Transport of rarefied gases inside a vortex tube induced by a surface wave

We derive the entrainment of rarefied gases induced by a surface wave (SW) propagating along the wall or interface of the vortex core in a rather long straight vortex-tube (vortex or vorticity filament) by using the perturbation method. The values of the critical reflux pressure-gradient for time-averaged macroscopic flows of rarefied gases decrease as the Knudsen number increases from zero. Nonlinear coupling due to the boundary effect and the streaming flow of the rarefied gases is observed as the Reynolds number (based on the wave speed) increases to 50 and the wave number of the surface wave is larger. We also address the zero-flux states of our results. Received: November 22, 2004; revised: May 17, 2005     

The Velocity of Viscous Vortex Rings

The motion of vortex rings of small cross section is considered. A formula is derived for the velocity of a ring in an ideal fluid with an arbitrary distribution of vorticity in the core. The effects of viscosity are then examined. A definition of the velocity of an unsteady diffusing ring is given and it is shown that the method used to calculate the ring speed in an ideal fluid can be extended to give the velocity of a vortex ring subject to viscous diffusion.     

梢涡流场中气泡轨迹及形态数值模拟

针对气泡在舰船尾迹涡流场运动特性,根据其是否为尾涡所捕获,将数值模拟过程分为两个阶段:准球状运动阶段和非球状运动阶段．分别应用单向耦合质点粒子追踪法（PTM）和边界元法（BEM）模拟这两个阶段,将第1阶段结束的物理量作为第2阶段的初始条件,从而完成整个数值模拟过程．在已有数值研究结果和实验数据基础上,探讨空化发生条件,追踪尾迹空泡运动轨迹,模拟尾迹气泡的运动、变形、溃灭等,以及被尾涡捕获后的撕裂等运动特性,旨在为优化设计尾流场提供参考．     

Numerical study of dynamics of single bubbles and bubble swarms

A systematic computational study of the dynamics of gas bubbles rising in a viscous liquid is presented. Two-dimensional simulations are carried out. Both the dynamics of single bubbles and small groups of bubbles (bubble swarms) are considered. This is a continuation of our previous studies on the two-bubble coalescence and vortex shedding [A. Smolianski, H. Haario, P. Luukka, Vortex shedding behind a rising bubble and two-bubble coalescence: a numerical approach, Appl. Math. Model. 29 (2005) 615–632]. The proposed numerical method allows us to simulate a wide range of flow regimes, accurately capturing the shape of the deforming interface of the bubble and the surface tension effect, while maintaining the mass conservation. The computed time-evolution of bubble’s position and rise velocity shows a good agreement with the available experimental data. At the same time, the results on the dynamics of bubble interface area, which are, up to our knowledge, presented for the first time, show how much the overall mass transfer would be affected by the interface deformation in the case of the bubble dissolution. Another set of experiments that are of interest for chemical engineers modelling bubbly flows concerns the bubble swarms and their behavior in different bubble-shape regimes. The ellipsoidal and spherical shape regimes are considered to represent, respectively, the coalescing and non-coalescing bubble swarms. The average rise velocities of the bubble swarms are computed and analyzed for both regimes.     

水下爆炸气泡与复杂弹塑性结构的相互作用研究

计及结构的弹塑性,将边界元法(BEM)与有限元法(FEM)耦合提出了气泡与弹塑性结构耦合动力学计算方法,并开发了全套的三维水下气泡分析程序（UBA）,计算值与实验值之间误差在10%以内．以水面舰船为例,将三维计算程序工程化．并分析了水下爆炸气泡载荷作用下船体的弹塑性响应,从船体结构典型单元上的应力时历曲线可以看出,在气泡坍塌时出现应力峰值,证实了气泡坍塌压力及射流引起的压力对舰船等结构造成严重毁伤．从气泡与舰船的相互作用中可以看出,舰船低阶垂向振型被激起,在气泡作用下呈鞭状运动,同时舰船随着气泡的膨胀和收缩作升沉运动,通过本文的分析得到了适合于工程应用的规律及结论．     

Hydrodynamics of a particle impact on a wall

The problem of a particle impacting on a wall, a common phenomenon in particle-laden flows in the minerals and process industries, is investigated computationally using a spectral-element method with the grid adjusting to the movement of the particle towards the wall. Remeshing is required at regular intervals to avoid problems associated with mesh distortion and the constantly reducing maximum time-step associated with integration of the non-linear convective terms of the Navier–Stokes equations. Accurate interpolation between meshes is achieved using the same high-order interpolation employed by the spectral-element flow solver. This approach allows the full flow evolution to be followed from the initial approach, through impact and afterwards as the flow relaxes. The method is applied to the generic two-dimensional and three-dimensional bluff body geometries, the circular cylinder and the sphere. The principal case reported here is that of a particle colliding normally with a wall and sticking. For the circular cylinder, non-normal collisions are also considered. The impacts are studied for moderate Reynolds numbers up to approximately 1200. A cylindrical body impacting on a wall produces two vortices from its wake that convect away from the cylinder along the wall before stalling while lifting induced wall vorticity into the main flow. The situation for a sphere impact is similar, except in this case a vortex ring is formed from the wake vorticity. Again, secondary vorticity from the wall and particle plays a role. At higher Reynolds number, the secondary vorticity tends to form a semi-annular structure encircling the primary vortex core. At even higher Reynolds numbers, the secondary annular structure fragments into semi-discrete structures, which again encircle and orbit the primary core. Vorticity fields and passive tracer particles are used to characterize the interaction of the vortical structures. The evolution of the pressure and viscous drag coefficients during a collision are provided for a typical sphere impact. For a Reynolds number greater than approximately 1000 for a sphere and 400 for a cylinder, the primary vortex core produced by the impacting body undergoes a short-wavelength instability in the azimuthal/spanwise direction. Experimental visualisation using dye carried out in water is presented to validate the predictions.     

The role of added mass in the theory of Hele-Shaw cell bubbles

Viscous bubbles in a Hele-Shaw cell are studied by two-dimensional theory. The motion is caused by buoyancy and/or a pressure gradient driving a uniform basic flow in the surrounding fluid. A formula for the velocity of a steady bubble is derived, involving the ratio between the added mass of the bubble and the displaced fluid mass.     

Prediction of initial motion of a gas bubble in liquids

Numerical predictions are presented for the motion and distortion of a single gas bubble rising through the liquid. The computations were made with an implicit finite-difference procedure which solves the transient equations of motion throughout the bubble and the liquid, such that the free surface between the gas bubble and the liquid is not a boundary of the computational domain.The predictions compare well with the experimental results of others. Computations are presented for bubble sizes from 0.02 to 0.05 m radius and for bubbles of different gas densities rising in liquids of different densities. Surface tension effects are neglected.     

On the Formation of Vortex Rings

The production of a vortex ring formed by using a piston to drive fluid through an orifice is considered. A cylindrical vortex sheet is supposed to be formed initially which rolls up into a vortex ring. Energy and momentum are conserved during rollup and determine the speed and size of the ring. It is shown that these quantities are independent of the vorticity distribution in the core of the ring. Reasonable agreement with experimental observations is found. A speculation is made about the criterion for the rings to be laminar or turbulent.     

Numerical modelling of bubbly flows with and without heat and mass transfer

In this paper, modelling gas–liquid bubbly flows is achieved by the introduction of a population balance equation combined with the three-dimensional two-fluid model. For gas–liquid bubbly flows without heat and mass transfer, an average bubble number density transport equation has been incorporated in the commercial code CFX5.7 to better describe the temporal and spatial evolution of the geometrical structure of the gas bubbles. The coalescence and breakage effects of the gas bubbles are modelled according to the coalescence by the random collisions driven by turbulence and wake entrainment while for bubble breakage by the impact of turbulent eddies. Local radial distributions of the void fraction, interfacial area concentration, bubble Sauter mean diameter, and gas and liquid velocities, are compared against experimental data in a vertical pipe flow. Satisfactory agreements for the local distributions are achieved between the predictions and measurements. For gas–liquid bubbly flows with heat and mass transfer, boiling flows at subcooled conditions are considered. Based on the formulation of the MUSIG (multiple-size-group) boiling model and a model considering the forces acting on departing bubbles at the heated surface implemented in the computer code CFX4.4, comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter, interfacial area concentration, and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Good agreement is achieved with the local radial void fraction, bubble Sauter mean diameter, interfacial area concentration and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress through the consideration of additional momentum equations or developing an algebraic slip model to account for the effects of bubble separation.     

Numerical modelling of EHD effects on heat transfer and bubble shapes of nucleate boiling

In this article, mathematical and numerical models are developed to study pure electrohydrodynamic (EHD) effects on heat transfer and bubble shapes when an initial bubble attached to a superheated horizontal wall in nucleate boiling. In the modelling of EHD effects on heat transfer, an undeformed bubble is considered; the electric body force and Joule heat are added to the momentum and energy equations; governing equations for heat, fluid flow and electric fields are coupled numerically and solved using a non-orthogonal body-fitted mesh system with necessary interfacial treatments at the gas–liquid boundary. While, to study the pure effect of EHD on the deformation of the bubble, the evaluation of a deformable bubble without heat transfer is simulated by volume of fluid (VOF) method based on an axial symmetric Cartesian coordinate system. The simulations indicate that EHD can effectively enhance heat transfer rate of nucleate boiling by influencing the motion of the ring vortex around the bubble and that bubble can be elongated due to the pull in axial direction and push in the negative radial direction by the electric field force.     

二维气固两相混合层中固粒对流场影响的研究

采用双向耦合模型对含有固粒的二维气固两相混合层流场进行了研究。流场采用拟谱方法直接数值模拟,固粒采用颗粒-轨道模型,在考虑流场对固粒作用的同时,考虑固粒对流场的反作用。结果发现固粒的浓度和Stokes数对流场影响明显。固粒的作用使涡量扩散加快,并阻碍流场的变化,减弱了流场中拟序结构的强度,缩短涡的生存期;固粒在流场中的分布规律与单相耦合所得结果相似。     

Ground-based measurement of ash distribution in volcanic plumes

Measurement of ash particle distribution within volcanic eruption plumes is important for volcanic hazard prediction, but is difficult because of the inherent danger and inaccessibility of volcanoes, and the three-dimensional time-dependent dynamics of turbulent eruption plumes. A combined study using a novel UV camera coupled with classical analysis of the dynamics of finite-volume buoyant plumes has been used to develop a detection algorithm for ground-based volcanic ash monitoring. The method provides the capability to observe and measure the internal structure of the plume, and processes occurring during plume rise, including concentration of ash over time into the plume ‘head’, increased ash at the plume edges during early formation and dilution at the top of the plume head as entrainment of surrounding air occurs. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stream-vorticity NS equation ADI scheme to investigate properties of impulsively started translatory flows around the rotational circular cylinder without wall vorticity conditions

The properties of flow around a circular cylinder impulsively started into translatory and, rotatory motion with rotational parameter a less than or equal to 8.0 and Reynolds number Re=100 and 200 are investigated in the present paper. The vorticity and stream function N-S equations are adopted here, with a 2nd-order spatial and temporal accuracy ADI (alternating direction implicit) scheme. Moreover the wall vorticity obtain through the principle of conservation of the total computational domain vorticity is determined by domain vorticity and stream function, therefore, through the wall vorticity iteration, the wall vorticity condition is not fixed during the time step. And the present model results indicate: (1) when α>4.0, vortex street suppression is obvious for the computational period (t<60) for all the Re numbers here studied; (2) the higher the αnumber for the same Reynolds number, the slower the upper main vortex proceeds; (3) the maximum instantaneous transverse coefficient exceeds the limitation 4π.     

LES and analyses on the vortex structure behind supersonic MVG with turbulent inflow

In this paper, an implicitly implemented high order large eddy simulation by using the fifth order bandwidth-optimized WENO scheme is applied to make comprehensive studies on ramp flows with and without control at Mach 2.5 and Re_θ = 5760. Flow control in the form of microramp vortex generators (MVG) is applied. The mechanism of vortex ring generation behind MVG has been studied in detail and shear layer instability has been studied and found as the mechanism of K–H vortex ring generation. A series of new observations on the flow around supersonic MVG have been made including inflection points (surface in 3-D), vorticity conservation, interaction of the primary vortex and new generated K–H vortex rings, and the K–H vortex ring structure. The numerical observations have been confirmed by the experimental work.     

Quadratic Volume-Preserving Maps: (Un)stable Manifolds, Hyperbolic Dynamics, and Vortex-Bubble Bifurcations

We implement a semi-analytic scheme for numerically computing high order polynomial approximations of the stable and unstable manifolds associated with the fixed points of the normal form for the family of quadratic volume-preserving diffeomorphisms with quadratic inverse. We use this numerical scheme to study some hyperbolic dynamics associated with an invariant structure called a vortex bubble. The vortex bubble, when present in the system, is the dominant feature in the phase space of the quadratic family, as it encloses all invariant dynamics. Our study focuses on visualizing qualitative features of the vortex bubble such as bifurcations in its geometry, the geometry of some three-dimensional homoclinic tangles associated with the bubble, and the “quasi-capture” of homoclinic orbits by neighboring fixed points. Throughout, we couple our results with previous qualitative numerical studies of the elliptic dynamics within the vortex bubble of the quadratic family.     

Vortex Filament Method

In this paper, the convergence of the vortex filament methodfor three-dimensional incompressible and inviscid fluid flowis proved. Properties of consistency and stability are analysed.The foundation for studying these properties is based on thecubature formulae with lines as well as on the specific useof the vector measure that transports the vorticity by the flow,preserving the filament structure of the solution of the problem.In this way, the method takes into account the stretching termimplicitly.