The influence of rotation on turbulent flow and heat transfer in an annulus between independently rotating tubes

Experimental and numerical investigations of turbulent flow and heat transfer have been performed in a concentric annulus between independently rotating tubes. Numerical predictions, applying a Reynolds stress turbulence model, are compared with experimental fluid flow and heat transfer results for the case of a heated outer tube and an adiabatic inner tube. Compared to the above mentioned boundary conditions for the conservation equation of energy, differences in heat transfer in case of a heated inner tube and an adiabatic outer one, are examined by analysis, applying a mixing length turbulence model. Numerical investigations with both kinds of models about the influence of annulus radius ratio make evident that due to different superimpositions of centrifugal force and additional shear stress there is a wide variation of effects on fluid flow and heat transfer caused by the rotation of the inner and the outer tube.     

Waves in thin-walled elastic tubes containing an incompressible inviscid fluid

The effect of the non-linearity of the governing equations on the propagation of waves in fluid filled elastic tubes is investigated. Results are obtained by the method of characteristics for a particular form of pressure pulse applied at the end of a semi-infinite initially uniform tube. An expression is obtained for the distance along the tube at which shock formation is predicted. Two different hyperelastic materials whose elastic properties model those of biological tissue are considered for the tube walls. Numerical results are presented in graphical form.     

CHAOTIC TRANSIENTS IN A CURVED FLUID CONVEYING TUBE

I. INTRODUCTIONChaotic motion is a kind of reciprocal non-periodic motion caused by a deterministic system. Itis very sensitive to the initial conditions, apparently random and incapable of long-term prediction.Chaotic transient is such a motion that the system will undergo a final steady state, which is one ofseveral or much more possible steady motions of the system. But this final steady state is very sensitiveto the initial conditions of the system. As it is e?ected by many uncertain…     

流固耦合地震波动问题的显式谱元模拟方法

流固耦合地震波动问题主要研究由流体和固体构成的复杂系统中地震波传播特性及其规律. 传统模拟方法中一般以声波方程、弹性波方程的数值解分别描述理想流体和弹性固体中的波动, 并实时地处理两种不同性质介质之间的相互耦合作用, 数值格式复杂且限制数值模拟精度与计算效率. 本文采用谱元法结合多次透射公式人工边界条件实现了一种流固耦合地震波动问题的高阶显式数值计算方法. 该方法利用了流固耦合问题统一计算框架,可将饱和多孔介质的Biot波动方程分别退化为理想流体的声波方程和弹性固体的弹性波方程. 通过P波垂直入射的水平成层理想流体-饱和多孔介质-弹性固体场地模型、P波斜入射的不规则层状界面以及任意形状界面的理想流体-饱和多孔介质-弹性固体场地模型等三个算例, 与传递函数法解析解以及集中质量有限元法计算结果进行对比分析, 证明了本文方法的正确性与有效性. 数值模拟结果表明, 本文方法相较传统有限元法可以少得多的节点数量获得更高的数值精度, 并且在较宽的频率范围内都能可靠地模拟出流固耦合系统的动力响应, 充分体现出本文方法兼顾高精度、计算效率和复杂场地建模灵活的特点.      

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研究了埋置于弹性地基内充液压力管道中非线性波的传播. 假设管壁是线弹 性的,地基反力采用Winkler线性地基模型,管中流体为不可压缩理想流体. 假定系统初始 处于内压为$P_0$的静力平衡状态,动态的位移场及内压和流速的变化是叠加在静 力平衡状态上的扰动. 基于质量守恒和动量定理,建立了管壁和流体耦合作用的非 线性运动方程组; 进而用约化摄动法, 在长波近似情况下得到了KdV方程,表征 着系统有孤立波解.     

Waves in nonlinear fluid filled tubes

Wave propagation and shock formation in nonlinear elastic and viscoelastic fluid filled tubes is discussed. For a Mooney-Rivlin material a simple exact solution exhibiting distortionless propagation is found.     

Fluid flow of incompressible viscous fluid through a non-linear elastic tube

The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well. The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung’s (Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain–energy density function. The fluid is described through a Navier–Stokes code coupled with a system of non linear equations, governing the interaction with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response.     

Wave propagation in an elastic tube: a numerical study

In this paper, a fluid–wall interaction model, called the elastic tube model, is introduced to investigate wave propagation in an elastic tube and the effects of different parameters. The unsteady flow was assumed to be laminar, Newtonian and incompressible, and the vessel wall to be linear-elastic, isotropic and incompressible. A fluid–wall interaction scheme is constructed using a finite element method. The results demonstrate that the elastic tube plays an important role in wave propagation. It is shown that there is a time delay between the velocity waveforms at two different locations and that the peak velocity increases while the low velocity decreases in the elastic tube model, contrary to the rigid tube model where velocity waveforms overlap each other. Compared with the elastic tube model, the increase of the wall thickness makes wave propagation faster and the time delay cannot be observed clearly, however, the velocity amplitude is reduced slightly due to the decrease of the internal radius. The fluid–wall interaction model simulates wave propagation successfully and can be extended to study other mechanical properties considering complicated geometrical and material factors.     

Motion equations of the dynamic theory of consolidation from the point of view of the theory of transient pipe flows

An elastic fluid-saturated porous medium is modeled as a bundle of parallel cylindrical tubes aligned in a direction parallel to the fluid movement. The pore space is filled with viscous compressible liquid. A cell model and the theory of transient pipe flow are used to derive one-dimensional governing equations in such media. All macroscopic constants in these equations are defined by the individual material constants of the fluid and solid. The interaction force includes an additional term not found in Biot's theory.     

THERMOELASTIC VIBRATION OF FLUID-CONVEYING MICROTUBES EMBEDDED IN ELASTIC MEDIUMS

研究热环境中被弹性介质包围的微米输流管道的横向振动问题. 根据Hamilton 原理及非线性热弹性理论建立管道横向振动控制方程,并利用复模态法对其进行求解,得到了系统的固有频率和屈曲失稳临界流速,讨论了环境温度和一些重要系统参数对管道振动特性的影响. 研究结果表明:环境温度变化、管道和流体的微尺度效应、管道外径及弹性介质刚度对输流微管道固有频率和临界流速都有很大影响.     

Solitary waves in initially stressed thin elastic tubes

In the present work, we study the propagation of non-linear waves in an initially stressed thin elastic tube filled with an inviscid fluid. Considering the physiological conditions of the arteries, in the analysis, the tube is assumed to be subjected to a uniform inner pressure P₀ and an axial stretch ratio λ_z. It is assumed that due to blood flow, a finite dynamical displacement field is superimposed on this static field and, then, the non-linear governing equations of the elastic tube are obtained. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the longwave approximation is investigated. It is shown that the governing equations reduce to the Korteweg-deVries equation which admits a solitary wave solution. It is observed that the present model equations give two solitary wave solutions. The results are also discussed for some elastic materials existing in the literature.     

Response of blood flow through an artery under stenotic conditions

This paper presents an analytical study on the behavoiur of blood flow in an artery having a stenosis. This is basically formulated through the use of a suitable mathematical model. The arterial segment under consideration is simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible fluid representing blood. The analysis is carried out for an artery with mild local narrowing in its lumen forming a stenosis. Particular emphasis has been paid to the effect of the surrounding connective tissues on the motion of the arterial wall. Blood is treated as a Newtonian fluid. The analysis is restricted to propagation of small amplitude harmonic waves, generated due to the flow of blood whose wave length is large compared to the radius of the arterial segment. The effect of the shape of stenosis on the resistance to blood flow has been well illustrated quantitatively through numerical computations of the resulting expressions. A quantitative analysis is also made for the variation of the phase velocity, as well as the velocity of wave propagation and the flow rate, in order to illustrate the applicability of the model.     

滞后细观模型在岩石力学中的应用

对以砂岩为代表的所谓``NME材料'的力学行为研究方面的一些新的概念和模型进行了评介.首先介绍了一种基于所谓``滞后单元'的描述滞后现象的物理模型------Preisach-Mayergoyz(P-M)模型,然后详细阐述了P-M模型应用于模拟岩石的非线性滞后应力应变关系的过程和结果.这种唯象模型很好地描述了宏观上的滞后表现和``离散记忆'效应.接着本文对应变能耗散的力学机制进行了简单分析. 最后,介绍了一种描述弹性波在``NME材料'中传播规律的数学方法, 该方法从一般的弹性波传播规律出发,分析了``NME材料'特殊的力学性质给弹性波传播带来的影响,揭示了产生特殊的弹性波传播规律的原因.      

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

NUMERICAL SIMULATION OF STEADY FLOW IN A COMPLIANT TUBE OR CHANNEL WITH TAPERED WALL THICKNESS

Flow through compliant tubes with linear taper in wall thickness is numerically simulated by finite element analysis. Two models are examined: a compliant channel and an axisymmetric tube. For verification of the numerical method, flow through a compliant stenotic vessel is simulated and compared to existing experimental data. Steady two-dimensional flow in a collapsible channel with initial tension is also simulated and the results are compared with numerical solutions from the literature. Computational results for an axisymmetric tube show that as cross-sectional area falls with a reduction in downstream pressure, flow rate increases and reaches a maximum when the speed index (mean velocity divided by wave speed) is near unity at the point of minimum cross-sectional area, indicative of wave-speed flow limitation or “choking” (flow speed equals wave speed) in previous one-dimensional studies. For further reductions in downstream pressure, the flow rate decreases. Cross-sectional narrowing is significant but localized. For the particular wall and fluid properties used in these simulations, the area throat is located near the downstream end when the ratio of downstream-to-upstream wall thickness is 2; as wall taper is increased to 3, the constriction moves to the upstream end of the tube. In the planar two-dimensional channel, area reduction and flow limitation are also observed when outlet pressure is decreased. In contrast to the axisymmetric case, however, the elastic wall in the two-dimensional channel forms a smooth concave surface with the area throat located near the mid-point of the elastic wall. Though flow rate reaches a maximum and then falls, the flow does not appear to be choked.     

Simultaneous solution of the Navier-Stokes and elastic membrane equations by a finite element method

Fluid flow through a significantly compressed elastic tube occurs in a variety of physiological situations. Laboratory experiments investigating such flows through finite lengths of tube mounted between rigid supports have demonstrated that the system is one of great dynamical complexity, displaying a rich variety of self-excited oscillations. The physical mechanisms responsible for the onset of such oscillations are not yet fully understood, but simplified models indicate that energy loss by flow separation, variation in longitudinal wall tension and propagation of fluid elastic pressure waves may all be important. Direct numerical solution of the highly non-linear equations governing even the most simplified two-dimensional models aimed at capturing these basic features requires that both the flow field and the domain shape be determined as part of the solution, since neither is known a priori. To accomplish this, previous algorithms have decoupled the solid and fluid mechanics, solving for each separately and converging iteratively on a solution which satisfies both. This paper describes a finite element technique which solves the incompressible Navier-Stokes equatikons simultaneously with the elastic membrane equations on the flexible boundary. The elastic boundary position is parametized in terms of distances along spines in a manner similar to that which has been used successfully in studies of viscous free surface flows, but here the membrane curvature equation rather than the kinematic boundary condition of vanishing normal velocity is used to determine these diatances and the membrane tension varies with the shear stresses exerted on it by the fluid motions. Bothy the grid and the spine positions adjust in response to membrane deformation, and the coupled fluid and elastic equations are solved by a Newton-Raphson scheme which displays quadratic convergence down to low membrane tensions and extreme states of collapse. Solutions to the steady problem are discussed, along with an indication of how the time-dependent problem might be approached.     

On the radial oscillations of incompressible, isotropic, elastic and limited elastic thick-walled tubes

The finite amplitude, free radial oscillations of a thick-walled circular cylindrical tube are studied for an arbitrary incompressible, isotropic and homogeneous rubber-like material having limiting molecular chain extensibility. First, based on classical results for hyperelastic tubes, some results for thick-walled Mooney-Rivlin tubes are described graphically in the phase plane. Then the periodicity of the finite amplitude, free oscillations of a general limited elastic, thick-walled tube is studied; and some analytical results for the Gent model are illustrated in several numerical examples. Results for thick-walled Gent tubes are compared with those for corresponding Mooney-Rivlin tubes; and the motion of thin-walled Gent tubes is illustrated in the phase plane. Physical conclusions are presented. The period of small amplitude oscillations of an arbitrary elastic or limited elastic tube is derived from relations obtained by a linearization of a general class of equations of which the tube problem is a special case. Classical results of the linear theory are thereby recovered and compared with results for Mooney-Rivlin and Gent tubes.     

FLUIDELASTIC ANALYSIS OF TUBE BUNDLE VIBRATION IN CROSS-FLOW

Tube bundles in cross-flow vibrate in response to motion-induced fluid-dynamic forces; hence, the resultant motions are considered to be a fluidelastic vibration. The characteristics of the vibration depend greatly on the features of the fluid-dynamic forces and the structure of the tube bundle. Therefore, in this study, the equations of motion of the tube bundle are derived. From the viewpoint of vibration, each tube is not independent of the surrounding tubes because its vibration is affected by fluid-dynamic coupling with the neighboring tubes. Thus, the equations are a set of coupled equations and the solution is obtained as an eigenvalue problem. The fluid-dynamic forces, which are indispensable in the calculation, have been obtained by experiments using a vibrating tube in the bundle; it was found that the forces depend strongly on the reduced velocity. Using these equations and the fluid forces, critical velocities of the tube bundle vibration are calculated, and it is found that the critical velocity is strongly dependent on the fluid-dynamic force characteristics, as they vary with the reduced velocity. Vibration tests of the tube bundle have also been conducted, and the critical velocities obtained in the tests are compared with the calculated values; agreement with the calculated values is good, demonstrating that the method of calculation is useful. The effects of mass ratio, frequency deviation and damping deviation of tubes in the bundle on the critical velocity are also examined theoretically. It is found that it is better to treat the mass ratio and the logarithmic decrement separately when the mass ratio is less than 10. Differences in natural frequencies make the critical velocity large. Similarly, differences in logarithmic decrement may distribute the vibration energy to other tubes and make the critical velocity large.     

Axisymmetric Vortex Fluid Flow in a Long Elastic Tube

A mathematical model for axisymmetric eddy motion of a perfect incompressible fluid in a long tube with thin elastic walls is proposed. Necessary and sufficient conditions for hyperbolicity of the system of equations of motion for flows with monotonic radial velocity profiles are formulated. The propagation velocities of the characteristics of the system under study and the characteristic shape of this system are calculated. The existence of simple waves continuously attached to a given steady shear flow is proved. The group of transformations admitted by the system is found, and submodels that determine invariant solutions are given. By integrating factorsystems, new classes of exact solutions of equations of motion are found.