New Two-Fluid Turbulence Model Based Numerical Simulation of Flow in a Flat Suddenly Expanding Channel

The purpose of the research was to numerically study the structure of the flow in a flat channel in the zone of its sudden step-like expansion. The results of the study are given in the paper. The calculations are carried out with the use of a new two-fluid turbulence model and are based on the numerical solution of a system of nonstationary equations. The profiles of axial velocity and turbulent stress in various sections of the channel before and after the step were obtained, as well as the dependence of the friction coefficient for the lower wall of the channel on the distance after the step. For the difference approximation of the initial equations, the control volume approach was applied; the relationship between the velocities and pressure was found using the SIMPLEC procedure. Meanwhile, the viscosity terms were approximated by the central difference, and for the convective terms the QUICK second-order accuracy scheme was used. To confirm the correctness of the numerical results, we compared them with the experimental data taken from the NASA database for the Reynolds number Re = 36,000. The results obtained using the SA and SST models are also given in the paper. Despite the coarse grid used for numerical calculations, the results based on the new two-fluid turbulence model are not less accurate than the results determined by the RANS models for predicting separated flows in the flat channel in the zone of its sudden backward-facing step expansion

Shaping the Combustion Chamber of a Piston Engine with Direct Injection of Gasoline

The object of the study was a six-cylinder in-line engine for land transport system with direct gasoline supply and forced ignition. The problem of shaping the combustion chamber is solved using the numerical control volumes method in a three-dimensional formulation. Nonstationary equations of energy, motion, diffusion and continuity in the Reynolds form, supplemented by the k-ζ-f model of turbulence, are used as a basis for modelling the engine operation. To model fuel combustion, an extended coherent flame model (ECFM) was used. Calculations were performed using the AVL FIRE software. The processes of mixture formation were optimized by considering the current lines and velocity fields of a moving charge, taking into account the geometry of the combustion chamber and intake and exhaust ports. As a result, the efficiency of the engine increased and the combustion process became more stable in the part load modes employing different fuel supply laws.

On some properties of the projection operator for a class of stabilization algorithms

Теоретически и численно исследуется оператор проектирования $Q[a]$, действующий из линейного пространства функций $a(x) \in \span \{\sin ix , \, i \ge 1\}$, заданных на отрезке $[0,\pi]$, на подпространство функций вида $\tilde a(x) \in \span \{\sin ix , \, i > i_0\}$. Соответствующая проекция выполняется вдоль подпространства $l(x) \in \span \left\{\,\psin ix , \, i=1,\ldots, i_0\right\}$, где $\psin ix = \chi_\delta(x) \sin i x$, $\chi_{\delta}(x)$ --- характеристическая функция интервала $[0,\delta)$. Полученные результаты применяются при решении задач стабилизации по начальным данным решений модельных нестационарных уравнений. The projection operator $Q[a]$ acting from the linear space of the functions $a (x) \in \span \{\sin i x,\; i \ge 1\}$ given on the segment $[0,\pi]$ onto the subspace of the functions $\tilde a(x) \in \span \{\sin i x,\; i > i_0\}$ is studied theoretically and numerically. The corresponding projection is performed along the subspace of the functions $l(x) \in \span \{{ \overline{\rm\, sin\, }} i x , \; i=1,\ldots, i_0\}$, where ${ \overline{\rm\, sin\, }} i x = \chi_\delta (x) \sin i x$ is the characteristic function $\chi_{\delta} (x)$ of the interval $[0,\delta)$. The obtained results are used to solve the problem of stabilization with respect to the initial data of solutions to the model nonstationary equations.

INVARIANT DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS WITH TRANSFORMATIONS OF INDEPENDENT VARIABLES

In this paper, invariant difference schemes for nonstationary equations under independent variables transformation constructed and investigated. Under invariance of difference scheme we mean its ability to preserve basic properties (stability, approximation, convergency, etc.) in various coordinate systems. Difference schemes of the second-order approximation that satisfy the invariance property are constructed for equations of parabolic type. Stability and convergency investigation of correspondent difference problems are carried out; a priori estimates in various grid norms are obtained.