Home – Home – Jornals – Thermophysics and Aeromechanics 2024 number 5

This paper presents the results of numerical simulation of magnetic field cumulation and the Joule heating of shaped-charge jets produced by explosive compression of a metal cone in which a magnetic field was preliminary generated. The problem is considered in an axisymmetric two-dimensional non-stationary formulation. The final electrical conductivity of the cone material is taken into account, and various methods of generating the initial magnetic field (using one or two solenoids) are considered. It is found that that during cone compression, the magnetic field induction can increase several hundred-fold. For a relatively low initial magnetic field induction on the cone axis (0.09-0.17 T), the temperature increase near the axis of the shaped-charge jet due to heating by eddy currents is 200-300 °C. This heating can be accompanied by thermal softening of the shaped-charge jet material and an increase in its ultimate elongation and hence penetration capability.

This paper presents preliminary results of refinement of the mathematical model of plasma transport in a helical open magnetic trap (HOMT). Plasma is contained in the device by transferring a magnetic field pulse with helical symmetry to the rotating plasma. The mathematical model is based on the stationary equation of plasma transport. The paper presents a method for taking into account the effect of the model coefficients using additional information. The calculated dependence of temperature on coordinates is obtained, which qualitatively agrees with the experimental data. Ordinary differential equations are obtained, which follow from the original model and can be used to refine the coefficients. The mathematical model is developed to predict the plasma confinement parameters in devices with a spiral magnetic field.

The crystallization of a gallium alloy in a rectangular flat cuvette located vertically under external electromagnetic influence has been studied experimentally. It has been shown that the speed of movement and shape of the crystallization front can be effectively controlled by changing the power parameters of the electromagnetic stirrer. A mode characterized by intense mixing flow and significant inhomogeneity of the crystallization front has been selected by varying the amplitude of electromagnetic forces. In this mode, changing the phase angles of the supply currents of the linear induction machine allows one to fundamentally change the topology of hydrodynamic melt flows at a constant power supply of the stirrer. This, in turn, leads to a change in heat and mass transfer characteristics and hence the conditions in the interfacial region, making it possible to indirectly control the homogeneity of the crystallization front and, to a lesser extent, the phase transition rate. The contribution of convection to flow formation and its influence on the crystallization process have been studied. In particular, it has been shown that thermal convection can lead to the formation of additional vortex structures near heat exchangers, which prevents metal crystallization.

Coupled aerodynamics and rigid body dynamics are used to develop a numerical method for the rigid motion of the object on the ground under shock waves based on the collision theory and dynamic mesh method. The effects of the mass and centroid height of the object on the rigid motion are analyzed. Furthermore, the effect of object motion on shock wave propagation is examined. The results suggest that the rigid motion behavior of the object remains similar under different positive pressure times; the motion laws of the object are similar under different masses, while a small mass can alter the rotational direction; increasing the centroid height can reverse the rotational direction, and diffraction may induce a further reversal when the centroid height increases to a certain value; the rigid motion reduces the pressure decay rate near the leeward side during shock wave propagation over the object.

The states of liquid albumin droplets sitting on a non-wetting horizontal elastic substrate which was first cyclically stretched and then relaxed have been studied experimentally. Multi-branch hysteresis of the states of the droplet gave been found. The number of hysteresis branches can be regulated by changing the law of motion of the substrate.

This paper describes the propagation of vertically polarized surface acoustic waves at an interface between porous media saturated with methane hydrate and ice (water), as well as horizontally polarized waves at an interface between a hydrate-saturated porous medium and a water-saturated porous medium. A mathematical model is developed for plane harmonic waves. The porous medium saturated with gas hydrate or ice (water) is assumed to be an elastic isotropic body. The mathematical model includes wave equations for scalar and vector potentials of wave velocities with account for displacement and stress vector components of the medium particles. Conditions for the continuity of displacements and stresses in porous media at the interface are given. The obtained dispersion equations are analyzed, and the results are compared with experimental data. It is revealed that the penetration depth of a transverse wave into hydrate-saturated sand is greater than the penetration depth of a longitudinal wave. It is proposed to determine the presence of hydrate-saturated sand at positive temperatures of bottom sediments by the penetration depth and the variation of the zero mode velocity of the horizontal polarization wave.

A setup for experimental studies of the structure, shape, and size of the gas-liquid interface under ultrasonic exposure and forced aeration has been developed. It has been found that ultrasonic exposure leads to a factor of about 1.5 increase in the interfacial area during aeration. The existence of an optimal intensity of ultrasonic exposure that provides maximum increase in interfacial area per unit supplied ultrasonic energy has been found.

The paper presents solutions to problems of nonstationary filtration to an imperfect well with an arbitrary angle of inclination from the vertical, allowing for the interpretation of data based on pressure transient test and production forecasting. Solutions are obtained for various conditions on the top and bottom of the reservoir, while two algorithms are implemented to describe the bottom-hole pressure: a multi-segment and a single-segment algorithm with the determination of an equal pressure point. A computational experiment shows that the calculation results obtained using single- and multi-segment algorithms are in good agreement.

Results of studying an oblique impact of heavy solid spheres 6 mm in diameter onto an undisturbed surface of water by the method of high-speed visualization are reported. The dynamics of interaction of the body with the liquid in the cases of sphere ricochet and immersion is compared. It is found that air bubbles are intensely captured in the wake behind the body in situations with body immersion owing to a collision of the edges of the “crown” generated at the cavity boundaries and to formation of a jet penetrating through the cavity bottom and entraining air bubbles. The effects of the sphere material density and of the impact velocity and angle on the scenario of sphere-liquid interaction are studied. Comparisons with previous experiments show that a decrease in the sphere size leads to reduction of the critical angle, while the opposite effect (increase in the critical angle) is observed if the impact velocity is increased. Such effects cannot be explained by theoretical approaches developed earlier for impacts of large spheres because these approaches ignore the dynamics of the liquid jet generated ahead of the body and the changes in the flow pattern as a whole.

The influence of various individual and phantom boundary conditions on the results pre-operative numerical simulations of hemodynamics of a fusiform aneurysm of cerebral vessels is numerically simulated. It is found that allowance for individual mechanical properties of the aneurysm tissue affects the results of predicting the aneurysm status, but does not affect predicting the rupture zone, which can be detected by using the CFD approach under the assumption of rigid walls with phantom boundary conditions and with the condition of the maximum shear stresses on the wall as a criterion of rupture zone determination.

Results of a methodical study aimed at modeling a spatially inhomogeneous transition line are reported. The results are obtained by an in-house software module for the CFD package and an in-house program for predicting the laminar-turbulent transition based on the  e<i>^N</i>-method. Numerical simulations are performed for a hybrid laminar-turbulent transition, where the regular and bypass transition scenarios take place in different regions of the flow in the boundary layer on a swept wing.

A method is developed for determining residual stresses in a thin metal plate via shot peening of its surface. The reference configuration of the plate is assumed to be flat with a layer of hardened material of known thickness with a uniform longitudinal initial stress; its value is determined by solving the inverse problem of establishing the equilibrium state of a bent plate. The problem of bending a plate with initial stresses is solved numerically by the finite element method using the model of an isotropic hypoelastic material. As a result of solving the problem, a residual stress field is determined, allowing one to estimate the degree of danger of positive principal stresses that can lead to destruction of the plate material.

One of the most important factors determining dental implants' longevity and effectiveness is the connection between the abutment and the implant. This investigation focuses on studying how bone shielding is affected by the interface between dental implants and abutments. In a computer-aided design (CAD) environment, three dental implant connectors and carbon-reinforced PEEK are modeled. A comparison is made between the modern dental implant locking mechanism and the more traditional internal hexagonal and conical abutment interfaces to evaluate the former's effectiveness. ANN is employed in the process of developing the precise modulus of the dental implant material for the human jaw. Studying the von Mises stress and deformation of dental interface materials makes it possible to discover a unique locking system that exhibits the highest von Mises stress and deformation, virtually on par with the bone. However, the carbon-reinforced PEEK composite material demonstrates high bone shielding.

A method for selecting an appropriate ice model and its parameters using numerical simulation is developed. The process of low-velocity impact of a spherical indenter with an ice plate is studied, and numerical calculation data are compared with experimental data. This paper describes well-known rheological models of elastoplasticity with the von Mises and von Mises-Schleicher yield criteria, as well as an elasticity model with a constant-size elastoplastic inclusion. A system of isotropic linear elasticity equations, solved by the grid-characteristic method, is used as the determining system of equations. The effect of the model parameters on the calculated instantaneous velocities and coordinates of the ball is investigated. Criteria for selecting the model characteristics are formulated, and approximations of dependences of these criteria on various parameters are constructed.

A single integral form of the postulates of continuum mechanics in the form of laws of change (conservation) of certain quantities is represented as a table of postulates. It is assumed that in a continuous medium, both purely mechanical and various non-mechanical interactions occur, which are described by scalar, vector, and second-rank tensor energetically conjugate pairs of quantities, one of which characterizes a process and the other defines the response of the environment to this process. The first three rows of the table of postulates are used to construct the fourth and fifth rows corresponding to the laws of change in internal energy and the quantity that, in the case of the thermodynamic pair “temperature-entropy” coincides with entropy. It is shown that the assignment of sources, flows through the boundary, and productions in the fourth and fifth rows of the table of postulates actually makes these rows definitions. The principles used in nonisothermal mechanics to construct constitutive relations linking dependent and independent state variables for each type of interaction are generalized.

The problem of determining the parameters of a large system of non-autonomous differential equations consisting of subsystems connected in an arbitrary order by non-local boundary conditions is solved. Unknown parameters participate both in differential equations and in boundary conditions. The problem under study is reduced to a parametric optimal control problem with a mean-square residual criterion estimating the degree of non-fulfillment of additionally specified boundary conditions. To apply first-order numerical methods, analytical formulas for the components of the gradient of the objective functional in the space of optimized parameters are obtained. The analysis of the obtained results of computer experiments is made using a test problem as an example.

This paper aims to provide an efficient numerical method based on the second Chebyshev wavelets for solving the fractional Langevin equation. Applying this operational matrix of fractional-order integration of second Chebyshev wavelets converts the original problem into a system of algebraic equations, which could be solved by the Newton method. After analyzing the method, the error bound is estimated. Moreover, the method's efficiency through a few numerical examples is evaluated.

We consider nonlinear dynamical systems as a model of interaction of components of a gene network which regulates early stages of an embryonic stem cells state. A parametric analysis of these dynamical systems is performed in order to describe the (non)uniqueness and stability of their equilibriums. We have obtained a criterion of existence of periodic trajectories near these points and localized these oscillations on the phase portraits of dynamical systems which describe these processes. A special software for cloud numerical experiments with these systems has been elaborated.

This article explores the computational intricacies of H. Rutishauser's quotient-difference (Q-D) algorithm and C programming code, a revolutionary advancement in polynomial analysis. Our specific focus is on cubic polynomials featuring absolute, distinct non-zero real roots, emphasizing the algorithm's distinctive capability to simultaneously approximate all zeros independently of external data. Notably, it proves invaluable in diverse domains, such as determining continuous fraction representations for meromorphic functions and serving as a powerful tool in complex analysis for the direct localization of poles and zeros. To bring this innovation into practice, the article introduces a meticulously crafted C language program, complete with a comprehensive algorithm and flowchart. Supported by illustrative examples, this implementation underscores the algorithm's robustness and effectiveness across various real-world scenarios.

Rational techniques for verifying the congruence of complex matrices are discussed. An algorithm is said to be rational if it is finite and uses only arithmetical operations. An important part in verifying the congruence of nonsingular matrices play their cosquares. The verification gets complicated if there are eigenvalues of modulus 1 in the spectrum of cosquares; this is especially true if such eigenvalues are defective. In this direction, the most advanced result is the rational algorithm for matrices A and B whose cosquare is the direct sum J_m (1) ⊕ J_m (1). Here, this algorithm is extended to the case where the cosquare is the direct sum of two Jordan blocks of distinct orders. This extension is heavily dependent on additional facts concerning the solutions to the matrix equation X - J^Τ_m(1)XJ_m(1) = 0. found in the present paper.

Traditionally, to solve the hydrodynamic equations a Godunov method is used, whose main component is the solution of a Riemann problem to compute the fluxes of the conservative variables through the interfaces. Most numerical Riemann solvers are based on partial or full spectral decompositions of the Jacobian matrix with the spatial derivatives. However, when using complex hyperbolic models and various types of equations of state, even partial spectral decompositions are quite difficult to find analytically. Such hyperbolic systems include the equations of special relativistic magnetic hydrodynamics. In this paper, a numerical Riemann solver is constructed by means of a viscosity matrix on the basis of Chebyshev polynomials. This scheme does not require information about the spectral decomposition of the Jacobian matrix, while considering all types of waves in its design. To reduce the dissipation of the numerical solution, a piecewise parabolic reconstruction of the physical variables is used. The behavior of the numerical method is studied by using some classical test problems.

A process of searching on the sphere for the best (in a sense) cubature formulas that are invariant under the transformations of different dihedral rotation groups is described. The parameters of the new cubature formulas of the 6th, 10th, and 12th order of accuracy are given to 16 significant digits. A table which contains the main characteristics of all the best to date cubature formulas of the dihedral rotation group up to the 29th order of accuracy is given.

For the case of two spatial variables, a finite-difference scheme of the predictor--corrector type is constructed for solving nonlinear dispersion equations of wave hydrodynamics with a higher order of approximation of the dispersion relation. The numerical algorithm is based on splitting the original system of equations into a hyperbolic system and a scalar equation of the elliptic type. Two methods of approximating the elliptic part are considered. For each of the variants of the difference scheme, dissipation and dispersion analysis is performed, stability conditions are obtained, formulas for the phase error are analyzed, and the behavior of the harmonic attenuation coefficient is studied. A comparative analysis is carried out to identify the advantages of each of the schemes.

The flows of a viscous liquid film along the outer surface of a vertical cylinder are considered. The study employs a model nonlinear evolutionary equation for film thickness deviation from the undisturbed level. It is valid for describing long-wave perturbations in the case of small fluid flows and large cylinder radii. The branching of spatial wave regimes from the undisturbed flow regime is investigated. Particular attention is paid to special cases when the values of the radii of the cylinders lie in the vicinity of some specific critical points. To study such cases, a model system of equations is obtained from the initial equation. Several solutions of this system are given.

Analytical and numerical solutions for the heating of a composite "hydrocarbon - water" drop with a water microdroplet located in the center of a spherical drop of hydrocarbon are compared. The conjugation conditions are fulfilled at the interface: continuity of temperature and heat flux. At the outer boundary of the droplet, a condition of heat exchange with a hot gas streamlining the droplet is set. The analytical formula is based on the decomposition of the solution in a series of eigenfunctions of the Sturm-Liouville problem. An original conservative difference scheme for the numerical integration of the equations of thermal conductivity inside a composite droplet is constructed to take into account the abrupt change in thermophysical properties at the interface of hydrocarbon-water media. The calculation results obtained using the analytical formula and the numerical integration method are consistent with each other. The numerical scheme includes radiative heat transfer and the effect of evaporation on the heat transfer coefficient. A comparison of the simulation results with experimental data is presented.

High-speed shadow imaging of a gas-droplet flow from a microchannel nozzle device was performed by varying the liquid flow rate from 1 to 50 ml/min and the gas pressure drop from 0.5 to 8 bar. For this purpose, an optical system with a stereomicroscope was assembled to ensure a large depth of field and relatively high resolution. The outflow was studied for two types of nozzles: a three-nozzle device with an internal channel diameter of 200 μm and a custom-made nozzle with a microchannel silicon membrane of 243 μm thickness and a microchannel size of 10×10 μm². Spray angles for a single nozzle and an angle averaged over three nozzles were determined. Dependences of the angles on liquid flow rate for each pressure drop and dependences on pressure drop with varying liquid flow rate were obtained. It is shown that a uniform gas-droplet flow can be organized at the nozzle edge with small droplets using a microchannel membrane.

The results of an experimental investigation on heat transfer and critical heat flux during surface cooling with a dispersed flow of deeply subcooled liquid are presented. The study was carried out using a pressure nozzle with a mass flow rate of water of 24.2 g/s. A record critical heat flux of 13.2 MW/m² was achieved in these experiments. The findings indicate that the onset of boiling within the liquid film formed on the impact surface during spray irrigation leads to a notable reduction in the temperature non-uniformity across the heater.

The paper presents an updated physical-mathematical model for a stationary flow of a water-oil flow through the porous space of a rock core (this space is described as an array of capillary clusters). Here we consider an isothermal statement of problem: the temperature is the key parameters for fluid properties and for the value of pressure drop caused by interaction between the fluid phases. The developed model ensures calculating the relative permeability at different temperatures; this approach is based on standard laboratory data for core testing and on experimental data for single-phase filtration of the fluid at different temperatures (or substituted with appropriate formulas). This model was applied for calculating the relative phase permeabilities at different temperatures for the case of weakly-cemented rock formation. This sample was taken from one of Siberian oil fields with a high viscosity oil. The numerical study was conducted on the effect of temperature on the flow pattern in a variable cross-section capillary channel. Simulation was conducted using the OpenFOAM platform. The temperature-caused change in fluid properties alleviates the intensity of a train flow and promotes the transition of the train flow to the droplet flow.

The paper investigates the possibility to control the two-phase flow of immiscible liquids with a high viscosity ratio of the carrier and dispersed phases in a T-type microchannel, with the dispersed phase being a ferromagnetic liquid, by means of a constant magnetic field. The effects of separation of slugs and microdrops of a ferrofluid, as well as the controllability of the structure of the parallel flow of immiscible liquids, have been found. The obtained results may be used to design microfluidic systems in order to efficiently sort particles, as well as intensify heat and mass transfer processes.

Various approaches to oil film visualization of the flow on the cylinder surface aligned transversely in a supersonic flow in a pulsed wind tunnel are compared. Two types of fine-particle coloring pigments Al₂O₃ and TiO₂ are considered. Two methods of pigment application are used: sprinkling onto the model surface pre-coated with an oil film and applying a mixture of the pigment and oil onto the model surface. The mass fraction of the pigment in the mixture for oil film visualization is varied from 10 to 20%. Photographs of the dynamics of variation of the oil film coating on the model surface are presented, which are taken immediately after application, during the experiment, and upon its completion. Based on the results of the present study, recommendations are formulated on using surface flow oil film visualization with due allowance for specific features of application of this method for experiments in pulsed supersonic wind tunnels.

The present study deals with optical and thermophysical properties of nanofluids based on spherical carbon nanoparticles stabilized in water by sodium dodecyl sulfate. Nanoparticles with the mean diameter of 11 nm are synthesized by means of electric arc spraying in helium at a pressure of 3 Torr. For the concentration of carbon nanoparticles in the nanofluid equal to 0.01%, the extinction coefficient varies from 400 to 200 m^-1 in the wavelength range of 180 - 1100 nm. For mass fractions of nanoparticles within 0 - 0.04%, the viscosity is not found to depend on the concentration. With an increase in the concentration, the thermal conductivity of nanofluids in the same range of concentrations is found to be lower than the thermal conductivity of water by up to 4%.

The paper presents the results of numerical simulation of a round turbulent jet propagation in confined space: the jet at Re = 5.4·10⁴ is supplied into a rectangular cavity with a height to width ratio of 0.16. The URANS and LES calculations reproduce the self-oscillating regime, registered previously in the experiments by Lawson et al. (2005). A significant rearrangement of the flow structure and pressure field occurring at a low-flow jet supply from the narrow side wall allows controlling self-oscillations up to their complete suppression. A map of flow regimes has been obtained for three various positions of the opening, supplying the control jet, depending on the control and primary jets momentum ratio. The calculated data provide a quantitative assessment of the flow controllability by injecting a low-flow jet into the zone of the primary jet propagation perpendicular to its axis.

The paper presents the results of the experimental study of the structure of a liquid microlayer at the base of vapor bubbles during water pool boiling using the method of light-emitting diode (LED) interferometry and a transparent design of the heating surface. Microlayer profiles were obtained at different time moments and the effect of heat flux density on its characteristics was analyzed. It is shown that the applied technique with a fairly simple optical scheme allows obtaining of up-to-date information on the structure and dynamics of the microlayer under bubbles during boiling.

The paper considers experimental data of superfluid helium dynamics in a U-shaped cylindrical channel filled with a backfill of metal balls. An experimental cell is presented, and the results of study are shown in the form of a time dependence for the position of vapor-liquid interface. The differences between the oscillations in a free channel and in confined conditions are discussed. For a channel with a finely dispersed porous structure, the oscillation amplitude significantly reduces and a stationary state of the interfacial surface is possible.

This paper presents the development of active control methods for vortex phenomena in hydro turbines. The flow pattern downstream of a simplified turbine runner was studied under conditions typical of a hydro turbine operating at partial load, which are prone to generating large-scale vortex structures and inducing powerful pressure pulsations. Active control was achieved through the injection of additional air jets into the center of the runner cone. The results of experiments covering velocity distributions, velocity pulsations, and pressure pulsations following the injection of jets are presented. Control jets, regardless of their orientation, successfully suppress pressure pulsations. However, jets oriented radially provide the most effective suppression of vortices and reduce the total flow swirl in the draft tube. The pattern of jet supply directly affects the formation of a recirculation zone downstream of the runner. Experimental data on optimal injection align with previous theoretical estimates based on flow linear stability analysis.

The results of an experimental study of the normal integral emissivity (NIE) of lithium, sodium, and potassium during melting and in the liquid state are presented. The research is realized by the radiation method. The experimental results are compared with the theoretical calculation of the NIE from the Foot approximation and analyzed. The behavior of the main thermophysical properties of metals in the melting point region is generalized for the position of alkali metals in the Periodic Table.

The results of an experimental study of the flow around a sharp cone with an opening angle of 10° in two large-scale TsAGI wind tunnels are presented. The Mach and Reynolds numbers of the free-stream flow varied in a wide range of M=0.2÷6 and Re=3÷34 million. The drag, lift and side force coefficients were measured. The behavior of the pitching, rolling, and yawing moment coefficients was studied. The distribution of static pressure on the cone surface and pressure fluctuations were analyzed. A physical model of the cone streamlining was constructed. An ordered system of data was prepared to contain both the results of experiments and test calculations, intended for the validation of computer programs and models.

(To the 110th anniversary of the birth of Academician S.S. Kutateladze) The paper presents the contribution of Academician S.S. Kutateladze to the substantiation and development of engineering methods for calculating electric-arc plasmatorches based on the approaches of the similarity theory and dimensional analysis. Generalized volt-ampere and thermal characteristics of a single-chamber plasmatorch with both conventional water and porous anode cooling are presented, as well as some investigation results on high-temperature, underexpanded supersonic low-density jets, including the plasma ones.

The influence of the change in the velocity profile on stability of the Tollmien-Schlichting waves in the Blasius boundary layer is studied experimentally. The experiment is performed with a flat plate model in a low-turbulence wind tunnel T-324 at the freestream velocity U_∞ = 9 m/s. Hot-wire anemometry is applied for measurements. The results show that a distributed action on the Blasius boundary layer through a hydrodynamically smooth surface leads to attenuation of the amplitude of the naturally excited Tollmien-Schlichting wave almost by two orders of magnitude. This distributed action leads to changes in flow stability. The experimental results reveal that the distributed action is more effective than the action onto the flow through a slot, other conditions being identical.

The results of experimental and computational studies for the coolant flows mixing at different temperatures for standard operational parameters of a nuclear power unit (NPU) are presented in this paper. Experiments were performed using an upgraded version of measurement model. This study defines a temperature filed in the mixing zone and offers the optimal set of operation parameters calculated from the condition of maximum temperature pulsation within the mixing zone. Simulation was performed using a software kit Ansys Fluent. The grid model is based on the block structure in Ansys ICEM code. Numerical simulation was performed for unsteady problem statement based on the LES WALE turbulence model. Analysis of simulation and experimental fields for flow velocity and temperature confirmed the validity of the developed numerical method. A qualitative compliance for the probability density distribution and the spectral-correlation characteristics for temperature signals in the mixing zone was observed. The spectral power density for calculated temperature and velocity distributions fits the case of 1D energy spectrum of developed isotropic turbulence.