Numerical Simulation of the Protective Effect of Complex Boundaries Toward Shock Waves in a 3D Explosive Field

A numerical method is presented that simulates 3D explosive field problems. A code MMIC3D using this method can be used to simulate the propagation and reflected effects of all kinds of rigid boundaries to shock waves produced by an explosive source. These numerical results indicate that the code MMIC3D has the ability in computing cases such as 3D shock waves produced by air explosion, vortex region of the shock wave, the Mach wave, and reflected waves behind rigid boundaries.

Direct numerical simulation of shock wave/boundary layer interaction controlled by steady microjet in a compression ramp

Shock wave/boundary layer interaction in a 24°turning angle of the compression ramp at Mach number 2.9 controlled by steady microjet is investigated using direct numerical simulation.Three different jet spacings which are termed as sparse,moderate and dense are considered,and the induced vortex system and shock structures are compared.A moderate jet spacing configuration is found to generate counter-rotating vortex pairs that transport high-momentum fluid towards the vicinity of wall and strengthen the boundary layer to resist separation,reducing the separation region.The dense jet spacing configuration creates a larger momentum deficit region,reducing the friction downstream of the corner.Analysis of pressure and pressure gradient reveals that dense jet spacing configuration reduces the intensity of separation shock.The impact of varying jet spacings on the turbulent kinetic energy transport mechanism is also investigated by decomposing the budget terms in the transport equation.Furthermore,the spectral characteristics of the separation region are studied using power spectral density and dynamic mode decomposition methods,revealing that moderate jet spacing configuration suppresses low-frequency fluctuations in the separation region.

The criterion of the existence or inexistence of transverse shock wave at wedge supported oblique detonation wave

A simplified theoretic method and numerical simulations were carried out to investigate the characterization of propagation of transverse shock wave at wedge supported oblique detonation wave.After solution validation,a criterion which is associated with the ratio Φ （u 2 /u CJ） of existence or inexistence of the transverse shock wave at the region of the primary triple was deduced systematically by 38 cases.It is observed that for abrupt oblique shock wave （OSW）/oblique detonation wave （ODW） transition,a transverse shock wave is generated at the region of the primary triple when Φ 〈 1,however,such a transverse shock wave does not take place for the smooth OSW/ODW transition when Φ 〉 1.The parameter Φ can be expressed as the Mach number behind the ODW front for stable CJ detonation.When 0.9 〈 Φ 〈 1.0,the reflected shock wave can pass across the contact discontinuity and interact with transverse waves which are originating from the ODW front.When 0.8 〈 Φ 〈 0.9,the reflected shock wave can not pass across the contact discontinuity and only reflects at the contact discontinuity.The condition （0.8 〈 Φ 〈 0.9） agrees well with the ratio （D ave /D CJ） in the critical detonation.

Direct numerical simulation of impinging shock wave and turbulent boundary layer interaction over a wavy-wall

The interaction of an impinging oblique shock wave with an angle of 30°and a supersonic turbulent boundary layer at Ma_(∞)=2.9 and Re_(θ)=2400 over a wavy-wall is investigated through direct numerical simulation and compared with the interaction on a flat-plate under the same flow conditions.A sinusoidal wave with amplitude to wavelength ratio of 0.26 moves in the streamwise direction and is uniformly distributed across the spanwise direction.The influences of the wavy-wall on the interaction,including the characterization of the flow field,the skin-friction,pressure and the budget of turbulence kinetic energy,are systematically studied.The region of separation grows slightly and decomposes into four bubbles.Local peaks of skin-friction are observed at the rear part of the interaction region.The low-frequency shock motion can be seen in the wall pressure spectra.Analyses of the turbulence kinetic energy budget indicate that both diffusion and transport significantly increase near the crests,balanced by an amplified dissipation in the near-wall region.Proper orthogonal decomposition analyses show that the most energetic structures are associated with the separated shock and the shear layer over the bubbles.Only the bubbles in the first two troughs are dominated by a low-frequency enlargement or shrinkage.

NUMERICAL SIMULATION OF 1-D UNSTEADY TWO-PHASE FLOWS WITH SHOCKS

In the present paper, random-choice method (RCM) and second-order GRP difference method, which are high resolution methods used for pure gas flows with shocks, are extended and employed to study the problem of one-dimensional unsteady two-phase flows. The two-phase shock wave and the flow field behind it in a dusty gas shock tube are calculated and the time-dependent change of the flow parameters for the gas and particle phase are obtained. The numerical results indicate that both the two methods can give the relaxation structure of the two-phase shocks with a sharp discontinuous front and that the GRP method has the advantages of less time-consuming and higher accuracy over the RCM method.

THE INTERACTION BETWEEN SHOCK WAVES AND FOAM IN A SHOCK TUBE

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.

Numerical simulation for deformation of multi-layer steel plates under underwater impulsive loading

To further understand the dynamic deformation and impact resistance of thin-plate hull structure under impulse wave,the deformation of multi-layer steel plates under underwater impulsive loading has been studied by AUTODYN V6.1.In order to verify the validity of numerical methods,the experimental results are compared with the simulation results.The multi-layer plate types include 1 mm + 3 mm,2 mm + 2 mm,3 mm + 1 mm double-layer,and 4 mm monolayer annealed 304 stainless steel plates.Each type of target plates has four flyer plate's velocities.There are 150,200,250 m /s and 300 m /s.The pressure wave histories in water and deformation of specimens have been predicted and measured by numerical simulations.The simulation results demonstrate that the protective capacity of 2mm + 2mm double-layer annealed 304 stainless steel plates is the best one in this velocity range of flyer plate,as the integral deformation is the smallest among the four structure types.

Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil

Numerical and experimental study to evaluate aerodynamic characteristics in supersonic ow over a double wedge airfoil is carried out using Fluent software and a supersonic wind tunnel, respectively. The Schlieren visualization method was also used to develop the experimental step of this study. The supersonic wind tunnel reached a proximately a Mach number of 1.8. The result got showed oblique shock waves visualization on double-wedge airfoil and the numerical simulation, the flow behavior as function of Mach number, pressure, temperature and density in the flow field on the computational model. The simulation allowed to observe the shock wave and the expansion fan in the leading and tailing edge of double-wedge airfoil. From the numerical and experimental comparison, an agreement at the shock wave angle and Mach number was observed, with a difference about 1.17% from the experimental results.

Study of Variation Patterns of Shock Wave Control by Different Plasma Aerodynamic Actuations

Demonstrative experiments on the variation patterns of the position, angle, and intensity of shock wave are presented. Different means of aerodynamic actuation, such as variations of the distance between discharge channels, the number of discharge channels, the DC discharge voltage, the angle of ramp, and the application of magnetic field, in a supersonic flow of M = 2.2 are employed. Results of both the schlieren and pressure test indicated that when the plasma aerodynamic actuation is applied, the starting point of the shock wave was shifted 1 mm to 8 mm upstream on average, the shock wave angle was reduced 470 to 8% on average, and the shock wave intensity was decreased by 8% to 26%. The local plasma aerodynamic actuation could generate an extrusive plasma layer with high temperature and pressure. This plasma layer caused an upstream-shift of the separating point of the boundary layer. which changed the structure of the original shock wave. Moreover, in a simulation study, the plasma aerodynamic actuation was simplified as a thermal source term added to the Navier-Stokes equations, after all, the results obtained showed consistency with the experimental results.

Further studies on the numerical simulation of bubble plumes in the cold seepage active region

Using the occurrence characteristics of bubble plumes in the South China Sea as a reference, this paper continues to study the seismic responses produced by bubble plumes in the cold seepage active region. To make the plume modelling scheme more reasonable, we modified the original modelling scheme and reconstructed a plume water body model based on the variation of its radius as bubbles rise in seawater. The plume seismic records of shot gathers were obtained by forward simulation. The seismic records of single shot show obvious characteristics of a scattering wave field and the periodic characteristics of the model. Seismic records of shot gathers were processed using prestack depth migration. The boundary of its imaging section has a good convergence effect. The migration sections can be imaged distinctly with higher accuracy. The aforementioned studies once again laid a foundation for the further study of the seismic responses produced by plumes. They also gradually probed a more suitable seismic data processing method for plumes and provided a theoretical guidance for the identification of plumes.

Flame behavior, shock wave, and instantaneous thermal field generated by unconfined vapor-liquid propylene oxide/air cloud detonation

Energy output and heating effects are essential for vapor-liquid fuel/air cloud detonation in the fuel-air explosive(FAE) applications or explosion accidents. The purpose of this study is to examine the dynamic large-size flame behavior, shock wave propagation law, and instantaneous thermal field generated by unconfined vapor-liquid propylene oxide(PO)/air cloud detonation. Based on computational fluid dynamics(CFD) and combustion theory, a numerical simulation is used to study the detonation process of a PO/air cloud produced by a double-event fuel-air explosive(DEFAE) of 2.16 kg. The large-scale flame behavior is characterized. The flame initially spreads radially and laterally in a wing shape. Subsequently,the developed flame increases with a larger aspect ratio. Moreover, the propagation laws of shock waves at different heights are discussed. The peak pressure of 1.3 m height level with a stepwise decline is obviously different from that of the ground with an amplitude of reversed ’N’ shape. In the vast majority of the first 6.9 m, the destructive effect of the shock wave near the ground is greater than that of the shock wave at 1.3 m height. Furthermore, the dynamic instantaneous isothermal field is demonstrated.The scaling relationship of various isotherms in the instantaneous thermal field with the flame and initial cloud is summarized. The comprehensive numerical model used in this study can be applied to determine the overpressure and temperature distribution in the entire fuel/air cloud detonation field,providing guidance for assessing the extent of damage caused by DEFAE detonation.

Study on the Propagation Law of Shock Wave Pressure in Tunnels with Different Materials

The propagation of shock wave pressure in the tunnel is greatly affected by the tunnel structure,shape,material and other factors,and there are great differences in the propagation law of shock wave pressure in different kinds of tunnels.In order to study the propagation law of shock wave pressure in tunnels with different materials,taking the long straight tunnel with the square section as an example,the AUTODYN software is used to simulate the explosion of TNT in the concrete,steel and granite tunnel,and study on the variation law of shock wave pressure in tunnels with different materials.By using dimensional analysis and combined with the results of numerical simulation,a mathematical model of the propagation law of shock wave pressure in the tunnel is established,and the effectiveness of the mathematical model is verified by making the explosion test of the warhead in the reinforce concrete tunnel.The results show that the same mass of TNT explodes in the tunnel with different materials,and the shock wave overpressure peak at the same measuring point is approximate in the near field.However,there is a significant difference in the middle-far fields from the explosion center,the shock wave overpressure peak in the steel tunnel is 20.76%and 34.82%higher than that of the concrete and the granite tunnel respectively,and the shock wave overpressure peak in the concrete tunnel is 24.91%higher than that in the granite tunnel.Through the experimental verification,getting the result that the maximum relative deviation between the measured value and the calculated value of the shock wave overpressure peak is 11.85%.Therefore,it is proved that the mathematical model can be used to predict the shock wave overpressure peak in the tunnel with different materials,and it can provide some reference for the power evaluation of warhead explosion in the tunnel.

Modeling on the shock wave in spheres hypervelocity impact on flat plates

In hypervelocity impacts of projectiles into thin flat targets,shock initiation and interaction dominate the responses of projectiles and targets,and especially dominate the features of the debris cloud.To estimate the geometric features of the wave front during the first complete propagation in the sphericalprojectile,the Geometric Propagation Model(GPM)is built in this paper to describe the geometry of the shock wave front,which proposes an ellipse contour as a function of time and equivalent speed.The GPM identifies the geometric features of the wave front as a function of time and impact velocity successfully.Combined with the GPM and SPH simulation,the shock pressure distribution and attenuation in the spherical-projectile have been obtained.Meanwhile,the attenuation of shock pressure and speed are presented as a function of impact velocity,respectively,and a method for obtaining the equivalent speed of the shock wave is proposed by the GPM.The GPM may be applicable to hypervelocity events involving any monolithic materials as long as the equivalent speed could be supplied from numerical simulation.The GPM proposed in this paper and the corresponding shock wave analysis provide a new insight into the processes of the quantitative analysis of the initiation of the debris cloud.

Modeling of the whole process of shock wave overpressure of freefield air explosion

The waveform of the explosion shock wave under free-field air explosion is an extremely complex problem.It is generally considered that the waveform consists of overpressure peak,positive pressure zone and negative pressure zone.Most of current practice usually considers only the positive pressure.Many empirical relations are available to predict overpressure peak,the positive pressure action time and pressure decay law.However,there are few models that can predict the whole waveform.The whole process of explosion shock wave overpressure,which was expressed as the product of the three factor functions of peak,attenuation and oscillation,was proposed in the present work.According to the principle of explosion similarity,the scaled parameters were introduced and the empirical formula was absorbed to form a mathematical model of shock wave overpressure.Parametric numerical simulations of free-field air explosions were conducted.By experimental verification of the AUTODYN numerical method and comparing the analytical and simulated curves,the model is proved to be accurate to calculate the shock wave overpressure under free-field air explosion.In addition,through the model the shock wave overpressure at different time and distance can be displayed in three dimensions.The model makes the time needed for theoretical calculation much less than that for numerical simulation.

Numerical Simulation of Bubble Plumes and an Analysis of Their Seismic Attributes

To study the bubble plume's seismic response characteristics,the model of a plume water body has been built in this article using the bubble-contained medium acoustic velocity model and the stochastic medium theory based on an analysis of both the acoustic characteristics of a bubble-contained water body and the actual features of a plume.The finite difference method is used for forward modelling,and the single-shot seismic record exhibits the characteristics of a scattered wave field generated by a plume.A meaningful conclusion is obtained by extracting seismic attributes from the pre-stack shot gather record of a plume.The values of the amplitude-related seismic attributes increase greatly as the bubble content goes up,and changes in bubble radius will not cause seismic attributes to change,which is primarily observed because the bubble content has a strong impact on the plume's acoustic velocity,while the bubble radius has a weak impact on the acoustic velocity.The above conclusion provides a theoretical reference for identifying hydrate plumes using seismic methods and contributes to further study on hydrate decomposition and migration,as well as on distribution of the methane bubble in seawater.

Centrifuge Model Tests and Numerical Simulations of the Impact of Underwater Explosion on an Air-Backed Steel Plate

Damage and threats to hydraulic and submarine structures by underwater explosions(UNDEXs)have raised much attention.The centrifuge model test,compared to prototype test,is a more promising way to examine the problem while reducing cost and satisfying the similitude requirements of both Mach and Froude numbers simultaneously.This study used a systematic approach employing centrifuge model tests and numerical simulations to investigate the effects of UNDEXs on an air-backed steel plate.Nineteen methodical centrifuge tests of UNDEXs were conducted.The shock wave pressure,bubble oscillation pressure,acceleration and the strain of the air-backed steel plate were recorded and compared with numerical studies using the finite element analysis(FEA)commercial software ABAQUS.By implementing empirically derived and physically measured pressures into the numerical models,the effects of the shock wave and bubble oscillation on the steel plate were investigated.Generally,the numerical results were in agreement with the experimental results.These results showed that the peak pressure of an UNDEX has a significant effect on the peak acceleration of the steel plate and that the impulse of the UNDEX pressure governs the peak strain of the steel plate.

Numerical Simulation of Lateral Jet Interaction

Jet interaction effects on aerodynamic characteristics of aircraft in subsonic/transonic compressible crossflow are investigated numerically. The high reliable CFD method is established and compared with existing experimental results. The lateral jet interaction characteristics of lateral jet in subsonic/ transonic compressible crossflow on an ogive-cylinder configuration are simulated numerically. Variation characteristics of normal force amplification factor, pitching moment and amplification factor are analyzed and compared with the results at supersonic condition. Research results and some useful conclusions can be provided for the design of RCS aircraft control system as basis and reference in subsonic/transonic compressible crossflow.

Interaction of strong converging shock wave with SF6gas bubble

Interaction of a strong converging shock wave with an SF6 gas bubble is studied, focusing on the effects of shock intensity and shock shape on interface evolution. Experimentally, the converging shock wave is generated by shock dynamics theory and the gas bubble is created by soap film technique. The post-shock flow field is captured by a schlieren photography combined with a high-speed video camera. Besides, a three-dimensional program is adopted to provide more details of flow field. After the strong converging shock wave impact, a wide and pronged outward jet, which differs from that in planar shock or weak converging shock condition, is derived from the downstream interface pole. This specific phenomenon is considered to be closely associated with shock intensity and shock curvature. Disturbed by the gas bubble, the converging shocks approaching the convergence center have polygonal shapes, and the relationship between shock intensity and shock radius verifies the applicability of polygonal converging shock theory. Subsequently, the motion of upstream point is discussed, and a modified nonlinear theory considering rarefaction wave and high amplitude effects is proposed. In addition, the effects of shock shape on interface morphology and interface scales are elucidated. These results indicate that the shape as well as shock strength plays an important role in interface evolution.

Effect of expansion waves on cowl shock wave and boundary layer interaction in hypersonic inlet

The interaction of cowl shock wave and boundary layer has a crucial effect on the stability,operability and performance of hypersonic inlets.Many studies on inhibiting the sep-aration and managing the strength of the interaction of the shock wave and boundary layer with expansion corner have been conducted.However,the expansion waves near the circular arc shoulder to effectively control the interaction and cowl shock arrangement is little investigated.Therefore,the interaction of the cowl shock wave and boundary layer under thefluence of the expansion waves is studied by inviscid and viscous numerical simulations.The results reveal that the expansion waves have an important impact on the interaction between the cowl shock wave and boundary layer and the strength of shock wave,and that there are four types of inter-action processes with the change of the relative impingement positions of cowl shock wave.The expansion waves have a different influence on the shock wave and boundary layer inter-action at different incident points.When the incident point of the cowl shock wave goes far downstream from the end of the circular arc shoulder,the influence of expansion waves is weakened,and the magnitude of separation zone increases.However,when the expansion waves are applied to the interaction of the cowl shock wave and boundary layer on the circular arc shoulder,the separation can be effectively controlled.In particular,while the expansion waves interact with the shock wave and boundary layer in the back half of the circular arc shoulder,the separation is best inhibited.Compared with the upstream and downstream inci-dent points,the scale of separation area in the optimal control region is reduced by 65.3%at most.Furthermore,the total pressure recovery coefficientfirst increases and then decreases when the cowl moves from upstream to downstream,and the total pressure recovery coefficient reaches the maximum value of 68.36%at the incident position of cowl shock wave d Z 8.09d0.

Numerical simulation of bubble plumes in overlying water of gas hydrate in the cold seepage active region

To study the seismic responses produced by gas hydrate bubble plumes in the cold seepage active region, we constructed a plume water body model based on random medium theory and acoustic velocity model of bubble medium. The plume water body model was forward simulated by finite difference. Seismic records of single shot show the scattered waves produced by the plume. The scattered wave energy is strong where the plume exists. Where the scattered wave energy is stronger, the minimum of travel time is always above the plume, which has no relationship with the shot's position. Seismic records of shot gathers were processed by prestack time migration. The migration section shows that the scattered waves produced by plumes can be imaged distinctly with higher accuracy. These researches laid a foundation for further study on the seismic responses produced by plumes and provided a new approach for the identification of gas hydrate.