Strong Detonation Wave Research Articles

Real Gas Effect on Motion of Self-gravitating Cylindrical Detonation Waves

Abstract: The effect of real gas on the adiabatic propagation of strong cylindrical imploding detonation waves in the nonhomogeneous medium having power varying density distribution. Ignoring the effect of overtaking disturbances the CCW solution has been obtained for the problem at the detonation waves are initially in Chapman-Jouguet state. The analytical expressions for the detonation velocity just behind the front along with other flow variables are derived. The expressions for the freely propagating velocity of detonation front are derived. Using the jump condition across the strong detonation front, the numerical values of the pressure and density across the front have been computed with the help of the software MATLAB. It is observed that the variation of flow parameters with convergence of detonation front is depend upon the change in Alfven Mach number, the parameters of realness of the gas and initial density distribution. Finally, it is found that change in parameter of realness of the medium plays an important role on the post flow variables. The effect of change in Alfven Mach number and density parameter is also discussed through graphs. The outcome of the present study is compared with the results for the case of ideal reacting gas.

Imploding Detonation Waves in Self-gravitating Ideal Gas

In the present paper, the propagation of strong spherical imploding detonation waves in a reacting ideal gas under the effect of self-gravitation of the non-homogeneous medium has been investigated, by the help of Chester-Chisnell-Whitham (CCW) theory. It is considered that detonation wave is initially Chapman-Jouguet. Initial taking the density distribution law as power decreasing with distance, the analytical expressions for the detonation velocity just behind the front along with other flow variables are derived. Neglecting the effect of overtaking disturbances the variation of non-dimensional detonation velocity, the pressure and density with the propagation distance have been calculated numerically. The effect of change in density parameter at different Alfven Mach number on the convergence of detonation front have been discussed through graphs in details. Finally, it is found that density parameter and Alfven Mach number of gas have a significant role on propagation of strong spherical detonation front in reacting ideal gas with gravitation effect on all the post-flow variables. The software MATLAB have been used for computation of the problem. Keywords: Self-gravitating gas, Strong detonation waves, CCW theory.

Stability of strong detonation waves for Majda’s model with general ignition functions

For strong detonation waves of the inviscid Majda model, spectral stability was established by Jung and Yao for waves with step-type ignition functions, by a proof based largely on explicit knowledge of wave profiles. In the present work, we extend their stability results to strong detonation waves with more general ignition functions where explicit profiles are unknown. Our proof is based on reduction to a generalized Sturm-Liouville problem, similar to that used by Sukhtayev, Yang, and Zumbrun to study spectral stability of hydraulic shock profiles of the Saint-Venant equations.

Investigation of dual ignition for a detonation-driven shock tunnel in forward driving mode

A detonation-driven shock tunnel is useful as a ground test facility for hypersonic flow research. The forward detonation driving mode is usually used to achieve high-enthalpy flows due to its strong driving capability. Unfortunately, the strong detonation wave front results in diaphragm fragments that disturb the test flow and scratch the nozzle or test models. In this study, a dual ignition system was developed to burst a metal diaphragm without fragmentation in the forward driving mode. A series of experiments were conducted to validate the proposed technique. The influences of the delay time setting on the test conditions were investigated in detail. Numerical simulations were also conducted to obtain a better understanding of the wave processes in the shock tube. The results showed that the dual ignition system solved the diaphragm issues in the forward driving mode. The test time was shortened due to the additional ignition close to the primary diaphragm; the smaller the delay time, the shorter the effective test time. However, a small amount of time loss is considered worthwhile because the severe diaphragm problems have been solved.

Spherical detonation waves of the Chapman–Jouguet combustion model

The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we construct rigorously self-similar detonation wave solutions to a Riemann initial–boundary value problem for the spherically symmetric Chapman–Jouguet combustion model. We give a detailed analysis to show that the problem does not have a strong detonation wave solution but has a Chapman–Jouguet detonation wave solution. We also obtain detailed structures of the Chapman–Jouguet detonation wave solution besides the existence.

Fast Ignition by a Proton Beam and Burning of a DT Cylindrical Shell Target

Edge ignition of a cylindrical shell target by a proton beam with a small mass heating depth of about 0.5 g/cm2 is analyzed for two values of the initial mass density of the DT fuel, $${{\rho }_{0}} \approx 110$$ and 22 g/cm3, and given beam parameters (the intensity $$J \propto {{\rho }_{0}}$$ and impact time $$\Delta {{t}_{{{\text{pr}}}}} \propto \rho _{0}^{{ - 1}}$$ ). By comparing results obtained using different models of heat transfer through the fuel–shell interface, it is shown that application of a strong magnetic field that suppresses heat transfer but does not affect the trajectories of the α-particles produced in the DT reaction reduces the ignition energy by only about 10%. The unsteady detonation wave generated in the course of ignition transforms into a steady-state fast shockless burning wave, in which the cold fuel is heated by α-particles. The wave parameters depend on the deposited energy. As the wave propagates through the fuel, the α-particles escaping from the fuel volume carry away about one-half of their initial power. For one of the simulation versions, the target length H is determined ( $${{\rho }_{0}}H \approx 10$$ g/cm2) at which the gain reaches a value of $$G = 1250$$ . An approximate formula is derived that relates the slope of the pressure profile in a steady-state wave to the wave velocity and the heating power per unit mass of the fuel near the wave front. The applicability of the formulas relating the pressure and velocity at the Chapman–Jouguet point to the propagation velocity of a strong detonation wave is demonstrated.

Experimental research on ignition, quenching, reinitiation and the stabilization process in rotating detonation engine

This paper presents an experimental research on ignition, quenching, reinitiation and the stabilization process in hydrogen-air rotating detonation engine with an array of injection holes. The stabilization process can be divided into six sections, including deflagration, deflagration to detonation transition (DDT) process, coexistence of detonation with deflagration, coexistence of strong & weak detonations, unstable to stable detonation transition and stable detonation. The phenomenon of single-double-single wave transition is found and analyzed for the first time in the experiment. During the transition, the initial strong detonation wave weakens until it disappears, and the weak detonation wave becomes stronger until it propagates steadily. The reinitiation phenomenon is related to the injection pressures of the propellant. Increasing the injection pressure helps to reinitiate, thus avoiding the occurrence of the quenching phenomenon.

Transmission of a detonation across a density interface

The present study investigates the transmission of a detonation wave across a density interface. The problem is first studied theoretically considering an incident Chapman–Jouguet (CJ) detonation wave, neglecting its detailed reaction-zone structure. It is found that, if there is a density decrease at the interface, a transmitted strong detonation wave and a reflected expansion wave would be formed; if there is a density increase, one would obtain a transmitted CJ detonation wave followed by an expansion wave and a reflected shock wave. Numerical simulations are then performed considering that the incident detonation has the Zel’dovich–von Neumann–Doring reaction-zone structure. The transient process that occurs subsequently to the detonation-interface interaction has been captured by the simulations. The effects of the magnitude of density change across the interface and different reaction kinetics (i.e., single-step Arrhenius kinetics vs. two-step induction–reaction kinetics) on the dynamics of the transmission process are explored. After the transient relaxation process, the transmitted wave reaches the final state in the new medium. For the cases with two-step induction–reaction kinetics, the transmitted wave fails to evolve to a steady detonation wave if the magnitude of density increase is greater than a critical value. For the cases wherein the transmitted wave can evolve to a steady detonation, the numerical results for both reaction models give final propagation states that agree with the theoretical solutions.

Uniform formula for the riemann solutions of a scalar combustion model

In this paper, we construct a uniform formula for the Riemann solutions of the simplified Chapman-Jouguet model. Firstly, we define a new functional, and then, we obtain that the Riemann solutions can be expressed by the maximum value point of this functional, while Riemann solutions may contain some of strong detonation waves, Chapman-Jouguet detonation waves and contact discontinuities. Finally, Chapman-Jouguet deflagration waves are also discussed.

Attenuation and recovery of detonation wave after passing through acoustically absorbing section in hydrogen-air mixture at atmospheric pressure

The deceleration and attenuation of a detonation wave in a hydrogen-air mixture were experimentally studied in a cylindrical channel. The inner walls of an extended section of the channel were covered with an acoustically absorbing layer. Experiments were carried out in an undiluted by inert gases mixture at atmospheric pressure and 295 K temperature. Ignition of the hydrogen-air mixture was carried out by a spark gap at a closed end of the detonation tube, and the second end of the tube was opened. A strong detonation wave was formed before entering the section with the acoustically absorbing layer on the walls. The dependence of velocity and pressure at the front of the detonation/shock wave on the thickness of the acoustically absorbing material and mixture composition (equivalence ratio) was presented. The results demonstrate that increasing the thickness of the porous material on the walls lead to further attenuation of the detonation wave to the point where it is not re-initiated at the distance of 15 calibers from the porous section. It was found that the recovery of the detonation wave after the passage of the acoustically absorbing section can happen if the shock wave velocity does not drop below Chapman-Jouguet acoustic velocity.

Computational study of non-ideal and mildly-unstable detonation waves

This paper deals with some salient features of numerical detonation modeling, whose shock dynamics exhibits mildly oscillations behavior. The study is based on the integration of the hyperbolic equations with source terms, using a fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme for the convective flux and a third-order Runge–Kutta scheme for time advancement. Strang’s splitting technique is used for the integration of the source terms. The computations are performed for both stable and mildly unstable detonation waves. The study shows that the rate of convergence depends on the smoothness of the solution and that in presence of strong detonation waves, the accuracy is much lower than commonly believed. To improve the computation accuracy, a simple algorithm for shock detection is proposed along with a chemical activator for weak activation energies. A mesh refinement is also employed to achieve high resolution computations. It is found that a resolution of 66 points per half reaction zone is required to correctly capture the main structure of the detonation front and the associated flow instabilities. Examples are carried out to show that the proposed model yield accurate results. In particular, as the friction and the heat losses increase, the mean detonation velocity decreases and a series of period-doubling self sustained oscillations appears. It is also found that non-adiabatic conditions play a crucial role on the dynamics of the shock front, by enhancing the fluctuations. This aspect should be properly accounted for when dealing with multi-dimensional detonations.

Monotonic derivative correction for calculation of supersonic flows with shock waves

Subject of Research. Numerical solution methods of gas dynamics problems based on exact and approximate solution of Riemann problem are considered. We have developed an approach to the solution of Euler equations describing flows of inviscid compressible gas based on finite volume method and finite difference schemes of various order of accuracy. Godunov scheme, Kolgan scheme, Roe scheme, Harten scheme and Chakravarthy-Osher scheme are used in calculations (order of accuracy of finite difference schemes varies from 1st to 3rd). Comparison of accuracy and efficiency of various finite difference schemes is demonstrated on the calculation example of inviscid compressible gas flow in Laval nozzle in the case of continuous acceleration of flow in the nozzle and in the case of nozzle shock wave presence. Conclusions about accuracy of various finite difference schemes and time required for calculations are made. Main Results. Comparative analysis of difference schemes for Euler equations integration has been carried out. These schemes are based on accurate and approximate solution for the problem of an arbitrary discontinuity breakdown. Calculation results show that monotonic derivative correction provides numerical solution uniformity in the breakdown neighbourhood. From the one hand, it prevents formation of new points of extremum, providing the monotonicity property, but from the other hand, causes smoothing of existing minimums and maximums and accuracy loss. Practical Relevance. Developed numerical calculation method gives the possibility to perform high accuracy calculations of flows with strong non-stationary shock and detonation waves. At the same time, there are no non-physical solution oscillations on the shock wave front.

Stability of Viscous Weak Detonation Waves for Majda’s Model

Continuing the program initiated by Humpherys, Lyng, & Zumbrun [17] for strong detonation waves, we use a combination of analytical and numerical Evans-function techniques to analyze the spectral stability of weak detonation waves in a simplified model for gas-dynamical combustion. Combining these new spectral stability results with the pointwise Green function analysis of Lyng, Raoofi, Texier, & Zumbrun [22], we conclude that these waves are nonlinearly stable. The principal novelty of this analysis is the treatment of weak detonation waves. In contrast to the case of strong detonation waves, weak detonation waves are undercompressive and the stability of these waves is delicate and has not been treated by standard weighted-norm techniques. The present analysis thus provides a case study illustrating the flexibility and power of the Evans-function- based approach to stability. As in the case of strong detonations, we find that all tested waves are spectrally stable, hence nonlinearly stable.

Combining Discrete Equations Method and Upwind Downwind-Controlled Splitting for non-reacting and reacting two-fluid computations: Two dimensional case

This work deals with impermeable and permeable interfaces and the design of numerical strategies allowing multi-dimensional propagation of these interfaces on general unstructured grids. The numerical context is the (Reactive) Discrete Equations Method (DEM/RDEM) for the Baer–Nunziato type non-equilibrium multiphase model allowing a diffused interface, and meanwhile preserving the global conservation, which is of fundamental importance for studying long term combustion phenomena in large-scale geometries. Another advantage of RDEM for combustion lies in its ability to compute both deflagration and detonation, provided an appropriate reactive Riemann solver is inserted within the method. The present paper is a sequel to the recent publication (Tang et al., 2014) [35] where an anti-diffusive approach and an original Upwind Downwind-Controlled Splitting method (UDCS) were combined with the 1D formulation of the DEM and RDEM. The method successfully developed in 1D for computing inert interfaces (e.g. impermeable water gas shock tube problem) and flame interfaces (e.g. Chapman–Jouguet deflagration and strong detonation wave) with excellent robustness and accuracy properties is extended here to two dimensional problems. The proposed low- and anti-diffusive versions of the multi-D UDCS strategy form an original contribution to the modeling of multifluid flows on unstructured grids. This multi-D extension relies on a general derivation of the Downwind Factors involved in the formulation of UDCS. In particular, the proposed UDCS anti-diffusive algorithm represents a new alternative to the “Extended–Vofire” solver (Faucher and Kokh, 2013) [15] for unstructured meshes. Numerical experiments performed for non-reacting gas–gas and liquid–gas shock bubble interactions as well as for a model combustion problem demonstrate the combination of DEM/RDEM with UDCS yields excellent robustness/accuracy properties. Some remaining issues linked to the modeling of flame propagation in multi-dimensional cases are eventually discussed.

Combining Discrete Equations Method and upwind downwind-controlled splitting for non-reacting and reacting two-fluid computations: One dimensional case

The Discrete Equations Method (DEM) (Abgrall and Saurel, 2003) relies on integrating the solutions of interface problems over a two-phase control volume with these solutions provided by Riemann solvers. The method was next extended to reacting flows (RDEM) by Le Métayer et al. (2005). The objective of the present work is to compute high speed combustion waves in a robust and accurate way using RDEM. Several ingredients need to be implemented within the RDEM framework to achieve this goal and they are successively assessed on non-reacting interface problems using DEM and on reacting flows using RDEM. These ingredients are: the anti-diffusive approach developed in Després and Lagoutière (2002), the Large Time Step generalization of Godunov’s method proposed by LeVeque and an original upwind downwind-controlled spitting method (UDCS). Numerical experiments performed on one-dimensional non-reacting (water gas shock tube problem) and reacting (Chapman–Jouguet deflagration, strong detonation wave) flows demonstrate the combination of DEM/RDEM with UDCS and the anti-diffusive approach yields excellent robustness and accuracy properties.

Viscous Hyperstabilization of Detonation Waves in One Space Dimension

It is a standard practice to neglect diffusive effects in stability analyses of detonation waves. Here, with the aim of quantifying the impact of these oft-neglected effects on the stability characteristics of such waves, we use numerical Evans-function techniques to study the (spectral) stability of viscous strong detonation waves---particularly traveling-wave solutions of the Navier--Stokes equations modeling a mixture of reacting gases. Our results show a surprising synergy between the high-activation-energy limit typically studied in stability analyses of detonation waves and the presence of small but nonzero diffusive effects. While our calculations do show a modest delay in the onset of instability in agreement with recently reported calculations by direct numerical simulation of the physical equations, our Evans-function-based approach provides additional spectral information. In particular, for each of the families of detonation waves in our computational domain, we find an unexpected kind of hysteresis in the limit of increasing activation energy; that is, our calculations suggest that, whenever diffusive effects are present, there is a return to stability as activation energy is further increased, with unstable eigenvalues returning to the stable complex half-plane.

Comparative characteristics of strong shock and detonation waves in bubble media by an electrical wire explosion

Strong shock and detonation waves in inert and chemically active bubble media, which are generated by a wire explosion initiated by a capacitor with a stored energy $$W_0 =12.3$$ –1,600 J, is experimentally studied. The measurements are performed near the wire and far from the wire in a vertical shock tube 4.5 m long with a volume fraction of the gas in the medium $$\beta _0 =1$$ –4 %. It is shown that in inert bubble medium, a short intensely decaying shock wave (SW) with intense pressure oscillations is formed in the vicinity of wire explosion point; near the explosion point at $$\beta _0 \le 2$$ % the SW propagates with the velocity of sound in a liquid. In chemically active bubble medium, an unsteady detonation wave generated by a wire explosion is formed. The pressure amplitude and the velocity of this wave are greater and the length is smaller than those of SW in an inert bubble medium in the same range of explosion energy. It is found that in the interval of low energy explosion from $${\sim }12$$ to 64 J, the formation of the bubble detonation wave occurs faster than that at high energies ( $$3\times 10^{2}$$ – $$10^{3}$$ J).

Numerical simulation of one-dimensional aluminum particle–air detonation with realistic heat capacities

Aluminum (Al) particle–air detonation is very complicated because it includes multi-phase combustion phenomenon. Thus numerical simulations are often over-simplified. Here, the detonation is simulated by solving one-dimensional equations with more realistic heat capacities that vary with the dust mixture temperature. The effect on detonation parameters from the realistic heat capacities for the solid particles is investigated with a hybrid combustion model. The calculated results indicate that the detonation pressure, temperature and velocity vary significantly with changes in the heat capacity. Except for the velocity, these parameters are overestimated in numerical simulations when a constant heat capacity of the pre-shock mixtures is used. Furthermore, the realistic heat capacities have a strong effect on small diameter particles, but a weak effect on large diameter particles. Thus, when constant heat capacities are used, the combustion characteristic lengths are a function of the particle diameters with a power dependence of 1.77, whereas the power dependence decreases to 1.49 when realistic heat capacities are used. Moreover, if realistic heat capacities are applied, an “abnormal” strong detonation wave may appear in a dust mixture having large diameter particles. This phenomenon is consistent with the current combustion model, but it indicates that the value of heat released should also vary with the gas temperature in a fashion similar to that of the heat capacities.

Structure of shock wave for a viscous combustion model

In this article, the existence of weak and strong detonation waves for a viscous combustion model is proved. In order to prove the existence of this kind of waves, it is necessary to consider a 3-dimensional system of ordinary differential equations and prove the existence of heteroclinic orbits of it. In order to prove this, topological arguments are mainly tools.

Stability of Detonation Profiles in the ZND Limit

Confirming a conjecture of Lyng–Raoofi–Texier–Zumbrun, we show that stability of strong detonation waves in the ZND, or small-viscosity, limit is equivalent to stability of the limiting ZND detonation together with stability of the viscous profile associated with the component Neumann shock. Moreover, on bounded frequencies the nonstable eigenvalues of the viscous detonation wave converge to those of the limiting ZND detonation, while on frequencies of order one over viscosity, they converge to one over viscosity times those of the associated viscous Neumann shock. This yields immediately a number of examples of instability and Hopf bifurcation of reacting Navier–Stokes detonations through the extensive numerical studies of ZND stability in the detonation literature.