Showing papers on "Shock (mechanics) published in 1995"

Time‐domain modeling of pulsed finite‐amplitude sound beams

Abstract: A time‐domain algorithm that solves the Khokhlov–Zabolotskaya–Kuznetsov (KZK) nonlinear parabolic wave equation is described. The algorithm models the propagation of pulsed finite amplitude sound beams radiated from axisymmetric sources in homogeneous, thermoviscous fluids. Numerical results are presented for waveform distortion and shock formation in directive beams radiated by pulsed circular pistons. Waveforms are calculated through the shock region and out to far‐field locations where they are dominated by the nonlinearly generated low‐frequency components. Effects of pulse duration, frequency modulation, and noise are examined. Methods for including relaxation and focusing are described.

Shock absorbing cushion

Abstract: A shock absorbing cushioning device suitable for products, objects and footwear which is comprised of a compressible insert encapsulated within an elastomeric barrier member The elastomeric barrier member is secured to the compressible insert by a plurality of tensile members having a first portion embedded in the elastomeric material and a second portion embedded in the compressible insert The elastomeric member is also filled with a fluid, preferably a compressible gas

Laser shock peening for gas turbine engine vane repair

Abstract: A wide gap braze repair, particularly for a gas turbine engine vane or a component in the hot section of the engine. The repair is characterized by a braze filled void in a damaged area of the component, a laser shock peened surface over the repaired area of the braze filled void, and a region of deep compressive residual stresses imparted by laser shock peening (LSP) extending from the laser shock peened surface into the repair.

Devices and methods for evaluating athletic performance

Abstract: The present invention provides for electrical devices and methods for evaluating athletic performance. A shock sensor is attached to an athlete or a suitable target such as a punching bag. When the athlete subjects the shock sensor to a shock with a magnitude which equals or exceeds the shock sensor sensitivity, an electrical effect is generated which is processed by a control means. The control means can be programmed for a delay period which precedes the performance evaluating cycle. The athlete's reaction time and shock magnitude can be measured and displayed. The devices and methods are suitable for evaluating athletic performance even if the athlete does not contact a target or an another object such as in simulated martial arts combat wherein there is no body contact between the athletes.

The First Second of a Type-II Supernova: Convection, Accretion, and Shock Propagation

Abstract: One- and two-dimensional hydrodynamical simulations of neutrino-driven supernova explosions are discussed. The simulations cover the phase between the stagnation of the prompt shock and about one second after core bounce. Systematic variation of the neutrino fluxes from the neutrino sphere shows that the explosion energy, explosion time scale, initial mass of the protoneutron star, and explosive nucleosynthesis of iron-group elements depend sensitively on the strength of the neutrino heating during the first few 100 ms after shock formation. Convective overturn in the neutrino-heated region behind the shock is a crucial help for the explosion only in a narrow window of neutrino luminosities. Here powerful explosions can be obtained only in the multi-dimensional case. For higher core-neutrino fluxes also spherically symmetrical models yield energetic explosions, while for lower luminosities even with convection no strong explosions occur.

On the exponentially slow motion of a viscous shock

Abstract: Using formal asymptotic methods, we study the internal layer behavior associated with the following viscous shock problem in the limit e 0: The convex nonlinearity f(u) satisfies f(α) = f(–α) For the steady problem, we show that the method of matched asymptotic expansions fails to uniquely determine the location of the equilibrium shock layer solution This indeterminacy, resulting from neglecting certain exponentially small effects, is eliminated by using the projection method, which exploits certain properties of the spectrum associated with the linearized operator For the time dependent problem, we show that the viscous shock, which is formed from initial data, drifts towards the equilibrium solution on an exponentially long time interval of the order O(eC/e), for some C > 0 This exponentially slow behavior is analyzed by deriving an equation of motion for the location of the viscous shock For Burgers equation (f(u) = u2/2), the results give an analytical characterization of the slow shock layer motion observed numerically in Kreiss and Kreiss; see [11] We also show that the shock layer behavior is very sensitive to small changes in the boundary operator In addition, using a WKB-type method, the slow viscous shock motion is studied numerically for small e, the results comparing favorably with corresponding analytical results Finally, we relate the slow viscous shock motion to similar slow internal layer motion for the Allen-Cahn equation

Nonlinear sawtooth-shaped waves

Abstract: This survey is devoted to experimental and theoretical results on interaction and self-action processes of strongly distorted waves containing shock fronts. Such sawtooth-shaped disturbances can be formed during the propagation of the wave through media where the nonlinearity predominates over competitive factors like dispersion, diffraction, and absorption. The specificity of nonlinear processes for sawtooth-shaped waves is particularly emphasised. The recently observed phenomena such as self-action of beams, self-refraction of shock pulses and saturation of the signal in focus, as well as current applied problems, are described.

High‐speed photography of compressive failure waves in glasses

Abstract: A mechanism for the compressive failure of soda‐lime and borosilicate glasses is proposed based upon high‐speed photography of impact on glasses. Shock loading was produced by the impact of a 50 mm diameter projectile so inducing shock states of one‐dimensional strain in glass targets. The shock waves and failure fronts were visualised using the shadowgraph technique. The failure appeared to occur at discrete nucleation sites and propagated out to form a continuous front. The velocity of this front increased with higher impact stresses and varied with the glass composition.

Injection and acceleration of interstellar pickup ions at the heliospheric termination shock

Abstract: We have used a one-dimensional hybrid code (macro-ions, massless electron fluid) in order to study the interaction of an interstellar pickup ion distribution with the heliospheric termination shock. The shock is generated by reflecting the solar plasma at a rigid wall. The interstellar pickup ions are additional populations modeled as spheres in velocity space with radii given by the solar wind speed, comoving with the solar wind. The pickup ions are located on the outer shell of the spheres. We have determined the reflection rates of the pickup ions, which have been defined as the ratio of the reflected to the incident pickup ions at the shock. The dependence of these reflection rates on the shock normal angle Θ Bn and on an upstream imposed turbulence has been investigated. No backscattered pickup ions are found for Θ Bn greater than 70° and the reflection rates decrease with increasing level of upstream imposed turbulence. The dependence of the reflection rate on the ratio of the upstream pickup proton density to the upstream solar wind density has been investigated. Since this ratio is proportional to the heliospheric distance of the termination shock we have been able to investigate the reflection rates of the pickup ions at different heliospheric locations of the termination shock. Based on these hybrid simulations a model for the acceleration of anomalous component of the cosmic rays has been developed which is able to explain the differential flux of anomalous helium at the termination shock needed in modulation calculations to fit observations in the inner heliosphere. In this model we have not included the influence of the anomalous component on the shock structure. From comparison with modulation calculations it is concluded that the location of the termination shock is at distances between 80 and 120 AU.

Dynamic properties of ceramic materials

Abstract: The present study offers new data and analysis on the transient shock strength and equation-of-state properties of ceramics. Various dynamic data on nine high strength ceramics are provided with wave profile measurements, through velocity interferometry techniques, the principal observable. Compressive failure in the shock wave front, with emphasis on brittle versus ductile mechanisms of deformation, is examined in some detail. Extensive spall strength data are provided and related to the theoretical spall strength, and to energy-based theories of the spall process. Failure waves, as a mechanism of deformation in the transient shock process, are examined. Strength and equation-of-state analysis of shock data on silicon carbide, boron carbide, tungsten carbide, silicon dioxide and aluminum nitride is presented with particular emphasis on phase transition properties for the latter two. Wave profile measurements on selected ceramics are investigated for evidence of rate sensitive elastic precursor decay in the shock front failure process.

Demonstration of an Automotive Semi-Active Suspension Using Electrorheological Fluid

Abstract: A prototype semi-active suspension system using fast, continuously variable, electrorheological (ER) shock absorbers was installed on a demonstration vehicle. The shock absorbers had no moving parts other than the piston/rod moving relative to the body of the device. Damping was obtained by controller/power supplies individually applying voltages to the four shock absorbers as determined by a modified sky-hook algorithm. This included control of heave, pitch and roll body motions. The damping parameters could be adjusted to tuning ride and handling characteristics. The system was designed to respond in less than 10 ms with an average power requirement of less than 40 W for normal road surfaces and handling. Data are presented that document the performance of the demonstration vehicle. Within the optimal temperature range of the system, the suspension performed as designed. (A) For the covering abstract of the conference see IRRD 875861.

One-dimensional front tracking based on high resolution wave propagation methods

Abstract: A simple approach to shock tracking is presented in conjunction with conservative high resolution shock-capturing methods in one space dimension. An underlying uniform grid is used with additional grid interfaces introduced at appropriate points for tracked shocks. Conservative high resolution methods based on the large time step wave propagation approach are used on the resulting nonuniform grid. This method is stable even if some of the small cells created by the tracked interface are orders of magnitude smaller than the regular cells used to determine the time step. A fractional step method is used to handle source terms. Several calculations are presented to demonstrate the effectiveness of the method, including an unstable detonation wave calculation where mesh refinement in the reaction zone is required in addition to shock tracking. Stability and accuracy results of the method are also shown for some sample problems. The basic ideas described here can be extended to two space dimensions, as will be...

An aspect of sonoluminescence from hydrodynamic theory

Abstract: Sonoluminescence (SL), the phenomenon of light emission associated with the collapse of bubble oscillating under ultrasonic pressure field has been studied by solving the conservation equations for the gas inside bubble analytically. Heat transfer in the liquid layer adjacent to the bubble wall has also been considered in this analysis. It has been found that the gas behavior is neither adiabatic nor isothermal for a bubble under ultrasound conditions. In this analysis, the launch condition and the Hugoniot curve for the shock propagation have been identified, and the shock duration of 2.7 to 17 ps, which is comparable to experimental result, has been obtained with the use of a similarity solution for converging spherical shock. For SL, the gas temperature after the shock focusing has been found to be 7000 K∼ 44000 K, depending on the equilibrium bubble radius and the driving amplitude of ultrasound. It has also been found that the heat flux at bubble collapse is as large as 47 GW/m 2 , which could be mor...

The numerical simulation of shock bifurcation near the end wall of a shock tube

Abstract: The reflection of a normal shock wave from the end wall of a two‐dimensional channel has been numerically simulated to investigate the unsteady, viscous interaction aspects of shock bifurcation. The numerical simulation implements a data‐parallel version of the Flux‐Corrected Transport algorithm that has been coupled to the viscous transport terms of the Navier–Stokes equations. All numerical simulations were performed on the Connection Machine, the CM‐5. The results indicate that the shear layer in the bifurcation zone is unstable, and the large and small scale vortices lead to complex flow patterns. In addition, the high‐speed, essentially inviscid flow, which is adjacent to the shear layer, is deflected over this region. As a result, weak shock and expansions waves are generated and a reattachment shock is formed at the trailing edge of the interaction region. The impact of heat transfer, Reynolds number, and incident shock strength on the viscous interaction is also investigated. Heat transfer to the ...

Nonlinear stability of an undercompressive shock for complex Burgers equation

Abstract: Though there is strong numerical evidence for the stability of undercompressive shocks, their stability has not been verified analytically. In particular, the energy methods used to analyze stability of standard shocks do not apply. Here, we present the first proof of stability for a particular undercompresive shock, the real Burgers shock considered as a solution of the complex Burgers equation. Our analysis is by direct calculation of the Green's function for the linearized equations, combined with pointwise estimates of nonlinear effects. A benefit of this method is to obtain fairly detailed information about the solution, includingL1 behavior, and rates of decay in different regions of space.

Shock layer movement for Burgers' equation

Abstract: This paper considers the motion of the shock layer exhibited by the solution of the initial-boundary value problem for the equation $\epsilon u_{xx} + uu_x = u_t $ with small values of $\epsilon > 0$. This Burgers’ equation occurs as a model for a number of physical problems and is representative of many convection-dominated evolution equations. A specific example will be solved explicitly using the Cole–Hopf transformation. The result suggests a corresponding asymptotic approach which provides the shock layer location $x_\epsilon ( t )$ as the solution of an initial value problem. That method, which can be applied to a far wider class of equations, also shows how the steady-state shock location can be changed substantially by asymptotic exponentially small perturbations.

Laser shock peening surface enhancement for gas turbine engine high strength rotor alloy repair

Abstract: A metallic article and method for producing such an article, having a metallic substrate, at least one metallic layer sprayed onto a laser shock peened surface area of the substrate, and a region having deep compressive residual stresses imparted by laser shock peening extending into the substrate from the laser shock peened surface. The metallic substrate and or layer may be made from an alloy such as a Cobalt or a Nickel based superalloy. The substrate may be made from Nickel Base forgings or Titanium base forgings. An exemplary embodiment of the present invention is a gas turbine engine rotor component such a disk and, more particularly, a turbine disk suitable for use in a hot section of a gas turbine engine. The invention may be used for new or refurbished parts to restore dimensions of the component and, in particular, radial dimensions.

Distortion control for laser shock peened gas turbine engine compressor blade edges

Abstract: A method for counteracting distortion of the airfoil caused by laser shock peening a gas turbine engine compressor metallic airfoil along its leading and/or trailing edge to form laser shock peened surfaces extending radially along at least a portion of the edges with a region having deep compressive residual stresses imparted by laser shock peening (LSP) extending into the airfoil from the laser shock peened surfaces.

Head biomechanics: from the finite element model to the physical model

Abstract: The objectives of this work are: (1) to characterize the human head dynamic response under shock conditions by a new three-dimensional (3D) finite element model (FEM); and (2) to transfer the results to a physical model intended for "measuring" the shock severity. The proposed 3D FEM distinguishes the different anatomical features of the cerebral matter. Model validation is based on it's theoretical modal analysis compared to the in vivo mechanical impedance recordings of the head. Modal analysis of the model shows three vibration modes. The mode shapes are illustrated by brain rotations around the Z1, Y1-Y'1 and X1 axis. The new proposed physical head model has an internal mass modeling the cerebral mass. The modelling of the mechanical liaisons between the brain and skull was achieved by visco-elastic liaisons. The adjustable elastic component permits 3 degrees of freedom relative to the brain-skull movement (two X, Y translations and the rotation around Z). The resonance frequencies of these three degrees of freedom were fixed by the theoretical modal analysis of the 3D FEM. These new head models are especially suitable for distinguishing the risk of focal lesion or sub-dural haematoma from diffuse axonal injury (DAI) risks. (A) For the covering abstract of the conference see IRRD 896323.

Approximate cylindrical blast theory: Near‐field solutions

Abstract: A method for analyzing strong cylindrical blasts in cases where the source mass is not negligible is presented. Analytic expressions for the shock position as a function of time and shock speed and pressure as functions of position are derived. An approximation to classical Taylor–Sedov theory is extended to the near‐field regime where the source mass is not negligible. Results from example calculations are compared to Taylor–Sedov theory as well as thermodynamic free expansion.

High-Frequency Heat Flux Sensor Calibration and Modeling

Abstract: A new method of in-situ heat flux gage calibration is evaluated for use in convective facilities with high heat transfer and fast time response. A Heat Flux Microsensor (HFM) was used in a shock tunnel to simultaneously measure time-resolved surface heat flux and temperature from two sensors fabricated on the same substrate. A method is demonstrated for estimating gage sensitivity and frequency response from the data generated during normal transient test runs. To verify heat flux sensitivity, shock tunnel data are processed according to a one-dimensional semi-infinite conduction model based on measured thermal properties for the gage substrate. Heat flux signals are converted to temperature, and vice versa. Comparing measured and calculated temperatures allows an independent calibration of sensitivity for each data set. The results match gage calibrations performed in convection at the stagnation point of a free jet and done by the manufacturer using radiation. In addition, a finite-difference model of the transient behavior of the heat flux sensor is presented to demonstrate the first-order response to a step input in heat flux. Results are compared with shock passing data from the shock tunnel. The Heat Flux Microsensor recorded the heat flux response with an estimated time constant of 6 μs, which demonstrates a frequency response covering DC to above 100 kHz.

Two-dimensional weak shock-vortex interaction in a mixing zone

Abstract: The interaction between a vortex or a pair of vortices and a shock is studied by using two-dimensional direct numerical simulation. The deformation of the shock structure is analyzed and the mechanisms leading to the formation of triple points are underscored. It is shown that they are related to the appearance of pressure gradients in the direction parallel to the shock resulting from the shock-vortex interaction. A distribution of an inert chemical species, i.e., mixture fraction, is prescribed within the vortex. From its time evolution, one analyzes the coupling between the response of the shock to the disturbance and the change in mixing rate. Modifications of the maximum of the scalar gradient are observed in the direction perpendicular to the shock and also, to a smaller extent, in the direction parallel to the shock. Nomenclature A(s) = stretching function of the mesh a,b,c,d = coefficients of the FADE scheme D = diffusion coefficient of the inert chemical species L = reference length of the problem M = Mach number N = total number of grid points in streamwise direction P = pressure Pr = Prandtl number q, qr = mesh stretching ratio and stretching rate R = radius of the vortex Re = acoustic Reynolds number (r, ft) = polar coordinates s = position on the uniform mesh

Diffusive Shock Acceleration Simulations: Comparison with Particle Methods and Bow Shock Measurements

Abstract: Direct comparisons of diffusive particle acceleration numerical simulations have been made against Monte Carlo and hybrid plasma simulations by Ellison {\it et. al.} (1993) and against observations at the earth's bow shock presented by Ellison {\it et. al.} (1990). Toward this end we have introduced a new numerical scheme for injection of cosmic-ray particles out of the thermal plasma, modeled by way of the diffusive scattering process itself; that is, the diffusion and acceleration across the shock front of particles out of the suprathermal tail of the Maxwellian distribution. We find that all of these computational methods (diffusion-advection, two-fluid, Monte Carlo and hybrid) are in substantial agreement on the issues they can simultaneously address, so that the essential physics of diffusive particle acceleration is adequately contained within each. This is despite the fact that each makes what appear to be very different assumptions or approximations.

Diffusive shock acceleration simulations: Comparison with particle methods and bow shock measurements

Abstract: Direct comparisons of diffusive particle acceleration numerical simulations have been made against Monte Carlo and hybrid plasma simulations by Ellison {\it et. al.} (1993) and against observations at the earth's bow shock presented by Ellison {\it et. al.} (1990). Toward this end we have introduced a new numerical scheme for injection of cosmic-ray particles out of the thermal plasma, modeled by way of the diffusive scattering process itself; that is, the diffusion and acceleration across the shock front of particles out of the suprathermal tail of the Maxwellian distribution. We find that all of these computational methods (diffusion-advection, two-fluid, Monte Carlo and hybrid) are in substantial agreement on the issues they can simultaneously address, so that the essential physics of diffusive particle acceleration is adequately contained within each. This is despite the fact that each makes what appear to be very different assumptions or approximations.