Home – Home – Jornals – Thermophysics and Aeromechanics 2020 number 2

We study the natural vibrations of the liquid column in a vertical oil well that occur during a sharp shutdown or opening of the well (water hammer). In this case, the period of vibrations and the intensity of their damping are determined not only by the length and diameter of the liquid column in the well and the rheological properties of the liquid, but also by the reservoir characteristics of the bottomhole formation zone (in particular, permeability coefficients, quality of well perforation and properties of the fractures formed). Solutions to the problem of natural damping vibrations of the liquid column in the well are found using a mathematical model describing the movement of the liquid column in the well and the filtration in the bottomhole zone. Characteristic equations for determining complex frequencies (frequency of vibration and damping coefficient) are obtained. The dependences of vibration frequency, damping coefficient and damping decrement on reservoir permeability values are studied; the amplitude of vibrations at different points of the well is found.

The shock wave (SW) propagation in an aqueous foam layer is investigated for the conditions of new published experimental data with visualization of the dynamics of the foam's volume liquid fraction under SW impact. A mathematical model has been developed that describes the behavior of the foam as a non-Newtonian fluid taking into account the effective Herschel-Bulkley viscosity, interfacial heat transfer processes according to the Ranz-Marshall model and realistic equations of state that describe the thermodynamic properties of aqueous foam components. The model is numerically implemented in the solver created by the authors in the OpenFOAM package. The influence of the behavior of the aqueous foam on the SW evolution is analyzed.

A modified Rayleigh-Lamb equation is obtained, which takes into account the radial vibrations of a liquid drop that is covered by a viscoelastic shell, whose center contains a gas bubble, and which is placed in a viscoelastic medium. For the case of small vibrations of the inclusion, the heat transfer problem for gas, liquid phase, viscoelastic shell, and carrier liquid is solved. A dispersion equation is derived for a bubble medium. The influence of the inclusion shell and the viscoelasticity of the carrier phase on the dynamics of acoustic waves is investigated. Calculation results are compared with experimental data.

This study describes the propagation of harmonic and pulsed waves in a layered porous medium, with one of its layers containing gas hydrate. It is shown that the resulting wave pattern makes it possible to predict the presence of a hydrate in a layer and its thickness provided that thermobaric conditions for the existence of the gas hydrate are fulfilled.

We consider the interaction between two spherical bubbles of variable radii during their movement along their centerline in a viscous fluid. A stream function that satisfies the Stokes equation is found in bispherical coordinates as an expansion in Gegenbauer polynomials. Viscous forces that act on the sphere are exactly presented as infinite series. Asymptotic expressions of these forces near the bubble contact zone are derived.

In this study, miscible viscous fingering instability is examined numerically by using the two-phase Darcy's law and transport equations. The effects of the viscosity ratio, anisotropic permeability, and porosity on instabilities are investigated. The finger patterns and their splitting and spreading in the domain are discussed. An image processing algorithm is applied to concentration contours to quantify instability parameters, such as the breakthrough time, efficiency, and fractal dimension. It is revealed that more complex fingers are obtained as the viscosity ratio increases, while the efficiency and the breakthrough time decrease. It is demonstrated that high permeability perpendicular to the flow direction leads to instability intensification and to an increase in the fractal dimension, whereas changing the porosity does not have any considerable impact on viscous fingering instability.

Results of an experimental study of the normal collision of cylindrical impactors with sea ice are presented. The dynamics of wave process development in the thickness of a salt ice obstacle and the behavior of the forces of resistance to impactor penetration are analyzed at different impact velocities. The possibility of using induction cross sections for determining the position of impactors in the obstacle in a range of initial velocities of 800-1500 m/s. Pulsed X-ray diffraction is used to obtain motion diagrams (depth versus time) and the dimensions of cavities formed

A method is proposed for reducing the characteristic time of action of the pulse produced by explosive magnetic generators. The practical implementation of this method has been confirmed by the results of experiments.

An approximate analytical solution to the heat transfer problem for a moving fluid in a cylindrical channel is obtained using an additional new function and additional boundary conditions in the heat balance integral method and taking into account energy dissipation under a first-order boundary condition that varies along the longitudinal coordinate. The use of the additional new function that determines the temperature change along the longitudinal variable in the center of the channel makes it possible to reduce the solution of the partial differential equation to the integration of the ordinary differential equation. The additional boundary conditions are found in such a way that their satisfaction for the new solution is equivalent to the satisfaction of the differential equation at boundary points.

Single-stage synthesis of composite nanoparticles of titanium dioxide and silicon dioxide in the test section of a plasma-chemical reactor with the use of a chloride method based on simultaneous oxidation of titanium and silicon tetrachlorides with preliminary mixing of the reactants by means of bubbling is simulated. Within the framework of the model developed in the study, data on the size of the composite particle core, particle shell thickness, and number of particles with and without the shell are obtained.

Small-scale air-water experiments reported here contain all the important features of the industrial caster, the mold feed pipe, and the nozzles associated with it. The liquid is introduced into the feed pipe through an annulus with the gas entering at the center. The liquid travels down the walls of the feed pipe as a film until it encounters the pipe section containing a two-phase (air-water) bubbly mixture. Drift-flux relations are derived to compute the flow parameters (gas void fraction, horizontal velocity of the jet, etc.), which are found to be in good agreement with observations. The direction of the two-phase bubbly jet emerging from the nozzle is quantified, showing an improved downward deflection angle.

A method is developed for solving a boundary-value problem of residual stress relaxation in a surface-reinforced hollow cylinder under combined loading by an axial force, torque, and internal pressure. Methods for determining the stress-strain state after reinforcement and its kinetics during creep are proposed. The effect of internal pressure along with a tensile load or torque on a thick-walled cylindrical sample made of ZhS6KP alloy after air-shot peening is investigated. Computational diagrams for stress tensor components under instantaneous temperature-force loading during creep and after unloading are given and analyzed. The behavior of unreinforced and reinforced samples at the stage of steady creep after complete residual stress relaxation is compared.

A system for automated investigations of pulsed fluid flows in channels with the use of a special test rig is presented. In this system, a specially developed computer code defines the pulsed flow rate of the fluid and traces whether the task is performed. The test rig is tested with the use of a flowmeter.

In this paper, we consider the classical methods of surface damping of bending vibrations of thin-walled structures and a promising integral method of a damping coating consisting of two layers of material with pronounced viscoelastic properties between which a thin reinforcing layer of high modulus material is located. A finite element with 14 degrees of freedom has been developed for modeling an elongated plate with the specified damping coating taking into account the effect of transverse compression of the damping layers under high-frequency oscillations of the plate. A generalized problem of complex eigenvalues in the lower part of the spectrum of complex forms and frequencies of free vibrations of a damped plate is solved using iterations with consideration of the frequency dependence of the dynamic elastic moduli of the material. The damping properties of the plate are determined from the imaginary parts of the complex eigenfrequencies and the relative energy dissipation at resonance.

Three methods of approximation of lower non-differential terms in equations of dynamic problems of mechanics of deformable solids are studied with the use of explicit algorithms of the numerical solution based on several local approximations of each of the sought functions by linear polynomials. Additional equations based on the energy conservation law are formulated in the course of algorithm construction. The properties (dissipativity, monotonicity, and stability) of the proposed schemes are studied. Results of the numerical solution of the problem of deformation of an elastic plate with constant shear strains over the plate thickness (Timoshenko model) are presented. Results of the numerical solution of the problem of deformation of an elastic disk under pulsed loading are compared with the analytical solution of this problem.

This paper considers a model that can be used to describe polymorphic phase transition in a shock wave based on experimental data on the compression of material by a shock wave. It is assumed that the phase transition in a non-porous material has a martensitic character and occurs in the stationary shock wave that arises in the immediate vicinity behind the first one. Conditions for the occurrence of this shock wave are determined. The model has been tested for non-porous pyrolytic graphite. It has been shown that the model satisfactorily describes the experimental results obtained in various studies for this type of graphite.

Three-dimensional explicit dynamic simulations are carried out to study the failure of hybrid bolted-bonded vertical T- and L-joints under noncontact underwater explosion shock pressure. In this modelling, adherends are fibrous laminated composites having an orthotropic behavior, while bolts and adhesive layers exhibit an isotropic behavior. It is found that hybrid vertical T- and L-joints display appreciably higher joint resistance to underwater explosion shock pressure than adhesive T- and L-joints.

A plane elastoplastic problem related to stress distribution in a thin plate with a circular hole is considered with account for nucleation and development of cracks in an elastic region. It is assumed that the circular hole is located in the plastic deformation region. It is considered that loading is accompanied by crack nucleation and the fracture of the plate material in the elastic deformation region of the plate. The problem is solved using the perturbation theory and the theory of singular integral equations.

In this paper, the nonlinear dynamic behavior of an immersed dagger-shaped atomic force microscope cantilever in different liquids has been investigated for the first time. The Timoshenko beam theory, which considers rotatory inertia and shear deformation effects, has been used for modeling the cantilever. The nonlinear tip-sample interaction force has been modeled by using the Hertzian contact theory. Water, methanol, acetone, and carbon tetrachloride are considered as the immersion environments. In most cases, the softening behavior has been observed for the cantilever. The resonant frequency is found to decrease with an increase in the liquid viscosity. The experimental results have been compared with the theoretical predictions and are found to be in good agreement.

In this paper, the influence of the dynamic stress concentration in a piezoelectric material with a non-circular hole subjected to a shear wave polarized so that its particle motion and direction of propagation contained in a horizontal plane (SH-wave) is investigated. The boundary conditions of the non-circular hole can be mapped into a unit circle by applying complex variables and conformal mapping. The analytical solution of the dynamic stress concentration factor is determined by the unknown mode coefficients obtained by using the boundary conditions. Numerical examples are presented to analyze the influence of the incident wave number, piezoelectric constant of the material, and eccentricity ratio of the hole on the distribution of the dynamic stress concentration factor. The analysis reveals that the distribution of the dynamic stress concentration factor on the incident direction of the SH-wave is significantly different from that on the other side.

On the basis of a micromechanical model of the tensile strength of a polymer composite, it is shown that, in contrast to the case of adhesion between two polymers, when a linear dependence of the thickness of the interfacial region on the degree of interfacial adhesion is observed, the strength of the material of the interfacial region in nanocomposites of the polymer - high modulus filler type decreases as its thickness increases. ... Using a fractal model of interphase interactions, estimates of the threshold values of the volume fractions of nanoclusters of the epoxy polymer matrix and metal nanoparticles of the filler are obtained, upon passing through which the process of transfer of mechanical stress from the polymer matrix to the filler is weakened. It is shown that exceeding the threshold value of the volume fraction of the filler leads to a violation of the aggregate stability of the filler and a decrease in the values of the dimensionless parameter of the micromechanical model, which characterizes the degree of interfacial adhesion. With a further increase in the volume fraction of the filler, the values of this parameter become negative, while the strength of the composite practically does not increase.

Experiments are performed on dilute polymer solutions jetting into quiescent air with a jet velocity range of 30-87 m/s. Polymer solutions are those with several hundred ppm concentrations of long-chain polyoxyethylene (millions of molecular weight) dissolved in purified water. The breakup characteristics of the jets were recorded by high-speed photography from four observation windows along the jet direction. The breakup morphologies of dilute polymer solution jets are significantly different from that of Newtonian fluids. Small-scale interfacial disturbances are suppressed, while a twisted liquid column waving with large amplitudes is observed. When the jet velocity exceeds a critical value, liquid films and filaments are peeled off successively from the liquid column. Four different breakup patterns are distinguished. The diameters of the central liquid column and the principal liquid filament are observed to decrease with increasing jet velocity.

This paper deals with the to boundary value problems for pseudoparabolic equations of fractional order with the Bessel operator with variable coefficients with non-local boundary conditions of the integral type and difference methods for their solutions. To solve the considered problems a priori estimates in differential and difference interpretations are obtained, which means the uniqueness and stability of solutions by initial data and the right-hand side, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem.

Analytical and numerical methods for solving inverse problems of logarithmic and the Newtonian potentials are investigated. The following contact problem in the case of a Newtonian potential is considered. In the domain Ω{Ω: -l ≤ x,y ≤ l, H υ(x,y) ≤ z ≤ H}, sources with the density ρ(x,y), perturbing the Earth’s gravitational field, are distributed. Here, υ(x,y) is a non-negative finite function with the support Ω = [l,l]², 0 ≤ υ(x,y) ≤ H. It is required to simultaneously restore the depth H of the occurrence of the contact surface z = H, the density ρ(x,y) of sources, and the function υ(x,y). The methods of simultaneous determination are based on the use of nonlinear models of potential theory which are developed in the paper. The following kinds of information are used as the basic ones: 1) values of the gravity field and its first and second derivatives; 2) values of the gravity field at the different heights. The possibility of the simultaneous recovery of the functions ρ( x,y), υ(x,y) and the constants H in the analytical form is demonstrated. Iterative methods for their simultaneous recovery. The model examples demonstrate the effectiveness of the proposed numerical methods are constructed.

For one of cubic equations of state, the Redlich-Kwong, the inverse curve, which characterizes a change in a sign of the Joule-Thomson coefficient, has been constructed. The range of reduced pressure and temperature corresponds to the values intrinsic of technological changes in production and transport systems of natural gas.

In this paper, an operator iterative procedure for constructing of the orthogonal projection of a vector on a given subspace is proposed. The algorithm is based on the Euclidean ortogonalization of power sequences of a special linear transformation generated by the original subspace. For consistent systems of linear algebraic equations, a numerical method based on this idea is proposed. Numerical results are presented.

The shallow gas in the ground geological layers of the water space is of great danger for the drilling rigs in the case of an accident opening of the gas deposits. Gas starts rising towards the surface of water, and sooner or later, the gas emission into the atmosphere threatens the environment. It is very important to be able to forecast the gas emissions in order to prevent the catastrophic consequences with the destruction of drilling rigs and people fatalities. This paper presents the results for the numerical modeling of seismic waves propagation in models with gas deposits through the layered soil towards the surface of water for the 3D case. The modeling was carried out for the 4-year period for the layers, which are located at the depth of 1000 m from the bottom of the sea. The results of the computations (the wave pictures and seismograms) show the approach of gas to the surface of water for the 4th year of the computations. The consistency of the results for the 3D problem with the results for the 2D problem, early obtained by the authors, is very important for the further research into the area in question.

We investigate the influence of the Wiener and the Poisson random noises on the behavior of the linear and Van der Pol oscillators with the help of the statistical modeling method. For a linear oscillator, the analytical expression of the autocovariance function of the solution to stochastic differential equation (SDE) is obtained. This expression along with the formulas of mathematical expectation and variance of the SDE solution allows us to carry out the parametric analysis and to investigate the accuracy of estimates of moments of the numerical solution to the SDE obtained with the help of the generalized Euler explicit method. For the Van der Pol oscillator, the influence of the Poisson component on the oscillation nature of the first and the second moments of the SDE solution with a large value of jumps is numerically investigated.

Here, we consider the empirical relationships presented earlier in the literature that describe the thermophysical properties of H₂O + Al₂O₃ nanofluids, such as viscosity and heat conductivity coefficients. The main parameters affecting these properties of nanofluid are considered to be the volume fraction of particles φ, fluid temperature T, and particle size d_p. The suitability of approximation formulas for calculating the viscosity and heat conductivity coefficients is determined by comparing the data calculated by these formulas with the experimental results. The behavior of the analytical curves of thermophysical coefficients is analyzed in the following ranges of influencing parameters: 0 < φ &8804; 0.1, 280 K &8804; Т &8804; 360 K, 1 nm &8804; d_p &8804; 100 nm. Estimates of the degree of dependence of calculation results on the values of these parameters are given. Conclusions on the qualitative and quantitative reliability of the correlation formulas proposed in the literature, as well as on the limits of their applicability in the ranges of variation of the influencing parameters are drawn.

The results of a parametric study of hydrodynamic stability in linear formulation of the Blasius boundary layer stability over two-layer compliant coatings are presented. In the calculations, experimental data for real silicon rubbers of several types on the elasticity modulus and the loss factor as functions of deformation frequency are used. Eight pairs of the coatings have been considered. The effect of coating layer thickness and external flow velocity on flow stability, in particular, on the behavior of the critical Reynolds number, has been studied parametrically. The regions of the critical Reynolds number of nonmonotonic nature, characteristic of most of coatings under consideration, have been found. A qualitative explanation of this effect is given. An analysis of the behavior of the critical Reynolds number allows determination of the optimal ratio of coating thicknesses for interaction with the flow.

The results of investigating the physical and chemical processes in the wall boundary layer on graphite specimens in a nitrogen flow are reported. The effect of the catalytic wall on the heat flux is considered. The emphasis is on analyzing the distribution of the chemical species concentrations across the boundary layer based on a detailed consideration of the mechanism of heterogeneous catalytic reactions under the surface mass flux conditions. The distributions of the chemical species concentrations over the boundary layer thickness at the stagnation point of a blunted graphite body for a particular flight path segment are presented.

The paper presents a theoretical study for a supersonic boundary layer over a flat plate in a stream of air at Mach number M = 2 under the conditions of surface sublimation. The sublimation-prone material is naphthalene (C₁₀ H₈ ). Calculations demonstrated that at a higher surface temperature the mass flowrate of naphthalene evaporation is increasing. This reduces the wall temperature in comparison with a similar flow without sublimation. The high molecular mass of naphthalene (vs. air) and reduction of wall temperature due to the wall material evaporation creates a higher density of the binary gas mixture (air and naphthalene vapor) near the wall. This modification of the boundary layer profiles induces a significant reduction of instability growth rate. This fact was confirmed by calculations based on the linear stability theory. It was found that boundary layer stabilization occurs for growing sublimation surface temperature; it becomes a maximum near the triple point temperature of the coating material. The e^N method gives the estimates of the Reynolds number for laminar-turbulent transition. This shows a theoretical possibility of extension of the laminar boundary layer above a model with sublimation coating.

The mathematical model of unsteady heat transfer in the thermionic thermal protection system during high-enthalpy heating is studied numerically. The effect of evaporation of electrons from the emitter surface on reduction of the temperature of the multilayered shell of the thermionic thermal protection system is demonstrated. The influence of some heat transfer agents in the composite shell on the regimes of heat transfer in the body is considered. Qualitative agreement of the calculated results with available data is obtained.

Results of a physical experiment aimed at measuring the profile of relative excess pressure on a control surface in the near zone of the disturbed region of a schematized model of supersonic passenger aircraft (SPA) are reported. Tests in the test section of the T-313 wind tunnel, aimed at identification of the optimum mounting of SPA-model suspension and ensuring measurements of the full profile of the disturbed-pressure wave involving the leading, intermediate, and closing shock waves, were carried out. Comparisons of calculated data with experimental results are presented. Using the revealed optimum model suspension, measurement results in good agreement with the results of numerical calculations are obtained. The numerical solution to the problem about the flow around the geometric model was obtained and the necessary measurements in the experiment were carried out at freestream Mach number M_¥ = 2.04 and angle of attack a = 4°.

The paper studies turbulent mixing in thermoviscous fluid flow in a 3D cubic domain which is extended periodically in two directions (X and Y). The flow turbulization develops under the impact of two-dimensional chaotic disturbances at mass average Reynolds number Re₁ = 4704. The vortex field structure is discussed in terms of an isosurface of Q-criterion and local enstrophy z_l. For the advanced stages of flow evolution, the study considers Eulerian correlation coefficients for velocity fluctuations (auto-correlation functions) and the cross-correlations of pressure and temperature. The Eulerian correlation coefficient is split for analysis of correlation characteristics in periodicity and wall-normal directions. The integral scale is evaluated depending on the distance to the walls. The flow analysis is performed in the terminology of viscous scale. The mesh resolution is evaluated for the flow regions corresponding to the logarithmic boundary layer and the near-wall thermal layers.

The paper presents a study of the slip velocity for almost spherical bubbles in a downward laminar tube flow. The local slip velocity is defined as a difference between the mean liquid velocity (measured with electrodiffusional method) and the mean bubble velocity (measured with a modified LDA tool with a small size of measurement volume). The law for slip velocity for downward flow is significantly different from a similar law for upward flow. This reveals that the bubble flow motion is rather random than structured in the downward flow.

The flow modes of a vapor-drop mixture in a regasifier-heater of liquefied natural gas are numerically studied on the basis of the model that takes into account polydispersity, power and thermal interaction of phases, processes of breakup, coalescence, evaporation of droplets and condensation of steam. The dynamics of the carrier medium is described by the system of Navier-Stokes equations for a compressible gas, taking into account the exchange of mass, momentum, and energy with a dispersed phase that includes several fractions differing in the size of droplets. Each fraction is described by a system of equations consisting of the continuity equation for the average density, the conservation equations for the momentum components, and the thermal energy conservation equation, taking into account the interfacial exchange of mass, momentum, and energy with the carrier medium. Systems of equations of motion for the carrier medium and fractions of the dispersed phase are solved by the explicit McCormack method with the spatial operator splitting in directions and a scheme of nonlinear correction. At each time step, the main part of the computational algorithm is supplemented with models of breakup, coalescence, evaporation of droplets and vapor condensation, followed by correction of the hydro- and thermodynamic parameters of the mixture. The calculation of the flow modes of the vapor-drop mixture0020in the channel of the regasifier-heater of liquefied natural gas is performed based on the described model.

Results of a study of the air-plasma spraying of cavitation- and hydroabrasive-resistant coatings from powder materials are reported. A method of laboratory (bench) testing of coatings for resistance under pulsed impact loads is proposed. The bench is a laboratory impact tester that strikes an indenter brought in permanent contact with the sample. A measure of the damage inflicted to the surface hardened by a wear-resistant coating is the diameter of the hole produced by the indenter. The moment of coating destruction is the time at which cracks appear in the coating or the peeling occurs. The developed technique of the bench tests for the pulsed impact loading of wear-resistant coatings imitates the operating conditions of the blades of a high-speed propeller of a water-jet propulsion device in shallow water. The method of air-plasma spraying of powder materials as protective coatings was successfully tested when hardening the propeller blades of a water-jet propulsor of a KS-101D river ship.

A method for rapid determination of diffusion coefficients of polar solvents in anisotropic porous materials, making it possible to control the state of products prepared from such materials without destruction, is reported. For implementation of the proposed method, no preliminary calibration of the local solvent concentration in solid phase for the used converter and each new “porous material-solvent” system is required; that circumstance largely increases the research productivity of the method. The method possesses flexibility in terms of the possibility for measuring the values involved in the calculation expression on curve sections with a high sensitivity to parameter changes and in the range with a stable and noise-protected output signal of the concentration converter, which fact ensures an in-creased control accuracy.

This paper presents the results of numerical simulation of air flow with suspended particles through a human nasal cavity. The stationary and nonstationary problem statements were considered. Within the nonstationary case, two variants were studied: for the first variant, the breath cycle is taken with symmetric inhale/exhale, and for the second variant, we modelled a real asymmetric breath cycle. The solution was based on Navier-Stokes equations for laminar flow of incompressible gas. Particle flow is described using the Lagrangean approach with account for Brownian motion. Numerical simulation results were compared with experimental and simulation data from other authors. Results for different variants of problem statement were compared. Asymmetry of breath cycle should be accounted in calculation of particle deposition efficiency. A simple rule was found that replaces the computation-consuming nonstationary calculation with three stationary flow calculations.