

2016 year, number 1
Yu. V. Yulmukhametova
Mavlyutov Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa 450054, Russia
Keywords: подмодели ранга два газовой динамики, линейное поле скоростей, плоский коллапс политропного газа, rank two submodels of gas dynamics, linear velocity field, planar collapse of a polytropic gas
Abstract >>
A method for finding exact solutions of the equations of gas dynamics with a linear velocity field is proposed. This method was used to find exact solutions for one submodel of the evolutionary type which was fully integrated for the case of a polytropic gas. Examples of particle motion for the obtain exact solutions are given.

V. M. Belolipetskii^{1,2}, P. V. Belolipetskii^{1,3}
^{1}Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia ^{2}Siberian Federal University, Krasnoyarsk, 660041 Russia ^{3}Institute of Biophysics, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia
Keywords: стратифицированные озера, ветровые течения, критерий смены режимов течений, stratified lakes, wind flows, criterion of change in flow regime
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Wind flows in meromictic saline lakes in which the water column does not mix to the bottom for at least one year are studied. This leads to the formation of the upper and depth layers with small density gradients, between which there is a water layer with a large density gradient. It has been shown that, depending on the density stratification and the wind speed, wind flows (in a vertical plane) of two types are possible: with one or two circulation zones. For a twolayer lake model, a criterion for the change in the wind flow regime is proposed.

E.P. Magdenko
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia
Keywords: критические числа Марангони, деформируемая свободная плоская граница, конвекция, метод разделения переменных, critical Marangoni number, deformable free flat boundary, convection, method of separation of variables
Abstract >>
This paper considers a liquid in a finitesize cylinder in which Marangoni instability occurs. The upper boundary of the liquid is free and deformable. The problem of the occurrence of convection in a cylindrical container is solved using the method of separation of variables. A homogeneous differential equation of the sixth order with constant coefficients and complex boundary conditions is obtained. In the case of monotonic perturbations, an analytical expression for critical Marangoni numbers is derived. The case of a weightless liquid in the cylinder is considered.

F. Bouras^{1,2}, F. Khaldi^{1}
^{1}University of HLBatna, 05000 Batna, Algeria ^{2}University of HLEl Oued, 039000 El Oued, Algeria
Keywords: производство энтропии, турбулентный режим горения, необратимый термодинамический процесс, численные методы гидродинамики, entropy generation, turbulent combustion, thermodynamic irreversibility, computational fluid dynamics
Abstract >>
Thermodynamic irreversibilities generated by the combustion process are evaluated and analyzed numerically. The numerical simulation is performed for a reference case study for which experimental data are available in the literature: diffusion flame properties in a common burner configuration are studied by the Fluent software with the standard k e turbulence model and twostep chemical reaction. The study quantifies the contribution of each mechanism to entropy generation, i.e., friction, heat conduction, species diffusion, and chemical reaction. The chemical reaction and heat conduction are found to be the major sources of entropy production. Preheating of air reduces thermodynamic irreversibilities within the combustor.

A. S. Butt, A. Ali
QuaidiAzam University, Islamabad, Pakistan
Keywords: энтропия, свободная конвекция, осциллирующая пластина, магнитное поле, entropy, free convection, oscillating plate, magnetic field
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An unsteady free convective flow of a viscous fluid past an oscillating plate is considered, and the effects of entropy generation are investigated. The governing partial differential equations are normalized by using suitable transformations, and an exact solution of the problem is obtained by using the Laplace transformation technique. The expressions for the velocity and temperature are then used to compute the skin friction, Nusselt number, local entropy generation number, and Bejan number.

N. T. M. Eldabe, G. M. Moatimid, M. A. Hassan, D.R. Mostapha
Ain Shams University, Roxy, Cairo, Egypt
Keywords: перистальтическое течение, модель Олдройда, конусообразная артерия, течение в сужающемся канале, электрогидродинамика, теплообмен, явление захвата, peristaltic flow, Oldroyd model, tapered artery, stenosis flow, electrohydrodynamics, heat transfer, trapping phenomena
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The effect of a vertical alternating current, electric field, and heat transfer on a peristaltic flow of a dielectric viscoelastic Oldroyd fluid is studied. This analysis involves uniform and nonuniform annuli having a mild stenosis. The analytical solutions of equations of motion are based on the perturbation technique. This technique depends on two parameters: amplitude ratio and small wave number. Numerical calculations are performed to obtain the effects of several parameters, such as the electrical Rayleigh number, temperature gradient, Reynolds number, wave number, maximum height of stenosis, and Weissenberg numbers, on the distributions of velocity, temperature, electric potential, and wall shear stress. It is found that the abovementioned distributions in the case of a convergent tapered tube are larger than those in the case of a nontapered one as well as a diverging tapered tube.

R. Mohebbi^{1}, M. Nazari^{2}, M. H. Kayhani^{2}
^{1}Damghan University, Damghan, Iran ^{2}Shahrood University of Technology, Shahrood, Iran
Keywords: вынужденная конвекция, степенные жидкости, метод решеточных уравнений Больцмана, метод конечных элементов, forced convection, powerlaw fluid, lattice Boltzmann method, finite element method
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A detailed comparison between the lattice Boltzmann method and the finite element method is presented for an incompressible steady laminar flow and heat transfer of a powerlaw fluid past a square cylinder between two parallel plates. Computations are performed for three different blockage ratios (ratios of the square side length to the channel width) and different values of the powerlaw index n covering both pseudoplastic fluids (n<1) and dilatant fluids (n>1). The methodology is validated against the exact solution. The local and averaged Nusselt numbers are also presented. The results show that the relatively simple lattice Boltzmann method is a good alternative to the finite element method for analyzing nonNewtonian fluids.

A. V. Seryakov
Medgaz Research and Production Company, Moscow 121471, Russia
Keywords: низкотемпературные тепловые трубы, коническое сопло, емкостный датчик конденсации, lowtemperature heat pipes, conical nozzle, capacitive condensation sensor
Abstract >>
This paper presents the results of experimental and numerical studies of heat transfer and swirling pulsating flows in short lowtemperature heat pipes whose vapor channels have a conical nozzle shape. It has been found that as the evaporator of the heat pipe is heated, pressure pulsations occur in the vapor channel starting at a certain threshold value of the heat power, which is due to the start of boiling in the evaporator. The frequency of the pulsations was measured, and their dependence on the superheat of the evaporator was determined. It is found that in heat pipes with a conical vapor channel, pulsations occur at lower evaporator superheats and the pulsation frequency is greater than in heat pipes of the same size with a standard cylindrical vapor channel. It is shown that the curve of the heattransfer coefficient versus heat load on the evaporator has an inflection corresponding to the start of boiling in the capillary porous evaporator of the heat pipe.

G. A. Koval'skaya, A. K. Petrov
Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: нелинейные осцилляторы, долгоживущие колебательные состояния, локальные моды, внутримолекулярный переход энергии, nonlinear oscillators, longlived vibrational states, local modes, intramolecular energy transition
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Nonlinear vibrations in a closed system of coupled nonlinear oscillators are studied using acetylene type molecules as an example. A criterion for the stable existence of longlived vibrational states  local modes  in one of the oscillators is obtained. It is shown that the disappearance of a local mode, as well as its appearance, proceeds abruptly, and the mechanism of stabilization of these excitations is due to the presence or absence of internal resonances of an oscillatory system such as any polyatomic molecule. Energy values needed to excite vibrations in which local modes can appear are determined. It is shown that calculation results agree with experimental data.

H. M. Sedighi, A. Yaghootian
Shahid Chamran University of Ahvaz, Ahvaz, Iran
Keywords: метод разложения по параметру, частотная кривая, углеродные нанотрубки, нелокальная теория упругости, силы притяжения ВандерВаальса, неустойчивость процесса притягивания, графитовые листы, parameter expansion method, frequencyamplitude relationship, carbon nanotubes, nonlocal elasticity theory, van der Waals attraction, pullin instability, graphite sheets
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This article presents a new asymptotic method to predict dynamic pullin instability of nonlocal clampedclamped carbon nanotubes (CNTs) near graphite sheets. Nonlinear governing equations of carbon nanotubes actuated by an electric field are derived. With due allowance for the van der Waals effects, the pullin instability and the natural frequencyamplitude relationship are investigated by a powerful analytical method, namely, the parameter expansion method. It is demonstrated that retaining two terms in series expansions is sufficient to produce an acceptable solution. The obtained results from numerical methods verify the strength of the analytical procedure. The qualitative analysis of system dynamics shows that the equilibrium points of the autonomous system include center points and unstable saddle points. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits.

A. G. Greshilov
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090
Keywords: изгибногравитационные колебания, собственные колебания, гидроупругость, мелкая вода, круглая пластина, bendinggravitational oscillations, natural oscillations, hydroelasticity, shallow water, circular plate
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This papers the results of the numerical and analytical study of natural and quasinatural bendinggravitational oscillations of a circular elastic ice plate floating on the liquid surface and frozen to a cylindrical vertical support. In the framework of the theory of long waves in shallow water for limited and unlimited reservoirs, the dependence of natural and quasinatural frequencies of the geometrical parameters of the oscillation region is studied.

M. I. A. Othman^{1}, Y. Q. Song^{2}
^{1}Zagazig University, P.O. Box 44519, Zagazig, Egypt ^{2}Xi' an Jiaotong University, Xi'an, 710049, People's Republic of China
Keywords: микрополярная электромагнитная термоупругость, теория ЛордаШульмана, теория ГринаЛиндсея, анализ нормальных колебаний, micropolar electromagnetothermoelasticity, LordShulman theory, GreenLindsay theory, normal mode analysis
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The model of generalized micropolar magnetothermoelasticity for a thermally and perfectly conducting halfspace is studied. The initial magnetic field is parallel to the boundary of the halfspace. The formulation is applied to the generalized thermoelasticity theories of Lord and Shulman, Green and Lindsay, as well as to the coupled dynamic theory. The normal mode analysis is used to obtain expressions for the temperature increment, the displacement, and the stress components of the model at the interface. By using potential functions, the governing equations are reduced to two fourthorder differential equations. By numerical calculation, the variation of the considered variables is given and illustrated graphically for a magnesium crystal micropolar elastic material. Comparisons are performed with the results predicted by the three theories in the presence of a magnetic field.

J. Alinejad
Islamic Azad University, Sari, Iran
Keywords: метод сеточных уравнений Больцмана, изотермические цилиндры, вихревая дорожка, число Рейнольдса, lattice Boltzmann model, isothermal cylinders, vortex shedding, Reynolds number
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The lattice Boltzmann method is employed to simulate heat transfer in the flow past three arrangements of elliptical and circular cylinders under an isothermal boundary condition. The lattice Boltzmann equations and the BhatnagarGrossKrook model are used to simulate twodimensional forced convection at 30 ≤ Re ≤ 100 and Pr = 0.71. Pressure distributions, isotherms, and streamlines are obtained. Vortex shedding maps are observed in detail for several cases. The present results are in good agreement with available experimental and numerical data.

L. M. Kotlyar, N. M. Minazetdinov
Kazan Federal University, 423810 Naberezhnye Chelny, Russia
Keywords: электрохимическая обработка металлов, потенциал, гидродинамическая аналогия, свободная поверхность, electrochemical machining of metals, potential, hydrodynamic analogy, free surface
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An analytical solution of the problem of electrochemical machining of metals by a curvilinear cathode tool with allowance for a discontinuous function that describes the dependence of the current efficiency on the current density is obtained. According to the hydrodynamic itnerpretation, the original problem reduces to the problem of the theory of ideal fluid flows with a free surface. It is demonstrated that the use of the proposed dependence of the current efficiency on the current density ensures the existence of three domains on an unknown treated surface; these domains have different laws of the distribution of the charge fraction spent on metal dissolution. Results calculated for various particular cases are presented.

Ya. A. Lyashenko^{1,2}
^{1}Sumy State University, Sumy 40007, Ukraine ^{2}Technical University of Berlin, Berlin 10623, Germany
Keywords: система Лоренца, сдвиговые напряжения и деформации, граничное трение, кинетические режимы трения, моделирование, дифференциальные уравнения в частных производных, самоорганизация, Lorenz system, shear stresses and strains, boundary friction, kinetic friction regimes, modeling, partial differential equations, selforganization
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This paper presents a synergetic model that can be used to describe the boundary friction of two atomically smooth solid surfaces separated by an ultrathin lubricant layer. The model is constructed using the Lorenz equations, which are parameterized by shear stresses, shear strains, and the lubricant temperature. Given the spatial heterogeneity of these parameters, it is shown that a structure with two types of domains is formed during friction on the contact plane. Time dependences of the fractal dimensions of the domain distributions over the contact plane are calculated, and it is shown that there exists a time when the fractal dimensions take minimum values. During the evolution, the system tends to a homogeneous state in which the entire contact area is subjected to constant shear stresses which determine the relative velocity of motion of the friction blocks.

A. V. Shuvalov, N. A. Tokmak, N. I. Pis'mennyi, G. S. Kochubei
Institute of Technical Mechanics, National Academy of Sciences of Ukraine, Dnepropetrovsk, 49005 Ukraine
Keywords: намагниченное тело, гиперзвуковой поток разреженной плазмы, магнитное поле, magnetized body, hypersonic rarefied plasma flow, magnetic field
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Dependences of the drag and lift force coefficients of a magnetized sphere in a hypersonic rarefied plasma flow on the angle between the plasma flow velocity and the intrinsic magnetic induction vector of the body are obtained in a wide range of the ratio of the magnetic pressure to the plasma flow pressure. It is shown that by changing the orientation of the magnetic field vector of the body and the incoming flow velocity, it is possible to control the dynamic interaction in the plasmabody system, namely, to decelerate and accelerate the magnetized sphere in the rarefied hypersonic plasma flow.

V. A. Gorelov, A. Yu. Kireev
Central Aerohydrodynamic Institute, Zhukovskii, 140180 Russia
Keywords: ударная волна, неравновесность, физикохимические модели, ионизирующее излучение, shock wave, nonequilibrium, physicochemical models, ionizing radiation
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A physicochemical model of generation of nonequilibrium molecular radiation in the vacuum ultraviolet (VUV) spectral range behind the shock wave in air for shock wave velocities of 4.5 to 9.5 km/s is developed. Experimental results obtained in a shock tube in investigations of photoionization of air ahead of the shock wave front are used for verification of the numerical model of VUV radiation in the wavelength range from 85 to 105 nm. Model calculations show that nonequilibrium VUV radiation arises in a very thin hightemperature layer behind the shock wave front and is affected by the presence of electrons.

E. A. Batyaev^{1,2}, T. I. Khabakhpasheva^{1,2}
^{1}Lavrent'ev Institute of Hydrodynamics, Siberian Branch Russian Academy of Sciences, Novosibirsk 630090, Russia ^{2}Novosibirsk State University, Novosibirsk 630090, Russia
Keywords: взаимодействие тела и жидкости, удар по тонкому слою жидкости, метод сращиваемых асимптотических разложений, метод плоских сечений, удлиненный эллипсоид, body and liquid interaction, impact on a thin liquid layer, matched asymptotic expansions, plane section method, elongated ellipsoid
Abstract >>
The problem of the impact of an elongated solid body with a flat bottom on a thin layer of an ideal incompressible liquid is considered in the case where the horizontal component of the body velocity is substantially greater than its vertical component. The initial stage of the impact is studied in which the a priori unknown contact area between the body and the liquid is rapidly expanding. The loads on the body are determined by the plane section method. The method of matched asymptotic expansions is used to determine the position and size of the contact spot in each section. The coupled problem is solved: the liquid flow due to the motion of the body and the body motion itself are determined simultaneously. A system of integrodifferential equations was obtained and used for numerical investigation of the body motion under the action of hydrodynamic loads, and the hydrodynamic pressure distribution over the contact spot was determined.

T. Hayat^{1,2}, M. Hussain^{3}, S. A. Shehzad^{4}, A. Alsaedi^{2}
^{1}QuaidIAzam University 45320, Islamabad, 44000 Pakistan ^{2}King Abdulaziz University, Jeddah, 21589 Saudi Arabia ^{3}University of Engineering and Technology (RCET Campus), Lahore, 54890 Pakistan ^{4}Comsats Institute of Information Technology, Sahiwal 57000, Pakistan
Keywords: наночастицы, реологический степенной закон для жидкости, конвективное граничное условие, nanoparticles, powerlaw fluid, convective boundary condition
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A boundary layer flow of a nonNewtonian fluid in the presence of nanoparticles is examined. The flow is caused by a vertical stretching sheet. Convergence of the solution obtained is checked. The values of velocity, temperature, skin friction, and Nusselt number in the boundary layer are obtained.

V. I. Terekhov, Ya. I. Smul'skii, K. A. Sharov
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: турбулентный поток, отрывное течение, обратный уступ, пассивное возмущение, ребро, turbulent flow, separated flow, backwardfacing step, passive disturbance, rib
Abstract >>
The flow in a channel with a backwardfacing step and a rib mounted upstream of the step and generating flow disturbances is studied experimentally by the method of particle image velocimetry. It is demonstrated that mounting of a single rib leads to deformation of the profiles of the mean streamwise velocities and turbulent fluctuations. The effect of the position and height of a single rib on the recirculation region behind the backwardfacing step is analyzed. Reduction of the recirculation region size behind the step in the case of flow reattachment upstream of the step is validated.

S. N. Aristov^{1}, K. G. Shvarts^{2}
^{1}Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, 614013 Perm, Russia ^{2}Russian Presidential Academy of National Economy and Public Administration, 119571 Moscow, Russia
Keywords: термокапиллярная адвекция, вращение, точное решение, thermocapillary advection, rotation, accurate solution
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This paper presents a new accurate solution of the Navier Stokes equations in the Boussinesq approximation that describes the thermocapillary advective flow in a slowly rotating horizontal layer of incompressible liquid with free boundaries. Such a flow emerges in the case of linear temperature distribution over horizontal coordinates or in the case of heat flux distribution on the layer boundaries. The influence of the Taylor, Marangoni, Grashof, and Biot numbers on the flow and temperature velocity profiles is studied.

