Chaotic behavior of gas bubble in non-Newtonian fluid: a numerical study

In the present paper, the nonlinear behavior of bubble growth under the excitation of an acoustic pressure pulse in non-Newtonian fluid domain has been investigated. Due to the importance of the bubble in the medical applications such as drug, protein or gene delivery, blood is assumed to be the reference fluid. Effects of viscoelasticity term, Deborah number, amplitude and frequency of the acoustic pulse are studied. We have studied the dynamic behavior of the radial response of bubble using Lyapunov exponent spectra, bifurcation diagrams, time series and phase diagram. A period-doubling bifurcation structure is predicted to occur for certain values of the effects of parameters. The results show that by increasing the elasticity of the fluid, the growth phenomenon will be unstable. On the other hand, when the frequency of the external pulse increases the bubble growth experiences more stable condition. It is shown that the results are in good agreement with the previous studies.     

Numerical simulation and hydrodynamic visualization of transient viscous flow around an oscillating aerofoil

Unsteady viscous flow around a large-amplitude and high-frequency oscillating aerofoil is examined in this paper by numerical simulation and experimental visualization. The numerical method is based on the combination of a fourth-order Hermitian finite difference scheme for the stream function equation and a classical second-order scheme to solve the vorticity transport equation. Experiments are carried out by a traditional visualization method using solid tracers suspended in water. The comparison between numerical and experimental results is found to be satisfactory. Time evolutions of the flow structure are presented for Reynolds numbers of 3 × 10³ and 10⁴. The influence of the amplitude and frequency of the oscillating motion on the dynamic stall is analysed.     

Numerical study around the corotational Maxwell model for the viscoelastic fluid flows

We present numerical results for the FEM (finite element method) presented in [Comput. Methods Appl. Mech. Engrg. 191 (2002) 5045–5065]. This method is devoted to the approximation of fluid flows obeying the Oldroyd model. A particularity of this method, is to take into account the purely viscoelastic case, the so-called Maxwell model, important in practice. Numerical results are given for a fluid flowing in an abrupt plane 4 to 1 contraction. We use the corotational Maxwell model as benchmark in the choice of our computations. Results are also given for the upper convected Maxwell model. Interesting effects appear on the velocity profile: a phenomenon of quasi slip at the downstream wall.     

Numerical study of homogeneous bubbly flow: Influence of the inlet conditions to the hydrodynamic behavior

This paper discusses the role of the gas injection pattern on the large scale structures in a homogeneous pseudo-2D bubble column operated at relatively high gas hold-ups up to 8%. Seven cases with different inlet configuration have been studied experimentally by Harteveld et al. Each of these cases has been simulated using a (parallel) Euler–Lagrange model developed by Darmana et al. The presence of coherent structures for both uniform and non-uniform gas injection is studied. Furthermore, the influence of the gas injection pattern on the dynamics is investigated, while the statistical (average and fluctuating) quantities are compared with the PIV/PTV and LDA measurement data of Harteveld et al. The results show that the model resembles the observed experimental flow structures to a large extent.     

Numerical modeling of the laminar-turbulent transition control using a dielectric barrier discharge

The control of laminar-turbulent transition driven by Tollmien–Schlichting waves is studied. The control is realized by means of accelerating the boundary layer flow using a dielectric barrier discharge. As distinct from the previous studies based on the solution of the boundary layer equations, the discharge effect on the main flow and unstable disturbances are described by the Navier–Stokes equations.     

Experimental study of the gravity influence on the periodic thermocapillary convection around a bubble

The 3D periodic state, following the steady thermocapillary convection state, around an air bubble immersed in a low-Prandtl-number silicone oil layer under a heated wall was experimentally investigated on the ground and during parabolic flights. This oscillation was observed under reduced gravity conditions for the first time. Consequently, the initiation of this oscillation seems to be independent of gravity and so of buoyancy convection. The reduced and increased gravity conditions showed that the gravity level modifies the oscillation. Its frequency increases with the gravity level. The comparison with the results obtained on the ground shows the bubble aspect ratio is not a relevant parameter when the gravity varies. Received: 27 November 2000/Accepted: 25 May 2001     

Birefringence measurements in extensional flow of polyisobutylene around an expanding bubble

Birefringence in liquid polymers offers the possibility of obtaining information about stress in complex flows. In this work, this is done for extensional flows of polyisobutylene in a “breathing bubble” rheometer. In this type of rheometer, a bubble consisting of an incompressible, low-viscosity fluid (usually water) is injected into the sample with a nozzle. Expanding or collapsing the bubble by adding or removing water induces biaxial or uniaxial extension in the surrounding sample. The pressure difference between the bubble and the surroundings can be measured and compared to the predictions of constitutive equations. This measurement only gives one integral value for a complex flow history. In this paper, the birefringence around the bubble is measured in order to learn more about the flow. This is done by comparing pressure and birefringence results to those of standard constitutive equations for a polyisobutylene sample. A good agreement between the pressure and optical measurements and the theory is found with a single value of the stress-optical constant. Received: 25 June 1997 Accepted: 12 November 1997     

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。

     

Numerical modeling of the free rise of an air bubble

The results of a numerical investigation of the dynamics of a single air bubble rising in water are presented. The bubbles, 1, 2.5, 3, 5, 8, and 10 mm in diameter, are considered. An analysis is based on the numerical solution of the complete three-dimensional system of Navier–Stokes equations for a two-phase medium using an implicit approach with the automatic tracking of the gas-water interface by means of separating the volume fractions. Emphasis is placed on an examination of the local physical characteristics of the motion. The calculated mean rise velocities are compared with experimental data. The rising bubble trajectories are shown to be periodic, zigzag or helical in shape, which is due to the variation in their form and the generation of a characteristic turbulent wake behind them. The bubble rise velocities are correlated with the forces acting on the bubbles.     

Experimental study of the falling film of liquid around a Taylor bubble

The present work reports an experimental study of the falling liquid film around single Taylor bubbles rising in vertical tubes filled with stagnant liquids by using a pulse-echo ultrasonic technique. The experiments were carried out in acrylic tubes 2.0  m long, with inner diameters of 0.019, 0.024 and 0.034  m, with five water-glycerin mixtures, corresponding to inverse viscosity number ranging from 15 to 22422. The rising bubble and the falling liquid film were measured by using ultrasonic transducers located at the one side of the tube. The velocity and profile of the Taylor bubble, and the development length and equilibrium thickness of the falling liquid film around the bubble were obtained by the ultrasonic signals processing. Based on the experimental results of the present study, several correlations available to estimate the equilibrium thicknesses of liquid films falling around Taylor bubbles were evaluated and new correlations were proposed to estimate the dimensionless equilibrium film thickness and the film development length respectively.     

Nonlinear problem of an electrical discharge in a flow

The shape of the shoulder of a forming, filling and closing machine is calculated, based on geometrical considerations, first for a circular and subsequently for a rectangular (superelliptic) section. It appears to be possible to formulate a feasible solution for a model represented by a flat triangular region in the centre, which connects two truncated cones; for each cone one half of the intersection of shoulder and cylinder acts as the directrix of the cone. The solutions are formulated in terms which permit direct application in machine construction. Verification of the theory with the help of paper models and with real shoulders on machines shows a very good agreement between theory and practice. In addition practical tests produce excellent results as well.     

Nonlinear problem of an electrical discharge in a flow

The nonlinear intial boundary value problem describing the relaxation of a quasi-neutral discharge in a gas flow with coplanar, heated and nonheated electrodes of finite extension is formulated in the diffusion approximation. Relaxation occurs from an initial breakdown to a steady-state or zero discharge in a weak electric field. A nonlinear transformation is applied to get an equivalent nonlinear problem, where nonlinearity is treated as a small perturbation. An analytic solution is obtained and criterions for existence and sustainment of a steady-state discharge against plasma losses due to convection, diffusion and recombination is discussed. Some numerical results are exhibited.     

Determination of hydrodynamic load on the wall of a wellbore formed by an electric discharge

Hydrodynamic processes in the discharge chamber of a device intended to increase the fluid conductivity of the porous medium in the well bottom zone are studied. Spatial and temporal characteristics of the pressure waves resulting from an electric discharge in a fluid are determined. The effect of the performance of the electricdischarge device and the wellbore fluid pressure on the dynamic load acting on the wellbore wall are determined.     

Numerical and experimental study of the heat transfer and fluid flow by thermocapillary convection around gas bubbles

 At liquid–gas or liquid–liquid interfaces thermocapillary or Marangoni convection develops in the presence of a temperature or concentration gradient along the interface. This convection was not paid much attention up to now, because under terrestrial conditions it is superimposed by the strong buoyancy convection. In a microgravity environment, however, it is the remaining mode of natural convection. During boiling in microgravity it was observed at subcooled conditions. Therefore the question arises about its contribution to the heat transfer. Thus the thermocapillary convection was intensively studied at single gas bubbles in various liquids both experimentally and numerically. Inside a temperature gradient chamber, the overall heat transfer around single bubbles of different volume was measured with calorimetry and the liquid flow with PIV and LDV. In parallel to the experiment, a 2-dimensional mathematical model was worked out and the coupled heat transfer and fluid flow was simulated with a CV-FEM method both under earth gravity level and under microgravity. The results are described in terms of the dimensionless Nusselt-, Peclet-, Marangoni-, Bond- and Prandtl-number. Received on 23 August 1999     

Viscoelasticity of a dielectric fluid in nonuniform electric fields generated by electrodes with flocked fabrics

The rheological behavior of a dielectric fluid is studied in nonuniform electric fields which are generated by an electrode covered with flocked fabrics. Although no electrorheological (ER) effects are observed in uniform fields between metal electrodes with smooth surfaces, striking increases in viscosity and elastic response are induced by the electrode with flocked fabrics. The presence of flocked fabrics does not have a significant effect on the fluid rheology without electric fields. The ER behavior and current density are influenced by the fiber length even at a constant field strength. When a very small amount of fine particles is introduced in the electrified fluid without shear, we can see the rapid and large-scale motion of particles between the tips of fibers and plate electrode. In high DC fields, the Coulomb force acting on a free charge often gives rise to the secondary motion of fluid. The local motion of fluid in high electric fields is refereed to as electrohydrodynamic (EHD) convection. The additional energy may be required to change the periodic patterns of EHD convection by forced shear. Therefore, the ER effect demonstrated by the modification of electrode with flocked fabrics can be attributed to a combined effect of EHD convection and external shear. Received: 10 March 1998 Accepted: 1 June 1998     

Approximate calculation of the hydrodynamic characteristics of a long electrical discharge in water in the presence of a transverse magnetic field

This paper considers a range of physical phenomena that occur during electrical discharge in water in the presence of a transverse magnetic field. An approximate equation of energy balance is obtained using assumptions based on the well-known hydrodynamic concepts of a long electrical discharge in water. An experimental estimate of the reaction force impulse in a limited medium is obtained.     

Numerical study of the influence of boundary conditions on the dynamic behavior of a cylindrical shell conveying a fluid

We consider a finite element algorithm intended to study the dynamic behavior of an elastic cylindrical shell filled with an immovable or flowing fluid. To describe the fluid, we use the perturbed velocity potential whose equations with the corresponding boundary conditions are solved by the Bubnov-Galerkin method. To describe the shell, we use the variation principle, which includes the linearized Bernoulli equation for calculating the hydrodynamic pressure acting on the shell on the side of the fluid. Solving the problem is reduced to calculating and analyzing the eigenvalues of the coupled system of equations obtained as a result of combining the equations for the perturbed velocity potential and the shell displacements. We consider several test problems in which, along with the comparison of the computational results with the earlier published experimental, analytic, and numerical data, we also study the dynamic behavior of the “shell-fluid” system for various boundary conditions for the perturbed velocity potential.