Calculation algorithm and software for pipeline vibrations with consideration of internal flow

This paper discusses the development of calculation complex (model, algorithm and software) needed to investigate vibration parameters (amplitudes of displacements, internal forces and support responses) of a constant cross-section pipeline with a perfect incompressible fluid flowing inside it. This paper presents a pipeline model as quasi-monomeric finite-element system. Presently, the study discusses vibration of a straight constant cross-section pipeline resting on two elastic supports. Calculation algorithm is based on the discrete variant of partial-response method. The effect of fluid flow is taken into account as an additional inertial load incorporated, in its turn, by means of corrections and modifications of inertia & stiffness parameters of pipeline model. The study gives calculation expressions for partial responses and partial parameters, needed to implement the algorithm suggested by the authors. The problem formulated in this paper was solved as per specially developed mathematical model taking into account the forces due to the flow in the pipe. The paper also suggests calculation algorithm for vibration parameters of the adopted model. These vibration parameters were obtained in specially developed Koriolis software. The study also investigated the effect of additional inertial load components upon vibration parameters and natural frequencies of the structure at question. All these activities made it possible to accomplish the task of the whole study, i.e. to develop the calculation complex for determination of pipeline vibration parameters.

Deformation of cylindrical cavities in plane-parallel potential flows with circulation and under the action of mass forces

Рассматриваются задачи формирования кумулятивных струй в плоскопараллельных потенциальных течениях идеальной несжимаемой жидкости внутри цилиндрических полостей. На основе метода граничных элементов строится численный алгоритм решения. При аппроксимации используются квадратурные формулы без насыщения. Новизна работы заключается в исследовании потенциальных течений с ненулевой циркуляцией и выводе аналога закона сохранения импульса для таких течений. Кроме того, рассматривается задача всплытия полости в тяжелой жидкости. The problems of cumulative jet formation in plane-parallel potential flows of a perfect incompressible fluid within cylindrical cavities are considered. A new numerical algorithm is proposed on the basis of the boundary element method. The approximation is based on quadrature formulas without saturation. The novelty of this paper is to study the potential flows with nonzero circulation and to derive an analog of the momentum conservation law for such flows. The process of the cavity rise in a heavy fluid is also studied.

Invariant solutions and shock atmospheric waves in a thin circular layer

The objective of this paper is to investigate the nonlinear mathematical model describing equatorial waves from Lie group analysis point of view in order to understand the nature of shallow water model theory, which is associated to planetary equatorial waves. Such waves correspond to the Cauchy–Poisson free boundary problem on the nonstationary motion of a perfect incompressible fluid circulating around a solid circle of a large radius.

STOCHASTIC PROCESSES ON GROUPS OF DIFFEOMORPHISMS AND VISCOUS HYDRODYNAMICS

The viscous hydrodynamics is investigated via the studying diffusion processes on groups of Hs Sobolev diffeomorphisms of a flat n-dimensional torus (s > ½n + 1). A certain stochastic perturbation of the curve on the above groups, describing the motion of perfect incompressible fluid (or of the diffuse matter), is constructed such that it satisfies a certain stochastic analogue of the geodesic equation and the expectation of its "backward velocity" in the tangent space at identical diffeomorphism (algebra of the group) is a solution of Navier–Stokes (or Burgers, respectively) equations. In particular, the existence of solutions of those equations for lower s is proved. Some other approaches to stochastic presentation of viscous hydrodynamics, using the groups of diffeomorphisms, are also discussed.