IMPACT OF A PLANAR SHOCK ONTO SIDE-BY-SIDE DROPLETS: A 3D NUMERICAL STUDY
-
摘要: 采用三维守恒清晰界面数值方法, 研究平面激波冲击并排液滴的动力学过程. 研究的焦点在于激波接触液滴后的复杂波系结构生成, 以及并排液滴相互耦合作用诱导的单个液滴非对称界面演化. 首先, 分析并排液滴之间界面通道内的波系结构发展, 发现在冲击初期由于反射激波相交而形成新的反射激波以及马赫杆; 这些流动现象与液滴另外一侧 (非通道侧) 由激波反射所形成的弯曲波阵面截然不同, 而且所导致的液滴横向两侧流场差异是中后期冲击过程液滴两侧界面非对称演化的主要原因. 其次, 研究冲击中期时, 特别是入射激波已运动至液滴下游并远离并排液滴, 界面形态的演化过程和规律, 揭示通道下游出口处由于气流膨胀导致的界面闭合、以及随后气流阻塞导致的界面破碎等新的流动现象. 最后, 研究液滴间距对并排液滴相互作用的影响规律, 发现液滴间距大小与通道内压力峰值具有明显的关联关系. 研究表明, 更小的液滴间距不仅带来更大的压力峰值, 而且使得峰值出现的时间更早.Abstract: In this paper we investigate the evolution dynamics of side-by-side droplets after being impacted by a planar shock by using a three-dimensional conservative sharp interface method. Our research mainly focuses on the development of wave structures after the shock impact and the asymmetric interface evolution of single droplet induced by the coupling between the side-by-side droplets. Firstly, we analyze the development of the wave system including those inside and outside the channel between the side-by-side droplets. We find that at the early stage of impact, the intersection of reflected shock waves accounts for the formation of new reflected shock waves and Mach rods. This is quite different from the curved wave front formed by the reflected shock wave on the other side of the droplet transversely opposite to the channel. The difference of the flow field on the two sides of the droplet is responsible for the asymmetric interface evolution of the droplet in the middle stage of the droplet-shock interaction. Secondly, we investigate the interface morphology and its evolution in the middle stage of shock impact, especially when the incident shock wave moves to the downstream of and is far away from the droplets, and report the occurrence of new flow phenomena at the downstream outlet of the channel, such as interface coalescence caused by airflow expansion and subsequent interface fragmentation owing to airflow blockage. Finally, the effect of the gap between the side-by-side droplets on the droplet interaction is studied. We find that the gap size has a significant effect on the occurrence of pressure peaks in the channel. Specifically, a smaller gap not only brings higher pressure peak, but also makes the peak appear at an earlier time.
-
图 1 激波冲击并排液滴的二维示意图
Figure 1. Two-dimensional sketch of shock waves impacting onto side-by-side droplets
图 2 冲击初期波系演化过程 (L/R = 1)
Figure 2. The evolution of wave structures at the early stage of impact (L/R = 1)
图 3 并排液滴与激波相互作用早期的压力云图 (L/R = 1)
Figure 3. The evolution of wave structures at the early stage of impact (L/R = 1)
图 4 并排液滴的三维形态演化及X-Y平面(Z = 0)上的压力与马赫数分布, 标号为1的列为液滴侧面, 标号为2的列为液滴正面(L/R = 1)
Figure 4. Three-dimensional morphological evolution of side-by-side droplets, pressure and Mach number contours in the X-Y plane (Z = 0). The column with label 1 corresponds to the side of the droplet, and the column with the label 2 corresponds to the front of the droplet (L/R = 1)
图 5 激波冲击并排液滴(L/R = 1)后界面三维形态演化及X-Y 平面(Z = 0)上的压力与马赫数分布. 其中液滴侧面视图标号为 1, 液滴正面标号为 2
Figure 5. Snapshots of side-by-side droplets (L/R = 1) after being impacted by a planar shock, pressure and Mach number contours in the X-Y plane (Z = 0). The column with label 1 shows the side view of the droplet, and the column with the label 2 shows the front view
图 6 并排液滴两侧半径(L/R = 1)及单液滴半径随时间的变化
Figure 6. The radius evolution of side-by-side droplets (L/R = 1) and single droplet
图 7 不同液滴间距下X-Y平面(Z = 0)液滴的截面图
Figure 7. The cross-sectional profile of droplets in the X-Y plane (Z = 0) with different droplet gaps
图 8 不同通道间距下, 并排液滴的压力云图. 标号为2的列为L/R = 0.2
Figure 8. Pressure contours of side-by-side droplets under different channel spacing. The column labeled 1 corresponds to L/R = 0.5 and the column labeled 2 corresponds to L/R = 0.2
图 9 不同L/R下通道中心(X = Y = Z = 0)处压力值随时间变化
Figure 9. Time variation of pressure at the channel center (X = Y = Z = 0) with different L/R
图 10 t = 19 μs时刻的液滴的三维界面形态(L/R = 0.2)
Figure 10. Snapshot of the two droplets with L/R = 0.2 at t = 19 μs
-
[1] Taylor GI. The shape and acceleration of a drop in a high-speed air stream. The Scientific Papers of GI Taylor, 1963, 3: 457-464 [2] Harper EY, Grube GW, Chang ID. On the breakup of accelerating liquid drops. Journal of Fluid Mechanics, 1972, 52(3): 565-591 [3] Hinze JO. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE Journal, 1955, 1(3): 289-295 doi: 10.1002/aic.690010303 [4] 陆守香, 秦友花. 激波诱导的液滴变形和破碎. 高压物理学报, 2000, 14(2): 151-154 (Lu Shouxiang, Qin Youhua. Deformation and breakup of droplets behind shock wave. Chinese Journal of High Pressure Physics, 2000, 14(2): 151-154 (in Chinese) [5] Pilch M, Erdman CA. Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. International Journal of Multiphase Flow, 1987, 13: 741-757 doi: 10.1016/0301-9322(87)90063-2 [6] Guildenbecher D, Lopez-Rivera C, Sojka P. Secondary atomization. Experiments in Fluids, 2009, 46(3): 371-402 doi: 10.1007/s00348-008-0593-2 [7] Gelfand BE. Droplet breakup phenomena in flows with velocity lag. Progress in Energy and Combustion Science, 1996, 22(3): 201-265 doi: 10.1016/S0360-1285(96)00005-6 [8] Wierzba A. Deformation and breakup of liquid drops in a gas stream at nearly critical weber numbers. Experiments in Fluids, 1990, 9(1): 59-64 [9] Dai Z, Faeth GM. Temporal properties of secondary drop breakup in the multimode breakup regime. International Journal of Multiphase Flow, 2001, 27(2): 217-236 doi: 10.1016/S0301-9322(00)00015-X [10] 杨威, 贾明, 孙凯等. 液滴变形-袋式-多模式破碎转换研究. 工程热物理学报, 2017, 38(2): 416-420 (Yang Wei, Jia Meng, Sun Kai, et al. Investigation on transitions of deformation-bag-multimode breakup for liquid droplets. Journal of Engineering Thermophysics, 2017, 38(2): 416-420 (in Chinese) [11] Hanson AR, Domich EG, Adams HS. Shock tube investigation of the breakup of drops by air blasts. Physics of Fluids, 1963, 6: 1070-1080 doi: 10.1063/1.1706864 [12] Nicholls JA, Ranger AA. Aerodynamic shattering of liquid drops. AIAA Journal, 1969, 7(2): 285-290 doi: 10.2514/3.5087 [13] 楼建锋, 洪滔, 朱建士. 液滴在气体介质中剪切破碎的数值模拟研究. 计算力学学报, 2011, 28(2): 210-213 (Lou Jianfeng, Hong Tao, Zhu Jianshi. Numerical study on shearing breakup of liquid droplets in gas medium. Chinese Journal of Computational Mechanics, 2011, 28(2): 210-213 (in Chinese) [14] Waldman GD, Reinecke WG, Glenn DC. Raindrop breakup in the shock layer of a high-speed vehicle. AIAA Journal, 1972, 10(9): 1200-1204 doi: 10.2514/3.50350 [15] Simpkins PG, Bales EL. Water-drop response to sudden accelerations. Journal of Fluid Mechanics, 1972, 55(4): 629-639 doi: 10.1017/S0022112072002058 [16] Joseph DD, Belanger J, Beavers GS. Breakup of a liquid drop suddenly exposed to a high-speed airstream. International Journal of Multiphase Flow, 1999, 25(6): 1263-1303 [17] 耿继辉, 叶经方, 王健等. 激波诱导液滴变形和破碎现象实验研究. 工程热物理学报, 2003, 24(5): 797-800 (Geng Jihui, Ye Jingfang, Wang Jian, et al. Experimental investigation on phenomena of shock wave-induced droplet deformation and breakup. Journal of Engineering Thermophysics, 2003, 24(5): 797-800 (in Chinese) [18] Theofanous TG, Li GJ, Dinh TN. Aerobreakup in rarefied supersonic gas flows. Journal of Fluids Engineering, 2004, 126(4): 516-527 doi: 10.1115/1.1777234 [19] Liu Z, Reitz RD. An analysis of the distortion and breakup mechanisms of high speed liquid drops. International Journal of Multiphase Flow, 1997, 23(4): 631-650 doi: 10.1016/S0301-9322(96)00086-9 [20] Theofanous TG, Li GJ. On the physics of aerobreakup. Physics of Fluids, 2008, 20(5): 52-103 [21] Sembian S, Liverts M, Tillmark N, et al. Plane shock wave interaction with a cylindrical water column. Physics of Fluids, 2016, 28(5): 56-102 [22] Meng JC, Colonius T. Numerical simulation of the aerobreakup of a water droplet. Journal of Fluid Mechanics, 2018, 835: 1108-1135 doi: 10.1017/jfm.2017.804 [23] Liu N, Wang ZG, Sun MB, et al. Numerical simulation of liquid droplet breakup in supersonic flows. Acta Astronautica, 2018, 145: 116-130 doi: 10.1016/j.actaastro.2018.01.010 [24] Dorschner B, Biasiori-Poulanges L, Schmidmayer K, et al. On the formation and recurrent shedding of ligaments in droplet aerobreakup. Journal of Fluid Mechanics. 2020, 904(A20): 2020699 [25] Yoshida T, Wierzba A, Takayama K. Breakup and interaction of two droplets columns in a shock wave induced high-speed air flow. Transactions of the Japan Society of Mechanical Engineers, 1989, 55(514): 1607-1612 doi: 10.1299/kikaib.55.1607 [26] Igra D, Takayama K. Experimental investigation of two cylindrical water columns subjected to planar shock wave loading. Journal of Fluids Engineering, 2003, 125(2): 325-331 doi: 10.1115/1.1538628 [27] Chen H, Liang SM. Flow visualization of shock/water column interactions. Shock Waves, 2008, 17(5): 309-321 doi: 10.1007/s00193-007-0115-9 [28] Nourgaliev RR, Din TN, Theofanous TG. Adaptive characteristics-based matching for compressible multifluid dynamics. Journal of Computational Physics, 2006, 213: 500-529 doi: 10.1016/j.jcp.2005.08.028 [29] Chang CH, Deng X, Theofanous TG. Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method. Journal of Computational Physics, 2013, 242: 946-990 doi: 10.1016/j.jcp.2013.01.014 [30] Shen Y, Ren Y, Ding H. A 3D conservative sharp interface method for simulation of compressible two-phase flows. Journal of Computational Physics, 2020, 403: 109107 doi: 10.1016/j.jcp.2019.109107 [31] Osher S, Sethian JA. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 1988, 79: 12-49 doi: 10.1016/0021-9991(88)90002-2 [32] 林健宇. 切割网格方法及激波与气泡相互作用研究. [博士论文]. 合肥: 中国科学技术大学, 2016Lin Jianyu. Development of cut-cell method and dynamics of shock-bubble interactions. [PhD Thesis]. Hefei: University of Science and Technology of China, 2016 (in Chinese) [33] 沈毅. 守恒型尖锐界面方法及激波诱导的含泡液滴演化动力学. [博士论文]. 合肥: 中国科学技术大学, 2020Shen Yi. Conservative sharp interface method and shock-induced dynamics of droplet containing a bubble. [PhD Thesis]. Hefei: University of Science and Technology of China, 2020 (in Chinese) [34] Liou MS. A sequel to AUSM, part ii: AUSM+-up for all speeds. Journal of Computational Physics, 2006, 214(1): 137-170 doi: 10.1016/j.jcp.2005.09.020 [35] Osher S, Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces. New York: Springer, 2003: 17-90 [36] Sussman M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics, 1994, 114(1): 146-159 doi: 10.1006/jcph.1994.1155 [37] Russo G, Smereka P. A remark on computing distance functions. Journal of Computational Physics, 2000, 163(1): 51-67 doi: 10.1006/jcph.2000.6553 [38] Min C. On reinitializing level set functions. Journal of Computational Physics, 2010, 229(8): 2764-2772 doi: 10.1016/j.jcp.2009.12.032 [39] Theofanous TG, Mitkin VV, Ng CL, et al. The physics of aerobreakup ii. viscous liquids. Physics of Fluids, 2012, 24(2): 22-104 -
下载:
点击查看大图
计量
- 文章访问数: 554
- HTML全文浏览量: 176
- PDF下载量: 155
- 被引次数: 0
