Two-dimensional nonstationary gas dissipation into a vacuum from a plane or axisymmetric channel

The nonstationary escape of an ideal polytropic gas from a plane or axisymmetric channel is investigated. It is hence assumed that the gas is initially at rest, and the diaphragm separating it from the vacuum can be at any section of the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–83, January–February, 1976.     

高压气体驱动二级轻气炮发射过程的数值模拟方法及应用

二级轻气炮是一种常见的超高速发射装置,多年来其数值研究大多采用简化一维模型,鲜有三维有限元模型。以14 mm口径高压气体驱动二级轻气炮为研究对象,采用耦合欧拉-拉格朗日（coupled Eulerian-Lagrangian, CEL）算法,根据膜片破裂与否,将二级轻气炮模型解耦为2个分级三维数值模型。为确定实验难以测得的参数（材料摩擦因数和膜片破膜压力）,设计正交试验,拟合确定活塞与泵管间摩擦因数为0.82,弹丸与发射管摩擦因数为0.30和膜片破膜压力为11.73 MPa。正交结果表明,摩擦因数对计算结果影响较大,在高压气体驱动二级轻气炮的计算中不应忽略。通过上述方法建立数字化高压气体驱动二级轻气炮,完整复现气炮发射过程,计算的弹丸终速与实验结果吻合度高。选取验证工况详细分析了气炮发射过程内流场变化,并呈现关键时刻的压力云图。该气炮简化方法、分级思想和关键参数确认方法可推广应用于固体发射药驱动、爆轰驱动等其他驱动形式的二级/多级轻气炮。

     

On the shape of a slender axisymmetric nonstationary cavity

Very few studies have been made of three-dimensional nonstationary cavitation flows. In [1, 2], differential equations were obtained for the shape of a nonstationary cavity by means of a method of sources and sinks distributed along the axis of thin axisymmetric body and the cavity. In the integro-differential equation obtained in the present paper, allowance is made for a number of additional terms, and this makes it possible to dispense with the requirement ¦ In ¦ 1 adopted in [1, 2]. The obtained equation is valid under the weaker restriction 1. In [3], the problem of determining the cavity shape is reduced to a system of integral equations. Examples of calculation of the cavity shape in accordance with the non-stationary equations of [1–3] are unknown. In [4], an equation is obtained for the shape of a thin axisymmetric nonstationary cavity on the basis of a semiempirical approach. In the present paper, an integro-differential equation for the shape of a thin axisymmetric nonstationary cavity is obtained to order ² ( is a small constant parameter which has the order of the transverse-to-longitudinal dimension ratio of the system consisting of the cavity-forming body, the cavity, and the closing body). A boundary-value problem is formulated and an analytic solution to the corresponding differential equation is obtained in the first approximation (to terms of order ² In ), A number of concrete examples is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 38–47, July–August, 1980.I thank V. P. Karlikov and Yu. L. Yakimov for interesting discussions of the work.     

Spatial distribution of the gas phase in an axisymmetric submerged impact jet

Experimental data on the spatial distribution of the gas phase in an axisymmetric impact jet are obtained by the particle image velocimetry/laser-induced fluorescence (PIV/LIF) method. It is shown that the distribution of bubbles in the flow is determined by the dynamics of vortex structures. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 33–38, July–August, 2009.     

Forced nonstationary axisymmetric vibrations of a piezoceramic thin bimorph plate

We consider a nonstationary axisymmetric problem for a thin axially polarized bimorph plate whose end surfaces are under the action of an electric potential, which is an arbitrary function of the radial coordinate and time. On the basis of Timoshenko theory, the finite integral transformation method is used to construct a new closed solution. The obtained computational relations allow one to study the stress-strain state of piezoceramic elements with continuous and split circular electrodes.     

Identification of nonstationary axisymmetric load distributed along a cylindrical shell

The paper outlines a procedure to identify the space-and time-dependent external nonstationary load acting on a closed circular cylindrical shell of medium thickness. Time-dependent deflections at several points of the shell are used as input data to solve the inverse problem. Examples of numerical identification of various nonstationary loads, including moving ones are presented. The relationship between the external load and the stress-strain state of the shell is described by the Volterra equation of the first kind. The identification problem is solved using Tikhonov's regularization method and Apartsin's h-regularization method __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 91–100, July 2008.     

Determining the limiting solutions of nonstationary axisymmetric Hele-Shaw problems

Numerical solution of the Hele-Shaw problem reduces to solution of three boundary-value problems of determining analytic functions of a complex variable in each time step: conformal mapping of the range of the parametric variable to the physical plane, the Dirichlet problems for determining the electric-field strength, and the Riemann-Hilbert problem for calculating partial time derivatives of the coordinates of points of the interelectrode space (the images of the points on the boundary of the parametric plane are fixed). Unlike in the two-dimensional problem, the electric-field strength is determined using integral transformations of an analytic function. Approximation by spline function is performed, and more accurate and steady (than the well-known ones) general solution algorithms for the nonstationary axisymmetric problems are described. Results of a numerical study of the formation of stationary and self-similar configurations are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 87–99, July–August, 2009.     

Finite-amplitude instability of axisymmetric submerged jets

The effects associated with the finite-amplitude instability of submerged jets are numerically modeled. The investigation is carried out within the framework of the Euler inviscid model using the Bubnov-Galerkin method. The stability of an axisymmetric air jet submerged in an infinite fluid volume is considered with allowance for surface tension forces. The nonlinear evolution of a large-scale sinusoidal disturbance, stable according to the linear theory, is traced. The effect of an intense small-scale surface ripple on the development of the large-scale disturbance is studied, together with the reaction of the latter on the amplitude of the small-scale ripple.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 100–107, January–February, 1990.     

Calculations of two-dimensional nonstationary flows of a viscous gas blown into a short cylindrical channel

An investigation was made of the nonstationary problem of laminar axisymmetric flow of a viscous gas in a short cylindrical channel at one end of which the gas is blown in at an increasing rate with parabolic flow-rate profile; the other end is open. The problem was solved numerically on the basis of the complete two-dimensional system of Navier-Stokes equations for an ideal gas at the characteristic numbers M = 0.2, Pr = 1, Re = 20, 200, 2000. An investigation was made into the nonlinear process of pulsed excitation of longitudinal acoustic oscillations, which for Re = 2 000 give rise to separation flows. In this case, secondary oscillatory phenomena are observed in the separated viscous shear layers. The damping of the oscillations is treated on the basis of the proposed nonlinear model of the sound absorbing end wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. I, pp. 9–17, January–February, 1979.I thank G. I. Petrov for his interest in the work and valuable comments.     

Numerical modeling of impulsive jets of a viscous heat-conducting gas

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 4, pp. 93–99, July–August, 1992.     

Numerical analysis of supersonic viscous gas flow past axisymmetric nonpointed bodies

Supersonic viscous homogeneous gas flow past axisymmetric smooth nonpointed bodies is analyzed numerically for widely varying Mach and Reynolds numbers and flow geometry. The initial equations of a viscous shock layer are solved by the stabilization method. The effect of the determining parameters on the flow character and the heat transfer distribution along the surface is analyzed. The accuracy and domain of applicability of several approximate approaches to the solution of the problem are estimated. Tomsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–117, January–February, 1999. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00298).     

Numerical solution to the problem of gas exhausting from planar and axisymmetric vessels

A study is made of a gas jet exhausting from an infinite vessel with planar or axisymmetric walls whose generator makes angles ± with the symmetry axis of the jet. The flow regime is determined by the pressure ratio _a = P_a/P_O, where P_O is the pressure in the vessel and P_a the pressure in the surrounding space.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 174–176, March–April, 1982.We thank M. E. Deich for interest in the work and helpful discussions of the results.