Описан процесс построения новой модели (бифуркационной модели турбулентности), описывающей течение сплошной среды как в ламинарном, так и турбулентном режимах. Главной ее особенностью является ламинарно-турбулентный переход, возникающий как новое решение уравнения для напряжений Рейнольдса, замыкающего систему RANS (Reynolds-averaged Navier-Stokes). Статья состоит из трех основных разделов. В первом рассказывается о схемах замыкания второго порядка уравнений Навье-Стокса, осредненных по Рейнольдсу. Во втором разделе изложен вывод уравнений модели турбулентного течения в сдвиговом слое. Третий раздел содержит описание модели турбулентного пограничного слоя на плоской пластине. Приводятся расчеты рассматриваемых течений, результаты сравниваются с экспериментальными.

In this article, we describe a new mathematical model (bifurcational turbulence model) and justify its suitability for the prediction of laminar and turbulent boundary layer characteristics. The main specific feature of the model is the laminar-turbulent transition, arising as a new solution of the equation for Reynolds stresses, closing the system of Reynolds-averaged Navier-Stokes (RANS) equations. The article is divided into three main parts. The first part describes the RANS and second-order closure conditions together with the premises that we use to obtain the model equations in the closed form. In the second part, we derive the equations of the turbulent-flow model in the shear layer. In the third part, we consider the boundary-layer turbulence transition over a flat plate and present the results of numerical simulations compared with the experimental data.

In the case of a variable period (wavelength) of a perturbed interface, the instability and stability of Richtmyer–Meshkov vortices in perfect gas and incompressible perfect fluid, respectively, are investigated numerically and analytically. Taking into account available experiments, the instability of the interface between the argon and xenon in the case of a relatively small period is modeled. An estimate of the magnitude of the critical period is given. The nonlinear (for arbitrary initial conditions) stability of the corresponding steady-state vortex flow of perfect fluid in a strip (vertical periodic channel) in the case of a fairly large period is shown.

By means of single-, double-, and three-dimensional simulation, the dynamic processes occurring at a high speed impact of two metal plates of different densities are investigated. It is shown that in the process of collision, the Rayleigh-Taylor instability is developed on the boundary of the metals, which leads to the formation of three-dimensional ring structures on the surface of the metal with a lower density. The comparative characteristic of the deformation processes on the metal boundary in the spatial case is given by the use of various equations of the state of matter.

Как альтернативное дополнение к используемым моделям, основанным на турбулентной вязкости, для течений в плоском канале с постоянным градиентом давления и сдвиговом слое с постоянным давлением рассматривается простая схема замыкания RANS (Reynolds – averaged Navier–Stokes, система уравнений Навье–Стокса, осредненная по Рейнольдсу), позволяющая производить расчеты течений при любом числе Рейнольдса, в частности в области ламинарно-турбулентного перехода. Библ. 14. Фиг. 5.

For plane channel flows with a constant pressure gradient and for constant-pressure shear layer flows, a simple closure scheme for the Reynolds-averaged Navier-Stokes equations is proposed as an alternative to eddy-viscosity-based models. The closure scheme makes it possible to compute flows at any Reynolds number, including near the laminar-turbulent transition.

The evolution of an initial perturbation in an axisymmetric subsonic normal inviscid gas flow through a pipe is directly simulated. The basic (unperturbed) flow has a zero radial velocity component, while its axial velocity component (along the axis of symmetry) increases or decreases linearly with the radius. The perturbation is specified as a swirl (rotation about the axis) with a positive or negative velocity vanishing on the central axis and the lateral surface. Irrespective of its direction, the swirl gives rise to a steady-state vortex carried by the flow. It shape is spherical (contiguous to the rotation axis) or circular (sliding along the impermeable lateral surface).

We present a linear model for the numerical simulation of antisymmetric countercurrent flow in a gas centrifuge which has high computation speeds. A model describing the mechanics and thermodynamics of a gas is proposed with an equation for the concentration of separated components. Numerical examples are presented. We conclude that this technique is capable of accurately predicting the performance of a wide variety of machines under all operating conditions of interest.

The countercurrent flow in a gas centrifuge is simulated. Mechanical and thermal methods for its excitation are discussed; thermal restructuring, the thermal control of the velocity field, and a shift in the inversion point are analyzed; and the formation of overtone flows in the rarefaction zone is studied.