Liquid single- and gas—liquid two-phase flows of magnetic fluid in the presence of a high non-uniform parallel magnetic field

The effect of a non-uniform parallel high magnetic field on flow control characteristics is investigated experimentally for a magnetic fluid single-phase flow and an air—magnetic fluid two-phase flow in a vertical channel. It is found that as the magnetic field strength is increased, the friction factor of the single-phase flow increases significantly. For the two-phase flow, the friction pressure loss and the head pressure loss, which is smaller than the friction loss, are negligibly small compared with the magnetic pressure loss. In the case where air is injected 27.9d upstream from the maximum magnetic field, the air flow is blocked by the magnetic force in the entrance of the magnetic field, which leads to increases in both local void fraction and pressure drop there. In the case where air is injected 1.43d downstream from the maximum magnetic field, the air flow is accelerated, resulting in a decrease in void fraction and an increase in pressure rise. In the latter case and under the present range of experimental conditions, the magnetic pumping head reaches 0.02 MPa at the highest, and the maximum circulation flow rate reaches twice as high as non-magnetically driven flow rate.     

Hydrodynamics of two-phase flow in vertical up and down-flow across a horizontal tube bundle

Flow patterns, void fraction and friction pressure drop measurements were made for an adiabatic, vertical up-and-down, two-phase flow of air–water mixtures across a horizontal in-line, 5×20 tube bundle with a pitch-to-diameter ratio of 1.28. The flow patterns in the cross-flow zones were obtained and flow pattern maps were constructed. The data of average void fraction were less than the values predicted by a homogenous flow model and showed a strong mass velocity effect, but were well-correlated in terms of the Martinelli parameter X_tt and liquid-only Froude number Fr_LO. The two-phase friction multiplier data could be well-correlated with the Martinelli parameter.     

An impedance method for the measurement of liquid hold-up in two-phase flow

A liquid hold-up gauge based on the measurement of the electrical impedance has been developed for application in gas-liquid pipe flow. The gauge consists of two ring electrodes mounted flush to the pipe wall. The impedance (capacitance or conductance) seen by the electrodes depends on the distance between them and on the liquid hold-up. For distances above three tube diameters, the impedance is independent of the flow configuration for all separated flow patterns and, with good approximation, also for intermittent flows. Moreover, capacitance or conductance are linearly related to the liquid hold-up. The impedance under bubble flow conditions closely follows the theoretical predictions due to Maxwell. Also for the other flow configurations (annular, stratified, intermittent) the results of static and/or dynamic calibration agree closely with theoretical models.     

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.     

An investigation of void fraction in liquid slugs for horizontal and inclined gas—liquid pipe flow

The void fraction in liquid slugs has been determined for air—water fiow in horizontal and near-horizontal pipes by a newly-developed conductance probe technique. A semi-empirical correlation has been developed and compared with the present measurements and available data. This correlation predicts reasonably well the observed effects of diameter, inclination and physical properties.     

An experimental study on developing air-water two-phase flow along a large vertical pipe: effect of air injection method

The flow structure in a developing air-water two-phase flow was investigated experimentally along a large vertical pipe (inner diameter, D_h: 0.48 m, ratio of length of flow path L to D_h: about 4.2). Two air injection methods (porous sinter injection and nozzle injection) were adopted to realize an extremely different flow structure in the developing region. The flow rate condition in the test section was as follows: superficial air velocity: 0.02–0.87 m/s (at atmospheric pressure) and superficial water velocity: 0.01–0.2 0.01–0.2 m/s, which covers the range of bubbly to slug flow in a small-scale pipe (D_h about 0.05 m).

No air slugs occupying the flow path were recognized in this experiment regardless of the air injection methods even under the condition where slug flow is realized in the small-scale pipe. In the lower half of the test section, the axial distribution of sectional differential pressure and the radial distribution of local void fraction showed peculiar distributions depending on the air injection methods. However, in the upper half of the test section, the effects of the air injection methods are small in respect of the shapes of the differential pressure distribution and the phase distribution. The comparison of sectional void fraction near the top of the test section with Kataoka's correlation indicated that the distribution parameter of the drift-flux model should be modeled including the effect of D_h and the bubble size distribution is affected by the air injection methods. The bubble size distribution is considered to be affected also by L/D_h based on comparison of results with Hills' correlation.     

A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow

A separated flow model has been developed that is applicable to vertical annular two-phase flow in the purely convective heat transfer regime. Conservation of mass, momentum, and energy are used to solve for the liquid film thickness, pressure drop, and heat transfer coefficient. Closure relationships are specified for the interfacial friction factor, liquid film eddy-viscosity, turbulent Prandtl number, and entrainment rate. Although separated flow models have been reported previously, their use has been limited, because they were tested over a limited range of flow and thermal conditions. The unique feature of this model is that it has been tested and calibrated against a vast array of two-phase pressure drop and heat transfer data, which include upflow, downflow, and microgravity flow conditions. The agreements between the measured and predicted pressure drops and heat transfer coefficients are, on average, better or comparable to the most reliable empirical correlations. This separated flow model is demonstrated to be a reliable and practical predictive tool for computing two-phase pressure drop and heat transfer rates. All of the datasets have been obtained from the open literature.     

Resonance behaviour of viscoelastic fluid in Poiseuille flow in the presence of a transversal magnetic field

The oscillatory flow of a viscoelastic fluid in a circular pipe under the influence of a transversal magnetic field is studied. Exact solutions for the axial velocity and flow rate are presented. The velocity enhancement and the resonance behaviour are analysed both numerically and asymptotically in the case of small pipe radii. Approximations for the resonance frequencies and the achievable velocity enhancements are derived. Copyright © 2005 John Wiley & Sons, Ltd.     

Effect of the magnetic field on the pulsatile flow through a rigid tube

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Rheological behaviour of two-phase flow of solid particles in a gas

The present investigation was concerned with the rheological behaviour of dilute suspensions of solid particles in a gas in a vertical cocurrent flow moving upwards. Starting from the experimentally determined dependence of the pressure drop on the concentration of solid particles and the Reynolds number of the carrier medium in the steady flow region, the rheological parameters were estimated using pseudo-shear diagrams. Air was the carrier medium and the dispersed phase was one of six fractions of polypropylene powder and five fractions of glass ballotini. The results show that the investigated two-phase systems have pseudoplastic character which becomes more pronounced with increases in concentration, equivalent diameter and density of solid particles in the flowing suspension. C _d coefficient of particle resistance - d _e equivalent diameter of particles - D column diameter - Fr Froude number - g gravitational acceleration - K rheological parameter - L length - n rheological parameter - p _t pressure drop due to friction - p _m total pressure drop - p _ag pressure drop due to acceleration of the gas phase - p _as pressure drop due to acceleration of the solid phase - p _g hydrostatic pressure of the gas phase - p _s specific effective weight of the dispersed phase - r radius - Re Reynolds number - Re _p Reynolds number of a particle - Re _G generalized Reynolds number - Re _G1 generalized Reynolds number relating to the end of the laminar flow region - Re _G2 generalized Reynolds number relating to the beginning of the turbulent flow region - w _z axial component of velocity - u _t steady free-fall velocity of a single particle - w average velocity - w _g average velocity of the gas phase - w _s average velocity of the dispersed phase of solid particles - relative mass fraction of solid particles - x _s volume fraction of solid particles - _g coefficient of pressure drop due to friction - µ dynamic viscosity - _g density of the gas phase - _m density of the suspension - _s density of solid particles - _ds density of the dispersed phase - _w shear stress at the wall     

MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field

The problem of the steady magnetohydrodynamic (MHD) stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.     

Effect of magnetic Reynolds number on the two‐dimensional hydromagnetic flow around a cylinder

Numerical experiments have been conducted to study the effect of magnetic Reynolds number on the steady, two‐dimensional, viscous, incompressible and electrically conducting flow around a circular cylinder. Besides usual Reynolds number Re, the flow is governed by the magnetic Reynolds number R_m and Alfvén number β. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The pressure Poisson equation is solved to find the pressure fields in the entire flow region. The effects of the magnetic field and electrical conductivity on the recirculation bubble, drag coefficient, standing vortex and pressure are presented and discussed. For low interaction parameter (N<1), the suppression of the flow‐separation is nearly independent of the conductivity of the fluid, whereas for large interaction parameters, the conductivity of the fluid strongly influences the control of flow‐separation. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of induced magnetic field on peristaltic flow of Johnson-Segalman fluid in a vertical symmetric channel

In this paper, the influence of heat transfer and induced magnetic field on peristaltic flow of a Johnson-Segalman fluid is studied. The purpose of the present investigation is to study the effects of induced magnetic field on the peristaltic flow of non-Newtonian fluid. The two-dimensional equations of a Johnson-Segalman fluid are simplified by assuming a long wavelength and a low Reynolds number. The obtained equations are solved for the stream function, magnetic force function, and axial pressure gradient by using a regular perturbation method. The expressions for the pressure rise, temperature, induced magnetic field, pressure gradient, and stream function are sketched and interpreted for various embedded parameters.     

液态金属熔池中气泡-液体两相湍流的数值模拟研究

应用欧拉-欧拉双流体模型,以及分别描述气泡和液体湍流的两相湍流模型,描述液态金属中气体射流发泡过程的两相流动及气泡分布。与实验结果的对比表明,本模型的预测能力优于前人未考虑气相湍流的模型。考查了液体物性和气泡尺寸对流场特性的影响,结果发现,液体密度越低,气泡尺寸越小,气泡分布就越均匀。     

The effect of magnetic fields on low frequency oscillating natural convection with pressure gradient

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The influence of low-frequency varying magnetic field on the pulsatile flow in a rigid round tube

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Full-scale two-phase flow measurements on Athena research vessel

Measurements of gas volume fraction, bubble velocity, chord length and bubble size distributions were performed on the research vessel Athena II operating in Saint Andrew Bay in the gulf coast near Panama City, FL. Double tipped sapphire optical local phase-detection probes were used to acquire indicator functions downstream of the breaking bow wave, behind the masker and at the stern. These indicator functions were also taken at different depths, operating speeds and headings respect to the waves. The data processing includes the computation of velocity of individual bubbles and chord lengths, resulting in chord length distributions. These chord length distributions are used to obtain bubble size distributions using a novel procedure described in detail herein. Uncertainty analysis is performed for gas volume fraction, average bubble velocity and chord length. The results indicate that air entrainment increases with ship speed and sailing against the waves at all positions. The bow wave exhibits unsteady breaking that creates bubble clouds, which were characterized and identified by signal processing. At the stern a very strong dependence of bubble size with depth was found, with evidence that small bubbles (smaller than 500 μm) are transported through the bottom of the hull and reach the transom. The roller present at the transom, the associated strong unsteadiness and bubble entrainment are well captured, as indicated by the stern results, showing the frothy nature of the upper layer.     

气液混输悬链线立管系统两相流特性实验

严重段塞流是海洋工程气液混输管线--立管系统中常见的一种特殊有害流动现象, 采用水平--下倾--悬链线立管气液混输组合管道系统, 通过系列实验在悬链线立管中获得了严重段塞流、间歇流和震荡流等流型, 阐述了这些流动现象的形成机理, 提出了能够产生严重段塞流的判定准则. 结果表明, 悬链线立管严重段塞流具有明显周期性, 在一个周期内的流动特征可分为液塞形成、液体出流、液气喷发及液体回流等4个阶段, 进而给出了各阶段中相关流动参数的变化规律. 在实验中同时还对悬链线与垂直立管中严重段塞流形成机理进行了比较分析, 发现两者在液塞形成阶段有显著差别. 其中, 在悬链线立管中液塞形成之前首先需要经历一个气液混合液塞形成过程, 而垂直立管则没有这个过程.      

Prediction of liquid level distribution in horizontal gas-liquid stratified flows with interfacial level gradient

A one-dimensional momentum equation has been derived based on a two-fluid model and used to predict the axial distribution of liquid level or void fraction in steady, cocurrent, gas-liquid stratified flows in horizontal circular pipes and rectangular channels. The equation is carefully formulated to incorporate the effect of interfacial level gradient. Two different critical liquid levels are found from the momentum equation and are adopted as a boundary condition to calculate the liquid level or void fraction distribution upstream of the channel exit. The predicted void fraction distributions are compared with the experimental data obtained in a rectangular channel in this work and other data reported for large-diameter pipes. Good agreement is shown for air-kerosene, air-water and stream-water stratified flows with a smooth gas-liquid interface.     

The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media

We consider the one-dimensional two-phase flow including capillary effects through a heterogeneous porous medium. The heterogeneity is due to the spatial variation of the absolute permeability and the porosity. Both these quantities are assumed to be piecewise constant. At interfaces where the rock properties are discontinuous, we derive, by a regularisation technique, conditions to match the values of the saturation on both sides. There are two conditions: a flux condition and an extended pressure condition. Applying these conditions we show that trapping of the wetting phase may occur near heterogeneities. To illustrate the behaviour of the saturation we consider a time-dependent diffusion problem without convection, a stationary convection-diffusion problem, and the full time-dependent convection-diffusion problem (numerically). In particular the last two problems explicitly show the trapping behaviour.