Nonlinear dynamics of cantilevered extensible pipes conveying fluid

In this paper the nonlinear planar dynamics of a fluid-conveying cantilevered pipe is investigated. The centreline of the pipe is considered to be extensible; i.e., coupled longitudinal and transverse displacements are considered. The extended version of the Lagrange equations for systems containing non-material volumes is employed to derive the equations of motion, resulting directly in a set of coupled nonlinear ordinary differential equations. The pseudo-arclength continuation technique along with direct time integration are used to solve these equations. Bifurcation diagrams of the system are constructed as the flow velocity is increased; these diagrams are supplemented by time traces, phase-plane portraits, and fast Fourier transforms for some sets of system parameters. As opposed to the case of an inextensible pipe, an extensible pipe elongates in the axial direction as the flow velocity is increased from zero; depending on the system parameters, this static elongation can be considerable. At the critical flow velocity, the system loses stability via a supercritical Hopf bifurcation, emerging from the trivial solution for the transverse displacement and leading to a flutter.     

用晶格玻尔兹曼方法研究血液在分岔管中的栓塞

血液栓塞形成机理一直是学术界研究的热点.本文将以圆形刚性颗粒在分岔管中的运动模拟血液在微血管中的运动,对血液在分岔管中的栓塞现象作了初步研究.重点研究了当血管发生分岔时,血管中血液流速的变化以及血栓形成的概率.得出结论,压积越大越容易发生栓塞,压差越大越不易发生栓塞.分岔管的入口和分岔处最容易发生栓塞.血液经分岔管后,大管中的压积比小管的高.     

动态冰浆流动的浓度分布及粘性研究

动态冰浆是一种固-液两相流体。文中采用理论模型研究了动态冰浆在非均质流动情况下的冰晶浓度分布,分析了冰晶浓度、冰浆流速、管道直径、冰晶粒径大小对冰浆的动态粘度的影响。分析表明:在高冰晶浓度、低流速情况下,冰浆的平均粘度不仅和冰晶浓度和载流溶液的粘度相关,还受到冰浆流速、管道直径和冰晶颗粒大小的影响。     

Transmission of sound through pipe walls in the presence of flow

The transmission of sound through pipe walls was studied experimentally under no-flow conditions as well as with steady air flow velocities up to 120 m/s. The test specimens were commercial pipe and tube of diameter ranging from 0·07 to 0·3 m, and thickness-to-diameter ratios from 0·12 to 0·2. The technique involved two reverberant rooms, one traversed by the test pipe to measure externally radiated sound, and one in which the test pipe terminated to measure internally propagated sound. Vibration of the pipe wall was also monitored to determine radiation efficiency.The results show that no-flow transmission loss (TL) is higher than predicted by available theoretical expressions, but that TL decreases strongly with increasing flow velocity. A qualitative explanation for the latter is offered. Radiation efficiency was found to be independent of flow velocity. The scaling of results between “similar” specimens was moderately successful. The results are documented in sufficient detail to permit their use for forming empirical models as well as for testing future theoretical predictions.     

Phase velocities of plane waves in a pipe with a flow whose velocity varies along the radius

The phase velocities of plane waves in a pipe filled with a moving acoustic medium are studied for different laws of flow velocity variation along the pipe radius. The wave equation is solved by the discretization method, which breaks the entire pipe volume into individual cylinders under the assumption that, within each of the cylinders, the flow velocity of the medium is constant. This approach makes it possible to reduce the solution to the wave problem to solving Helmholtz equations for individual cylinders. Based on boundary conditions satisfied at the boundaries between neighboring cylinders, a homogeneous system of linear algebraic equations is obtained. From this system, with the use of the scattering matrices, a simple dispersion equation is derived for determining the phase velocities of plane waves. The stability of the numerical solution to the dispersion equation with respect to the number of cylinders is investigated. The phase velocities of quasi-homogeneous and inhomogeneous waves in a pipe are numerically calculated and analyzed for different velocities of a moving medium and different laws of flow velocity variation along the radius. It is shown that the variation that occurs in the phase velocity of a homogeneous plane wave in a pipe due to the motion of the medium is identical to the mean flow velocity for different laws of flow velocity variation along the radius. For inhomogeneous plane waves, the phase velocity increment exceeds the mean flow velocity several times and depends on both the law of wave amplitude distribution along the radius and the law of the flow velocity variation along the radius.     

Particle Mass Loading Effect on a Two-Phase Turbulent Downward Jet Flow

The particle mass loading effect on the flow structure of a two-phase turbulent jet flow was studied. A particle mass loading ratio ranging from 0 to 3.6 was used as the control parameter. The polystyrene solid particles used had nominal diameters of 210 and 780 μm. The flow Reynolds number, which was based on the pipe nozzle diameter and the fluid-phase centerline mean velocity, was 2 × 10⁴ in the current test. A two-color laser Doppler anemometer (LDA), combined with the amplitude discrimination method and the velocity filter method, was employed to measure the mean velocity distributions for the particle and fluid phases, and the turbulent intensities and Reynolds stresses of the flow. The two-phase jet flow field was measured from the initial pipe exit to 90 D downstream. Another one-component He? Ne laser LDA system was also applied to obtain the energy spectra and temporal correlations of the two-phase jet flow.     

Visualization of molten pools and invisible laser beam profiles using an ultraviolet CCD camera

Experiments were conducted on the effects of a wall distance and velocity ratio of suction flow to injection flow on the flow and heat transfer characteristics of a circular impinging jet accompanying an annular suction flow. As a result, it is found that in the case of accompanying suction flow, a higher Nusselt number can be obtained compared with in the case without suction flow, under a condition of the wall distance within eight times of injection pipe diameter from the near pipe exit edge. In addition, when the effect of velocity ratio is examined at a fixed arbitrary wall distance, it is found that there exists an optimum velocity ratio where the Nusselt number becomes the maximum. It is shown that these heat transfer characteristics are closely associated with the fluctuating velocity and the mean velocity in the two-dimensional velocity field observed by Particle Image Velocimetry (PIV).     

The self-similarity of wall-bounded temporally accelerating turbulent flows

From the study of viscous flow it is known that certain time-dependent laminar problems, such as the impulsively started flat plate and the diffusion of a vortex sheet, possess self-similar solutions. Previous studies of turbulent channel and pipe flows accelerating between two steady states have shown that the flow field evolves in three distinct stages. Furthermore, recent direct numerical simulations have shown that the perturbation velocity, i.e. the surplus velocity from the initial value, in an impulsively accelerating turbulent channel and pipe flow also possesses a self-similar distribution during the initial stage. In here, these results are developed analytically and it is shown that accelerating flows in which the centreline velocity develops as U^∧_c(t) = U₀(t/t₀)^m will possess a self-similar velocity distribution during the initial stage. The displacement thickness of the perturbation velocity is shown to be dependent only on the type of acceleration, and not on the initial Reynolds number, the acceleration rate or the change in Reynolds number. The derived formulas are verified with good agreement against measurements performed in a linearly accelerating turbulent pipe flow and with data from channel flow simulations.     

托卡马克真空室内线圈水冷管道接头强化二次流的数值研究

基于计算流体力学(CFD)理论,研究了不同曲率半径的螺旋导流片的托卡马克真空室内线圈水冷管道接头。利用湍流数值模拟方法,分析了线圈管道接头导流片曲率半径比、冷却水入口流速对线圈管道内流体平均雷诺数分布的影响。结果表明,不同导流片曲率半径比的线圈管道内的流体雷诺数分布曲线相似,平均雷诺数随入口流速的增加而增大,管道接头出口雷诺数随导流片曲率半径比的增大而减小,导流片曲率半径比小的管接头更适用于线圈水冷曲线管的二次流强化。此外,还为导流片曲率半径比为0.2的管接头拟合了管接头出口雷诺数与入口流速的关系式,为进一步研究类似于托卡马克真空室内线圈管道的曲线管接头的二次流强化提供理论基础。     

Experimental examination of vortex-sound generation in an organ pipe: A proposal of jet vortex-layer formation model

Aero-dynamical models of sound generation in an organ pipe driven by a thin jet are investigated through an experimental examination of the vortex-sound theory. An important measurement requirement (acoustic cross-flow as an irrotational potential flow reciprocating sinusoidally) from the vortex-sound theory is carefully realized when the pipe is driven with low blowing pressures of about 60 Pa (jet velocities of about 10 m/s). Particle image velocimetry (PIV) is applied to measure the jet velocity and the acoustic cross-flow velocity over the mouth area at the same phase by quickly switching the jet drive and the loudspeaker-horn drive. The vorticity of the jet flow field and the associated acoustic generation term are evaluated from the measurement data. It is recognized that the model of the “jet vortex-layer formation” is more relevant to the sound production than the vortex-shedding model. The acoustic power is dominantly generated by the flow–acoustic interaction near the edge, where the acoustic cross-flow velocity takes larger magnitudes. The acoustic generation formula on the vortex sound cannot deny the conventional acoustical volume-flow model because of the in-phase relation satisfied between the acoustic pressure at the mouth and the acoustic volume flow into the pipe. The vortex layers formed along both sides of the jet act as the source of an accelerating force (through the “acceleration unbalance”) with periodically alternating direction to oscillate the jet flow and to reinforce the acoustic cross-flow at the pipe mouth.     

Three-dimensional phase contrast velocity mapping acquisition improves wall shear stress estimation in vivo

The purpose of this study was to evaluate and apply high-resolution three-dimensional phase contrast mapping for estimation of wall shear stress in vivo. A silicon pipe of 8 mm diameter with a 8.3 ml/s steady flow and the entrance of the carotid bifurcation in 10 young healthy volunteers aged 23.6 +/- 3.1 years was studied. Very high resolution three-dimensional and two-dimensional phase contrast mapping sequences with spatial resolutions of 0.31 x 0.31 x 1.5 mm(3) and 0.31 x 0.31 x 3 mm(3), respectively, were compared in vivo and in vitro. Wall shear stress was calculated using multi-sectored, three-dimensional paraboloid fitting. In comparison to the two-dimensional measurements, the three-dimensional method with only half the slice thickness gave higher signal-to-noise ratio and velocity-to-noise ratios both in vivo and in vitro. Wall shear stress derived from the three-dimensional velocity measurements did not differ from the two-dimensional velocity measurements either in vitro or in vivo. Mean wall shear stress was lowest and oscillatory shear index was highest at the outer wall, towards the carotid bifurcation. Three-dimensional velocity mapping increases resolution and image quality and allows estimation of wall shear stress patterns circumferentially and longitudinally in human arteries.     

气力提升系统气液两相流数值模拟分析

污水处理、油田采油、液态金属冷却反应堆和磁流体动力转换器等领域采用气力提升系统有其显著优势.由于不同液体介质与气体介质密度对气力提升系统性能影响较大,因此本文基于Fluent仿真软件,采用欧拉模型、k-ω剪切应力输运湍流模型数值模拟了氮气-水、氮气-煤油、氮气-水银及空气-水、氩气-水、氮气-水下气力提升系统内气液两相流动行为,分析了系统稳定时提升立管内气相体积分数、提升液体流量、提升效率、提升管出口处液体径向速度的变化规律.研究结果表明:1)氮气-水、氮气-煤油、氮气-水银系统中,提升管内液体介质密度越大,提升管内气相体积分数越小、提升液体流量越大、提升效率越高;2)空气-水、氩气-水、氮气-水系统中,提升管内气体介质密度越大,提升管内气相体积分数越小、提升液体流量越大、提升效率峰值越小;3)提升管出口处提升液体径向速度随气体充入量的不断增加而整体波动升高,最终管轴中心附近液体速度较大,管壁附近液体速度较小.本文研究成果为污水处理、气举采油、液态重金属冷却核反应堆和磁流体动力转换器等应用领域的气力提升技术的优化提供科学的理论基础.     

Pipe flow measurement by using a side-scattering holographic particle imaging technique

A side scattering holographic particle imaging technique has been developed and demonstrated to be a capable tool for obtaining good quality images of a particle field in a high Reynolds number pipe flow. Instantaneous three-dimensional velocity components can be measured. The streamwise velocity error is estimated to be about 5%. Limitations of this optical set-up are discussed. The methodology and results presented will be of use for designing a pulsed laser holographic technique for turbulent velocity measurement or particle diagnostics in a pipe flow.     

螺旋管内气液固三相流颗粒相分布规律

为了深入认识螺旋管多相流相分离现象,并为新型螺旋管除砂器设计提供指导,本文应用马尔文粒度仪,测量了螺旋管气水砂三相流底部水平段液膜中的颗粒浓度和粒度分布。研究表明:在泡状流和分层流条件下,螺旋管底部水平段可形成稳定的连续液膜流动;在宽广的气速范围内,液膜中的颗粒浓度分布规律均为内弯侧较低、外弯侧较高,说明螺旋管除砂器对于实际生产中流动工况的变化具有良好的适应性;泡状流中提高气速有利于分离;分层流中在中等气速条件下外弯侧颗粒浓度最大,中等气速是相分离的最佳操作工况。     

Laser anemometry measurements in a gas-solid suspension flow

A laser anemometer has been used to measure local solid particle velocities and turbulence intensities, mean particle velocity and particle wall velocity for a fully developed gas-solid suspension flowing in a vertical pipe. The technique, which does not disturb the flow and requires no calibration, can be used successfully for internal pipe flow measurements where the solids to air mass loading ratio is below about two.     

Entrance Length of Polymer Flow Through a Contraction Die: Comparison of Calculation from an Equation and Flow Induced Birefringence Measurements

When a polymeric melt flows through a contraction die, it experiences a certain distance in the slit before a fully developed flow is achieved, which is defined as the entrance length. Here, an equation for calculation of the entrance length was proposed based on an assumption that the pressure drops in an exponential function way along the flow direction in the contraction die from the entrance to the fully developed flow. The entrance length could be calculated from the flow parameters, such as volumetric flow rate, the pressures at the entrance and at the defined point in the fully developed flow. The entrance lengths of a low-density polyethylene (LDPE) and a high-density polyethylene (HDPE) melt were calculated from this equation with the measured flow parameters at various flow rates. The results are quite close to those measured from flow induced birefringence and similar to that reported in a published study by Martyn et al., which suggested that the equation could be used to describe the relation between the entrance length and the flow parameters.     

管内超临界压力水的混和对流换热

本文利用FLUENT6.0软件,数值研究了超临界压力下水在光管内作层流流动和换热特性,着重考察了重力引 起的二次流的影响。研究发现垂直管中由于浮力作用,速度曲线不再是抛物线,而成M状,并在壁面附近出现峰值;重 力作用下,物性的剧烈变化在水平管垂直流动方向引起了很强的二次流,从而影响了阻力特性和换热特性。     

New Equation for Predicting Pipe Friction Coefficients Using the Statistical Based Entropy Concepts

In general, this new equation is significant for designing and operating a pipeline to predict flow discharge. In order to predict the flow discharge, accurate determination of the flow loss due to pipe friction is very important. However, existing pipe friction coefficient equations have difficulties in obtaining key variables or those only applicable to pipes with specific conditions. Thus, this study develops a new equation for predicting pipe friction coefficients using statistically based entropy concepts, which are currently being used in various fields. The parameters in the proposed equation can be easily obtained and are easy to estimate. Existing formulas for calculating pipe friction coefficient requires the friction head loss and Reynolds number. Unlike existing formulas, the proposed equation only requires pipe specifications, entropy value and average velocity. The developed equation can predict the friction coefficient by using the well-known entropy, the mean velocity and the pipe specifications. The comparison results with the Nikuradse’s experimental data show that the R2 and RMSE values were 0.998 and 0.000366 in smooth pipe, and 0.979 to 0.994 or 0.000399 to 0.000436 in rough pipe, and the discrepancy ratio analysis results show that the accuracy of both results in smooth and rough pipes is very close to zero. The proposed equation will enable the easier estimation of flow rates.     

Localized velocity and turbulence measurement in turbulent swirling flows using laser Doppler anemometry

Turbulent swirling water flow in a pipe has complex velocity distributions with special measurement problems tor experimental work. Some of these problems are described in the introduction to the paper along with comments on the basic characteristics of turbulent swirling flow.The form of laser Doppler anemometer used is briefly noted, with some special optical features developed to suit this class of flow. Experience during some two years of comprehensive experimentation is then outlined, including comment on the data processing system.Results from experiments with tangentially injected water flow in 50 mm bore pipes up to 60 diameters long are reported, with local measurements of mean velocity and turbulence intensity. The variation of mean velocity components and turbulence intensity with radius and distance along the pipe are discussed with a few comparisons of results obtained from other experimental techniques, e.g. pitot-static probe and hot films.For the particular problem examined here it would have been difficult, if not impossible, to obtain the measurements using a technique other than laser anemometry.     

Flow-induced oscillations of a cantilevered pipe conveying fluid with base excitation

It is known that a plain cantilevered pipe conveying fluid loses its stability by a Hopf bifurcation, leading to either planar or non-planar flutter for flow velocities beyond the critical flow velocity for Hopf bifurcation. If an external mass is attached to the end of the pipe (an end-mass), the resulting dynamics become much richer, showing 2D and 3D quasiperiodic and chaotic oscillations at high flow velocities. In this paper, a cantilevered pipe, with and without an end-mass, subjected to a small-amplitude periodic base excitation is considered. A set of three-dimensional nonlinear equations is used to analyze the pipe?s response at various flow velocities and with different amplitudes and frequencies of base excitation. The nonlinear equations are discretized using the Galerkin technique and the resulting set of equations is solved using Houbolt?s finite difference method. It is shown that for a plain pipe (with no end-mass), non-planar post-instability oscillations can be reduced to planar periodic oscillations for a range of base excitation frequencies and amplitudes. For a pipe with an end-mass, similarly to a plain pipe, three-dimensional period oscillations can be reduced to planar ones. At flow velocities beyond the critical flow velocity for torus instability, the three-dimensional quasiperiodic oscillations can be reduced to two-dimensional quasiperiodic or periodic oscillations, depending on the frequency of base excitation. In all these cases, a low-amplitude base excitation results in reducing the three-dimensional oscillations of the pipe to purely two-dimensional oscillations, over a range of excitation frequencies. These numerical results are in agreement with the previous experimental work.