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Journal of Applied Mechanics and Technical Physics

2016 year, number 2

Viscous Liquid Film Flow Down an Inclined Corrugated Surface. Calculation of the Flow Stability to Arbitrary Perturbations using an Integral Method

Yu. Ya. Trifonov1,2
1Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: течение пленок, нелинейные волны, устойчивость, film flow, nonlinear waves, stability

Abstract >>
Viscous liquid film flow along an inclined corrugated (sinusoidal) surface has been studied. Calculations were performed using an integral model. The stability of nonlinear steady-state flows to arbitrary perturbations was examined using the Floquet theory. It has been shown that for each type of corrugation there is a critical Reynolds number for which unstable perturbations occur. It has been found that this value greatly depends on the physical properties of the liquid and geometric parameters of the flow. In particular, in the case of film flow down a smooth wall, the critical wave-formation parameter depends only on the angle of inclination of the flow surface. The values of the corrugation parameters (amplitude and period) were obtained for which the film flow down a wavy wall is stable to arbitrary perturbations up to moderate Reynolds numbers. Such parameter values exist for all investigated angles of inclination of the flow surface.

Use of Shutdown of the Capacitive Storage in Implementing Electrical Action on Metallic Shaped-Charge Jets

S. V. Fedorov
Bauman Moscow State Technical University, Moscow, 105005 Russia
Keywords: взрыв, кумулятивная струя, глубина проникания, импульс тока, электродинамическое воздействие, емкостный накопитель, разрядный контур, explosion, shaped-charge jet, penetration depth, current pulse, electrodynamic action, capacitive storage, discharge circuit

Abstract >>
To improve the efficiency of electrical action on metallic shaped-charge jets, it is proposed to use shutdown of the capacitive storage at the time when the voltage on it during passage of an alternating discharge becomes zero. It has been shown that using this expedient eliminates recharging of the capacitive storage and provides better matching between the current pulse and the time of motion of various parts of the shaped-charge jet through the electrode gap. Studies have been conducted using a computational procedure in which the development of magnetohydrodynamic instability of the jet and the dispersion of its material are considered possible physical mechanisms reducing the penetration capability of shaped-charge jets under the action of high current pulses.

Test of a New Tip Material for Langmuir Probe Diagnostic

M. Y. Naz1,2, S. Shukrullah1,2, A. Ghaffar2, N. U. Rehman3,4, Y. Khan5
1Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Malaysia
2University of Agriculture, Faisalabad, 38040 Pakistan
3King Saud University, Riyadh, 11451 Kingdom of Saudi Arabia
4COMSATS Institute of Information Technology, Islamabad, Pakistan
5King Saud University, Riyadh, 11451 Saudi Arabia
Keywords: многоэлектродные зонды, плотность электронов, электронная температура, радиочастотная плазма, multi-tip probes, electron number density, electron temperature, radio frequency plasmas

Abstract >>
The objective of the work is to test a nickel-chrome alloy as a probe tip material for characterization of discharge plasmas. In order to meet the objective, a symmetric triple Langmuir probe diagnostic system and an associated driving circuit are designed and tested in an inductively coupled plasma generated by a 13.56-MHz radio frequency source coupled with an automated impedance match network. This probe is used to measure the electron temperature, electron number density, and ion saturation current as functions of the input power of the radio frequency source and the filling gas pressure. An increasing trend is noticed in the electron temperature and electron number density with an increase in the input power, whilst a decreasing trend is evident in these parameters with an increase in the nitrogen gas pressure. The overall inaccuracies in electron temperature and electron number density measurements are 5-12% and 3-13%, respectively.

Uniqueness of Solution and Well-Posedness of the Problem of Determining the Fastening Parameters of a Pipe Containing Flowing Fluid

A. M. Akhtyamov1,2, G. F. Safina3
1Bashkir State University, Ufa, 450076 Russia
2Mavlyutov Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa, 450054 Russia
3Bashkir State University, Neftekamsk, 452680 Russia
Keywords: труба с текущей в ней жидкостью, частоты колебаний, краевые условия, параметры упругого закрепления, задача диагностирования, единственность решения, компакт, pipe containing flowing fluid, vibration frequency, boundary conditions, elastic fastening parameters, diagnostics problem, uniqueness of solution, compact

Abstract >>
The inverse problem of determining the type and parameters of fastening of the pipe ends from the natural frequencies of the pipe flexural vibrations is formulated and solved for the case of fluid flowing through the pipe. The uniqueness of the solution of the problem is proved, and the Tikhonov well-posedness of the problem is shown. A method for solving the inverse problem is proposed, and examples of the solution are given.

Water Surface Waves in a Horizontally Oscillating Container

V. I. Bukreev
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: колебания лотка с водой, гравитационные волны, резонанс, кумулятивные струи, oscillations of container with water, gravity waves, resonance, cumulative jets

Abstract >>
This paper presents the results of experimental verification of Sretenskii's linear theory of gravity waves in a container partially filled with water and oscillating horizontally according to the harmonic law. It has been shown that this theory predicts the existence of an infinite ordered countable set of generation modes of unstable waves. It has been experimentally confirmed that the waves are unstable if the container oscillation frequency is equal to the frequency of any odd standing-wave mode. At even eigenfrequencies of container oscillations, the theory predicts wave amplitudes up to a constant term. Experiment has shown that, in this case, the waves are stable and have minimum amplitudes.

On the Mechanism of Self-Oscillations of a Supersonic Radial Jet Exhausting into an Ambient Space

S. P. Kiselev1,2, V. P. Kiselev1, V. N. Zaikovskii1
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State Technical University, Novosibirsk, 630092 Russia
Keywords: перерасширенная сверхзвуковая струя, радиальное сопло, автоколебания, ударная волна, supersonic overexpanded jet, radial nozzle, self-oscillations, shock wave

Abstract >>
Results of an experimental study and numerical simulation of self-oscillations of a supersonic radial jet exhausting from a plane radial nozzle into an ambient space are reported. It is demonstrated that flexural oscillations develop in the jet, leading to its destruction. Feedback ensured by acoustic waves in the gas surrounding the supersonic jet is found to play a key role in the emergence of self-oscillations.

Linear Stability of the Couette Flow of a Vibrationally Excited Gas. 2. Viscous Problem

Yu. N. Grigor'ev1,2, I. V. Ershov1
1Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: линейная теория устойчивости, колебательная релаксация, уравнения двухтемпературной аэродинамики, моды возмущений, linear stability theory, vibrational relaxation, two-temperature aerodynamics, disturbance modes

Abstract >>
Based on the linear theory, stability of viscous disturbances in a supersonic plane Couette flow of a vibrationally excited gas described by a system of linearized equations of two-temperature gas dynamics including shear and bulk viscosity is studied. It is demonstrated that two sets are identified in the spectrum of the problem of stability of plane waves, similar to the case of a perfect gas. One set consists of viscous acoustic modes, which asymptotically converge to even and odd inviscid acoustic modes at high Reynolds numbers. The eigenvalues from the other set have no asymptotic relationship with the inviscid problem and are characterized by large damping decrements. Two most unstable viscous acoustic modes (I and II) are identified; the limits of these modes were considered previously in the inviscid approximation. It is shown that there are domains in the space of parameters for both modes, where the presence of viscosity induces appreciable destabilization of the flow. Moreover, the growth rates of disturbances are appreciably greater than the corresponding values for the inviscid flow, while thermal excitation in the entire considered range of parameters increases the stability of the viscous flow. For a vibrationally excited gas, the critical Reynolds number as a function of the thermal nonequilibrium degree is found to be greater by 12% than for a perfect gas.

Motion of a Viscous Fluid and a Wall in the Presence of a Stationary Wall

V. L. Sennitskii1,2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: вязкая жидкость, "свободная'' и закрепленная твердые стенки, затухающее движение, резкое торможение гидромеханической системы, viscous fluid, free and fixed rigid walls, damping motion, abrupt deceleration of hydromechanical system

Abstract >>
The problem of damping motion of a hydromechanical system consisting of a viscous fluid and its bounding rigid walls is solved. A condition under which there is an abrupt deceleration of the hydromechanical system is determined.

Steady Flow of a Power-Law Non-Newtonian Fluid Across an Unconfined Square Cylinder

A. Pantokratoras
Democritus University of Thrace, Xanthi, 67100 Greece
Keywords: цилиндр с квадратным поперечным сечением, степенной закон, коэффициент сопротивления, вихревой след, square cylinder, power law, drag coefficient, wake

Abstract >>
A two-dimensional flow of a non-Newtonian power-law fluid directed normally to a horizontal cylinder with a square cross section is considered in the present paper. The problem is investigated numerically with a finite volume method by using the commercial code Ansys Fluent with a very large computational domain so that the flow could be considered unbounded. The investigation covers the power-law index from 0.1 to 2.0 and the Reynolds number range from 0.001 to 45.000. It is found that the drag coefficient for low Reynolds numbers and low power-law index ( n ≤ 0.5) obeys the relationship CD = A / Re. An equation for the quantity A as a function of the power-law index is derived. The drag coefficient becomes almost independent of the power-law index at high Reynolds numbers and the wake length changes nonlinearly with the Reynolds number and power-law index.

Theoretical-Experimental Method of Determining the Drag Coefficient of a Harmonically Oscillating Thin Plate

A. G. Egorov1, A. M. Kamalutdinov1, V. N. Paimushin2, V. A. Firsov2
1Kazan' Federal University, Kazan', 420008 Russia
2Kazan' National Research Technical University named after A. N. Tupolev, Kazan', 420111 Russia
Keywords: свободные механические колебания, коэффициент сопротивления, вязкая несжимаемая жидкость, демпфирование, декремент колебаний, free mechanical oscillations, drag coefficient, viscous incompressible fluid, damping, decrement of oscillations

Abstract >>
A method for determining the drag coefficient of a thin plate harmonically oscillating in a viscous incompressible fluid is proposed. The method is based on measuring the amplitude of deflections of cantilever-fixed thin plates exhibiting damping flexural oscillations with a frequency corresponding to the first mode and on solving an inverse problem of calculating the drag coefficient on the basis of the experimentally found logarithmic decrement of beam oscillations.

Three-Dimensional Flow of a Magnetohydrodynamic Casson Fluid over an Unsteady Stretching Sheet Embedded into a Porous Medium

A. S. Butt1, M. N. Tufail1,2, Ali Asif1,2
1Quaid-I-Azam University, Islamabad, 44000 Pakistan
2Prince Muhammad Bin Fahd University, Al Khobar, 31952 Saudi Arabia
Keywords: растягивающаяся пластина, жидкость Кэссона, метод гомотопического анализа, stretching sheet, Casson fluid, homotopy analysis method

Abstract >>
A three-dimensional flow of a magnetohydrodynamic Casson fluid over an unsteady stretching surface placed into a porous medium is examined. Similarity transformations are used to convert time-dependent partial differential equations into nonlinear ordinary differential equations. The transformed equations are then solved analytically by the homotopy analysis method and numerically by the shooting technique combined with the Runge-Kutta-Fehlberg method. The results obtained by both methods are compared with available reported data. The effects of the Casson fluid parameter, magnetic field parameter, and unsteadiness parameter on the velocity and local skin friction coefficients are discussed in detail.

Flow around a Cylinder at the Beginning of the Critical Region

K. G. Dobrosel'skii1,2
1Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk National Research State University, Novosibirsk, 630090 Russia
Keywords: гидродинамический стенд, цилиндр, PIV-метод, кавитация, пограничный слой, коэффициент сопротивления, hydrodynamic testbench, cylinder, PIV, cavitation, boundary layer, drag coefficient

Abstract >>
Results of experiments with a turbulent flow around a transversely aligned circular cylinder located at identical distances from the walls of a rectangular channel are reported. Data on averaged velocity fields around the cylinder are obtained by means of particle image velocimetry (PIV). Based on these fields, the near wake behind the cylinder is studied, and the kinematic characteristics for flow regimes with and without cavitation are compared. Based on the vector fields of averaged velocity, the angles of separation of the boundary layer from the cylinder surface in the considered flow regimes are determined. The drag coefficients of the cylinder for different flow regimes are calculated. It is demonstrated that the vortex region behind the cylinder and the drag coefficient of the cylinder increase in the case with cavitation. It is also shown that vortex shedding from the cylinder may be irregular, despite the fact that this process is quasi-periodic for most of the time.

Study of Unsteady Performance of a Twin-Entry Mixed Flow Turbine

M. M. Bencherif, M. K. Hamidou, M. Hamel, M. Abidat
University of Science and Technology Mohamed Boudiaf, BP-1505 Oran El M'Naouer, Algeria
Keywords: двигатель внутреннего сгорания, газовая турбина, сдвоенный вход, internal combustion engine, gas turbine, twin entry

Abstract >>
The aim of this investigation is to study the performance of a twin-entry turbine under pulsed flow conditions. The ANSYS-CFX code is used to solve three-dimensional compressible turbulent flow equations. The computational results are compared with those of a one-dimensional model and experimental data, and good agreement is found.

Melting Heat Transfer in an Axisymmetric Stagnation-Point Flow of the Jeffrey Fluid

M. Nawaz1, T. Hayat2, A. Zeeshan3
1Institute of Space Technology, Islamabad, 44000 Pakistan
2Quaid-I-Azam University 45320, Islamabad, 44000 Pakistan
3International Islamic University, Islamabad, 44000 Pakistan
Keywords: теплообмен при плавлении, течение вблизи точки торможения, жидкость Джеффри, число Нуссельта, melting heat transfer, stagnation-point flow, Jeffrey fluid, Nusselt number

Abstract >>
This investigation explores the characteristics of melting heat transfer in a boundary layer flow of the Jeffrey fluid near the stagnation point on a stretching sheet subject to an applied magnetic field. The governing boundary layer equations are transformed to ordinary differential equations by similarity transformations. Resulting nonlinear problems are solved analytically by the homotopy analysis method. It is noticed that an increase in the melting parameter decreases the dimensionless velocity and temperature, while an increase in the Deborah number increases the velocity and momentum boundary layer thickness.

Radiative Mixed Convection Flow of an Oldroyd-B Fluid over an Inclined Stretching Surface

Ashraf M. Bilal1, T. Hayat2, A. Alsaedi3
1COMSATS Institute of Information Technology, Wah Cantt, 47040 Pakistan
2Quaid-i-Azam University, Islamabad, 44000 Pakistan
3King Abdulaziz University, Jeddah, 21589 Saudi Arabia
Keywords: наклонная растягивающаяся поверхность, течение при наличии теплового излучения, жидкость Олдройда-B, inclined stretching surface, radiative flow, Oldroyd-B fluid

Abstract >>
A mixed convection flow of an Oldroyd-B fluid in the presence of thermal radiation is investigated. The flow is induced by an inclined stretching surface. The boundary layer equations of the Oldroyd-B fluid in the presence of heat transfer are used. Appropriate transformations reduce partial differential equations to ordinary differential equations. A computational analysis is performed for convergent series solutions. The values of the local Nusselt number are numerically analyzed. The effects of various parameters on velocity and temperature are discussed.

Non-Fourier Heat Conduction in an Exponentially Graded Slab

M. R. Raveshi
Toosi University of Technology, Tehran, Iran
Keywords: функционально-градиентный материал, не подчиняющаяся закону Фурье теплопроводность, метод дифференциального преобразования, плита, функция, экспоненциально зависящая от расстояния, functionally graded material, non-Fourier heat conduction, differential transformation method, slab, exponential location-dependent function

Abstract >>
The present article investigates one-dimensional non-Fourier heat conduction in a functionally graded material by using the differential transformation method. The studied geometry is a finite functionally graded slab, which is initially at a uniform temperature and suddenly experiences a temperature rise at one side, while the other side is kept insulated. A general non-Fourier heat transfer equation related to the functionally graded slab is derived. The problem is solved in the Laplace domain analytically, and the final results in the time domain are obtained by using numerical inversion of the Laplace transform. The obtained results are compared with the exact solution to verify the accuracy of the proposed method, which shows excellent agreement.

Thermophoretic Motion of Large Heated Aerosol Spherical Particles

N. V. Malai1, A. V. Limanskaya1, E. R. Shchukin2
1Belgorod State National Research University, Belgorod, 308007 Russia
2Joint Institute of High Temperatures, Moscow, 125412 Russia
Keywords: термофорез нагретых сферических частиц, движение нагретых сферических частиц в поле градиента температуры, thermophoresis of heated spherical particles, motion of heated spherical particles in a gradient temperature field

Abstract >>
The stationary motion of a large spherical aerosol particle in the external field of a temperature gradient in zero gravity is theoretically described using the Stokes approximation and the assumption that the average temperature of the particle surface differs considerably from the temperature of the surrounding gaseous medium. The gas dynamics equations are solved taking into account the power-law temperature dependence of the molecular transport coefficients (viscosity, thermal conductivity) and the density of the gaseous medium. Numerical estimates show that the dependence of the thermophoretic force and velocity on the average temperature of the particle surface is nonlinear.

Convective Heat Transfer \\in a Rotating Horizontal Cylindrical Fluid Layer

A. A. Vyatkin, A. A. Ivanova, V. G. Kozlov
Perm' State Humanitarian Pedagogical University, Perm', 614990 Russia
Keywords: вибрационная тепловая конвекция, вращение, цилиндрический слой, теплоперенос, thermal-oscillatory convection, rotation, cylindrical layer, heat transfer

Abstract >>
This paper describes the thermal convection and heat transfer in a cylindrical fluid layer rotating around a horizontal axis, with various constant temperatures set at the layer boundaries. The influence of the rotational speed of the cylindrical fluid layer on the convective heat transfer in this layer is studied. The study results are presented according to the dimensionless parameters that characterize the action of two convective mechanisms: centrifugal and thermal-oscillatory. It is shown that, with low rotational speed, the heat transfer is determined by quasistationary gravitational convection.

Temperature-Strain Rate Deformation Conditions of Aluminum Alloys

D. A. Kitaeva1, Sh. T. Pazylov2, Ya. I. Rudaev2
1St. Petersburg State Polytechnical University, St. Petersburg, 195251 Russia
2Kyrgyz-Russian Slavic University, Bishkek, 720000 Kyrgyzstan
Keywords: динамическая сверхпластичность, температурно-скоростное деформирование, деформационная анизотропия, коэффициент анизотропии, алюминиевые сплавы, равноосная мелкозернистая структура, dynamic superplasticity, temperature-strain rate deformation conditions, deformation anisotropy, anisotropy factor, aluminum alloys, fine-grained equiaxed structure

Abstract >>
This paper presents the results of an experimental study of the deformation and structural parameters of 1561 anisotropic alloy. It has been found that the lowest anisotropy factor corresponds to the formation of an ultrafine-grained equiaxed structure under temperature-strain rate conditions of superplasticity.

Frictionless Contact of an Elastic Punch Subject to the Normal Load and Bending Moment

X. Jiang1,2, G. Shao1, L. Zhu1
1Xidian University, Xi'an, China
2Xi'an Jiaotong University, Xi'an, China
Keywords: асимптотическое решение, полный контакт, контакт с отставанием, наклонный штамп, asymptotic solution, complete contact, receding contact, tilted punch

Abstract >>
A two-dimensional contact problem of a trapezium shaped punch pressed into a frictionless, elastically similar half-plane and subject sequentially to the normal load and bending moment is considered. The model of a tilted flat punch is used to evaluate the pressure distribution and the contact deformation within the contact zone. Comparisons of the results generated by the analytical technique to those computed by the finite element method demonstrate the high level of accuracy attained by both methods. The presented numerical results illustrate the effects of the normal load, bending moment, and internal angles of the punch geometry on the contact stresses.

Technique for Selecting the Functions of the Constitutive Equations of Creep and Long-Term Strength with One Scalar Damage Parameter

E. B. Kuznetsov, S. S. Leonov
Moscow Aviation Institute, Moscow, 125993 Russia
Keywords: ползучесть, разрушение, параметр поврежденности, продолжение решения по параметру, наилучшая параметризация, методика определения функциональных зависимостей, системы дифференциальных уравнений, creep, fracture, damage parameter, solution continuation with respect to a parameter, the best parameterization, technique for determining functional dependences, systems of differential equations

Abstract >>
The strain-strength characteristics of aerostructures made of hardening materials under uniaxial tension in creep conditions are determined. The problem is reduced to a system of ordinary differential equations of the kinetic theory of creep with one scalar damage parameter. The approximate solutions of the problem are obtained with the help of the implicit Euler method and of the arc length method in combination with the explicit methods of the Runge-Kutta family for cylindrical St.45 steel samples and 3V titanium alloy plates.

Numerical Analysis on the Cutting and Finishing Efficiency of Mraff Process

F. L. Lih
Center of General Education, Republic of China Military Academy, Kaohsiung 83059, Taiwan, Republic of China
Keywords: магнитогидродинамика, магнитореологическая жидкость, численное моделирование, магнитореологический абразивный поток, многофазный поток, MHD, magnetorheological fluid, CFD, MRAFF, multiphase flow

Abstract >>
The aim of the present research is to conduct a numerical study of the characteristic of a two-phase magnetorheological fluid with different operation conditions by the finite volume method called SIMPLE with an add-on MHD code.