基于EFEM和气泡统一方程的双气泡耦合效应研究

许流逸; 李世民; 王诗平; 刘云龙; 张阿漫

doi:10.21656/1000-0887.450018

基于EFEM和气泡统一方程的双气泡耦合效应研究

doi: 10.21656/1000-0887.450018

哈尔滨工程大学船舶工程学院, 哈尔滨 150001

(我刊青年编委刘云龙、编委张阿漫来稿)

基金项目:

国家自然科学基金 51925904

国家自然科学基金 52088102

中国博士后科学基金 2024T171136

黑龙江省博士后资助项目 LBH-Z23115

国家资助博士后研究人员计划 GZB20230942

详细信息

作者简介:
许流逸(1998—)，男，博士(E-mail: liuyi980211@126.com)

通讯作者:
李世民(1996—)，男，讲师，博士(通讯作者. E-mail: lishimien@126.com)

中图分类号: O351.2
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- 文章访问数: 247
- HTML全文浏览量: 118
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- 被引次数: 0
出版历程
- 收稿日期: 2024-01-25
- 修回日期: 2024-04-02
- 刊出日期: 2024-07-01

Investigation of Coupling Effects of Double Bubbles Based on the EFEM and the Unified Bubble Equation

College of Shipbuilding Engineering, Harbin Engineering University,Harbin 150001， P.R. China

(Contributed by LIU Yunlong, M.AMM Youth Editorial Board & ZHANG Aman, M.AMM Editorial Board)

摘要

摘要: 基于Euler有限元方法(EFEM), 建立了双气泡水下脉动轴对称数值模型，通过与气泡统一方程和实验结果的对比，该模型的准确性和网格的收敛性得到了充分验证. 计算结果表明，相比其他气泡理论，气泡统一方程对气泡动力学行为和流场中压力载荷的预测更为准确. 结合EFEM和气泡统一方程，研究了浮力参数δ和强度参数ε对双气泡耦合规律的影响. 当δ≤0.15时，上气泡在下气泡的作用下会产生垂直向下的射流，此时下气泡边界与固壁边界相似；而当δ增大至0.2时，下气泡对上气泡的影响减弱，浮力效应占据主导地位，上气泡的射流方向垂直向上. ε对气泡间的耦合作用未造成明显影响，但当ε≥150时，其对气泡射流速度的作用会明显减弱.
- 气泡动力学 /
- EFEM /
- 气泡统一方程 /
- 气泡耦合
Abstract: Based on the Eulerian finite element method (EFEM), an axially symmetric numerical model was established for 2-bubble underwater pulsation. The accuracy of the model and the convergence of the mesh were fully verified by comparison with the unified bubble equation and experimental results. The calculation results show that, the unified bubble equation is more accurate than other bubble theories in predicting the bubble dynamic behavior and the pressure load in the flow field. Combined with the EFEM and the unified bubble equation, the effects of buoyancy parameter δ and strength parameter ε on the coupling law of double bubbles were studied. For buoyancy parameter δ≤0.15, the upper bubble will produce a vertical downward jet under the action of the lower bubble, and the lower bubble boundary is like the solid wall boundary. For δ increasing to 0.2, the influence of the lower bubble on the upper bubble weakens, the buoyancy effect becomes more prominent and the jet direction of the upper bubble is vertical upward. Strength parameter ε has no obvious effect on the coupling between bubbles, but its effect on the bubble jet velocity decreases significantly for ε≥150.
- bubble dynamics /
- EFEM /
- unified bubble equation /
- bubble coupling
edited-by

edited-by
注释:

1) (我刊青年编委刘云龙、编委张阿漫来稿)

HTML全文

图 1 自由场中的双气泡脉动示意图

Figure 1. Diagram of double bubble pulsation in a free field

下载: 全尺寸图片幻灯片

图 2 实验结果^[47]与数值结果的对比

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 2. Comparison of experimental results^[47] with numerical results

下载: 全尺寸图片幻灯片

图 3 气泡1半径和迁移时历曲线数值与理论计算^[19]对比

Figure 3. Comparison of numerical and theoretical results^[19] of bubble 1 radius and migration time curves

下载: 全尺寸图片幻灯片

图 4 气泡2半径和迁移时历曲线数值与理论计算^[19]对比

Figure 4. Comparison of numerical and theoretical results^[19] of bubble 2 radius and migration time curves

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图 5 δ=0.05时的自由场同相双气泡脉动过程

Figure 5. The in-phase double bubble pulsation process in the free field for δ=0.05

下载: 全尺寸图片幻灯片

图 6 δ=0.20时的自由场同相双气泡脉动过程

Figure 6. The in-phase double bubble pulsation process in the free field for δ=0.20

下载: 全尺寸图片幻灯片

图 7 不同理论计算^[18-19]及不同浮力参数下的流场压力时历曲线

Figure 7. Histories of flow-field pressure under different theoretical calculations^[18-19] and different buoyancy parameters

下载: 全尺寸图片幻灯片

图 8 不同理论计算及不同浮力参数下的气泡半径时历曲线

Figure 8. Histories of bubble radii under different theoretical calculations and different buoyancy parameters

下载: 全尺寸图片幻灯片

图 9 不同理论计算及不同浮力参数下的气泡迁移时历曲线

Figure 9. Histories of bubble migration under different theoretical calculations and different buoyancy parameters

下载: 全尺寸图片幻灯片

图 10 δ=0.05, 0.10, 0.15和0.20时的双气泡射流速度时程

Figure 10. Double bubble jet velocity histories for δ=0.05, 0.10, 0.15 and 0.20

下载: 全尺寸图片幻灯片

图 11 ε=200时的自由场同相双气泡脉动过程

Figure 11. The in-phase double bubble pulsation process in the free field for ε=200

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图 12 不同强度参数下的流场压力时历曲线

Figure 12. Histories of bubble radii under different strength parameters

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图 13 不同强度参数下的气泡半径时历曲线

Figure 13. Histories of bubble radii under different strength parameters

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图 14 不同强度参数下的气泡迁移时历曲线

Figure 14. Histories of bubble migration under different strength parameters

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图 15 ε=50, 100, 150和200时气泡射流速度时程

Figure 15. Double bubble jet velocity histories for ε=50, 100, 150 and 200

下载: 全尺寸图片幻灯片

表 1 基本物理量的无量纲化

Table 1. Non-dimensionalization of fundamental physical quantities

time	velocity	mass	acceleration	internal energy
$ R_{\mathrm{m}} \sqrt{\frac{\rho_{\mathrm{w}}}{P_{\infty}}}$	$ \sqrt{\frac{P_{\infty}}{\rho_{\mathrm{w}}}}$	$ \rho_{\mathrm{w}} R_{\mathrm{m}}^3$	$ \frac{P_{\infty}}{R_{\mathrm{m}} \rho_{\mathrm{w}}}$	$ P_{\infty} R_{\mathrm{m}}^3$

下载: 导出CSV

表 2 气泡1水平方向最大长度及其出现时刻实验^[47]与数值结果对比

Table 2. Comparison of the maximum length of bubble 1 in the horizontal direction and its appearance time between experimental results^[47] and numerical results

bubble 1	experimental result^[47]	numerical result	error
maximum length in the horizontal direction	13.8 mm	14.8 mm	7.2%
appearance time of the maximum length	1.473 ms	1.533 ms	4.1%

下载: 导出CSV

表 3 气泡最大半径及迁移误差对比

Table 3. Comparison of relative errors of maximum bubble radii and migrations

parameter	error
parameter	L_e=0.01R_m	L_e=0.02R_m	L_e=0.04R_m
maximum radius of bubble1	1.59%	2.01%	2.27%
maximum migration of bubble 1	1.81%	7.84%	19.25%
maximum radius of bubble 2	1.97%	2.23%	2.49%
maximum migration of bubble 2	8.84%	4.96%	18.35%

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表 4 不同计算情况下气泡1的脉动周期和最小半径对比

Table 4. Comparison of pulsation periods and minimum radii of bubble 1 under different calculations

case	pulsation period of bubble 1	minimum radius of bubble 1
unified bubble equation^[19], δ=0.05	2.240	0.219
Keller equation^[18], δ=0.05	2.243	0.206
EFEM, δ=0.05	2.219	0.246
EFEM, δ=0.10	2.201	0.223
EFEM, δ=0.15	2.155	0.192
EFEM, δ=0.20	2.106	0.168

下载: 导出CSV

表 5 不同计算情况下气泡2的脉动周期, 最小和最大半径对比

Table 5. Comparison of pulsation periods, minimum and maximum radii of bubble 2 under different calculations

case	pulsation period of bubble 2	minimum radius of bubble 2	maximum radius of bubble 2
unified bubble equation^[19], δ=0.05	2.225	0.231	0.999
Keller equation^[18], δ=0.05	2.228	0.216	0.999
EFEM, δ=0.05	2.212	0.255	0.993
EFEM, δ=0.10	2.162	0.270	0.979
EFEM, δ=0.15	2.069	0.282	0.953
EFEM, δ=0.20	1.954	0.289	0.922

下载: 导出CSV

表 6 不同强度参数下的压力峰值对比

Table 6. Comparison of pressure peaks under different strength parameters

strength parameter	shockwave pressure		pressure peak value of bubble pulsation
strength parameter	the 1st peak value	the 2nd peak value	pressure peak value of bubble pulsation
ε=50	3.668	5.560	3.182
ε=100	5.282	7.663	3.889
ε=150	6.601	9.040	4.327
ε=200	7.764	10.090	4.690

下载: 导出CSV

表 7 不同强度参数下气泡1和气泡2的脉动周期和最小半径对比

Table 7. Comparison of pulsation periods and maximum radii of bubbles 1 and 2 under different strength parameters

strength parameter	bubble 1		bubble 2
strength parameter	pulsation period	minimum bubble radius	pulsation period	minimum bubble radius
ε=50	2.242	0.262	2.205	0.307
ε=100	2.201	0.223	2.163	0.270
ε=150	2.177	0.204	2.138	0.251
ε=200	2.169	0.193	2.131	0.240

下载: 导出CSV

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