Session H35: Detonation and Explosions

Theory of weakly nonlinear self sustained detonations

We derive a new weakly non-linear asymptotic model of detonation waves capable of capturing the rich dynamics observed in solutions of the reactive Euler equations, both in one and multiple space dimensions. We then investigate the travelling wave solutions of the asymptotic model, together with their linear stability. Finally, we study the non-linear dynamics through numerical simulations, and present a quantitative comparison between the asymptotic equations and the full system they are expected to approximate.   

Acoustic timescale characterization of asymmetric hot spot detonation initiation

Hot spots and temperature gradients are often used to model detonation initiation processes. Traditionally the focus of the analysis is on the critical gradient conditions necessary to facilitate detonation formation. However, hot spots usually have a local maximum of some finite size at the center. In previous work, acoustic timescale analysis has been used to characterize the behavior of a one-dimensional hot spot where a linear temperature gradient is joined with a constant temperature plateau. In the present work, the effects of multiple dimensions are analyzed by considering hot spots whose plateau and gradient regions are modeled as circles and ellipses. Even with clear differences in behavior between one and two dimensions, the {\it a priori} prescribed hot spot acoustic timescale ratio is shown to characterize the 2-D gasdynamic response. In asymmetric hot spots, it is shown that the behavior along the semi-minor axis is similar to the one-dimensional model over a limited period of time.   

Linear Theory for the Interaction of Small-Scale Turbulence with Overdriven Detonations

To complement our previous analysis of interactions of large-scale turbulence with strong detonations, the corresponding theory of interactions of small-scale turbulence is presented here. Focusing most directly on the results of greatest interest, the ultimate long-time effects of high-frequency vortical and entropic disturbances on the burnt-gas flow, a normal-mode analysis is selected. The interaction of the planar detonation with a monochromatic pattern of perturbations is addressed first, and then a Fourier superposition for two-dimensional and three-dimensional isotropic turbulent fields is employed to provide integral formulae for the amplification of the kinetic energy, enstrophy, and density fluctuations. Effects of the propagation Mach number and of the chemical heat release and the chemical reaction rate are identified, as well as the similarities and differences from the previous result for the thin-detonation (fast-reaction) limit.   

Nonlinear dynamics of hydrogen-air detonations with detailed kinetics and diffusion

We consider the calculation of unsteady detonation in a mixture of calorically imperfect ideal gases with detailed kinetics. The use of detailed kinetics introduces multiple reaction length scales, and their interaction gives rise to complex dynamics. These are predicted using a wavelet-based adaptive mesh refinement technique and includes multi-component species, momentum, and energy diffusion, as well as DuFour and Soret effects. In the one-dimensional limit, we predict a transition from stability to unstable limit cycles as a driving piston velocity is lowered. At low overdrive, energy is partitioned into a variety of high frequency oscillatory modes. For weak low frequency instabilities, the dynamics are largely explained by a competition between advection and reaction time scales, with diffusion serving to perturb the dynamics. For higher frequency instabilities, the influence of diffusion is larger. We present new extensions to two-dimensional dynamics.   

Numerical study of detonation ignition via converging shock waves

In this talk we present results of a numerical study on gaseous detonation ignition via converging shock waves in reflectors. In our study, chemical kinetics is modelled by a three-step chain-branching mechanism possessing an explosion limit. According to our simulations, as soon as the shock reflects from the apex of the domain, the temperature and pressure behind it can exceed the explosion limit, thus initiating rapid burning. However, the subsequent expansion of the reflected shock might eventually inhibit detonation ignition. To explore further the interplay between these mechanisms, we discuss results of parametric studies with respect to confinement geometries and present estimates for the minimum shock strength required for detonation ignition.   

Mechanisms of strong pressure wave generations during knocking combustion: compressible reactive flow simulations with detailed chemical kinetics

Knocking is a very severe pressure oscillation caused by interactions between flame propagation and end-gas autoignition in spark-assisted engines. In this study, knocking combustion modeled in one-dimensional space is simulated using a highly efficient compressible flow solver with detailed chemical kinetics for clarifying the process of knocking occurrence. Especially, mechanisms of strong pressure wave generation are addressed. A robust and fast explicit integration method is used to efficiently handle stiff chemistry, and species bundling for effectively estimating the diffusion coefficients. The detailed mechanisms such as n-butane of 113 species and n-heptane of 373 species are directly applied. Results demonstrate that the negative temperature coefficient (NTC) region of n-heptane significantly influence the knocking timing and intensity. In the NTC region, stronger pressure wave is generated due to rapid heat release of a very small portion in the end-gas, which is attributed to low temperature oxidation and inhomogeneous temperature distributions in the end-gas. The knocking intensity is thus amplified in the NTC region, taking a maximum value. In the case of n-butane with no NTC region, relatively weak knocking intensity is observed in all conditions with no clear peak.   

Chemical Kinetics in the expansion flow field of a rotating detonation-wave engine

Rotating detonation-wave engines (RDE) are a form of continuous detonation-wave engines. They potentially provide further gains in performance than an intermittent or pulsed detonation--wave engine (PDE). The overall flow field in an idealized RDE, primarily consisting of two concentric cylinders, has been discussed in previous meetings. Because of the high pressures involved and the lack of adequate reaction mechanisms for this regime, previous simulations have typically used simplified chemistry models. However, understanding the exhaust species concentrations in propulsion devices is important for both performance considerations as well as estimating pollutant emissions. A key step towards addressing this need will be discussed in this talk. In this approach, an induction parameter model is used for simulating the detonation but a more detailed finite-chemistry model is used in the expansion flow region, where the pressures are lower and the uncertainties in the chemistry model are greatly reduced. Results show that overall radical concentrations in the exhaust flow are substantially lower than from earlier predictions with simplified models. The performance of a baseline hydrogen/air RDE increased from 4940 s to 5000 s with the expansion flow chemistry, due to recombination of radicals and more production of H2O, resulting in additional heat release.   

A Common Initiation Criterion for CL-20 EBW Detonators

In an effort to better understand the initiation mechanisms of hexanitrohexaazaisowurtzitane (CL-20) based Exploding Bridgewire (EBW) detonators, a series of studies were performed comparing electrical input parameters and detonator performance. Traditional methods of analysis, such as burst current and action, do not allow performance to be compared across multiple firesets. A new metric, electrical burst energy density ($E_{\rho })$, allows an explosive train to be characterized across all possible electrical configurations (different firesets, different sized gold bridges, different cables and cable lengths); by testing one electrical configuration, performance across all others is understood. This discovery has implications for design and surveillance, and for the first time, presents a link between modeling of electrical circuits (such as in ALEGRA) and explosive performance.   

Plasma Sensor Measurements in Pulse Detonation Engines

Measurements have been conducted in a pulse detonation and rotating detonation engine using a newly developed plasma sensor. This sensor relies on the novel approach of using an ac-driven, weakly-ionized electrical discharge as the main sensing element. The advantages of this approach include a native high bandwidth of 1 MHz without the need for electronic frequency compensation, a dual-mode capability that provides sensitivity to multiple flow parameters, including velocity, pressure, temperature, and gas-species, and a simple and robust design making it very cost effective. The sensor design is installation-compatible with conventional sensors commonly used in gas-turbine research such as the Kulite dynamic pressure sensor while providing much better longevity. Developmental work was performed in high temperature facilities that are relevant to the propulsion and high-speed research community. This includes tests performed in a J85 augmentor at full afterburner and pulse-detonation engines at the University of Cincinnati (UC) at temperatures approaching $2760^{\circ}$C ($5000^{\circ}$F).