Flows: Detonations, Explosions and DDT

Impact of operator splitting schemes on detonation convergence

In reacting flow simulations, operator splitting allows one to treat the impact of chemical reactions, which represents an extremely stiff dynamical system, with a stiff time integration scheme in isolation by considering each cell in the domain as a local reactor. As such, in standard operator split implementations, the coupling due to convection and diffusion is misrepresented. Despite its widespread use, this decoupling has been shown to introduce splitting errors that may eventually lead to unphysical results that can corrupt simulations, such as incorrect autoignition or extinction times. In this presentation, we focus on isolating the impact of these splitting errors in convection-dominated compressible reacting flow problems, namely detonations. More specifically, through a grid convergence analysis of quantities of interest in the detonation structure, various integration schemes (Strang splitting, balanced splitting, spectral deferred correction) are compared with fully coupled unsteady baselines and steady state detonation profiles.   

Development and validation of numerical tools for the Detonation Research Test Facility

This presentation describes recent progress in the development of a new multidimensional compressible reactive-flow solver for the Navier-Stokes equations (LRFPFCT) that aims to study interactions of shocks, detonations, and turbulence. LRFPFCT implements the 3D Flux Corrected Transport algorithm to solve the conservation equations and uses the Chemical-Diffusive model (CDM) for conversion of fuel to products with energy release. LRFPFCT is built on AMReX, the adaptive mesh refinement framework and has been tested on GPU architectures. One particular use of this tool is to support the development of the new experimental facility, the Detonation Research Test Facility (DRTF), now under construction at Texas A&M University. Here we describe a series of numerical simulations for typical combustion applications including interactions of flames, shocks and detonations. These results are compared with experimental data and benchmark simulation results.   

Numerical simulations of flame acceleration and transition to detonation using the chemical-diffusive model

We describe the results of numerical simulations of flame acceleration and transition to detonation in a stoichiometric hydrogen-air mixture using different versions of the chemical-diffusive model (CDM). The CDM is an alternative approach to including the effects of chemical reactions and diffusive transport in compressible reactive Navier-Stokes solvers. CDM parameters are calibrated to reproduce selected combustion properties that are most important to flames and detonations. There are now two types of CDMs available for the simulations of the deflagration to detonation transition (DDT): one type is calibrated for the theoretical half-reaction distance of the Zel'dovich-Neumann-D\"oring detonation and the other is calibrated to reproduce the experimental detonation cell size. This presentation compares the results of simulations for stoichiometric hydrogen-air mixtures using these two CDMs for DDT in obstacle-laden channels with different geometrical configurations. The results are compared to experiments, and show that for channels whose widths are close to the critical size for onset of DDT, the CDM that reproduces the half-reaction distance tends to over-predict the likelihood of DDT. The CDM that reproduces the detonation cell size results in improved predictions.   

Mechanism of detonation development in hydrogen (H2)/methane (CH4) - air mixtures in the presence of non-thermal reactivity

The binary fuel blend of H₂/CH₄ is one of the most favored hydrogen-enriched hydrocarbon fuels in spark-ignition (SI) engines. Yet, the undesirable phenomenon of “superknock”, which can severely and instantaneously damage an SI engine, limits its widespread adoption. Moreover, there is still a lack of consensus on the precise mechanism by which this phenomenon occurs i.e. via flame acceleration or spontaneous ignition, despite numerous previous investigations. Meanwhile, recent chemistry studies have demonstrated a high probability of occurrence of non-thermal reactions in practical flames due to the presence of non-trivial concentrations of reactive radicals including H, O and OH in addition to O₂. In this study, the mechanism of detonation formation in different blends of H₂/CH₄ in air under SI engine conditions was examined through fully resolved, constant volume 1D simulations with and without non-thermal reactivity. Non-thermal reactions were included in the macroscopic kinetic model as chemically termolecular reactions facilitated by radical-radical recombination and radical-molecule association reactions. Sensitivity analysis was performed to quantify the effects of non-thermal reactions on the duration of heat release and thereby the mechanism of detonation formation.

    

Investigation of finite reaction zone effects on the calibration of the condensed-phase high explosive products equation of state

The prediction of high explosive (HE) performance in engineering geometries requires precise knowledge of the HE’s constitutive relations. Specifically, the detonation products equation-of-state (EOS) is key in determining the explosive’s ability to accelerate surrounding materials. Though the products EOS can be generated using theoretical thermochemical equilibrium approaches and knowledge of the molecular constituents, this does not generally achieve the needed predictive accuracy in many engineering design applications. Instead, the products EOS is directly calibrated to cylinder expansion experiments via the use of iterative continuum-level hydrodynamic multi-material simulations. In these experiments, an axisymmetric cylindrical charge confined by a copper liner is detonated and the expanding outer wall trajectory is measured, in order to constrain the detonation products EOS. Due to the large number of required simulations, the hydrodynamic flow in the HE is calculated using efficient, sub-scale Programmed Burn (PB) methodologies which separately set the detonation’s progress and energy delivery. However, the PB methods available to model the flow in the HE have expanded in number and complexity since this methodology was first established. Here, we produce a suite of calibrated products EOS models generated using a variety of HE flow treatments in the detonating explosive, spanning classical (i.e. infinitely thin reaction zone limit) to modern PB methods which incorporate finite reaction zone effects. The predictive capability of each constitutive model variant is then investigated and compared.   

Structure and Dynamics of 2D and 3D Detonations in Ethylene-Air Mixtures

Recent years have seen an increasing interest in using ethylene as an alternate fuel to heavy hydrocarbons for detonative propulsion due to its better detonability. In this work, we present a brief summary of recent effort to perform the first systematic numerical exploration of the properties of detonations in ethylene-air mixtures across a wide range of conditions (pressures, equivalence ratios, fuel preheat) in 2D and 3D geometries using complex multi-step chemical kinetics and high-fidelity numerical simulations. In particular, we study the properties of these detonations as a function of the equivalence ratio to determine lean detonability limits. We also study the propagation limits of 2D detonations in channels of varying width. Overall, we observe that cells are highly irregular, and smaller than the expected experimental cell size. Hierarchy of cell sizes is observed due to frequent failure/re-ignition events resulting in the periodic formation of transverse detonations. These events lead to a complex detonation structure with various flow features that are typical in unstable detonation mixtures. Finally, we conclude by presenting a comparison between 2D and 3D ethylene/air detonations at similar conditions in rectangular channels in the presence of wall loss effects.   

The Theory of Turbulence in Supersonic Combustion in the Absence of Solid Walls

It is commonly believed that the higher the Reynolds number of a flow, the larger the separation between the large (integral) and the small (Kolmogorov) scales, and consequently, the stronger the turbulence intensity. What is not commonly appreciated, however, is that flows in the high-speed regime, where the Reynolds number is practically infinite, is more likely going to be laminar! The implication for supersonic combustion problems is that the large velocities in the flow do not imply large turbulence intensities. The disconnect apparently has its origin from the fact that classical turbulence theories are based on low-speed flows. In a supersonic combustion model without solid walls and with negligible buoyancy production of turbulence, we investigate shear production. The shock waves in such a system play the role of a solid wall as far as shear generation of turbulence is concerned. But then, this is a porous wall as per the Rankine-Hugoniot relations, so that the efficiency of turbulence generation will be relatively poor, and the turbulence will be mostly transitional and highly localized. A few results that demonstrate the phenomenon will be discussed.   

Computational investigation of the chemical dynamics in detonation development at SI engine conditions

This study employs algorithmic tools from the computational singular perturbation (CSP) approach and statistics to investigate detonation development in SI engines using 2D simulations at different intensity levels – strong and mild detonations. The setups are based on the Zel’dovich theory and Bradley diagram to predict detonability using two non-dimensional parameters ε, ξ. Several 1D cut lines extracted from 2D contours are used to track the detonation propagation and all related dynamics. The evaluation of the chemical dynamics of both detonation events with the use of the CSP tools highlights that the strong detonation case exhibits a more pronounced explosive character. The comparative analysis using the CSP tools also reveals that the action of strong dissipative modes which tends to cancel the explosive ones. The chemical dynamics are further evaluated using the tangential stretching rate (TSR) metric. The statistical analysis of TSR in a temperature-based progress variable space largely displays the dominance of the strong detonation TSR values over the ones of the mild detonation. The PDF’s of TSR identify a trend favoring the high intensity detonation event.   

Study of Shockwave interaction with non-metallic solid bodies

Nuclear explosion in a densely populated area is the worst can happen to any country in the world due to enormous loss of life, property and severe economic damage. Nuclear explosion immediately causes radiological damage and destruction of infrastructure. Hydro-magnetic shock propagation due to blast gives rise to simultaneous signals around the world. A better understanding of the effects of shock wave interactions with complex boundary conditions and deformable/breakable objects can facilitate both prevention and mitigation of nuclear explosion damage. This study focuses on the effects of the shock wave on solid bodies made from different materials and placed in a variety of formations. Experiments are conducted in a horizontally placed shock tube, with a solid body holder on the floor of the test section. Solid bodies are mounted on this holder and attached to the test section. These solid bodies are then impacted with a planar shock wave at several different Mach numbers. Visualization of this shock waveinteraction with solid bodies is accomplished by planar laser-induced fluorescence (PLIF) with a high-powered Nd:YAG ultraviolet laser and an DSLR camera. Visualization of the resulting instabilities is achieved by using a tracer gaseous medium injected into the test section. Representative results of these experiments are reported here along with a review of previous works in this area