Topological structure bifurcation of temperature field of deformable drop in Marangoni migration

The unsteady processes of the Marangoni migration of deformable liquid drops are simulated numerically in a wider range of Marangoni number (up to Ma = 500) in the present work. A steady terminal state can always be reached, and the scaled terminal velocity is a monotonic function decreasing with increasing Marangoni number, which is generally in agreement with corresponding experimental data. The topological structure of flow field in the steady terminal state does not change as the Marangoni number increases, while bifurcation of the topological structure of temperature field occurs twice at two corresponding critical Marangoni numbers. A third critical value of Marangoni number also exists, beyond which the coldest point jumps from the rear stagnation to inside the drop though the topological structure of the temperature field does not change. It is found that the inner and outer thermal boundary layers may exist along the interface both inside and outside the drop if Ma > 70. But the thickness decreases with increasing Marangoni number more slowly than the prediction of potential flow at large Marangoni and Reynolds numbers.     

Numerical simulation of Reynolds number effects on velocity shear flow around a circular cylinder

Three-dimensional Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are performed to investigate the shear effects on flow around a circular cylinder at Reynolds numbers of Re=60–1000. The shear parameter, β, which is based on the velocity gradient, cylinder diameter and upstream mean velocity at the center plane of the cylinder, varies from 0 to 0.30. Variations of Strouhal number, drag and lift coefficients, and unsteady wake structures with shear parameter are studied, along with their dependence on Reynolds number. The presented simulation provides detailed information for the flow field around a circular cylinder in shear flow. This study shows that the Strouhal number exhibits no significant variation with shear parameter. The stagnation point moves to the high-velocity side almost linearly with shear parameter, and this result mainly influences the aerodynamic forces acting on a circular cylinder in shear flow. Both the Reynolds number and shear parameter influence the movement of the stagnation point and separation point. Mode A wake instability is suppressed into parallel vortex shedding mode at a certain shear parameter. The lift force increases with increasing shear parameter and acts from the high-velocity side to the low-velocity side. In addition, a simple method to estimate the lift force coefficient in shear flow is provided.     

Numerical simulation of laminar flow past a circular cylinder with slip conditions

The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical Simulation of the Unsteady Laminar Flow Past a Circular Cylinder with a Perforated Sheath

The unsteady two-dimensional laminar flow past a circular cylinder encased in a perforated sheath is numerically simulated. On the basis of the calculated results a technique for controlling the wake flow by diverting a portion of the flow from the forward stagnation point through internal ducts to orifices in the sheath located in the separation zone, is analyzed.     

Numerical study of single bubble motion in liquid metal exposed to a longitudinal magnetic field

The paper presents numerical simulations modeling the ascent of an argon bubble in liquid metal with and without an external magnetic field. The governing equations for the fluid and the electric potential are discretized on a uniform Cartesian grid and the bubble is represented with a highly efficient immersed boundary method. The simulations performed were conducted matching experiments under the same conditions so that sound validation is possible. The three-dimensional trajectory of the bubble is analyzed quantitatively and related to the flow structures in the wake. Indeed, the substantial impact of the magnetic field in the bubble trajectory results from its influence on the wake. Quantitative data describing the selective damping of vortex structures are provided and discussed. As a result of applying a longitudinal field, the time-averaged bubble rise velocity increases for large bubbles, it reaches a maximum and then decreases when further increasing the magnetic interaction parameter. For small bubbles, the time-averaged bubble rise velocity decreases when increasing the magnetic field. The bubble Strouhal number as a dimensionless frequency is reduced with the application of a magnetic field for all bubbles considered and the zig–zag trajectory of the bubble becomes more rectilinear.     

Experimental study of low precessing frequencies in the wake of a turbulent annular jet

This paper investigates the flow structure in the wake behind the centrebody of an annular jet using time-resolved stereoscopic PIV measurements. Although the time-averaged flow field is symmetric, the instantaneous wake is asymmetric. It consists of a central toroidal vortex (CTV), which closes downstream at the stagnation point. This stagnation point lies off-axis and hence the axis of the CTV is tilted with respect to the central axis of the geometry. The CTV precesses around the central axis, corresponding to a Strouhal number of 2.5 × 10⁻³. The phase averaging technique is used to study this large-scale motion as it can separate the precession from the turbulence in the flow field. It is found that the precession creates a highly three-dimensional flow field and for instance near the stagnation point, up to 45% of the rms velocity fluctuations are attributed to it.     

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES) method at a Reynolds number Re = 8 500. The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric. The proper orthogonal decomposition(POD) analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1% of the turbulent kinetic energy, and hence their impact on the wake dynamics is studied. The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point. The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction. In addition, the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.     

Multi-resolution analysis of the large-scale coherent structure in a turbulent separation bubble affected by an unsteady wake

Multi-resolution analysis (MRA) was applied to the large-scale coherent structure in a turbulent separation bubble affected by an unsteady wake. The unsteady wake was generated using a spoked-wheel type wake generator, which was installed in front of the separation bubble. The wake generator was rotated either clockwise (CW) or counter-clockwise (CCW) with a normalized passing frequency of St_H=0.2. The Reynolds number based on the half-thickness of the blunt body was Re_H=5600. To show the unsteady dynamic flow structures between the ‘cutting’ and ‘wrapping’ regimes, a MRA using the maximal overlap discrete wavelet transform (MODWT) was performed. This method enabled delineation of the coherent structure of the turbulent separation bubble through a scale-resolved analysis. Reconstruction of the flow field in combination with conditional averaging was attempted. Flapping motions as well as sawtooth movements of the unsteady separation bubble were analyzed using the MODWT. The unsteady wakes decayed faster in the system with CCW rotation than in that with CW rotation.     

Stabilization of cylinder wakes in shallow water flows by means of roughness elements: an experimental study

Shallow wakes that occur in a wide range of natural flows tend to generate instabilities that develop into large, 2D coherent structures (2DCS). We present the results of an experimental study to stabilize shallow wakes by local, enhanced bottom roughness. Two successful stabilization strategies are compared to a base case of an unsteady bubble wake. First, localized bed roughness is placed in the lateral shear layers near the shoulders of the cylinder. Second, a local roughness element is placed at the end of the recirculation bubble, in the downstream region where large-scale vortices would normally shed. Dye visualization is used to assess the qualitative behavior of the wake, and two-component laser Doppler velocimetry (LDV) measurements are made to measure the Reynolds stress distributions and time-averaged velocity profiles. In both stabilization cases, a minimum patch size of the enhanced roughness elements is required for stabilization, which depends on the momentum thickness of the shear layers and the locations of enhanced Reynolds shear stresses. The main effect of the wake stabilization is a reduction in momentum exchange with the ambient flow due to damping of the large 2DCS. This reduction in eddy diffusivity results in a narrower wake and a slower decay of the centerline velocity deficit with downstream distance compared to the base case of an unsteady bubble wake.     

Study of vortex breakdown by particle tracking velocimetry (PTV) Part 3: Time-dependent structure and development of breakdown-modes

This third part of the study deals with the time-dependent nature of vortex breakdown. The results show the unsteady velocity and vorticity field of the initiation and development of breakdown and transition between both predominant breakdown modes, the bubble and the spiral. During the development to breakdown, the generated amount of circumferential vorticity follows the theoretical prediction by Brown and Lopez (1990). This confirms the idea of positive feedback as the key-mechanism leading to vortex breakdown. We regard the bubble-type as the fundamental breakdown type, that is stationary and nearly axisymmetric. The circumferential vorticity is distributed in a form of an elliptical vortex-ring-like structure. Starting from this stage, an increase of volume flux to a higher Reynolds number leads to the transition to the spiral-type with an initial stretching of the vortex ring-like structure and a subsequent change to an asymmetric circumferential vorticity distribution. This in combination with the inductive effect causes the front stagnation point to be deflected radially away and later to rotate around the centerline. Consequently the approaching vortex core is radially deflected in opposite direction and evolves in a spiral path. The idea of a second positive feedback-mechanism gives a possible explanation for the transition. Following this theory the asymmetry of circumferential vorticity will trigger itself at a certain degree by the interaction with the inductively affected stagnation point and its influence on the approaching vortex core. This self-enhancing process will finally lead to the spiral-type breakdown in which the radial distance between rotating stagnation point and deflected vortex core is of the order of the characteristic vortex core radius. The reversed transition from the spiral to a stable bubble-type can be regenerated by decreasing the Reynolds number down to the value that corresponds to the stable bubble state. The flow structure evolves nearly in the time-reversed way as during transition from bubble towards the spiral.     

旋转圆柱绕流流场特性分析

对雷诺数Re = 20000 ~ 90000、相对转速ɑ = 0 ~ 0.72的旋转圆柱后方流场进行了实验测量, 分析了旋转圆柱后方不同剖面处的速度分布规律和湍流度分布规律. 采用LES方法对旋转圆柱绕流问题进行了数值模拟, 分析旋转圆柱周围流场特性和自由剪切层变化规律, 最后通过理论模型对流场变化进行分析, 得出如下结论: 当圆柱逆时针旋转时, 同一雷诺数下随着相对转速的增加, 旋转圆柱尾迹区域下方速度突变处的位置随着相对转速的增加而上移, 而上方速度突变处的位置不变, 雷诺数的增加使旋转圆柱尾迹区域下方速度突变处位置有小幅度的下移. 通过数值模拟发现, 圆柱旋转之后, 圆柱后方下侧涡的位置明显上移, 且幅度较大. 下方的自由剪切层有明显的上移, 上方的自由剪切层位置变化较小. 最后通过理论分析发现, 圆柱后侧下方涡位置的上移对圆柱升力影响十分显著, 在高雷诺数、低相对转速的条件下, 旋转圆柱后侧下方涡位置的改变对旋转圆柱的升力、尾流区自由剪切层的变化起到了重要的影响.      

NUMERICAL ANALYSIS ON THE VELOCITY AND PRESSURE FIELDS INDUCED BYMULTI-OSCILLATIONS OF AN UNDERWATER EXPLOSION BUBBLE

假设水下爆炸气泡的内部气体在膨胀收缩过程中满足绝热条件,周围流体无黏无旋不可压缩. 基于势流理论,采用边界元法研究气泡动力学行为,重点关注气泡引起的流场脉动载荷以及滞后流特性,给出了相关的理论推导和数值计算方法. 通过将数值结果与解析解、实验值进行对比,数值模型的收敛性和有效性能够得到保证. 利用编写的程序进行计算和分析,发现在气泡加速膨胀阶段,流场压力在气泡径向不一定是逐渐衰减,还有可能以先增后减的规律变化;气泡射流后,为了能够继续描述环状气泡的运动以及流场特性,将此时的流场分为无旋场和一个布置在气泡内部涡环的叠加,计算过程中采用了一些数值技巧处理气泡的拓扑结构,得以连续模拟多个周期的气泡运动. 环状气泡具有相对较高的上浮迁移速度,而且在其顶部和底部附近分别形成两个高压区,顶部的高压区峰值相对较大,底部的高压区范围相对较大. 环状气泡中心轴上的流场速度会在气泡中心有一个加速过程,在气泡顶部附近又迅速减小.     

气泡多周期运动时引起的流场压力与速度

假设水下爆炸气泡的内部气体在膨胀收缩过程中满足绝热条件,周围流体无黏无旋不可压缩. 基于势流理论,采用边界元法研究气泡动力学行为,重点关注气泡引起的流场脉动载荷以及滞后流特性,给出了相关的理论推导和数值计算方法. 通过将数值结果与解析解、实验值进行对比,数值模型的收敛性和有效性能够得到保证. 利用编写的程序进行计算和分析,发现在气泡加速膨胀阶段,流场压力在气泡径向不一定是逐渐衰减,还有可能以先增后减的规律变化;气泡射流后,为了能够继续描述环状气泡的运动以及流场特性,将此时的流场分为无旋场和一个布置在气泡内部涡环的叠加,计算过程中采用了一些数值技巧处理气泡的拓扑结构,得以连续模拟多个周期的气泡运动. 环状气泡具有相对较高的上浮迁移速度,而且在其顶部和底部附近分别形成两个高压区,顶部的高压区峰值相对较大,底部的高压区范围相对较大. 环状气泡中心轴上的流场速度会在气泡中心有一个加速过程,在气泡顶部附近又迅速减小.      

A rising bubble in a polymer solution

We propose a boundary integral method to study the shape of a bubble rising under gravity in a dilute polymer solution. Constitutive properties are modelled using a FENE model [M.D. Chilcott, J.M. Rallison, J. Non-Newtonian Fluid Mech. 29 (1988) 381] with a pure surface tension interface. We employ a birefringent strand representation [O.G. Harlen, J.M. Rallison, M.D. Chilcott, High-Deborah-number flows of dilute polymer, J. Non-Newtonian Fluid Mech.34 (1990) 319–349] of the wake to simulate the shape and the time-dependent motion of the bubble. Steady and non-steady solutions reproduce qualitatively the bubble deformation seen in experiment with a small region of very high curvature near the rear stagnation point of the bubble. We find a limit point for steady axisymmetric solutions if the polymer concentration is increased or the surface tension is decreased. Rise speed jump discontinuities were not found.     

Evaluation of bubble-induced turbulence using direct numerical simulation

The presented research evaluates the interaction between a single bubble and homogeneous turbulent flow using direct numerical simulation (DNS) approach. The homogeneous single-phase turbulence is numerically generated by passing a uniform flow through grid planes. The turbulence decay rate is compared with experiment-based correlation. The single phase turbulence is then used as an inflow boundary condition for a set of single bubble studies. By estimating the turbulent field around the fully resolved bubble, the effects of bubble deformability, turbulent intensity and relative velocity on the bubble-induced turbulence are investigated. The existence of bubble creates new vortices in the wake region and the enhancement of turbulence is observed in the region behind the bubble. The results show that the magnitude of the turbulence enhancement would increase as the bubble encounters larger liquid turbulent intensity or higher relative velocity. Set of bubble Weber numbers from 0.34 to 3.39 are used to investigate the effect of bubble deformability. The more deformable bubble is the higher the increase in the magnitude of the turbulence enhancement behind the bubble. This research provides systematic insight on the bubble-induced turbulence (BIT) mechanism and is important for multiphase computational fluid dynamics (M-CFD) closure model development.     

Large-scale vortical structure of turbulent separation bubble affected by unsteady wake

The large-scale vortical structure of a turbulent separation bubble under the influence of an unsteady wake was investigated. The unsteady wake was generated by a spoked-wheel type wake generator installed in front of the separation bubble. This wake generator was rotated either clockwise or counter-clockwise at Re _H=5.600. The mechanism of vortex shedding from the separation bubble was analyzed in detail by taking a conditional average as well as a phase average. Spatial box filtering (SBF) was used to extract the large-scale vortical structure from the turbulent separation bubble affected by the unsteady wake. To elucidate the influence of the unsteady wake on the large-scale vortical structure, conditional averages of the velocity, vorticity and turbulent kinetic energy were calculated. The nature of the convection of the vortical structure under the influence of an unsteady wake was analyzed. The dipole acoustic pressure level was predicted using Curle's integral of wall-pressure fluctuations.     

On the origin of wake-induced vibration in two tandem circular cylinders at low Reynolds number

We numerically investigate flow-induced vibrations of circular cylinders arranged in a tandem configuration at low Reynolds number. Results on the coupled force dynamics are presented for an isolated cylinder and a pair of rigid cylinders in a tandem configuration where the downstream cylinder is elastically mounted and free to vibrate transversely. Contrary to turbulent flows at high Reynolds number, low frequency component with respect to shedding frequency is absent in laminar flows. Appearance and disappearance of the vorticity regions due to reverse flow on the aft part of the vibrating cylinder is characterized by a higher harmonic in transverse load, which is nearly three times of the shedding frequency. We next analyze the significance of pressure and viscous forces in the composition of lift and their phase relations with respect to the structural velocity. For both the isolated and tandem vibrating cylinders, the pressure force supplies energy to the moving cylinder, whereas the viscous force dissipates the energy. Close to the excitation frequency ratio of one, the ratio of transverse viscous force to pressure force is found to be maximum. In addition, movement of stagnation point plays a major role on the force dynamics of both configurations. In the case of isolated cylinder, displacement of the stagnation point is nearly in-phase with the velocity. During vortex-body interaction, the phase difference between the transverse pressure force and velocity and the location of stagnation point determines the loads acting on the cylinder. When the transverse pressure force is in-phase with velocity, the stagnation point moves to higher suction region of the cylinder. In the case of the tandem cylinder arrangement, upstream vortex shifts the stagnation point on the downstream cylinder to the low suction region. Thus a larger lift force is observed for the downstream cylinder as compared to the vibrating isolated cylinder. Phase difference between the transverse load and the velocity of the downstream cylinder determines the extent of upstream wake interaction with the downstream cylinder. When the cylinder velocity is in-phase with the transverse pressure load component, interaction of wake vortex with the downstream cylinder is lower compared to other cases considered in this study. We extend our parametric study of tandem cylinders for the longitudinal center-to-center spacing ranging from 4 to 10 diameter.     

The interaction of background ocean air bubbles with a surface ship

A two-fluid model suitable for the calculation of the two-phase flow field around a naval surface ship is presented. This model couples the Reynolds-averaged Navier–Stokes (RANS) equations with equations for the evolution of the gas-phase momentum, volume fraction and bubble number density, thereby allowing the multidimensional calculation of the two-phase flow for monodisperse variable size bubbles. The bubble field modifies the liquid solution through changes in the liquid mass and momentum conservation equations. The model is applied to the case of the scavenging of wind-induced sea-background bubbles by an unpropelled US Navy frigate under non-zero Froude number boundary conditions at the free surface. This is an important test case, because it can be simulated experimentally with a model-scale ship in a towing tank. A significant modification of the background bubble field is predicted in the wake of the ship, where bubble depletion occurs along with a reduction in the bubble size due to dissolution. This effect is due to lateral phase distribution phenomena and the generation of an upwelling plume in the near wake that brings smaller bubbles up to the surface. © 1998 John Wiley & Sons, Ltd.     

Viscid contributions to the hydrodynamic flows past a rising spherical gas bubble with a time-dependent radius

We study the effect of the viscosity on the hydrodynamic flow fields past the interface of a spherical deforming gas bubble impulsively started at a constant velocity in a viscous liquid of large extent at rest. Exact solutions for the unsteady inner and outer flow fields within the boundary layers are obtained making appropriate scalings on the position, velocity and time variables in the non-linear Navier-Stokes equations. These theoretical results apply to any slowly deforming fluid sphere, whatever the time-dependence of its radius, provided that the internal circulation is complete, the flow separation is negligible, the Reynolds numbers are large and the bubble retains its spherical shape. A numerical application to the case of deforming air bubble in water is discussed.