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Journal of Applied Mechanics and Technical Physics

2014 year, number 3

Experimental Study of the Laminar-Turbulent Transition on a Blunt Cone

E. A. Aleksandrova1,2, A. V. Novikov1,2, S. V. Utyuzhnikov2,3, A. V. Fedorov1,2
1Joukowski Central Aerohydrodynamic Institute, Zhukovskii, 140180 Russia
2Moscow Institute of Physics and Technology, Dolgoprudnyi, 141700 Russia
3The University of Manchester, M13 9PL Manchester, UK
Keywords: Laminar-turbulent transition, hypersonic flows, blunt cone, reverse of the laminar-turbulent transition, "blunt body paradox", experiment

Abstract >>
Results of an experimental study of the laminar-turbulent transition in a hypersonic flow around cones with different bluntness radii at a zero angle of attack, free-stream Mach number M = 6, and unit Reynolds number in the interval Re∞, 1 = 5.79 · 1065.66 107 m-1 are presented. Flow regimes in which a reverse of the laminar-turbulent transition (decrease in the length of the laminar segment with increasing bluntness radius) are studied. Heat flux distributions over the model surface are obtained with the use of temperature-sensitive paints. Lines of the beginning of the transition in the boundary layer are analyzed by using heat flux fields. The critical Reynolds number Re∞, R ≈ 1.3 105 beginning from which the laminar-turbulent transition substantially depends on uncontrolled disturbances, such as the model tip roughness, is found. In supercritical regimes, the line of the transition beginning is shifted in most cases toward the model tip (reverse of the transition). The results obtained are compared with available experimental data.

Stability of a Vertical Liquid Film with Consideration of the Marangoni Effect and Heat Exchange with the Environment

O. A. Burmistrova
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: liquid film, free surface, small perturbations, solution stability, interfacial heat transfer, thermocapillary effect

Abstract >>
The stability of a free vertical liquid film under the combined action of gravity and thermocapillary forces has been studied. An exact solution of the Navier-Stokes and thermal conductivity equations is obtained for the case of plane steady flow with constant film thickness. It is shown that if the free surfaces of the film are perfectly heat insulated, the liquid flow rate through the cross section of the layer is zero. It is found that to close the model with consideration of the heat exchange with the environment, it is necessary to specify the liquid flow rate and the derivative of the temperature with respect to the longitudinal coordinate or the flow rate and the film thickness. The stability of the solution with constant film thickness at small wave numbers is studied. A solution of the spectral problem for perturbations in the form of damped oscillations is obtained.

Vibrations of a Circular Cylinder Submerged in a Fluid with a Non-Homogeneous upper Boundary

I. V. Sturova
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: linear wave theory, submerged cylinder vibrations, non-homogeneous upper boundary, multipole expansion method, hydrodynamic load

Abstract >>
The results of solving a linear problem on steady vibrations of a horizontal cylinder submerged in a fluid, whose upper boundary is partially closed by a solid lid, whereas the rest of the surface is free, are presented. Multipole and eigenfunction expansion methods are used. Reciprocity relations are derived. The added-mass and damping coefficients and the wave amplitudes on the free fluid surface are calculated.

Nonlinear-Dispersive Shallow Water Equations on a Rotating Sphere and Conservation Laws

Z. I. Fedotova, G. S. Khakimzyanov
Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: shallow water equations on a sphere, surface waves, nonlinear dispersive equations, Boussinesq type equations, energy conservation law

Abstract >>
Nonlinear dispersive shallow water equations on a sphere are obtained without using the potential flow assumption. Boussinesq-type equations for weakly nonlinear waves over a moving bottom are derived. It is found that the total energy balance holds for all obtained nonlinear dispersive equations on a sphere.

Determination of Bottom Pressure in River Flow over an Obstacle

V. A. Shlychkov
Novosibirsk Branch of the Institute of Water and Environmental Problems, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: river watercourse, flow over obstacles, hydrodynamic equations, incompressible fluid, pressure gradient, resistance of bottom soil

Abstract >>
Free-surface flow in natural watercourses was investigated using two-dimensional incompressible fluid equations written for a longitudinal vertical plane. Within the framework of similarity theory, expanding the unknown variables in power series of given structure reduces the problem to a sequence of ordinary differential equations for which an analytical solution is obtained. The solution reproduces the spatial pattern of the flow over the bottom surface of arbitrary geometry. The results of calculation of the pressure field near an underwater pipeline are presented which can be used in the stability analysis of pipeline-bottom soil systems in the case of scouring.

Occurrence of Quasiperiodic Flows between Two Rotating Permeable Cylinders

V. V. Kolesov, M. N. Romanov
Federal University, Rostov-on-Don, 344090 Russia
Keywords: permeable cylinders, secondary steady flow, azimuthal waves, bifurcations, amplitude system, limit cycles, quasiperiodic flows

Abstract >>
This paper considers viscous incompressible fluid flows between two infinite rotating permeable concentric cylinders near the bifurcation point, which result in secondary steady flow and oscillations with azimuthal waves. Steady periodic and quasiperiodic fluid flow regimes with two, three, and four independent frequencies are obtained by methods of the theory of codimension-two bifurcations of hydrodynamic flows having cylindrical symmetry.

Falling of a Body with a Flat Elastic Bottom on a Thin Liquid Layer at a Small Angle

L. A. Tkacheva
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: impact, jet formation, nonlinear shallow water equations, separation of liquid from body, elastic plate, method of matched asymptotic expansions

Abstract >>
Nonlinear shallow water equations and the method of matched asymptotic expansions are used to solve the problem of the impact of a box-type body with a flat bottom on a thin elastic liquid layer at a small angle in the plane formulation. It is established that, at certain values of the input parameters of the problem, the liquid pressure near the body edges becomes less than atmospheric pressure, and the liquid separates from the bottom of the box. Calculations demonstrating the influence of elastic bottom and liquid separation on the body motion are performed. It is shown that the presence of an elastic bottom significantly changes the hydrodynamic pressure distribution and can cause loads higher than in the case of a rigid body.

Evolution of Deviations from the Spherical Shape of a Vapor Bubble in Supercompression

R. I. Nigmatulin1,2, A. A. Aganin3, M. A. Il'gamov4, D. Yu. Toporkov3
1Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, 117997 Russia
2Lomonosov Moscow State University, Moscow, 119991 Russia
3Institute of Mechanics and Engineering, Russian Academy of Sciences, Kazan', 420111 Russia
4Mavlyutov Institute of Mechanics, Russian Academy of Sciences, Ufa, 450054 Russia
Keywords: bubble dynamics, spherical shape stability, acoustic cavitation, bubble collapse

Abstract >>
This paper considers the evolution of small deviations of a cavitation bubble from a spherical shape during its single compression under conditions of experiments on acoustic cavitation of deuterated acetone. Vapor motion in the bubble and the surrounding liquid is defined as a superposition of the spherical component and its non-spherical perturbation. The spherical component is described taking into account the nonstationary heat conductivity of the liquid and vapor and the nonequilibrium nature of the vaporization and condensation on the interface. At the beginning of the compression process, the vapor in the bubble is considered an ideal gas with a nearly uniform pressure. In the simulation of the high-rate compression stage, realistic equations of state are used. The non-spherical component of motion is described taking into account the effect of liquid viscosity, surface tension, vapor density in the bubble, and nonuniformity of its pressure. Estimates are obtained for the amplitude of small perturbations (in the form of harmonics of degree n = 2, 3,… with the wavelength λ = 2π R/n, where R is the bubble radius) of the spherical shape of the bubble during its compression until reaching extreme values of pressure, density, and temperature. These results are of interest in the study of bubble fusion since the non-sphericity of the bubble prevents its strong compression.

Experimental Determination of the Boundaries of the Region of Existence of Anomalous Convection Flow in an Tilted Cube

A. N. Sharifulin1, A. N. Poludnitsin2
1Perm' National Research Polytechnic University, Perm', 614990 Russia
2Perm' State National Research University, Perm', 614990 Russia
Keywords: anomalous air convection, experimental study, tilted cubic cavity, bifurcation

Abstract >>
This paper presents an experimentally study of the bifurcation of steady-state air convection in a cubic cavity heated from below under controlled deviations from equilibrium heating conditions due to a slow quasisteady-state tilt of the cavity at a predetermined angle a. It is found that in the supercritical range of Rayleigh numbers Ra at a tilt of the cavity not exceeding 7°, the existence of two stable steady-state convection regimes (normal and anomalous) with circulation in opposite directions is possible. A study is made of the transformations of the temperature distribution in the middle (with respect to the planes in which heat exchangers are located) plane during transition from the anomalous flow regime to the normal regime by instantaneous rotation of the entire mass of air in the cavity around the vertical axis by an angle of 90 to 135. It is shown that this rotation occurs when the tilt of the cavity exceeds a critical value αcr (Ra), which was determined experimentally for Rayleigh numbers 0 < Ra < 25 Racr , where Racr is the critical Rayleigh number for stability of mechanical equilibrium for heating from below.

Method of Molecular Dynamics in Mechanics of Deformable Solids

S. P. Kiselev
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: method of molecular dynamics, symplectic difference schemes, energy conservation law, EAM and MEAM potentials, pressure, temperature, stress tensor, copper, molybdenum, fracture, plastic deformation

Abstract >>
The basic principles of the method of molecular dynamics are analyzed. Symplectic difference schemes for the numerical solution of molecular dynamics equations are considered. Stability is studied, and the errors in the energy conservation law, which are induced by using these schemes, are estimated. Equations of mechanics of continuous media are derived by means of averaging over the volume of an atomic system. Expressions for the stress tensor are obtained by using the virial principle and the method of averaging over the volume. The principles of construction of EAM and MEAM potentials of atomic interaction in crystals are analyzed. Two problems of fracture of copper-molybdenum composites are solved by the method of molecular dynamics.

Constructing Generalized Cesàro Formulas for Finite Plane Strains

D. V. Georgievskii
Lomonosov Moscow State University, Moscow, 119991 Russia
Keywords: kinematics, Cauchy relations, finite strain tensors, Cesàro formulas, invariant, plane strain

Abstract >>
The problem of finding the displacement vector from a system of nonlinear differential equations which includes displacement gradient components is studied. Expressions on the right side of this system for certain parameter values have the kinematic sense of Lagrange and Euler finite strain tensors. The task is to construct generalized Cesàro formulas for finite strains. The construction of the solution consists of two stages (algebraic and differential), and the second is performed for space whose dimension is greater than or equal to two. An algorithm for the inversion of the original system is proposed, and analytical constructions for the case of two-dimensional space are performed. The problem is solved at the first (algebraic) stage, i.e., an exact analytical expression for the displacement vector components is derived through the known finite strain tensor and an unknown scalar function having the kinematic sense of rotation. Necessary conditions for the existence of this relationship are formulated.

Reconstruction of Inhomogeneous Characteristics of a Transverse Inhomogeneous Layer in Antiplane Vibrations

A. O. Vatul'yan1, P. S. Uglich2
1South Federal University, Rostov-on-Don, 344006 Russia
2South Mathematical Institute of the Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, 362027 Russia
Keywords: inverse coefficient problem, layered structures

Abstract >>
Direct and inverse problems of forced antiplane vibrations of a transverse inhomogeneous elastic layer are considered. The mechanical characteristics of the layer (density and shear modulus) are considered to be functions of the transverse coordinate. A method for solving the direct problem, based on using the integral Fourier transform and solving the boundary problem by the shooting method, is proposed. The inverse problem of determining the distributions of the mechanical parameters based on the known information on the wave field on some part of the upper surface is considered. Iterative sequences of integral equations are constructed. Results of numerical experiments and recommendations on the optimal choice of the vibration frequency and the interval, on which the displacements are determined, are given.

Steady-State Creep of Bent Reinforced Metal-Composite Plates with Consideration of Their Reduced Resistance to Transverse Shear. 1. Deformation Model

A. P. Yankovskii
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: reinforced metal-composites, plates, steady-state creep, Timoshenko theory

Abstract >>
The problem of deformation of reinforced metal-composite plates is formulated in rectangular Cartesian coordinates using the second version of Timoshenko theory and taking into account the reduced transverse shear resistance of the plates under steady-state creep conditions. A similar model problem of axisymmetric bending of reinforced plates is considered in polar coordinates.

Model of Stepwise Propagation of the Tip of a Hydraulic Fracture in the Absence of Filtration

V. M. Kornev, A. G. Demeshkin
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: brittle fracture, necessary fracture criterion, hydraulic fracturing crack, stepwise propagation of the crack tip

Abstract >>
Quasi-static stepwise propagation of a hydraulic fracture in rock with a regular structure in the absence of filtration is considered. It is proposed to use a brittle fracture diagram taking into account the hydraulic fracturing fluid pressure and the confining pressure. Fracture curves describing the brittle rock fracture where the hydraulic fracturing fluid partially fills the fracture are constructed and used to predicted the possibility of stepwise propagation of hydraulic fracturing in the case where the fluid gradually flows into the fracturing crack. The regularity of the structure of the brittle rocks fracture is estimated from the results of two full-scale experiments: the critical stress intensity factor and the tensile strength limit of the rock. Experiments on pulsed loading of polymethylmethacrylate samples with stepwise crack propagation along concentric circular arcs were performed. The results of the experiments are consistent with theoretical predictions.

Nondestructive Evaluation of the Carbon Content in Steel

A. Badidi Bouda, H. Belkhelfa, W. Djerir, R. Halimi
Centre de Recherche Scientifique et Technique en Soudage et Contrôle, Chéraga, Algiers
Keywords: carbon content, steel, ultrasonic waves

Abstract >>
The aim of this work is to propose an experimental method to evaluate the steel carbon content by ultrasound. The sample is immersed in a water tank in order to analyze it under various incidences of sound waves. Longitudinal wave velocities are measured by immersion by using a 5-MHz frequency probe. Transverse wave velocities are measured in a contact mode by using a 4-MHz transverse wave transducer. The attenuation coefficients of ultrasonic longitudinal and transverse waves are deduced from three successive basic echoes through the sample. The effects of some heat treatments on ultrasonic parameters are also studied. The measurement of ultrasonic parameters in steel offers an interesting possibility of tracing the carbon content and, at the same time, provides information on the steel structure and its elasticity.

Effect of Mechanical Stresses on the Magnetic Characteristics of Pipe Steel

E. S. Gorkunov1, S. M. Zadvorkin1, A. N. Mushnikov1, S. V. Smirnov1, E. I. Yakushenko2
1Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, Ekaterinburg, 620049 Russia
2Naval Polytechnic Institute, St. Petersburg, 196604 Russia
Keywords: tension, compression, torsion, internal pressure, coercive force, residual induction, maximum magnetic permeability

Abstract >>
The effect of elastic deformation in tension (compression) torsion, internal pressure loading, and their combination on the magnetic characteristics of 09G2S pipe steel is studied. It is found that in the cases of compression, torsion, and internal pressure loading, the coercive force, residual induction, and maximum magnetic permeability are uniquely dependent on the stress. It is shown that the strength of the applied magnetic field in which the magnetostriction becomes negative decreases under the action of tensile stresses. It is found that in the case of combined tension (compression) and torsion, shear stresses weaken the effect of normal stresses on the magnetic properties. In the case of a combination of all three types of loading, increasing internal pressure leads to an increase in the coercive force and a decrease in the residual induction and maximum magnetic permeability. Measurement results were used to plot the dependence of the stress intensity on the coercive force for different values of the Lode parameter, which determines the type of stress state of the object.

Coupled Model of Coating Formation on a Cylindrical Substrate

S. A. Shanin1, A. G. Knyazeva1,2
1Tomsk Polytechnic University, Tomsk, 634004 Russia
2Institute of Strength Physics and Materials Science, Tomsk, 634021 Russia
Keywords: coating deposition, cross effects, chemical transformations, coupled model

Abstract >>
A coupled model of coating formation on the surface of a part of a cylindrical shape during deposition from the plasma is proposed. This model takes into account the phenomena of thermal diffusion, diffusive thermal conductivity, and mass transfer under the action of the stress gradient, and the formation of chemical compounds. The coating growth rate is considered to be a given function of the particle velocity and particle concentration near the surface of the growing coating. The problem is solved numerically. It is shown that diffusion cross-fluxes, diffusive thermal conductivity, and thermal diffusion during the growth process reduce the width of the transition zone between the substrate and the coating. This effect becomes most essential if the substrate has a low thermal conductivity. Accounting for stresses arising in the coating-substrate system during the deposition process changes the effective transfer coefficients and significantly affects the result of modeling the distribution of chemical elements and their compounds in the coating.