翼型空化绕流数值研究

空化是发生在流体机械上的复杂过程，理论研究遇到很大困难。本文引入合适的空化数值模型，将空腔界面近似为自由面，用界面构造精度较高的流体体积方法求解空腔位置，通过直接求解原始变量的NavuerStokes方程，数值模拟了无界域中空化在翼型上发生、发展和脱落的周期过程；并分析了空化产生对翼型表面的压力分布、翼型收到的阻力和升力的影响。结果表明，空化出现在翼型上表面；由于空化的产生，翼型表面压力分布不稳定，导致升力、阻力和流场压力出现波动，这是实际中产生噪声和损失的主要原因。     

Calculation of the characteristics of a gas-dynamic laser

The dependence of the radiated power on the characteristics of optical cavities in the case of flow systems has been investigated in a number of papers [1–3], in which it is assumed that population inversion of the laser levels is obtained until entry into the cavity. The operation of a cavity is analyzed in [1] in the geometric-optical approximation with allowance for vibrational relaxation in the gas flow. A simplified system of relaxation equations is solved under steady-state lasing conditions and an expression derived for the laser output power on the assumption of constant temperature, density, and flow speed. The vibrational relaxation processes in the cavity itself are ignored in [2, 3]. It is shown in those studies that the solution has a singularity at the cavity input within the context of the model used. In the present article the performance characteristics of a CO₂-N₂-He gas-dynamic laser with a plane cavity are calculated. A set of equations describing the processes in the cavity is analyzed and solved numerically. Population inversion of the CO₂ laser levels is created by pre-expansion of the given mixture through a flat hyperbolic nozzle. The dependence of the output power on the reflectivities of the mirrors, the cavity length, the pressure, and the composition of the active gas medium is determined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi FiziM, No. 5, pp. 33–40, September–October, 1972.     

Dynamics of a flat cavity in a low-viscosity liquid

The problem of the motion of a cavity in a plane-parallel flow of an ideal liquid, taking account of surface tension, was first discussed in [1], in which an exact equation was obtained describing the equilibrium form of the cavity. In [2] an analysis was made of this equation, and, in a particular case, the existence of an analytical solution was demonstrated. Articles [3, 4] give the results of numerical solutions. In the present article, the cavity is defined by an infinite set of generalized coordinates, and Lagrange equations determining the dynamics of the cavity are given in explicit form. The problem discussed in [1–4] is reduced to the problem of seeking a minimum of a function of an infinite number of variables. The explicit form of this function is found. In distinction from [1–4], on the basis of the Lagrauge equations, a study is also made of the unsteady-state motion of the cavity. The dynamic equations are generalized for the case of a cavity moving in a heavy viscous liquid with surface tension at large Reynolds numbers. Under these circumstances, the steady-state motion of the cavity is determined from an infinite system of algebraic equations written in explicit form. An exact solution of the dynamic equations is obtained for an elliptical cavity in the case of an ideal liquid. An approximation of the cavity by an ellipse is used to find the approximate analytical dependence of the Weber number on the deformation, and a comparison is made with numerical calculations [3, 4]. The problem of the motion of an elliptical cavity is considered in a manner analogous to the problem of an ellipsoidal cavity for an axisymmetric flow [5, 6]. In distinction from [6], the equilibrium form of a flat cavity in a heavy viscous liquid becomes unstable if the ratio of the axes of the cavity is greater than 2.06.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 15–23, September–October, 1973.The author thanks G. Yu. Stepanov for his useful observations.     

Plane-parallel flow around a gas cavity

The stationary motion of a gas cavity in an ideal incompressible fluid is studied taking account of surface tension by using a variational equation. Approximate analytical dependences of the dimensionless parameters on the degree of cavity deformation are obtained. It is shown that the variational equation admits of an exact analytical solution. The stability of motion corresponding to the exact solution is proved relative to arbitrary perturbations in the cavity shape. A solution is given for the problem of stationary motion of an elliptical cavity in a gravity viscous fluid and the stability problem is investigated. Dependences are found for the velocity of cavity rise, the Reynolds number, and the Froude number as a function of the cavity size.     

Dynamics of a Fluid in a Rotating Horizontal Cylinder

The behavior of a low-viscosity fluid in a rotating horizontal circular cylinder is investigated experimentally. The stability of the centrifuged layer, the motion of the fluid with respect to the cavity, the excitation of inertial waves on the fluid surface, and the effect of the waves on the stability and flow structure are studied over a wide region of relative occupancy of the cavity. The results are analyzed from the viewpoint of vibrational mechanics in which the motion is generated by the oscillations of the fluid with respect to the cavity and the gravity force plays the role of the force oscillating in the cavity reference system.     

Modeling the effect of diffusion of the ambient medium on the long-term strength of a hollow cylinder under uniaxial tension

The problem of the long-term strength of an extended thick-walled tube containing a corrosive medium in the internal cavity is solved. The diffusion of this medium into the tube material is analyzed. The diffusion equation is solved approximately by introducing the diffusion front, and the error of the solution is estimated. The dependence of the time of fracture of the tube on the variable tensile stress and the concentration of the medium filling the cavity is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 88–93, July–August, 2007.     

Collapse of a cylindrical cavity in a fluid layer under impact

The case of impact on a thin annular fluid layer with a gas-filled cavity is considered. The solution of the problem reduces to integrating a system of two first-order ordinary differential equations. The equations are analyzed qualitatively, and some exact solutions are found. Cases are noted of pulsation of the cavity, and the influence of counter-pressure and viscosity is investigated. The experimental results obtained are in agreement with the numerical computations carried out herein.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 98–106, November–December, 1970.The authors are grateful to A. M. Kogan and L. V. Mostovaya for performing the computations.     

Potential flow model of cavitation-induced interfacial fracture in a confined ductile layer

Fracture of a thin ductile layer sandwiched between stiff substrates often results from growth and coalescence of microscopic cavities ahead of an extending crack. Cavitation induced by plastic flow in a confined, ductile layer is analyzed here to evaluate the interfacial fracture toughness of such sandwich structures. For rigid-plastic materials, a new method is proposed in which the potential flow field of a fluid is used to approximate the plastic deformation. The principle of virtual work rate is applied to determine the equivalent traction-separation law. The method is demonstrated and validated for spherically symmetric cavity growth, for which an exact solution exists. We then study in detail the growth of an initially spherical cavity in a cylindrical bar of finite length subject to uniform traction at its ends. The results show that the stress-separation curves depend strongly on initial cavity size and the strain-hardening exponent, and weakly on the nominal strain. The method has clear advantages over numerical methods, such as finite-element analysis, for parametric study of cavity growth with large plastic deformation.     

Dynamic stress of a circular cavity buried in a semi-infinite functionally graded piezoelectric material subjected to shear waves

The paper presents a theoretical method to investigate the multiple scattering of shear waves and dynamic stress around a circular cavity in a semi-infinite functionally graded piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary condition of the semi-infinite structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the buried depth of the cavity, the incident wave number and the nonhomogeneous parameter of materials on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of intermediate frequency and the effect increases with increasing wave number. When the nonhomogeneous parameter of materials is less than zero, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of the dynamic stress around the cavity. When the nonhomogeneous parameter of materials is greater than zero, it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.     

月牙形空腔结构金属靶的抗弹性能分析

为提高金属靶的抗弹性能,设计了一种含有月牙形空腔结构的金属靶。利用ABAQUS软件对月牙形空腔结构在12.7 mm穿甲燃烧弹弹芯侵彻下的弹体偏转性能进行了数值模拟研究,讨论了月牙形状、弹着点和空间排布对弹体偏转效果的影响。结果表明:月牙形状对弹体的偏转效果有显著的影响;空腔结构在不同弹着点表现出不同的弹体偏转性能,处于空腔胞元最薄弱处附近的弹着点弹体偏转角度明显小于其他位置;空腔胞元空间排布的非对称化处理能够提升空腔结构对子弹的偏转效果。     

Nature of the state of the medium in the neighborhood of a cavity expanding into a dilating medium

Substantial changes in the state of a solid medium can occur under the expansion of a gas cavity therein. In particular, rupture of the brittle rock occurs. The nature of the motion of the ruptured rock differs substantially from the nature of the motion of the unruptured medium. Thus, a change in the density of the ruptured rock occurs under shear strains. This phenomenon is usually called dilatancy [1]. In addition, the strength characteristics also change under rupture of the rock. The stress state of a medium in the neighborhood of an expanding cavity at the time of cessation is analyzed in this paper. The influence of the ruptured rock characteristics on the magnitude of the residual stress is investigated. The radius of the rupture zone is determined and its dependence on the characteristics of the medium is investigated. The volume of the threshold space in the neighborhood of the cavity being formed because of dilatancy is calculated. The nature of the stress state in elastic-plastic media which do not dilate under plastic flow is also investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 143–152, May–June, 1979.     

Multiple scattering of electro-elastic waves from a buried cavity in a functionally graded piezoelectric material layer

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and the dynamic stress around a buried cavity in a functionally graded piezoelectric material layer bonded to a homogeneous piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the cavity. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the position of the cavity in the layer, the incident wave number and the material properties on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of higher frequencies, and the effect increases with the decrease of the thickness of FGPM layer. If the material properties of the homogeneous piezoelectric material are greater than those at the surface of the structure, the dynamic stress resulting from the piezoelectric property is greater. The effect material properties at the two boundaries of FGPM layer on the distribution of dynamic stress around the cavity is also examined.     

Stokes waves on a cavity surface in a rotating fluid

The axisymmetric flow of an inviscid incompressible fluid rotating about a cavity with constant pressure is considered. Due to the centrifugal force, on the cavity surface waves may exist, in particular, waves with a break in the wave base where the cavity meridional sections form the angle 2/3, i.e. Stokes waves. A method of finding these waves from the boundary-value problem for the fluid velocity potential is described. For an infinite cavity, the dependence of the wave parameters on the cavitation number, calculated using the pressure in the cavity, is given.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 105–110, November–December, 1996.     

Numerical heat transfer in a cavity with a solar control coating deposited to a vertical semitransparent wall

A transient two‐dimensional computational model of combined natural convection, conduction, and radiation in a cavity with an aspect ratio of one, containing air as a laminar and non‐participating fluid, is presented. The cavity has two opaque adiabatic horizontal walls, one opaque isothermal vertical wall, and an opposite semitransparent wall, which consists of a 6‐mm glass sheet with a solar control coating of SnS–Cu_xS facing the cavity. The semitransparent wall also exchanges heat by convection and radiation from its external surface to the surroundings and allows solar radiation pass through into the interior of the cavity. The momentum and energy equations in the transient state were solved by finite differences using the alternating direction implicit (ADI) technique. The transient conduction equation and the radiative energy flux boundary conditions are coupled to these equations. The results in this paper are limited to the following conditions: 10⁴≤Gr≤10⁶, an isothermal vertical cold wall of 21°C, outside air temperatures in the range 30°C≤T₀≤40°C and incident solar radiation of AM2 (750 W m⁻²) normal to the semitransparent wall. The model allows calculation of the redistribution of the absorbed component of solar radiation to the inside and outside of the cavity. The influences of the time step and mesh size were considered. Using arguments of energy balance in the cavity, it was found that the percentage difference was less than 4 per cent, showing a possible total numerical error less than this number. For Gr=10⁶ a wave appeared in the upper side of the cavity, suggesting the influence of the boundary walls over the air flow inside the cavity. A Nusselt number correlation as a function of the Rayleigh number is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Creeping flow of viscoplastic materials through a planar expansion followed by a contraction

In this work, the creeping flow of a viscoplastic fluid through a planar channel with an expansion followed by a contraction is analyzed numerically. The solution of the conservation equations of mass and momentum is obtained via the finite volume method. In order to model the non-Newtonian behavior of the fluid, it was used the generalized Newtonian fluid constitutive equation. The viscosity function was the one proposed by Souza Mendes and Dutra [Souza Mendes, P.R., Dutra, E.S.S., 2004. Viscosity function for yield-stress liquids. Appl. Rheol. 14, 296–302]. The yielded and unyielded regions are obtained for several combinations of rheological parameters. The influence of these parameters on pressure drop through the cavity is also obtained and analyzed.     

Identification of a cavity in an elastic rod in the analysis of transverse vibrations

The direct and inverse problems of the steady-state transverse vibrations of a cylindrical rod with a defect in the form of a cavity of small relative size are considered. An approach to determining the location and volume of the cavity of arbitrary shape is proposed. Results of computational experiments are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 152–158, November–December, 2008     

Small oscillations of a liquid in a partitioned cylindrical vessel

The equations of motion of a rigid body whose cavity is partially filled with an ideal fluid have been obtained in works of Moiseev [1, 2, 3], Okhotsimskii [4], Narimanov [5], and Rabinovich [6]. All the equation coefficients have been calculated for a cavity in the form of a circular cylinder or two concentric cylinders.The problem of fluid motion in a partitioned cylindrical cavity was considered by Rabinovich [7]. It was also considered by Bauer [8], who analyzed the particular case of vessel motion in the plane of one of the partitions.In the following we consider the two-dimensional motion of a cylinder with radial and annular baffles, and a definition is given of the velocity potential in the case of arbitrary positioning of the radial baffles with respect to the motion plane. Formulas are obtained for determining the parameters of a mechanical analog of the wave oscillations, which consists of two mathematical pendulum subsystems.     

Analysis of Momentum Transfer in a Lid-Driven Cavity Containing a Brinkman–Forchheimer Medium

The CE/SE (the space-time conservation element and solution element method) scheme with the second-order accuracy has been proposed. And the pretreatment method has been introduced to convert the parabolic equations to the hyperbolic equations, which are accurately solved by the CE/SE method. The lid-driven rectangular cavity containing a porous Brinkman–Forchheimer medium is studied in this numerical investigation. The Brinkman–Forchheimer equation is used such that both the inertial and viscous effects are incorporated. The governing equations are solved by the improved CE/SE approach. The characteristics of the flow are analyzed with emphasis on the influence of the Darcy number and the cavity depth. It is found that the porous medium effect decreases both the strength and the number of eddies, especially for deep cavities.     

Oscillations of a vessel containing a viscous fluid

The oscillations of a rigid body having a cavity partially filled with an ideal fluid have been studied in numerous reports, for example, [1–6]. Certain analogous problems in the case of a viscous fluid for particular shapes of the cavity were considered in [6, 7]. The general equations of motion of a rigid body having a cavity partially filled with a viscous liquid were derived in [8]. These equations were obtained for a cavity of arbitrary form under the following assumptions: 1) the body and the liquid perform small oscillations (linear approximation applicable); 2) the Reynolds number is large (viscosity is small). In the case of an ideal liquid the equations of [8] become the previously known equations of [2–6]. In the present paper, on the basis of the equations of [8], we study the free and the forced oscillations of a body with a cavity (vessel) which is partially filled with a viscous liquid. For simplicity we consider translational oscillations of a body with a liquid, since even in this case the characteristic mechanical properties of the system resulting from the viscosity of the liquid and the presence of a free surface manifest themselves.The solutions are obtained for a cavity of arbitrary shape. We then consider some specific cavity shapes.     

Shock-initiated implosion of an elliptical cavity and detonation in a liquid layer

Many papers [1–9] have been devoted to the dynamical analysis of bubble implosion in a liquid layer. Experiments have shown that an initially circular cavity is displaced or transformed into an elliptical cavity during the implosion process due to instability, whereupon its further contraction produces cumulative jets. This problem is important in the study of surface wear in cavitation flow [7] and in the analysis of the impact sensitivity of liquid explosives [1–6]. The onset of accumulation is conveniently investigated by starting with an elliptical cavity or by displacing a circular cavity relative to the impact axis, thereby creating an asymmetrical pressure field about the center of the cavity. In the present article certain theoretical notions are advanced with regard to the onset of the cumulative jet in an elliptical or displaced cavity and its influence on the ignition of liquid explosives due to the formation of minute droplets [4] in the adiabatically heated gas inside the cavity. Experimental data on the jet formation time and the frequency of nitroglycerin detonations qualitatively support the theoretical predictions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 78–85, September–October, 1971.