Forced Convection with Laminar Pulsating Counterflow in a Saturated Porous Circular Tube

An analytical solution is obtained for forced convection in a circular tube occupied by a core–sheath-layered saturated porous medium with counterflow produced by pulsating pressure gradients. The case of the constant heat-flux boundary conditions is considered, and the Brinkman model is employed for the porous medium. A perturbation approach is used to obtain analytical expressions for the velocity, temperature distribution, and transient Nusselt number for convection produced by an applied pressure gradient that fluctuates with small amplitude harmonically in time about a non-zero mean. It is shown that the fluctuating part of the Nusselt number alters in magnitude and phase as the dimensionless frequency increases. The magnitude increases from zero, goes through a peak, and then decreases to zero. The height of the peak depends on the values of various parameters. The phase (relative to that of the steady component) decreases from π/2 to − π/2 as the frequency increases.     

Simulation of transverse self-oscillations for a free circular cylinder mounted with a narrow gap in a plane channel

The experimentally observed self-oscillations of a cylinder mounted with a narrow gap in a plane channel are simulated. The added masses of the cylinder are calculated in the framework of ideal fluid theory by a generalized image method. In order to describe the self-oscillations in a real fluid, some dissipative factors and an impulsive impact force exerted on the cylinder are introduced.     

Mechanism of self-oscillations in a supersonic jet impact onto an obstacle 1. Obstacle with a spike

Results of numerical simulations and experimental investigations of self-oscillations arising in the case of impingement of an overexpanded or underexpanded jet onto an obstacle with a spike are reported. The mechanisms of the emergence and maintaining of self-oscillations for overexpanded and underexpanded jets are elucidated. It is demonstrated that self-oscillations are caused by disturbances in a supersonic jet, which induce mass transfer between the supersonic flow and the region between the shock wave and the obstacle. The feedback is ensured by acoustic waves generated by the radial jet on the obstacle. These waves propagate in the gas surrounding the jet, impinge onto the nozzle exit, and initiate disturbances of the supersonic jet parameters. In the overexpanded jet, these disturbances penetrate into the jet core, where they are amplified in oblique shock waves.     

On the mechanism of self-oscillations of a supersonic radial jet exhausting into an ambient space

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.     

Forced Convection with Laminar Pulsating Flow in a Saturated Porous Channel or Tube

A perturbation approach is used to obtain analytical expressions for the velocity, temperature distribution, and transient Nusselt number for the problem of forced convection, in a parallel-plates channel or a circular tube occupied by a saturated porous medium modeled by the Brinkman equation, produced by an applied pressure gradient that fluctuates with small amplitude harmonically in time about a non-zero mean. It is shown that the fluctuating part of this Nusselt number alters in magnitude and phase as the dimensionless frequency increases. The magnitude increases from zero, goes through a peak, and then decreases to zero. The height of the peak decreases as the modified Prandtl number increases. The phase (relative to that of the steady component) decreases from π/2 to − π/2. The height of the peak at first increases, goes through a maximum, and then decreases as the Darcy number decreases.     

Synthesis of self-oscillations

The problem of construction of self-oscillations is solved as a control synthesis for a dynamical system in the presence of additive and parametric controls. Several mathematical models of such systems are discussed; self-oscillations with maximum amplitude are taken into account in these models. The orbital stability is proved; the domain of initiation of self-oscillations is constructed.     

Mechanism of self-oscillations in a supersonic jet impact onto an obstacle. 2. Obstacle with no spike

Results of the numerical solution of the problem of impingement of an overexpanded supersonic jet onto an obstacle are reported. The mass-flow-rate mechanism of self-oscillations is revealed. This mechanism consists of periodic changes in the regimes of gas inflow and outflow from the separation region to the jet around this region. It is shown that the shock-wave structure of the impinging supersonic jet exerts a significant effect on the amplitude of self-oscillations.     

Analytical Study of Quasilinear Self-Oscillations in the Helmholtz Resonator

A quasilinear model of the self-oscillations in the Helmholtz resonator is developed. The conditions of existence, uniqueness, and stability of periodic solutions are determined using the Lyapunov-Poincaré, local integral manifold, and averaging methods. In the first approximation, the basic parameters of the self-oscillations are calculated and their qualitative features are studied. A thermodynamic interpretation of the gas self-oscillations in the resonator is given.     

Passive Stabilization Conditions for a Rectilinearly Moving Wheelset

Nonlinear stability conditions for a wheelset are established in analytical form for some design restrictions. They permits assessing the influence of the parameters of the curvilinear wheel tread on the nature of self-oscillations     

Eigensolutions to a vibroacoustic interior coupled problem with a perturbation method

In this paper, an efficient and robust numerical method is proposed to solve non-symmetric eigenvalue problems resulting from the spatial discretization with the finite element method of a vibroacoustic interior problem. The proposed method relies on a perturbation method. Finding the eigenvalues consists in determining zero values of a scalar that depends on angular frequency. Numerical tests show that the proposed method is not sensitive to poorly conditioned matrices resulting from the displacement–pressure formulation. Moreover, the computational times required with this method are lower than those needed with a classical technique such as, for example, the Arnoldi method.     

Thermomechanical Self-Excited Oscillations of Current-Carrying Conductors

This paper presents a study of the self-excitation of thermomechanical self-oscillations of a current-carrying conductor which depend on its electrical resistance, power of joule heat generation, and the heat transfer from its surface. The conditions for the occurrence of self-oscillations are determined, and numerical simulation of the excitation of oscillations is performed.     

黏弹性层合圆柱壳的临界轴压分析

基于经典屈曲理论，研究了轴向受压黏弹性复合材料层合圆柱壳的临界屈曲载荷. 利用Boltzmann线性积分型本构关系描述铺设单层的各向异性黏弹性行为. 结合解析与数值 方法，由Donnell型屈曲控制方程以及边界条件的Laplace变换导出相空间的特征方程，根 据Laplace逆变换的极值定理，获得层合圆柱壳的瞬时弹性临界载荷与持久临界载荷. 针对 多组铺设方式，通过数值算例重点分析了临界载荷随铺设角的变化特征，两种临界载荷的峰 值点差异程度与铺设方式、几何参数以及材料类型的关系，得到了一些对黏弹性层合圆柱壳 的优化设计有参考价值的结论.     

Heat Transfer and Evaporation from a Plane Surface into a Half-Space upon a Sudden Increase in Body Temperature

The one-dimensional time-dependent problem of evaporation from a plane body surface into a half-space filled by a gas (condensed phase vapor) upon a sudden increase in the body surface temperature is studied. The evaporation coefficient is the problem parameter and may take arbitrary values within the limits from zero to unity. The problem is formulated for the kinetic equation and solved by the finite-difference method. It is shown that a deviation of the evaporation coefficient from unity considerably modifies the gas phase flow pattern. However, the evaporation rate divided by the rate of evaporation into a vacuum at the given surface temperature is only weakly dependent on the evaporation coefficient.     

Ideal Gas Outflow from a Cylindrical or Spherical Source into a Vacuum

The solutions of initial and boundary value problems of the outflow of an ideal (inviscid and non-heat-conducting) gas from cylindrical and spherical sources into a vacuum are obtained. Time is measured from the moment, when the source is turned on; at this moment the source is surrounded by a vacuum. The entropy, flow rate, and the Mach number of the gas outflowing from the source are given, together with the source radius; the Mach number can be greater of or equal to unity. If the source radius is greater than zero, then the flow domain in the “radial coordinate–time” plane consists of the stationary source flow and adjoining non-self-similar centered expansion wave consisting of C^?-characteristics. The stationary flow is described by the known formulas, while the expansion wave is calculated by the method of characteristics. The calculations by this method confirm the earlier obtained laws for large values of the radial coordinate. The interface between the vacuum and the expansion wave is the straight trajectory of particles and, at the same time, a unique rectilinear C^?-characteristic. For the source of zero radius (“pointwise” source) the velocity, density, and speed of sound of the outflowing gas are infinite. The gas velocity remains infinite everywhere, while the density and speed of sound become zero for any non-zero values of the radial coordinate. For the pointwise source the problem of outflow into a vacuum is self-similar. In the plane of the “self-similar” velocity and speed of sound its solution is given by three singular points of a differential equation in these variables. At one of these points the self-similar velocity is infinite, the self-similar speed of sound is zero, and the self-similar independent variable varies from zero to infinity, with the exception of the extreme values.     

Transport diffuse interface model for simulation of solid-fluid interaction

For solid-fluid interaction, one of the phase-density equations in diffuse interface models is degenerated to a "0 = 0" equation when the volume fraction of a certain phase takes the value of zero or unity. This is because the conservative variables in phasedensity equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves,such as shear waves in fluids, are introduced by the artificial treatment. In this paper,a transport diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, a new formulation for phase densities is derived, which is unrelated to volume fractions. Consequently, the new model is able to handle zero/unity volume fractions, and nonphysical waves caused by artificial volume fractions are prevented. One-dimensional and two-dimensional numerical tests demonstrate that more accurate results can be obtained by the proposed model.     

Choice of optimal blunting radius of axisymmetric body with account for surface radiation

We consider the problem of determining the optimal blunting with respect to heat transfer of an axisymmetric body in supersonic gas flow at zero angle of attack with account for body surface radiation. Results are presented of a calculation of the optimal blunting radius of a cone with half-angle 10° for various values of the ratio of convective heat flux at the stagnation point to the radiative heat flux. It is shown that for small values of this ratio the small bluntings are optimal.     

Aeroacoustic Self-Oscillations of the Gas Near Two Plates in a Channel

Aeroacoustic self-oscillations of the gas near two thin plates arranged in a tandem manner in a rectangular channel are studied in a two-dimensional formulation. A bifurcation of natural frequencies depending on the distance between the plates is detected, and the frequency of selfoscillations is found as a function of the plate length and the distance from the channel walls. The fields of pressure and gas velocities in the examined range of oscillations are constructed.     

State-space approach to thermoelastic interactions in generalized thermoelasticity type III

The present work is attempted to formulate the state-space approach to the problems of thermoelastic interactions with energy dissipation on the basis of the theory of generalized thermoelasticity type-III, recently developed by Green and Naghdi. The formulation is then applied to solve a boundary value problem of an isotropic elastic half space with its plane boundary subjected to two different types of boundary conditions: (1) sudden increase in temperature and zero stress and (2) sudden increase in load and zero temperature change. Integral transform method is applied to obtain the solution of the problem. The short time approximated solutions for the field variables have been constructed analytically for both the cases. The problem is illustrated with the help of different graphs of numerical values of the field variables.     

Nonlinearwaves in a liquid film-gas flow system

The instability and regular nonlinear waves in the film of a heavy viscous liquid flowing along the wall of a round tube and interacting with a gas flow are investigated. The solutions for the wave film flows are numerically obtained in the regimes from free flow-down in a counter-current gas stream to cocurrent upward flow of the film and the gas at fairly large gas velocities. Continuous transition from the counter-current to the cocurrent flow via the state with a maximum amplitude of nonlinear waves and zero values of the liquid flow rate and the phase velocity is investigated. The Kapitsa-Shkadov method is used to reduce a boundary value problem to a system of evolutionary equations for the local values of the layer thickness and the liquid flow rate.     

Self-oscillation regimes of the penetration of free conical thin-walled turbulent jets through a fluid surface

Certain results of an experimental investigation of hydrodynamic effects occurring, when free thin-walled turbulent jets issuing from a conical slot nozzle with a vertical axis penetrate through the surface of a fluid in a rectangular reservoir, are presented. The ranges of the jet flow rate and the spacing between the nozzle and the free surface, on which stable regular transverse self-oscillations of the boundaries of dome-shaped jets are observable, are determined. For fixed values of the conicity angle α = 60° and the nozzle slot width δ = 0.1 cm the characteristic form of the dependence of the self-oscillation period on the jet flow rate and the spacing between the slot nozzle and the free surface (dome height) is presented. The self-oscillation regime generation mechanism, together with the possible reasons for the revealed bifurcation changeover of the oscillation mode at certain values of the governing parameters and the hysteresis effects, are discussed. The salient features of the flows occurring on the surface and within the fluid beneath the dome are described.