Session Z13: Reacting Flows: Detonations, Explosions and DDT (12:15pm - 1:00pm CST)

Calibrating chemical-diffusive model for multidimensional combustion properties

We present model developments and tests that calibrate the chemical-diffusive model (CDM) with respect its ability to to reproduce multidimensional detonation properties. The CDM is a parameter-fitting approach for incorporating heat release and diffusive processes into fluid dynamics simulations. Reaction parameters are optimized to reproduce global or one-dimensional properties of a laminar flame and a ZND detonation. This work first examines the dependence of detonation cell size on the CDM parameters in multidimensional simulations. The correlation between the detonation cell width and the half-reaction distance of the ZND structure is then incorporated into the CDM optimization process. It is shown that computed detonation cells, with the modified CDM, show the same sizes as those found in experimental measurements. Further tests will recalibrate the new Navier-Stokes CDM combination for computing the the deflagration-to-detonation transition. The objective is to produce a reacting-flow model that can be used with confidence for flame acceleration, DDT, and detonation propagation and quenching.   

Dynamics of flame development at early stages of combustion inside a reverse-flow power generator model combustor

Effects of reverse-flow configuration on characteristics of premixed flame development inside a model combustor were investigated experimentally. Tests were performed for lean CH$_{\mathrm{4}}$-air flames with bulk flow velocities of 4.0 and 6.4 m/s. High-speed OH* chemiluminescence imaging synchronized with pressure measurements were performed. The results suggest, prior to appearance of thermoacoustics, three phases, namely, ignition, stabilization, and transition are observed. During the ignition phase, the normalized flame edge velocity can achieve relatively large maximum values owing to the reverse-flow configuration compared to that for closed chambers. The ignition phase is followed by the stabilization phase during which a Bunsen flame is formed on the flame-holder. During the transition phase, the flame chemiluminescence features a long-period sinusoidal oscillation, during which the flame is partially-detached from the holder. Despite significant influences of the reverse-flow configuration on flame dynamics during the ignition and stabilization phases, the spectral characteristics of pressure and flame chemiluminescence oscillations are not influenced by this configuration during the transition phase and are similar to those of unconfined flames.   

Detonation simulations by solving the spatially-filtered Euler equations

The presence of both shocks and chemical reactions in detonations poses a challenge for simulation efficiency. Detailed chemical kinetic models require one equation per chemical species in addition to the compressible Navier-Stokes equations, quickly increasing the computational cost. To model hydrogen combustion, nine species are needed; for hydrocarbon fuels, there may be hundreds or even thousands of species to consider. The cost of chemistry has been addressed for subsonic reacting flow simulations using the tabulated chemistry method, in which one (or a combination of) species mass fraction tracks the progress of reactions in a system. However, species concentrations also depend on the thermodynamic state, as temperature and pressure affect reaction rates. In compressible flows, these thermodynamic variables, along with the progress variable, are used to describe all other species mass fractions, greatly reducing the computational cost. This work extends the methodology that has been implemented for turbulent flames to include one-dimensional detonations. The reduced-order chemical model is validated against simulation data obtained with detailed chemistry.   

Dynamic mode decomposition (DMD) applications in spinning and standing waves in rotating detonation combustors

Rotating detonation combustors (RDC) are characterized by a supersonic combustion wave spinning around an annular combustion chamber at a characteristic frequency. Dynamic mode decomposition (DMD) should thus be a well-suited low-order tool to investigate the RDC's dynamics. However, other wave patterns are commonly observed, including counter-rotating, standing and clapping waves, which complicate the analysis. In this work, we investigate the applicability of DMD to RDC operating conditions in which multiple waveforms are simultaneously found. By processing high speed video imaging of the natural flame luminosity from the aft-end of the combustor, we (i) identify and separate the wave modes associated with longitudinal, spinning, standing and clapping phenomena and (ii) demonstrate successful reconstruction of the RDC dynamics using a small set of wave modes. We also demonstrate the applicability of DMD and preservation of the identified dynamics when reducing the processed dataset from the original two-dimensional Cartesian image of the annular combustor into 1D luminosity maps, averaged across the radial extension of the annulus. This significantly reduces the computational cost without affecting the DMD ability of isolating the most significant wave modes in an RDC.   

Supersonic Combustion Heat Flux in Rotating Detonation Engine

Rotating detonation engines (RDEs) have been investigated extensively in recent years as a candidate for a high thermodynamic efficiency air-breathing propulsion system. The propulsive performance of the engine has been studied a great deal, as have the effects of numerous parameters of the system, such as the dynamics of the detonation wave, the cellular structure, turbulence, injection flow rate, injector design, and numerous other factors. However, to the knowledge of the authors, the issue of heat transfer in the RDE system has not received enough attention, even though such a study would be quite valuable in determining the cooling requirements of the engine and the effects of system parameters on thermal management. This is particularly important because of the high temperatures involved in the RDE engine. The present study has been undertaken to address this knowledge gap using the large-eddy simulation approach to analyze the combustion in the system and determine the heat flux distributions that result. To the knowledge of the authors, no previous studies have addressed this issue to any significant extent.   

Assessment of low-speed mixing and diffusion models for detonating compressible turbulence

Several studies, for example, Ref [1], have shown that thermodynamic gradients caused by hot spots in reactive gas mixtures could lead to spontaneous initiation of detonation. These laminar-flow approach can predict the conditions for the onset of detonation in quiescent gas mixtures, and only forms detonation in localized and isolated hot spots on time scales shorter than, or comparable to, chemical and acoustic timescales. On the other hand [2], in highly turbulent autoignition flows, turbulence and compressibility together can generate non-monotonic temperature fields with tightly-spaced minima and maxima that vary over a wide range of length and time scales, including those much larger than chemical and acoustic length and time scales. Towery et al. [2] successfully pursued this possibility in their work, using DNS of compressible homogenous an isotropic turbulence. In the present work, the datasets generated in [2] are used to investigate some aspects of turbulence statistics, to understand previous mixing and diffusion models for reactive scalars, with a focus on the extension to reactive compressible turbulence. [1] Khokhlov, A., Astronomy and Astrophysics 246 pp. 211-214 (1991) [2] Towery, C. A. Z. et al., Combustion and Flame 213, pp. 172-183 (2020)   

Engine performance analysis for mode transition conditions in Rotating Detonation Engines using detailed numerical simulations

Mode Transition (MT) is a phenomenon of abrupt change in the number of detonation waves, occurring in a Rotating Detonation Engine (RDE), and is due to a change in inlet conditions, such as plenum pressure, fuel reactivity or mass flow rate. MT can result in sudden changes in engine performance$^{\mathrm{1}}$ or detonation failure. In this work, we report results from numerical simulations on the effect of MT on three, key engine performance parameters -- thrust, specific impulse and mass flow rate. The working fuel was stoichiometric H$_{\mathrm{2}}$-O$_{\mathrm{2}}$ mixture, while the N$_{\mathrm{2}}$ dilution was varied to trigger MT. Sensitivity of the new mode configuration on the N$_{\mathrm{2}}$ perturbation trajectory was also examined. It was observed that the engine thrust showed little variation with the change in N$_{\mathrm{2}}$ dilution. All the simulations were performed on a 2D unrolled RDE geometry with discrete nozzle injectors. The compressible Euler equations were solved using the FLASH$^{\mathrm{2}}$ code, with a Piecewise Parabolic Method on a cartesian mesh. $^{\mathrm{1}}$A. George et al., Proc. Comb. Inst., 36 (2), 2691, (2017). $^{\mathrm{2}}$B. Fryxell et al., Astrophys. J., Suppl. Ser. 131, 273 (2000).   

Analysis of Gas-Phase n-Dodecane-Air Cellular Detonations

Gas-phase detonations are found in a wide range of settings, including industrial explosions and advanced propulsion systems, such as detonation-based engines. The defining characteristic of detonations is their unstable nature, which is manifested in a complex cellular structure due to the interaction between transverse waves and the leading shock. Propulsion applications typically rely on heavy hydrocarbon fuels, similar in properties to n-dodecane. Detonation properties in such complex fuels remain virtually unexplored in detailed numerical studies. Here we present two-dimensional numerical simulations of gas-phase n-dodecane-air cellular detonations in stoichiometric and lean mixtures, which use a 24-species reduced chemical mechanism. Detailed investigation of different parameters, such as grid resolution and domain size, is performed. Detonation structure and dynamics are analyzed using numerical soot foils, as well as Lagrangian tracer particle analysis of thermochemical trajectories. Our findings reveal, for the first time, the typical cell size and structure produced by this highly unstable mixture. Finally, we discuss the implications of this study for the development of improved chemical mechanisms for heavy hydrocarbon detonations.   

Numerical simulations of flame acceleration and DDT in natural gas: the effects of trace propane and ethane

Natural gas is primarily composed of methane, but realistic mixtures usually contain trace amounts of higher hydrocarbons. Here we summarize results of numerical simulation of flame acceleration and subsequent deflagration-to-detonation transition (DDT) in channels with obstacles for methane-air mixtures diluted with varying trace amounts of ethane and propane. The simulations were performed with a fully compressible, unsteady, reactive flow code coupled to appropriate chemical diffusion models (CDM) which describe energy release, the diffusion processes, and the conversion of fuel to product. Various aspects of flame acceleration and DDT phenomena are examined, including the run-up distance to DDT and the detonation cell structure, a property characteristic of the reactive gas. Numerical simulation results show that the distance to DDT is only slightly reduced with the added hydrocarbons. The detonation cell size, however, does decrease significantly making the propagating detonation more robust and harder to extinguish.