Shape Of Shock Wave Research Articles

Experimental study on effect of elastic-rigid composite boundary on shockwave from cavitation bubble collapse

Understanding the mechanisms behind the cavitation erosion resistance of elastic materials is the basis for the development of new cavitation erosion resistance materials. This paper employs underwater low-voltage discharge to induce cavitation bubble, combined with high-speed photography, shadowgraph methods, and transient pressure measurement systems to experimentally investigate the evolution and intensity of shockwave from bubble collapse near elastic-rigid composite boundary. Under the condition of constant elastic material thickness, with the bubble–wall distance increasing, shockwave shape evolves from multi-layers to single-layer. The peak pressure of the shockwave shows a trend of decreasing, then increasing, and finally stabilizing with increase in the bubble–wall distance. Furthermore, it was found that the elastic-rigid composite boundary causes the shockwave to reflect twice. As the material thickness increases, the intensity of the first reflected shockwave from the elastic surface decreases initially, then increases, and eventually stabilizes. However, that of the second reflected shockwave decreases. The total energy of the two reflections at the elastic interface is less than 4% of the mechanical energy of the bubble at its maximum volume. Finally, after the energy dissipation by the two reflections and material deformation, the elastic layer substrate withstands over 70% of the total mechanical energy of the cavitation bubble. There is an optimal elastic material thickness to minimize the shockwave load on the elastic layer substrate under the condition that the elastic-rigid composite boundary does not affect the evolution of cavitation bubble shape. These findings are significant for understanding bubble dynamics near elastic-rigid composite boundaries and provide theoretical support for developing cavitation erosion-resistant materials in engineering.

Analysis of CFRP inter‐laminar cracking location under laser impacts

AbstractIn this study, a combination of theoretical analysis and experimental verification was used to investigate the effects of laser parameters and shock wave shape on the location of layer cracks in carbon fiber‐reinforced plastics specimens. Firstly, the propagation coupling process of trapezoidal, rectangular, and triangular pulses in the material was investigated based on the one‐dimensional stress wave propagation theory. The study analyzed the effects of shock wave pressure amplitude, pulse width, and other factors on the location of layer cracks in the material. Subsequently, laser impact experiments with varying energies and pulse widths were conducted on specimens of different thicknesses to investigate the impact of shock wave pressure amplitude and laser pulse width on the location of layer cracking. The results show that the theoretical analysis of triangular shock waves has broader applicability and can serve as a representative analytical model to describe single‐layer crack damage.Highlights Laser impact experiments with various specimen thicknesses. Laser pulse width determines the initial location of inter‐laminar cracking. The applicability of the triangular pulsed layer cracking formula. The effect of laser energy on pulse amplitude.

The aerodynamic optimization of hypersonic vehicles with the proper-orthogonal-decomposition-based CST method

The flight performance of traditional hypersonic vehicles is limited to a specified incoming flow condition, their aerodynamic performance significantly deteriorates outside of the design condition. We construct a data-driven design framework for aerodynamic shape optimization of hypersonic vehicles, which can be used to improve the current flexibility of designing hypersonic vehicles based on the existing shockwave shape or flowfield. The framework uses a class function/shape function transformation to set parameters for the control sections of the vehicle, then the dimensions of the parameter matrix are reduced by using the proper orthogonal decomposition, and the surrogate model with improved expectations is combined to carry out the aerodynamic shape optimization of hypersonic vehicles. The hypersonic aerodynamic optimization design of NACA 0012 airfoil is conducted, which verifies the high efficiency of the optimization method. The single-point and multi-point aerodynamic optimization designs for the Hypersonic Technology Vehicle-2 (HTV-2) type are conducted. The correlation analysis to the fundamental modes of control sections and lift-to-drag ratio is performed, which verifies the accuracy of the design. Completed the single-point and multi-point optimized design of the entire vehicle considering 48 design variables and geometry restrictions with volume not less than 95% of the baseline. The single-point optimization increases the lift-to-drag ratio by 10.91%, and the multi-point optimization ensures that the aerodynamic performance is improved at all flight conditions and reduces the drag coefficient by 4.1% at the large angle of attack condition. The vehicle shape change rule that is controlled by the positively correlated and negatively correlated fundamental modes for the three control sections coincides with the optimized trend. The study demonstrated the effectiveness and practicality of the framework in the aerodynamic design of hypersonic vehicles.

Mathematical-Physics Analyses of the Nozzle Shaping at the Aperture Gas Outlet into Free Space under ESEM Pressure Conditions.

The paper presents a methodology that combines experimental measurements and mathematical-physics analyses to investigate the flow behavior in a nozzle-equipped aperture associated with the solution of its impact on electron beam dispersion in an environmental scanning electron microscope (ESEM). The shape of the nozzle significantly influences the character of the supersonic flow beyond the aperture, especially the shape and type of shock waves, which are highly dense compared to the surrounding gas. These significantly affect the electron scattering, which influences the resulting image. This paper analyzes the effect of aperture and nozzle shaping under specific low-pressure conditions and its impact on the electron dispersion of the primary electron beam.

Experimental investigation on the characteristics of the shock wave emitted by the cavitation bubble near the air bubble

This study explores the mitigation of cavitation damage in hydraulic engineering through air entrainment. The primary aim is to experimentally analyze the shock wave characteristics emitted by cavitation bubbles adjacent to air bubbles affixed to a tube nozzle. The schlieren optical system is utilized to visualize the shock wave, while a hydrophone measures its pressure. Experiments are conducted on cavitation bubbles induced by the spark-generated method in the vicinity of air bubbles, varying the dimensionless distances and sizes of the air bubbles. The results indicate that (1) The introduction of an air bubble noticeably changes the morphology, kinematic behavior, and shock wave features of the cavitation bubble. (2) Four distinct shock wave patterns are identified based on the quantity and shape of the shock wave, with variations in the cavitation bubble's collapsing behavior and shock wave characteristics across different patterns. (3) The dimensionless distance γ and size δ exert significant influence on the shock wave's quantity, pressure peak, shape, and energy. With γ decreases or δ increases, the shock wave quantity increases while the shock wave intensity decreases. This investigation of the interaction between cavitation bubbles and air bubbles is essential for elucidating the mechanism through which air entrainment mitigates cavitation damage.

Geometry of the energy input of a shockwave generated by a nanosecond laser-induced breakdown

The spatio-temporal evolution of the shock wave generated by a laser induced breakdown is often investigated and interpreted in the framework of the theory of shock similarity solutions. This work is a discussion about the choice of the most relevant geometry (spherical or cylindrical) to be used in the Jones modelling to track the intermediate-strength shockwave trajectory coming from a laser-induced non-resonant breakdown in argon. Laser incident energies ranging from 10 to 200 mJ with initial pressure of argon from 250 to 2500 mbar are investigated using a Q-switched Nd:YAG laser operating at a wavelength of 532 nm with a 6 ns pulse duration. Experimental results show that using the radial component of the ellipsoidal shape of the shockwave with a cylindrical geometry best describes the shockwave trajectory over time. Moreover, the deduced characteristic length allows us to observe a shockwave shape similarity for all tested laser energies at a given pressure.

Effect of relativistic ponderomotive force on shock waves in a relativistic degenerate plasma

Abstract We investigate the effect of relativistic ponderomotive force on the propagation of shock waves in relativistic degenerate plasma, which is relevant to high-intensity laser-plasma experiments aimed at replicating extreme conditions on white dwarfs. We derive the KdV-Burger’s equation by incorporating the density modification induced by the ponderomotive force and hence demonstrate that this equation is a suitable model for shock waves affected by ponderomotive force. Unlike previous studies that use ponderomotive force as a source of nonlinearity to derive the nonlinear Schrödinger equation for envelope solitons, our study focuses on the effect of ponderomotive force on shocks produced by the intense laser. We show that the ponderomotive force can significantly modify the strength and shape of shock waves, providing insight into the underlying physics of shock waves in relativistic degenerate plasmas which may help to better understand experimental observations in this regime.

Applicability analysis of inverse method of characteristics

The inverse method of characteristics (iMoC) is often employed to simulate the axisymmetric flow behind a predefined shock wave shape. Firstly, two marching schemes of iMoC were compared in this work: the intersection of the left- and right-running Mach lines and the intersection of the left-running Mach line and streamline. The intersection of the left-running Mach line and streamline is discovered to be simpler and more stable. Following that, the applicability of iMoC was analyzed by dividing the shock wave shapes into concave and convex curves, respectively. Based on the oblique shock relations, it is proved mathematically that iMoC is capable of computing the flow behind a concave shock wave. However, for the convex shock wave, if the shock wave angle declines too much along the axial coordinate, the clusters of left-running Mach lines may intersect, leading to iMoC failure. Furthermore, a method for enabling the implementation of iMoC is proposed by generating an expansion fan to replace the infeasible segment of the convex shock wave. Finally, computational fluid dynamics techniques were applied to validate the proposed methods and analysis. This study provides theoretical support to promote the application of iMoC in waverider and inward inlet design.

Analysis of wave converging phenomena inside the shocked two-dimensional cylindrical water column

Due to the curvature of the droplet surface, the propagation of transmitted waves is complex inside a droplet impacted by an incident shock wave. The wave converging phenomena inside a two-dimensional water column impacted by different curved shock waves are explored in this paper by means of theoretical ray analysis and high-resolution numerical simulations. An analytical method describing the wave structure evolution characteristics inside the shocked water column is established. Hence, the morphological pattern and focus locations of these waves are theoretically obtained. The analysis shows that both the first and the second reflected waves focus inside the water column regardless of the convergent, planar or divergent nature of the incident shock wave shape. The dimensionless distances from focusing points to the column centre are derived as ${\kappa }/{( 3\kappa -{{M}_{0}}{{f}_{s}} )}$ for the former and ${\kappa }/{( 5\kappa -{{M}_{0}}{{f}_{s}})}$ for the latter, respectively. Here, $\kappa$ , $M_0$ and $f_s$ represent the sound-speed ratio of the two phases, the incident shock wave strength and a function characterising the shock wave shape effect, respectively. Moreover, highly negative pressures due to the first reflected wave focusing and significant pressure oscillations due to the second reflected wave focusing are numerically tracked for three shapes of the incident shock. The effects of the incident shock wave intensity on the pressure variations at focus points are further studied. As the incident shock wave intensity increases, stronger negative pressure and higher pressure oscillation are induced. The converged incident shock wave can enhance the above phenomena, but the diverged one can weaken them.

Effects of influencing factors on the performance and morphology of shock waves in ejectors: A review

This paper presents a detailed literature review on the studies carried out in the last three decades, for understanding the factors affecting the performance of the ejector. An ejector is one of the important components in many industrial applications in the field of refrigerant expansion, circulation of fluids, vacuum creation, etc. From the analysis of the reported works of the ejector, the CFD modeling has proved to be a convenient method for analyzing the complex phenomenon in the ejector like mixing process, turbulence characteristics, shock interactions, and condensation process. The first part of this paper discusses the operation of ejector, flow structure, parameters required for the computational modeling, governing equations, etc. The second part discusses the influence of geometrical parameters and various operating conditions on the ejector performance. The shape and position of shock waves in the ejector for various operating conditions are also narrated under the same section. Third part of this paper is devoted to discussions on advances in modeling to be considered for the performance improvement of ejectors. Finally, the paper concludes with clear guidelines for the effective ejector modeling. Future scope of ejector research, pathways to progress, etc., mentioned in the conclusion section should help researchers and designers in this field.

Principles of Magnetohydrodynamical Control of Internal and External Supersonic Flows

This paper demonstrates the possibility of active magnetohydrodynamic (MHD) control of supersonic flows containing shock waves. The shock wave configurations that occur at the inlet to a supersonic diffuser and in front of a streamlined semicylindrical model are used for the purpose of investigation. The impact is carried out by organizing local gas discharge regions when applying a magnetic field transverse to gas discharge currents. It has been shown that by changing the local region of application, the intensity and the direction of the gas discharge currents, it is possible to change the intensity and direction of the ponderomotive force acting on the gas flow during MHD interaction. The ponderomotive force control allows for acting locally on the shape and position of shock waves, the speed and direction of the flow, and the increase or reduction of pressure near the surface of the streamlined body. The experiments were carried out on a gas dynamic setup based on a shock tube in a gas dynamic path, capable of creating supersonic flows in a wide range of Mach numbers at M = 4–7. There was a possibility of organizing the electric and pulsed magnetic fields with an intensity of up to 1.5 T. The given experimental Schlieren flow patterns and the analysis of the obtained data demonstrate the MHD effect on: the change in the angle of inclination of the attached shocks, both into increase and decrease; the bow shock wave approaching the body or the removal from it; and the change in the aerodynamic drag and lift force of the streamlined bodies.

Effects of feeding pressures on the flowfield structures of three-dimensional film cooling

A Mach 2.6 annular supersonic nozzle was designed to protect a hypersonic cone. The annular nozzle is able produce tangential cooling film around the cone. Experiments were carried out in a hypersonic wind tunnel under different cooling film feeding pressures and different attack angles. Temperature-sensitive paint (TSP) was used to measure surface temperature of the cone body; schlieren method was applied to visualize the flow structures. TSP results showed that cooling film can obviously decrease surface heating load, but its efficiency was influenced by the angle of attack. Schlieren results showed that the shape of upper-lip shock wave is similar to an arc, and the reflected shock wave is more closer to a straight line; both the tilt rate of upper-lip shock wave and the reflected shock wave were increased exponentially with the rise of feeding pressure; a higher feeding pressure resulted in a larger curvature of upper-lip shock wave; compared with reflected shock wave, upper-lip shock wave and shearing layer were more easily affected by the feeding pressure. With higher feeding pressure, incidence point was moved to the further downstream location, and a fitting formula is given to express the relationship between the position of the shock wave incidence point and the feeding pressure.

Shock Wave Reflection from Rough-Surface Wedges

The present paper describes a numerical study of shock wave reflection from rough- surface wedges. For validating the reliability of the applied numerical scheme it is first employed for simulating available experimental findings. Thereafter, the effect of the wedge surface roughness on the pattern of the reflected shock wave shape and on the post shock flow is investigated by comparing it to a similar smooth-surface case. It is shown that the presence of roughness changes both the reflected shock wave’s geometry and the prevailing pressure acting on the wedge surface. In addition, at high wedge angles there is a kinked shock wave between the incident shock wave and the reflected shock wave. This wave structure is unique for the rough-surface wedge case, and its length increases with the increase in the wedge angle.

Interpretation of the flow field behind shock waves based on the results of shock wave shape visualization

Interpretation of the flow field behind shock waves based on the results of shock wave shape visualization

The shape of incident shock wave in steady axisymmetric conical Mach reflection

For internal flow with supersonic inflow boundary conditions, a complicated oblique shock reflection may occur. Different from the planar shock reflection problem, where the shape of the incident shock can be a straight line, the shape of the incident shock wave in the inward-facing axisymmetric shock reflection in steady flow is an unknown curve. In this paper, a simple theoretical approach is proposed to determine the shape of this incident shock wave. The present theory is based on the steady Euler equations. When the assumption that the streamlines are straight lines at locations just behind the incident shock is adopted, an ordinary differential equation can be derived, and the shape of the incident shock wave is given by the solution of this ordinary differential equation. The predicted curves of the incident shock wave at several inlet conditions agree very well with the results of the numerical simulations.

Analysis Methods for High Energy Line Break Jet Flows in Nuclear Power Plants

Abstract The effects of postulated accidents, including dynamic effects of pipe ruptures, must be analyzed for licensing of nuclear power plants (NPPs). Applicants and licensees of NPPs have struggled to address U.S. Nuclear Regulatory Commission (NRC) expectations to assess if high energy line break (HELB) jet impingement on structures and components can lead to dynamic amplification, and to accurately simulate blast wave-induced loadings. In this paper, evaluation of the potential for load amplification and occurrence of resonance conclusively demonstrates that the phenomenon does not occur. In a HELB, several physical parameters of jets issuing from a ruptured pipe—such as nonequilibrium condensation of steam, unsteady separation between the jet exit and target, nonorthogonal alignment of jet axis to impingement surface, uneven impingement surfaces, or mismatch of jet excitation frequency and target natural frequency—prevent occurrence of the phase lock conditions needed to initiate and maintain a resonance. The analytical approach to evaluate the blast wave-induced loading applied a pressure vessel burst (PVB) correlation instead of performing computational fluid dynamics (CFD) analysis for all break locations. Three-dimensional (3D) CFD analysis of blast wave transient propagation provided the basis to develop benchmarking factors for use with the PVB correlation. The simplified methodology utilizes shockwave reflection, shape, and environment factors for application to impacted targets, which significantly reduces the amount of time to evaluate all break locations. The modified PVB method is also more appropriate than an explosion-type correlation to model the blast wave pressures from steam pipe breaks.

Investigation of Shock Waves in Nonextensive Electron–Positron–Ion Plasma with Relativistic Ions

Nonlinear propagation of ion-acoustic (IA) shock wave in a nonextensive and relativistic plasma is investigated by deriving space fractional Korteweg–de Vries–Burgers (SFKB) equation. This unmagnetized and collisionless plasma contains relativistic thermal ions, q-distributed electrons, and positrons. A modified tanh-function method is presented to solve the obtained SFKB equation taking space fractional and relativistic parameters, electrons nonextensivity, positrons nonextensivity, and electron-to-positron temperature ratio. It is observed that the structure of the IA shock wave can be modified by space fractional parameters. On the other hand, the IA shock wave shape can be modulated using the space fractional parameter. Our results can help understand the astrophysical environments such as pulsar magnetospheres, quasars, and collimated jets.

Accurate detection of shock waves and shock interactions in two-dimensional shock-capturing solutions

This paper describes an innovative technique that is capable of automatically detecting shock-wave shapes and shock-interaction patterns by post-processing the results obtained from a shock-capturing calculation using any of the available, state-of-the-art, shock-detection techniques. This new technique makes use of the Hough transform, the least-squares fit and the fuzzy logic to post-process the data supplied by classical shock-detection techniques; it not only allows to significantly enhance the quality of the extracted shock-fronts, but, even more importantly, allows to recognize the different types of shock-shock and shock-wall interactions that may occur within the flowfield.

Investigation on energy output structure of explosives near-ground explosion

In order to give the energy output structure of typical explosives near-ground explosion in real ground conditions, the free-field shockwave, ground reflection shockwave and Mach wave overpressure time history of composition B explosive, RDX explosive and aluminized explosive were measured by air pressure sensors and ground pressure sensors. The shape of the free-field shock wave, ground reflection shock wave, and Mach wave and explosion flame were captured by high-speed camera. The experimental results show that, at the same horizontal distance from the initiation point, the peak overpressure of explosive shock wave of composition B explosive, both in the air and on the ground, is less than that of RDX and aluminized explosives. At a distance of 3.0 m from the initiation point, the peak overpressure of aluminized explosives is slightly less than that of RDX explosives. Owing to the exothermic effect of aluminum powder, the pressure drop of aluminized explosives is slower than that of RDX explosives. At 5.0 m from the initiation point, the peak overpressure of aluminized explosives is larger than that of RDX explosives. At the same position from the initiation point, among the three kinds of explosives, the impulse of aluminized explosives is the maximum and the impulse of composition B explosives is the minimum. With the increase of the horizontal distance from the initiation point, the height of Mach triple-points (Mach steam) of the three explosives increases gradually. At the same horizontal distance from the initiation point, there is poorly difference in the height of Mach triple-points between aluminized explosive and RDX explosive, and the height of Mach triple-points of composition B explosive is much smaller than that of other two explosives. The maximum diameter and duration of the fireball formed by aluminized explosives are the largest, followed by composition B explosive, and the maximum diameter and duration of the fireball formed by RDX explosive are the smallest.

The influence of flow separation mode on side-loads in a rocket nozzle

Side-loads in nozzle can cause serious structural damage. Owing to the presence of side-loads of a rocket nozzle in the actual environmental situation, the unsteady flow field of the nozzle, which is based on dynamic mesh technology, has been simulated by taking VOLVO S1 nozzle. The study calculates the flow field and side-load in the nozzle when the pressure ratio is from 4 to 16, and comprehensively studies the generation and evolution of the shock wave shape, so as to analyze the influence of the internal flow separation on the side-load under different conditions of the nozzle. The results show that the nozzle flow separation mode will significantly affect the side-load, mainly in the following: when the nozzle is in the free shock separation mode, the airflow in the nozzle passes through the shock wave, occurs separation and then no longer adheres to the wall surface, while the side-load is obvious. As the pressure ratio increases, the asymmetry of flow separation occurs inside the nozzle and the side-load gradually increases with it. The nozzle flow is close to the critical state of the conversion of the shock separation until NPR=7. The severe pressure asymmetry of the upper and lower walls occurs inside the nozzle, accompanied by serious side-load. Subsequently, the nozzle flow transforms into the restricted shock separation, which is uniform and stable, and the side-load tends to a small amount in value.