Finest Morse Decompositions for Semigroup Actions on Fiber Bundles

Let S{\mathcal{S}} be a semigroup acting on a topological space M. We study finest Morse decompositions for the action of S{\mathcal{S}} on M. This concept depends on a family of subsets of S{\mathcal{S}} . For certain semigroups and families it recovers the concept of Morse decomposition for flows and semiflows. This paper also studies the behaviour of Morse decompositions for semigroup actions on principal bundles and their associated bundles. The emphasis is put on the study of those decompositions considering their projections onto the base space and their intersections with the fibers.     

Experimental analysis of local void fractions measurements for boiling hydrocarbons in complex geometry

The present paper is part of a research program on two-phase flows and heat transfer studies in tube bundles. An experimental study was carried out to analyse the void fraction for vertical two-phase flows. Boiling across a horizontal tube bundle for three hydrocarbons (n-pentane, propane and iso-butane) under saturated conditions is investigated. The experiments were performed on a tube bundle with 45 plain copper tubes of 19.05 mm outside diameter in a staggered configuration with a pitch to diameter ratio of 1.33. An optical probe has been developed to determine the local void fraction at the minimum cross section between the tubes.     

Derivation of a linear theory for nonequilibrium and equilibrium flows

Conventional linear theory of nonequilibrium and equilibrium gas flows yields correct results only for very small deviations of the stream parameters from the unperturbed values. Moreover, if in linearization we take the coordinates in planar flow as independent variables, then the flow past concave and convex corners is described in exactly the same fashion. In this case the characteristic emanating from the corner is (depending on the type of corner) a compression or rarefaction shock. In the case of a break in the wall of an axisymmetric channel the shock intensity approaches infinity with approach to the centerline, which indicates a deficiency of this type of linear theory. In the following we use a modification which eliminates the deficiencies noted above. This involves conversion to new independent and dependent variables such that the coefficients of the exact equations being linearized become weakly varying functions of the unknown parameters, the linearized boundary conditions coincide with the exact conditions at all or part of the boundaries, and the rarefaction shocks become rarefaction wave bundles of finite width. The last condition is achieved as a result of the fact that, in accordance with the Lighthill method of deformable coordinates [1], we take as one of the independent variables a quantity which maintains a constant value on each characteristic of the bundle of characteristics emanating from the break point [for equilibrium flows the semicharacteristic (or characteristic) independent variables were used in deriving the linear theory, for example, in [2–4]]. The study was based on the example of two-dimensional stationary nonequilibrium flow of an inviscid and nonheatconducting gas. In this case we find that boththelinear equations at a finite distance from the walls and the boundary conditions for determining the potential and nonequilibrium parameters outside the rarefaction wave bundles coincide with the equations and the conditions of conventional linear theory [5], while the relations associating the values of the parameters on the closing characteristics of each bundle (outside the bundles the same value of the characteristic variable corresponds to these characteristics) at some distance from the axis or from some reflecting surface are identical to the conditions on the rarefaction shocks. This fact makes it possible to use several results of conventional linear theory.     

A Uniform Exponential Spectrum for Linear Flows on Vector Bundles

For linear flows on vector bundles we define a uniform exponential spectrum. For a compact invariant set for the projected flow we obtain this spectrum by taking all accumulation points for the time tending to infinity of the union over the finite time exponential growth rates for all initial values in this set. Using direct arguments we show that for a connected compact invariant set this spectrum is a closed interval whose boundary points are Lyapunov exponents. For a compact invariant set on which the flow is chain transitive we show that this spectrum coincides with the Morse spectrum. In particular, this approach admits a straightforward analytic proof for the regularity and continuity properties of the Morse spectrum without using cohomology or ergodicity results.     

Direct numerical simulation of fluid flow in a 5x5 square rod bundle

Characterization of parallel flow through rod bundles is of key importance in assessing the performance and safety of several engineering systems, including a majority of nuclear reactor concepts. Inhomogeneities in the bundle cross-section can present complex flow phenomena, including varying local conditions of turbulence. With the ever-increasing capabilities of high-performance computing, Direct Numerical Simulation (DNS) of turbulent flows is becoming more feasible. Through resolving all scales of turbulence, DNS can serve as a “numerical experiment,” and can provide substantial insight into flow physics, but at considerable computational cost. Thus to date, the DNS in open literature for rod bundle flows is relatively scarce, and largely limited to unit-cell domains. Since wall effects are important in rod bundle flows, a multiple-pin DNS study can expand understanding of rod bundle flows while providing valuable reference data for evaluating reduced-resolution techniques. In this work, DNS of a 5x5 square bare rod bundle representative of typical light water reactor fuel dimensions was performed using the spectral element code Nek5000. Turbulent microscales based on an advanced Reynolds-Averaged Navier–Stokes model were used to establish the required DNS resolution. Velocity and Reynolds stress fields are analyzed in detail, and invariant analysis is used for further investigation into flow physics. The results show stark changes in the structure of turbulence in the edge gaps, suggesting the presence of gap vortices in these regions. In addition, turbulent kinetic energy budgets are presented to more fully illustrate the various turbulent processes. These data can prove useful for rigorous evaluation of lower-fidelity turbulence modeling approaches.     

Modelling techniques for fluid–solid coupling dynamics of bundle tubes vibrating and colliding in fluids

Nonlinear vibrations that occur in such bundle structures caused collisions between tubes and cross flows of the surrounding fluid. This paper presents modeling techniques for simulating the FSI dynamics of bundle tubes vibrating and colliding in fluids. A typical configuration of a three-dimensional tube bundles submerged in fluid of a cylindrical container is studied. Coupling conditions of displacement, velocity and forces are considered on the fluid-structure coupling interfaces. Contacts boundary between tubes and topological domain changes of the fluid are also considered on the fluid-structure coupling interface. Modeling techniques and algorithm are then established for flow-induced vibrations of the tubes, and collisions between tubes in fluids. The examples are presented to demonstrate the effectiveness of the proposed techniques. It has confirmed that our code produces the correct physics of the FSI problem, and capable of revealing the complex nonlinear mechanism with solid-solid contacts together with fluid-solid interactions.     

Theoretical Approach of Bubble Entrapment Through Interconnected Pores: Supplying Principle

Fiber-reinforced composite materials are often composed of fibers collected in bundles that are stitched together. During the impregnation of a fibrous preform by a liquid resin, the multiscale porous medium leads to an heterogenous flow front, and therefore bubbles may be created and entrapped. Indeed, for a wetting system, capillary pressure is higher inside bundle, due to the microspace between fibers, than outside the bundles that represent the macrospace, thus, inducing an overflow between both pore scales. Motivated by the prediction of bubble formation during fiber fabric infiltration for composite materials, we attempt to determine the bubble rate in imbibition through a simple model network with two connected capillaries, called ??Pore Doublet Model?? (PDM). Our system is composed of two parts: a first part, continuously interconnected, in which the suppling mass to the microchannel from the macrochannel occurs, and a second part connected only by nodes. To quantify the leading flow front, a theoretical model based on the supplying principle and arranged Washburn equation is proposed. This approach has been conducted for wetting liquids, Newtonian flows, incompressible fluids and pores, no inertial and gravitational forces and no dynamic contact angle. The geometrical variability (channel radius and length) and the different configuration of connections (continuous and discrete) influence the entrapped bubble rate, leading to either microbubble in the microchannel or macrobubble in the macrochannel. The outcomes can contribute to the knowledge of void formation especially during the filling of fibrous preforms and may extend the previous works on the PDM in general.     

Streaming and mixing induced by a bundle of ciliary vibrating micro-pillars

Directional near-wall flow induced by the vibration of slender micro-pillars attached to a surface similar to ciliary structures or grafted filaments is studied experimentally. The micro-pillar arrays are arranged in the form of a “V” approximating an asymmetric fore-aft bundle shape often found in nature, too. A base-layer actuation is used to excite the micro-pillars to oscillate in a vibratory pattern with maximum amplitude at the tips. Due to the specific shape of the bundle structure and asymmetric boundary conditions of the oscillatory motion, the pillars perform a tilted beating motion—similar to cilia—with a forward power stroke and a backward oriented recovery stroke or vice versa, depending on the boundary conditions of the actuation. As a consequence of the cooperative beating motion and the fore-aft asymmetry of the shape of the bundle, a directional streaming motion is induced by the pillars which increase with increasing streaming Reynolds number Re _S . In addition to the net streaming effect, the flow in the space between the pillar bases exhibit a micro-scale swirling motion around each of the structures with an efficient mixing behavior. Applied to micro-channels or wall-bounded flows, such structures may act as locally distributed passive or active flow manipulation devices. The use of such cilia bundles in large numbers on surfaces as passive structures for near-wall control in of boundary layer flows is feasible, too.     

Numerical investigation of mixed convection heat transfer past an in-line bundle of cylinders

Two dimensional unsteady Navier-Stokes and the energy equations are solved using finite element method for the case of flow past five row deep in-line bundle of circular cylinders with pitch to diameter ratios (PDR) of 1.5 and 2.0. Numerical solutions of governing equations have been obtained using Euler's explicit algorithm. Analysis have been made for Reynolds number of 100 and Prandtl number of 0.71. The effect of Richardson number (Ri=Gr/Re ²) on the flow and heat transfer have been investigated forRi=?1.0, ?0.5, 0.0, +0.5 and +1.0. Streamlines, isovorticity lines, pressure and temperature contours, local and average Nusselt numbers, pressure and shear stress distribution around the cylinders are presented. Results obtained for forced convection (Ri=0.0) agree well with the available experimental and numerical results. There is considerable effect of buoyancy over tube bundles both in buoyancy aiding and opposing flows.     

基于CFD模拟的翅片管束多孔介质模型建立方法及流场模拟

为了利用多孔介质模型对翅片管束外流场进行计算,首先利用实体模型计算了局部管束的流场特性以获得多孔介质参数,在验证了多孔介质模型的准确性后,使用该模型对大尺度管束的流场特性进行了计算。结果表明:可以采用多孔介质模型对翅片管束进行简化计算,局部计算得到的多孔介质参数可以应用到增大长度、高度和宽度后的大尺度同型管束区域计算上,多孔介质模型与实体模型的误差基本在10%以内。     

Two-phase flow pattern identification in a tube bundle based on void fraction and pressure measurements,with emphasis on churn flow

Two-phase flow are frequently encountered in the industry. In particular, in steam generators of nuclear plants, water is heated so that at the top of the generator an important fraction of water flows as vapor. In this upper part, a rising co-current two phase flow transverse to the tube bundle takes place. Fluids exert significant forces on the tubes in this area which highly depend on the two-phase flow pattern. Thus, as a prerequisite, it is essential to gather information on the flow conditions associated with the different two-phase flow patterns, which can be bubbly, intermittent, or annular. Then we must analyze the potentially dangerous flow patterns. This paper presents an experimental campaign aimed at characterizing those flow patterns for a rising co-current transverse flow in a tube bundle representative of the geometry in a steam generator. A new methodology based on the understanding of key contributions to vertical two-phase flow pattern maps in tube bundles is proposed that leads to a more complete flow pattern map. Finally, the paper focuses on the churn flow, which is the flow pattern for which significant pressure fluctuations occur. For this pattern, important damages could be expected on the tubes of a steam generator. Different kinds of pressure fluctuations are observed at different frequencies depending on the flow rates and the location in the test section.     

Effect of Multi-Scale Porosity in Local Permeability Modelling of Non-Crimp Fabrics

The influence of multi-scale porosity of fibre reinforcements on local permeability is investigated, in order to determine the possibility of simplifying permeability models for more efficient permeability calculations. Unit cell models of a biaxial Non-Crimp Fabric are developed and used to investigate, whether or not the porous bundles can be excluded, when modelling the local permeability. Numerical accuracy of calculations is controlled to guarantee the quality of the results and the conclusions drawn from them. It is found that fibre bundles with high fibre density can be excluded from permeability models, while bundles with low fibre volume fractions need to be included. A new method to model the local permeability of multi-scale reinforcements is developed and verified for low fibre density in the bundles. In this method, the effects of the flow inside the fibre bundles are included through modifications of the boundary conditions of a single-scale model representing the interbundle regions. The local permeability of multi-scale reinforcements can, therefore, be calculated by models with simplified fluid domains for all fibre bundle porosities, instead of being calculated by models consisting of the entire multi-scale geometry.     

GEOMETRIC FRAMEWORK AND MINIMAL REALIZATIONS OF NONLINEAR SYSTEMS ON FIBRE BUNDLE

ＧＥＯＭＥＴＲＩＣＦＲＡＭＥＷＯＲＫＡＮＤＭＩＮＩＭＡＬＲＥＡＬＩＺＡＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＳＯＮＦＩＢＲＥＢＵＮＤＬＥＭｕＸｉａｏｗｕ（慕小武）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅｒｓ...     

PIV measurement of the vertical cross-flow structure over tube bundles

Shell and tube heat exchangers are among the most commonly used types of heat exchangers. Shell-side cross-flow in tube bundles has received considerable attention and has been investigated extensively. However, the microscopic flow structure including velocity distribution, wake, and turbulent structure in the tube bundles needs to be determined for more effective designs. Therefore, in this study, in order to clarify the detailed structure of cross-flow in tube bundles with particle image velocimetry (PIV), experiments were conducted using two types of model; in-line and staggered bundles with a pitch-to-diameter ratio of 1.5, containing 20 rows of five 15 mm O.D. tubes in each row. The velocity data in the whole flow field were measured successfully by adjusting the refractive index of the working fluid to that of the tube material. The flow features were characterized in different tube bundles with regards to the velocity vector field, vortex structure, and turbulent intensity.     

SIMULATION OF TUBE BUNDLE VIBRATIONS INDUCED BY CROSS-FLOW

A two-dimensional simulation model for flow-induced vibrations of tube bundles subjected to single-phase cross-flow is applied on six different bundles at realistic Reynolds numbers. The calculation scheme solves the unsteady Navier–Stokes equations, including turbulence modelling. Fluid forces, tube acceleration, tube velocity and tube displacements are computed after each time step due to the current flow field. The bundles are square and 30°-arrangements, with pitch-to-diameter ratios of 1·2 up to 2·4. The point of resonance or instability is determined by increasing the approach velocity step by step. The results are analysed and compared with experimental data and with design criteria proposed in the literature.     

Espaces d'écoulements dits « universels »Spaces of universal flows

An isochoric motion can be performed both in perfect fluid, in Newtonian fluid, in Maxwell fluid (slow motions) and in Rivlin–Ericksen fluid of second grade whatever be viscosities and viscometric coefficients, iff the motion is universal. Every universal motion with steady vorticity is a generalised Belrami flow, and fulfils the Stokes equation. If the velocity $\text{u}$ of an universal motion complies with $\text{rot}\text{[(?}{}^{\mathrm{<mtext>t</mtext>}}\text{(}\text{Δ}\text{u}\text{))}\text{u}\text{]=}\text{0}$, the motion stands for feasible motion in every second order fluid. Brothers of the potential flows, all the sets of universal motions make up bundles of linear or cono??d spaces with various dimensions, finite or infinite, issued from the rest $\text{u}\text{≡}\text{0}$. The structures appear by scanning parallel to the potential flows. To cite this article: M. Bouthier, C. R. Mecanique 331 (2003).     

Swirled flows and their generalizations

New swirled flows (flows in channels, flows around bodies of revolution, and flows with a sink or source on the axis of symmetry) are studied. Group solutions constructed from a supergroup, which are generalizations of conical flows, are considered.     

Experimental investigation on the influence of gap vortex streets on fluid-structure interactions in hexagonal bundle geometries

Gap vortex streets characterise many industrial applications involving rod bundle flows, such as heat exchangers and nuclear reactors. These structures, known as gap vortex streets, may excite the structural components of the bundle to resonance, leading to fretting and fatigue. This work aims to measure these coherent structures and the resulting displacement and oscillation frequency of the neighbouring rod, to provide unique data for fluid-structure interaction studies and to develop a general correlation for estimating the coherent structure’s wavelength. A water loop was built to host a hexagonal rod bundle. Fluorinated Ethylene Prophylene (FEP), a refractive index matching (RIM) material, was used to have undisturbed optical access in the area around the central rod. The flow was measured with Laser Doppler Anemometry (LDA) to detect coherent structures, while the vibrations were measured with a high speed camera. A new correlation for estimating the wavelength of the coherent structures is derived with dimensional analysis based on experimental evidence. The correlation is tested on different geometries: rectangular channels with single or half-rods, and two rod bundles, within the pitch-to-diameter ratio (P/D) range 1.02–1.2. Moreover fluctuations in the flow, given by the detected coherent structures, govern the structural response of the rod. The rod is excited to resonance if these fluctuations match twice the natural frequency of the rod.     

Mechanical properties of single-walled carbon nanotube bundles as bulk materials

Single-walled carbon nanotubes (SWNTs) in crystalline bundles may exhibit a transition in which the cross-sections of tubes turn from perfectly circular to hexagonal, depending upon the tube diameter and externally applied pressure, and this structural instability leads to an abrupt change in the bulk elastic properties of SWNT bundles. This paper presents a hybrid atom/continuum model to study the bulk elastic properties of SWNT bundles, and the predicted characteristics of this structural instability agree well with the experimental observations available in the literature. Linearized bulk elastic properties of SWNT bundles with respect to a stable configuration are transversely isotropic and hence can be characterized by five independent elastic moduli. A complete set of these five moduli is predicted for the first time. It is found that the deformability of tube cross-sections play a dominant role in characterizing the transverse moduli.