Effect of microbubbles on the structure of turbulence in a turbulent boundary layer

The time-averaged velocity and turbulence intensity distributions were measured by a laser Doppler velocimeter in a turbulent boundary layer filled with microbubbles. The void fraction distribution was also measured using a fiber-optic probe. The velocity decreased in the region below 100 wall units with an increase in bubble density. This led to a decrease in the velocity gradient at the wall, which was consistent with a decrease in shearing stress on the wall. The turbulence intensity in the buffer layer increased at a low microbubble density, and then began to decrease with an increasing microbubble density. Based on the present measurements, the mechanism of turbulence reduction by microbubbles is discussed and a model is proposed. Received for publication on Dec. 3, 1999; accepted on April 18, 2000     

Influence of microbubble diameter and distribution on frictional resistance reduction

Investigations into frictional resistance reduction by microbubbles were carried out using a two-dimensional channel. The flow velocity and the amount of air injected were varied, and the frictional resistance reduction was measured. The frictional resistance reduction increased with increasing mean void ratio. When the bubble diameter was changed, the influence on frictional resistance reduction was negligible. The influence of bubble distribution near a wall was also investigated. Although it is thought that the influence of microbubbles near a wall is large, further investigations are required. Received: February 6, 2002 / Accepted: April 30, 2002 Acknowledgments. This research was supported by a special research program of Toyo University, SR239 Research Committee of the Shipbuilding Research Association of Japan, and the Research Project on Smart Control of Turbulence. The authors express their sincere gratitude for these supports. Address correspondence to: H. Kato (kato@eng.toyo.ac.jp)     

微气泡减阻的二相湍流边界层模型计算

利用边界层中注入微气泡来降低固体壁面摩擦阻力是一项有实用价值且有待进一步研究的减阻技术.本文以含微气泡的湍流边界层为研究对象,以气液二相流理论为基础,对二相湍流边界层控制方程进行了详细讨论,并利用差分网格法进行了求解,计算结果表明微气泡具有明显的减阻效果.最后对影响减阻效果的因素进行了分析,指出了今后的研究方向.     

采用微气泡缩减高速船拖曳阻力(英文)

Ship hull form of the underwater area strongly influences the resistance of the ship.The major factor in ship resistance is skin friction resistance.Bulbous bows,polymer paint,water repellent paint(highly water-repellent wall),air injection,and specific roughness have been used by researchers as an attempt to obtain the resistance reduction and operation efficiency of ships.Micro-bubble injection is a promising technique for lowering frictional resistance.The injected air bubbles are supposed to somehow modify the energy inside the turbulent boundary layer and thereby lower the skin friction.The purpose of this study was to identify the effect of injected micro bubbles on a navy fast patrol boat(FPB) 57 m type model with the following main dimensions:L=2 450 mm,B=400 mm,and T=190 mm.The influence of the location of micro bubble injection and bubble velocity was also investigated.The ship model was pulled by an electric motor whose speed could be varied and adjusted.The ship model resistance was precisely measured by a load cell transducer.Comparison of ship resistance with and without micro-bubble injection was shown on a graph as a function of the drag coefficient and Froude number.It was shown that micro bubble injection behind the mid-ship is the best location to achieve the most effective drag reduction,and the drag reduction caused by the micro-bubbles can reach 6%-9%.     

含微气泡二相湍流边界层减阻理论计算

利用边界层中注入微气泡降低固体壁面摩擦阻力的方法是一项有实用价值且有待进一步研究的减阻技术.本文以含有微气泡的湍流边界层为研究对象,以气液二相流理论为基础,建立了二相湍流边界层控制方程,在对控制方程进行详细讨论的基础上,利用差分网格法进行了求解,计算结果表明微气泡具有明显的减阻效果.最后对影响减阻效果的因素进行了分析,并指出了今后的研究方向.     

气泡减阻实验研究

为研究气泡对航行体侧壁的减阻效果，设计一套试验装置。利用该装置，采用壁面通气法研究不同通气量、不同来流速度和不同通气角度对气泡减阻效果的影响。实验结果表明：在通气量和通气角度不变的条件下，减阻率随来流速度增加而增加；在来流速度和通气角度不变的条件下，随通气量增加，减阻率先增加然后变小；在来流速度和通气量不变的条件下，减阻率随通气角度的增大而减少；在一定的条件下，取得了20．34％的减阻率。     

Simple Lagrangian formulation of bubbly flow in a turbulent boundary layer (bubbly boundary layer flow)

For the theoretical consideration of a system for reducing skin friction, a mathematical model was derived to represent, in a two-phase field, the effect on skin friction of the injection of micro air bubbles into the turbulent boundary layer of a liquid stream. Based on the Lagrangian method, the equation of motion governing a single bubble was derived. The random motion of bubbles in a field initially devoid of bubbles was then traced in three dimensions to estimate void fraction distributions across sections of the flow channel, and to determine local bubble behavior. The liquid phase was modeled on the principle of mixing length. Assuming that the force exerted on the liquid phase was equal to the fluid drag generated by bubble slip, an equation was derived to express the reduction in turbulent shear stress. Corroborating experimental data were obtained from tests using a cavitation tunnel equipped with a slit in the ceiling from which bubbly water was injected. The measurement data provided qualitative substantiation of the trend shown by the calculated results with regard to the skin friction ratio between cases with and without bubble injection as function of the distance downstream from the point of bubble injection.List of symbols B law of wall constant - C _f local coefficient of skin friction - C _f0 local coefficient of skin friction in the absence of bubbles - d _b bubble diameter [m] - g acceleration of gravity [m/s²] - k ₁ k₄ proportional coefficient - k _L turbulent energy of the liquid phase [m²/s²] - L representative length [m] - l _b mean free path of a bubble [m] - m _A added mass of a single bubble [kg] - m _b mass of a single bubble [kg] - N _x ,N _y ,N _z force perpendicular to the wall or ceiling exerted on a bubble adhering to that wall or ceiling [N] - P absolute pressure [Pa] - Q _G rate of air supply [/min] - q _L ⁽ⁱ⁾ turbulent velocity at the ith time increment [m/s] - R> _ex Reynolds number defined by Eq. 32 - T _*L integral time scale of the liquid phase [s] - U velocity of the main stream [m/s] - ,¯v,¯w time-averaged velocity components [m/s] - u,v,w turbulent velocity components [m/s] - û _L ,v_L root mean square values of liquid phase turbulence components in thex- and y-directions [m/s] - V volume of a single bubble [m³] - X,Y,Z components of bubble displacement [m] - x _s ,y _s ,z _s coordinate of a random point on a sphere of unit diameter centered at the coordinate origin - root mean square of bubble displacement in they-direction in reference to the turbulent liquid phase velocity [m] - local void fraction - _m mean void fraction in a turbulent region - regular random number - R _v increment of the horizontal component of the force acting on a single bubble, defined by Eq. 22 [N] - t time increment [s] - ₁ reduction of turbulent stress [N/m²] - _L rate of liquid energy dissipation [m²/s³] - _m coefficient defined by Eq. 30 - law of wall constant in the turbulent region in absence of bubbles - ₁ law of wall constant in the turbulent region in presence of bubbles     

Distribution of void fraction in bubbly flow through a horizontal channel: Bubbly boundary layer flow, 2nd report

A method of enveloping the hull with a sheet of microbubbles is discussed. It forms part of a study on means of reducing the skin friction acting on a ship's hull. In this report, a bubble traveling through a horizontal channel is regarded as a diffusive particle. Based on this assumption, an equation based on flow flux balance is derived for determining the void fraction in approximation. The equation thus derived is used for calculation, and the calculation results are compared with reported experimental data. The equation is further manipulated to make it compatible with a mixing length model that takes into account the presence of bubbles in the liquid stream. Among the factors contained in the equation thus derived, those affected by the presence of bubbles are the change of mixing length and the difference in the ratio of skin friction between cases with and without bubbles. These factors can be calculated using the mean void fraction in the boundary layer determined by the rate of air supply into the flow field. It is suggested that the ratio between boundary layer thickness and bubble diameter could constitute a significant parameter to replace the scale effect in estimating values applicable to actual ships from corresponding data obtained in model experiments.List of symbols a ₁ proportionality constant indicating directionality of turbulence - B law-of-the-wall constant - C _f local skin-friction coefficient in the presence of bubbles - C _f0 local skin-friction coefficient in the absence of bubbles - d _b bubble diameter (m) - g acceleration of gravity (m/s²) - j _g flow flux of gas phase accountable to buoyancy (m/s) - j _t flow flux of gas phase accountable to turbulence (m/s) - k ₄ constant relating reduction of liquid shear stress by bubble presence to decrease of force imparted to bubble by its displacement due to turbulence - l _b mixing length of gas phase (m) - l _m mixing length of liquid phase (m) - l _mb diminution of liquid phase mixing length by bubble presence (m) - Q _G rate of air supply to liquid stream (l/min) - q _/g velocity of bubble rise (m/s) - 2R height of horizontal channel (m) - T _* integral time scale (s) - U _m mean stream velocity in channel (m/s) - U friction velocity in channel (m/s) - V volume of a bubble (m³) - u, ¯ v time-averaged stream velocities inx- andy-directions, respectively (m/s) - u, v turbulent velocity components inx- andy-directions, respectively (m/s) - v root mean square of turbulence component in they-direction (m/s) - root mean square of bubble displacement iny-direction with reference to turbulent liquid phase velocity (m) - y displacement from ceiling (m) - local void fraction - _m mean void fraction in boundary layer - _m constant relating local void fraction to law-of-the-wall constant - _t reduction of turbulent stress (N/m²) - law-of-the-wall constant in turbulent liquid region in absence of bubbles - ₁ law-of-the-wall constant in turbulent liquid region in presence of bubbles - ₂ law-of-the-wall constant in gas phase - _m constant indicating representative turbulence scale (m) - viscosity (Pa × s) - v kinematic viscosity (m²/s) - density (kg/m³) Suffixes G gas - L liquid - 0 absence of bubbles     

带附体潜艇绕流场数值计算与验证

采用κ-ε湍流模型和有限体积法用求解RANS方程的方法,对全附体的SUBOFF AFF-8潜艇模型三维粘性绕流场进行了数值模拟计算.一种结合增强型壁面函数的两层模型被采用,以便在近壁区域采用精细网格来模拟边界层内的流场流动特征.给出了雷诺数Re=1.2×107下模型表面纵中剖面线上半部分压力系数与摩擦阻力系数的分布,以及指挥台围壳与尾翼表面不同高度处的压力系数分布,同时计算了桨盘面处的尾流速度分布,并与有关文献给出的实测值进行了比较和验证,分布趋势基本一致,较相关文献给出的计算结果有相当大的改进,此外从指挥台围壳与尾翼后的速度矢量图观察到了与有关文献相同的涡旋流场结构,从而验证了该数值方法的有效性,为潜艇概念设计中评价设计方案优劣提供了重要的技术手段.     

壁面展向周期振动减阻机理及其二维波谱分析

利用直接数值模拟(DNS)对壁面作展向周期运动的槽道湍流进行研究,建立了槽道湍流数据库.通过改变振幅大小和振动周期,可以使壁面摩擦阻力明显减少.随着平均减阻率的增加,壁面阻力随时间的变化也更加稳定并呈现出较大周期的变化.将一个典型的阻力变化周期分成三个不同区域进行讨论,对湍流脉动能的二维波谱进行了定量分析,进一步揭示出壁面展向周期振动抑制湍流、实现减阻的内在机理.     

两相流相互作用下的船模微气泡减阻性能数值仿真

基于两相流理论,对集装箱船船模进行微气泡减阻性能数值仿真研究。分析船模在不同喷气口位置、流体含气率、不同喷射速度和角度下的流场分布和减阻效果。结果表明：当流体微气泡含量过高时,会增大船体摩擦阻力,流体含气率为10%~20%时,有较好的减阻效果,喷气口位置在距离球鼻艏后缘约三分之一船长附近具有较高的空气覆盖率,喷气口喷气方向垂直向下所产生的减阻效果比喷气方向偏向船侧效果要好,且船速较高时可允许较高含气率流体注入流场并增大减阻效果。     

A hybrid analytical model of sterilization effect on marine bacteria using microbubbles interacting with shock wave

The present paper reports on a hybrid analytical model consisting of a biological probability model and a physical impact model proposed to predict the cell viability ratio of a sterilization method for marine bacteria using microbubbles interacting with a shock wave. The physical impact model of interaction between a microbubble and a shock wave is developed on the basis of the bubble motion analysis with experimental pressure data and a one-dimensional numerical simulation. An underwater shock wave produced by microbubble motion is simulated using a second-order finite differential scheme by means of bubble surface velocity variation obtained from Herring’s bubble motion equation, and the radius of the sterilized space around a microbubble is estimated by the critical pressure that just causes cell wall damage of marine bacteria. The sterilization effect predicted by the present hybrid analysis shows a good agreement with the bio-experimental result.     

微气泡层减阻的边界层模型计算

以流体中光滑平板为例,建立微气泡层覆盖平板的气液简单边界层模型,采用平板层流理论,对给定的气泡喷射参数和流体特性参数计算了微气泡层状态下平板的摩擦阻力,结果显示微气泡层对平板有明显减阻效果;最后给出了气体边界层的速度分布和剪切应力分布.     

Experimental study on microbubble ejection method for frictional drag reduction

The formation of air bubbles ejected through a single hole in a flat plate was observed in uniform flow of 2–10 m/s It was confirmed that the size of the air bubbles was governed by main flow velocity and air flow rate. According to previous experiments, the size of the bubbles is an important factor in frictional drag reduction by microbubble ejection. Usually bubbles larger than a certain diameter (for example 1 mm) have no effect on frictional drag reduction. Three different methods were proposed and tested to generate smaller bubbles. Among them, a 2D convex (half body of an NACA 64-021 section) with ejection holes at the top was the best and most promising. The diameter of the bubbles became about one-third the size of the reference ejection on a flat plate. Moreover, the bubble size did not increase with increasing flow rate. This is a favorable characteristic for practical purposes. The skin friction force was measured directly with a miniature floating element transducer, and decreased drastically by microbubble ejection from the top of the 2D convex shape.     

基于水中气泡特性的舰船应用技术

水中气泡广泛应用于化工、环境及海洋等工程实践中,其动力学特性及与周围流体的相互作用是气液两相流领域研究的热点。本文分析了水中气泡的基础特性,以及少量存在的气泡对流场声学、光学等特性的影响,探讨了基于上述特性的舰船隔声降噪、舰船减阻、舰船尾流抑制等技术,可为水中气泡在船舶领域应用的进一步拓展提供参考。     

减压条件下深水圆柱附近气泡的运动特性

为深入探究气泡与附近潜艇的相互作用规律,采用电火花气泡发生装置与高速摄像分析系统,在减压环境中对近似潜艇的深水圆柱周围不同位置的气泡进行研究。并以气泡通过圆柱结构中心的铅垂线为界的分类情况讨论深水圆柱周围气泡的动态变化。实验结果表明：圆柱结构附近的气泡的运动主要取决于气泡与圆柱结构间相对的攻角以及气泡质心到就近圆柱壁面的无量纲距离这两种因素的影响。在此基础上同时考虑减压环境中浮力的因素分析了浮力参数及攻角和爆距半径比对气泡第一周期运动时间和位移的影响,并总结圆柱下侧气泡不同爆距半径比下射流宽度的作用范围变化规律。研究结论为圆柱状的潜艇结构在水下受到攻击时的毁伤状态提供了参考。     

超空泡回转体减阻特性研究

基于Fluent 6.0的气泡两相流模型对超空泡回转体的减阻特性进行了数值研究.内容包括:外形对阻力及超空泡形状的影响;超空泡控制;阻力系数随空泡数的变化规律;长细比对减阻率的影响.超空泡减阻机理的研究表明:超空泡不仅可以减小回转体的摩擦阻力,还可以减小回转体的压差阻力.在外形、长细比和空泡数以及工程可实现性等诸多因素中,存在着一个最佳组合,使减阻率最高.     

过渡型艇微气泡减阻喷缝尺度影响数值计算(英文)

针对一优良过渡型艇,为喷气需要进行船底断阶,采用有限体积法、SIMPLEC算法和k-ε两方程湍流模型,不计自由面影响,计及气泡与水的相对运动,数值求解包含气液两相流的雷诺平均控制方程组。获得不同喷缝宽度、不同傅汝德数和相对喷气速度下的船舶的阻力特性和气泡浓度分布规律并与模型实验结果进行对比分析。结果显示:在获得高减阻率条件下,Cn随Fr增加而呈非线性增加,当Fr=0.779时,Cn达到最大值;在获得25%减阻率的条件下,Fr=0.973时相对喷缝宽度为0.112所需喷气量最小即喷气所消耗功率最小。计算结果可为高速气泡船喷缝参数设计提供参考。     

超大型沉箱贮仓压力的数值模拟计算

通过ABAQUS有限元分析软件对一般沉箱和超大型沉箱的贮仓压力进行数值模拟,并对比分析数值模拟结果与按现行规范中贮仓压力公式的计算结果。经过对不同参数组计算结果的对比分析后发现:填料的内摩擦角、弹性模量、泊松比,以及填料与仓格边壁间的摩擦系数均是影响贮仓压力的主要参数。现行规范中的贮仓压力计算公式,仅考虑填料内摩擦角和填料与仓格边壁间摩擦系数的影响,而不考虑填料的弹性模量和泊松比影响的假设值得商榷。