数值模拟中低Reynolds数下简单剪切流流过单液滴的稳态流场(英文)

This work presents a numerical investigation on steady internal, external and surface flows of a liquid sphere im-mersed in a simple shear flow at low and intermediate Reynolds numbers. The control volume formulation is adopted to solve the governing equations of two-phase flow in a 3-D spherical coordinate system. Numerical re-sults show that the streamlines for Re=0 are closed Jeffery orbits on the surface of the liquid sphere, and also closed curves outside and inside the liquid sphere. However, the streamlines have intricate and non-closed struc-tures for Re≠0. The flow structure is dependent on the values of Reynolds number and interior-to-exterior vis-cosity ratio.     

Numerical study on steady and transient mass/heat transfer involving a liquid sphere in simple shear creeping flow

A numerical method is utilized to examine the steady and transient mass/heat transfer processes that involve a neutrally buoyant liquid sphere suspended in simple shear flow at low Reynolds numbers is described. By making use of the known Stokes velocity field, the convection‐diffusion equations are solved in the three‐dimensional spherical coordinates system. For the mass transfer either outside or inside a liquid sphere, Sherwood number Sh approaches an asymptotic value for a given viscosity ratio at sufficiently high Peclet number Pe. In terms of the numerical results obtained in this work, two new correlations are derived to predict Sh at finite Pe for various viscosity ratios. © 2013 American Institute of Chemical Engineers AIChE J, 60: 343–352, 2014     

Mass/heat transfer from a neutrally buoyant sphere in simple shear flow at finite Reynolds and Peclet numbers

Theoretical analyses of mass/heat transfer from a neutrally buoyant particle in simple shear flow indicate that mass/heat must diffuse across a region of closed streamlines of finite thickness at zero Reynolds number, whereas spiraling streamlines allow the formation of a thin mass transfer boundary layer at small but non‐zero Reynolds numbers (Subramanian and Koch, Phys Rev Lett. 2006;96:134503; Subramanian and Koch, Phys Fluids. 2006;18: 073302). This article presents the first numerical results for mass/heat transfer at finite Reynolds and Peclet numbers. The simulations indicate that fluid particles in the flow‐gradient plane spiral away from the particle for Reynolds numbers smaller than about 2.5 while they spiral toward the particle for higher Reynolds numbers. Solutions of the Navier‐Stokes equations coupled with a boundary layer analysis of mass transfer yield predictions for the rate of mass transfer at asymptotically large Peclet numbers and Reynolds numbers up to 10. Simulations of mass transfer for zero Reynolds number and finite Peclet numbers confirm Acrivos' (Acrivos, J Fluid Mech. 1971;46:233–240) prediction that the Nusselt number approaches a finite value with increasing Peclet number. Simulations at finite Reynolds numbers and Peclet numbers up to 10,000 confirm the theoretical predictions for the concentration gradient at the particle surface at angular positions away from the flow‐gradient plane. However, the wake near the flow‐gradient plane remains too large at this Peclet number to yield a quantitative agreement of the overall rate of mass transfer with the theory for asymptotically large Peclet number. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Numerical solution of viscous flow past a solid sphere with the control volume formulation

The control volume formulation with the QUICK finite difference scheme is used to solveincompressible liquid flow past a solid sphere in terms of stream function and vorticity.Several tech-nical points are addressed on improving the accuracy and efficiency of numerical simulation of similarproblems of fluid flow.In particular,the importance of suitable specification of the distortion func-tion to enforcing the far field boundarv conditions is emphasized.     

Modeling of unsteady flow around accelerating sphere at moderate reynolds numbers

The flow around an accelerating spherical particle of diameter ranging from 50 to 200 m?m is studied in the range of Reynolds number between 0.1 and 100. The flow around the sphere is assumed to be laminar and two-dimensional axisymmetric. The calculated drag coefficient is compared with the theoretical predictions of added mass term and Basset history term. Appropriate corrections for those two terms are proposed as function of the acceleration rate and the particle diameter.     

Mass and heat transfer from or to a single sphere in simple extensional creeping flow

The first detailed numerical investigation on the mass and heat transfer both outside and inside a solid or liquid sphere immersed in a simple extensional flow for a larger range of Peclet numbers (1–100,000) is presented. By making use of the known Stokes velocity field at small Reynolds numbers, a finite difference method with the control volume formulation is adopted to solve the convection‐diffusion transport equation. Simulation results show that the transport rate, which is represented by Sherwood number, is significantly affected by Peclet number and viscosity ratio. The flow direction, no matter a uniaxial extensional flow or a biaxial extensional flow, has no effect on the total transport rate but affects the concentration distribution a lot. Some comparisons between present simulations and previous studies are made to validate each other and confirm the reliability and applicable scopes of reported correlations. A few new correlations are put forward to predict the transfer rate at finite Peclet numbers for various values of viscosity ratios. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3214–3223, 2012     

剪切流场中聚乙烯结晶过程的建模与模拟

基于Eder模型推导了剪切流场中球晶、串晶形态演化的数学模型,将第一法向应力差作为串晶成核的驱动,并引入两相悬浮模型描述体系,认为其由无定形相和半结晶相组成,分别用FENE-P模型和刚性哑铃模型描述。基于上述数学模型,分别构造了捕捉球晶、串晶生长的Monte Carlo法与体系控制方程求解的有限差分法,成功模拟了二维剪切流场中聚乙烯的结晶过程,给出了球晶、串晶的形态演化,分析了剪切时间、剪切速率对串晶成核密度、结晶速率、流体黏度等的影响。数值结果表明:所构造的Monte Carlo法合理有效,不仅成功捕捉了晶体的生长与碰撞,而且较为准确地预测了结晶速率。此外,提高剪切时间或剪切速率,将增加串晶成核密度、提高结晶速率、使流体黏度突增的时间点提前。     

Numerical study on gas and liquid slugs for Taylor flow in a T-junction microchannel

The rapid development of microfabrication techniques creates new opportunities for applications of microchannel reactor technology in chemical reaction engineering. The extremely large surface-to-volume ratio and the short transport path in microchannels enhance heat and mass transfer dramatically, and hence provide many potential opportunities in chemical process development and intensification. Multiphase reactions involving gas/liquid reactants with a solid as a catalyst are ubiquitous in chemical and pharmaceutical industries. The hydrodynamics of the flow affects the reactor performance significantly; therefore it plays a prominent role in reactor design. For gas/liquid two-phase flow in a microchannel, the Taylor slug flow regime is the most commonly encountered flow pattern. The present study deals with the numerical simulation of the Taylor flow in a microchannel, particularly on gas and liquid slugs. A T-junction empty microchannel with varying cross-sectional width (0.25, 0.5, 0.75, 1, 2 and 3 mm) served as the model micro-reactor, and a finite volume based commercial computational fluid dynamics (CFD) package, FLUENT, was adopted for the numerical simulation. The gas and liquid slug lengths at various operating and fluid conditions were obtained and found to be in good agreement with the literature data. Several correlations in the T-junction microchannel were developed based on the simulation results. The slug flows for other geometries and inlet conditions were also studied.     

Numerical simulation of churn flow in a vertical pipe

A numerical simulation of the churn flow regime of air-water and R134a vapour-liquid mixtures by means of the volume of fluid (VOF) method is presented. The focus of the paper is on the inlet region of a vertical pipe. An axisymmetrical domain is used, reproducing the region next to the porous wall liquid injector of a typical test section for the investigation of vertical gas-liquid flows.A simplified model of the levitation process of the ring-type waves typical in churn flow is proposed. The influence of the gas Froude number on the waves amplitude is shown by means of the simplified model and used to explain the numerical results.A comparison of the numerical results with experimental wave frequency data and visualizations available in the literature is performed. The velocity field in the forming wave region and the pressure and shear stress variations along the interface are shown.Simulations have been performed at different liquid and gas superficial velocities and pipe diameters and the influence of these parameters on the gas-liquid interface is discussed.     

Heat/mass transfer from a neutrally buoyant sphere by mixed natural and forced convection in a simple shear flow

Building on the work of Yang et al. in 2011, the finite difference method and the Boussinesq approximation were applied to solve the time‐dependent Navier‐Stokes, convection diffusion and continuity equations in spherical coordinates. An idealized condition, the mass transfer from a neutrally buoyant sphere in a horizontal simple shear flow with natural convection was numerically simulated for the first time in this work. In the hybrid transfer case, the outwardly spiraling streamlines enhanced the transfer process, but the counter‐gravity spiraling streamlines near the sphere hindered the natural convection and the spatial dilution action weakened the natural convection transfer process. These competing effects led to nonmonotonic behavior of the Nusselt number with Reynolds number. Results from these previously undocumented cases were summarized into correlations for predicting Nusselt numbers at finite Reynolds numbers for various Grashof and Prandtl numbers. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2816–2827, 2018     

洗涤冷却环内液体冷态流动行为数值模拟

为了研究洗涤冷却环内冷却水流动的情况,借助计算流体力学软件Fluent建立了洗涤冷却环流体冷态流动的数学模型,同时为了验证模型的可靠性,对洗涤冷却环出口处的流动情况进行了实验研究,实验结果与模拟结果基本吻合。结果表明：因为洗涤冷却环的结构限制,其内部存在多处涡旋区域;内室入水口周向位置处的涡旋运动最为剧烈;受其影响,入水口周向位置的射流孔出口平均速度最小,两入水口之间周向位置的射流孔出口平均流速最大;槽缝出口的平均流速在周向上的分布与射流孔出口平均流速分布相同。     

90°弯管内湍流流动的数值模拟

进行了90°弯管内湍流流动的数值模拟实验。结果表明,切向速度在开始旋转阶段内侧的速度增大、压力减小,外侧速度降低、压力增大;当转过60°截面后,外侧的速度增大、压力减小,内侧速度降低、压力增大。弯管内流体旋转产生的离心力导致压力分布的变化,使得弯管内流体产生垂直于主流切向速度的轴向速度和径向速度,形成了二次流。90°弯管流场是主流切向速度与二次流的叠加,呈现出复杂的三维流动特性。     

Structural change of polydomain in the liquid crystalline polymers by weak shear flow

Steady-state shear stress (τ₁₂) and first normal stress difference (N₁) of liquid crystalline polymers at low shear rates were examined by using a mesoscopic constitutive equation set including the idea of initial domain size. For the applicability to the weak shear flow at low shear rates, a Hinch-Leal closure approximation was adopted in the calculation of the constitutive equation set. The steady-state rheological behaviors predicted by adopting the Hinch-Leal approximation were compared with those by the Doi simple decoupling approximation. It could be predicted from the plot of N₁ versus τ₁₂ that smaller domains distributed isotropically at a quiescent state might maintain the isotropic domain distribution even at the imposition of moderate shear rate, and then could be changed to the ordered (or partially elongated) domain phase by a further increase of shear rate. Such change of the polydomain structure with the increase in shear rate could be proved more precisely by the transient rheological behaviors of N₁ and τ₁₂ after the start-up of shear flow.     

Dissolution in film flow of shear thinning liquid on a horizontal rotating disk

The mass transfer from the surface of a horizontal rotating disk into a film flow of shear thinning liquid on the disk has been theoretically and experimentally investigated. Dissolution of gypsum in two aqueous polymer solutions has been used for the confirmation of the theory. It has been established that the disk speed of rotation is the most important operative parameter, intensifying the mass transfer. The effect of speed increase becomes stronger when the liquid index of rheology decreases. This “synergistic” effect is found to be higher than in the case of gas transfer to/from the film free surface previously reported.     

Numerical simulation of the two-dimensional flow in high pressure catalytic combustor for gas turbine

The objective of this paper is modeling the mechanism of high pressure and high temperature catalytic oxidation of natural gas, or methane. The model is two-dimensional steady-state, and includes axial and radial convection and diffusion of mass, momentum and energy, as well as homogeneous (gas phase) and heterogeneous (gas surface) single step irreversible chemical reactions within a catalyst channel. Experimental investigations were also made of natural gas, or methane combustion in the presence of Mn-substituted hexaaluminate catalysts. Axial profiles of catalyst wall temperature, and gas temperature and gas composition for a range of gas turbine combustor operating conditions have been obtained for comparison with and development of a computer model of catalytic combustion. Numerical calculation results for atmospheric pressure agree well with experimental data. The calculations have been extended for high pressure (10 atm) operating conditions of gas turbine.     

Deformation of an oil droplet on a solid substrate in simple shear flow

Displacement of immiscible fluids is important in sub-surface processes such as enhanced oil recovery, oil sand processing and detergency. In this study, simulation of an oil droplet deformation on a solid substrate in simple shear flow has been carried out using computational fluid dynamics tool (Fluent 6.3) and the shape of the oil droplet is compared with that of the experimental observation. The dynamic behavior of a two-dimensional oil droplet subject to shear flow in a closed channel is considered under the condition of negligible inertial and gravitational forces. The volume of fluid method is used in Fluent to determine the dynamics of free surface of the oil droplet during the fluid flow. The oil droplet deformation increases with the increase in capillary number, Reynolds number and size of the oil droplet. The deformation of an oil droplet attached to channel surface in simple shear flow is studied experimentally in laminar flow through visual observation using microscope (Ziess, SV11 APO) with high speed camera (PCO). Aniline and isoquinoline was used to form oil droplet and distilled water was used as shearing fluid. The deformation of aniline and isoquinoline droplets was recorded using a high speed camera connected to a PC. The recorded image was replayed and the deformation of aniline and isoquinoline droplets was analyzed using Axio Vision software and compared with the results obtained from CFD simulation. The deformation of different sizes of aniline and isoquinoline droplets at different flow rates of shearing fluid and with time are well predicted by the CFD simulation.     

Simulation and experiments of droplet deformation and orientation in simple shear flow with surfactants

The deformation and orientation behavior of three-dimensional (3D) viscous droplets with and without surfactants is studied in simple shear flow using simulations and experiments. Two added amounts of surfactants are considered, along with a range of viscosity ratios and capillary numbers. The numerical method couples the boundary integral method for interfacial velocity, a second-order Runge-Kutta method for interface evolution, and a finite element method for surfactant concentration. The algorithm assumes a bulk-insoluble, nonionic surfactant, and uses a linear equation of state to model the relationship between the interfacial tension and the surfactant concentration on the drop surface. The algorithm was validated by comparison with other numerical results and good agreement was found. The experiments are performed in a parallel-band apparatus with full optical analysis of the droplet. The simulated and measured 3D steady-state shape of the ellipsoidal drops and their orientation are in reasonably good agreement. It was found that the surfactants have a greater effect on drop geometry for smaller viscosity ratios and that the deformation increases as the transport of surfactant becomes more convection dominated. It was also found that surfactants cause the drops to align more in the flow direction and that, for both clean and surfactant-covered drops, this alignment increases with viscosity ratio. Finally, simulations showed a wider distribution of surfactant on the interface for smaller viscosity ratios.     

地下水数值模拟在液体矿采矿设计中的应用

青海钾肥二期工程设计中提出了井群集卤开采方案，为了解决多方案大规模并群计算中庞大的数据处理问题、了解开采生产后区域抽采漏斗的动态变化全过程，以便制定细致、合理的开采方案，引入了地下水数值模拟方法，在计算机上实现了各种方案开采状态的实时模拟。实践证明这一方法是可行的、先进的。     

Monte Carlo simulation of linear polymer melts in shear flow. Effect of shear stress and confined space on chain dynamics

Linear homopolymer melts under shear stress were studied using a Monte Carlo method in a dense system, using the cooperative motion algorithm. The simulations were performed in a plane-parallel geometry, between reflective walls, for chains up to 640 beads (entangled). Behavior of the melts under shear stress was simulated by appropriate biasing of the bead move probability. Chain dynamics was monitored during reaching the equilibrium flow in the step-shear experiment (creep) simulation, in the equilibrium flow and during melt relaxation. The results were compared with those obtained for non-flowing melt. Significant differences between step-shear and steady-state simulations were observed, while chain dynamics during recovery is almost identical with that in non-flowing melt. Dynamics of the melt depended strongly on the chain length and shear stress, showing nonlinear effects for long chains. Chain orientation, coil deformation and relaxation were analyzed. Relaxation time of long chain decreased by orders of magnitude under shear following the power law. Diffusion of beads and chains was analyzed and an anomalous diffusion was observed, also in the directions perpendicular to the flow direction. In the flowing melt the effect of confined space was important, even if the wall spacing was much bigger than R_g.