Response amplitude and hydrodynamic force for a buoy over a convex

A buoy as an offshore structure is often placed over a convex such as a caisson or a submerged island. The hydrodynamic fluid/solid interaction becomes more complex due to the convex compared with that on the flat. Both the buoy and the convex are idealized as vertical cylinders. Linear potential theory is used to investigate the response amplitude and the hydrodynamic force for a buoy over a convex due to diffraction and radiation in water of finite depth. These are derived from the total velocity potential. A set of theoretical added mass, damping coefficient, and exciting force expressions have been proposed. Analytical results of the response amplitude and hydrodynamic force are given. Finally, the numerical results show that the effect of the convex on the response amplitude and hydrodynamic force for the buoy is ignored if the size of the convex is relatively smaller.

INVESTIGATING A NEAR-BED SUBMARINE PIPELINE IN A CURRENT

This paper considers the lift forces acting on a pipeline with a small gap between the pipeline and the plane bottom or scoring bottom. A more reasonable fluid force on the pipeline has been obtained by applying the knowledge of modified potential theory (MPT), which includes the influences of the downstream wake. By finite element method, an iteration procedure is used to solve problems of the nonlinear fluid-structure interaction. Comparing the deflection and the stress distributions with the difference sea bottoms, the failure patterns of a spanning pipeline have been discussed. The results are essential for engineers to assess pipeline stability.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

大别山硬玉石英岩带中的水

The Dabie Mountains is a collisional orogenic belt between the North China and Yantze Continental plates. It is the eastern elongation of the Tongbai and Qingling orogen, and is truncated at its east end by the Tan-Lu fault. Jadeite-quartzite belt occurs in the eastern margin of UHPMB from the Dabie Mountains. Geochemical features indicate that the protoliths of the jadeite-quartzite and associated eclogite to be supracrustal rocks. The occurrence of micro-inclusions of coesite in jadeite and garnet confirmed that the continental crust can be subducted to great depth (8 0-100km) and then exhumed rapidly with its UHP mineral signature fairly preserved. Therefore, study of UHP jadeite-quartzite provides important information on subduction of continental crustal rocks and their exhumation histories, as well as the dynamics of plate tectonic processes at convergent margins. The purpose of this paper is to investigate the presence of hydrous component in the jadeite-quartzite belt, significant natural variations in the hydrous component content of UHP minerals and to discuss the role of water in petrology, geochemistry and micro-tectonic. On the basis of our previous studies, some new geological evidences have been found in the jadeite-quartzite belt by researches on petrography, mineralogy, micro-tectonic, hydrous component content of UHP minerals and combined with the study on rheology of materials using microprob, ER, TEM. By research and analysis of these phenomenona, the results obtained are as follows: 1. The existence of fluid during ultra-high pressure metamorphic process. Jadeites, omphacite, garnet, rutile, coesite and quartz from the jadeite-quartzite belt have been investigated by Fourier transform infrared spectrometer and TEM. Results show that all of these minerals contain trace amount of water which occur as hydroxyl and free-water in these minerals. The two-type hydrous components in UHP minerals are indicated stable in the mantle-depth. The results demonstrated that these ultra-high pressure metamorphic minerals, which were derived from continental crust protoliths, they could bring water into the mantle depth during the ultra-high pressure metamorphism. The clusters of water molecules within garnet are very important evidence of the existence of fluid during ultra-high pressure metamorphic process. It indicated that the metamorphic system was not "dry"during the ultra-high pressure stage. 2.The distribution of hydrous component in UHP minerals of jadeite-quartzite. The systematic distribution of hydrous components in UHP minerals are a strong indication that water in these minerals, are controlled by some factors and that the observed variations are not of a random nature. The distribution and concentration of hydrous component is not only correlated with composition of minerals, but also a function of geological environment. Therefore, the hydrous component in the minerals can not only take important part in the UHP metamorphic fluid during subduction of continental crustal rocks, but also their hydroxyl transported water molecules with decreasing pressure during their exhumation. And these water molecules can not only promote the deformation of jadeite through hydrolytic weakening, but also may be the part of the retrograde metamorphic fluid. 3.The role of water in the deformed UHP minerals. The jadeite, omphacite, garnet are strong elongated deformation in the jadeite-quartzite from the Dabie Mountains. They are (1) they are developed strong plastic deformation; (2) developed dislocation loop, dislocation wall; (3) the existence of clusters of water molecular in the garnet; and (4) the evolution of micero-tectonic from clusters of water molecular-dislocation loop in omphacite. That indicated that the water weakening controlled the mechanism of deformed minerals. Because the data presented here are not only the existence of clusters of water molecular in the garnet, but also developed strong elongation, high density of dislocation and high aspect ratios, adding microprobe data demonstrate the studied garnet crystals no compositional zoning. Therefore, this indicates that the diffusion process of the grain boundary mobility did not take place in these garnets. On the basis of above features, we consider that it can only be explained by plastic deformation of the garnets. The clusters of water molecules present in garnet was directly associated with mechanical weakening and inducing in plastic deformation of garnet by glissile dislocations. Investigate of LPO, strain analysis, TEM indicated that these clinopyroxenes developed strong elongation, high aspect ratios, and developed dislocation loop, dislocation wall and free dislocations. These indicated that the deformation mechanism of the clinopyroxenes plastically from the Dabie Mountains is dominant dislocation creep under the condition of the UHP metamorphic conditions. There are some bubbles with dislocation loops attached to them in the omphacite crystal. The bubbles attached to the dislocation loops sometimes form a string of bubble beads and some loops are often connected to one another via a common bubble. The water present in omphacite was directly associated with hydrolitic weakening and inducing in plastic deformation of omphacite by dislocations. The role of water in brittle deformation. Using microscopy, deformation has been identified as plastic deformation and brittle deformation in UHP minerals from the Dabie Mountains. The study of micro-tectonic on these minerals shows that the brittle deformation within UHP minerals was related to local stresses. The brittle deformation is interpreted as being caused by an interaction of high fluid pressure, volume changes. The hydroxyl within UHP minerals transported water molecules with decreasing pressure due to their exhumation. However, under eclogite facies conditions, the litho-static pressure is extreme, but a high fluid pressure will reduce the effective stress and make brittle deformation possible. The role of water in prograde metamorphism. Geochemical research on jadeite-quartzite and associated eclogite show that the protoliths of these rocks are supracrustal rocks. With increasing of temperature and pressure, the chlorite, biotite, muscovite was dehydrous reaction and released hydrous component during the subduction of continental lithosphere. The supracrustal rocks were transformed UHP rocks and formed UHP facies assemblage promotely by water introduction, and was retained in UHP minerals as hydrous component. The water within UHP minerals may be one of the retrograde metamorphic fluids. Petrological research on UHP rocks of jadeite-quartzite belt shows that there was existence of local fluids during early retrograde metamorphism. That are: (1) coronal textures and symplectite around relict UHP minerls crystals formed from UHP minerls by hydration reactions; (2) coronal textures of albite around ruitle; and (3) micro-fractures in jadeite or garnet were filled symplectite of Amp + PI + Mt. That indicated that the reactions of early retrograde metamorphism dependent on fluid introduction. These fluids not only promoted retrograde reaction of UHP minerals, but also were facilitate to diffuse intergranular and promote growth in minerals. Therefore, the hydrous component in the UHP minerals can not only take important part in the UHP metamorphic fluid during subduction of continental crustal rocks, but also their hydroxyl transport water molecules with decreasing pressure and may take part in the retrograde metamorphic fluid during their exhumation. 7. The role of water in geochemistry of UHP jadeite-quartzite. Geochemical research show that there are major, trace and rare earth element geochemical variations in the jadeite-quartzite from the Changpu district of Dabie Mountains, during retrograde metamorphic processes from the jadeite-quartzite--gneiss. The elements such as SiO_2、FeO、Ba、Zr、Ga、La、Ce、PTN Nd% Sm and Eu increase gradually from the jadeite-quartzite to retrograded jadeite-quartzite and to gneiss, whilst TiO_2. Na_2CK Fe2O_3、Rb、Y、Nb、Gd、Tb、Dy、Ho、Er、Tm、Yb decrease gradually. And its fO_2 keep nearly unchanged during early retrograde metamorphism, but decreased obviously during later retrograde metamorphism. These indicate that such changes are not only controlled by element transformation between mineralogical phases, but also closely relative to fluid-rock interaction in the decompression retrograde metamorphic processes.

Modeling, numerical methods, and simulation for particle-fluid two-phase flow problems

In this paper, we study the issues of modeling, numerical methods, and simulation with comparison to experimental data for the particle-fluid two-phase flow problem involving a solid-liquid mixed medium. The physical situation being considered is a pulsed liquid fluidized bed. The mathematical model is based on the assumption of one-dimensional flows, incompressible in both particle and fluid phases, equal particle diameters, and the wall friction force on both phases being ignored. The model consists of a set of coupled differential equations describing the conservation of mass and momentum in both phases with coupling and interaction between the two phases. We demonstrate conditions under which the system is either mathematically well posed or ill posed. We consider the general model with additional physical viscosities and/or additional virtual mass forces, both of which stabilize the system. Two numerical methods, one of them is first-order accurate and the other fifth-order accurate, are used to solve the models. A change of variable technique effectively handles the changing domain and boundary conditions. The numerical methods are demonstrated to be stable and convergent through careful numerical experiments. Simulation results for realistic pulsed liquid fluidized bed are provided and compared with experimental data. (C) 2004 Elsevier Ltd. All rights reserved.

Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.

Dynamic interaction of an elastic container with fluid

The vibration analysis of an elastic container with partially filled fluid was investigated in this paper. The container is made of a thin cylinder and two circular plates at the ends. The axis of the cylinder is in the horizontal direction. It is difficult to solve this problem because the complex system is not axially symmetric. The equations of motion for this system were derived. An incompressible and ideal fluid model is used in the present work. Solutions of the equations were obtained by the generalized variational method. The solution was expressed in a series of normalized generalized Fourier's functions. This series converged rapidly, and so its approximate solution was obtained with high precision. The agreement of the calculated values with the experimental result is good. It should be mentioned that with our method, the computer time is less than that with the finite-element method.

The interaction of two pairs of solitary waves in a two-fluid system

This paper deals with the interaction of solitary waves in a two-fluid system which consistsof two superimposed incompressible inviscid fluids with a free surface and a horizontal rigidbottom. Under the assumption of shallow water wave, we first derive the basic equationssuitable for the model considered, a generalized form of the Boussinesq equations, then usingthe PLK method and the reductive perturbation method, obtain the second-order approximatesolution for the head-on collision between two pairs of interface and surface solitary waves,and give their maximum amplitudes during the collision and the nonuniform phase shiftsafter the collision which lead to the distortion of the wave profiles.

Turbulent collision of inertial particles: point-particle based, hybrid simulations and beyond

Point-particle based direct numerical simulation (PPDNS) has been a productive research tool for studying both single-particle and particle-pair statistics of inertial particles suspended in a turbulent carrier flow. Here we focus on its use in addressing particle-pair statistics relevant to the quantification of turbulent collision rate of inertial particles. PPDNS is particularly useful as the interaction of particles with small-scale (dissipative) turbulent motion of the carrier flow is mostly relevant. Furthermore, since the particle size may be much smaller than the Kolmogorov length of the background fluid turbulence, a large number of particles are needed to accumulate meaningful pair statistics. Starting from the relative simple Lagrangian tracking of so-called ghost particles, PPDNS has significantly advanced our theoretical understanding of the kinematic formulation of the turbulent geometric collision kernel by providing essential data on dynamic collision kernel, radial relative velocity, and radial distribution function. A recent extension of PPDNS is a hybrid direct numerical simulation (HDNS) approach in which the effect of local hydrodynamic interactions of particles is considered, allowing quantitative assessment of the enhancement of collision efficiency by fluid turbulence. Limitations and open issues in PPDNS and HDNS are discussed. Finally, on-going studies of turbulent collision of inertial particles using large-eddy simulations and particle- resolved simulations are briefly discussed.

Dissipative particle dynamics simulation of wettability alternation phenomena in the chemical flooding process

Wettability alternation phenomena is considered one of the most important enhanced oil recovery (EOR) mechanisms in the chemical flooding process and induced by the adsorption of surfactant on the rock surface. These phenomena are studied by a mesoscopic method named as dissipative particle dynamics (DPD). Both the alteration phenomena of water-wet to oil-wet and that of oil-wet to water-wet are simulated based on reasonable definition of interaction parameters between beads. The wetting hysteresis phenomenon and the process of oil-drops detachment from rock surfaces with different wettability are simulated by adding long-range external forces on the fluid particles. The simulation results show that, the oil drop is liable to spread on the oil-wetting surface and move in the form of liquid film flow, whereas it is likely to move as a whole on the water-wetting surface. There are the same phenomena occuring in wettability-alternated cases. The results also show that DPD method provides a feasible approach to the problems of seepage flow with physicochemical phenomena and can be used to study the mechanism of EOR of chemical flooding.

simulation and interaction of fluid dynamics

In the fluid simulation, the fluids and their surroundings may greatly change properties such as shape and temperature simultaneously, and different surroundings would characterize different interactions, which would change the shape and motion of the fluids in different ways. On the other hand, interactions among fluid mixtures of different kinds would generate more comprehensive behavior. To investigate the interaction behavior in physically based simulation of fluids, it is of importance to build physically correct models to represent the varying interactions between fluids and the environments, as well as interactions among the mixtures. In this paper, we will make a simple review of the interactions, and focus on those most interesting to us, and model them with various physical solutions. In particular, more detail will be given on the simulation of miscible and immiscible binary mixtures. In some of the methods, it is advantageous to be taken with the graphics processing unit (GPU) to achieve real-time computation for middle-scale simulation.

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth

The linear water wave scattering and radiation by an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth is investigated by use of the multipole expansion method. The diffracted and radiated potentials are expressed as a linear combination of infinite multipoles placed at the centre of each cylinder with unknown coefficients to be determined by the cylinder boundary conditions. Analytical expressions for wave forces, hydrodynamic coefficients, reflection and transmission coefficients and energies are derived. Comparisons are made between the present analytical results and those obtained by the boundary element method, and some examples are presented to illustrate the hydrodynamic behavior of multiple horizontal circular cylinders in a two-layer fluid. It is found that for two submerged circular cylinders the influence of the fluid density ratio on internal-mode wave forces is more appreciable than surface-mode wave forces, and the periodic oscillations of hydrodynamic results occur with the increase of the distance between two cylinders; for four submerged circular cylinders the influence of adding two cylinders on the wave forces of the former cylinders is small in low and high wave frequencies, but the influence is appreciable in intermediate wave frequencies.

Theoretical calculation of Flory-Huggins and scattering interaction parameters by means of the lattice fluid theory for PVME/PSD blends

By fitting the spinodals of poly(vinyl methyl ether)/deuterated polystyrene (PVME/PSD) systems, the adjustable parameters epsilon (12)* and delta epsilon* in the Sanchez-Balasz lattice fluid (SBLF) theory could be determined for different molecular weights. According to these parameters, Flory-Huggins and scattering interaction parameters were calculated for PVME/PSD with different molecular weights by means of the SELF theory. From our calculation, Flory-Huggins and scattering interaction parameters are both Linearly dependent on the reciprocal of the temperature, and almost linearly on the concentration of PSD. Compared with the scattering interaction parameters, the Flory-Huggins interaction parameters decreased more slowly with an increase in the concentration for all three series of blends.