20世纪的流体力学大师--冯·卡门

纪念流体力学大师冯@卡门逝世40周年.     

Spin-down of the von Karman flow

The decay of the fluid flow due to a rotating disk is analysed when the disk is stopped suddenly. The interaction of the induced Rayleigh flow and the initial von Karman flow results in the establishment of a boundary layer whose characteristics are studied in detail. Solutions representing the initial and final stages of the spin-down are supplemented by the numerical solution of the governing equations.     

Implicit symmetrized streamfunction formulations of magnetohydrodynamics

We apply the finite element method to the classic tilt instability problem of two‐dimensional, incompressible magnetohydrodynamics, using a streamfunction approach to enforce the divergence‐free conditions on the magnetic and velocity fields. We compare two formulations of the governing equations, the standard one based on streamfunctions and a hybrid formulation with velocities and magnetic field components. We use a finite element discretization on unstructured meshes and an implicit time discretization scheme. We use the PETSc library with index sets for parallelization. To solve the nonlinear problems on each time step, we compare two nonlinear Gauss‐Seidel‐type methods and Newton's method with several time‐step sizes. We use GMRES in PETSc with multigrid preconditioning to solve the linear subproblems within the nonlinear solvers. We also study the scalability of this simulation on a cluster. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of the von Karman equations by group methods

One of the systems of equations approximating the large deflection of plates consists of two coupled non-linear fourth order partial differential equations, known as the von Karman equations. The full symmetry group for the steady equations is a finitely generated Lie group with ten parameters. For the time-dependent system the full symmetry group is an infinite parameter Lie group. Several subgroups of the full group are used to generate exact solutions of the time-independent and the time-dependent systems. These include the dilatation group (similar solutions), rotation group, screw group and others. Physical implications and applications are discussed.     

Nonregular interaction of shock waves in magnetohydrodynamics

The nonregular quasisteady interaction of plane-polarized shock waves in a magnetic field is considered. Within the framework of the magnetohydrodynamic approximation, a Mach interaction pattern is proposed and investigated. This pattern contains the Mach shock wave moving between the initial shocks and connecting their branch points. Unlike the gasdynamic case, in the vicinity of both branch points the flow contains, in addition to the Mach shock, up to five waves whose qualitative structure cannot be predicted in advance. Numerical methods of solving the problem are elaborated. The numerical simulations of the phenomenon under consideration were carried out by means of a specially designed software package with the entire range of all the upstream parameters being covered. It was found that the velocity and inclination of the Mach shock depend significantly on the vector of the magnetic induction in the initial state. The wave pattern of the developing flow is a function of all the key parameters, being particularly sensitive to the inclination of the magnetic field. The values of the parameters for which catastrophic restructurings of the wave pattern occur are determined. Sudden changes in the flow and the magnetic field occur in a zone behind the colliding shock waves. The interaction of the shock waves at different angles and for different magnetic fields are analyzed in detail.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 184–198, May–June, 1993.The authors wish to thank G. G. Chernyi, A. B. Vatazhin, A. G. Kulikovskii, and G. A. Lyubimov for helpful discussions of their results.     

磁流体动力学在航空工程中的应用与展望

介绍了磁流体动力学在航空工程中的主要应用方式,主要包括:磁流体冲压组合发动机、磁流体涡轮组合发动机、燃烧室后磁流体发电、表面磁流体发电、磁流体加速风洞、磁流体推力矢量、进气道大尺寸磁流体流动控制、边界层分离流动控制、边界层转捩控制、飞行器头部热流控制等;探讨了磁流体技术在应用中存在的关键科学与技术问题,对导电流体的产生、磁流体实验设备与实验技术、多场耦合机理及数值模拟方法等进行了分析;最后对磁流体技术在航空工程上的应用与发展进行了总结与展望.     

Extension of oblique-incidence method to photo-orthotropic elasticity

With the interpretation of isochromatic and isoclinic fringes in transparent, birefringent, orthotropic composites established, efforts have been in progress to determine the-individual values of the principal stresses or strains. Several methods have recently been proposed. Some of them utilize the photoelastic results only partially and rely on numerical procedures. Others have attempted to obtain the required information based entirely on experimental data. In this paper, the classical oblique-incidence technique is applied to transversely isotropic-birefringent composites. The proposed extension is verified by applying it to the problem of an orthotropic half-plane subjected to an edge-load.     

Stability of a system of two immiscible fluids in magnetohydrodynamics

Stability is investigated with allowance for the induced magnetic field and the force of gravity. Calculations are made for specific values of the parameters corresponding to the conditions in an electrolyzer. The parameters of a feedback regulator capable of stabilizing unstable steady states in accordance with the signals from a detector that measures the deviation of some parameter from the steady-state value are found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 88–94, November–December, 1991.     

Extension of Whittaker equations to non-holonomic mechanical systems

In 1904, using the energy integral Whittaker studied the reduction of a dynamical problem to a problem with fewer degrees of freedom for the holonomic conservative systems and obtained the Whittaker equation^[1].In this article, Whittaker equations are extended to non-holonomic systems and the generalized Whittaker equations are obtained. And then these equations are transformed into Kiel-sen’s form.Finally an example is given.     

Extension of Ovsyannikov's Analytical Solutions to Transonic Flows

The solution of the equation of the velocity potential of a steady axisymmetric ideal-gas flow in the neighborhood of a given point at the axis of symmetry in the form of a double series in powers of the distance to the axis of symmetry and its logarithm is considered. Recurrent chains of equations with arbitrariness in two analytical functions of the streamwise variable are obtained for coefficients of the series. Convergence of the constructed series is proved by the method of special majorants. The theorem of existence and uniqueness of the solution of the initial-boundary problem for this nonlinear differential equation in partial derivatives with a singularity at the axis of symmetry is obtained as an analog of Kovalevskaya's and Ovsyannikov's theorems. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 14–25, November–December, 2005.