Compensatory bellows oscillations as a corrugated shell with liquid inside

The paper deals with a relevant problem of shipbuilding, i.e. calculation of free and forced vibrations of pipeline compensatory bellows. These devices are used to reduce the vibration load caused by ship power machines. When analyzing the vibrations of the compensatory bellows, it is necessary to take into account the liquid contained in the bellows. In this work, the design model of the bellows is represented by a corrugated elastic shell as a material surface with five degrees of freedom. A variant of the classical theory of shells, built on the basis of Lagrangian mechanics, is used. The influence of the liquid is taken into account by two models. First, the liquid is considered to be ideal and incompressible and is considered through the attached mass to the shell. The shell is replaced by a cylindrical surface with a radius in the middle line of the corrugation. To account for the influence of the frequency of bellows oscillations on the attached inertia of the liquid in the calculation we also used the acoustic approximation; and derived a formula for a generalized attached mass of the ideal compressible liquid. The equations of the bellows oscillations under the periodic loading are obtained. The problem has been solved by the finite difference method. The values of natural frequencies of free vibrations are obtained for the compensatory bellows from the corrosion-resistant heat-resistant steel. It is shown that by taking account of the liquid, we significantly change the natural frequencies of the bellows. With high-frequency vibrations it is necessary to take into account the compressibility of the liquid. The problem of the forced vibrations of the bellows caused by a displacement of its end face by the harmonic law is solved. The internal forces and moments are determined, as well as occurring stresses by Mises criterion in the bellows. We found the critical value of the end face displacement at a frequency of 50 Hz, at which the bellows goes into a plastic state.

A Steady Flow of The Viscous Compressible Liquid in Vertical Pipe

In the study of the flow of gas-liquid mixture over circular vertical pipe rising from the deep zone to ground level, it is observed that, the velocity on surface of tube is much more than in the center of flow. Such a picture is seen also in the water filtration process in sands ordering from high permeability zone to lower. Same phenomena occur in transportation of the water carbon nana-tubes. In order to predict behavior of those processes in this paper, we have studied the compressible liquid flow over the circular vertical pipe ordered from the deep zone to the ground surface for some concrete inlet and outlet regimes of the pipe. The Navier-Stokes equations system as a model of study. For certain inlet and outlet regimes of the flow splitting the equation into the cross section and axes variables, the pressure and velocity distribution are found. The Lane-Emden equation arises for determining the pipe cross section velocity distribution, which is also justified by our calculations on the used model.

Application of Thermal and Cavitation Effects for Heat and Mass Transfer Process Intensification in Multicomponent Liquid Media

In this paper, the authors consider the processes of dynamic interaction between the boiling particles of the dispersed phase of the emulsion leading to the large droplet breakup. Differences in the consideration of forces that determine the breaking of non-boiling and boiling droplets have been indicated in the study. They have been determined by the possibility of using the model to define the processes of displacement, deformation, or fragmentation of the inclusion of the dispersed phase under the influence of a set of neighboring particles. The dynamics of bubbles in a compressible liquid with consideration for interfacial heat and mass transfer has also been analyzed in the paper. The effect of standard and system parameters on the intensity of cavitation processes is considered. Physical transformations during the cavitation treatment of liquid are caused not only by shock waves and radiated pressure pulses but also by extreme thermal effects. At the stage of ultimate bubble compression, vapor inside the bubble and the liquid in its vicinity transform into the supercritical fluid state. The model analyzes microflow features in the inter-bubble space and quantitatively calculates local values of the velocity and pressure fields, as well as dynamic effects.

Non-spherical nucleon clusters in the mantle of a neutron star: CLDM based on Skyrme-type forces

Neutron stars are superdense compact astrophysical objects. The central region of the neuron star (the core) consists of locally homogeneous nuclear matter, while in the outer region (the crust) nucleons are clustered. In the outer crust these nuclear clusters represent neutron-rich atomic nuclei and all nucleons are bound within them. Whereas in the inner crust some neutrons are unbound, but nuclear clusters still keeps generally spherical shape. Here we consider the region between the crust and the core of the star, so-called mantle, where non-spherical nuclear clusters may exist. We apply compressible liquid drop model to calculate the energy density for several shape types of nuclear clusters. It allows us to identify the most energetically favorable configuration as function of baryon number density. Employing four Skyrme-type forces (SLy4 and BSk24, BSk25, BSk26), which are widely used in the neutron star physics, we faced with strong model dependence of the ground state composition. In particular, in agreement with previous works within liquid drop model, mantle is absent for SLy4 (nuclear spheres directly transit into homogeneous nuclear matter; exotic nuclear shapes do not appear).

A Revisit of Implicit Monolithic Algorithms for Compressible Solids Immersed Inside a Compressible Liquid

With the development of mature Computational Fluid Dynamics (CFD) tools for fluids (air and liquid) and Finite Element Methods (FEM) for solids and structures, many approaches have been proposed to tackle the so-called Fluid–Structure Interaction or Fluid–Solid Interaction (FSI) problems. Traditional partitioned iterations are often used to link available FEM codes with CFD codes in the study of FSI systems. Although these procedures are convenient, fluid mesh adjustments according to the motion and finite deformation of immersed solids or structures can be challenging or even prohibitive. Moreover, complex dynamic behaviors of coupled FSI systems are often lost in these iterative processes. In this paper, the author would like to review the so-called monolithic approaches for the solution of coupled FSI systems as a whole in the context of the immersed boundary method. In particular, the focus is on the implicit monolithic algorithm for compressible solids immersed inside a compressible liquid. Notice here the main focus of this paper is on liquid or more precisely liquid phase of water as working fluid. Using the word liquid, the author would like to emphasize the consideration of the compressibility of the fluid and the assumption of constant density and temperature. It is a common practice to assume that the pressure variations are not strong enough to alter the liquid density in any significant fashion for acoustic fluid–solid interactions problems. Although the algorithm presented in this paper is not directly applicable to aerodynamics in which the density change is significant along with its relationship with the pressure and the temperature, the author did revisit his earlier work on merging immersed boundary method concepts with a fully-fledged compressible aerodynamic code based on high-order compact scheme and energy conservative form of governing equations. In the proposed algorithm, on top of a uniform background (ghost) mesh, a fully implicit immersed method is implemented with mixed finite element methods for compressible liquid as well as immersed compressible solids with a matrix-free Newton–Krylov iterative solution scheme. In this monolithic approach, with the simple modulo function, the immersed solid or structure points can be easily located and thus the displacement projections and force distributions stipulated in the immersed boundary method can be effectively and efficiently implemented. This feature coupled with the key concept of the immersed boundary method helps to avoid topologically challenging mesh adjustments and to incorporate parallel processing commands such as Message Passing Interface (MPI) and further vectorization of the numerical operation. Once these high-performance procedures are implemented coupled with the monolithic implicit matrix-free Newton–Krylov iterative scheme with immersed methods, effective and efficient reduced order modeling techniques can then be employed to explore phase and parametric spaces. The in-house developed programs are at the moment two-dimensional. Furthermore, based on the same approach implemented in one-dimensional test example with one continuum immersed in another continuum, such monolithic implicit matrix-free Newton–Krylov iterative approach can be extended for the study of composites with deformable aggregates and matrix.

Evaluation the effect of the ambient temperature on the liquid petroleum gas transportation pipeline

Liquefied petroleum gas (LPG) plays a major role in worldwide energy consumption as a clean source of energy with low greenhouse gases emission. LPG transportation is exhibited through networks of pipelines, maritime, and tracks. LPG transmission using pipeline is environmentally friendly owing to the low greenhouse gases emission and low energy requirements. This work is a comprehensive evaluation of transportation petroleum gas in liquid state and compressible liquid state concerning LPG density, temperature and pressure, flow velocity, and pump energy consumption under the impact of different ambient temperatures. Inevitably, the pipeline surface exchanges heat between LPG and surrounding soil owing to the temperature difference and change in elevation. To prevent phase change, it is important to pay attention for several parameters such as ambient temperature, thermal conductivity of pipeline materials, soil type, and change in elevation for safe, reliable, and economic transportation. Transporting LPG at high pressure requests smaller pipeline size and consumes less energy for pumps due to its higher density. Also, LPG transportation under moderate or low pressure is more likely exposed to phase change, thus more thermal insulation and pressure boosting stations required to maintain the phase envelope. The models developed in this work aim to advance the existing knowledge and serve as a guide for efficient design by underling the importance of the mentioned parameters.