Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza
Fluid Dynamics is the English version of the leading Russian journal Izvestia RAN, Mekhanika Zhidkosti i Gaza. It publishes original articles in the field of classical fluid and plasma dynamics, biomechanics of continuous media, flow in electro-magnetic fields, dynamics of multiphase and chemically reactive flow, including flow in porous media.
The journal publishes theoretical and experimental investigations. Numerical research should focus on new mechanical results with a short description of the numerical method itself.
The manuscripts are peer reviewed by two experts. In accordance with the "Statute of Scientific Journals of the Russian Academy of Sciences", the Editorial Board has the exclusive right to accept or reject manuscripts. According to the rules of our journal, authors will not be informed of the reasons for rejection. Papers are published free of charge to the authors and no fee is paid to them.
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No 1 (2025)
Articles
CONSTRUCTION OF THE THREE-DIMENSIONAL MINIMUM-WAVE-DRAG FOREBODY OF GIVEN LENGTH AND WITH A CIRCULAR BASE (REVIEW)
Abstract
We consider the problems occurring in constructing the nose parts (NP) of bodies of revolution realizing the wave drag minimum at a given body length and when the number of the planes of symmetry n ⩾ 2. The axisymmetric solution of this problem had been given by I. Newton in his Philosophiae Naturalis Principia Mathematica within the framework of his own Newton formula (NF) for the pressure on the windward side of a body in flow suggested in the same study. The solution given by Newton without any explanations was not at once understood by aerodynamicists who turned to the solution of this problem and its certain generalizations at the mid-twentieth century. Newton’s Principia were translated into Russian by A.N. Krylov, who gave also detailed commentaries to this treatise, including the problem under discussion. However, even these comments could not help to understand Newton’s solution and it was only the Soviet aerodynamicists who could cope with them. Nevertheless, before long the three-dimensional NPs could be constructed within the framework of the NF; the drag of those bodies, which had firstly star-shaped and then circular bases, was smaller than that of the axisymmetric Newtonian NPs of the same length at n ⩾ 2. The mathematicians, who started to deal with this problem at the end of the 20th century and the beginning of the 21st century, and had known nothing about the studies of aerodynamicists, turned to the same NF, prohibiting concave regions of the surfaces of the required NFs. The main result of their investigations within the framework of the NF is the NP that consists of n ⩾ 2 identical inclined planes, adjoining lineate surfaces, and a leading flat face — a regular n-gon (a rectilinear segment at n = 2). However, for both the theory and applications it is important to know how they behave in at least an inviscid flow. The results of calculations of these flows according to Euler equations presented below are intended to reply to this question.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):3-21
3-21
THE LAWS OF THE MATTER DISTRIBUTION IN A COLORED FREE-FALLING DROP IN A TRANSPARENT RECEIVING FLUID (REVIEW)
Abstract
The results of the visualization of the matter transfer processes in colored free-fall drops, which mix with a transparent receiving fluid are analyzed. The parametrization is carried out basing on the system of fundamental equations of fluid mechanics which includes the equations of state for the density and the Gibbs potential. The contribution of different mechanisms of energy transfer is discussed; these are the macroscopic (including flows, waves, and vortices) and microscopic (dissipative and conversional) ones. The radiation transfer effect is not considered. The technique of the present-day experiments is descried, which makes it possible to record accompanying acoustic signals together with the highly-resolving videorecording of colored flow pictures. The flow structure, dynamics, and energetics are analyzed for different density ratios of the confluent fluids and the kinetic and potential surface energies (PSE) of the drop. The conditions of the establishment of certain selected regimes, such as intrusive drop inflow, impact breakdown in fibers, and an intermediate hovering and rebound regime, are determined. A drop flowing smoothly into the fluid thickness at a small contact velocity in the intrusive regime forms a connected body. Thin jetlets containing the matter of both media are formed in the contact spot in the The fibrous wakes of the jetlets form lineate and reticular structures on the fluid surface and within its thickness. In the intermediate regime the drop can hover on the fluid surface, touch it, merge partially with it, and rebound with the loss of the matter. The evolution of gas cavities and bubbles radiating acoustic packets is traced. The necessity of taking account for all the mechanisms of total energy transfer in describing hydrodynamics and acoustics of drop flows is noted.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):22-65
22-65
STIMULATION OF THROMBUS DISSOLVINGBY MAGNETO-INDUCED CIRCULATION CURRENTS
Abstract
The theoretical model and the method of its approximate analysis dealing with flows induced by a rotating magnetic field in the channel occupied by a non-magnetic fluid with an embedded ferrofluid layer are proposed. One of the channel ends is assumed to be closed (thrombotic). Some estimates of the velocity of convective-diffusion flow of a neutral impurity (thrombolytic) onto a thrombus in the channel with magnetically induced circulation currents are obtained and the effect of these currents on the thrombus dissolution rate is studied.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):66-74
66-74
ENHANCEMENT OF SEPARATION FLOW AND HEAT TRANSFER IN A BOOMERANG-TYPE GROOVE ON THE CHANNEL WALL
Abstract
The self-organization of a tornado-like vortex enhanced by the formation of an extraordinary transverse pressure drop and the onset of a negative pressure pole in the tornado core is observed in the case of a 45∘ deviation of the inlet section of streamwise oriented groove on the heated wall of plane-parallel channel with increase in the relative length of the section ξ, starting from 0.15. Tornado generation leads to the development of abnormal separation flow and heat transfer enhancement in the inlet inclined part of the groove. It is known that in the inclined rectilinear grooves the abnormal enhancement of separation flow and heat transfer is characterized by weakening of vortex structures and suppression of heat transfer in the end part of the groove. It is found that at the optimum relative length ξ the orientation of the end section of the groove along the flow in the channel leads to the penetration of intense swirling flow into the end zone of the boomerang-type groove and enhances heat transfer here. The optimal length of the inlet section ξ = 0.35 is determined. At this length, a 29% increase in the maximum heat transfer from the inner groove surface compared to the plane channel wall is achieved. In this case, the heat removal inside the boomerang-type groove is 1.2 times higher than that for the straight groove at the 45∘ inclination angle. The critical length of the inlet section (ξ = 0.7) starting from which the swirling flow leaves the groove without reaching its end is found. The critical length is characterized by the minimum relative hydraulic losses for the section bounded by the contour of the groove spot.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):75-112
75-112
EXPERIMENTS ON THE NONLINEAR DEVELOPMENT OF CONTROLLED DISTURBANCES IN THE REGION OF ARTIFICIAL FLOW INHOMOGENEITY IN THE FLAT-PLATE BOUNDARY LAYER AT MACH NUMBER 2.5
Abstract
The results of the measurements of the time-periodic controlled disturbances in an inhomogeneous flat-plate boundary layer are considered at Mach number 2.5. The disturbances were introduced using a high-frequency flow discharge. The electric power of the discharge was recorded. The nonlinear downstream development of wave trains and a considerable effect of the unit Reynolds number on the nature of the disturbance interaction is found to exist under the experimental conditions. An analysis of the wave characteristics of the disturbances is carried out.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):113-128
113-128
DIFFUSION AND DEPOSITION OF BROWNIAN PARTICLES IN THE BOUNDARY LAYER IN FLOW OF A DISPERSED MIXTURE PAST A PERMEABLE SURFACE
Abstract
The effect of mass transfer (owing to fluid injection or suction) with a surface in disperse flow on the processes of diffusion and deposition of Brownian particles in the boundary layer is studied. The equations of motion and diffusion of a dispersed mixture are presented in the boundary layer approximation with regard for the dependence of the effective viscosity of the suspension on the volume particle content. The boundary value problem is formulated in self-similar variables with regard for the fluid suction (injection) rate on the permeable surface. An analysis of the diffusion equation is carried out at small and large Schmidt numbers and in these limiting cases approximations of its solutions are found. In particular, it is shown that in the boundary layer, in the limit as the Schmidt number increases indefinitely, the derivative of the particle concentration with respect to the independent self-similar variable tends to the Dirac delta function. The results of numerical solution of the formulated boundary value problem obtained at various values of the constitutive parameters are discussed with reference to the plate boundary layer. It is found that in the presence of injection there exists a characteristic Schmidt number (depending on the injection intensity) such that a region without particles appears in the boundary layer at the higher Schmidt numbers. The effect of the injection intensity on the dimensions of this region is studied. The dependences of the diffusion particle flow toward the plate surface on the Schmidt number are analyzed in the case of the presence or absence of injection (suction).
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):129-145
129-145
GAS-DROPLET TURBULENT JETS WITH PHASE TRANSITIONS AND DROPLET COLLISIONS
Abstract
The effect of phase transitions and droplet collisions on the parameters of a gas-droplet nonisothermal turbulent jet is studied numerically using the developed mathematical model of the jet. When carrying out the mathematical modeling of two-phase jet flow, the case of flow out of a heterogeneous medium from a nozzle into steady gas with the temperature significantly higher than the temperature of the phases at the nozzle exit is considered. The calculations carried out for various volume concentrations of droplets at the nozzle exit (in the initial jet cross-section) showed that at the concentration of the order of 10–4, the droplet collisions do not have a significant effect on the jet parameters; this effect begins to manifest itself at an initial droplet concentration of the order of 5 × 10–4 and becomes noticeable at the concentration equal to 10–3. As distinct from droplet collisions, phase transitions have a noticeable effect on the jet parameters over the entire considered range of variation in the initial droplet concentration from 10–4 to 10–3.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):146-160
146-160
METHOD OF TEMPERATURE CORRELATIONS FOR ESTIMATING THE LARGE-SCALE CIRCULATION RATE IN THE CASE OF TURBULENT CONVECTION OF LIQUID METALS IN AN INCLINED CYLINDER
Abstract
The potentials of the method of temperature correlations in determining the mean velocities of liquid metal turbulent flows are investigated. The method uses the signals from temperature transducers arranged in line in the direction of large-scale circulation motion. As distinct from other, more conventional techniques, this indirect method can be used in the measurements in melt metals, which represent aggressive opaque media. The method is based on the Taylor hypothesis of the temperature disturbance field freezing in the velocity field on a certain level of flow turbulence. By fixing the passage of such disturbances through temperature transducers it is possible to calculate the flow velocity. The flow in the actual setups is usually inhomogeneous and developed turbulence arises only locally in the cavity. For this reason, though the method is absolute and does not need calibration, its applicability should to be verified in each particular case. In this study the method is applied to the problem of turbulent convection of liquid sodium (Prandtl number Pr = 0.0083) in a cylinder, whose length is greater than its diameter by the factor of 5, heated from one end and cooled from the other end. In the flow regimes considered the cylinder is inclined to the vertical line by an angle β, 18∘ ⩽ β ⩽ 90∘. The Rayleigh number based on the cylinder diameter was 5 · 106. An analysis of the data of experimental investigations and three-dimensional numerical calculations is performed. In the latter case the flow velocity is known for a fact and can be directly compared with the estimates obtained using the crosscorrelation analysis. It is shown that the method of temperature correlations not always allows one to adequately estimate the mean velocities of regular large-scale sodium flows, that is, has its own restrictions. The method performs well in the conditions of moderate turbulent fluctuations of the temperature and velocity. The greatest error of the method takes place near the heat exchangers in the flow direction: a demonstrative explanation of the reasons for this error is proposed with reference to this example. The nonlinear dependence of the large-scale circulation amplitude on the angle of inclination of the cylinder is obtained; it has a maximum near 45∘. The location of the maximum of this dependence is different from that for the cylinder with the aspect ratio 20 (60∘–70∘).
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):161-173
161-173
DIFFRACTION OF OBLIQUE SURFACE WAVES BY AN ICE COVER IN THE PRESENCE OF A CURRENT WITH VELOCITY SHEAR
Abstract
The diffraction of oblique surface waves on the edge of an elastic semi-infinite plate floating on the surface of a fluid of finite depth in the presence of a current with linear velocity shear is studied. An exact analytical solution of this problem is constructed using the Wiener-Hopf technique. The frequency dependences of the reflection and transmission coefficients and angles are investigated at various angles of incident waves and the shear gradient.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):174-187
174-187
NUMERICAL STUDY OF THE TURBULENT BOUNDARY LAYER WITH AN ADVERSE PRESSURE GRADIENT IN COMPRESSIBLE GAS FLOW
Abstract
The turbulent boundary layer in supersonic flow with an adverse pressure gradient is numerically simulated using the three-parameter differential RANS turbulence model. The adverse pressure gradient is implemented by reducing the Mach number along the plate. The simulation is carried out for a number of values of the free-stream Mach number from 1.5 to 3.0 and the temperature factor equal to and different from unity. The results of calculating the integral and local flow characteristics testify that there is a significant effect of the adverse pressure gradient on the flow and heat transfer characteristics.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):188-201
188-201
INVESTIGATION OF A NANOSECOND SLIDING SURFACE DISCHARGE IN A TIME-DEPENDENT SUPERSONIC AIR FLOW IN A CHANNEL
Abstract
The regimes of development of a sliding surface discharge with a running time of about 500 ns are experimentally studied in time-dependent supersonic air flows in the channel of shock tube with a rectangular cross-section. The Mach numbers of the shock waves were from 2.30 to 5.00 at the initial air pressures from 2 to 100 Torr and the Mach numbers in the flow were from 1.18 to 1.66. A 100 mm-long sliding surface discharge was initiated at a given moment of time in different stages of the time-dependent supersonic flow after plane shock wave diffraction on an obstacle and in a quasistationary flow past the obstacle in the presence of an inclined shock wave. The discharge current and spatial radiation characteristics were analyzed. The high-speed shadow recording of the flow fields was carried out at the frequency up to 525,000 frames per second. The numerical modeling of the channel flow was performed within the framework of the Navier–Stokes equations. The comparison of the experimental and numerical results made it possible to establish the correlation between the parameters of a low-density zone formed as a result of the interaction between the oblique shock wave and a boundary layer and the regime in which the discharge current proceeds. The flow structure in the channel is analyzed after the discharge initiation, when a near-semi-cylindrical shock wave is formed. The comparison of the experimental and numerical results shows the thermal energy released in the discharge current region amounts to 0.15 to 0.36 J.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):202-213
202-213
FLOWS WITH AN OVERCOMPRESSED DETONATION WAVE IN VARIABLE-AREA CHANNELS
Abstract
Numerical simulation of flows of an inviscid chemically active hydrogen-air mixture with overcompressed detonation wave in the quasi-two-dimensional and two-dimensional formulations is carried out. Simulation is carried out by integrating Euler’s equations supplemented with the equations of physical and chemical kinetics of hydrogen combustion in air with 18 chemical reactions in a 9-component mixture. In the quasi-two-dimensional formulation, steady-state flows with overcompressed detonation wave are obtained for various values of the excess air coefficient. In the two-dimensional formulation, a solution with overcompressed detonation wave is obtained and the effect of mixture inhomogeneity on the flow with formation of a detonation wave and its cellular structure is studied.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):214-224
214-224
GENERATION OF THERMOGRAVITATIONAL CONVECTION AND CONVECTIVE DIFFUSION IN A RADIATION-HEATED REGION
Abstract
We present the results of the numerical investigation of the generation of thermogravitational convection and convective diffusion as a result of the radiation flux action on the internal boundaries of the walls of a closed rectangular region filled with the air. The conditions of the development and the characteristics of hydrodynamic and thermophysical processes occurring as a result of the heating of surface layers of the walls during the radiation heating are established. The relationship between the radiation heating strength and the convective heat and mass transfer is derived. The time-dependent fields of the temperature and the concentrations of anthropogenic gas admixture illustrate a considerably greater intensity of the heat transfer generated by the radiation heat flux compared with the conductive heat transfer and the convective diffusion compared with molecular diffusion.
Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza. 2025;(1):225-238
225-238