A Hybrid High-Order method for creeping flows of non-Newtonian fluids

In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for Leray-Lions scalar problems. A complete well-posedness and convergence analysis of the method is carried out under new, general assumptions on the strain rate-shear stress law, which encompass several common examples such as the power-law and Carreau-Yasuda models. Numerical examples complete the exposition.

Numerical simulation of underwater cable laying with account of non-uniform hydrostatic force at Arctic basin condition

Статья посвящена моделированию динамического равновесия установившегося движения протяженной кабельной линии с учетом действия гидродинамических сил сопротивления и неоднородной гидростатической силы. Учитывая различные условия и глубины укладки, а также требования функционального назначения и защиты от враждебных факторов морского дна, необходимо рассмотреть широкий диапазон кабелей с различными механическими характеристиками: трехжильный кабель с одиночным бронированием 2XS2YRAA, одножильный кабель с одиночным бронированием ZS-YJQ41 и одножильный кабель с двойным бронированием – аналог GASLMLTV. Целью работы является развитие цифровой технологии по моделированию укладки подводных коммуникационных и силовых кабелей, позволяющей учитывать многочисленные физико-механические явления, имеющие место при проведении реальных морских работ. Для достижения поставленной цели работы используется программная среда Matlab Math Works с использованием разработанного комплекса программ для инженерной оценки формы и натяжения провисающего участка кабеля. Научная новизна состоит в апробации модели подводной укладки кабеля, учитывающей действие неоднородной гидростатической силы. Результаты моделирования представлены в виде формы и натяжения провисающей части кабеля при различных углах схода кабеля с движущегося судна при различных механических параметрах кабелей. Практическое значение работы состоит в повышении эффективности освоения перспективных месторождений, путем определения характеристик укладки кабеля в условиях Арктического бассейна: газовое месторождение Лудловское, газоконденсатное месторождение Ленинградское, нефтяное месторождение Медынское-море. This article studies the numerical simulation of underwater steady motion of the cable line with account of hydrodynamic water resistance forces and non-uniform hydrostatic force. It is necessary to consider distinctive types of cables due to various depths, laying conditions, functional requirements and protection requirements against adverse factors of seabed. Three-core single armoured cable 2XS2YRAA, one-core single armoured cable ZS-YJQ41 and one-core double armoured cable – analogue GASLMLTV are considered in this article. The aim of the research consists in digital technology development for underwater cable laying modeling, which allows taking into account numerous physical and mechanical features. These features occur during real marine operations for communication and power cables. Programming and numeric computing platform Matlab Math Works with developed software package is chosen as the research method. Simulation results are presented in dimensionless form for cable shape and tension for engineering purposes. The novelty of the work consists in approbation of underwater cable laying analytical model considering non-uniform hydrostatic force. Simulation results are presented for underwater cable laying during reeling from spool mounted on the vessel, moving with constant speed for distinctive types of cables. The influence of the cable run-off angle on the investigated characteristics was also considered. The practical value of the research consists in increasing of efficiency of exploration of oil, gas and condensate fields by determining underwater cable laying characteristics for perspective fields. At the end of the paper, the results of estimation of the shape and tension of the cable being laid undersea were presented for several fields at Arctic basin condition: gas field Ludlovskoe, condensate field Leningradskoe and oil field Medinskoe sea.

Optimization of the trimming tilting angle of the electric tiltrotor propeller group

The paper examined the possibility of improving the energy efficient performance of an electric tiltrotor with a lift-propulsion propeller group for a steady flight mode by reducing the energy consumption of the propeller group per unit of time or per unit of the path traveled by the electric tiltrotor. This is achieved by selecting the optimal tilting angles of the electric tiltrotor total thrust vector. In the proposed approach, the trimming tilting angle of the propeller group is variable, depending on the aerodynamic characteristics of the electric tiltrotor, its propeller group. Since the propeller group is equipped with the drives for tilting them, this approach is easily implemented by the conventional facilities of the electric tiltrotor. The tilting of the total thrust vector, on the one hand, leads to an increase in the effective value of the aerodynamic lift coefficient and, on the other hand, it is accompanied by a decrease in the projection of the total thrust vector on the flight speed vector, a change in the drag and power required to create the thrust of the propeller group. This circumstance makes it necessary to solve the optimization problem in order to increase the maximum endurance and long-range capabilities in the cruise mode of the electric tiltrotor flight. The paper presents a method for calculating the optimal tilting angles of the total thrust vector based on the equations of steady motion of the electric tiltrotor in the cruise flight mode, the expression for the total power required for the rotation of the propellers of the propeller group. The analytical dependences for the optimal tilting angles of the total thrust vector are obtained depending on the ratio of the wing area to the total propeller-disk area of the propeller group and the aerodynamic quality of the electric tiltrotor.

Review on Ship Manoeuvrability Criteria and Standards

Possible reduction of the installed power on newly designed merchant ships triggered by requirements of the Energy Efficiency Design Indices (EEDI) raised concern in possible safety degradation and revived interest in manoeuvrability standards to make them capable to compensate for negative effects of underpowering. A substantial part of the present article presents a detailed analytical review of general principles laid in the foundation of consistent safety standards in the naval architecture and analysis of the existing IMO manoeuvrability criteria and standards. Possible ways of extension of the existing standards to embrace situations associated with adverse sea and wind conditions are discussed and modification of the present standards related to the directional stability is considered as one of the possible solutions. At the same time, it was found that introduction of additional standards for the ship controllability in wind is justified, and the second part of the contribution is dedicated to developing a theoretical basis useful for devising such standards. This includes obtaining a set of analytical solutions related to the steady motion in wind and analysis of wind-tunnel data which resulted in simple equations for conservative generalized envelopes for the aerodynamic forces which are especially convenient for standardizing purposes. Possible design decisions aimed at augmentation of the ship’s capacity to resist adverse environmental factors are outlined.

Optimal Stability Thresholds in Rotating Fully Anisotropic Porous Medium with LTNE

The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved. Article Highlights A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained. It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly. Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction.

Fundamentals of the Theory of Power Pulse Device

The article discusses a mathematical model of a power impulse device, which allows you to select the characteristics of the ejected liquid jet, such as the velocity at the moment of ejection, the pressure created in the nozzle of the power impulse device, etc., by changing the parameters of the device. A feature of the proposed mathematical model, which significantly distinguishes it from the previously considered models, is that the model was considered for the case of unsteady motion. This state of the medium in a power impulse device is the most characteristic, therefore the results obtained are more general. It is shown that, in contrast to the steady motion of a liquid, in the case of unsteady motion, an additional term appears, which can be defined as a head having an inertial character. It can be seen from the proposed mathematical model that the presence of an inertial head leads to the appearance of a flow deceleration effect, which, in turn, leads to an increase in the total liquid head in the direction of the flow. The pressure generated in the barrel acts against the direction of the hydraulic resistance. All of the above is applicable only for a certain moment in time or for the case when the acceleration of the fluid is constant. If the acceleration changes, then the action of the heads along the fluid flow is a function of time. This circumstance makes it possible to apply the result obtained with unsteady motion to create devices that form a high-pressure jet. A distinctive feature of the considered model is that it analyzes the behavior of the fluid in the power impulse device for two cases: 1. the volume of fluid in the barrel of the power impulse unit is greater than the volume of the nozzle; 2. the volume of fluid in the barrel is less than or equal to the volume of the nozzle. The results of the analysis showed that in the first case, the initial velocity of liquid ejection significantly exceeds this velocity in the second case. That is, it is the first case that is of practical importance.