Shock Waves In Fluids Research Articles

Model for explosive shock waves in fluids with relaxation

Model for explosive shock waves in fluids with relaxation

A MUSCL-SCNI approach for meshfree modeling of shock waves in fluids

A stable and nodally integrated meshfree formulation for modeling shock waves in fluids is developed. The reproducing kernel approximation is employed to discretize the conservation equations for compressible flow, and a flux vector splitting approach is applied to allow proper numerical treatments for the advection and pressure parts, respectively, based on the characteristics of each flux term. To capture the essential shock physics in fluids, including the Rankine–Hugoniot jump conditions and the entropy condition, local Riemann enrichment is introduced under the stabilized conforming nodal integration (SCNI) framework. Meanwhile, numerical instabilities associated with the advection flux are eliminated by adopting a modified upwind scheme. To further enhance accuracy, a MUSCL-type method is introduced in conjunction with an oscillation limiter to avoid Gibbs phenomenon and ensure monotonic piecewise linear reconstruction in the smooth region. The present meshfree formulation is free from tunable artificial parameters and is capable of capturing shock and rarefaction waves without over/undershoots. Several numerical examples are analyzed to demonstrate the effectiveness of the proposed MUSCL-SCNI approach in meshfree modeling of complex shock phenomena, including shock diffraction, shock–vortex interaction, and high energy explosion processes.

Shock-induced energy conversion of entropy in non-ideal fluids

From shaping cosmic structures in space to producing intense sounds in aircraft engines, shock waves in fluids ineluctably convert entropy fluctuations into swirling motions and sound waves. Studies of the corresponding conversion from internal energy to kinetic energy have so far been restricted to ideal (or idealised) fluids. Yet, many substances do not obey the ideal-gas law (including those in the above two examples). The present work demonstrates that non-ideal thermodynamic properties provide a remarkable degree of control over the conversion to solenoidal and dilatational kinetic energies. Of particular interest is the ability to suppress much of the emitted acoustic field whilst promoting mixing downstream of the shock. This is made possible by exploiting the convexity (or lack thereof) of the shock adiabats. Whilst illustrated here using dense vapours near the thermodynamic critical point, this ability to design and control specific shock-induced energy transfers extends beyond near-critical-point phenomena; e.g. shocked mixtures (high-speed dusty flows on Mars, nanoparticle formation in supersonic expanders for drug manufacturing), reacting fronts (supersonic combustion, rocket propulsion), ionising shocks (reentry systems, inertial confinement fusion) or fronts in active fluids (bacterial and crowd flows). This theoretical work, which demonstrates the predictive capabilities of linear theory, lays the foundation for future experimental investigations ultimately aimed at delivering novel shock-based flow-control strategies exploiting the thermodynamic properties of the fluid.

FSI simulation of hydrodynamic ram event using LS-Dyna software

In this study, the effects of hydrodynamic ram on a fuel tank are studied using finite element method. Considered fluid-structure interaction (FSI) problem is solved in an Eulerian-Lagrangian reference frame by using LS-Dyna software. By comparing of the results obtained from the simulations and the experimental data, it can be seen that LS-Dyna software is able to model the different phases of hydrodynamic ram event accurately. Also, comparison of the wall Von Mises stress contours for the fluid-filled tank and the empty tank signifies 30% growth of the maximum Von Mises stress in the wall of the fluid-filled tank compared to the maximum Von Mises stress generated in the wall of the empty tank. In addition, numerical results show that because fluid-filled tank walls are pre-stress due to the fluid shock waves; failure mode of fluid-filled tank is quite different with the failure mode of the empty tank. Finally the effect of variation of parameters such as bullet velocity, tank elastic modulus and fluid density on maximum stress generated on tank was investigated.

Dynamics of a Pipeline under the Action of Internal Shock Pressure

The static and dynamic bending of a pipeline in the vertical plane under the action of its own weight is considered with regard to the interaction of the internal pressure with the curvature of the axial line and the axisymmetric deformation. The pressure consists of a constant and timevarying parts and is assumed to be uniformly distributed over the entire span between the supports. The pipeline reaction to the stepwise increase in the pressure is analyzed in the case where it is possible to determine the exact solution of the problem. The initial stage of bending determined by the smallness of elastic forces as compared to the inertial forces is introduced into the consideration. At this stage, the solution is sought in the form of power series and the law of pressure variation can be arbitrary. This solution provides initial conditions for determining the further process. The duration of the inertial stage is compared with the times of sharp changes of the pressure and the shock waves in fluids. The structure parameters are determined in the case where the shock pressure is accepted only by the inertial forces in the pipeline.

Shock waves in the atmosphere, the body, and mercury

As the 1995/96 F.V. Hunt Fellow, I transferred skills acquired during my Ph.D., at the University of Texas at Austin, in developing a numerical models of sonic boom propagation in the atmosphere, in order to investigate how shock waves propagate through the body, in order to better understand lithotripsy the medical procedure where shock waves are used to fragment kidney stones, at the Applied Physics Laboratory at the University of Washington in Seattle. After my fellowship, I joined the faculty at Boston University where a collaboration with Oak Ridge National Laboratory resulted in a project to understand shock wave generation and propagation in liquid mercury. This talk will focus on the underlying nonlinear acoustics associated with shock waves in fluids and by use of nondimensionalization demonstrate the strong similarity in these three apparently disparate propagation problems. It will be then shown that even with modern computers the memory and calculation requirements associated with fully three-...

Recent progresses on numerical investigations of microscopic structure of strong shock waves in fluid

Shock wave appears widely in various complex systems and plays an important role in the fundamental research and engineering applications. Much effort has been devoted to getting insight into the microscopic structure and dynamic features on the shock front and obtaining the shock hugoniot of materials. The scope of this review would be limited to strong shock waves in fluid, considering that materials behave as fluid under strong impact loading. The development of methods used to study shock waves has been reviewed and the applicable conditions and features of these method has been summarized. The microscopic structures, non-equilibrium effects and dynamic processes on the shock front have been discussed, which have reference value for the modeling of shock wave in complex system.

Instability of mistuned tube-array structures with axial loads

This study examined the instability of mistuned tube-array structures with axial loads. The tube-array structures were used to simulate a heat exchanger. In a heat exchanger, the tubes are frequently affected by hot and cold fluid shock waves. Therefore, the tubes often wear out. This wear may affect the dynamic properties of the tubes and introduce mode localization in the system. This study examined the instability caused by mode localization in a heat exchanger. A system consisting of periodic cooling tubes was used to simulate a coupled periodic structure system. Because each tube is coupled to the adjacent tube through the water, the system can be regarded as a weakly coupled system. The equations of the mistuned system with reference to the fluid effect can be derived using the Galerkin method. The numerical results indicated that the wear may introduce mode localization and instability into a mistuned heat exchanger with fluid.

Symmetry group approach to the solution of generalized Burgers equation: Ut + UUx = \lambda Uxx

Symmetry of a system of differential equations is a transformation that maps any solution to another solution of the system. In Lie’s framework such transformations are groups that depend on continuous parameters and consist of point transformations (point symmetries), acting on the system’s space of independent and dependent variables, or, more generally, contact transformations (contact symmetries), acting on independent and dependent variables as well as on all first derivatives of the dependent variables. Lie groups, and hence their infinitesimal generators, can be naturally prolonged to act on the space of independent variables, dependent variables, and derivatives of the dependent variables. We present a Lie symmetry approach in solving Burgers Equation:Ut + UU x = λUxx which is a nonlinear partial differential equation, which arises in model studies of turbulence and shock wave theory. In physical application of shock waves in fluids, coefficient λ, has the meaning of viscosity. So far in both analytic and numerical approaches the solutions have only been established for 0 ≤ λ ≤ 1. In this paper, we give a global solution to the Burgers equation with no restriction on λ i.e. for λ ∈ (−∞, ∞).

Vibration of a Tube with the Axial Loads and Fluid

Vibration of a tube with the fluid and axial load is focused. In a heat exchanger, the tubes are frequently affected by external force and fluid shock waves. Thus, tubes are often found to be vibrated. This vibration may alter the performance of the tubes and global heat exchanger. That a heat exchanger system is weakly coupled as the each tube is coupled to the adjacent one through the fluid is found. To understand the global system dynamics, the dynamics of a tube must be investigated first. In this work, the dynamic properties of a tube with the axial loads are investigated. The Galerkin method employed, the equation of a tube with the fluid effect can be to derive. Numerical results reveal that the axial load and fluid effects may affect the dynamic properties of a tube with fluid significantly.

Well-posed two-temperature constitutive equations for stable dense fluid shock waves using molecular dynamics and generalizations of Navier-Stokes-Fourier continuum mechanics

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.

Dilution and hydrate forming process in shock waves

Process of dilution and hydrate forming beyond the front of the shock wave with moderate amplitude (moderate shock wave front) in water with carbonic gas bubbles at varying initial static pressures has been experimentally observed and studied. Influence of surfactants on dilution and hydrate forming process beyond the shock wave occurring in the medium has been scrutinized. It has been proved that beyond the moderate shock wave in fluid with carbonic gas bubbles intense process of dilution and hydrate forming occurs resulting in complete loss of gas phase for several milliseconds. Surfactants present in the medium proved to be insignificant for dilution and hydrate forming process in the studied time range. Dependence of dilution and hydrate forming process beyond the shock wave from wave and medium parameters has been revealed. Theoretical model of dilution and hydrate forming process beyond the shock wave in gas and fluid medium taking into account convective and molecular gas diffusion in fluid, convective and conductive heat exchange caused by heat release in interphase boundary resulted from dilution and hydrate forming has been offered. Close fit of experimental data and calculations has been achieved.

Modal localization in mistuned tube-array structures

An investigation of mode localization in mistuned tube-array structures is studied in this work. The continuous action of hot-cold fluid shock waves in tube-array heat exchangers results in a significant abrasive wear of the tubes, which in turn alters their dynamic behavior and may introduce an undesirable modal localization effect within the tube bundle. This study performs a numerical investigation into the problem of modal localization in mistuned tube-array heat exchangers, with cross-flow. In conducting the investigation, the heat exchanger is modeled as a bundle of periodically-arranged cooling tubes in which the vibrational displacements of the individual tubes are weakly coupled to those of their neighbors via a squeezed water film in the gap between them. In general, the numerical results reveal that damage to even a single tube within the array is sufficient to introduce a severe modal localization effect. Furthermore, due to the weak coupling effect of the fluid, the vibrational energy induced by modal localization is confined to the defected tube and its immediate neighbors, and hence the risk of further wear defected within the tube bundle is increased. The results suggest that the modal localization phenomenon is alleviated at higher values of the cross-flow velocity, but becomes more severe as the tube wall thickness is increased.

Initial value formalism for Lemaitre-Tolman-Bondi collapse

Formulating a dust-filled spherically symmetric metric utilizing the 3 + 1 formalism for general relativity, we show that the metric coefficients are completely determined by the matter distribution throughout the spacetime. Furthermore, the metric describes both inhomogeneous dust regions and also vacuum regions in a single coordinate patch, thus alleviating the need for complicated matching schemes at the interfaces. In this way, the system is established as an initial boundary value problem, which has many benefits for its numerical evolution. We show the dust part of the metric is equivalent to the class of Lemaitre-Tolman-Bondi (LTB) metrics under a coordinate transformation. In this coordinate system, shell crossing singularities (SCS) are exhibited as fluid shock waves, and we therefore discuss possibilities for the dynamical extension of shell crossings through the initial point of formation by borrowing methods from classical fluid dynamics. This paper fills a void in the present literature associated with these collapse models by fully developing the formalism in great detail. Furthermore, the applications provide examples of the benefits of the present model.

Mode localization of a component cooling water heat exchanger

In a nuclear power plant, the tubes of a component cooling water heat exchanger are frequently affected by cold and hot fluid shock waves. Thus, tubes are often found to be worn out. This wear may alter the dynamics of the tubes and introduce mode localization in the heat exchanger. This paper examines mode localization in a component cooling water heat exchanger. A heat exchanger, consisting of periodic cooling tubes is used to simulate as a coupled periodic structure system. Each tube is coupled to the adjacent one through the water, and so the system is weakly coupled. The Galerkin method is employed herein to derive the mode localization equations off the mistuned system, with reference to the fluid effect. Numerical results reveal that the wear may introduce mode localization into a mistuned heat exchanger with fluid.

A unified theory for the interpretation of total pressure and temperature in two-phase flows at subsonic and supersonic speeds

This paper presents a unified theory on the interpretation of total pressure and total temperature in multiphase flows. The present approach applies to both vapour-droplet mixtures and solid-particle laden gases, and at subsonic as well as supersonic velocities. It is shown here that the non-equilibrium processes occurring in the vicinity of a stagnation point are important. These processes may be responsible for the generation of entropy and affect the pressure and temperature at the stagnation point. They should be properly considered while inferring, say, flow velocity or entropy generation from Pitot measurements. By proper non-dimensionalization of the relevant parameters, it is possible to find a single (theoretically obtained) calibration curve for the total pressure as a function of the particle size, which is almost independent of the constituents of the multiphase mixture and of the flow conditions. The calibration curve is a plot of a pressure recovery factor versus Stokes number and specifies the total pressure under different non-equilibrium conditions. The total pressure, predicted by the present theory, varies monotonically between the two limiting values: the frozen total pressure (when there is no interphase mass, momentum and energy transfer in the decelerating flow towards the stagnation point) and the equilibrium total pressure (when the dispersed phase, either the liquid droplets or the solid particles, is always at inertial and thermodynamic equilibrium with the continuous vapour phase). The equilibrium total pressure is always higher than the frozen total pressure. It is shown that the equilibrium total temperature, on the other hand, may be higher or lower than the frozen total temperature. In addition, unlike the case of total pressure, the calibration curve for total temperature is not so universal, and the total temperature under non-equilibrium conditions is not necessarily bounded between the frozen and equilibrium values. It is further shown that the entropy of a multiphase mixture has to be carefully interpreted and is not unequivocally related to the total pressure even in steady adiabatic flow.

Measurement of energy conversion efficiency during laser ablation by a multiple laser beam deflection probe

We have developed a novel multiple-pass laser beam deflection (LBD) arrangement for detection of acoustic and weak shock waves in fluids. The arrangement gives us the possibility to acquire temporally resolved information (signal waveforms) on single and non-reproducible events in several points of space. We have applied the new arrangement to investigate spherical shocks generated during laser ablation of metallic targets in air. For each ablation event we determine shock transit times at several points in space and fit the data to the theoretical shock trajectory in order to determine the blast energy released in the shock wave. This multiple-point procedure improves the accuracy and reliability of blast energy measurement.

Multiple-pass laser beam deflection probe for detection of acoustic and weak shock waves in fluids

We examine a novel laser beam deflection arrangement for detection of acoustic and weak shock waves in fluids. Novelty of the arrangement is folding of the probe beam by two parallel plane mirrors in such a way that the probe beam passes the wave propagation region several times before it reaches the deflection-detecting photodetector. In this way the probed wave interacts with several segments of the probing beam in sequence. A single oscilloscope trace of the photodetector output thus gives us the possibility to study the evolution of the probed wave at several distances from the source. To demonstrate the potentials of the arrangement we present wave forms of spherical blast waves detected in air during laser ablation of solid samples. We also discuss a simple theoretical model that qualitatively explains the most characteristic features of this arrangement.

Structure of weak shocks in fluids having embedded regions of negative nonlinearity

The dissipative structure of weak shock waves in fluids in which the fundamental derivative is negative for a finite range of pressures and temperatures has been examined. Conditions under which the shock thickness increases with strength rather than decreases are delineated. Nonclassical features of the entropy distribution and variation of local Mach number are also described.

Evaluation of electrohydraulic lithotripsy as a means of gallstone fragmentation in a canine model

Electrohydraulic lithotripsy (EL) is defined as the fragmentation of calculi or stones by electrically induced fluid shock waves. The objective and rationale of EL is to reduce the size of large retained stones so that stone fragments can be removed without the inherent risks and morbidity of surgical intervention. Lithotripsy equipment consists of a power source generator and a bipolar coaxial electrode. The generator discharges a rapid series of sparks across the two poles of the electrode tip. When the electrode tip is placed in a solution and discharged, these high voltage sparks cause an explosive evaporation and sudden expansion of the surrounding fluid which initiates the creation of hydraulic shock waves. When a shock wave travels through a liquid medium, its energy can be absorbed by an abrupt increase in acoustical impedance or resistance such as a stone. Absorption of shock wave energy within the stone leads to a build-up of pressure gradients and formation of tear and shear forces which eventually cause fragmentation. For more than a decade EL has been used successfully in urology for cystoscopic disintegration of vesical calculi.,2 Urolithiasis and choledocholithiasis present similar clinical problems, i.e., if a stone does not pass spontaneously, pain, ductal obstruction, or infection force surgical intervention for stone removal. Endoscopic EL for biliary calculi fragmentation is not currently performed. We report the results of our preliminary studies using an animal model to evaluate EL as a potential means of gallstone fragmentation in the common bile duct.