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No 2 (2023)
Articles
Investigation of Flow and Spectral Characteristics in a Flow-Flow Hydrodynamic Generator of the Flat Type with Changes in the Degree of Flow Blockage
Abstract
The paper presents the results of studying the flow past cylindrical bodies located in a flattype flow-through hydrodynamic generator. The result were obtained on the hydrodynamic test bench of the experimental base of the Scientific Center of the Mechanical Engineering Research Institute of the Russian Academy of Sciences with the degree of flow blockage by the bluff bodies St /S0 = 10– 82%, the Re numbers (0.5–5) × 105 , and the inlet pressure Рin= 0.1–0.9 MPa. It was found that at certain values of the inlet/outlet pressure ratio, which are constant for each of the degrees of flow blockage, powerful resonant-type pressure peaks arise at frequencies of 0.5–5 kHz with the amplitude more than 4–5 times higher than the maximum inlet pressure.
3-8
Mathematical Modeling of the Effect of Cell Mobility and Active Intercellular Interactions on the Sorting of the Cells of Two Types in the Cultures of Biological Tissues
Abstract
The cell motion is at the bottom of many biological phenomena. An important role in controlling cell motions is played by active stresses developing in biological tissues as a result of mechanical intercellular interactions. An investigation of the evolution of the mixtures of cells of different types forming cell aggregates shows that active intercellular force interactions lead to the spatial separation of the cells of different types, or the cell sorting. Within the framework of the continuum model of biological media [24] (the cells of different types are regarded as separate phases), in this study we investigate the effect of the parameters characterizing various mechanisms of the development of
active intercellular stresses, as well as adhesion and cell mobility, on the process of the sorting of cells of two types that form an aggregate of spherical shape at the initial moment of time. It is shown that the sufficient condition for the sorting of cells of different types and the formation of a sharp boundary between the regions occupied by these cells is the absence of contracting interactions between the cells of different phases under the condition of asymmetry of the initial distributions of their concentrations or asymmetry of the parameters characterizing the development of active stresses in different phases. It is shown that the cells of the phase, where active contracting intercellular interactions are stronger (at the same values of the other parameters and the same initial distributions of phase concentrations for different cell phases), strive to occupy the central region of a spheroid. At the same time, the cells of the other phase, where the contracting interactions are weaker, are displaced to the periphery. An increase in the parameter characterizing cell repulsion leads to the displacement of this cell phase toward the periphery. Beside the active interaction forces, the cell motions can be controlled by both passive mechanical properties of the medium and the cell mobility. The asymmetry of the interphase distributions of these parameters can lead to the situation, when the cells that possess the greater contracting interactions will be displaced toward the cell spheroid periphery and surround the cells, the interaction between which is weaker
9-19
A Nonlinear Schrеdinger Equation for Gravity-Capillary Waves on Deep Water with Constant Vorticit
Abstract
The surface gravity-capillary waves on deep water with constant vorticity in the region
bounded by the free surface and the infinitely deep plane bottom are considered. A nonlinear Schrödinger equation is derived from a system of exact nonlinear integro-differential equations in conformal variables written in the implicit form taking into account surface tension. In deriving the nonlinear Schrödinger equation, the role of the mean flow is taken into account. The nonlinear Schrödinger equation is investigated for modulation instability. A soliton solution of the nonlinear Schrödinger equation that represents a soliton of the “ninth wave” type is obtained. bounded by the free surface and the infinitely deep plane bottom are considered. A nonlinear Schrödinger equation is derived from a system of exact nonlinear integro-differential equations in conformal
variables written in the implicit form taking into account surface tension. In deriving the nonlinear Schrödinger equation, the role of the mean flow is taken into account. The nonlinear Schrödinger equation is investigated for modulation instability. A soliton solution of the nonlinear Schrödinger equation that represents a soliton of the “ninth wave” type is obtained.
20-32
Evolution of Viscous Electrically Conducting Fluid Flow on a Rotating Wall in the Presence of a Magnetic Field with Account for the Induction and Diffusion Effects
Abstract
The evolution of a viscous conducting fluid flow on a rotating plate in the presence of a magnetic field is studied. The analytical solution of the three-dimensional time-dependent magnetohydrodynamics equations is found. In this case, the full magnetic induction equation is used, i.e., both the dissipation effect and the energy dissipation as a result of the electric current flow are taken into account. The fluid, together with the bounding plane, rotates as a whole at a constant angular velocity about a direction not perpendicular to the plane. The velocity field and the induced magnetic field in the flow of viscous electrically conducting fluid that occupies a half-space bounded by a flat wall are determined. The motion of wall is considered in a series of particular cases. Based on the results obtained, the individual structures of the near-wall boundary layers are investigated
33-45
Effective Tensor of the Relaxation Kernels of a Layered Medium Consisting of a Viscoelastic Material and a Viscous Incompressible Fluid
Abstract
The explicit formulas for calculating the components of the effective tensor of relaxation kernels of a two-phase layered medium with a periodic microstructure are derived. The first phase of such a medium consists of an isotropic viscoelastic material and the second phase consists of a viscous incompressible fluid. In particular, it is established that the components of this tensor depend on the volume fraction of the fluid inside a periodicity cell and do not depend on the number of layers and the distances between them.
46-54
Pulsating Turbulent Flows through a Square Pipe
Abstract
Pulsating turbulent flows in a square pipe are studied numerically. The flow dominance regime in which the fluid flow rate remains positive in all phases of the oscillatory cycle is considered. The flows are studied at several oscillation frequencies. The results are compared with oscillating laminar flows and a steady turbulent flow in a square pipe, as well as with pulsating turbulent flows in a round pipe. The integral and fluctuating characteristics of turbulence and their dependence on the oscillation frequency are determined. In particular, it is found that at the considered Reynolds number Re = 2200 the friction coefficient in pulsating flows turns out to be lower than that in the stationary flows. The drag reduction increases with growth of the oscillation period and reaches 14.7%. A distinctive feature of turbulent flows in pipes of rectangular cross-section is the occurrence of secondary flows of Prandtl’s 2nd kind. The details of secondary flows under the pulsating flow conditions are studied at length.
55-71
Flow Structure and Transition to Local Turbulence Downstream of an Asymmetric Narrowing that Imitates Arterial Stenosis
Abstract
The results of experimental studies and numerical simulation of the flow structure in the separation region downstream of an asymmetric narrowing of smooth canal that simulates 70% onesided stenosis of the artery are presented. The Reynolds number was equal to 1800. The instantaneous flow velocity vector fields were measured using the SIV technique. The numerical solution was obtained by the large eddy simulation (LES) method. Setting the disturbances in numerical simulation close to the experimental conditions made it possible to obtain a satisfactory agreement between the calculated and experimental velocity fields and the components of the Reynolds stress tensor. The data on formation of the local flow turbulence region behind the constriction and subsequent downstream flow relaminarization are obtained. It is shown that a pair of secondary eddies localized within the region of flow separation is formed near the throat of the constriction.
72-84
Flow past Rankine’s Half-Body of Revolution
Abstract
An axisymmetric incompressible flow past Rankine’s half-body of revolution is investigated at high Reynolds numbers. It is established that the solution of the problem for the system of boundary layer equations does not involve the line of zero surface friction. The low under consideration is separationless, which is in complete agreement with the available experimental data.
85-89
Fluid Flow to a Well through a Radial Hydraulic Fracture in a Porous Medium at Constant Flow Rate
Abstract
The problem of fluid withdrawal from a reservoir into a well or injection of fluid from a well into a reservoir in the presence of a hydraulic fracture perpendicular to the wellbore is considered in the constant flow rate regime. Analytical solutions that describe the evolution of pressure in the fracture at a constant reservoir-to-well fluid flow rate are obtained. Approximate solutions are constructed using the method of successive change of stationary states (SCSS). A comparison of the numerical results of the exact and approximate solutions shows that these solutions are almost identical. The influence of the reservoir features of the stratum and fracture on the evolution of pressure in the fracture and well is analyzed.
90-101
Experimental Study of Energy Separation in Compressible Air Cross Flow Over a Pair of Side-by-Side Circular Cylinders
Abstract
The influence of the distance between two circular side-by-side cylinders in a cross flow on the surface distribution of temperature and static pressure is experimentally studied. The studies were carried out at free-stream Mach numbers M equal to 0.295 and 0.365 and Reynolds numbers ReD equal to 6.4 × 104 and 7.9 × 104, respectively. The surface distributions of the pressure coefficient and the temperature recovery factor for one of the cylinders are obtained. It is shown that, depending on the distance between the cylinders, the pressure coefficient and temperature recovery factor can be both higher and lower than the values obtained in the flow over a single cylinder with the same free-stream parameters.
102-112
Motion of a Load on an Ice Cover in the Presence of a Current with Velocity Shear
Abstract
The behavior of an ice cover on the surface of an ideal incompressible fluid of finite depth under the action of a pressure domain that moves rectilinearly at a constant velocity in the presence of a current with velocity shift is studied. Fluid flow is not potential. The ice cover is modeled by a thin elastic plate with account for uniform compression. The motion of the load can occur at an arbitrary angle to the direction of current. It is assumed that the ice deflection is steady in the coordinate system moving with the load. The Fourier transform method is used within the framework of the linear wave theory. The critical velocities and the deflection of ice cover are studied depending on the current velocity gradient, the direction of motion, and the compression ratio.
113-122
NON-EQUILIBRIUM SUPERSONIC FLOW AROUND A BLUNT
Abstract
The computational model designed for studying the processes of non-equilibrium physicochemical gas dynamics in supersonic rarefied-air flow past a blunt plate of finite dimensions under the laboratory experiment conditions is formulated. The computational model is based on the two-dimensional Navier–Stokes equations, the energy conservation laws for the translational degrees of freedom of atoms and molecules and the vibrational degrees of freedom of diatomic molecules, and the chemical kinetics and diffusion equations for individual components of partially ionized gas flow. The basic gas dynamic and kinetic processes in flow past a blunt plate are analyzed at the Mach numbers M = 10 and 20. It is shown that regions of thermal nonequilibrium are formed.
123-137
Comparison of the Eulerian and Lagrangian Approaches to Studying the Peculiarities of the Interstellar Dust Distribution in the Heliosphere in the Framework of the Cold Gas Model
Abstract
Interstellar dust grains penetrate into the heliosphere (region in which the solar wind propagates) due to the relative motion of the Sun and the Local Interstellar Medium (LISM). Inside the heliosphere, the motion of dust particles is mainly governed by the electromagnetic force determined by the heliospheric magnetic field. Under the action of this force, the trajectories of dust grains experience intersections with each other and self-intersections. As a result, dust density accumulation regions appear. These regions are of a great interest in the context of theoretical studying and planning of upcoming space missions. The main aim of the present study is to model the interstellar dust distribution in the heliosphere and investigate the peculiarities of the number density distribution. To describe the dusty component, the cold gas model is used, while to compute the interstellar dust distribution two approaches are considered, namely, the Eulerian and Lagrangian approaches. For solving the continuity equation in the Lagrangian coordinates, the full Lagrangian method or the Osiptsov method is used. As a result, all the peculiarities of the dust distribution are investigated and it is found that they are located on caustics, i.e., the envelopes of interstellar dust trajectories. Besides it, the regular regions of overdensity (without singularities in the number density) are discovered. It is shown that the dust component accumulation regions are located in a small neighborhood of the heliospheric current sheet, at which the magnetic field changes its polarity, and in the tail of the heliosphere. The effectiveness of the Osiptsov method of solving the continuity equation is compared with the widely used Monte Carlo method (Eulerian approach). It is shown that Monte Carlo method requires extremely high resolution of computational grid to reach the level of accuracy comparable with the Osiptsov method.
138-150