Universal regularities of hydraulic fracturing within the framework of the Perkins-Kern-Nordgren model

An algorithm that permits one to find a solution of the Perkins-Kern-Nordgren problem for standard regimes of hydraulic fracturing is suggested. The universal qualitative specifics, of the behavior of a crack is shown; in particular, the asymptotics of crack opening at the tip is found, and it is shown that the character of the crack is determined by the rate of increase or decrease in the crack size. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 149–157, May–June, 1998.     

Three-dimensional imaging of a turbulent jet using shearing interferometry and optical tomography

The 3-D density field of a round, neutrally buoyant turbulent jet is obtained using a finite-fringe, shearing interferometer. A He–Ne laser beam (λ=632.8 nm) is subdivided into six beams of equal intensity, which intersect a helium–argon jet flowing from a vertical nozzle. Two-dimensional projection data of the jet are captured simultaneously from six viewing directions distributed over 140°. The desired phase is removed from the spatial carrier using the Fourier transform method. A tomographic reconstruction technique, using a truncated Fourier–Bessel expansion is performed to obtain the complete 3-D density field. The Reynolds number, based on the exit mean velocity and the nozzle diameter, is 5890. Received: 22 December 1999/Accepted: 20 January 2000     

A comparison of three adsorption equations and sensitivity study of parameter uncertainty effects on adsorption refrigeration thermal performance estimation

This paper presents isosteric-based adsorption equilibrium tests of three activated carbon samples with methanol as an adsorbate. Experimental data was fitted into Langmuir equation, Freundlich equation and Dubinin-Astakov (D–A) equation, respectively. The fitted adsorption equations were compared in terms of agreement with experimental data. Moreover, equation format’s impacts on calculation of the coefficient of performance (COP) and refrigeration capacity of an adsorption refrigeration system was analyzed. In addition, the sensitivity of each parameter in each adsorption equation format to the estimation of cycle’s COP and refrigeration capacity was investigated. It was found that the D–A equation is the best form for presenting the adsorptive property of a carbon-methanol working pair. The D–A equation is recommended for estimating thermal performance of an adsorption refrigeration system because simulation results obtained using the D–A equation are less sensitive to errors of experimentally determined D–A equation’s parameters.     

Equations of foam hydrodynamics

A closed system of differential equations describing a foam as a viscoelastic compressible continuum is obtained on the basis of the general theory of the mechanics of deformable continua [3–5]. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–95, September–October, 1988.     

Prediction of separation flows around a 6：1 prolate spheroid using RANS/LES hybrid approaches

This paper presents hybrid Reynolds-averaged Navier–Stokes (RANS) and large-eddy-simulation (LES) methods for the separated flows at high angles of attack around a 6:1 prolate spheroid. The RANS/LES hybrid methods studied in this work include the detached eddy simulation (DES) based on Spalart–Allmaras (S–A), Menter’s k–ω shear-stress-transport (SST) and k–ω with weakly nonlinear eddy viscosity formulation (Wilcox–Durbin+, WD+) models and the zonal-RANS/LES methods based on the SST and WD+ models. The switch from RANS near the wall to LES in the core flow region is smooth through the implementation of a flow-dependent blending function for the zonal hybrid method. All the hybrid methods are designed to have a RANS mode for the attached flows and have a LES behavior for the separated flows. The main objective of this paper is to apply the hybrid methods for the high Reynolds number separated flows around prolate spheroid at high-incidences. A fourth-order central scheme with fourth-order artificial viscosity is applied for spatial differencing. The fully implicit lower–upper symmetric-Gauss–Seidel with pseudo time sub-iteration is taken as the temporal differentiation. Comparisons with available measurements are carried out for pressure distribution, skin friction, and profiles of velocity, etc. Reasonable agreement with the experiments, accounting for the effect on grids and fundamental turbulence models, is obtained for the separation flows. The project supported by the National Natural Science Foundation of China (10502030 and 90505005).     

Conformational evolution under steady shear flow: a comparison between cyclic and linear block copolymers

Cyclic block copolymer is a special type of block copolymer having no free ends. Comparison of the dynamic behavior between cyclic and linear block copolymers enables an understanding of the role of chain ends in dynamics of the latter. In relation to this point, analysis was made on the conformational dynamics for a cyclic bead-spring type diblock copolymer chain, AoB, under the steady shear flow. Further comparison was made on the conformational behavior of the AoB chain and that of two symmetric linear triblock copolymer chains, A–B–A and B–A–B. For these chains, the mobility was set to be higher for the A segments than the B segments. Thus, for the AoB chain under the steady shear flow, the segments of the A block exhibit less orientational anisotropy than those of the B block. This orientational contrast is enhanced for the A–B–A chain partly because the constraint for the motion of the segments is less near the chain ends than near the chain center. Nevertheless, for the B–A–B chain, the segmental orientation over the A block becomes more anisotropic than that over the B block. Detailed analysis shows that this result is attributable to a high orientational correlation for the segments of two end B blocks, in particularly for those near the block junctions. The correlated B segments exert a tensile force on the A block thereby significantly enhancing the orientational anisotropy of the A segments.     

Development and validation of a thermo-mechanical finite element model of the steel quenching process including solid–solid phase changes

A computational thermo-metallographic and thermoelastoplastic model for the analysis of the quenching process is developed and validated. The diffusive transfor-mations are modeled according to the Johnson–Mehl–Avrami–Kolmogorov model and the Scheil’s additivity rule. Two different models are investigated for the non-diffusive transformation—the Koistinen–Marburger model and the Yu model. A large displacement formulation is assumed for the deformation analysis, modeling the plastic behavior of the material according to the Prandtl–Reuss model. Two different bilinear hardening models—the isotropic and the kinematic hardening model—are used and compared. The model allows to evaluate the transient stress and strain distributions during the quenching process, the final phases and hardness distributions, and to predict the residual stress and the final deformation of the processed part. A good agreement between computational results and reference data is found     

On a Generalized Nonlinear K–ε Model and the Use of Extended Thermodynamics in Turbulence

A resent extension of the nonlinear K–ε model is critically discussed from a basic theoretical standpoint. While it was said in the paper that this model was formulated to incorporate relaxation effects, it will be shown that the model is incapable of describing one of the most basic such turbulent flows as is obvious but is described for clarity. It will be shown in detail that this generalized nonlinear K–ε model yields erroneous results for the Reynolds stress tensor when the mean strains are set to zero in a turbulent flow – the return-to-isotropy problem which is one of the most elementary relaxational turbulent flows. It is clear that K–ε type models cannot describe relaxation effects. While their general formalism can describe relaxation effects, the nonlinear K–ε model – which the paper is centered on – cannot. The deviatoric part of the Reynolds stress tensor is predicted to be zero when it actually only gradually relaxes to zero. Since this model was formulated by using the extended thermodynamics, it too will be critically assessed. It will be argued that there is an unsubstantial physical basis for the use of extended thermodynamics in turbulence. The role of Material Frame-Indifference and the implications for future research in turbulence modeling are also discussed. Received 19 February 1998 and accepted 23 October 1998     

Charging and coagulation of water aerosols with a small admixture of highly radioactive droplets

The mechanism of electrocoagulation of water aerosols with a small admixture of highly radioactive droplets is examined. A corresponding mathematical model describing the processes of ionization, electrization and coagulation of radioactive water aerosols is developed. The time dependence of the ion concentration and the charge and concentration of the nonradioactive droplets and of the charge and radius of the radioactive droplets is numerically investigated for a number of typical aerosols. It is shown that the electrocoagulation process may lead to an increase in the radius of the droplets from 5–10 to 30–40μm in ≃10⁴ sec ≃3 h and, consequently, may play a significant part in the development of aerosols with a droplet radius of up to 20μm, when gravitational coagulation is unimportant. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 90–96, March–April, 1994.     

Numerical investigation of the convective flow in the toroidal gap

A numerical investigation of the convective flow in the toroidal gap is presented. A new formulation of the incompressible Navier–Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation [Weinen and Liu in Commun Math Sci 1(2):317–332, 2003] has been used. The gauge freedom allows simple boundary conditions to be formulated for the auxiliary field, as well as the gauge field. The gauge field eliminates the pressure distribution in the Navier–Stokes equation. The influence of the geometric parameters and the Prandtl number is discussed.     

Possibility of gas washout from a gas-hydrate massif by circulation of warm water

A possibility of gas extraction from a gas-hydrate massif by means of warm water circulation through a system of wells is demonstrated. A technological scheme and a theoretical model of this process are proposed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 100–111, July–August, 2009.     

Criterion of formation of a shock wave reflected from a cloud of particles

The problem of the formation of a “collective” shock wave reflected from a cloud of particles, which was previously observed in experiment, is considered. A criterion of formation of a reflected shock wave is obtained based on the numerical and analytical solutions of the problem. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 44–51, May–June, 1998.     

On the problem of controlling the efficiency of action of shaped-charge jets

It is suggested that noncontact action of a magnetic field on shaped-charge jet elements be used to decrease the penetration depth. A decrease in the depth is attained. A physicomathematical model for the process is constructed that allows one to optimize performance of devices used to realize the action of an external magnetic field. Lykov Academic Scientific Complex “Institute of Heat and Mass Exchange,” Minsk 220072. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 36–43, May–June, 1998.     

Motion of a sphere in a vibrating liquid in the presence of a wall

A solution is obtained for the problem of the motion of a sphere in an ideal liquid bounded from outside by a wall which performs specified vibrations far from the sphere. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences. Novosibirsk 630090, Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 125–132, July–August. 1999.     

Structure of a supersonic erosion plasma jet

A supersonic erosion plasma jet was generated in a heavy-current discharge in a capillary. The jet development diagram is presented. A spectral study of the jet flowing from the capillary is conducted and densitograms of the negatives are presented. The temperatures and electron and ion concentrations are determined. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 181–185, January–February, 1997.     

Motion of an inclusion in uniformly and nonuniformly vibrating liquids

An approach to constructing the quantitative nonuniformity characteristics of liquid vibrations is proposed. A new problem of the motion of an inclusion in a vibrating liquid is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 79–85, January–February, 2007.     

Modeling the spread of an oil slick on the sea surface

The spread of an oil slick in the sea is considered. A mathematical model of the process is proposed and a formulas for determining the oil slick sizes in explicit form are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 127–130, May–June, 2009.     

Measurement and chemical kinetic model predictions of detonation cell size in methanol–oxygen mixtures

In this study, detonation cell sizes of methanol–oxygen mixtures are experimentally measured at different initial pressures and compositions. Good agreement is found between the experiment data and predictions based on the chemical length scales obtained from a detailed chemical kinetic model. To assess the detonation sensitivity in methanol–oxygen mixtures, the results are compared with those of hydrogen–oxygen and methane–oxygen mixtures. Based on the cell size comparison, it is shown that methanol–oxygen is more detonation sensitive than methane–oxygen but less sensitive than hydrogen–oxygen.