Extensional flow of a viscoelastic filament governed by the FENE-CR model

A thin filament model is used to analyze the extensional flow of a viscoelastic thread governed by the FENE-CR model. The problem is solved numerically by finite differences using a third-order upwind scheme in space and a second order Runge-Kutta scheme in time. The behavior of the filament is controlled by the competing effects of surface tension and axial normal stresses which are characterized in terms of three-dimensional groups, the Deborah number De, the extensibility parameter L and the capillary number Ca. Surface tension has a destabilizing effect causing the filament to thin in the mid-section leading to a rupture. On the other hand normal stresses tend to stabilize the filament. If axial normal stresses are sufficiently large the filament deforms almost uniaxially due to strain hardening.     

Extensional flow of polymer solutions through porous media

The flow behaviour of various polymer solutions of non-hydrolyzed polyacrylamide, hydrolyzed polyacrylamide, polyox and Xanthan was investigated in a plexiglass column having a succession of enlargements and constrictions, and compared with the flow behaviour and mechanical degradation of a solution of non-hydrolyzed polyacrylamide in a packed column of non-consolidated sand. The flow behaviour of this solution was found to be very similar in both the sand pack and plexiglass pore.Apart from the Xanthan solution, all other polymer solutions showed a viscoelastic behaviour in the plexiglass pore. The onset of viscoelastic behaviour, which has previously been defined using the shear rate ( ), stretch rate ( _s ) and Ellis number (E ₁), could be more precisely evaluated using a modified stretch rate (S _G). The pressure losses across the plexiglass pore for different polymer solutions of the same type were found to follow a unique curve provided the suggested group (S _G) was used, a situation which was not achieved with the other rheological parameters.The multipass mechanical degradation of the non-hydrolized polyacrylamide was tested through the sand pack against the suggested group (S _G) and Maerker's group (M _a). It was found that the loss of the solution viscoelasticity due to multipass mechanical degradation was better represented usingS _G thanM _a. A cross-sectional area (cm²) - C ^* critical concentration of polymer (ppm) - d plexiglass pore enlargement diameter - D average sand grain diameter (cm) - e equivalent width for the plexiglass pore - E ₁ Ellis number (a Deborah number) - F _R resistance factor - F _Ri resistance factor at the first pass - h height of the flow path of the plexiglass pore - K power-law constant - K _h,K _w effective permeability to hydrocarbon and water, respectively (10^–8 cm²) - M _a Maerker's group for a given porosity (s^–1) - M _ai value ofM _a at the first pass - N _D Deborah number - n power-law index - Q flow rate (cm³/s) - R capillary radius (cm) - R _g radius of gyration - S _G suggested group of rheological parameters representing a modified maximum stretch rate (s^–1) - S _Gi value ofS _G at the first pass - T _R,t characteristic time for the fluid (s) - t _s residence time (s) - V ₀ superficial velocity (cm/s) - V mean velocity of flow through a porous medium (cm/s) - average axial velocity in the enlargement section of the plexiglass pore (cm/s) - V ₁,V ₂ maximum velocity at a plexiglass enlargement neck and centre - [] intrincis viscosity - viscosity (mPa s) - _r relative viscosity (ratio of the viscosity of the polymer solution to that of the solvent) - shear rate (s^–1) - _s stretch rate (s^–1) - characteristic time for the polymer solution (s)     

Single cavitation bubble generation and observation of the bubble collapse flow induced by a pressure wave

This study utilizes a U-shape platform device to generate a single cavitation bubble for a detailed analysis of the flow field characteristics and the cause of the counter jet during the process of bubble collapse caused by sending a pressure wave. A high speed camera is used to record the flow field of the bubble collapse at different distances from a solid boundary. It is found that a Kelvin–Helmholtz vortex is formed when a liquid jet penetrates the bubble surface after the bubble is compressed and deformed. If the bubble center to the solid boundary is within one to three times the bubble’s radius, a stagnation ring will form on the boundary when impinged by the liquid jet. The fluid inside the stagnation ring will be squeezed toward the center of the ring to form a counter jet after the bubble collapses. At the critical position, where the bubble center from the solid boundary is about three times the bubble’s radius, the bubble collapse flow will vary. Depending on the strengths of the pressure waves applied, the collapse can produce a Kelvin–Helmholtz vortex, the Richtmyer–Meshkov instability, or the generation of a counter jet flow. If the bubble surface is in contact with the solid boundary, the liquid jet can only move inside-out without producing the stagnation ring and the counter jet; thus, the bubble collapses along the radial direction. The complex phenomenon of cavitation bubble collapse flows is clearly manifested in this study.     

Evolution of flow structure in impinging three-dimensional axial and radial jets

Direct numerical simulations of the flow field of an element of banks of impinging axial and radial slot jets for different Reynolds number are presented. Simulations have been obtained from the solution of the Navier–Stokes equations. Results show for the chosen geometry a transition from steady to periodic to chaotic flow with increasing Reynolds number. The transition Reynolds number is nearly 50% smaller for the radial jet than for the axial jet. Period doubling has been observed for both cases, but only the radial jet shows periodic windows of chaos. © 1997 John Wiley & Sons, Ltd.     

Towards numerical simulations of supersonic liquid jets using ghost fluid method

A computational tool based on the ghost fluid method (GFM) is developed to study supersonic liquid jets involving strong shocks and contact discontinuities with high density ratios. The solver utilizes constrained reinitialization method and is capable of switching between the exact and approximate Riemann solvers to increase the robustness. The numerical methodology is validated through several benchmark test problems; these include one-dimensional multiphase shock tube problem, shock–bubble interaction, air cavity collapse in water, and underwater-explosion. A comparison between our results and numerical and experimental observations indicate that the developed solver performs well investigating these problems. The code is then used to simulate the emergence of a supersonic liquid jet into a quiescent gaseous medium, which is the very first time to be studied by a ghost fluid method. The results of simulations are in good agreement with the experimental investigations. Also some of the famous flow characteristics, like the propagation of pressure-waves from the liquid jet interface and dependence of the Mach cone structure on the inlet Mach number, are reproduced numerically. The numerical simulations conducted here suggest that the ghost fluid method is an affordable and reliable scheme to study complicated interfacial evolutions in complex multiphase systems such as supersonic liquid jets.     

Propagation characteristics of pressure disturbances originated by gas jets in fluidized beds

An experimental investigation has been carried out on velocities and amplitudes of pressure disturbances in fluidized beds made of 100–200 μm glass ballotini. Disturbances were originated by gas jetting in a 0.35 m i.d. fluidized bed. A fluidization tube 0.10 m i.d. has also been used. Different types of disturbances have been induced in the bed contained in this tube: injection of a freely rising bubble and of a captive bubble; injection of a bubble chain; and compression of the bed free surface. The dynamic wave character of the disturbances has been shown. Velocities and amplitudes of waves moving through the beds have been measured. In particular, wave velocities have been compared with theoretical results obtained by the application of “pseudo-homogeneous” and “separated phase flow” models.     

Enhancement of shock waves in a porous medium saturated with a liquid containing soluble-gas bubbles

Evolution of a moderate-intensity shock wave and its enhancement after reflection from a rigid surface embedded in a porous medium are studied experimentally. The medium is saturated with a liquid that has bubbles of a soluble gas. A physical mechanism of shock wave enhancement in a saturated porous medium is proposed. Experimental data on the amplitude and velocity of reflected waves are compared with results of theoretical modeling. The process of gas bubble dissolution behind a shock wave is studied.     

Pumping of a fluid through a microchannel by means of a bubble driven by a light beam

A new method of pumping a fluid through a microchannel device using a gas bubble-piston, set in motion by the thermocapillary force induced by a light beam, is proposed. To demonstrate the method, a model micropump has been assembled. The model consists of two reservoirs connected by two channels with a bubble-piston driven by a light beam. The pumping rate and the volume per piston stroke are evaluated experimentally. The method proposed is compared with known microfluid pumping methods. Some advantages of the new method are indicated.     

Film thickness measurements in liquid–liquid slug flow regimes

At present there is significant interest in the development of small scale medical diagnostic equipment. These devices offer faster processing times and require smaller sample volumes than equivalent macro scale systems. Although significant attention has been focused upon their outputs, little attention has been devoted to the detailed fluid mechanics that govern the flow mechanisms within these devices. Conventionally, the samples in these small scale devices are segmented into distinct discrete droplets or slugs which are suspended in an organic carrier phase. Separating these slugs from the channel wall is a very thin film of the organic carrier phase.The magnitude of this film is the focus of the present study and the effects of sample slug length and carrier phase fluidic properties on the film are examined over a range of Capillary numbers. A non-intrusive optical technique was used to capture images of the flow from which the magnitude of the film was determined.The experimental results show that the film is not constant along the length of the slug; however above a threshold value for slug length, a region of constant film thickness exists. When compared with existing correlations in the literature, the experimental data showed reasonable agreement with the Bretherton model when the Capillary number was calculated based on the mean two phase flow velocity. However, significant differences were observed when the Capillary number was redefined to account for the mean velocity at the liquid interface, i.e., the mean slug velocity.Analysis of the experimental data revealed that it fell into two distinct flow regimes; a visco-capillary regime and a visco-inertial regime. A modified Taylor expression is presented to estimate the magnitude of the film for flows in the visco-capillary regime while a new model is put forward, based on Capillary and Weber numbers, for flows in the visco-inertial regime. Overall, this study provides some novel insights into parameters, such as aqueous slug length and carrier phase fluidic properties, that affect the thickness of the film in liquid–liquid slug flow regimes.     

水下爆炸中气泡射流壁压特性实验研究

水下爆炸气泡射流载荷是中近场水下爆炸壁压载荷的重要组成部分, 将水下爆炸气泡射流简化为一段高速水柱来研究水下爆炸气泡射流载荷特性是研究水下爆炸气泡射流载荷的主要手段。本文基于腔内爆炸提出了一种新的高速水射流实验方法,并给出了实验装置设计、实验方法以及实验系统。基于实验系统,开展了不同工况下高速水射流的实验研究,研究了腔口位置、腔深对水射流形态的影响,并对水射流的形态形成因素进行了分析。使用压电型壁压传感器测得了水射流冲击壁压,给出了水射流冲击壁压的特性及其特点。实验结果表明：腔口位置与腔深是影响水射流端面形态的重要因素;生成的高速水射流冲击壁压峰值满足水锤理论。基于腔内爆炸的高速水射流实验方法能够应用于包括水下爆炸气泡射流在内的高速水射流形态、壁压特性的研究。

     

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.     

Numerical study of elbow erosion due to sand particles under annular flow considering liquid entrainment

Sand particle erosion is always a challenge in natural gas production. In particular, the erosion in gas–liquid–solid annular flow is more complicated. In this study, a three-phase flow numerical model that couples the volume of fluid multiphase flow model and the discrete phase model was developed for prediction of erosion in annular flow. The ability of the numerical model to simulate the gas–liquid annular flow is validated through comparison with the experimental data. On the basis of the above numerical model, the phase distribution in the pipe was analyzed. The liquid entrainment behavior was reasonably simulated through the numerical model, which guaranteed the accuracy of predicting the particle erosion. Additionally, four erosion prediction models were used for the erosion calculation, among them, the Zhang et al. erosion model predicted the realistic results. Through the analysis of the particle trajectory and the particle impact behavior on the elbow, the cushion effect of the liquid film on the particles and the erosion morphology generation at the elbow were revealed.     

CFD based mini- vs. micro-system delineation in elongated bubble flow regime

Delineation of mini- and micro-scale channels with respect to two-phase flow has been the subject of many research papers. There is no consensus on when the small channel can be characterized as a mini-channel or micro-channel. The idea proposed by this paper is to use the normalized bubble nose radius, liquid film thickness top over bottom ratio, and bubble shape contour, which are found under normal gravity conditions in slug flow through a horizontal adiabatic channel, as the delineation criteria. The input parameters are bubble nose radius and bubble nose velocity as the characteristic length scale and characteristic velocity scale respectively. 3D numerical simulation with ANSYS FLUENT was used to obtain the necessary data. Following CFD practice, a mesh independence study and a numerical model validation against published experimental data were both conducted. Analysis of the numerical simulation results showed that channels with D ⩽ 100 μm can be characterized as a micro-system, while channels with D ⩾ 400 μm belong to mini-systems. The region 200 μm ⩽ D ⩽ 300 μm represents a transition from the micro-scale to mini-scale.     

Formation of radially expanding liquid sheet by impinging two round jets

A thin circular liquid sheet can be formed by impinging two identical round jets against each other. The liquid sheet expands to a certain critical radial distance and breaks. The unsteady process of the formation and breakup of the liquid sheet in the ambient gas is simulated numerically. Both liquid and gas are treated as incompressible Newtonian fluids. The flow considered is axisymmetric. The liquid-gas interface is modeled with a level set function. A finite difference scheme is used to solve the governing Navier-Stokes equations with physical boundary conditions. The numerical results show how a thin circular sheet can be formed and break at its circular edge in slow motion. The sheet continues to thin as it expands radially. Hence, the Weber number decreases radially. The Weber number is defined as ρu 2 h/σ, where ρ and σ are, respectively, the liquid density and the surface tension, and u and h are, respectively, the average velocity and the half sheet thickness at a local radial location in the liquid sheet. The numerical results show that the sheet indeed terminates at a radial location, where the Weber number reaches one as observed in experiments. The spatio-temporal linear theory predicts that the breakup is initiated by the sinuous mode at the critical Weber number We c =1, below which the absolute instability occurs. The other independent mode called the varicose mode grows more slowly than the sinuous mode according to the linear theory. However, our numerical results show that the varicose mode actually overtakes the sinuous mode during the nonlinear evolution, and is responsible for the final breakup. The linear theory predicts the nature of disturbance waves correctly only at the onset of the instability, but cannot predict the exact consequence of the instability.     

Primary instabilities of liquid film flow sheared by turbulent gas stream

Evolution of excited waves on a viscous liquid film has been investigated experimentally for the annular gas–liquid flow in a vertical tube. For the first time the dispersion relations are obtained experimentally for linear waves on liquid film surface in the presence of turbulent gas flow. Both cocurrent and countercurrent flow regimes are investigated. As an example of comparison with theory, the experimental data are compared to the results of calculations based on the Benjamin quasi-laminar model for turbulent gas flow. The calculation results are found to be in good agreement with experiments for moderate values of film Reynolds number.     

Investigation on development of free-surface structures in turbulent liquid lithium flow

The liquid lithium film thickness facing the Deuterium beam of the International Fusion Material Irradiation Facility (IFMIF) determines the neutron flux to be generated. Hence, apart from its thickness also its spatio-temporal behaviour plays a decisive role in the performance of the target. Two aspects contributing to the free surface shape are the evolution of the viscous wall boundary layer in the nozzle and the development of turbulence downstream the nozzle exit, which are analysed here numerically by means of a fluid dynamic Large Eddy Simulation (LES). The numerical method is validated by experiments conducted at Osaka University with respect to mean and turbulent flow quantities in a broad spectrum of mean flow velocities. Thereby, both a qualitative and a quantitative agreement have been attained identifying different flow regimes and, moreover, allowing for a more refined, realistic IFMIF target prediction performance.     

The EHD-driven fluid flow and deformation of a liquid jet by a transverse electric field

The aim of this study is to investigate the effect of a uniform transverse electric field on the steady-state behavior of a liquid cylinder surrounded by another liquid of infinite extent. The governing electrohydrodynamic equations are solved for Newtonian and immiscible fluids in the framework of leaky-dielectric theory and in the limit of small electric field and fluid inertia. A detailed analysis of the electrical and hydrodynamic stresses acting on the interface separating the two fluids is presented, and an expression is found for the interface deformation for small distortions from a circular shape. The electrical stresses acting on the interface of two leaky-dielectric liquids are compared with those acting on an interface separating a perfect dielectric or infinitely conducting core fluid cylinder from a surrounding perfect dielectric fluid. A comparison is made between the results of this study and those of a similar study for fluids with permeable interfaces and the classical results for liquid drops.