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1、SIMULATION OF COALESCENCE AND BREAKUP OFDISPERSED WATER DROPLETS IN CONTINOUS OIL PHASEP连续油相中分散水滴聚结和破裂模拟Shuxia Yuan, Ramin Dabirian, Ram S. Mohan Ovadia ShohamProceedings of the ASME 2018 5th Joint US European Fluids Engineering Summer Conference. FEDSM2018.July 15-20, 201 8, Le Centre Sheraton Mont
2、real, Montreal, Quebec, Canada. FEDSM2018-83314 ABSTRACT 摘要Petroleum industry uses shear devices such as chokes, valves, orifices and pumps, which cause droplet coalescence and breakup making the downstream separation process very challenging. Droplet droplet coalescence leads to formation of larger
3、 droplets, which accelerate the phase separation, whereas the breakup of larger droplets into smaller ones delays the separation process.石油行业使用节流阀、阀门、孔板和泵等剪切装置导致液滴聚结和破裂，使下游别离 过程非常具有挑战性。液滴聚结导致形成较大的液滴，加速相别离，而较大的液滴破裂为 较小的液滴会延迟别离过程。Computational Fluid Dynamic (CFD) simulations are conducted by ANSYS Flu
4、 ent software to track the droplet breakup and droplet-droplet coalescence, where the interfaces between the two phases are tracked by the Volume of Fluid (VOF) model. The material of droplet is water while the continuous phase is oil. In this study, the effect of variables such as droplet diameter,
5、 droplet relative velocities as well as droplet motion directions on the time evolution of droplet droplet coalescence and breakup is evaluated.计算流体动力学(CFD)模拟采用ANSYS Fluent软件进行，跟踪液滴破裂和液滴-液 滴聚结，其中两相之间的界面由流体体积(VOF)模型跟踪。液滴的材料是水，而连续相 为油。在这项研究中，评估液滴直径、液滴相对速度以及液滴运动方向等变量对液滴聚结 和破裂时间变化的影响。The simulation resu
6、lts confirm that smaller droplet collisions lead to coalescence under wide ranges of droplet relative velocities, while larger droplet collisions result in droplet breakup at higher relative velocities During coalescence, two droplets combine into one droplet, which 响、为保证破裂后的附属液滴都在研究范围内，连续相的尺寸为液滴直径的
7、10倍，连续 相边界为IODxIOD正方形，其中D是液滴的直径THE COMPUTATIONAL DOMAIN 计算域In order to determine the mesh size the models were simulated in the equivalent cases with different mesh sizes. Comparing the snapshots of each time showed that the simulation results do not change when the meshes size is equal or less than
8、 D /40 if coalescence happened whereas the meshes size should be equal or less than D /60 if breakup happened. Therefore, the meshes size of D 6 0 was selected to generate the cell for the simulations, and the total cell numbers are about 260 000.为了确定网格尺寸，模型在不同网格尺寸的等效情况下模拟。比照每个时间的快照， 说明，如果发生聚结，网格尺寸等
9、于或小于D/40时，模拟结果不会改变，而如果发生破 裂，那么网格尺寸应等于或小于D/60o因此，选择D60的网格尺寸，生成模拟单元，总 单元数约为260 000oAll the outer boundaries of the continuous phase are defined as walls. The initial time is identified as t = 0 and the initial relative velocity between the droplet s is no where the values of i)o are 0.25m /s, 0.5m s,
10、Im/s, 2m/s, 4m/s and 8m/s. The droplet is water, while the continuous phase is oil, which their physical properties are shown in Table 1连续相的所有外边界定义为壁。初始时间确定为t = 0,液滴之间的初始相对速度为v 0,其中i)o的分别为025m/s、05m/s、lm/s 2m/s、4m/s和8s/s。液滴为水，而是连续 相为油，其物理性质见表1。TABLE 1 SIMULATION P ARAMETERS 模拟参数Solve Methods求解方法Para
11、meters 参数Continuous phase连续相Droplet 液滴Density 密度(kg/n?)875998.2Viscosity 粘度(kg/m.s)0.0020.001Surface tension外表张力 (N/m)0.07194Velocities速度(m/s)00.25, 0.5, 1,2, 4, and 8Diameters 直径(pm)50, 200 and 800The Explicit Interpolation Scheme is used to solve the volume fraction equation, and the volume fracti
12、on values are computed through equation (8).显式插值方案用于求解体积分数方程，体积分数值通过式(8)计算。P P z P P/+ Z(4%琮/ ) = 0In equation (8), “n+1 is the index fbr new (current) time step, n” is the index for previous time step, and At is the time step size. The variable ap,f is the face value of the volume fraction of water
13、, Uf is the volume flux through the face based on normal velocity, V is the volume of cell and f is the face number. The scheme of geometric reconstruction, which was proposed by Youngs209 is applied as the interpolation method near the interface. For this scheme, the interface between fluids is obt
14、ained utilizing a piecewise-linear approach, see Fig. 2.在式(8)中，“n+1”是新(当前)时间步长的索引，“n”是前一个时间步长索引，At是(b) Geometric reconstruction (piecewise-linear) scheme(b) Geometric reconstruction (piecewise-linear) scheme见图2o时间步长大小。变量（Xp,f是 水的体积分数的面值，Uf是 基于法向速度的通过面的体 积通量，V是单元体积，f是 面数。Youngs提出的几何重 构方案用作近界面的插值方 法。对
15、于这一方案，流体之间 界面采用分段线性方法取得,COMPARISON BETWEEN ACTUAL VOF INTERFACE AND GEOMETRIC RECONSTRUCTION SCHEME实际VOF界面与几何重构方案比照MODEL VALIDATION模型验证As mentioned, the coalescence and breakup behaviors of two droplets colliding in gas have been studied experimentally and theoretically by several researchers, where
16、by the collision regimes of coalescence, bounce or breakup after the collision are considered. However the collision between two droplets in liquid is studied just from recent years, thus the experimental data are lacked. Therefore, the collision of droplets in a gas is studied in this paper and the
17、 results are compared with the experimental data of Qian and Lawl to validate the developed simulations. Then the same model is used to study the collision behavior of droplets in a liquid. The material of droplets is tetradecane with the density (pp) of 762.8kg/m35 viscosity (|ip) of 0.00213Pa-s, a
18、nd the surface tension (o) of 0.0265N/m. The gas is nitrogen with the density (p) of 1.138kg/m39 and viscosity (ji) of 1.663xl0 5 Pa-s.如前所述，一些研究人员实验和理论上研究了气体中两个液滴碰撞的聚结和破裂特性, 其中考虑了碰撞后聚结、反弹或破裂的碰撞机制。但是，近几年才开始研究液体中两个液 滴之间的碰撞，因此，缺乏实验数据。因此，本文研究了气体中液滴的碰撞，并将结果与实验数据比照，验证开发的模拟。之后使用相同模型，研究液滴在液体中的碰撞特性。液 滴材料为十四烷
19、,密度(pp)为762.8kg/m3,粘度(即)为0.00213Pas,外表张力为0.0265N/mo 气体为氮气,密度(p)为1.138kg/m3,粘度)为1.663x10-5 pa.s。The comparison between the experiment datel and the results of numerical simulation are presented in Fig. 3, where the Weber number (We) is 0.2, the droplet Reynolds number (Rep) is 14.89 the off-center pa
20、rameter (B) is 0.20, and droplet radius (R) of the two droplets is 120|im.实验数据与数值模拟结果比照见图3,其中Weber数(We)为0.2,液滴雷诺数(Rep) 为14.8,偏心参数(B)为0.20,两个液滴dl液滴半径(R)为120pm。The Weber number, the Reynolds number, and the off-center parameter are defined as equation (9), (10), and (11). In equation (11), % is the di
21、stance between the centers of the two droplet in vertical direction.Weber数、雷诺数和偏心参数定义为式(9)、(10)和(11)。在式(11)中，5c是两 个液滴中心的垂直方向距离。(9)(10)(H)We oc pp6/pAVp /(7R?p = PpWpdp I &B = /HRThen the relative velocity between the two droplets can be calculated from the Weber number and Reynolds number reported b
22、y Qian and Lawl9 and it is vO = 0.17m/s. It can be known from Fig. 3 that the simulation results have a good agreement with the experiment data collected by Qian and Law 1. The method used to simulate the collision of droplets in a liquid is exactly the same, only the physical properties of the cont
23、inuous phase are changed.之后可由报告的Weber数和雷诺数计算 出两个液滴之间的相对 速度，vo = 0.17m/So 从 图3可以看出，模拟结 果与提供的实验数据非 常一致。用于模拟液体0.0 ms0.68 ms1.21 ms1.41 ins000.91 ms1.15 ms2.11 ms81.79 ms001.92 ms2.21 ins2.05 ms2.38 ms2.45 ins2.57 ins3.09 ins(a) Experiment data of Qian and Law 1 c o0.0 ms0.68 ms0.91 ms( IV J1.15 ms1.21
24、ms( k )1.41 ms/1.79 msxx/ /I1.92 ms2.05 msc )2.11 ms/(a2.21 ms(JV2.38 msC /2.45 ms()2.57 ins( 3.09 ins(b) Simulation results using the same condition with (a中液滴碰撞的方法完全相同，只是改变了连续相的物理性质。FIG.3 DROPLETS BEHAVIORSC OMPARISON BETWEEN THE EXPERIMENTDATA PRESENTED BY QIAN AND LAW 1 AND THE RESULTS OF SIMUL
25、ATIONS给出的实验数据与模拟结果的液滴特性比照RESULTS AND DISCUSSION结果和讨论The simulation models discussed previously are used, and the head on collision of the droplets with three different sizes, i.e. 50(im9 200 |im, and 800 pm, under different relative velocities are investigated. The possibility of droplet coalescence
26、 after collision depends on the fact that the kinetic energy can drain the continuous phase between them out. If the kinetic energy is enough, the two droplets combine into one droplet. Whether the combined droplet recovers its shape or break is determined by Weber number, which is the ratio between
27、 the inertial force and surface tension as expressed in equation 9 The greater the inertia force is, the more easily the breakup happens, and the greater the surface tension is, the more easily fbr the droplet to recover the shape. There are many factors, which affect droplet coalescence and breakup
28、 process, including droplet sizes, droplet and continuous phase physical properties (density, viscosity, and surface tension), collisio n relative velocities and so on. In this study, the influence of two parameters such as droplet sizes and velocities are discussed in this study.采用前面讨论的模拟模型，研究了三种不同
29、尺寸液滴在不同相对速度下的正面头部, 即50国11、200 nm和800 pim。碰撞后液滴和聚结的可能性取决于可排出之间连续相互动 能的事实。如果动能足够，那么两 个液滴结合并为一个液滴。合并 液滴是否恢复其形状或破裂由 Weber数决定，后者是惯性力与 外表张力的比值，如式9所示。惯性力越大，越易于发生破裂， 而外表张力越大，液滴越易于恢 复形状。影响液滴聚结和破裂过 程的因素很多，包括液滴尺寸、 液滴和连续相的物理性质(密度、Relative velocity (m，s)0.125 OO OO Qmso 0O CO Q 0175 OO。0 Ojo oo Q O 0225 OO 0 O|
30、0250 O 0。I g o o o0.4500Q0。4”0OO0 50QQO0J30.51.0o-o OO OG OO 0.025 0 OO OO o.o5o O0 OO 0.075 OO OO 30.00.100.200.300.400.500.60ORO1.01.201.401.601.802.02.202.402.602.803.03.203.40Relative velocity (tns) 0.2S051.02.00000000000000000000C 原硒q多r-w;./%v.D,QG4O 3 d aO.。.0.aooQooO2HO0。 M X 工IGOQR 麒点:vvv 00
31、凶 2 OA YOOVAX30do.oodo$00.00.8.00dododo.o 000000008。88000 OOO0OOO 000000008000 000 00 0000 00 0。 oo0000ooooWOTOOOOOOOOOOOOO 40802060o40qs2080,44)2.03.20,80,40o.o,60,80 aal-L2245.兀 &10I213I51618202123”(SIU) 9EURelative velocity 0.250.51.02.0408.0粘度和外表张力）、碰撞相对速度等。在本研究中，研究中讨论了液滴大小和速度两个参数的影响。FIG. 4 SNAP
32、SHOTS OF DROPLETS COLLISION IMAGES CHANGING WITHTIMES UNDER DIFFERENT VELOCITIES不同相对速度下液滴碰撞图像快照随时间的变化The Influence of Relative Velocity 相对速度的影响The relative velocity of droplets determines the kinetic energy. The droplets require sufficient kinetic energy to drain the continuous phase between them ou
33、t, whereas too large kinetic energy may cause the droplet break up. Fig. 4 (a) to (c) shows the snapshots of the head on collision between the two equal size droplets under di昧rent relative velocities. The diameters of the droplets in Fig. 4 (a) to (c) are 50|im, 200(im and 800|im respectively. Acco
34、rding to the definition of this paper, coalescence time includes the collision time (including the time to drain the continuous phase out) and the shape recovery time. With the increase in relative velocities, the collision time becomes shorter. When the relative velocity increases to a certain valu
35、e, it increas s the shape recovery time and even makes the droplet broken When the relative velocity is 2m/s9 the two droplets with the diameter of 200|im collide in only 0.2ms. However, the combined droplet undergoes serious deformation due to the higher kinetic energy. To explain this process in d
36、etails, the forces acting on the droplets are shown in Fig. 5. The kinetic energy makes the droplets deformed while the surface tension recovers the droplet shape. Under these actions, the droplet deforms in the two perpendicular directions alternately several times, and finally recovers the shape t
37、o a quasispherical shape or break into several droplets.液滴相对速度决定动能。液滴需要足够的动能排出之间的连续相，而太大的动能可能 导致液滴破裂。图4(a)到(c)显示了不同相对速度下两个相等大小液滴正面碰撞的快 照。图4 (a)至(c)中液滴的直径分别为50|im、200plm和800pm。根据本文的定义, 聚结时间包括碰撞时间(包括排出连续相的时间)和形状恢复时间。随着相对速度增加， 碰撞时间变短。当相对速度增加到一定值时，形状恢复时间增加，甚至使液滴破裂。当相对速度为2m/ s,两个直径为200|im的液滴仅 在0.2ms内发生碰撞
38、。但是，由于较高的动能， 合并后的液滴发生严重的变形。为了详细解释这 一过程，作用在液滴上力见图5。动能使液滴变 形，而外表张力恢复液滴形状。在这些作用下, 液滴在两个垂直方向交替变形数次，最终恢复形 状为准球形，或破裂为数个液滴。FIG. 5 SCHEMATIC OF DROPLETS DEFORMATION AFTER COLLOSION 碰撞后液 滴变形示意图The comparisons of collision time, shape recovery time and coalescence time for dropletswith the diameter of 50(im5
39、200|im9 and 800Plm are shown in Fig. 6 (a) to (c), respectively. Two curves represent the droplets collision time and the coalescence time, respectively, and the difference between them is the shape recovery time.(A) 50pm(B) 200pm(C) 800pm之间的差是形状恢复时间。50|im、200|im 和 800|im直径液滴的碰 撞时间、形状恢复时间 和聚结时间的比照见
40、图6 (a)至(c)所示。 两条曲线分别代表液 滴碰撞时间和聚结时间,THE COMPARISONS OF COLLISION TIME, SHAPE RECOVERY TIME ANDCOALESCENCE TIME碰撞时间、形状恢复时间和聚结时间比照As shown in Fig. 4, the droplet collision time decreases with the increase in relative velocity, while the shape recovery time may become longer with the increase in relativ
41、e velocity. When the relative velocity increases to a certain value, the collided droplet needs more time to recover the shape due to the serious deformation caused by the high velocity, and the increase in shape recovery time increases the coalescence time again.如图4所示，液滴碰撞时间随着相对速度的增加而减少，而形状恢复时间可能随着
42、 相对速度加而变长。当相对速度增加到一定值时，由于高速引起的严重变形，碰撞的液滴 需要更多时间恢复形状，形状恢复时间增加再次增加聚结时间。For the biggest droplet size, namely, 800 |im, the rate of increasing shape recovery factor is low because the coalescence occurs at low relative velocity, whereby the deformation is not significant. For particle sizes of 50 and 20
43、0 jim, the coalescence time decrease s with the increase in relative velocity firstly, and then increase with the increase in relative velocity.对于最大的液滴尺寸，即800 |im,由于聚结发生在较低的相对速度下，因此变形不 显著，形状恢复因子增加率较低，。对于50和200 gm的粒径，聚结时间先随着相对速 度的增加而减少s,然后随着相对速度的增加而增加。The longer shape recovery time corresponds to the
44、 high Weber number, which means that the droplets are prone to break. For a specific diameter, the shortest coalescence time is achievedat a moderate relative velocity, and the high relative velocity may in crease the possibility of breakup.较长的形状恢复时间对应于较高的Weber数，这意味着液滴易于破裂。对于特定直径, 在中等相对速度下实现最短聚结时间，而
45、较高的相对速度可能增加破裂的可能性。The Influence of Droplet Diameter 液滴直径的影响It can be seen from Fig. 4 (a) to (c) that the larger droplet size, the longer the coalescence time. The increase in droplet coalescence time is not only due to increase in the collision time, but also in the shape recovery time, whereby lar
46、ge droplets require more time to recover their shape. Fig. 7 presents the time cost of the collision stage and shape recovery stage. It can be seen from Fig. 7 (a) that the droplet collision time is almost proportional to R, especially when the relative velocity is low. This phenomenon is obvious be
47、cause the initial distance between the two droplets is specified to the equivalent radius of two droplets (R) , which the collision time is proportional to the initial distance. However, the shape recovery time shown in Fig. 7 (b) is obviously not proportional to the radius of the droplet, and the l
48、arger droplets need a longer recovery time. In addition, Fig. 7 (b) also shows that the shape recovery time does not change with the relative velocity.从图4 (a)到(c)可以看出，液滴尺寸越大，聚结 时间越长。液滴聚结时间增加不仅是由于碰撞时间增加, 而且是由于形状恢复时间增加，因此，大液滴需要更长 时间恢复其形状。图7显示碰撞和形状恢复阶段所用 时间。从图7 (a)可以看出，液滴碰撞时间几乎与R成 正比，尤其是在相对速度较低时。由于两个液滴之间的 初始距离指定为两个液滴的等效半径(R),其碰撞时间 与初始距离成正比，这种现象明显。但是，图7 (b)所 示的形状恢复时间显然并非与液滴半径成正比，较大的 液滴需要较长的恢复时间。另外，图7 (b)也说明形状(A) COLLISION STAGE(A) COLLISION STAGE(B