Behavior of a small single bubble rising in a rotating flow field

A small single bubble was generated with a single-hole nozzle facing upward in a water bath contained in a rotating cylindrical vessel. The bubble size falls in the surface tension force dominant regime. The vertical, radial, and tangential migration velocities of the bubble were measured with two CCD cameras and a high-speed video camera. The tangential velocity component of water flow was measured with particle image velocimetry. A helical motion of the bubble was observed under every experimental condition. The direction of the helical motion was the same as that of the tangential velocity component. This helical motion is associated with the large initial shape deformation of the bubble near the nozzle exit and the subsequent regular shedding of vortices behind it. The period and amplitude of the helical motion were obtained by analyzing the trajectory of the bubble. These quantities were non-dimensionalized by the volume equivalent bubble diameter and the terminal bubble velocity in the vertical direction and correlated as functions of the Eotvos number. Empirical equations were proposed for the period and amplitude. Originally published in the Journal of JSEM, Vol. 4, No. 2, pp. 38–45 (2004).     

On the dynamics of bubbles in polymer aqueous solutions

By analysing experimentally the rheological behaviors of polyethylene oxide solutions, polyacrylamide solutions, carboxymethylcellulose solutions, and hydroxyethylcellulose solution, a rheological model is proposed. The effect of various polymer additives on an air-liquid surface tension is made clear. The equation of motion for a bubble and the pressure equation are derived by using the new rheological expression, and then the effects of a kind of polymer and a polymer concentration on the bubble radius-time history and impulse pressure are numerically examined.     

Effects of atmospheric pressure and air concentration in the fluid on the motion of a rigid sphere along a wall (experiment)

The effects of the dissolved air concentration and atmospheric pressure on the motion of a rigid sphere along a wall in a fluid are studied experimentally. These effects are the result of the occurrence of a gas bubble in the lubrication layer between the moving sphere’s and the wall. It is found that, depending on the air concentration in the fluid and the atmospheric pressure, during the sphere motion the bubble volume may either increase or remain constant. From the observations, it is clear that the variation of the bubble volume is associated with the unsteady motion of the sphere.     

An Experimental Study of the Modulation of the Bubble Motion by Gas–Liquid-Phase Interaction in Oscillating-Grid Decaying Turbulence

The purpose of the present research is to understand dynamic bubble–liquid interaction in a bubbly flow based on the experimental results of the modulation of the bubble motion in oscillating-grid decaying turbulence. By comparing the experimental results obtained from stagnant water and those from oscillating-grid decaying turbulence, we discussed and described detailed process of the modulation of the bubble motion in a water vessel. We discussed the enhancement of the transition of the bubble motion from 2D to 3D by combining the liquid-phase motion obtained through particle imaging velocimetry/laser-induced fluorescence (PIV/LIF) measurement and the bubble wake motion captured through the LIF/HPTS (8-hydroxypyrene-1, 3, 6-trisulfonic acid) method, under both conditions (in the stagnant water and in the oscillating-grid decaying turbulence) in which the initial bubble formation and the bubble motion (gravity-center motion and surface oscillation) were considered to be the same. In addition, by using PIV/LIF measurement along with an infrared shadow technique, we simultaneously obtained the bubble motion (2D zigzagging motion in stagnant water, and 3D motion in the decaying turbulence) and the standard deviation of the liquid-phase motion (the bubble Reynolds number: 775; the turbulent Reynolds number: 62.2). Taking all of the results together, the modulation of the bubble motion in the decaying turbulence, and the dynamic interaction between the bubble and the liquid-phase motion were experimentally and carefully investigated. Consequently, the enhancement and the modulation of the bubble wake motion were considered to be triggered by the collapse of the symmetric property of the bubble–liquid (i.e. ambient liquid-phase turbulence) interaction.     

简单Green函数法模拟三维水下爆炸气泡运动

假定水下爆炸气泡脉动阶段的流场是无旋、不可压缩的,运用势流理论导出气泡边界面运动的控制方程,采用高阶曲面三角形单元离散了维气泡表面,用边界积分法求解气泡的运动．并将计算结果与Rayleigh-Plesset气泡模型和试验数据进行对比分析,分析结果表明高阶曲面单元能够高精度的模拟水下爆炸气泡运动,且比线性单元有多方面的优越性．分别模拟了有、无重力场和刚壁时对气泡运动的影响,并预测了气泡在流场中膨胀、坍塌、迁移、射流形成等苇要动力学行为,同时建立了水下爆炸气泡与圆柱简相互作用的三维模型,模拟了自由液面、圆柱筒附近三维气泡的动力学特性．     

Bubble deformation and flow structure measured by double shadow images and PIV/LIF

An experiment on bubble motion in a simple shear layer was performed in order to obtain fundamental knowledge of the force on the bubble and its lateral motion induced by the surrounding flow field. We explored the flow structure in the vicinity of the bubble in one plane and its deformation in two planes by particle image velocimetry (PIV)–laser-induced fluorescence (LIF) and a projection technique for two perpendicular planes, respectively. For our experiment, we chose a single air bubble with an equivalent bubble diameter D _eq of 2~6 mm in a vertical shear flow. Velocity measurements were made using a digital high-speed CCD camera for PIV with fluorescent tracer particles. The second and third CCD cameras were used to detect the bubbles shape and motion via backlighting from an array of infrared LEDs. We quantitatively studied the three-dimensional wake structure from measurements of the two-dimensional vortex structure and approximated three-dimensional shape deformation arranged from two perpendicular bubble images.     

Interchangeability of vortex-breakdown types

In order to investigate the connection between the bubble and the spiral form of vortex breakdown, experiments were conducted: an external disturbance in the form of an azimuthally spinning waveform was imposed in a pipe. The azimuthal wave number was varied by adjusting the phase difference among four oscillating pistons mounted circumferentially on the pipe. By imposing a disturbance of zero azimuthal wave number, a spiral was transformed into a bubble, and this occurred only for selective piston frequencies; the vortex breakdown which altered from the spiral to the bubble moved upstream, where it remained as a bubble as long as the external disturbance remained. Once the disturbance was removed, the bubble returned to a spiral. By imposing a disturbance of azimuthal wave number +1 (the first circumferential mode rotating in the same direction as the mean swirl), a bubble was transformed into a spiral for selective piston frequencies, and the spiral moved downstream. These preferred frequencies were found to be the same as the unexcited frequencies observed in the spiral in its natural state. As long as the external disturbance was imposed, the breakdown altered from the bubble to the spiral remained as a spiral; once the disturbance was removed, the spiral reverted to a bubble. By imposing a disturbance with azimuthal wave number -1 (the first circumferential mode rotating in the opposite direction to the mean swirl), no change was detected in either a bubble or a spiral. By imposing a disturbance with azimuthal wave number 2 (the second circumferential mode), for selective piston frequencies a bubble was transformed into what appears to be the so-called two-tailed type. Thus, it appears that hydrodynamic instability plays a role in interchanging vortex breakdown types, and a comparison with available stability theories is discussed.     

垂直壁面附近上升单气泡的弹跳动力学研究

采用高速摄影技术结合阴影法,对静止水中垂直壁面附近上升单气泡运动进行实验研究,对比气泡尺度及气泡喷嘴与壁面之间的初始无量纲距离 ($S^{\ast}$)对气泡上升运动特性的影响,分析气泡与壁面碰撞前后,壁面效应与气泡动力学机制及能量变化规律.结果表明,对于雷诺数$Re \approx 580 \sim 1100$,无量纲距离$S^{\ast } <2 \sim3$时,气泡与壁面碰撞且气泡轨迹由无约束条件下的三维螺旋转变成二维之字形周期运动;当$S^{\ast } >2 \sim3$时,壁面效应减弱,有壁面约束的气泡运动与无约束气泡运动特性趋于一致.气泡与壁面碰撞前后,壁面效应导致横向速度峰值下降为原峰值的70%,垂直速度下降50%;气泡与壁面碰撞前,通过气泡中心与壁面距离($x/R$)和修正的斯托克斯数相关式可预测垂直速度的变化规律.上升气泡与壁面碰撞过程中,气泡表面变形能量单向传输给气泡横向动能,使得可变形气泡能够保持相对恒定的弹跳运动.提出了气泡在与壁面反复弹跳时的平均阻力系数的预测模型,能够很好地描述实验数据反映出的对雷诺数${Re}$、韦伯数${We}$和奥特沃斯数${Eo}$等各无量纲参数的标度规律.      

水下爆炸气泡射流载荷计算的新方法研究

由于存在强冲击、多相界面复杂运动等强非线性效应,目前对于水下爆炸气泡运动的计算方法无法给出较为可信的水射流运动特征及其载荷形式.本文基于多相可压缩流体的five-equation计算模型,引入界面函数和界面密度压缩技术,采用5阶WENO重构与HLLC近似Riemann求解器进行空间离散,时间离散采用3阶TVD Rung...     

Forced convective flow and heat transfer of upward cocurrent air–water slug flow in vertical plain and swirl tubes

This experimental study comparatively examined the two-phase flow structures, pressured drops and heat transfer performances for the cocurrent air–water slug flows in the vertical tubes with and without the spiky twisted tape insert. The two-phase flow structures in the plain and swirl tubes were imaged using the computerized high frame-rate videography with the Taylor bubble velocity measured. Superficial liquid Reynolds number (Re_L) and air-to-water mass flow ratio (AW), which were respectively in the ranges of 4000–10000 and 0.003–0.02 were selected as the controlling parameters to specify the flow condition and derive the heat transfer correlations. Tube-wise averaged void fraction and Taylor bubble velocity were well correlated by the modified drift flux models for both plain and swirl tubes at the slug flow condition. A set of selected data obtained from the plain and swirl tubes was comparatively examined to highlight the impacts of the spiky twisted tape on the air–water interfacial structure and the pressure drop and heat transfer performances. Empirical heat transfer correlations that permitted the evaluation of individual and interdependent Re_L and AW impacts on heat transfer in the developed flow regions of the plain and swirl tubes at the slug flow condition were derived.     

Interaction of heat release and vortex breakdown during flame flashback driven by combustion induced vortex breakdown

The interaction of heat release by chemical reaction and the flow dominates flame transition in swirling flows caused by combustion induced vortex breakdown (CIVB). The simultaneous application of 1 kHz high-speed particle imaging velocimetry (PIV) for the analysis of the flow field and OH planar laser-induced fluorescence for the detection of the flame front is particularly useful for the improvement of the understanding of the observed fast CIVB driven flame propagation. For the first time, the combination of both techniques was successfully applied to confined swirling flows. In the study, the flow field characteristics of an aerodynamically stabilized burner system with CIVB are analyzed in great depth. The influence of geometric parameters of the swirl generator was investigated and conclusions concerning the proper burner design of vortex breakdown premix burners are drawn from the experimental results. In particular, the effect of the vortex core with respect to the stability of the swirl stabilized burner is analyzed. The contribution of combustion to vortex breakdown is shown comparing isothermal and reacting flows. The presented data reveals that at the onset of CIVB driven flame transition, the azimuthal vorticity leads to the formation of a closed recirculation bubble at the tip of the internal recirculation zone. Once this bubble propagates upstream, the flame is able to follow and propagate relative to the bulk flow velocity with a velocity far beyond the turbulent flame speed. The interaction of reaction and flow was observed for different volumetric heat releases. The experiments confirm the CIVB theory of the authors, which was initially developed on the basis of a CFD study alone. Both the volume expansion and the baroclinic torque have an effect on whether fast flame propagation occurs. Whereas the volume expansion caused by the heat release stabilizes the flow field and the reaction, the baroclinic torque stimulates flame transition. For upstream propagation the flame tip has to have a position downstream of the stagnation point of the bubble. Else, the required transition inducing force is insufficient and the flame remains stable. In case the flame reaches positions too close or even upstream of the stagnation point, the fast propagation is interrupted or even prohibited. The key finding that the relative position of flame and stagnation bubble governs CIVB is discussed on the basis of high-speed LIF/PIV data as well as chemiluminescence. Since essentially the same behavior has been observed before in tests of a totally different swirler design and flow field, the conclusion can be made that the root cause for CIVB independent of the special geometry has been found.     

A computational study of the effect of initial bubble conditions on the motion of a gas bubble rising in viscous liquids

In order to examine the influence of initial bubble conditions on bubble rise motion, two-dimensional direct numerical simulations of the motion of a gas bubble rising in viscous liquids were carried out by a coupled level set/volume-of-fluid (CLSVOF) method. For dimensionless groups predicting a “spherical-cap bubble shape” (high Eötvös and low Morton numbers), we have found computationally that solutions depend on initial bubble conditions. Specifically, for spherical-cap bubble areas, we could obtain computational results of toroidal bubbles or spherical-cap bubbles depending on initial bubble conditions. On the other hand, we showed for low Eo and high M conditions that initial bubble conditions did not affect the final state of bubble rise motion.     

Direct numerical simulation of confined swirling jets

This study investigates the Lagrangian acceleration and velocity of fluid particles in swirling flows via direct numerical simulation. The intermittency characteristics of acceleration and velocity of fluid particles are investigated at different swirl numbers and Reynolds numbers. The flatness factor and trajectory curvature are used to analyse the effect of Lagrangian intermittency. The joint probability density function of Lagrangian acceleration and turbulence intensity is shown to explain the augmentation effect of Lagrangian intermittency by the strongly swirling levels under the relatively low intensity of turbulence. In addition, the correlation between the Lagrangian acceleration and the turbulence intensity is enhanced as the swirl level increases. It shows the important effect of swirl on the motion behaviour of fluid particles in the strongly swirling flows.     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

On coherent structures and mixing characteristics in the near field of a rotating-pipe jet

Mixing characteristics and coherent structures populating the near-nozzle area of a rotating-pipe jet at the Reynolds number of 5300 were studied by Large-eddy simulation (LES). The swirl rate, defined as the ratio of the tangential velocity of the inner pipe wall to the bulk axial velocity, varied from 0 to 1, corresponding to a weak-to-moderate swirl intensity, insufficient to induce reverse flow near the nozzle. The visualization shows that for the non-swirling jet the near-wall streaky structures generated in the pipe interact with the shear layer, evolving into hairpin-like structures that become tilted at low rotation rates. For higher swirl, they cannot be recognized as they are destroyed at the nozzle exit. No large-scale coherent structures akin to Kelvin–Helmholtz vortical rings in the ‘top-hat’ jets are identifiable close to the nozzle. Using the single and joint probability density functions of velocity and passive scalar (temperature) fields we quantify the events responsible for the intensive entrainment at various swirl numbers. The isosurface of the temperature field indicates the meandering and precessing motion of the rotating jet core at the axial distance of 6D downstream, where D is the diameter of the pipe. The Fourier analysis with respect to the azimuthal angle and time reveals an interplay between the co- and counter-rotating modes. These findings explain the previously detected but not fully clarified phenomenon of the weakly counter-rotating jet core at low swirl rates.     

Unsteady separated and reattaching turbulent flow over a two-dimensional square rib

The spatio-temporal characteristics of the separated and reattaching turbulent flow over a two-dimensional square rib were studied experimentally. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. Profiles of time-averaged streamwise velocity and wall-pressure fluctuations showed that the shear layer separated from the leading edge of the rib sweeps past the rib and directly reattaches on the bottom wall (x/H=9.75) downstream of the rib. A thin region of reverse flow was formed above the rib. The shedding large-scale vortical structures (fH/U₀=0.03) and the flapping separation bubble (fH/U₀=0.0075) could be discerned in the wall-pressure spectra. A multi-resolution analysis based on the maximum overlap discrete wavelet transform (MODWT) was performed to extract the intermittent events associated with the shedding large-scale vortical structures and the flapping separation bubble. The convective dynamics of the large-scale vortical structures were analyzed in terms of the autocorrelation of the continuous wavelet-transformed wall pressure, cross-correlation of the wall-pressure fluctuations, and the cross-correlation between the wall pressure at the time-averaged reattachment point and the streamwise velocity field. The convection speeds of the large-scale vortical structures before and after the reattachment point were U_c=0.35U₀ and 0.45U₀, respectively. The flapping motion of the separation bubble was analyzed in terms of the conditionally averaged reverse-flow intermittency near the wall region. The instantaneous reattachment point in response to the flapping motion was obtained; these findings established that the reattachment zone was a 1.2H-long region centered at x/H=9.75. The reverse-flow intermittency in one period of the flapping motion demonstrated that the thin reverse flow above the rib is influenced by the flapping motion of the separation bubble behind the rib.     

Large Eddy Simulations of Unconfined Non-reacting and Reacting Turbulent Low Swirl Jets

The low swirl flow is a novel method for stabilizing lean premixed combustion to achieve low emissions of nitrogen oxides. Understanding the characteristics of low swirl flows is of both practical and fundamental interest. In this paper, in order to gain better insight into low swirl stabilized combustion, large eddy simulation and dynamically thickened flame combustion modeling are used to characterize various features of non-reacting and reacting low swirl flows including vortex breakdown, shear layers’ instability, and coherent structures. Furthermore, four test cases with different equivalence ratios are studied to evaluate the effects of equivalence ratio on the flame and flow characteristics. A finite volume scheme on a Cartesian grid with a dynamic one equation eddy viscosity subgrid model is used for large eddy simulations. The obtained results show that the combustion heat release and increase in equivalence ratio toward the stoichiometric value decrease the local swirl number of the flow field, while increasing the flow spreading at the burner outlet. Results show that the flame becomes W shaped as the equivalence ratio increases. Moreover, the combination of the swirling motion and combustion heat release temporally imposes a vortex breakdown in the post-flame region, which leads to occurrence of a transient recirculation zone. The temporal recirculation zone disappears downstream of the burner outlet due to merging of the inner shear layer from all sides at the centerline. Also, various analyses of shear layers’ wavy and vortical structures show that combustion heat release has the effect of decreasing the instability amplitude and vortex shedding frequency.     

Marangoni效应下气泡上升过程的FTM模拟

采用界面跟踪法FTM(Front-Tracking Method),并结合CSF(continuum surface force)模型,研究了在垂直方向上温度分布不均匀的对称流场中由Marangoni效应引起的气泡上升运动问题。模拟了在不同的M a数和Pr数下单气泡及同轴双气泡的运动。研究结果表明,在不同的M a数下气泡的运动差异较大,M a数越大,气泡运动至稳态时的速度越大,且气泡运动的最大速度值与M a数呈正相关关系;增大Pr数所造成的粘度增大或热扩散率减小将削弱气泡的迁移运动;Marangoni对流中双气泡的局部运动证实了温度梯度和气泡运动速度紧密相关。     

Study on heat transfer performance of spray cooling: model and analysis

In consideration of droplet–film impaction, film formation, film motion, bubble boiling (both wall nucleation bubbles and secondary nucleation bubbles), droplet–bubble interaction, bulk air convection and radiation, a model to predict the heat and mass transfer in spray cooling was presented in this paper. The droplet–film impaction was modeled based on an empirical correlation related with droplet Weber number. The film formation, film motion, bubble growth, and bubble motion were modeled based on dynamics fundamentals. The model was validated by the experimental results provided in this paper, and a favorable comparison was demonstrated with a deviation below 10%. The film thickness, film velocity, and non-uniform surface temperature distribution were obtained numerically, and then analyzed. A parameters sensitivity analysis was made to obtain the influence of spray angle, surface heat flux density, and spray flow rate on the surface temperature distribution, respectively. It can be concluded that the heat transfer induced by droplet–film impaction and film-surface convection is dominant in spray cooling under conditions that the heated surface is not superheated. However, the effect of boiling bubbles increases rapidly while the heated surface becomes superheated.     

电场作用下气泡上升行为特性的数值计算研究

利用电场控制气泡形态及运动,强化气液相间传热传质是电流体动力学的重要研究内容之一. 然而目前多数研究集中在非电场下的气泡动力学上,对于电场下的气泡行为特性及电场的作用机制仍需开展深入研究. 本研究对电场作用下单个气泡在流体中上升过程的动力学行为进行了数值模拟研究. 在建立二维模型的基础上求解电场方程与Navier-Stokes方程,并采用水平集方法捕捉了上升气泡的位置及形状. 模拟结果的准确性与有效性通过与前人实验和数值结果进行对比得到了验证. 通过改变雷诺数、邦德数和电邦德数等不同参数研究了电场下液体黏度、表面张力和电场力对气泡运动变形的影响. 计算结果表明,电场对气泡的动态特性有显著影响. 非电场情况下液体黏度和表面张力较大时气泡基本维持球状,反之气泡发生变形并逐步达到稳定状态. 此外,电场作用使气泡在初始上升阶段发生剧烈形变,随着不断上升,气泡形变程度不断减小,且气泡的上升速度和长径比均出现振荡. 垂直电场使气泡的上升速度有较大的提高,且随着电邦德数的增大,难以达到相对稳定的状态.