NUMERICAL INVESTIGATION OF TOROIDAL SHOCK WAVES FOCUSING USING DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD

A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.

DETONATION INITIATION INDUCED BY FLAME IMPLOSION AND SHOCK WAVE FOCUSING

Computational simulations on structurally different detonation generator are carried out to study the phenomena,the mechanism and the gas dynamics characteristics of flame implosion and shock wave focusing.Two-dimensional axisymmetric and unsteady Navier-Stokes equations are numerically solved and detailed chemical reaction kinetics of hydrogen/air mixture is used.The simulation results show that the laminar flame generated by low energy spark in the jet flame burner is accelerated under the narrow channel,the jet flame impinging on the axis strengthens shock wave and the shock wave enhances flame acceleration.Under the function of multiple shock waves and flame,a number of hot spots appear between the wave and the surface.The spots enlarge rapidly,thus forming an over-drive detonation with high pressure,and then declining to stable detonation.Through calculation and analysis,the length of detonation initiation and stable detonation are obtained,thus providing the useful information for further experimental investigations.

Deflagration and detonation induced by shock wave focusing at different Mach numbers

Shock wave focusing is an effective way to create a hot spot or a high-pressure and hightemperature region at a certain place,showing its unique usage in detonation initiation,which is beneficial for the development of detonation-based engines.The flame propagation behavior after the autoignition induced by shock wave focusing is crucial to the formation and self-sustaining of the detonation wave.In this study,wedge reflectors with two different angles(60°and 90°)and a planar reflector are employed,and the Mach number of incident shock waves ranging from 2.0 to 2.8 is utilized to trigger different flame propagation modes.Dynamic pressure transducers and the high-speed schlieren imaging system are both employed to investigate the shock-shock collision and ignition procedure.The results reveal a total of four flame propagation modes:deflagration,DDT(Deflagration-to-Detonation Transition),unsteady detonation,and direct detonation.The detonation wave formed in the DDT and unsteady detonation mode is only approximately 75%-85%of the Chapman-Jouguet(C-J)speed;meanwhile,the directly induced detonation wave speed is close to the C-J speed.Transverse waves,which are strong evidence for the existence of detonation waves,are discovered in experiments.The usage of wedge reflectors significantly reduces the initial pressure difference ratio needed for direct detonation ignition.We also provide a practical method for differentiating between detonation and deflagration modes,which involves contrasting the speed of the reflected shock wave with the speed of the theoretically nonreactive reflected shock wave.These findings should serve as a reference for the detonation initiation technique in advanced detonation propulsion engines.

Focus Reflective Shock Wave Interaction with Flame

An experiment on deformation of flame under the effect of focusing shock wave reflection is performed with the help of multiple-spark camera to understand the flame instability of the deformation process. Methane and oxygen are mixed stoichiometrically to be used in the experiment. Based on Navier-Strokes equations,two-dimensional axisymmetric elementary reactions are numerically simulated. And the simulation results are solved by optical calculation. Shaded pictures by simulation fit well with experimental photos. Focusing reflecton shock waves can affect the flame,which accelerates the deformation of flame and renders violent burning in high-energy flammable gases behind waves. Therefore anticlockwise whirlpool appears. It clusters around the external surface of flame and has a tendency to develop toward the right. Finally,the whirlpool focuses on the right side of the flame,which involves the fresh unfired gases into the whirlpool circle,and consequently the head of mushroom cloud is formed. Meanwhile,when shock wave passes through the flame,the intensity of the shock waves on the axis is strengthened.

The influence of radial entrance width of the circular cavity on incident shock wave focusing

Despite the achievement of shock wave focusing with certain reflectors,the influence of the radial entrance width of a circular cavity on the flow field has yet to be addressed.In this study,we systematically investigated the effects of the shock wave focusing process in a cavity based on the radial entrance widths.An experimental system was installed to research the evolution of the flow field under conditions with different radial entrance widths of 3.0,11.1,19.5,and 33.0 mm.A schlieren system was used to photograph the structures of the flow field in the cavity,and a data acquisition system was used to record the dynamic pressure histories of different points.A numerical simulation was carried out to investigate greater details of the shock wave focusing process.A third-order strong stability-preserving Runge-Kutta method,third-order weighed essential non-oscillation scheme,and an adaptive mesh refinement algorithm were adopted to simulate the shock wave reflection,diffraction,and focus process.Good agreement between the experimental and numerical results was observed.By comparing the evolution process of the flow field under the conditions of four different entrance cavity widths,we found that when the entrance width was 19.5 mm,there was the stronger intensity of the shock wave focusing in the focal region,and the larger pressure value at the apex of the cavity than the other three entrance widths,occur.This study improves our understanding of shock wave focusing.

Computational study of planar shock wave interacting with elliptical heavy gas bubble

High-precision numerical methods are utilized to study the shock waves interacting with an elliptical heavy bubble.The influence of different bubble gases(SF6 and R22)and shock intensities(Ma=1.21 and Ma=2.1)is analyzed qualitatively and quantitatively.The results show that the focusing position is farther from the right bubble interface in the SF6 bubble(case 1)than in the R22 bubble(case 2)when Ma=1.21;thus,case 2 exhibits an outward jet structure,while case 1 does not.When Ma=2.1(case 3),the shock wave propagates faster,and the shock focusing is nearer to the right bubble interface.Finally,outward jet structures form on the bubble interfaces.The maximum values of density and pressure of shock focusing are different in the three cases,which imply that different gas densities and shock intensities significantly affect the shock-bubble interaction.The effective bubble volume and gases mixing degree are both smaller in case 2 than in case 1,but the trends over time are essentially the same.The increased shock intensity in case 3 leads to a smaller effective bubble volume than in case 1,but a much greater gases mixing degree.In all three cases,the compression term plays a more important role in the vorticity development than the other terms.