Home – Home – Jornals – Numerical Analysis and Applications 2019 number 2

This paper describes different types of modern magneto-cumulative generators, their operating principles, design, and main characteristics. Application areas of the generators for fundamental and applied studies in high-energy density physics are considered. Some investigation results are presented. Prospects for the further development of the MCG facilities designed in VNIIEF are discussed.

The energy capabilities of acceleration devices are theoretically analyzed, including various ramjet-in-tube options for gas-dynamic acceleration of massive (1 to 40 kg) bodies under ground conditions up to velocities of 2-3 km/s. Simple quasi-one-dimensional models for a perfect gas are used in the computations. It is demonstrated that the use of a ramjet-in-tube with a closed exit allows the velocities of acceleration of massive bodies to be increased to 3 km/s, which is twice greater than the values that can be obtained with available gunpowder-based methods.

The limiting possibilities and energy efficiency of single-stage acceleration of solid by compressed gas in a pipe (ballistic Lagrange problem) is under study. An exact partial solution of the ballistic Lagrange problem in a homogeneous deformation approximation is obtained. The calculation results are compared by different methods with the experimental data and the calculation results from other papers. It is shown that using an efficiency coefficient as a criterion for choosing an optimal solution prevents from using the effective configurations of ballistic devices.

The influence of a sudden change in the external magnetic field on the flow of an electrically conducting Bingham fluid in a two-dimensional channel is considered. It is demonstrated that a method of independent descriptions of the flow in plastic and viscous regions can be used for studying magnetohydrodynamic flows of the Bingham fluid. An exact equation is derived for the position of the plastic flow region boundary as a function of time and magnetic field induction. It is shown that the corresponding Cauchy problem has a unique asymptotically stable solution. Results of numerical integration for some values of parameters are presented; these result confirm the qualitative conclusions.

Results of direct numerical simulations of the roughness-induced development of instability and transition to turbulence in a supersonic boundary layer on a blunted cone for the free-stream Mach number M¥ = 5.95 are presented. The flow parameters and model geometry are consistent with the conditions of the experiments performed in the study. The following roughness types are considered: random distributed roughness, individual roughness elements of different shapes, and a group of regularly arranged roughness elements. The processes of the instability development and transition for different roughness types are compared, and possible mechanisms of the roughness influence on the stability of boundary layers on blunted bodies are discussed.

A mathematical model for reducing the pressure of natural gas in a direct acting pressure regulator is developed. It is shown that, if an output-input pressure ratio typical for practice is lower than a critical value, the pressure reduction process comes down to two stages: partial expansion of gas with throttling in the orifice plate of the pressure regulator and subsequent expansion in its casing. The values of the gas temperature in the characteristic sections of the pressure regulator are determined. It is established that the temperature drops at the first stage of pressure reduction and rises as the flow in the pressure regulator casing expands and decelerates. A method for minimizing the possibility of formation of gas hydrates in the pressure regulator is proposed.

This paper presents the results of an analysis of field measurements of a wave bore in the pycnocline of a shallow sea using vertical located thermistors. Hydrodynamic interpretation of the space-time structure of the bore is performed using a mathematical model of a weakly dispersed shallow sea which takes into account the influence of cubic nonlinearity and low-frequency dispersion. The limiting amplitude and minimum duration of the soliton solutions of the model are determined. An algorithm for evaluating these parameters based on measurements of the pulsations of isotherms induced by the bore is proposed. The limiting amplitude and minimum duration of solitary waves in the pycnocline in the coastal the Sea of Japan are evaluated.

The problem of waves generated in a fluid and an ice sheet by a pressure region moving on the free surface of the fluid along the edge of the semi-infinite ice sheet was solved using the Wiener-Hopf method. The load applied in some region simulates an air cushion vehicle, and the ice sheet is modeled by a thin elastic plate of constant thickness on the surface of an ideal incompressible fluid of finite depth. In a moving coordinate system, the plate deflection and the fluid elevation are assumed to be steady. The wave forces, the elevation the free surface of the fluid, the deflection and deformation of the plate at various speeds of the load were investigated. It has been found that at near-critical load speeds, the ice sheet has a significant effect on the wave forces (wave resistance and side force) acting on the body moving on the free surface, and this effect is most pronounced at small distances from the edge. It has been shown that for some values of the speed, ice thickness, and load pressure, breaking of the ice sheet near the edge is possible.

The propagation of weak disturbances in a superheated water-air bubble medium is considered in the case where the bubbles contain, in addition to water vapor, an inert gas (e.g., air) which is not involved in phase transitions. Maps of stability zones of the investigated systems depending on the degree of superheating of the liquid are constructed. The influence of the initial degree of superheating on the evolution of harmonic waves is analyzed. For unstable systems, the dependence of the increment on bubble radius with increasing degree of water superheating is studied

During the recently passed last few years, viscous flows due to continuously shrinking surfaces have become very much popular among the researchers working in this particular area. Based upon the literature published over these years, it has been established that, different from the continuous stretching surface case, the flow due to a continuous shrinking surface does not admit a meaningful solution in the absence of sufficient wall suction and does admit multiple solutions if a sufficient amount of wall suction velocity is introduced. Furthermore, it has also been believed that shrinking surface flows offer more nonlinear phenomena by exposing the “interesting” characteristics of the boundary-layer flow. Using a correct self-similar formulation for the two-dimensional shrinking sheet flow, the objective of this study is to prove that all the so-called “interesting” features of the shrinking sheet flow discovered in the previous studies are also exhibited by the stretching sheet flow. This fact consequently negates all such fascinations attributed to the shrinking sheet flow.

Plane-parallel steady motion of a viscous incompressible fluid that partially fills a cylindrical rotating cavity is under consideration. The region occupied by the fluid is simply connected, with two points of a sliding three-phase contact, and the edge angles at which the fluid approaches the walls are specified at these points. The free boundary of the fluid is curvilinear. There is a slip condition at the interface between the fluid and solid wall, which corresponds to proportionality of tangential stresses of a velocity difference of the solid and fluid particles. The flow region is conformally mapped onto a rectangular. The vortex and current function with a given slip coefficient and different rotation velocities of the cylinder are calculated.

A computational experiment has been performed to study the effect of the change in the main pipeline cross section due to hydrate formation on hydraulic resistance and the temperature and pressure dynamics taking into account quasi-stationary heat exchange with permafrost ground. The case is considered where wet gas is supplied to the pipeline and the dynamics of hydrate formation is determined along with other parameters. The calculations are carried out until the outlet pressure becomes lower than standard one. The experiment showed that a model in which the hydraulic resistance coefficient is considered constant leads to a significant underestimation of the permissible pipeline operation time. Consequently, in mathematical modeling of hydrate formation in natural gas pipelines, taking into account the relationship between heat transfer and viscous friction is critical.

A mathematical model of vertical interference testing of a gas reservoir penetrated by an imperfect vertical well is considered. The effect of the vertical and horizontal permeability and the degree of reservoir penetration on the pressure variation curves in the active and responding well intervals is investigated. A method for interpreting the results of vertical interference testing of a gas reservoir based the theory of inverse problems is proposed. It is shown that the results of vertical interference testing of a gas well can be used to estimate the vertical and horizontal permeability and porosity of the reservoir in the case of its full penetration.

This paper presents the theoretical description of steady motion of a moderately large spherical aerosol particle in the external field of a temperature gradient in the Stokes approximation with Reynolds and Peclet numbers much smaller than unity. It is assumed that the average temperature of the particle surface significantly differs from the temperature of its gaseous environment. Gas dynamics equations are solved with account for the power dependence of molecule transport coefficients (viscosity and thermal conductivity) and the density of the gaseous environment on temperature. Boundary conditions are written in the linear approximation based on the Knudsen number. It is shown that the thermophoretic force and velocity substantially depend on the Knudsen number and the average temperature of the particle surface.

A single-stage gas-driven setup is developed, which allows 0.5-kg projectiles to be accelerated to velocities of the order of 1200 m/s. Experiments with penetration of steel projectiles into a massive ice target are performed. The experimental data are compared with the results of computations performed by the REACTOR software system and numerical calculations of destruction of a finite-thickness ice target under the impact of one projectile and several projectiles. It is demonstrated that an impact of a steel ring onto a finite-thickness ice target leads to knock-out of the maximum volume of ice and almost complete loss of the kinetic energy of the ring.

Experimental dependences of the strength of frozen sandy soil on strain rate are analyzed using a structural-temporal approach. Results of dynamic uniaxial compression tests at a temperature of -18oC and strain rates of 400 to 2600 s-1 of frozen sandy soil samples of two types with a mass fraction of ice of 10 and 18% measured at room temperature are presented. The strain rate dependence of the at different temperatures of freezing of frozen sand with a mass fraction of ice of 30% was studied using known experimental data.

Available results of laboratory investigations of the dynamic strength of various rock types are analyzed with the use of the incubation time criterion in both compression and tension cases. Based on this approach, a theoretical curve is constructed, which describes the increase in the ultimate stress of sample fracture for some types of sandstone. Incubation times for all materials considered in the study are estimated.

This paper proposes a refined formulation of linearized problems of internal nonuniformly scaled flat buckling modes of a rigid monolayer consisting of fibers and fiber bundles with allowance for their interaction with the surrounding matrix. Fibers are the structural elements of fibrous composites and in a subcritical (unperturbed) state under the action of shear stresses and tensile (compression) stresses in the transverse direction. The problems are formulated using equations constructed by reducing the version of geometrically nonlinear equations of the elasticity theory to one-dimensional equations of the theory of rectilinear rods. These equations are based on the use of the refined Timoshenko shear model with allowance for tension-compression strains in the transverse direction for the rigid monolayer and the transverse-soft layer model with immobile boundary planes in a perturbed state for the epoxy layers. It is shown that loading samples with a structure is accompanied by constant changes in the composite structure due to implementation and alternation of the internal buckling modes with a varying wave formation parameter. This particularly allows explaining the changing of the effective shear modulus of the fibrous composite with increasing shear strains.

In this paper, we consider conditions under which the gas enclosed in the main crack located at the edge of a coal or rock formation can produce fracture of the formation. Kinetic theory is developed for two competing physical processes: formation unloading due to rock pressure and gas filtration from the crack cavity into the surrounding massif. The first process promotes fracture, and the second leads to a decrease in the gas pressure causing he fracture. The evolution of the crack is determined by the ratio of the rates of these processes. It is found that a modified Griffiths criterion is a necessary but not sufficient condition for fracture. For formation fracture, it is also necessary that the unloading rate to the filtration rate exceed a certain threshold value.

A size-dependent cracked Timoshenko beam model is established based on the nonlocal strain gradient theory and flexibility crack model. Expressions of the higher-order bending moment and shear force are derived. Analytical expressions of the deflection and rotation angle of the cross section of a simply supported microbeam with an arbitrary number of cracks subjected to uniform loading are obtained. The effects of the nonlocal parameter, the material length scale parameter, the presence of the crack, and the slenderness ratio on the bending behaviors of the cracked microbeam are examined. It is found that the material length scale parameter plays an important role in the cracked microbeam bending behavior, while the nonlocal parameter is not decisive. Furthermore, the cracked microbeam also exhibits a stiffening or softening effect depending on the values of the two scale parameters; if the two parameters are equal, the bending deformation of the nonlocal cracked microbeam may not be reduced to that of the classical elastic cracked Timoshenko beam. Additionally, the influence of the size effect on beam stiffening and softening becomes more significant as the slenderness ratio decreases.

A model of disk-like cracks based on amplitude-frequency spectra of acoustic emission, detected in the fracture of a concrete sample, is used to restore their size distribution function, as well as corresponding distributions of porosity and specific area of internal surface of the material. Changes in these characteristics of a solid in a time interval between the instances of detection of the spectra are studied.

A prototype of a pulsed X-ray apparatus with and operating voltage of 600-800 kV based on a combined helical generator has been developed and tested. Compared to the classical helical generator, the total length of the helical winding is increased by adding a single-bus line, which allows matching of the wave propagation time along the helical generator line to the oscillation period in the generator with a Tesla transformer. It is shown that the proposed transformer has high efficiency. A theoretical model describing the operation of the combined generator is proposed.

We consider two related discrete optimization problems of searching for a subset in a finite set of points in the Euclidean space. Both problems are induced by the versions of the fundamental problem in data analysis, namely, by selecting a subset of similar elements in a set of objects. In each problem, an input set and a positive real number are given, and it is required to find a cluster (i.e., a subset) of the largest size under constraints on the value of a quadratic clusterization function. The points in the input set which are outside the sought for subset are treated as the second (complementary) cluster. In the first problem, the function under the constraint is the sum over both clusters of the intracluster sums of the squared distances between the elements of the clusters and their centers. The center of the first (i.e., the sought) cluster is unknown and determined as the centroid, while the center of the second one is fixed at a given point in the Euclidean space (without loss of generality in the origin). In the second problem, the function under the constraint is the sum over both clusters of the weighted intracluster sums of the squared distances between the elements of the clusters and their centers. As in the first problem, the center of the first cluster is unknown and determined as the centroid, while the center of the second one is fixed in the origin. In this paper, we show that both problems are strongly NP-hard. Also, we present the exact algorithms for the cases of these problems in which the input points have integer components. If the space dimension is bounded by some constant, the algorithms are pseudopolynomial.

An automated system for identifying the conditions of homogeneous and heterogeneous reactions includes mathematical modeling of a chemical reaction, determination of optimization criteria conditions for variable parameters, setting and multipurpose optimization problem solution and an optimal control problem, development of efficient algorithms for a computing experiment. Modeling and optimization of a homogeneous and heterogeneous catalytic reactions are carried out. Optimal conditions for carrying out reactions to achieve the specified criteria are determined.

Using additional boundary conditions and additional unknown functions in the integral method of heat balance, we consider the method of obtaining analytical solutions to the thermal conductivity problem associated with the separation process of thermal conductivity of two phases with respect to time, which allows reducing the solution of partial differential equations to the integration of two ordinary differential equations for some additional desired functions. The first stage is characterized by a rapid convergence of the analytical solution to an exact one. For the second stage, the exact analytical solution has been obtained. Additional boundary conditions for both phases are in such a form that their execution by a desired solution be equivalent to realization of the original equation at boundary points and at a front of the temperature perturbations. It is shown that the implementation of the equations at the boundary points leads to its execution also inside the domain.

In this paper, we present a two-grid scheme for a semilinear parabolic integro-differential equation using a new mixed finite element method. The gradient for the method belongs to the space of square integrable functions instead of the classical H (div;Ω) space. The velocity and the pressure are approximated by a P ₀²- P ₁ pair which satisfies an inf-sup condition. Firstly, we solve the original nonlinear problem on the coarse grid in our two-grid scheme. Then, to linearize the discretized equations, we use Newton's iteration on the fine grid twice. It is shown that the algorithm can achieve an asymptotically optimal approximation as long as the mesh sizes satisfy h = O ( H ⁶ |ln H |²). As a result, solving such a large class of nonlinear equations will not be much more difficult than solving one linearized equation. Finally, a numerical experiment is provided to verify the theoretical results of the two-grid method.

Randomized algorithms of Monte Carlo method are constructed by the combined realization of the base probabilistic model and its random parameters for investigation of the parametric distribution of linear functionals. The optimization of algorithms with the use of the statistical kernel estimator for the probability density is presented. The randomized projection algorithm for estimating a nonlinear functional distribution as applied to the investigation of criticality fluctuations for the particles multiplication process in a random medium is formulated.

An adaptive analog of the Nesterov method for variational inequalities with a strongly monotone operator is proposed. The main idea of the method proposed is the adaptive choice of constants in maximized concave functional at each iteration. In this case there is no need in specifying an exact value of this constant, because the method proposed makes possible to find a suitable constant at each iteration. Some estimates for the parameters determining the quality of the solution of the variational inequality depending on the number of iterations have been obtained.

In this article, a weighted finite difference scheme is proposed for solving a class of parameterized singularly perturbed problems (SPPs). Depending upon the choice of the weight parameter, the scheme is automatically transformed from the backward Euler scheme to a monotone hybrid scheme. Three kinds of nonuniform grids are considered: a standard Shishkin mesh, a Bakhavalov-Shishkin mesh, and an adaptive grid. The methods are shown to be uniformly convergent with respect to the perturbation parameter for all three types of meshes. The rate of convergence is of first order for the backward Euler scheme and of second order for the monotone hybrid scheme. Furthermore, the proposed method is extended to a parameterized problem with mixed type boundary conditions and is shown to be uniformly convergent. Numerical experiments are carried out to show the efficiency of the proposed schemes, which indicate that the estimates are optimal.

For the mathematical model of the sea thermodynamics, developed in the Institute of Numerical Mathematics of the Russian Academy of Sciences, the problem of variational assimilation of the sea surface temperature data is considered, with allowance for the observation data error covariance matrices. Based on the variational assimilation of satellite observation data, the inverse problem of restoring a heat flux on the sea surface is solved. The sensitivity of functionals with respect to observation data in a problem of variational assimilation is studied, and the results of numerical experiments for the model of the Baltic Sea dynamics are presented.

Combustion of tapes in air, rolled from titanium powder, and the delay time of the combustion front motion in the presence of a one-sided partition, which limits the access of an oxidizer to the surface. It is shown that the combustion front is aligned with respect to the tape thickness at a long distance from the partition, which is two order of magnitude larger than its thickness. The critical width of the two-sided partition is determined. The largest portion of the tape, where the front is aligned with respect to the tape thickness with a one-sided partition, and the small critical width of the two-sided partition are due to the surface combustion.

X-ray diffraction with the help of synchrotron radiation is used to analyze a sequence of phase formation in the oxidation of original and modified Al powders in the case of heating in oxidizing gaseous media with rates of 10 and 100 K/min. It is established that an increase in the heating rate of the modified ASD-4 powder leads to an active growth of metastable phase (  - and  '-Al₂O₃) of aluminum oxide except for the  -Al₂O₃ phase. There are assumptions on the forms of existence of vanadium in the interaction products. It is shown that diffusion limitations in the core - shell system (Al-Al₂O₃) can be removed under the action of an oxidizing aluminum particle on physicochemical processes at interphase boundaries.

Combustion of a Ti + 0.5C granulated mixture with a varying rate of the concurrent flow of nitrogen is under consideration. Experimental data are used to determine the gas flow parameters responsible for the transition from conductive to convective propagation of the combustion wave, which is characterized by a stronger dependence of the burning rate on the value of the gas flow. A simple model for calculating the burning rate in convective combustion, and a method for determining the boundary between combustion regimes is developed. In accordance with this model, the burning rate not only depends on the combustion temperature of the mixture, but also on the ignition temperature of the mixture components in the flow of active gas.

A method of preliminary mechanical activation is used to perform the combustion of a Ti + Ni mixture, which does not burn at room temperature. The dependences of the burning rate, maximal temperature of combustion, and elongation of samples on the mechanical activation time of the Ti + Ni powder mixture are described for the first time. Moreover, the microstructure and phase composition of activated mixtures of their combustion products are studied. The mechanical activation time (9 min) during which the burning rate of the mixture and the content of the main phase (TiNi intermetallide) in the combustion products is experimentally determined. In these conditions, the combustion propagates within a narrow zone - the maximal temperature corresponds to that in the combustion front.

Thermal decomposition of disubstituted salts of high-energy 5,5'-azotetrazolate (sodium, ammonium, hydrazine, guanidinium, aminoguanidinium, and triaminoguanidinium salts) under isothermal and nonisothermal conditions in solid and liquid phases is studied. The relationship between the avidity and the thermal stability of the 5,5'-azotetrazolate salt is demonstrated. The boundary of possible existence of 5,5'-azotetrazolate salts in terms of the avidity index p K _a is determined. Gaseous and condensed products of decomposition are analyzed, and a mechanism of thermal decomposition of 5,5'-azotetrazolate is proposed. The enthalpies of formation of some 5,5'-azotetrazolate salts are determined, and the most reliable values are chosen on the basis of the analysis of the data obtained in the present study and those available in publications.

The standard enthalpies of formation of the compounds 1-(2,2-bis(methoxy-NNO-azoxy)ethyl)pyrazole, 1-(2,2-bis(methoxy-NNO-azoxy)ethyl)-3-nitropyrazole, and 1-(2,2-bis(methoxy-NNO-azoxy)ethyl)-4-nitropyrazole were measured experimentally to be 273.6 ± 6.7, 231.0 ± 3.3 and 213.8 ± 7.9 kJ/mol, respectively. These enthalpy values were used to determine the contribution of the replacement of H atoms at N atoms in heterocycles by CH₂CH(N₂O₂Me)₂ groups (151.9 kJ/mol). Calculations have shown that compared to HMX, 1-(2,2-bis(methoxy-NNO-azoxy)ethyl derivatives of pyrazole, 3- and 4-nitropyrazole, 3,4-diniteopyrazole, 3,4,5-ttrinitropyrazole, the bis-derivative bis-furazano[3,4-b;3',4'-e] piperazine are worse gasifying components of solid composite propellants in metal-free compositions with an active binder. Only the derivative 3,4-dinitropyrazole, which at low content and combined with ammonium perchlorate provides a specific impulse of 249 s in aluminum-free propellant compositions. Key

This paper presents a review of studies of the combustion of composite propellants containing a fuel based on aluminum and boron. A method for studying the combustion of large particles of a combined Al + B fuel in air is presented. Burning Al/B particles 300-700 m in diameter of agglomeration origin were obtained by ignition of miniature pieces of a mixed composition containing 32% binder and 68% micron size aluminum and boron powders in the ratio Al/B = 81/19 placed in a burning metal-free sample. Agglomerates formed by the merger of many small particles burned in free fall in air. The procedures for processing video records of the combustion process and studying condensed combustion products (residues of burning agglomerates) to determine the burning time and analyze the transformation of the combined fuel into oxide are described.

The combustion of Al/B agglomerates (0.81/0.19) with a diameter of 320-780 m in free fall in air was first studied by the method of model monodisperse agglomerates method. The dependence of the burning time on size was determined. Burning residue particles were subjected to morphological, chemical, mass, particle size, and elemental (EDS method) analyses. It has been found that the essential features of the combustion mechanism of Al/B agglomerates compared to aluminum are long combustion; the specific core-shell structure of the particles, with boron present in the core and absent in the shell; a slight change in mass and diameter of particles during combustion.

The achievement of stable colloidal suspensions of reactive metal powders in liquid propellants is crucial for obtaining enhanced thrust per unit mass. Aluminium is of interest due to its availability, stability, and high combustion enthalpy (32000 J/g). In this manuscript, ultrafine spherical aluminium particles with the average size of 15 m are produced by wet milling. Aluminium particles are effectively surface-modified with a polymeric surfactant and sterically stabilized in an organic solvent (toluene). Organically modified aluminium demonstrates a drastic change in surface properties from hydrophilic to hydrophobic, with effective transfer from the aqueous to organic phase. The stabilized particles are effectively dispersed in a liquid rocket propellant (hydrazine). The impact of aluminium particles on hydrazine combustion characteristics is evaluated by using a thermodynamic code named ICT (Institute of Chemical Technology in Germany, 2008). Aluminium particles offer an increase in the combustion temperature, oxygen balance, characteristic exhaust velocity, and specific impulse. The optimum solid loading level of aluminium in the hydrazine fuel is found to be 6 wt%.

By considering the parametric variation of an individual boron particle in a boron agglomerate, the heat transfer, and the mass transfer between the boron particle agglomerate and the surroundings, an ignition and combustion model of a boron agglomerate is proposed. An experiment of a ramjet combustor using a boron-based slurry fuel is designed and operated for the purpose of validating the ramjet configuration and verifying the combustion of boron particles. Then a mathematical model for simulating a multiphase reacting flow within the combustor of a boron-based slurry fuel ramjet is established. Kerosene droplets and boron particles are injected discretely to the burner flowfield, and their trajectories are traced using the discrete phase model. The influence of the agglomerate size, bypass air mass flow rate, initial boron particle diameter, and boron particle content on the combustion efficiency of the slurry fuels is analyzed in detail. The results show that the combustion efficiency decreases with an increase in the agglomerate radius, initial boron particle diameter, and boron particle content. The combustion efficiency increases with an increase in the mass flow rate of bypass air. If the agglomerate diameter is greater than 100 m or the bypass air mass flow rate is smaller than 50 g/s, the boron particles cannot be fully burned.