A discontinuous shapeless particle method for the quasi-linear transport

This paper considers a new version of the discontinuous particle method, whose higher accuracy is based on the “predictor-corrector” scheme. The peculiarity of this version is a new criterion of rearranging particles at the “corrector” stage. In contrast to the previously used version with the analysis of overlapping particles, which required an assumption about their form, we use another key characteristic of particles, namely, their mass, more precisely, the assumption that in the nonlinear elastic transport not only particle masses are conserved but also the mass located between the centers of these particles. This requirement leads to the fact that changing a distance between particles in the process of their movement and conservation of mass in the space between them, lead to a change in the density of one of the particles. A new version arose in the solution of the two-dimensional transport problems. We emphasize that the discontinuity is smeared into a single particle, which indicates to a high accuracy of the method. The construction of the method for a simple nonlinear transport problem is a necessary step to simulate the complex gas dynamics problems.

Investigation of the influence of boundary conditions in the numerical solution of a vortex tube model

The applicability of various boundary conditions in the computational simulation of a Ranque–Hilsch vortex tube is investigated. A review of existing works on the effect of geometry and various thermodynamic parameters on the efficiency of the pipe is made. The substantiation of the possibility of introducing additional computational domains when moving the boundaries to study the influence of boundary conditions when modeling gas dynamics problems is given. To simulate the dynamics of a gas in a vortex tube, a mathematical model is written that includes the Navier–Stokes system of equations describing a compressible viscous fluid, which is closed by the equation of state of an ideal gas. Existing methods for calculating turbulent flows are considered. The applicability of various semi-empirical models of turbulence for modeling a vortex tube is described. The possibility of using the selected k−ε model and its description is argued. The boundary conditions characteristic of the vortex tube model are described, and the boundary conditions most combined in the simulation of gas dynamics problems are also shown. Presents a grid that takes into account the area formed by the removal of boundaries. The solution is based on the sonicFoam algorithm in the OpenFOAM package. Utilities of the postprocessor are used when preparing the model for calculations on a high-performance cluster and utilities for averaging the obtained physical quantities. The simulation results for different combinations of boundary conditions and models with remote boundaries are given. Comparison of the results obtained. It is shown that the geometrical dimensions have a strong influence on the operation of the pipe; the correct choice of boundary conditions makes it possible to obtain the values of physical quantities that are closest to the known experimental ones. Moving the boundaries away from direct exits provides an opportunity to more accurately estimate the effects that arise near the real boundaries of the vortex tube, especially affecting the magnitude of the Ranque–Hilsch effect.

Visualization of numerical results obtained for gas-particle flows using Lagrangian approaches to the dispersed phase description

Рассматриваются вопросы, связанные с визуализацией течений, содержащих твердые частицы или жидкие капли, в различных практических приложениях. Приводятся примеры визуального представления решений ряда задач двухфазной газовой динамики, связанных с расчетами течений в каналах и вихревых структурах и полученных при помощи лагранжевых подходов. Помимо традиционных подходов к визуализации вихревых течений с частицами и каплями, основанных на построении линий уровня различных характеристик потока, фазовых траекторий и распределений концентрации дискретных включений, применяются сечения Пуанкаре и метод локальных показателей Ляпунова, а также различные критерии идентификации вихревых образований в поле течения. Обсуждается дисперсия частиц в турбулентном потоке и формирование областей с повышенным содержанием дисперсной фазы. В логическом отношении лагранжевый подход к описанию двухфазных течений является простым, но в вычислительном отношении достаточно трудоемким, поскольку для имитации движения примеси требуется проведение большого числа траекторных расчетов пробных частиц. Дополнительные вычислительные трудности связаны с необходимостью локализации частиц в контрольных объемах неструктурированной сетки и восполнением параметров несущего потока. Some issues related to the implementation and physical and mathematical support of computational experiments on the investigation of fluid and gas flows containing Lagrangian coherent vortex structures are considered. Methods and tools designed to visualize vortical flows arising in various practical applications are discussed. Examples of visual representation of solutions of gas dynamics problems computed with Lagrangian approaches to the description of flows of fluid and gas are provided. In addition to traditional approaches to the visualization of vortex flows based on the construction of contours of various flow quantities, the phase trajectories of Lagrangian particles, the Poincare section, and the local Lyapunov exponent method are applied. The Lagrangian approach to the description of two-phase flows is relatively simple, but time-consuming from the computational point of view, because it requires a large number of trajectory calculations of sample particles. Additional computational difficulties come from the need of localization of particles in the control volumes of unstructured mesh and interpolation of flow quantities of gas phase.