Numerical simulation of thermo‐solutal‐capillary migration of a dissolving drop in a cavity

In the present paper the thermo‐solutal‐capillary migration of a dissolving liquid drop, composed by a binary mixture having a miscibility gap, injected in a closed cavity with differentially heated end walls, is studied. The main goal of the analysis is to clarify if and how the drop migration is affected by the dissolution process. The numerical code is based on a finite volume formulation. A level‐set technique is used for describing the dynamics of the interface separating the different phases. A thermodynamic constraint fixes the concentration jump between the interface sides. This jump, together with that of the concentration normal derivatives, in turn defines the entity of the dissolution cross‐flow through the interface and the interface velocity relative to the fluid. Since the jump singularity of normal derivatives cannot be easily mollified, while retaining the necessary accuracy, a scheme for the species equation is elaborated that allows sharp jumps and has subcell resolution. Steady migration speeds are determined after the start‐up phase for different radii and temperature differences. The results will be used for the preparation of a sounding rocket space experiment. Copyright © 2003 John Wiley & Sons, Ltd.     

Unsteady model of drop Marangoni migration in microgravity

The experiments of drop Marangoni migration have been performed by the drop shift facility of short period of 4.5 s, and the drop accelerates gradually to an asymptotic velocity during the free fall. The unsteady and axisymmetric model is developed to study the drop migration for the case of moderate Reynolds numberRe=O(1), and the results are compared with the experimental ones in the present paper. Both numerical and experimental results show that the migration velocity for moderate Reynolds number is several times smaller than that given by the linear YGB theory. The project supported by the National Natural Science Foundation (19789201) and the Ministry of Science and Technology of China (95-Yu-34)     

高温激波管化学非平衡流动数值模拟研究

为了预测氢氧定容燃烧驱动的高温激波管性能,需要准确分析激波管非定常化学非平衡流动过程.本文在破膜前的驱动段定容燃烧以及破膜后的化学非平衡流动数值模拟中,引入双时间步长方法,发展高温激波管化学非平衡流动数值模拟方法,该方法在时间上具有二阶精度.计算结果与目前存在的激波管流动解析解以及零维化学反应系统的数值解进行了比较,吻合较好.对于典型高温激波管状态,采用有限体积方法离散准一维流动Euler控制方程,并通过将流动过程和化学反应动力学过程耦合求解,获得了激波管内部的化学非平衡流动特征.     

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.     

Pressure drop caused by flow area changes in capillaries under low flow conditions

Single-phase and two-phase flow pressure drops caused by flow area expansion and contraction were measured using air and water. The test section consisted of two capillaries with 0.84 mm and 1.6 mm diameters. For single-phase flow, the Reynolds numbers defined based on the smaller diameter capillary covered the range 160–11,000. For two-phase flow, the all-liquid Reynolds number based on the smaller capillary varied in the 410–1020 range, and the flow quality varied in the 0.018–0.2 range. The single-phase flow loss coefficients for both flow area expansion and contraction were empirically correlated. For two-phase flow, the data indicated the occurrence of significant velocity slip, and the one-dimensional homogeneous flow model utterly disagreed with the data. For flow area expansion the one-dimensional slip flow model along with an Armand-type slip ratio correlation could predict the data well. For flow area contraction, the one-dimensional slip flow model along with the slip ratio expression of Zivi agreed with the data very well, provided that no vena-contracta was considered.     

Numerical simulation of lateral migration of red blood cells in Poiseuille flows

A spring model is applied to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the RBC rheology in two‐dimensional Poiseuille flows using an immersed boundary method. The lateral migration properties of the cells in Poiseuille flows have been investigated. The simulation results show that the rate of migration toward the center of the channel depends on the swelling ratio and the deformability of the cells. We have also combined the above methodology with a fictitious domain method to study the motion of RBCs in a two‐dimensional micro‐channel with a constriction with an application to blood plasma separation. Copyright © 2010 John Wiley & Sons, Ltd.     

激波诱导高速气流中液滴的初期变形

基于激波管平台和高速摄影方法对平面激波诱导高速气流中液滴的早期变形现象进行实验研究。研究发现在相近的We数或Re数下,实验参数的改变可导致液滴形态发展出现显著差异。这种差异主要体现在背风面的脊状环形突起、褶皱区以及后驻点区的凹凸形态。对刚性圆球外流的数值模拟显示,液滴变形早期形态与外流场结构和表面气动力分布之间存在鲜明的对应关系。最后采用简化理论推导出一组估测液滴早期变形的表达式。将数值模拟所得气动力数据代入计算发现:导致液滴变形的主要驱动力是液滴表面不均匀压力的挤压效应,而不是界面剪切摩擦所引起的切向流动堆积效应,前者高出后者约2个数量级;此外,采用压力作用理论计算所得液滴外形在主要变形特征和变形量级上均可与实验图像很好地吻合。     

Numerical simulation of axisymmetric turbulent jets

The flow in axisymmetric turbulent jets is numerically simulated with the use of a semi-empirical second-order turbulence model including differential transport equations for the normal Reynolds stresses. Calculated results are demonstrated to agree with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 55–60, September–October, 2008.     

Numerical simulation of a drop undergoing large amplitude oscillatory shear

Direct numerical simulations are conducted for a Newtonian drop in a Newtonian matrix subjected to large amplitude oscillatory shear flows. In the experimental study of Guido et al. (in Rheol Acta 43:575–583, 2004), the drop shape is found to oscillate at higher harmonics of the forcing frequency when the capillary number is increased. Their phenomenological model requires a much smaller capillary number for predicting the harmonic nature of the experimental data. In this paper, computational results on the evolution of drop length and inclination angle are obtained at the same fluid and flow properties as the experiments, and are shown to reasonably reproduce the experimental data. In particular, the computed velocity fields around the drop are shown to elucidate the over-rotation, which is a mechanism for the experimentally observed harmonics.     

Supercomputer simulation of liquid drop formation on a solid surface

Using a molecular-dynamics-type approach, we show how to simulate the formation of a liquid drop on a solid surface. Application is made to the case in which the liquid is water and the solid is graphite. The dynamical equations are large systems of nonlinear, ordinary differential equations which must be solved numerically. CRAY X-MP/24 simulations and related contact angle calculations are described and discussed.     

Level‐set based numerical simulation of a migrating and dissolving liquid drop in a cylindrical cavity

In the present paper the dissolution of a binary liquid drop having a miscibility gap and migrating due to thermo‐solutal capillary convection in a cylindrical cavity is studied numerically. The interest in studying this problem is twofold. From a side, in the absence of gravity, capillary migration is one of the main physical mechanisms to set into motion dispersed liquid phases and from the other side, phase equilibria of multi‐component liquid systems, ubiquitous in applications, often exhibit a miscibility gap. The drop capillary migration is due to an imposed temperature gradient between the cavity top and bottom walls. The drop dissolution is due to the fact that initial composition and volume values, and thermal boundary conditions are only compatible with a final single phase equilibrium state. In order to study the drop migration along the cavity and the coupling with dissolution, a previously developed planar two‐dimensional code is extended to treat axis‐symmetric geometries. The code is based on a finite volume formulation. A level‐set technique is used for describing the dynamics of the interface separating the different phases and for mollifying the interface discontinuities between them. The level‐set related tools of redistancing and off‐interface extension are used to enhance code resolution in the critical interface region. Migration speeds and volume variations are determined for different drop radii. Copyright © 2004 John Wiley & Sons, Ltd.     

扰动风作用下微型旋翼流场的数值模拟及流动控制研究

对于处在低雷诺数下的微型旋翼,扰动风对其流场影响很大。本文基于动态嵌套网格技术的双时间法,采用网格速度法模拟扰动风,研究了不同频率和幅值的正弦式扰动风下三维微型旋翼上的拉力系数响应情况,并采用变形网格方法模拟了旋翼桨叶的周期性边距运动对扰动风的流动控制,为今后旋翼机的主动控制研究提供了线索。研究结果表明,低雷诺数下,旋翼在周期性扰动风作用下的拉力响应曲线拟合函数与扰动风函数形式相同,响应曲线函数同样具有周期性变化趋势,波动幅值与扰动风幅值成正比例关系;对不同飞行状态下的旋翼,采用周期等角变距方式,能够找到一个适合的控制参数使得旋翼在正弦式扰动风环境下旋翼的拉力波动在一定范围内得到有效抑制。     

MOTION AND DEFORMATION OF VISCOUS DROP IN STOKES FLOW NEAR RIGID WALL

A boundary integral method was developed for simulating the motion and deformation of a viscous drop in an axisymmetric ambient Stokes flow near a rigid wall and for direct calculating the stress on the wall. Numerical experiments by the method were performed for different initial stand-off distances of the drop to the wall, viscosity ratios, combined surface tension and buoyancy parameters and ambient flow parameters. Numerical results show that due to the action of ambient flow and buoyancy the drop is compressed and stretched respectively in axial and radial directions when time goes. When the ambient flow action is weaker than that of the buoyancy the drop raises and bends upward and the stress on the wall induced by drop motion decreases when time advances. When the ambient flow action is stronger than that of the buoyancy the drop descends and becomes flatter and flatter as time goes. In this case when the initial stand-off distance is large the stress on the wall increases as the drop evolutes but when the stand-off distance is small the stress on the wall decreases as a result of combined effects of ambient flow, buoyancy and the stronger wall action to the flow. The action of the stress on the wall induced by drop motion is restricted in an area near the symmetric axis, which increases when the initial stand-off distance increases. When the initial stand-off distance increases the stress induced by drop motion decreases substantially. The surface tension effects resist the deformation and smooth the profile of the drop surfaces. The drop viscosity will reduce the deformation and migration of the drop.     

注塑成型三维流动的数值模拟

建立了非等温、粘性、不可压缩、非牛顿流体流动的控制方程。为了避免同时求解耦合的压力场、速度场,本文通过修改Galerkin方法的变分方程,导出了关于压力场的拟Poisson方程,用迭代法独立地求解连续性方程、动量方程,并进行速度一粘度迭代求出最终的压力场、速度场。由于直接使用Galerkin方法求解能量方程容易引起温度场的振荡,本文采用隐式格式及“上风”法离散能量方程,用超松驰迭代法求解温度场的代数方程组。比较了模拟结果与等温管道流动的解析解及法兰的实际注射结果,算例表明本文方法可以预测注射成型流动过程中的一些重要特征。与传统Galerkin方法相比,本文方法可以减少内存,提高数值方法的稳定性。     

Evaluation analysis of prediction methods for two-phase flow pressure drop in mini-channels

Two-thousand and ninety-two data of two-phase flow pressure drop were collected from 18 published papers of which the working fluids include R123, R134a, R22, R236ea, R245fa, R404a, R407C, R410a, R507, CO₂, water and air. The hydraulic diameter ranges from 0.506 to 12 mm; Re_l from 10 to 37,000, and Re_g from 3 to 4 × 10⁵. Eleven correlations and models for calculating the two-phase frictional pressure drop were evaluated based upon these data. The results show that the accuracy of the Lockhart–Martinelli method, Mishima and Hibiki correlation, Zhang and Mishima correlation and Lee and Mudawar correlation in the laminar region is very close to each other, while the Muller-Steinhagen and Heck correlation is the best among the evaluated correlations in the turbulent region. A modified Chisholm correlation was proposed, which is better than all of the evaluated correlations in the turbulent region and its mean relative error is about 29%. For refrigerants only, the new correlation and Muller-Steinhagen and Heck correlation are very close to each other and give better agreement than the other evaluated correlations.     

Numerical simulation of elongational flow behaviour in the cross cell experiments

In this work, numerical simulation of an elongational flow of polymer solutions is tried. The flow field is computed in a cell of simple geometry for newtonian, non-newtonian inelastic and non-newtonian elastic fluids. For the latter, an Oldroyd four-constant-model was adopted. The results are qualitatively in good agreement with the experimental results.     

后台阶流动的数值模拟

访述了大涡模拟的基本思想，指出大涡模拟的效率主要取决于四个因素，即流动中须有大尺度涡存在、合理的计算格式、合适的滤波器和亚格子应力模型。在深入考虑粘性不可压缩流Navier—Stokes方程各个子项作用的基础上，提出二阶全展开Euler—Taylor—Galerkin有限元方法作为大涡模拟的离散格式，并采用Gauss滤波器，对典型算例——后台阶处的流动进行大涡模拟，计算结果与相关文献符合的很好。从计算结果还可以看出大涡模拟与二阶全展开ETG有限元方法的结合在捕捉涡系及反映涡动时变过程方面具有明显的优势，说明大涡模拟适合于边界几何形状复杂区域流动的模拟。同时应用二阶全展开ETG有限元方法对低雷诺数粘性不可压缩后台阶流动进行了计算，得到与相关文献符合良好的计算结果，即该方法也可独立用于对低雷诺数粘性不可压缩流动的计算。     

Numerical simulation of three-dimensional free surface flow in isopycnal co-ordinates

In this paper a semi-implicit method for three-dimensional circulation in isopycnal co-ordinates is derived and discussed. It is assumed that the flow is hydrostatic and characterized by isopycnal surfaces which can be represented by explicit, single-valued functions. The hydrostatic pressure is determined by using the conjugate gradient method to solve a block pentadiagonal linear system. The horizontal velocities are determined by solving a large set of tridiagonal systems. The stability of the resulting algorithm is shown to be independent of the surface and internal gravity wave speeds. © 1997 John Wiley & Sons, Ltd.     

Numerical simulation of the flow in straight blade agitator with the MPS method

The three‐dimensional flow in a straight blade agitator with free surface on top is simulated using a grid‐free method named moving particle semi‐implicit method. The agitator has six rotor blades matched with six stationary guide blades. The mechanism and phenomena of the flow are investigated in the area between two adjacent stationary guide blades. Eddies near each tip of the rotational blades are predicted, and they move with the motion of the rotor blades but in opposite rotation direction of the rotor. The rotation axis of the eddies is traced and annular vortices, which are made by the eddies, are studied. The pressure pulsation in the rotation process is also predicted with this particle method. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulation of flow in Hartmann resonance tube and flow in ultrasonic gas atomizer

The gas flow in the Hartmann resonance tube is numerically investigated by the finite volume method based on the Roe solver.The oscillation of the flow is studied with the presence of a needle actuator set along the nozzle axis.Numerical results agree well with the theoretical and experimental results available.Numerical results indicate that the resonance mode of the resonance tube will switch by means of removing or adding the actuator.The gas flow in the ultrasonic gas atomization (USGA) nozzle is also studied by the same numerical methods.Oscillation caused by the Hartmann resonance tube structure,coupled with a secondary resonator,in the USGA nozzle is investigated.Effects of the variation of parameters on the oscillation are studied.The mechanism of the transition of subsonic flow to supersonic flow in the USGA nozzle is also discussed based on numerical results.