Parametric vibrations of flexible hoses excited by a pulsating fluid flow,Part II: Experimental research

The paper presents the results of experimental studies of vibrations of an elastic hose which are induced by a pulsating fluid flow. It was found that there is a possibility of parametric resonances: principal and combination associated with certain modes of vibrations. The influence of frequency and the amplitude of pulsation, average flow velocity, pressure inside pipe, the length of the hose, and the temperature on the ranges of parametric vibrations were analysed. The character of vibrations in resonance ranges was determined by showing time histories and the results of spectral analyses. A flexible hose applied in high-pressure hydraulic systems was used as an object of research. The values of basic parameters which describe the hose׳s mechanical properties were identified experimentally. The results of the experiments were compared with the results of numerical simulations conducted on the basis of the methodology proposed in Part I of this paper.     

The effect of internal surface modification on flow instabilities in forced convection boiling in a horizontal tube

This paper presents the experimental result of a study on the effects of heat transfer enhancement on two-phase flow instabilities in a horizontal in-tube flow boiling system. Five different heat transfer surface configurations and five different inlet temperatures are used to observe the effect of heat transfer enhancement and inlet subcooling. All experiments are carried out at constant heat input, system pressure and exit restriction. Dynamic instabilities, namely pressure-drop type, density-wave type and thermal oscillations are found to occur for all the investigated temperatures and enhancement configurations, and the boundaries for the appearance of these oscillations are found. The effect of the enhancement configurations on the characteristics of the boiling flow dynamic instabilities is studied in detail. The comparison between the bare tube and the enhanced tube configurations are made on the basis of boiling flow instabilities. Differences among the enhanced configurations are also determined to observe which of them is the most stable and unstable one. The amplitudes and periods of pressure-drop type oscillations and density-wave type oscillations for tubes with enhanced surfaces are found to be higher than those of the bare tube. The bare tube is found to be the most stable configuration, while tube with internal springs having bigger pitch is found to be the most unstable one among the tested tubes. It is found that system stability increases with decreasing equivalent diameter for the same type heater tube configurations; however, on the basis of effective diameter there is no single result such as stability increase/decrease with increasing/decreasing effective diameter.     

An experimental investigation of the effect of a constriction on turbulent pipe flow

Measurements have been made of the distributions of the mean-velocity and the axial turbulence velocity component in a cross-section of a circular tube at various distances downstream from a number of different constrictions. Also spectral distributions of the turbulence velocity have been measured in the axis of the tube and in a point very close to the wall. The constrictions had a contraction ratio of 0.25 except one which had a ratio of 0.5. One of the constrictions was made of a thin rubber hose. When for this constriction the contraction ratio was reduced to a value smaller than 0.25, self-excited vibrations of the hose took place, producing an oscillating flow of the air in the tube. The Reynoldsnumber was kept at roughly 5,000. As could be expected, after 40 tube diameter distance downstream from the constrictions an almost complete recovery of the disturbed turbulent flow, as far as the distributions of the mean velocity and relative turbulence intensity are concerned, was obtained. Depending on the shape of the constriction even a shorter distance appeared to be sufficient. The flexible constriction then was in the non-vibrating condition. However, the spectral distributions showed in some cases still a difference with the undisturbed case, in particular in the low frequency range. If the flexible constriction was vibrating, the induced oscillations of the flow which showed up as discrete peaks in the spectral distributions, persisted over the entire length of the tube, again as expected.     

HPAM溶液在石英微圆管中的流动实验

针对HPAM溶液在油藏孔隙中的复杂渗流特性问题,在内径为10～350μm微圆管中进行了部分水解聚丙烯酰胺(HPAM)溶液的流动实验.实验结果表明:在本文实验条件下,HAPM溶液在管径尺度较小的微圆管内的流动规律明显偏离常规尺度下的非牛顿流体力学流动规律,其截面平均流速高于按照常规尺度流动推算出的结果,且管径越小,偏离程度越大,微尺度效应越强.     

The viscous flow through a slightly distorted flexible tube

The high Reynolds number structure is examined for a viscous Newtonian flow through a thin axisymmetric flexible Hookean tube. Linear and nonlinear solutions are examined for a number of cases encompassing both large and small tube compliances. Particular cases studied are a flexible tube with a flexible stenosis/dilatation and a flexible tube supported between two rigid tubes. Novel vacillating free-interactions are identified at low tube compliances. These free-interfactions are believed to have application to general viscous-inviscid interactions. Solutions are also found which appear to terminate at a critical level of tube dilation for the slightly constricted tube.This study was supported by a National Science Foundation Presidential Young Investigator Award.     

Drop size measurements for annular two-phase flow in a 20 mm diameter vertical tube

As part of a study on the effect of tube diameter on the mean drop size and liquid film flow rate in annular two-phase flow, data was obtained for the vertical upflow of an air-water system in a 20 mm internal diameter tube, held at a pressure of 1.5 bar and ambient temperature. This complements data taken in earlier experiments on 10 and 32 mm tubes. Increases in the superficial gas velocity caused reductions in the mean drop size whilst increasing the liquid mass flux in all but the lowest gas velocity case, caused the drop size to rise. Comparisons were made between the current drop size data and that from a 10 mm and 32 mm internal diameter tube, for similar conditions of temperature and pressure. The current drop size measurements, which fall between those from earlier work, confirm the dependence of drop size on tube diameter. The performance of several drop size correlations have been tested. Because the correlations do not account for the influence of tube diameter, they fail to predict the drop size data accurately. The influence of gas and liquid flow rate on the measured film flow rate show trends similar to those seen in data from the 10 mm and 32 mm diameter tubes. Models, to calculate the entrained liquid mass flux were tested; good predictions were given.     

Entrainment in condensing annular flow

Experiments were carried out on low pressure, steam-water, condensing annular flow in a 38.1 mm i.d. horizontal tube. The velocity of the steam at inlet was in the range 97–186 m/s.Measurements of the liquid film flow rate at the end of the test section, which arose as a result of condensation, entrainment, and deposition, were made by extracting the film through a porous sinter bush. The liquid flow rate in the vapour core at exit was deduced from these measurements together with a heat balance on the condenser section.These results were compared with three correlations for entrainment developed from air-water studies. On the basis of the experimental data available, there was sufficient agreement in one case to warrant further investigation.     

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.     

An experimental study of drag on a single tube and on a tube in an array under two-phase cross flow

In this work, the drag coefficient and the void fraction around a tube subjected to two-phase cross flow were studied for a single tube and for a tube placed in an array. The drag coefficients were determined by measuring the pressure distribution around the perimeter of the tube. Single tube drag data were taken when the tube was held both rigidly and flexibly. The test tube was made of acrylic and was 2.2 cm in diameter and 20 cm in length. In the experiments, liquid Reynolds number ranged from 430 to 21,900 for the single tube and liquid gap Reynolds number ranged from 32,900 and 61,600 for the tube placed in a triangular array. Free stream void fraction was varied from 0 to 0.4. At low Reynolds numbers, the ratio of two-phase to single-phase drag coefficient is found to be a strong function of εGr/Re2. However, at high Reynolds numbers only void fraction is the important parameter. Empirical correlations have been developed for the ratio of two-phase drag on a single tube and on a tube placed in an array.     

Acceleration of a sphere behind planar shock waves

The paper presents the results of an investigation on the motion of a spherical particle in a shock tube flow. A shock tube facility was used for studying the acceleration of a sphere by an incident shock wave. Using different optical methods and performing experiments in two different shock tubes, the trajectory and velocity of a spherical particle were measured. Based upon these results and simple one-dimensional calculations, the drag coefficient of a sphere and shading effect of sphere interaction with a shock tube flow were studied.     

The effect of flexible tube vibration on pressure drop and heat transfer in heat exchangers considering viscous dissipation effects

The pressure drop and heat transfer coefficient in tube bundle of shell and tube heat exchangers are investigated considering viscous dissipation effects. The governing equations are solved numerically. Because of temperature-dependent viscosity the equations should be solved simultaneously. The flexible tubes vibration is modeled in a quasi-static method by taking the first tube of the row to be in 20 asymmetric positions with respect to the rest of the tubes which are assumed to be fixed and time averaging the steady state solutions corresponding to each one of these positions .The results show that the eccentricity of the first tube increases pressure drop and heat transfer coefficients significantly comparing to the case of rigid tube bundles, symmetrically placed. In addition, these vibrations not only compensate the effect of viscous dissipations on heat transfer coefficient but also increase heat transfer coefficient. The constant viscosity results obtained from our numerical method have a good agreement with the available experimental data of constant viscosity for flexible tube heat exchangers.     

Effect of diameter on two-phase pressure drop in narrow tubes

The effect of tube diameter on two-phase frictional pressure drop was investigated in circular tubes with inner diameters of 0.6, 1.2, 1.7, 2.6 and 3.4 mm using air and water. The gas and liquid superficial velocity ranges were 0.01-50 m/s and 0.01-3 m/s, respectively. The gas and liquid flow rates were measured and the two-phase flow pattern images were recorded using high-speed CMOS camera. Unique flow patterns were observed for smaller tube diameters. Pressure drop was measured and compared with various existing models such as homogeneous model and Lockhart-Martinelli model. It appears that the dominant effect of surface tension shrinking the flow stratification in the annular regime is important. It was found that existing models are inadequate in predicting the pressure drop for all the flow regimes visualized. Based on the analysis of present experimental frictional pressure drop data a correlation is proposed for predicting Chisholm parameter “C” in slug annular flow pattern. For all other flow regimes Chisholm’s original correlation appears to be adequate except the bubbly flow regime where homogeneous model works well. The modification results in overall mean deviation of pressure drop within 25% for all tube diameters considered. This approach of flow regime based modification of liquid gas interaction parameter appears to be the key to pressure drop prediction in narrow tubes.     

Interference effect of an upstream larger cylinder on the lock-in vibration of a flexibly mounted circular cylinder

Experiments have been carried out to investigate the flow-induced vibration response of a flexibly mounted circular cylinder located in the vicinity of a larger cylinder and subjected to cross-flow. The interfering larger cylinder was placed upstream and had a diameter twice that of the vibrating cylinder. Complex interaction was observed between the flow over the two cylinders. The vibration responses of the flexible cylinder were classified into different regimes according to the relative positions of the two cylinders. In the-side-by-side arrangement and the tandem or near-tandem arrangement, flow-induced vibrations of the flexible cylinder were greatly suppressed. In the staggered arrangement which covered a large portion of the relative cylinder positions being investigated, vibrations of the smaller cylinder were greatly amplified. The vibration response curves were also largely modified with a broadening of the lock-in resonance range. A shift of the peak reduced velocity for maximum vibration response was also found. Flow visualizations and wake velocity measurements suggested that the modifications of the vibration responses were related to the presence or absence of constant or intermittent flow through the gap region between the two cylinders. The proposed mechanisms of flow interactions and the resulting vibration response characteristics could explain previous observations on flow-induced vibrations of two equal-sized circular cylinders reported in the literature.     

An experimental study of nonrheometric flows of viscoelastic fluids: II. Flow in a liquid jet exiting from a vertical tube

A laser anemometer has been used to study the region of accelerating shear flow near the exit of a vertical tube. It is in this region that the transition between steady laminar shear flow in the upstream tube and elongational flow in the downstream liquid jet takes place.Downstream velocity profiles were measured for solutions of 0.9% polyacrylamide in 85% glycerol/water and 0.9% polyacrylamide in water. Reynolds numbers (based on wall conditions in the fully developed upstream flow) ranged from 45 to 310 and Froude numbers from 0.294 to 4.11. Tubes, having sharpedged and rounded exit corners, with diameters of 1.25 cm and 1.90 cm were usedUpstream velocity profiles were measured for a solution of 0.9% polyacrylamide in water. Reynolds numbers ranged from 16 to 670. Only tubes having sharp-edged exit corners were used.It was found that the transition region did not extend upstream into the tube but was confined to the downstream jet. The transition took place over a distance of about 3–5 tube diameters depending upon the value of the Froude number. The axial distance downstream from the tube exit plane at which the velocity profile first became flat increased with increasing Froude number. The magnitude of the jet velocity at this point decreased with increasing Froude number.The condition of the tube exit corner was found to influence the flow in the transition region. Downstream velocity profiles obtained using tubes having rounded exit corners initially develop more slowly than, but soon catch up with and eventually overtake, the corresponding profiles obtained using tubes with sharp-edged exit corners.Downstream velocity profiles obtained for the 0.9% polyacrylamide in 85% glycerol/water solution were found to develop smoothly. The transition from steady shear flow in the tube to elongational flow in the jet took place through the combined processes of acceleration of the outer layers of the jet due to radial transfer of momentum with adjacent inner layers, the process spreading steadily inwards with increasing axial distance from the tube exit plane, and acceleration of the whole due to gravity. However, the velocity profiles obtained for the 0.9% polyacrylamide in water solution did not always develop so smoothly. At a Reynolds number of 310 and Froude number of 2.06 the radial momentum transfer process was restricted to a narrow outer region of the jet until a downstream axial distance of about 2 tube diameters was reached. Thereafter, the transition to a flat profile took place smoothly.     

A SIMULATION OF THE TURBULENCE RESPONSE OF HEAT EXCHANGER TUBES IN LATTICE-BAR SUPPORTS

Tube failures due to excessive flow-induced vibrations are a major concern with regards to the operation of heat exchangers in nuclear power and chemical process plants. Among the possible excitation mechanisms, turbulence-induced forces have a persistent effect and thus are an important factor in determining the long-term reliability of heat exchangers. Impact forces which occur when tube/support collisions take place play a vital role in determining tube wear. To address this issue, a tube/support interaction model was implemented in an in-house finite element program and validated against three published examples. Pseudo-forces in conjunction with modal superposition were utilized in solving the nonlinear equations of motion of loose tubes in lattice-bar supports. Time-domain simulations of the nonlinear response of the tube are presented to determine the effect of various tube and support parameters on the vibratory characteristics of the systems. Special attention was paid to the effect of increased clearance on the response of tubes in lattice-bar supports. The tube response, impact force and contact ratio were analysed and represented in dimensionless form. The dimensionless parameters developed proved effective in collapsing the data pertaining to different flow velocities over single curves. These are useful in identifying the roles of several key variables in altering tube dynamics. Moreover, these parameters may also be used to scale the results to account for differences in geometrical and material properties.     

An experimental study of nonrheometric flows of visco-elastic fluids: I. flow into a re-entrant tube

A laser anemometer has been used to study the developing flow both upstream and downstream from the entry plane in a re-entrant tube geometry. A 0.75% polyacrylamide/water solution was used and Reynolds numbers (based on wall conditions in the fully developed downstream flow) in the range 100–500 were obtained in 1.82-cm and 2.40-cm-diameter tubes.The shear stress-shear rate relationship for the fluid was measured using a cone and plate geometry in conjunction with a Weissenberg rheogoniometer. Theoretical fully developed velocity profiles were calculated numerically from these measurements. The measured fully developed velocity profiles were found to be in excellent agreement with those calculated.Velocity profiles measured at the tube entry plane showed the pronounced wall region distortion typically predicted by recent numerical solutions of the flow of purely-viscous fluids through an abrupt tube contraction.It was found that the major velocity rearrangements were achieved within only a few diameters (both upstream and downstream) of the entry plane. In particular, the velocity distribution near the tube wall varied negligibly over the relatively longer distance (many diameters) that it took for the centreline velocity to achieve its fully developed value. Entry lengths were found to be only about half those for purely-viscous fluids.Calculation of the time of flight along the central streamline confirmed that the major rearrangements of velocity suffered by the fluid occurred over a relatively short time period. This indicates that hereditary integral constitutive equations may have to be used in theoretical analyses of this type of flow situation.     

Measurement of the liquid film thickness in micro tube slug flow

Slug flow is one of the representative flow regimes of two-phase flow in micro tubes. It is well known that the thin liquid film formed between the tube wall and the vapor bubble plays an important role in micro tube heat transfer. In the present study, experiments are carried out to clarify the effects of parameters that affect the formation of the thin liquid film in micro tube two-phase flow. Laser focus displacement meter is used to measure the thickness of the thin liquid film. Air, ethanol, water and FC-40 are used as working fluids. Circular tubes with five different diameters, D = 0.3, 0.5, 0.7, 1.0 and 1.3 mm, are used. It is confirmed that the liquid film thickness is determined only by capillary number and the effect of inertia force is negligible at small capillary numbers. However, the effect of inertia force cannot be neglected as capillary number increases. At relatively high capillary numbers, liquid film thickness takes a minimum value against Reynolds number. The effects of bubble length, liquid slug length and gravity on the liquid film thickness are also investigated. Experimental correlation for the initial liquid film thickness based on capillary number, Reynolds number and Weber number is proposed.     

Effect of heat transfer augmentation on two-phase flow instabilities in a vertical boiling channel

The effect of different heater surface configurations on two-phase flow instabilities has been investigated in a single channel, forced convection, open loop, up-flow system. Freon-11 is used as the test fluid, and six different heater tubes with various inside surface configurations have been tested at five different heat inputs. In addition to temperature and pressure recordings, high speed motion pictures of the two-phase flow were taken for some of the experiments to study the two-phase flow behavior at different operating points. Experimental results are shown on system pressure drop versus mass flow rate curves, and stability boundaries are also indicated on these curves. Comparison of different heater tubes is made by the use of the stability boundary maps and the plots of inlet throttling necessary to stabilize the system versus mass flow rate. Tubes with internal springs were found to be more stable than the other tubes.     

An experimental investigation of pulsatile flow through a smooth constriction

Measurements of flow disturbances in the downstream region of modeled stenoses in a rigid tube, with upstream pulsatile flow are reported. Experiments were conducted over physiologically relevant mean Reynolds numbers of 600; based on the tube diameter and the time-averaged value of upstream centerline velocity. Contoured constrictions with 25%, 50% and 75% area reductions were investigated and velocity data were obtained from ensemble averaging techniques (phase-locked waveform). Experimental data over extensive spatial regions of poststenotic fields were taken, employing a two-component laser Doppler velocimeter LDV. Constant time sampling techniques for performing data or frequency analyses were used to avoid velocity bias and to study the evolution of poststenotic flow disturbances. It is found that different types of flow disturbances exist downstream of the constriction. Data analysis methods with the aid of flow visualization allow accurate classification of the disturbances which are sensitive indicators of mild to moderate constrictions. Although the present study was motivated by a biological situation, sufficient data were reported in detail that they may also be used by investigators working in computational fluid dynamics.     

Wave behavior in horizontal annular air–water flow

In this study, non-intrusive pressure drop, liquid base film thickness distribution, and wave behavior measurements have been obtained for 206 horizontal annular two-phase (air–water) flow conditions in 8.8, 15.1, and 26.3 mm ID tubes. Reliable wave velocity measurements are available for 185 of these flow conditions, while 131 flow conditions allow for reliable wave frequency measurements. The wave velocity is found to be predicted to within 9% by gas friction velocity and 6% by an optimized correlation of similar structure. Wave frequency can also be predicted with a simple correlation to within 5% for the 8.8 and 15.1 mm tubes, but a separate relation is required to explain 26.3 mm frequency data. The differences in wave behavior between the annular and wavy-annular/wavy regimes are also discussed.