On the temperature rise at the tip of a fast running crack2

The high energy concentration at the tip of a running crack leads to irreversible deformations, and a great amount of the deformation energy is set free as heat. Assuming that this moving heat source is of circular shape, the temperature distribution around the crack tip has been calculated. The temperatures are dependent on the radius of the heat source and the crack velocity. Some examples for the material glass are given. The very high temperatures computed lead to the supposition that the observed light emission during fast fracture is of thermal origin.     

Some peculiarities of two-phase flow in nozzles

Calculations are conducted for unidimensional two-phase flow in nozzles for a wide range of particle concentrations and dimensions. It is established that there exists a maximum in loss of specific momentum due to a lag in particle velocity and temperature relative to the gas. The results obtained are compared with calculations using linearized theory as well as with experimental data. The agreement between calculation and experiment is noted. Equilibrium flow of a two-phase mixture with solidification of liquid particles is considered. The presence of an anomalous flow region is established, where in the model of an ideal unidimensional equilibrium flow in a nozzle with discharge into a vacuum the presence of two successively located minimum sections is necessary.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 50–57, May–June, 1973.     

Multi-Stage Upscaling: Selection of Suitable Methods

Reservoirs are often composed of an assortment of rock types giving rise to permeability heterogeneities at a variety of length-scales. To predict fluid flow at the full-field scale, it is necessary to be aware of these different types of heterogeneity, to recognise which are likely to have important effects on fluid flow, and to capture them by upscaling. In fact, we may require a series of stages of upscaling to go from small-scales (mm or cm) to a full-field model. When there are two (or more) phases present, we also need to know how these heterogeneities interact with fluid forces (capillary, viscous and gravity). We discuss how these effects may be taken into account by upscaling. This study focusses on the effects of steady-state upscaling for viscous-dominated floods and tests carried out on a range of 2D models are described. Upscaling errors are shown to be reduced slightly by the increase in numerical dispersion at the coarse scale. We select a combination of three different upscaling methods, and apply this approach to a model of a North Sea oil reservoir in a deep marine environment. Six different genetic units (rock types) were identified, including channel sandstone and inter-bedded sandstone and mudstone. These units were modelled using different approaches, depending on the nature of the heterogeneities. Our results show that the importance of small-scale heterogeneity depends on the large-scale distribution of the rock types. Upscaling may not be worthwhile in sparsely distributed genetic units. However, it is important in the dominant rock type, especially if there is good connectivity through the unit between the injector wells (or aquifer) and the producer wells.This revised version was published online in May 2005. In the previous version one of the authors name was missing.     

Dynamics of oblique detonations in ram accelerators

Time-accurate numerical simulations are used to study the dynamic development of oblique detonations on accelerating projectiles in ram accelerators. These simulations show that the oblique detonation can be stabilized on the projectile. The high pressure generated behind the detonation can result in accelerations up to 10⁶G and propel the projectile to velocities higher than 4.0 km/s. The detonation structure on the projectile is sensitive to the projectile geometry. A small change in the projectile shape is sufficient to alter the overall detonation structure and significantly affect the pressure distribution on the projectile. In order to maximize the thrust, an appropriate projectile shape has to be chosen to generate the detonation structure just behind the widest part of the projectile body. The projectile acceleration also has strong effects on the flow field and the detonation structure. During the acceleration, the location of the oblique detonation moves upstream from one reflected shock to another. However, one the detonation is stabilized behind the upstream shock, it remains at the new location until the transition to the next upstream shock occurs. In the simulations, the Non-Inertial-Source (NIS) technique was used to accurately represent of the projectile acceleration. Also, the Virtual-Cell-Embedding (VCE) method was employed to efficiently treat the complex projectile geometry on cartesian grids.     

Influence of a magnetic field on the thermoacoustic stability of a high-temperature heat releasing gas

The conditions of thermoacoustic stability are found for a high-temperature electrically conducting gas with internal heat release in a constant magnetic field which transforms acoustic waves into fast and slow magnetoacoustic oscillations, and also introduces Joule dissipation. The investigation is by means of the energy balance method, and also by direct solution of the equations for small perturbations in the special case of wavelengths of the acoustic oscillations that are short compared with the inhomogeneity scales in the region of heat release. The limits of stability with respect to fast and slow magnetoacoustic oscillations are found.Translated from Izvestiya Akademii Nauk SSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 102–107, July–August, 1979.     

Microprojectile velocities in a gas driven launcher

Microprojectile methods of genetic engineering sometimes employ a macroprojectile which launches the microprojectiles when it hits a stopping plate. A study has been made of the relationship between the velocities of the macroprojectile and the microprojectile it launches. Macroprojectile velocities were measured using a beam blanking method and the microprojectile velocities were measured with a laser Doppler anemometer. Particles of tungsten, titanium dioxide and silicon carbide were investigated as microprojectiles. The microprojectile velocity was found to depend not only on the macroprojectile velocity but also on the microprojectile size and material, the bond strength with the macroprojectile and the gas flow that develops ahead of the macroprojectile. On average the microprojectile launch velocity was similar to the macroprojectile velocity. However, some tungsten particles had velocities twice this value. Experimental evidence suggests that these higher velocities were caused by early break-way of particles from the macroprojectile followed by further acceleration by aerodynamic drag arising from the gas flow ahead of the macroprojectile.We are especially grateful for the advice of Dr. M. Gharib on the use of the HSI color system. John Lyons provided expert help in the laboratory and materials for and advice on photography. We thank the staff of the SIO Hydraulics Laboratory for making the wind-wave channel available for our use, and the staff of UCSD library for enabling us to use the Barneyscanner photometer-digitizer. We thank an anonymous reviewer who pointed out a numerical error and improved the clarity of the text.     

Electrochemical monitoring of aging embrittlement of steel for gas-cooled reactor pressure boundary components

The nondestructive testing technique is applied to evaluate the temper embrittlement of normalized and tempered steel; it is based on the anodic polarization behavior in calcium nitrate solution. The steel specimen is aged at a stress of 210 MPa at 450°C for up to 8800 h in order to examine the effect of applied stress on the enhancement of intergranular segregation of phosphorus. The secondary peak observed in the polarization curve for the material aged under stress was compared with that for the non-stressed. It can be quantified with the degree of intergranular segregation of phosphorus. The data suggest that the enhancement of phosphorus segregation due to the applied stress is only recognized after 3000 h of aging. This effect diminishes with increasing aging time.     

On the existence of infinite-dimensional invariant tori of nonlinear countable systems of difference-differential equations

In the space of bounded number sequences, we establish sufficient conditions for the existence of invariant tori for nonlinear countable systems of difference-differential equations defined on infinite-dimensional tori and containing an infinite set of constant deviations of a scalar argument.     

The Hall effect in an electrically conducting fluid for variable magnetic field and high magnetic Reynolds numbers

Hall phenomena in an electrically conducting fluid with a variable magnetic field were considered in [1]. In that paper the basic characteristics of the above-mentioned phenomena are determined, with certain unimportant constraints, for the case of fluid motion along a channel of rectangular cross section in a traveling magnetic field. The magnetic Reynolds number was assumed to be small, and a solution was given for the induction field in the form of a series in powers of the indicated parameter. Quantitative estimates based on the data of [1] are impossible in the case of relatively high electrical conductivity of the fluid, although certain conclusions of a qualitative nature remain valid. There is thus reason to consider the case of high magnetic Reynolds numbers. This will also allow a fuller picture of the characteristic Hall effect phenomena to be constructed for a variable magnetic field.     

Localization of fringes produced by rotation of the recording plate in focused-image holography

The equations determining the localization of interference fringes produced by rotation of the photographic plate in ‘focused-image holography’ are derived for an arbitrary cylindrical surface. The important properties of fringe localization are discussed and are experimentally verified.