The expansion of salts extraction and production has created a need for new spent brine disposal methods. This task is complicated by the fact that “heavy” brines due to the suppression of vertical turbulent pulsations can spread over considerable distances without a significant reduction in their concentration. Based on numerical modeling, we put forward some suggestions for optimizing exhaust structures designed to discharge the wastewater containing heavy impurities. The calculations performed in the framework of a three-dimensional statement for various conditions of discharge of wastewater show that the structures which provide for the location of exhaust devices near the surface of the reservoir turned out to be the most effective ones. However, such structures are difficult to implement in a certain reservoir section. Easy-to-implement and at the same time quite effective is a scheme that includes bottom arrangement of exhaust devices and selective intake of highly saline wastewater from sludge storage facilities. Regardless of the selected scheme for the disposal of highly mineralized wastewater, their discharge must be carried out in strict coordination with the hydrological regime of the water intake. This will provide the most efficient use of the assimilative capacity of a water body and the best way to reduce environmental stress.

Technology for producing parts from composite materials with a thermoplastic binder differs from traditional manufacturing methods which use thermosetting resins and therefore it requires new design and technological solutions. The approach proposed in this paper involves coating carbon filaments with a layer of thermoplastic melt at the prepreg preparation stage to ensure its more uniform distribution and deeper impregnation at the product molding stage. To describe the rheological properties of a polyether ether ketone melt (PEEK), a generalized Carreau model was applied and its material constants were determined. Based on the finite element method, a numerical model of the process of applying a layer of thermoplastic on a carbon filament in an axisymmetric die was constructed. The velocity, pressure and temperature fields are calculated, and the effect of applied pressure and core drawing speed on the applied layer thickness is determined. The required layer thickness is determined from an equality of the cross-sectional areas of the applied layers and the total area of voids between the filaments and between the carbon fibers. The dependence of the resulting thickness of the applied layer on the filament drawing speed and inlet pressure is determined. Based on the analytical solution of the flat-radial filtration problem, a dimensionless equation is obtained for determining the front of impregnation of a porous carbon fiber under external pressure linearly distributed along the die channel. The proposed mathematical model allows one to determine pressure and temperature fields, kinematics of fluid flow, to evaluate the influence of technological parameters on the thickness of the thermoplastic layer applied on the filament and to predict the degree of homogeneity of the finished product.

This chapter discusses a more general large-rotation and large-deformation finite element formulation. It also discusses the displacement field and coordinates of the finite element. The virtual work of the inertia and elastic forces of the element is used to formulate the virtual work expression of the equations of motion of the finite element. The chapter briefly reviews the basic differential geometry theories of curves and surfaces in order to help the reader better understand the modes of deformations of beams, plates, and shells. It discusses the performance of the finite elements, including topics such as the patch test; shear, membrane, and volumetric locking; and reduced and selective integrations. The chapter also reviews other large-deformation finite element formulations used in the literature and compares with the absolute nodal coordinate formulation (ANCF). It also compares the formulations of the dynamic equations obtained using the updated Lagrangian and Eulerian approaches.

At present, a significant weakening of the intensity of transverse mixing at the confluence of large rivers, which is observed in a number of cases, is widely discussed. Since the observed features of the confluence of large watercourses are not only of research interest, but also of significant economic importance associated with the characteristics of water management at these water bodies, a large number of works are devoted to their study. To explain this interesting phenomenon important from the point of view of ecology, a wide range of hypotheses is proposed, up to the negation of turbulence in rivers. One of the possible mechanisms for explaining the “suppression” of transversal mixing can be the presence of transverse circulation, manifested as Prandtl’s secondary flows of second kind. The characteristic velocity of these circulation flows is very small and difficult to measure directly, but they can significantly complicate the transverse mixing of the flow. In the present work, this hypothesis is tested on the basis of computational experiments in a three-dimensional formulation, performed for the configuration modeling of the Kama river at its confluence with the Vishera river. Calculations have shown that, at sufficiently large flow rates the two waters practically do not mix in the horizontal direction throughout the depth over long distances from the confluence. The reason for the weakening of transversal mixing is the formation of a two-vortex flow in the cross section below the confluence place. The fluid motion in vortices is such that, near the free surface, the fluid moves from the banks to the middle of the river.

In this paper, the process of surfactant diffusion through the vertical interphase boundary in the system of two immiscible liquids filling a horizontal channel was studied in a two-dimensional formulation. Densities of the base liquids were initially set equal to the surfactant density. Therefore, all subsequent changes of density in the system were caused only by the effect of contraction. At the nonunifrom diffusion, the interfacial tension is the function of the local surfactant concentration, which gives rise to the Marangoni convection. Since the system contained uncontrolled surface-active impurities, the capillary flow was initiated in a threshold manner. It was shown that at the initial stage, despite the action of the gravitational force, the Marangoni convection occurred in the form of a series of periodic, paired vortices located symmetrically about the channel axis (the same as under zero gravity). As the vertical density difference increased, the number of vortex pairs reduced to a single pair. The results of numerical simulation were verified by performing a full-scale experiment, during which visualization of the flow structure and surfactant concentration fields near the interface was realized. The dynamics of the oscillatory convection mode was studied. The analysis of the results of the numerical and full scale experiments revealed their qualitative agreement. For a few values of the Marangoni and Grashof numbers, the patterns of surfactant concentration fields and stream functions were constructed in addition to the plot of variation of the stream function maximum versus time. It was found that at rather high values of the Marangoni number (Ma≥50000) the diffusion process in the system of immiscible liquids and a soluble surfactant of equal densities leads to the onset of instability even in the absence of the contraction effect.

РАВНОВЕСНЫЕ ФОРМЫ ЖИДКОСТИ НА ВНУТРЕННЕЙ ПОВЕРХНОСТИ ВРАЩАЮЩЕГОСЯ ЦИЛИНДРА И ИХ УСТОЙЧИВОСТЬО.А

ДИНАМИЧЕСКАЯ ЗАДАЧА ТЕРМОЭЛЕКТРОУПРУГОСТИДЛЯ ФУНКЦИОНАЛЬНО-ГРАДИЕНТНОГО СЛОЯ А.О.Ватульян 1,2 , С.А.Нестеров 21 Южный федеральный университет, Ростов-на-Дону, Российская Федерация 2 Южный математический институт ВНЦ РАН, Владикавказ, Российская Федерация Приведена общая постановка задачи движения неоднородного термоэлектроупругого тела.Требуется определить наведенный в результате пироэффекта потенциал, возникающий на поверхности материала из пьезокерамики класса 6 mm.В качестве примера рассмотрена задача теплового удара по функционально-градиентному слою.При этом одна плоскость слоя заземлена, а на другой, в силу пироэффекта, наводится электрический потенциал.Осуществляется обезразмеривание начально-краевой задачи термоэлектроупругости, в результате которого выделяются параметры связанности.Исключение из постановки электрического потенциала позволяет преобразовать задачу термоэлектроупругости в задачу термоупругости с модифицированными коэффициентами.После применения к полученной задаче преобразования Лапласа задача термоупругости записывается в трансформантах, а затем сводится к системе интегральных уравнений Фредгольма 2-го рода.Система интегральных уравнений решается численно методом коллокаций с использованием квадратурной формулы трапеций.Оригиналы решений находятся на основе теория вычетов.На примере однородного слоя, изготовленного из титаната бария, проведено сравнение результатов численного и аналитического решений.Изучена связь характера наведенного потенциала с наиболее распространенными на практике типами тепловой нагрузки.Выяснено, как параметр дискретизации системы интегральных уравнений Фредгольма 2-го рода и разрядность чисел, которые задаются компьютеру, отражаются на точности численного решения.Исследована зависимость наведенного потенциала от распределения неоднородности в классах степенных и экспоненциальных функций.Выяснено, что вид законов распределения неоднородности коэффициента теплопроводности и удельной теплоемкости существенно влияет на форму наведенного потенциала.Показано, что вид законов распределения неоднородности модуля упругости, плотности материала и коэффициента температурного напряжения на форме наведенного потенциала не сказывается.Установленные результаты

ФЛАТТЕР ЗАЩЕМЛЕННОЙ ОРТОТРОПНОЙ ПРЯМОУГОЛЬНОЙ ПЛАСТИНЫС.О

The problem of joint oscillations of a thin infinite cylindrical Kirchoff-Love shell is considered. The free vibrations of the system are found. The propagating waves and energy flux are analyzed. Much attention is given to the exploration of waves with negative group velocity in the neighborhood of the bifurcation point of dispersion curves. The asymptotics of dispersion curves are used in the neighborhood of the bifurcation point for this case. The interval of system parameters (the relation of lengths of circle waves and lengths of waves along cylinder to the relative thickness of the cylinder) is estimated when the negative group velocity arises. The range of frequencies and wavenumbers where this effect is observed is also estimated. The difference in the kinds of asymptotics for the regular case and the case of bifurcation is discussed. The analysis of arising effects is carried out in terms of kinematic and dynamic variables and in terms of energy flux. Relative advantages and disadvantages of these approaches are discussed. Comparison of the contributions of various mechanisms of energy transmission in the shell to the integral energy flux is performed. A special role of the rotational component in the occurrence of a subzero integrated energy flux is analyzed. The dependence of subzero energy flux and dynamic and kinematic variables on the relative thickness of the shell, the mode number and other parameters of the system is considered. The proportionality of the energy flux and its components for various modes is analyzed. The possible fields of application of the obtained effects are established.

ФЛАТТЕР ЗАЩЕМЛЕННОЙ ОРТОТРОПНОЙ ПРЯМОУГОЛЬНОЙ ПЛАСТИНЫС.О