Transverse Wave Structure Research Articles

Numerical study on transverse wave structure and blast dynamics of spinning detonation in a square tube

Three-dimensional numerical simulation of spinning detonation in a square tube is carried out using the time-dependent, reactive Euler equations with detailed H2/air chemistry. A two-dimensional simulation of single-head detonation is also performed at similar conditions for the purpose of comparison with three-dimensional simulation. The pseudo-detonation phenomenon that appears in the flow field of spinning detonation at low resolution is revealed by a resolution study, indicating that a suitable grid resolution is necessary for reproducing the real spinning detonation under present conditions. Subsequently, a representative pattern of helical strips left by the spinning detonation on the wall of square tube is carefully analyzed under limiting propagation conditions. Our results show that the transverse wave structure behind the detonation front for both two- and three-dimensional cases can be featured by a second kind of strong transverse wave structure defined in this paper, and such structure lead to the generation of a number of unreacted pockets downstream the front. Furthermore, the results demonstrate that the blast dynamics instead of the transverse detonation wave dominates the propagation of spinning detonation in present study. The blast kernels, including line blast kernels and point blast kernels, promote the heat release and subsequently support the spinning detonation in the square tube. Finally, the results indicate that the out-of-phase collisions between the triple lines on the leading shock front lead to the resonant coupling between the reaction surface and the shock front, permitting the detonation to propagate self-sustainingly in the lowest mode within a square tube.

Numerical simulation on the operating characteristics of rotating detonation ramjet engines at high flight mach number

For high-Mach-number incoming flow circumstances, a rotating detonation ramjet engine configuration is proposed in this research. By installing supporting blocks at the rear of the combustor, this configuration achieves continuous rotating detonation operation. Based on the Comparison of the flow structures obtained from the engine configuration with and without the supporting block before and after detonation ignition respectively, we obtain the intrinsic mechanism of detonation wave's propagation and re-initiation under the action of the supporting block. The supporting block creates a deflagration wave that is almost stationary before detonation ignition. In the detonation-ignited state, the deflagration wave is continually formed and traveling upstream under the influence of the supporting block, which is analogous to the periodical before detonation ignition of a transverse wave structure. The dynamic deflagration wave will cause the incomplete reactants behind the detonation wave to burn as the intensity of the detonation wave decreases. As a result, the incident shock wave is transformed into a Mach stem to achieve the re-initiation of the detonation wave.

MHD effects in continuous spin detonation

Conversion possibility of the chemical energy of combustion products of a hydrogen–oxygen mixture into electrical energy with the use of continuous spin detonation has been demonstrated for the first time in an MHD system. The specific conductivity of detonation products in the region of rotation of the detonation front was measured to be ~3 · 10–2 Ω–1 m–1. The structure of transverse detonation waves was examined, their velocity was measured (2220 ± 50 m/s), and the flow in their vicinity was studied.

A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals

In this paper, we propose a Petrov-Galerkin finite element interface method (PGFEIM) to solve the elliptic and elastic interface problems with Bloch-periodic boundary conditions. The main idea of this method is to choose the standard finite element basis independent of the interface to be the test function basis, and choose a piecewise linear function satisfying the jump conditions across the interface to be the solution basis. The grid we use is a non-body-fitted grid. The PGFEIM is capable of dealing with sharp-edged interface problems with matrix coefficients and nonhomogeneous jump conditions. Further, we extend this method to compute the band structure of anti-plane transverse waves and in-plane elastic waves in phononic crystals. Different acoustic impedance ratios, arbitrary complex scatterer geometries and various material properties are considered and discussed. Numerical experiments demonstrate that the PGFEIM is nearly second order accurate in the L∞ norm for interface problems, and it is accurate and efficient for computing the band structure of phononic crystals.

Fluctuation splitting Riemann solver for a non-conservative modeling of shear shallow water flow

In this paper we propose a fluctuation splitting finite volume scheme for a non-conservative modeling of shear shallow water flow (SSWF). This model was originally proposed by Teshukov (2007) in [14] and was extended to include modeling of friction by Gavrilyuk et al. (2018) in [7]. The directional splitting scheme proposed by Gavrilyuk et al. (2018) in [7] is tricky to apply on unstructured grids. Our scheme is based on the physical splitting in which we separate the characteristic waves of the model to form two different hyperbolic sub-systems. The fluctuations associated with each sub-systems are computed by developing Riemann solvers for these sub-systems in a local coordinate system. These fluctuations enable us to develop a Godunov-type scheme that can be easily applied on mixed/unstructured grids. While the equation of energy conservation is solved along with the SSWF model in [7], in this paper we solve only SSWF model equations.We develop a cell-centered finite volume code to validate the proposed scheme with the help of some numerical tests. As expected, the scheme shows first order convergence. The numerical simulation of 1D roll waves shows a good agreement with the experimental results. The numerical simulations of 2D roll waves show similar transverse wave structures as observed in [7].

Experimental characterization of RDE combustor flowfield using linear channel

An experimental study was conducted to characterize fundamental behavior of detonation waves propagating across an array of reactant jets inside a narrow channel, which simulated an unwrapped rotating detonation engine (RDE) configuration. Several key flow features in an ethylene-oxygen combustor were explored by sending detonation waves across reactant jets entering into cold bounding gas as well as hot combustion products. In this setup, ethylene and oxygen were injected separately into each recessed injector tube, while a total of 15 injectors were used to establish a partially premixed reactant jet array. The results revealed various details of transient flowfield, including a complex detonation wave front leading a curved oblique shock wave, the unsteady production of transverse waves at the edge of the reactant jets, and the onset of suppressed reactant jets re-entering the combustor following a detonation wave passage. The visualization images showed a complex, multidimensional, and highly irregular detonation wave front. It appeared non-uniform mixing of reactant jets lead to dynamic transverse wave structure. The refreshed reactant jets evolving in the wake of the detonation wave were severely distorted, indicating the effect of dynamic flowfield and rapid pressure change. The results suggest that the mixing between the fuel and oxidizer, as well as the mixing between the fresh reactants and the background products, should affect the stability of the RDE combustor processes.

Multilevel detonation cell structures in methane-air mixtures

High-resolution numerical simulations of two-dimensional detonations in a methane-air mixture with extremely high activation energy show the formation of multiple levels of cellular structures caused by the propagation of triple-shock configurations. Two main types of these configurations were observed based on the structure of transverse waves behind the leading edge of the detonation. Collisions were observed between two triple-shock configurations with attached transverse detonations, two triple-shock configurations with inert transverse waves, and one of each of these types. These collisions give rise to the formation of highly irregular, and, in some cases incomplete, cells. Smoke foils obtained from detonation of a near-stoichiometric mixture of natural gas and air show similar results. Estimates of the width of the experimental cells qualitatively match those inferred from the calculations.

Transverse wave band gaps and longitudinal wave band gaps in solid phononic crystals

Based on the properties of transverse (divergenceless) waves and longitudinal (irrotational) waves, we divided the transverse wave modes and longitudinal wave modes from the mixed eigen modes in solid phononic crystals. By investigating the transverse wave and longitudinal wave band structures at low frequency, we found that transverse bands and longitudinal bands exhibit different behaviors in solid systems including spherical scatterers. Phononic crystal with a large density ratio of solid spheres to the background can guarantee both the large longitudinal and large transverse band gap, but solid spheres with a small ratio of longitudinal wave velocity to transverse wave velocity can only help to enlarge the longitudinal band gap, and do not help to enlarge the transverse band gap.

Realization and modeling of continuous spin detonation of a hydrogen-oxygen mixture in flow-type combustors. 2. Combustors with expansion of the annular channel

Results of a comprehensive numerical and experimental study of continuous spin detonation of an H2-O2 mixture in flow-type annular combustors with channel expansion are presented. In these experiments, oxygen is supplied as a continuous flow through an annular slot, and hydrogen is injected through injectors. Combustion of hydrogen-oxygen mixtures in continuously rotating (spinning) and pulsed detonation waves with exhaustion of the products into an evacuated tank with increasing counterpressure and into the atmosphere was realized and studied in such combustors for the first time. The domain of realization of continuous detonation is determined. Verification of the mathematical model is performed on the basis of experimental results, and reasonable agreement is reached for the basic detonation parameters: structure of transverse detonation waves, their velocity, and pressures in the combustor and in the injection system.

Reaction Mechanism of Aluminum-Particle-Air Detonation

Both in-tube and unconfined experimental evidence showed strong dependence of micrometric aluminum-air detonability on initial pressure and highly nonlinear behavior of abrupt deflagration-to-detonation transition, thus indicating dependence of the aluminum reaction mechanism of the detonation waves on chemical kinetics. On the other hand, the observed aluminum―air detonation manifested itself in a weak transverse wave structure, as revealed by the small-amplitude oscillation that rapidly degenerates behind the shock front in the pressure histories. This suggests a functional dependence that is weaker than the nonlinear Arrhenius kinetic behavior for the later aluminum combustion. Hence, a surface kinetic oxidation and diffusion hybrid reaction model with a degree of condensed detonation products was suggested, and the unsteady two-phase fluid dynamics modeling showed the success of the hybrid reaction model, capable of capturing both the kinetics-limited transient processes of detonation initiation, abrupt deflagration-to-detonation transition and detonation instability, and the diffusion-limited combustion of aluminum in the long reaction zone, supporting the weak transverse wave structure.

Observations of three‐dimensional Langmuir wave structure

Measurements of the three‐dimensional structure of solar wind Langmuir waves made by the STEREO spacecraft are presented. Langmuir wave structure is studied using hodograms classified as one‐, two‐, or three‐dimensional. Multi‐dimensional Langmuir waves are both less‐often observed than one‐dimensional events and clustered in time. These observations show that a minority of Langmuir waves have electric fields transverse to the local magnetic field direction. We present a new explanation for this transverse structure based on an interpretation of Langmuir waves as eigenmodes of solar wind density cavities. These new observations are compared with previous theories for transverse wave structure and the eigenmode interpretation is found to be consistent with STEREO observations.

Deflagration to detonation transition in aluminum dust–air mixture under weak ignition condition

Deflagration to detonation transition (DDT) in flake aluminum dust–air mixture was studied in a 199 mm inner diameter and 29.6 m long horizontal tube. 40 sets of dust dispersion system were used to disperse flake aluminum into the experimental tube. An electric spark of 40 J was used to ignite the aluminum–air mixture. Self-sustained detonation was observed and the characteristics of deflagration to detonation transition process were studied. Contributed to the transverse wave and cellular structure of detonation wave front in aluminum–air mixture, the propagation velocity of detonation wave ranges from 1480 m/s to 1820 m/s and the maximum overpressure oscillates between 40 and 102 bar. Single head spinning detonation wave in aluminum dust–air mixture was observed and the cell size was evaluated.

Mathematical model of continuous detonation in an annular combustor with a supersonic flow velocity

A two-dimensional unsteady mathematical model of a continuous spinning detonation wave in a supersonic incoming flow in an annular combustor is formulated. The wave dynamics in a combustor filled by a gaseous hydrogen-oxygen mixture is studied. The possibility of continuous spin detonation with a supersonic flow velocity at the diffuser entrance is demonstrated numerically for the first time; the structure of transverse detonation waves and the range of their existence depending on the Mach number are studied.

Continuous Spin Detonations

Results on controlled continuous spin detonation of various fuels in liquid-propellant rocket motors and ramjet combustors are reported. Schemes of chambers, combustion in transverse detonation waves, and typical photographic records of transverse detonation waves are given. The flow structure, existence conditions, and basic properties of continuous detonation are considered. An analysis of physical, chemical, and geometric parameters determining spin detonation is presented. Results of studying continuous spin detonation of C 2 H 2 + air and H 2 + air mixtures in an annular ducted chamber 30.6 cm in diameter are reported. The range of existence of continuous spin detonation in fuel-air mixtures is determined as a function of the governing parameters. In the case of high-quality mixing, the transverse detonation wave velocity and structure are extremely stable in a wide range of the ratios of propellant components and in the examined range of pressures in the chamber.

Continuous Spin Detonation in Annular Combustors

An acetylene-oxygen mixture is burned in two annular chambers 100 mm in diameter in the spin detonation regime with supercritical and subcritical differences of oxygen pressure in the annular slot. By varying the flow rates of components of the mixture, width of the slot for oxidizer injection, point of fuel injection, and initial ambient pressure, the regions of existence and the structure of transverse detonation waves are studied, and the limits of existence of continuous detonation in terms of pressure in the chamber are determined. The losses of the total pressure in the flow in oxygen-injection slots and in fuel-injector orifices are estimated.

Resonant X-ray magnetic scattering studies of the TmNi 2B 2C spin density wave

We report on polarisation resolved, resonant X-ray magnetic scattering (RXMS) studies of the spin density wave (SDW) formed in the TmNi 2B 2C superconductor. From this high wave-vector resolution investigation, we find the incommensurate magnetic SDW propagation vector to be ( 0 ± τ 0 ± τ 0 ) with τ = 0.096 rlu , slightly larger than the value previously deduced from magnetic neutron studies ( τ = 0.093 rlu ). The widths of the SDW peaks at 1 K are consistent with long-range magnetic order and we have deduced a magnetic correlation length of ∼1200 Å. When the incident photons are tuned to the Tm L 3 absorption edge, the RXMS energy response consists of a double peak feature, arising from both dipole (E1) transitions, probing the 5d conduction band polarisation, and quadrupole (E2) transitions, probing the Tm 4f magnetic moments. The RXMS wave-vector dependences of the (0± τ 0± τ L) SDW satellites are consistent with the transverse spin-density wave structure, with moments orientated along the crystallographic c-axis, originally proposed from neutron-scattering measurements. Our RXMS data are also in good agreement with the magnetic neutron-scattering response for the thermal evolution of the magnetic moments down to 1 K and in deducing a Nèel temperature of T N = 1.5 K . However, the RXMS probe reveals a small shift of the magnetic propagation vector of the order 3×10 −3 rlu along the (1 1 0) direction, on decreasing temperature below T N. Using very high-resolution X-ray studies with a conventional Si(1 1 1) analyser, no change in width or position is found below T N or T c. We have also not observed any charge modulation peaks at 2 τ , indicating that the SDW does not couple to the lattice.

The failure mechanism of gaseous detonations: experiments in porous wall tubes

To clarify the important role of the transverse wave structure in real detonations, we conducted experiments in porous wall tubes, as to attenuate the detonation’s transverse waves. Flow visualization and measurements of the attenuation and failure processes for three typical unstable mixtures (oxy-acetylene, oxy-methane, and oxy-propane mixtures), characterized by their highly irregular frontal structure, revealed the ongoing competition between transverse wave elimination at the porous wall and re-amplification of triple points within the reaction zone. At critical conditions, when these two effects balance, a unique failure limit is found, namely d∗ ≈ 4λ. Below this limit, the detonations fail. These experiments thus illustrate that transverse wave interactions are essential in the ignition and propagation mechanism for such unstable detonations. In comparison, experiments with argon-diluted detonations displaying a regular cellular structure with weaker transverse waves indicate that their transverse waves do not play a significant role in their propagation mechanism. The failure of these stable detonations is due to the global curvature mechanism caused by the mass divergence into the porous wall, leading to the slow distribution of frontal curvature. The results obtained in diluted and undiluted mixtures are also compared with a model taking into account the mass divergence at the permeable tube walls. Very good agreement is found for the argon-diluted mixtures, while the agreement for the unstable mixtures is very poor. This further indicates that the weak transverse wave structure in argon-diluted detonations, unlike the undiluted ones, does not significantly contribute to the ignition mechanism. Hence these argon-diluted detonations can be well approximated by a ZND reaction zone structure.

Transverse waves in numerical simulations of cellular detonations

In this paper the structure of strong transverse waves in two-dimensional numerical simulations of cellular detonations is investigated. Resolution studies are performed and it is shown that much higher resolutions than those generally used are required to ensure that the flow and burning structures are well resolved. Resolutions of less than about 20 numerical points in the characteristic reaction length of the underlying steady detonation give very poor predictions of the shock configurations and burning, with the solution quickly worsening as the resolution drops. It is very difficult and dangerous to attempt to identify the physical structure, evolution and effect on the burning of the transverse waves using such under-resolved calculations. The process of transverse wave and triple point collision and reflection is then examined in a very high-resolution simulation. During the reflection, the slip line and interior triple point associated with the double Mach configuration of strong transverse waves become detached from the front and recede from it, producing a pocket of unburnt gas. The interaction of a forward facing jet of exploding gas with the emerging Mach stem produces a new double Mach configuration. The formation of this new Mach configuration is very similar to that of double Mach reflection of an inert shock wave reflecting from a wedge.

A numerical simulation of reflection processes of a detonation wave on a wedge

Abstract. A two dimensional numerical simulation has been performed to study reflection processes of detonation waves on a wedge. The numerical scheme adopted is the flux corrected transport scheme and a two-step chemical reaction is assumed for a stoichiometric oxyhydrogen mixture diluted with argon. Transverse wave structures of the detonation are produced by artificial disturbances situated in front of a one-dimensional Chapman-Jouguet detonation wave. Numerical grids are generated by solving a Laplace equation. Results show that in the case where Mach reflection occurs, the cells in the Mach stem are smaller than those in the incident wave and are distorted in shape. There is also an initiating stage during which the cells in the Mach stem are created. The critical angle beyond which Mach reflection cannot occur is discussed.

Numerical simulation of detonation reignition in H $_2$ -O $_2$ mixtures in area expansions

Time-dependent, two-dimensional, numerical simulations of a transmitted detonation show reig- nition occuring by one of two mechanisms. The rst mechanism involves the collision of triple points as they expand along a decaying shock front. In the second mechanism ignition results from the coalescence of a number of small, relatively high pressure regions left over from the decay of weakened transverse waves. The simulations were performed using an improved chemical kinetic model for stoichiometric H2- O2 mixtures. The initial conditions were a propagating, two-dimensional detonation resolved enough to show transverse wave structure. The calculations provide clarication of the reignition mechanism seen in previous H2-O2-Ar simulations, and again demonstrate that the transverse wave structure of the detonation front is critical to the reignition process.