Showing papers on "Shock (mechanics) published in 1972"

Determination of magnetohydrodynamic shock normals.

Abstract: A method for determining many new magnetohydrodynamic shock normal expressions is described that uses both magnetic-field and plasma-flow parameters. These shock normal expressions are useful as a check on the usual magnetic coplanarity expression or for cases in which the most reliable data are mixed. For high Alfven Mach numbers, the exact results are well approximated by the simple velocity coplanarity formula. This is illustrated by calculating shock normals for the 1965 bow shock crossing of Pioneer 6.

Determination of Material Relaxation Properties from Measurements on Decaying Elastic Shock Fronts

Abstract: A theoretical method for the reduction of measurements on the decay of elastic precursor shock fronts is presented. The method yields values of the initial pressure‐volume relaxation path behind the front; it requires no assumptions about the form of the constitutive relation. The method is illustrated by application to data on lithium fluoride.

Propagation of weak shock waves through turbulence

Abstract: The effect of turbulence on the structure of weak shock waves is investigated. The equilibrium structure is shown to be governed by a balance between nonlinear steepening and the turbulent scattering of acoustic energy out of the main wave direction. The scattered energy appears as perturbations behind the shock front. For conditions typical of sonic booms in atmospheric turbulence the wave structure is governed by a Burgers equation similar to that describing viscous shocks, except that parameters related to the turbulence appear instead of the viscosity coefficient. The magnitude of the perturbations following a shock is estimated from first-order scattering applied to a thickened shock. Predictions of shock thicknesses and perturbations compare favourably with available experimental data.

Approximate Blast Wave Theory and Experimental Data for Shock Trajectories in Linear Explosive‐Driven Shock Tubes

Abstract: An approximate theory is presented for predicting the trajectories of gas shocks driven by solid high explosives in linear shock tubes. Theoretical calculations are compared to results of experiments, where agreement within 10% is found.

Interplanetary shock waves and the structure of solar wind disturbances

Abstract: Observations and theoretical models of interplanetary shock waves are reviewed, with emphasis on the large-scale characteristics of the associated solar wind disturbances and on the relationship of these disturbances to solar activity. The sum of observational knowledge indicates that shock waves propagate through the solar wind along a broad, roughly spherical front, ahead of plasma and magnetic field ejected from solar flares. Typically, the shock front reaches 1 AU about two days after its flare origin, and is of intermediate strength. Not all large flares produce observable interplanetary shock waves; the best indicator of shock production appears to be the generation of both type 2 and type 4 radio bursts by a flare. Theoretical models of shock propagation in the solar wind can account for the typically observed shock strength, transit time, and shape.

Thoughts and Afterthoughts About Shock Computations.

Abstract: : Typical one-dimensional, unsteady flow problems are considered to support shock-fitting concepts as the best way to handle shocked flows. Shock-captureing experiments are discussed; their results are concluded to be unsatisfactory. Various methods to predict the formation of a shock are suggested. Four shock-fitting methods are discussed, two of them considering the shock as a boundary between regions of continuous flow and two letting the shock move between mesh points. (Author)

Binary index for assessing local bow shock obliquity

Abstract: The earth's collisionless plasma bow shock has, overall, a nonuniform structure whose magnetic profile is simultaneously that of a monotonic or laminar perpendicular shock and of a multigradient oblique shock, depending on the local orientation of the interplanetary field to the nominal shock surface. A 'pulsation index' Ip has been devised from empirical results to provide a simple convenient means of assessing the probable local character of the shock's structure; Ip = 0 or 1, according to whether local field geometry favors perpendicular or oblique structure, respectively, at a chosen point of observation on the nominal shock surface.

Magnetohydrodynamic theory for the interaction of an interplanetary double-shock ensemble with the Earth's bow shock

Abstract: The interactions between interplanetary shocks and the earth's bow shock are formulated first on a gas-dynamic basis. The problem is repeated on a magnetohydrodynamic (MHD) basis for the special case of perpendicular shocks. In particular, an interplanetary double-shock ensemble (composed of forward and reverse shocks) is allowed to interact with the earth's bow shock. It is found that the collision of a forward shock with the bow shock creates two shocks and a contact surface; the symbolism S→S← → S←CS→ is used to represent this particular interaction. The collision of a reverse shock with the bow shock, hitherto not discussed, yields a shock, contact surface, and rarefaction wave: S←S← → S←CR→. The results of the interactions are discussed on the basis of several representative computations. An order-of-magnitude increase of thermal pressure is the major consequence of the ‘shock-on-shock’ interaction. The effect of the magnetic field is minor; for example, the bow-shock velocity after impact of a forward shock is only ∼10% less than the velocity computed on the basis of ordinary gas dynamics. Interaction dynamics are applied, in the case of the geomagnetic storm's sudden commencement, to the characteristic time and energy of the instantaneous compression. Several magnetic-storm sudden-commencement events (including the March 8, 1970, event) are discussed on the basis of spacecraft plasma observations and magnetogram records on the earth. Comparison of available diagnostics with the theory suggests the physical plausibility of the present fluid-dynamic study.

Beam‐Generated Collisionless Ion‐Acoustic Shocks

Abstract: A numerical study of a one‐dimensional collisionless ion‐acoustic shock generated by an injection of a plasma beam is presented. The electrons are assumed to be hot and isothermal, and obey the Boltzmann distribution; the ions are described by the Vlasov equation which is solved by a direct finite difference scheme. There is a threshold beam velocity ubm, above which shock is not generated. ubm is a function of the beam‐background density ratio and the electron‐ion temperature ratio, and is larger than the limit of the ion‐ion two‐stream instability uts. For beam velocities ranging from zero to uts a shock is observed followed by a region of fully developed two‐stream instability. For beam velocities between uts and ubm, a shock and a phase‐space vortex are formed and in between them a quiescent region grows. A stable two‐stream remains behind the vortex.

Mod-wall concrete

Abstract: A CONCRETE COMPSOITION DEVELOPED TO PROVIDE A MATERIAL OF CONSTRUCTION WHICH CAN BE UTILIZED TO BUILD ESSENTIALLY ALL TYPES OF STRUCTURES, INCLUDING HOUSES, OFFICE BUILDINGS, AND THE LIKE, WHICH IS CAPABLE OF BEING WET MIXED AND SUBSEQUENTLY MOLDED INTO CONVENIENT AND USEFUL SHAPES. THE COMPOSITION HAS GREAT STRENGTH, EXCELLENT SHRINK RESISTANCE PROPERTIES, IS SHOCK RESISTANT, AND PROVIDES GOOD INSULATION FOR STRUCTURES, AND IS ADAPTED FOR USE WITH SUITABLE MOLDS TO FORM THE ENTIRE WALL, SLAB AND ROOF STRUCTURE OF A HOUSE OR OTHER BUILDING IN A SINGLE POURING.

Switched numerical Shuman filters for shock calculations

Abstract: When using Shuman's filtering operator in the numerical computation of shock waves, nonlinear instabilities are prevented, but high order accuracy is lost even in smooth regions. In order to preserve second or higher order accuracy in these regions, an automatic switched Shuman filter is constructed. Nonsteady shock calculations in one and two spatial dimensions, demonstrate the usefulness and accuracy of the method, including examples with third and fourth order accurate finite difference schemes.

Observation of nonuniform structure of the Earth's bow shock correlated with interplanetary field orientation

Abstract: Explorer 33 and 35 magnetometers, on the western and eastern flanks of the earth's bow shock, respectively, observed the boundary concurrently between 0130 and 0430 UT, Oct. 30, 1968. Contrasting shock structures were recorded. Explorer 35 saw a quiet abrupt shock, whereas Explorer 33 saw an irregular noisy boundary with much upstream wave activity. The interplanetary field was roughly in the average archimedean spiral angle and was therefore approximately tangent to the shock at Explorer 35 and normal to the shock at Explorer 33. Gross motions and variable tilting of the aberrated shock probably contributed to the peculiar sequence of shock crossings at the two spacecraft. The observations support a model of the shock in which perpendicular and oblique collisionless structures coexist and form a nonuniform magnetosheath outer boundary.

Steady Shock Waves in Composite Materials

Abstract: The shock wave generated by a planar impact of a flyer plate and propagated along the direction of the fibers of a composite was studied. The sample composite used in the experiments was made of unidirectional aluminum fibers cast in an Epoxy matrix. Both the shock‐wave velocity and the free surface velocity were measured by means of an optical technique. The shock front in the composite was found to be steady. The results of the measured Hugoniot also give a satisfactory comparison with those obtained from an analysis proposed earlier. The observation of a steady shock in the present work is significant in treating problems involving composite materials.

Vehicle safety system

Abstract: A vehicle safety system for protecting a person in a vehicle from impact shock due to collision with an object comprises a gas bag. An obstacle detecting sensor predicts a collision prior to such occurrence. An impact detecting sensor detects the shock of impact upon collision. The gas bag is actuated incrementally by incremental operation of the obstacle detecting sensor and the impact detecting sensor.

Shock Waves, Jump Relations, and Structure

Abstract: Publisher Summary The chapter presents a local study of shock waves, introducing the basic concepts and ideas that arise in the theory of shocks with a simple mathematical model related to a single conservation law. The study emphasizes on shock relations for a physical phenomenon governed by conservation laws and the classification of shocks. The chapter provides examples in some detail, in particular taken from classical gas dynamics and magneto fluid dynamics. Problems related to the structure of a shock are considered, where some examples are provided in order to show that quite different behaviors may be found. Asymptotic expansions have been mentioned, which describe completely the behavior of the solution in the neighborhood of a shock. For simplicity, the analysis is restricted to the case of classical gas dynamics.

Shock and vibration technology with applications to electrical systems

Abstract: A survey is presented of shock and vibration technology for electrical systems developed by the aerospace programs. The shock environment is surveyed along with new techniques for modeling, computer simulation, damping, and response analysis. Design techniques based on the use of analog computers, shock spectra, optimization, and nonlinear isolation are discussed. Shock mounting of rotors for performance and survival, and vibration isolation techniques are reviewed.

Ogo 5 magnetic‐field data near the Earth's bow shock: A correlation with theory

Abstract: Magnetic-field data obtained in the earth's bow-shock region with a high-resolution triaxial fluxgate magnetometer aboard the Ogo 5 satellite have been correlated with a theory of Tidman and Northrop (1968) These authors have shown that either of two hypotheses about the nature of low-frequency magnetic waves could be invoked to explain previous observations We have observed exponentially decaying upstream waves that are consistent with only one of these hypotheses This observation allows use of the theory to infer the local shock velocity and frequency of driving currents within the shock This method of finding the shock velocity is less sensitive to errors in the plasma parameters than is the method based on the Rankine-Hugoniot relations

Frequency Stability of Methane‐Stabilized He–Ne Lasers

Abstract: Free‐running laser stabilities of 1.5×10−11 for the millisecond region and methane‐locked stabilities of 10−13 for 10‐sec averaging time are achieved with a minimum of shock and vibration isolation in an ordinary laboratory environment. Superior stability performance is obtained with dc excitation as compared to rf excitation. The experimental setup is described in some detail.

The boundary layer in a shock tube

Abstract: The boundary layer that forms on the walls of a shock tube, after the diaphragm which initially separates two gases at different pressures is burst, is investigated. Both the driver and driven gases are assumed to have the same thermal properties and the shock tube wall is maintained at constant temperature. Crocco variables are used and a method is presented for solving the compressible boundary-layer equations within the tube in similarity variables. Three cases, corresponding to different initial pressure ratios of the driver and driven gases, are calculated which are representative of weak and medium-strength shock and expansion waves.

Comparison of characteristics and shock capturing methods with application to the space shuttle vehicle.

Abstract: A critical appraisal is presented of a method-of-characteristics (MOC) and a shock-capturing technique (SCT) for calculating three-dimensional supersonic flow. Detailed comparisons are made for pointed and blunt-nosed bodies with a thick delta wing at angles of attack from 5 to 15 deg. The results show excellent agreement between the methods and with experiment. It is established that the SCT code yields accurate shock locations and jump conditions. The SCT code typically requires about three times as many mesh points as the MOC code in order to resolve the bow shock, but the total computation time is about the same. On a point for point basis, the SCT code is about four times faster than the MOC code.

Nonlinear U(u) Hugoniots of Liquids at Low Pressures

Abstract: Low pressure (<15 kbar) shock compression experiments were performed on the liquids CS2, C6H14 (n‐hexane), CH2I2, CHCl3, C6H6, and C6H12 (cyclohexane). In each case, the shock velocity‐particle velocity, U(u), Hugoniot was nonlinear and the shock velocity smoothly approached the sonic velocity as the shock pressure approached zero. Enthalpy‐pressure‐volume equation of state parameters are given for CS2, C6H14, C6H6, and C6H12.

Propagation of a blast wave in uniform or non-uniform media: a uniformly valid analytic solution

Abstract: The shock propagation theory of Brinkley & Kirkwood (1947) is extended to provide a uniformly valid analytic solution of point-explosion problems both when the undisturbed medium is uniform and when it is stratified. This is achieved mainly by selecting the parameter expressing a similarity restraint in this theory such that initially it gives precisely the Taylor–Sedov solution, while asymptotically, in the weak regime, still retaining the well-known Landau–Whitham–Sedov form of the solution for shock overpressure. The shock overpressure, as calculated by the present method for spherical and cylindrical blast waves in the entire regime from the point of explosion to where they have become very weak, shows excellent agreement with that from the exact numerical solutions of Lutzky & Lehto (1968) and Plooster (1970). The solution for a spherical shock propagating in an exponential atmosphere stratified by a constant acceleration due to gravity also shows a good agreement with the exact numerical solution of Lutzky & Lehto.

Empirical formulas for locating shock waves in a jet impinging on a barrier at right angles

Abstract: Empirical relations are derived for determining the ranges of stable and unstable interaction between a jet and a barrier and for determining the displacement of the central compression shock and of the triple point from the barrier.

Shock wave-turbulent boundary layer interactions in rectangular channels.

Abstract: Interaction regions created by the impingement of full span, externally generated, shock waves on a nozzle wall boundary layer were investigated. Incident shock strength was varied to produce unseparated, incipient, and fully separated flow fields. Significant departures from two-dimensionality were observed over the entire range of shock strengths tested and were identified with sidewall and corner boundary layer effects. However, comparisons of present centerline results with published two-dimensional data, obtained under similar test conditions and geometrical constraints, showed excellent agreement (e.g., incipient separation pressure levels, wall pressure distributions, free-interaction, and scale of the interaction region). This raises some question concerning the degree of two-dimensionality achieved in these previous investigations.

Influence of thermal anisotropy on best‐fit estimates of shock normals

Abstract: The influence of thermal anisotropy on the estimates of interplanetary shock parameters and the associated normals is discussed. A practical theorem is presented for quantitatively correcting for anisotropic effects by weighting the before and after magnetic fields by the same anisotropy parameter h. The quantity h depends only on the thermal anisotropies before and after the shock and on the angles between the magnetic fields and the shock normal. The theorem can be applied to most slow shocks, but in those cases h usually should be lower, and sometimes markedly lower, than unity. For the extreme values of h, little change results in the shock parameters or in the shock normal.