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# Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2015 number 2

## Journal of Applied Mechanics and Technical Physics

### 2015 year, number 2

#### 1.Effect of the Type of Boundary Conditions on the Three-Phase Contact Line on the Flow Characteristics during Filling of the Channel

E. I. Borzenko, G. R. Shrager
Tomsk State University, Tomsk, 634050 Russia
Keywords: three-phase contact line, free boundary, no-slip, slip, calculation method, dissipation function, shear stress, convergence

Abstract >>
The effect of various models of the dynamics of the three-phase contact line on the flow characteristics during filling of a plane channel is investigated. The system of constitutive equations is solved numerically using a technique based on the combined use of the SIMPLE algorithm and the method of invariants. Different methods for calculating the motion of the contact point for slip and no-slip conditions for a dynamic contact angle θ = π, neglecting surface tension on the free boundary are considered. It is shown that in the whole computational domain, except in a small vicinity of the contact point, the kinematic characteristics of the flow and the distributions of the dissipation function and shear stress are slightly dependent on the selected calculation method of the motion of the contact point.

DOI: http://dx.doi.org/10.1134/S0021894415020017

#### 2.Nonisothermal Two-Phase Flow in a Vertical Well

R. F. Sharafutdinov, T. R. Khabirov, A. A. Sadretdinov
Bashkir State University, Ufa, 450000 Russia
Keywords: temperature, pressure, bubble flow, heat transfer, borehole

Abstract >>
This paper presents a mathematical model for bubble flow in a vertical borehole under non-isothermal conditions and the results of calculations of the volume fraction and temperature of the phases. The influence of the bubble size on the formation phase of the temperature fields of the phases.

DOI: http://dx.doi.org/10.1134/S0021894415020029

#### 3.Investigation of the Effect of Roughness of Duct Surfaces of a Supersonic High-Pressure Stage of an Axial Compressor on Its Characteristics

A. A. Inozemtsev, A. I. Plotnikov
Open Joint-Stock Company ”Aviadvigatel”, Perm', 614990 Russia
Keywords: axial compressor, high-pressure wide-chord stage, three-dimensional calculation, stable operation, equivalent surface roughness, identification, compressor characteristic

Abstract >>
Results of calculations and experimental investigations of characteristics of a supersonic high-pressure wide-chord stage of an axial compressor are presented. The influence of surface roughness on the characteristics of this stage are analyzed. A method of identification of aerodynamic flow parameters in the compressor duct is described.

DOI: http://dx.doi.org/10.1134/S0021894415020030

#### 4.Experimental and Numerical Study of Turbulent Mixing at the Contact Boundaries of Three-Dimensional Gas Systems

N. V. Nevmerzhitskii, A. N. Razin, E. D. Sen'kovskii, E. A. Sotskov, A. A. Nikulin, L. V. Tochilina, O. L. Krivonos, E. V. Shaporenko
Institute of Experimental Physics (VNIIEF), Sarov, 607188 Russia
Keywords: òðåõñëîéíûå ãàçîâûå ñèñòåìû, íåóñòîé÷èâîñòü Ðèõòìàéåðà - Ìåøêîâà, òóðáóëåíòíîå ïåðåìåøèâàíèå, three-layer gas systems, Richtmyer-Meshkov instability, turbulent mixing

Abstract >>
This work presents the results of experimental and numerical studies on the process of turbulent mixing ocurring at the contact boundaries of three-layer gas systems during the passage of a stationary shock wave with a Mach number M ≈ 1.3. The experiments are carried out in an air shock tube. The working gases are air, F6, and He. The flow structure is recorded by a schlieren method with laser illumination. The data on the nature of turbulent mixing in two-dimensional flows are obtained.

DOI: http://dx.doi.org/10.1134/S0021894415020042

#### 5.Bubble Migration during Hydrate Formation

V. Sh. Shagapov, A. S. Chiglintseva, A. A. Rusinov
Birsk Branch of the Bashkir State University, Birsk, 452453 Russia
Keywords: hydrate particles, gas bubble migration, hydrate formation

Abstract >>
A model of the process of migration of methane bubbles in water under thermobaric conditions of hydrate formation is proposed. The peculiarities of the temperature field evolution, migration rate, and changes in the radius and volume fraction of gas hydrate bubbles are studied. It is shown that, with a constant mass flow of gas from the reservoir bottom, for all parameters of the surfacing gas hydrate disperse system, there is a quasistationary pattern in the form of a "step"-like wave. Depending on the relationship of the initial gas bubble density with the average gas density in the hydrate composition determined by the depth from which bubbles rise to the surface, the final radius of hydrate particles may be larger or smaller than the initial gas bubble radii. It is established that the speed at which gas hydrate inclusions rise to the surface decreases by several times due to an increase in their weight during hydrate formation. The influence of the depth of the water reservoir whose bottom is a gas flow source on the dynamics of hydrate formation is studied.

DOI: http://dx.doi.org/10.1134/S0021894415020054

#### 6.Visual Characterization of Heated Water Spray Jet Breakup Induced by Full Cone Spray Nozzles

M. Y. Naz, S. A. Sulaiman, B. Ariwahjoedi, K. Zilati
Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia
Keywords: fluid dynamics, airless sprays, thermal energy, high-speed imaging

Abstract >>
The present work with specific objectives places a greater emphasis on measurements of the breakup lengths and phenomenological analysis of a hot water jet under reduced pumping pressures in still environment. Therefore, visual and comparative studies are conducted on full cone jet disintegration of heated water for low pumping pressures. A further analysis of the grabbed images confirms the strong influence of the input processing parameters on full cone spray patternation. It is also predicted that the heated liquids generate a dispersed spray pattern by utilizing partial evaporation of the spraying medium. The radial spray cone width and angle do not vary significantly with increasing Reynolds and Weber numbers at early injection phases, leading to enhanced macroscopic spray propagation. The discharge coefficient, mean flow rate, and mean flow velocity are significantly influenced by the load pressure, but less affected by the temperature. The fine scale image analysis also predicts toroidal-shaped vortex formation in the spray structure near the water boiling point.

DOI: http://dx.doi.org/10.1134/S0021894415020066

#### 7.Effect of Junction Configurations on Microdroplet Formation in a T-Junction Microchannel

F. L. Lih1, J. M. Miao2
1Center of General Education, R.O.C. Military Academy, Kaohsiung, 83059 Taiwan, R.O.C
2Department of Biomechatronics Engineering, National Pingtung University of Science and Technology, Pingtung, 91201 Taiwan, R.O.C
Keywords: CFD, T-junction microchannel, VOF scheme, microdroplet, capillary number

Abstract >>
This study investigates the dynamic formation process of water microdroplets in a silicon oil flow in a T-junction microchannel. Segmented water microdroplets are formed at the junction when the water flow is perpendicularly injected into the silicon oil flow in a straight rectangular microchannel. This study further presents the effects of the water flow inlet geometry on hydrodynamic characteristics of water microdroplet formation. A numerical multiphase volume of fluid (VOF) scheme is coupled to solve the unsteady three-dimensional laminar Navier-Stokes equations to depict the droplet formation phenomena at the junction. Predicted results on the length and generated frequency of the microdroplets agree well with experimental results in a T-junction microchannel with straight and flat inlets (the base model) for both fluid flows. Empirical correlations are reported between the volumetric flow ratio and the dimensionless microdroplet length or dimensionless frequency of droplet generation at a fixed capillary number of 4.7 × 10–3. The results of this study indicate a reduction in the droplet length of approximately 21% if the straight inlet for the water flow is modified to a downstream sudden contraction inlet for the water flow.

DOI: http://dx.doi.org/10.1134/S0021894415020078

#### 8.MHD Flow and Heat Transfer of a Viscous Fluid over a Radially Stretching Power-Law Sheet with Suction/Injection in a Porous Medium

M. Khan1, A. Munir1, A. Shahzad1,2, A. Shah3
1Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000 Pakistan
2University of Engineering and Technology, Taxila, Pakistan
3Department of Mathematics, COMSAT Institute of Information Technology, Islamabad, Pakistan
Keywords: axisymmetric flow, heat transfer, suction/injection

Abstract >>
A steady boundary layer flow and heat transfer over a radially stretching isothermal porous sheet is analyzed. Stretching is assumed to follow a radial power law, and the fluid is electrically conducting in the presence of a transverse magnetic field with a very small magnetic Reynolds number. The governing nonlinear partial differential equations are reduced to a system of nonlinear ordinary differential equations by using appropriate similarity transformations, which are solved analytically by the homotopy analysis method (HAM) and numerically by employing the shooting method with the adaptive Runge-Kutta method and Broyden's method in the domain [0, ∞). Analytical expressions for the velocity and temperature fields are derived. The influence of pertinent parameters on the velocity and temperature profiles is discussed in detail. The skin friction coefficient and the local Nusselt number are calculated as functions of several influential parameters. The results predicted by both methods are demonstrated to be in excellent agreement. Moreover, HAM results for a particular problem are also compared with exact solutions.

DOI: http://dx.doi.org/10.1134/S002189441502008X

#### 9.Boundary Layer Flow due to a Stretching Sheet with a Variable Thickness and Slip Velocity

M. M. Khader1,2, A. M. Megahed2
1Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
2Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
Keywords: Newtonian fluid, stretching sheet, Chebyshev spectral method, slip velocity, variable thickness

Abstract >>
This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet with a power-law surface velocity, slip velocity, and variable thickness. The flow is caused by nonlinear stretching of the sheet. The governing partial differential equations are transformed into a nonlinear ordinary differential equation with appropriate boundary conditions for various physical parameters. The remaining ordinary differential equation is solved numerically by using the Chebyshev spectral method. The effects of the slip parameter and the wall thickness parameter on the flow profile and local skin friction are presented. A comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted.

DOI: http://dx.doi.org/10.1134/S0021894415020091

#### 10.Influence of the Initial Parameters of Liquid Droplets on Their Evaporation Process in a Region of High-Temperature Gas

R. S. Volkov, G. V. Kuznetsov, P. A. Strizhak
Tomsk Polytechnic University, Tomsk, 634050 Russia
Keywords: heat and mass transfer, evaporation, high-temperature gases, atomized water, drops, optical methods of diagnostics of gas-vapor-liquid mixtures

Abstract >>
This paper presents an experimental study of the influence of the main initial parameters (characteristic size, temperature, velocity) of droplets of an atomized liquid (water) on the process of their evaporation in gases at temperatures up to 1000 K. The limiting values of the initial parameters of liquid droplets at which the rate of evaporation reaches maximum and minimum values were determined.

DOI: http://dx.doi.org/10.1134/S0021894415020108

#### 11.Laminar Natural Convection Heat Transfer and Air Flow in Three-Dimensional Cubic Enclosures with a Partially Heated Wall

S. Mellah, N. Ben-Cheikh, B. Ben-Beya, T. Lil
DÃ©partement de Physique, FacultÃ©des Sciences de Tunis, Campus Universitaire, 2092, El-Manar II, Tunisia
Keywords: natural convection, three-dimensional enclosures, partially heated wall, heat transfer, numerical computation

Abstract >>
In the present study, a finite volume computational procedure and a full multigrid technique are used to investigate laminar natural convection in partially heated cubic enclosures. Effects of heated strip disposition in the enclosure on the heat transfer rate are studied. Results are presented in the form of flow lines, isotherms plots, average Nusselt numbers, and average temperature on the heat source surface. Statistical distributions of temperature and average velocity fields and their root-mean-square values are presented and discussed.

DOI: http://dx.doi.org/10.1134/S002189441502011X

#### 12.Nonlinear Thermal Analysis of a Hollow Functionally Graded Cylinder with Temperature-Variable Material Properties

M. Arefi
University of Kashan, Kashan, 87317-51167 Iran
Keywords: nonlinear thermal analysis, temperature-dependent thermal conductivity, functionally graded materials, Adomian decomposition method

Abstract >>
A nonlinear thermal analysis of a hollow functionally graded cylinder is performed in the present paper. A power function distribution is used for simulation of non-homogeneity of the material used. A temperature dependence is employed for the thermal conductivity. These simulations reduce the problem to a nonlinear differential equation with a variable coefficient. A semi-analytical method of successive approximations is employed for solving this equation. The convergence of the method is studied for different parameters of the problem by checking two criteria: convergence of the sum of the infinite series and condition of smallness of the residual of the responses. An exponentially function is used for simulation of the nonlinear dependence of cylinder material properties on temperature.

DOI: http://dx.doi.org/10.1134/S0021894415020121

#### 13.On the Tolerance Modelling of Heat Conduction in Functionally Graded Laminated Media

C. Wozniak1, M. Wagrowska2, O. Szlachetka2
1Technical University Architecture and Environmental Engineering, Lodz, Poland
2University of Life Sciences, Warsaw, Poland
Keywords: heat conduction, functionally graded laminate, tolerance modelling

Abstract >>
The object of analysis is a heat conduction problem within the framework of tolerance modelling in laminated media with a functional gradation of effective properties. In contrast to the known asymptotic models (based on the homogenization technique), the characteristic feature of the tolerance model equations is that they make it possible to analyze the effect of the microstructure size on the overall behavior of the laminate. The proposed model equations describe heat conduction in laminates by mean of partial differential equations with smooth and slowly varying functions. This paper describes a certain extension of the unified tolerance modelling procedure, which makes it possible to analyze specific problems of heat conduction in laminates with a transversal gradation of effective properties.

DOI: http://dx.doi.org/10.1134/S0021894415020133

#### 14.Rabotnov Damageparameter and Description of Delayed Fracture: Results, Current Status, Application to Fracture Mechanics, and Prospects

L. V. Stepanova, S. A. Igonin
Samara State University, Samara, 443011 Russia
Keywords: damage parameter, tensor measure of damage, long-term disruption, creep, continuum damage mechanics, computer simulation

Abstract >>
This paper presents a review of studies of delayed fracture and fracture mechanics problems in which the hypotheses and ideas of Yu. N. Rabotnov and L. M. Kachanov on the mechanisms of delayed fracture under creep conditions are extended to describe fracture processes using scalar and tensor measures of damage. The results of current research in the theory of elasticity, the mathematical theory of plasticity and creep, the mechanics of composites, and linear and nonlinear fracture mechanics, with material damage taken into account.

DOI: http://dx.doi.org/10.1134/S0021894415020145

#### 15.Flow of an Elastoviscoplastic Material between Rotating Cylindrical Surfaces with Nonrigid Cohesion

A. S. Begun1,2, A. A. Burenin3, L. V. Kovtanyuk1
1Institute of Automation and Control Processes, Far East Branch, Russian Academy of Sciences, Vladivostok 690041, Russia
3Institute of Engineering and Metallurgy, Far East Branch of Russian Academy of Sciences, Komsomolsk-on-Amur, 681005 Russia
Keywords: elasticity, viscoplasticity, large deformations, viscometric flows

Abstract >>
The theory of large deformations is used to construct exact solutions of a sequence of one-dimensional boundary-value problems of the occurrence, development, and subsequent deceleration of viscometric flow of an elastoviscoplastic incompressible material located in the gap between rotating rigid coaxial cylindrical surfaces. In the quasistatic approximation allowing for slip of the material on its solid boundaries, the flow initiation conditions in the deformed material and the laws of motion of the boundary surfaces of the flow of this material both during its development and deceleration are determined. The parameters of the stress-strain states in the regions of reversible deformation and flow in all stages of the process, including the cessation of the flow and the complete unloading by rotation of the solid boundary in the opposite direction, are calculated.

DOI: http://dx.doi.org/10.1134/S0021894415020157

#### 16.Effect of the Amplitude of Vibrations on the Pull-in Instability of Double-Sided Actuated Microswitch Resonators

H. M. Sedighi, K. H. Shirazi, M. Changizian
Shahid Chamran University, Ahvaz, Iran
Keywords: Hamiltonian approach, frequency-amplitude relationship, microbeam vibration, double-sided actuated microswitch, pull-in instability

Abstract >>
This paper exhibits the effect of the amplitude of vibrations on the pull-in instability and nonlinear natural frequency of a double-sided actuated microswitch by using a nonlinear frequency-amplitude relationship. The nonlinear governing equation of the microswitch pre-deformed by an electric field includes even and odd nonlinearities with a quintic nonlinear term. The study is performed by a new analytical method called the Hamiltonian approach (HA). It is demonstrated that the first term in series expansions is sufficient to produce an acceptable solution. Results obtained by numerical methods validate the soundness of the asymptotic procedure.

DOI: http://dx.doi.org/10.1134/S0021894415020169

#### 17.Experimental and Theoretical Studies of the Influence of a Tensile Load on the Relaxation of Residual Stresses in a Hardened Cylindrical Specimen under Creep Conditions

V. P. Radchenko1, E. P. Kocherov2, M. N. Saushkin1, V. A. Smyslov1
1Samara State Technical University, Samara, 443100 Russia
2Kuznetsov Company, Samara, 443009 Russia
Keywords: cylindrical specimen surface plastic strain, residual stress, tensile load, creep, relaxation

Abstract >>
This paper presents an experimental and theoretical study of the influence of a tensile load on the relaxation of residual stresses in a hardened cylindrical specimen of ZhS6KP alloy under creep conditions at 800 oC. An experimental study was conducted to investigate the distribution of the axial residual stress tensor component across the thickness of the hardened layer after hardening by air shot blasting using microbeads and after creep loading for 50 and 200 h under a tensile load of 150 and 250 MPa. A detailed theoretical analysis of the problem was performed. In all loading regimes, the calculated and experimental values of the residual stresses were found to be in good agreement. It was shown that at low tensile load, the relaxation rate decreased in comparison with the case of thermal exposure in the absence of a tensile load and, with increasing load intensity, it increased.

DOI: http://dx.doi.org/10.1134/S0021894415020170

#### 18.Choosing an Optimal Shape of thin Rigid Inclusions in Elastic Bodies

V. V. Shcherbakov1,2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: thin rigid inclusion, crack, nonlinear boundary conditions, variational inequality, optimal control

Abstract >>
The optimal control problem for a three-dimensional elastic body containing a thin rigid inclusion as a surface is studied. It is assumed that the inclusion delaminates, which is why there is a crack between the elastic domain and the inclusion. The boundary conditions on the crack faces that exclude mutual penetration of the points of the body and inclusion are considered. The cost functional that characterizes the deviation of the surface force vector from the function prescribed on the external boundary is used; in this case, the inclusion shape is considered as a control function. It is proven that a solution of the described problem exists.

DOI: http://dx.doi.org/10.1134/S0021894415020182

#### 19.Determination of Parameters of the Johnsonâ€“Cook Model for the Description of Deformation and Fracture of Titanium Alloys

A. E. Buzyurkin1, I. L. Gladky2, E. I. Kraus1
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, 630090 Novosibirsk, Russia
2Open Joint-Stock Company ”Aviadvigatel”, Perm', 614990 Russia
Keywords: deformation, fracture, strain rate, Johnsonâ€“Cook model

Abstract >>
Stress-strain curves of dynamic loading of VT6, OT4, and OT4-0 titanium-based alloys are constructed on the basis of experimental data, and the Johnson-Cook model parameters are determined. Results of LS-DYNA simulations of the processes of deformation and fracture of the fan casing after its high-velocity impact with a fan blade simulator are presented.

DOI: http://dx.doi.org/10.1134/S0021894415020194

#### 20.Vibrations in an Elastic Beam with Nonlinear Supports at Both Ends

Yi-Ren Wang, Zhi-Wei Fang
Department of Aerospace Engineering, Tamkang University, NewTaipei City, Tamsui Dist., 25137 Taiwan
Keywords: vibration, nonlinear boundary conditions, elastic beam

Abstract >>
Vibrations in an elastic beam supported by nonlinear supports at both ends under the influence of harmonic forces are analyzed in this study. It is hypothesized that the elastic Bernoulli-Euler beam is supported by cubic springs to simulate nonlinear boundary conditions. The dynamic behavior of the beam is described by using the Fourier expansion and the Bessel functions. The Hankel transform is then applied to obtain particular (nonhomogeneous) solutions. This study succeeds in describing the ``jump" phenomenon (instantaneous transition of the system from one position to another) of the vibrating system at certain frequencies. Models based on linear boundary conditions are unable to capture this phenomenon. A larger modulus of elasticity in nonlinear supports increases the frequency of unstable vibrations in the first mode and also widens the frequency region of system instability. This influence is less prominent in the second mode, in which the largest amplitude is smaller than those observed in the first mode.

DOI: http://dx.doi.org/10.1134/S0021894415020200