Session T34: Reacting Flows: Detonations, Explosions and DDT

Theoretical and Numerical Framework for Characterizing Multidimensional Detonation Wave-Turbulence Interactions

Detonation waves are inherently multidimensional due to intrinsic flow instabilities and turbulence. The two-way coupled interaction between turbulence and detonation wave structure is not well understood. Often, simulations invoked simplifying assumptions for turbulence or detonation structure that did not capture the fundamental physics. This study proposes a theoretical framework to probe the interaction between detonation wave structure and turbulence. A detonation regime diagram is developed which relates qualitatively the turbulence intensity to integral length scale, both normalized by detonation properties (CJ velocity and induction length, respectively). Different regions of detonation wave structure exist based on the relative size of the detonation induction length compared to the Kolmogorov length scale. To test the numerical framework, Direct Numerical Simulations (DNS) with detailed chemistry and transport are performed for different conditions within the detonation regime diagram.   

A parametric study of the interaction between a detonation and a bow shock

The interaction of a detonation with the flow field generated by objects moving at supersonic speeds has applications in the fields of industrial safety and in the transportation and storage of gaseous fuels such as hydrogen and natural gas. This is a complex interaction where the detonation propagates through a leading shock, interacts with the object, and diffracts into the wake where it encounters large-scale flow structures and gradients in reactant concentration. The passage of the detonation through this complex flow field distorts the detonation front, affecting the cellular structure. Here, we perform a parametric study to understand the behavior of the flow field for different obstacle geometries, sizes, and speeds. The multidimensional, compressible, reacting, Navier-Stokes equations are solved using AMRFCT where the chemical heat release and diffusive processes are modeled using the Chemical-Diffusive Model (CDM). The results of the two-dimensional interaction provide important insights which will guide future three-dimensional computations.   

A Discontinuous Galerkin spectral-element method for high-speed reacting flows

A high-order discontinuous Galerkin spectral element method (DGSEM) is developed to solve the chemically reactive Euler equations. The numerical method, based on the spectral element solver Nek5000, includes detailed chemistry and thermodynamics to enable computations of chemically reactive flows, such as those encountered in high-speed combustion. To prevent aliasing errors associated with the high-order advection terms, the discontinuous Galerkin (DG) method employs a summation-by-parts (SBP) operator for the volumetric contribution, and the interface Riemann problem is treated with a local Lax-Friedrichs Flux (LFF). To handle flow discontinuities such as those encountered in shock waves, an entropy residual-based artificial viscosity is used. Unphysical oscillations are suppressed through a conservative positivity-preserving limiter. A validation study is first conducted for a one-dimensional H₂-O₂-Ar detonation, and the results are compared with the steady Zeldovich-von Neumann-Döring (ZND) solution. Following the successful code validation, an unsteady simulation of a two-dimensional detonation is performed with the same unburned mixture. Both qualitative and quantitative analyses are conducted to demonstrate the solver’s capability to adequately capture the detonation cellular structure as well as the temperature and species profiles throughout the detonation.   

Three dimensional numerical simulations of liquid-fueled Rotating Detonation Engines

Rotating Detonation Engines (RDEs) powered by liquid fuels have gained significant interest in recent years due to their compact design, safety and high efficiency. However, the complex multiphase effects and associated heterogeneity can result in less efficient detonative combustion. In this work, we focus on comparing the properties of RDEs operating on liquid n-Dodecane fuel with those using purely gaseous fuel. Detailed 3D numerical simulations were performed using the FLASH¹ code using a two-way coupled Euler-Lagrange framework, accounting for droplet deformation, breakup, and evaporation². A 3D unrolled configuration of an RDE was used with uniform injection of premixed 20 μm n-Dodecane liquid fuel droplets and pure oxygen. Due to the presence of unburnt fuel droplets and parasitic combustion, the liquid fuel RDE exhibited lower thrust, a weaker detonation wave, and a lower detonation wave velocity compared to the pure gas phase fuel case. These preliminary results suggest fuel droplet breakup effects significantly impact the performance of RDEs. Understanding these multiphase effects are critical to the design of liquid-fueled RDEs.

¹B. Fryxell et al., Astrophys. J., Suppl. Ser. 131, 273 (2000).

²B. J. Musick et al., Combust. Flame, Suppl. 257, 113035 (2023).   

Droplet Breakup Process in Liquid Fueled Detonation

This talk will examine detonation induced droplet breakup phenomena through numerical simulations and experimental observation of liquid-fueled detonations. Current theoretical understanding and modeling approaches, based on droplet breakup induced by planar shock wave, lack the consideration of the extreme conditions behind the detonation front, characterized by high pressure, temperature and unsteady velocity regimes. A new droplet deformation and breakup model based on the evolution of surface instabilities in instantaneously changing background conditions will be presented. Euler-Lagrange simulations of liquid-fueled (n-Dodecane/Oxygen) small droplet (< 50 micron) detonations is carried out, in the hydrodynamic code FLASH, and compared with experimental observations. Experiments are run for various n-Dodecane fuel droplet size distributions where Mie-scattering and CH* imaging techniques are used to determine the droplet breakup and evaporation distance and reaction front location. Equivalence ratio measurements were used to estimate the velocity deficit from the Chapman-Jouguet (CJ) value for and equivalent gaseous detonation. In addition to the global features of the detonation, such as wave speeds, the droplet lag distance and child droplet cloud size will be compared between experiments and simulation for various parameters.   

Analysis of Mixing Efficiency and Detonation Wave Structure during Wave Splitting in a Hydrogen-Fueled Rotating Detonation Engine Combustor

The Rotating Detonation Engine (RDE) is a promising alternative to conventional deflagration-based combustion devices. This study examines the mixing efficiency and detonation wave structure in a practical hydrogen-fueled RDE combustor. Our computational setup replicates a previous experimental study, employing Unsteady Reynolds Averaged Navier Stokes (URANS) simulations with adaptive mesh refinement and detailed chemical kinetics. Initially, a single detonation wave structure at an equivalence ratio of = 1 is observed, consistent with experimental findings. By varying the mass flow rates of fuel and oxidizer while maintaining , the simulation reveals the transition from a single to a double co-rotating detonation wave structure. We comprehensively analyze the reacting flow field during this wave splitting, focusing on the interplay between pressure, heat-release rate, and thermo-chemical quantities. Additionally, we evaluate the spatial variation of the fuel/air mixing process in terms of mixing efficiency, a key metric for non-premixed RDE systems. Finally, we explore the state-space representation of the detonation structure to gain deeper insights into the mixing and combustion processes during wave splitting.   

Response of Non-premixed Jet Flames to Blast Waves

The work investigates the response dynamics of non-premixed jet flames to blast waves that are incident along the jet axis. In the present study, blast waves, generated using the wire-explosion technique, are forced to sweep across a non-premixed jet flame that is stabilised over a nozzle rim positioned at a distance of 264 mm from the source of blast generation. The work spans a wide range of fuel jet Reynolds numbers (Re) and incident blast wave Mach numbers (M_s,r). The interaction imposes a characteristic flow field over the jet flame, marked by a sharp discontinuity followed by a decaying profile and a delayed second spike. The second spike in the flow field profile corresponds to the induced flow that follows the blast front. While the response of the flame to the blast front was minimal, it was found to detach from the nozzle rim and lift off following the interaction with the induced flow. Subsequently, the lifted flame was found to re-attach back at the nozzle or extinguish, contingent on the operating Reynolds number and incident blast wave Mach numbers. Alongside flame lift-off, flame tip flickering was aggravated under the influence of the induced flow. A simplified theoretical model was developed to estimate the change in flickering timescales and length scales and was favourably compared against experimental observations.