Unsteady Detonation Waves Research Articles

Numerical study on flow and combustion properties of oblique detonation engine in a wide speed range

Ensuring safe flight is a fundamental prerequisite for developing hypersonic propulsion systems. A comprehensive investigation of the steady boundary associated with oblique detonation wave in a wide speed range was conducted, with the aim of exploring the feasibility of oblique detonation engine across a diverse array of flight conditions. In this study, the wedge angle applicable in a wide-speed range was acquired via the analysis of oblique detonation wave polar curve. The configuration of the internal injection oblique detonation engine was subsequently designed and established, considering the effect of fuel-air inhomogeneity and complex wave system interactions within a confined combustor. The compressible Euler equations coupled with a 9-species and 19-step chemical reaction mechanism are employed to simulate the oblique detonation process. Ultimately, the safe flight envelope of an air-breathing vehicle equipped with the internal injection oblique detonation engine is mapped across a broad range of Mach numbers, demonstrating the engine’s capability to operate within the Mach 8 to 12 range. Furthermore, the findings reveal that decreasing either the flight Mach number or altitude results in unsteady oblique detonation wave within the internal injection oblique detonation engine combustor, however, reducing the equivalence ratio can stabilize the oblique detonation wave once again. This study provides valuable guidance for the design and wide-speed-range operation of an internal injection oblique detonation engine.

Actual schemes of supersonic ramjet on detonation combustion. Unsteady detonation waves.

Actual schemes of supersonic ramjet on detonation combustion. Unsteady detonation waves.

Numerical investigation of one-dimensional unsteady detonation wave characteristics of magnesium particle-air mixture

In this paper, a one-dimensional unsteady model is established for the detonation of magnesium particle-air mixture. Through numerical simulation, the influences of the loss caused by the side wall of the detonation tube, the diameter of the magnesium particles, the initial equivalent ratio of the magnesium particles, and the deposition process on the surface of the particles, and the ignition energy on the structure and development of the detonation wave and the distribution of the flow field parameters inside the detonation wave are obtained. The studies show that there appear oscillations during the propagation of the fully developed one-dimensional unsteady detonation wave of magnesium particle-air mixture, but the amplitude is less than 1 m/s. Considering the loss of the wall, the pressure and temperature inside the detonation wave decrease with the inner diameter of the detonation tube decreasing, thus leading the propagation velocity and the thickness of the detonation wave decreasing. In the case without the wall loss, as the initial particle size increases, the detonation wave velocity remains unchanged, and the detonation wave thickness monotonically increases. With the wall loss taken into consideration, the stable velocity and thickness of detonation wave are lower than without considering the wall loss under the same initial conditions. Both the difference between the velocities and the difference between thickness values under the conditions with and without considering the wall loss increase as initial particle size increases. The detonation wave thickness with a double-size-distribution initial particle size is more than that with an equivalent single-size-distribution. Meanwhile the stable propagation velocity of the former is less than that of the latter. In the range of initial particle equivalent ratio of 0.5–2, as the initial equivalent ratio increases, the stable velocity of ideal detonation wave first increases and then decreases, and the thickness of the detonation wave first decreases and then increases. Considering the loss of the wall, with the increase of the initial equivalence ratio, the stable velocity of detonation wave first decreases and then increases and the thickness of the detonation wave monotonically decreases. When the initial equivalence ratio of the initial particles is in a lower range (0.337–0.382), the melting of MgO occurs near the CJ plane. As a result, the melting process of MgO has no significant effect on the stability of the detonation wave propagation, but has a greater influence on the structure of the detonation wave: when the initial equivalence ratio is lower in the above range, MgO in the detonation wave is partially melted and then re-solidified. When the initial equivalence ratio is higher in the above range, the MgO at the CJ plane is still in the melting process, and there is a low-strength secondary compression process in the detonation wave. Considering the fact that the combustion products are deposited on the particle surface, the detonation wave velocity increases while the corresponding thickness of the detonation wave remains almost unchanged with the increase of the deposition rate. The parameters of the ignition region have no influence on the final stable propagation state of the detonation wave, but will affect the development process of the detonation wave. Selecting appropriate paraneters of ignition zone can shorten the distance of denotation wave reaching to the steady propagation.

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.

Shock-wave processes in wire explosion in water and bubbly media

The structure of unsteady shock waves and bubble detonation waves generated by electrical explosion of a wire in water and chemically inert and reactive bubbly media was studied at a capacitor energy storage of 8–81 J. The formation and expansion of a plasma bubble after wire explosion in water and bubble media was investigated using optical recording. The formation of cavitation zones and the breakdown characteristics of the liquid and bubbly media in short strong shock waves were established. It is proved that the initiation of bubble detonation by wire explosion occurs by a resonance shock-wave mechanism. A comparative frequency Fourier analysis of shock waves in an inert bubble medium and bubble detonation waves was performed.

Qualitative modeling of the dynamics of detonations with losses

We consider a simplified model for the dynamics of one-dimensional detonations with generic losses. It consists of a single partial differential equation that reproduces, at a qualitative level, the essential properties of unsteady detonation waves, including pulsating and chaotic solutions. In particular, we investigate the effects of shock curvature and friction losses on detonation dynamics. To calculate steady-state solutions, a novel approach to solving the detonation eigenvalue problem is introduced that avoids the well-known numerical difficulties associated with the presence of a sonic point. By using unsteady numerical simulations of the simplified model, we also explore the nonlinear stability of steady-state or quasi-steady solutions.

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).

Preliminary study of a pulse normal detonation wave engine

A novel pulse normal detonation wave engine (PNDWE) is investigated from the viewpoint of entropy generation associated with combustion, whereas entropy production is detrimental to the efficiency of propulsion systems. To evaluate the relative advantages of different combustion modes for propulsion, the engine is studied in a given flight situation for a fixed amount of energy release during the combustion. Preliminary analysis suggests that compared with conventional subsonic combustion ramjet and Scramjet, PNDWE has superiority in theory, even though steady normal detonation engine is much inferior to the deflagration-based engine, for a given flight condition and a given amount of heat release. The principle of selecting the Mach number before unsteady detonation wave is also given. The superior range of flight Mach number for PNDWE is concluded to be about 3 to 7. Additionally, the influence of the exit boundary on the pulse normal detonation wave is discussed.

Modelling detonation waves in condensed energetic materials: multiphase CJ conditions and multidimensional computations

A hyperbolic multiphase flow model with a single pressure and a single velocity but several temperatures is proposed to deal with the detonation dynamics of condensed energetic materials. Temperature non-equilibrium effects are mandatory in order to deal with wave propagation (shocks, detonations) in heterogeneous mixtures. The model is obtained as the asymptotic limit of a total non-equilibrium multiphase flow model in the limit of stiff mechanical relaxation only (Kapila et al. in Phys Fluids 13:3002–3024, 2001). Special attention is given to mass transfer modelling, that is obtained on the basis of entropy production analysis in each phase and in the system (Saurel et al. in J Fluid Mech 607:313–350, 2008). With the help of the shock relations given in Saurel et al. (Shock Waves 16:209–232, 2007) the model is closed and provides a generalized ZND formulation for condensed energetic materials. In particular, generalized CJ conditions are obtained. They are based on a balance between the chemical reaction energy release and internal heat exchanges among phases. Moreover, the sound speed that appears at sonic surface corresponds to the one of Wood (A textbook of sound, G. Bell and Sons LTD, London, 1930) that presents a non-monotonic behaviour versus volume fraction. Therefore, non-conventional reaction zone structure is observed. When heat exchanges are absent, the conventional ZND model with conventional CJ conditions is recovered. When heat exchanges are involved interesting features are observed. The flow behaviour presents similarities with non ideal detonations (Wood and Kirkwood in J Chem Phys 22:1920–1924, 1950) and pathological detonations (Von Neuman in Theory of detonation waves, 1942; Guenoche et al. in AIAA Prog Astron Aeronaut 75: 387–407, 1981). It also present non-conventional behaviour with detonation velocity eventually greater than the CJ one. Multidimensional resolution of the corresponding model is then addressed. This poses serious difficulties related to the presence of material interfaces and shock propagation in multiphase mixtures. The first issue is solved by an extension of the method derived in Saurel et al. (J Comput Phys 228(5):1678–1712, 2009) in the presence of heat and mass transfers. The second issue poses the difficult mathematical question of numerical approximation of non-conservative systems in the presence of shocks associated to the physical question of energy partition among phases for a multiphase shock. A novel approach is used, based on extra evolution equations used to retain the information of the material initial state. This method insures convergence in the post-shock state. Thanks to these various theoretical and numerical ingredients, one-dimensional and multidimensional unsteady detonation waves computations are done, eventually in the presence of material interfaces. Convergence of the numerical hyperbolic solver against ZND multiphase solution is reached. Material interfaces, shocks, detonations are solved with a unified formulation where the same equations are solved everywhere with the same numerical scheme.

Theory of Detonation with an Embedded Sonic Locus

A steady planar self-sustained detonation has a sonic surface in the reaction zone that resides behind the lead shock. In this work we address the problem of generalizing sonic conditions for a three-dimensional unsteady self-sustained detonation wave. The conditions are proposed to be the characteristic compatibility conditions on the exceptional surface of the governing hyperbolic system of reactive Euler equations. Two equations are derived that are necessary to determine the motion of both the lead shock and the sonic surface. Detonation with an embedded sonic locus is thus treated as a two-front phenomenon: a reaction zone whose domain of influence is bounded by two surfaces, the lead shock surface and the trailing characteristic surface. The geometry of the two surfaces plays an important role in the underlying dynamics. We also discuss how the sonic conditions of detonation stability theory and detonation shock dynamics can be obtained as special cases of the general sonic conditions.

Numerical Simulation of Pulse Detonation Engine Phenomena

This computational study examines transient, reactive compressible flow phenomena associated with the pulse detonation wave engine. The PDWE is an intermittent combustion engine that relies on unsteady detonation wave propagation for combustion and compression elements of the propulsive cycle. The present computations focus on high order numerical simulations of the generic PDWE configuration with simplified reaction kinetics, so that rapid, straightforward estimates of engine performance may be made. Both one- and two-dimensional simulations of the high speed reactive flow phenomena are performed and compared to determine the applicability of 1D simulations for performance characterization. Examination of the effects of the combustion reaction mechanism and the use of a pressure relaxation length for 1D simulations is made. Characteristic engine performance parameters, in addition to engine noise estimates within and external to the detonation tube, are presented.

Wave angle for oblique detonation waves

The flow field associated with a steady, planar, oblique detonation wave is discussed. A revision is provided forβ-θ diagrams, whereβ is the wave angle andθ is the ramp angle. A new solution is proposed for weak underdriven detonation waves that does not violate the second law. A Taylor wave, encountered in unsteady detonation waves, is required. Uniqueness and hysteresis effects are also discussed.

Numerical Computation of Two-Dimensional Unsteady Detonation Waves in High Energy Solids

We are concerned with theoretical modelling of unsteady, two-dimensional detonation waves in high energy solids. A mathematical model and a numerical method to solve the associated hyperbolic system of equations are presented. The model consists of the Euler equations augmented bby extra conservation laws and source terms to accoxint for chemical reaction and tracking of materials. Both the thermodynamics and the chemistry are treated in a simple way. Using a detonation analogue due to Fickett, we test several numerical methods and assess their performance in modelling the essential features of detonation waves. The numerical method selected for the full model is an extension of the conservative, shock capturing technique of Roe, together with an adaptive mesh refinement procedure that allows the resolution of fine features such as reaction zones. Results for some typical tests problems are presented. Starting in 1946 as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in 1969. In 1993 it changed its name to Cranfield University.

Numerical computation of two-dimensional unsteady detonation waves in high energy solids

We are concerned with theoretical modelling of unsteady, twodimensional detonation waves in high energy solids. A mathematical model and a numerical method to solve the associated hyperbolic system of equations are presented. The model consists of the Euler equations augmented by extra conservation laws and source terms to account for chemical reaction and tracking of materials. Both the thermodynamics and the chemistry are treated in a simple way. Using a detonation analogue due to Fickett, we test several numerical methods and assess their performance in modelling the essential features of detonation waves. The numerical method selected for the full model is an extension of the conservative, shock capturing technique of Roe, together with an adaptive mesh refinement procedure that allows the resolution of fine features such as reaction zones. Results for some typical tests problems are presented.

Calculations of detonation waves in gas-droplet systems

The results of computations of steady and unsteady detonation waves in a heterogeneous medium, i.e. the mixture of liquid fuel drops and gaseous oxidizer, are presented. Inside the reaction zone the following processes are taken into account: deformation and acceleration of drops, break-up of a drop into smaller droplets at the instant when the critical stage of deformation has been reached, boundary layer stripping and, evaporation of the remains of drops at the last stage of dispersion (in a steady problem). To describe the deformation, a new approximate equation was introduced using the energetic approach. Several models of the reaction zone in a steady wave have been studied. The resulting numerical solution for the problem of point blast in a two-phase reacting medium shows that the velocity of the wave passes through a minimum and then increases, slowly approaching from below, the value of the steady Chapman-Jouguet detonation velocity.