我国大部分深部煤层瓦斯赋存具有高瓦斯、高应力、低渗透特征，尤其是低渗透特性，采用常规钻孔预抽煤层瓦斯效果不理想。为提高煤层瓦斯预抽率、缩短预抽时间，需对煤层采取强化增透措施，其中超声波致裂煤层增透作为具有多种效应（空化效应、机械振动效应、热效应）等协同作用的技术，逐渐受到重视。超声空化效应中空化泡溃灭时会产生巨大压力及冲击力，增强对煤体致裂效果，但冲击力致裂范围及其力值大小都缺乏具体量化分析，空化泡溃灭冲击力变化规律及多因素对空化泡动力学影响规律有待研究。针对这一问题，本文采用理论、实验和模拟相结合的方式，分析不同压裂液环境下不同频率超声波、功率激励煤体时超声波空化泡运动规律及溃灭冲击力演化规律，获得空化泡溃灭时液体流场压强变化规律，完善多因素影响下超声空化效应致裂煤体相关理论，为超声波致裂煤体压裂液及超声波参数选择提供依据。研究主要结论如下：

利用自制的超声空化泡溃灭冲击力测试实验台开展超声空化泡溃灭压力测定实验，获得不同影响因素对空化泡溃灭冲击力的作用规律。研究表明，传感器与工具头之间距离和空化泡溃灭冲击力成反比，超声工具头正下方的传感器测得冲击力比侧面传感器测得冲击力平均大13.205N；随着压裂液表面张力的增加，超声空化泡溃灭冲击力逐渐减小；粘度与超声空化泡溃灭冲击力呈负相关关系；超声波功率的增加能够提高超声空化泡溃灭冲击力，20 kHz、28 kHz、40 kHz下，随着超声功率的增加，冲击力增加梯度分别为80.23%、129.91%、102.84%；超声波频率与超声空化泡溃灭冲击力呈负相关关系。

超声激励改善煤体的结构并增加煤体渗透率，本研究通过核磁共振实验研究超声波激励前后煤体孔隙结构演化规律，采用蔡司 Stemi508 显微镜分析超声波激励后的煤体表面形貌变化规律。研究表明，超声激励能够有效增加煤体微小孔隙，激励后氢原子信号强度的总峰面积增加比例为26.31% ~ 48.72%，第一峰的面积增加比例为24.70% ~ 40.86%。煤体孔隙随着表面张力和粘度的增加而降低，随超声波功率的增加而增加。超声波能够影响煤体表面形态，随着压裂液的粘度和表面张力的增加，分形维数都有所增加。

采用公式推导的方法，通过冲击力和压强的计算公式获得了空化泡溃灭冲击力和压强的大小，并分析二者之间的转换关系。计算获得不同压裂液质量分数、超声频率和功率下压强，压强变化趋势和冲击力的变化趋势一致，随着交联瓜尔胶质量分数由0.01%变为0.1%，压强增加了18600 Pa；随着超声波频率的增加，压强的增幅也随之增加，在滑溜水中，20 kHz、28 kHz和40 kHz的压强增幅分别达到了45.42%、45.04%、52.26%。

基于能量守恒和单空化泡的受力分析，对空化泡的运动方程进行了推导，采用数值模拟的方法对方程计算。研究表明，声压幅值的增加会引起空化泡膨胀半径增加，增幅在73%~151%，；半径变化幅度随频率的增加而减小，半径减小幅度由30.72%增至57.33%；随着初始半径增大，最大膨胀比逐渐减小，从5 μm增加至20 μm时减小了9.67；当粘度逐渐增加，半径变化幅度随之减小，最大半径的降幅由12.19%增加至24.70%，最大膨胀比逐渐减小，0.001Pa·s最大半径比与0.003Pa·s的差值为3.22；当表面张力逐渐增加，最大半径比逐渐减少，最大半径比的降幅为1.19。

基于三大守恒理论建立了单空化泡动力学模型，探究了空化泡周围流场压强变化规律。研究表明，空化泡压缩至最小半径时泡内压强呈现最大值（8064145 Pa）；流场内流体的压强以空化泡中心为球心向外递减，监测点a0处最大压强是a6处 的1.41倍；空化泡半径极大值和极小值随时间变化呈现指数函数关系；随着液体表面张力、液体粘度、超声波频率、初始半径增加，超声空化泡产生的压强最大值减小；随着声压幅值增加，超声激励下空化泡产生的压强最大值增大。

本文通过实验室实验、理论推导和数值模拟等多种方法，获得了空化泡溃灭产生的冲击力，分析了压裂液参数、超声参数和空化泡自身参数对其运动及压裂液中压强场和空化泡溃灭时产生的冲击力影响规律；推导了单空化泡的运动学特性和空化泡外压强变化规律，完善了单空化泡受到声压幅值、频率、粘度、表面张力和初始半径等因素影响下空化泡的半径变化和压强变化。研究结果对完善超声空化效应理论，超声致裂煤体促进瓦斯开采技术的推广应用提供了科学参考。

Most of the deep coal seams in China have the characteristics of high gas, high stress and low permeability, especially low permeability, so the effect of pre-pumping coal seam gas by conventional drilling is not ideal. In order to improve the pre-pumping rate and shorten the pre-pumping time, it is necessary to take enhanced anti-reflection measures for coal seams. As a synergistic technology with various effects (cavitation effect, mechanical vibration effect, thermal effect), ultrasonic cracking anti-reflection has been paid more and more attention. In ultrasonic cavitation effect, huge pressure and impact force will be generated when the cavitation bubble collapses, which will enhance the cracking effect on the coal body. However, the cracking range and force value of the impact force lack specific quantitative analysis, and the change law of the collapse impact force of the cavitation bubble and the influence law of multiple factors on the dynamics of the cavitation bubble need to be studied. To solve this problem, this paper adopts the method of combining theory, experiment and simulation to analyze the movement law of ultrasonic cavitation bubble and the evolution law of collapse impact force when the coal body is stimulated by ultrasonic wave of different frequencies and power under different fracturing fluid environments, obtain the pressure change law of liquid flow field when the cavitation bubble collapses, and improve the relevant theory of cracking coal body caused by ultrasonic cavitation effect under the influence of multiple factors. It provides the basis for the selection of ultrasonic fracturing fluid and ultrasonic parameters. The main conclusions of this study are as follows:

The bursting pressure test of ultrasonic cavitation bubble was carried out by using a self-made ultrasonic cavitation bubble bursting force test bench, and the law of different influencing factors on the bursting force of cavitation bubble was obtained. The results show that the distance between the sensor and the tool head is inversely proportional to the cavitation bubble collapse impact force. The impact force measured by the sensor directly below the ultrasonic tool head is 13.205N larger than that measured by the side sensor. As the surface tension of fracturing fluid increases, the bursting force of ultrasonic cavitation bubble decreases gradually. There is a negative correlation between viscosity and bursting force of ultrasonic cavitation bubble. The bursting impact force of ultrasonic cavitation bubble can be improved with the increase of ultrasonic power. There is a negative correlation between ultrasonic frequency and bursting force of ultrasonic cavitation bubble.

Ultrasonic stimulation improves the structure of coal and increases the permeability of coal. In this study, the pore structure evolution law of coal before and after ultrasonic stimulation is studied by nuclear magnetic resonance experiment, and the surface morphology change law of coal after ultrasonic stimulation is analyzed by Zeiss Stemi508 microscope. The results show that ultrasonic excitation can effectively increase the tiny pores of coal, and the total peak area of hydrogen signal intensity increases by 26.31% ~ 48.72%, and the area of the first peak increases by 24.70% ~ 40.86%. The porosity of coal decreases with the increase of surface tension and viscosity, and increases with the increase of ultrasonic power. Ultrasonic wave can affect the surface morphology of coal, and the fractal dimension increases with the increase of the viscosity and surface tension of fracturing fluid.

Using a formula derivation method, the size of the cavitation bubble collapse impact force and pressure were obtained through the calculation formulas of impact force and pressure, and the conversion relationship between them was analyzed. The pressure changes trend and the change trend of impact force were consistent when the calculation was carried out at different concentrations of fracturing fluid, ultrasonic frequency and power. With the increase of crosslinked guar gum concentration from 0.01% to 0.1%, the pressure increased by 18,600 Pa; with the increase of ultrasonic frequency, the pressure increase also increased. In the slippery water, the pressure increase was 45.42%, 45.04%, and 52.26% at 20 kHz, 28 kHz, and 40 kHz, respectively.

Based on the principle of energy conservation and the analysis of the force acting on a single cavitation bubble, the motion equation of the cavitation bubble was derived, and the equation was calculated using numerical simulation methods. The research shows that the increase of acoustic pressure amplitude will cause the cavitation bubble to expand, with an increase of 73% to 151% in the radius; the change amplitude of the radius will decrease as the frequency increases, and the decrease in radius from 30.72% to 57.33%; as the initial radius increases, the maximum expansion ratio gradually decreases, from 5 μm to 20 μm, the decrease is 9.67; as the viscosity increases, the change amplitude of the radius decreases, the decrease in the maximum radius is 12.19% to 24.7%, and the maximum expansion ratio gradually decreases, the difference between the maximum radius ratio with 0.001 Pa·s and 0.003 Pa·s is 3.22; as the surface tension increases, the maximum radius ratio gradually decreases, and the decrease in the maximum radius ratio is 1.19.

Based on the three conservation theories, the dynamics model of the single cavitation bubble is established, and the pressure variation law of the flow field around the cavitation bubble is investigated. The results show that when the cavitation bubble is compressed to the minimum radius, the pressure inside the bubble presents the maximum value (8064145 Pa). The pressure of the fluid in the flow field decreases outward with the center of the cavitation bubble as the center of the sphere. The maximum pressure at the monitoring point a0 is 1.41 times that at a6. The maximum and minimum values of cavitation bubble radius show an exponential function relationship with time. With the increase of liquid surface tension, liquid viscosity, ultrasonic frequency and initial radius, the maximum pressure generated by ultrasonic cavitation bubble decreases. With the increase of sound pressure amplitude, the maximum pressure generated by cavitation bubble under ultrasonic excitation increases.

In this paper, the impact force caused by cavitation bubble collapse was obtained through laboratory experiments, theoretical derivation and numerical simulation, and the influence law of fracturing fluid parameters, ultrasonic parameters and cavitation bubble parameters on its movement, pressure field in fracturing fluid and the impact force caused by cavitation bubble collapse was analyzed. The kinematic characteristics of the single cavitation bubble and the variation law of the external pressure of the cavitation bubble are deduced, and the change of the radius and pressure of the single cavitation bubble under the influence of the factors such as the amplitude of sound pressure, frequency, viscosity, surface tension and initial radius are perfected. The research results provide a scientific reference for improving the theory of ultrasonic cavitation effect and promoting the popularization and application of ultrasonic cracking coal mining technology.

[1] 《中国能源统计年鉴2021》编辑出版人员. 胡汉舟总编, 中国能源统计年鉴, 中国统计出版社, 2021, 4-5, 年鉴.

[2] Shengming, W., Ke, Z., & Qian, L. (2019, January 1). A discussion on CBM development strategies in China based upon a case study of PetroChina Coalbed Methane Co., Ltd. Tianranqi Gongye, 39(5), 129–136.

[3] 赵馨悦, 韦波, 袁亮, 等. 煤储层水文地质特征及其瓦斯开发意义研究述评[J/OL]. 煤炭科学技术: 1-18[2022-11-29].

[4] 国土资源部油气资源战略研究中心. 全国瓦斯资源评价[Ｍ]. 北京:中国大地出版社, 2009: 256.

[5] 张千贵, 李权山, 范翔宇, 等. 中国煤与瓦斯共采理论技术现状及发展趋势[J]. 天然气工业, 2022, 42(06): 130-145.

[6] 秦勇, 申建, 李小刚. 中国瓦斯资源控制程度及可靠性分析[J]. 天然气工业, 2022, 42(06): 19-32.

[7] 朱昌海. 我国瓦斯产业已进入商业开发拐点[J]. 中国石油企业, 2022(08): 62.

[8] 朱苏阳, 孟尚志, 彭小龙, 等. 煤岩润湿性对瓦斯赋存的影响机理[J]. 油气藏评价与开发, 2022, 12(04): 580-588+595.

[9] 肖晓春, 潘一山. 低渗煤储层气体滑脱效应实验研究[J]. 岩石力学与工程学报, 2008(S2): 3509-3515.

[10] Zhang L, Ye Z W, Tang J, et al. Comparative Experiment Study on Nitrogen Injection and Free Desorption of Methane-Rich Bituminous Coal Under Triaxial Loading[J]. Nephron Clinical Practice, 2017, 62(4): 911-928.

[11] 褚怀保, 王昌, 杨小林, 等. 煤体高压空气爆破模拟实验研究[J]. 振动与冲击, 2022, 41 (20): 54-60+157.

[12] 李波, 张路路, 孙东辉, 等. 水力冲孔措施研究进展及存在问题分析[J]. 河南理工大学学报(自然科学版), 2016, 35(1):16-22.

[13] Xu J Z, Zhai C, Liu S, et al. Investigation of temperature effects from LCO2 with different cycle parameters on the coal pore variation based on infrared thermal imagery and low-field nuclear magnetic resonance[J]. Fuel, 2018, 215(1):528-540.

[14] 宋维源, 王忠峰, 唐巨鹏. 水力割缝增透抽采煤层瓦斯原理及应用[J]. 中国安全科学学报, 2011, 21(4):78-82.

[15] 卢红奇, 邓增社, 聂百胜, 等. 高压电脉冲致裂实验及其在瓦斯开采中的应用分析[J]. 煤矿安全, 2017, 48(10): 13-16.

[16] 姜永东, 宋晓, 崔悦震, 等. 声场作用下煤中甲烷解吸扩散的特性[J]. 煤炭学报, 2015, 40(3):623-628.

[17] 史小卫, 林萌, 王思鹏. 低渗煤层井下水力压裂增透技术应用研究[J]. 中国煤炭, 2011, 37(04): 7-9+31.

[18] 白云峰. 水力压裂增透瓦斯抽采存在问题及对策[J]. 中国石油和化工标准与质量, 2022, 42(14): 114-115.

[19] Ye L Z, Zhu X J, Liu Y. Numerical study on dual-frequency ultrasonic enhancing cavitation effect based on bubble dynamic evolution[J]. Ultrasonics Sonochemistry, 2019, 59:104744.

[20] 于国卿. 超声波对煤体孔隙结构影响规律研究[D]. 中国矿业大学, 2018.

[21] 姜永东, 李业, 崔悦震, 等. 声场作用下煤储层渗透性实验研究[J]. 煤炭学报, 2017, 42(S1): 154-159.

[22] 张文亮, 辛公锋, 宋雷, 等. 混凝土非均匀性对超声波衰减作用的模拟分析[J]. 科学技术与工程, 2022, 22(21): 9044-9053.

[23] 蔡峰, 袁媛, 刘泽功, 等. 超声波在煤矿井下环境中的传播与衰减特性[J]. 中国矿业大学学报, 2021, 50 (04): 685-690.

[24] 雷晨阳, 薛凯茹, 王丹彤, 等. 琼脂凝胶中气泡含量及间距对超声波衰减特性的影响[J]. 传感器与微系统, 2024, 43 (02): 57-60.

[25] 顾兴宇, 李树伟, 董侨, 等. 沥青混凝土超声波检测的衰减特征与影响因素研究[J]. 中国公路学报, 2020, 33 (10): 316-326.

[26] 曹彦涛, 彭晓星, 徐良浩, 等. 水翼空化瞬态特征与空化冲击关系实验研究[J]. 船舶力学, 2024, 28(03): 392-399.

[27] 顾嘉阳. 激光诱导空泡空化强化机理及化学效应研究[D]. 江苏大学, 2023.

[28] 韩磊, 张敏弟, 黄国豪等. 自由场空泡溃灭过程能量转化机制研究[J]. 力学学 报, 2021, 53(5): 1288-1301.

[29] 孙毅, 鲁沛奇, 毛亚郎, 等. 近壁面空化冲击颗粒破碎效果的影响因素研究[J]. 高技术通讯, 2023, 33(04): 402-410.

[30] 曾卿丰. 近凹陷空化泡动力学特性研究[D]. 哈尔滨工业大学, 2022.

[31] Jing Luo, Weilin Xu, Boo Cheong Khoo. Stratification effect of air bubble on the shock wave from the collapse of cavitation bubble[J]. Journal of Fluid Mechanics, 2021, 919, A16.

[32] Fujikawa S., Akamatsu T.. Experimental investigations of cavitation bubble collapse by a water shock tube[J]. Jsme International Journal Series B-fluids and Thermal Engineering, 1978, 21: 223-230.

[33] 马平川. 基于激光空化瞬态力学效应的微造型实验及仿真研究[D]. 江苏大学, 2022.

[34] Petkovšek M, Hočevar M, Dular M. Visualization and measurements of shock waves in cavitating flow[J]. Experimental Thermal and Fluid Science, 2020, 119: 110215.

[35] Zhong Xiaoxu, Eshraghi J, Vlachos P, et al. A model for a laser-induced cavitation bubble[J]. International Journal of Multiphase Flow, 2020, 132: 103433.

[36] Trummler T, Schmidt S, Adams N. Numerical investigation of non-condensable gas effect on vapor bubble collapse[J]. Physics of Fluids, 2021, 33(9): 096107.

[37] Dnestrovskij A, Voropaev S, Dushenko N, et al. Conditions of the Formation of a Shock Wave under Cavitation in Hydrocarbon Solutions[J]. Doklady Physics, 2020, 65(1): 8-11.

[38] Brujan E A, Ikeda T, Matsumoto Y. On the pressure of cavitation bubbles[J]. Experimental Thermal and Fluid Science, 2008, 32(5):1188-1191．

[39] 胡影影. VOF方法的改进及空泡溃灭和空化流的数值研究[D]. 北京: 清华大学, 2001.

[40] 闻仲卿. 泡群溃灭的直接数值模拟及统计特性分析[D]. 杭州: 浙江大学, 2013.

[41] 张洪峰. 超薄壁材料的激光空化冲击微成形机理及特性研究[D]. 镇江: 江苏大学, 2020.

[42] 赵付建. 自激振荡射流空化诱发空泡运移与溃灭特性分析[D]. 江苏大学, 2022.

[43] 刘亚喆. 介观尺度矩形织构对空化和微空泡溃灭影响的研究[D]. 大连海事大学, 2020.

[44] 葛亮. 水下冲击波与复杂物质界面作用动力学特性研究[D]. 哈尔滨工程大学, 2021.

[45] Holzfuss J, Rüggeberg M, Billo A. Shock wave emissions of a sonoluminescing bubble[J]. Physical Review Letters, 1998, 81(23): 5434-5437.

[46] Minsier V, Proost J. Shock wave emission upon spherical bubble collapse during cavitation-induced megasonic surface cleaning[J]. Ultrasonics Sonochemistry, 2008, 15(4): 598-604.

[47] 刘海军, 安宇. 空化单气泡外围压强分布[J]. 物理学报, 2004, 53(5): 1406-1412.

[48] 田红. 超声波在城市剩余活性污泥中的传输特性的模拟及实验研究[D]. 重庆: 重庆大学, 2010.

[49] Brennen C. Cavitation and bubble dynamics[M]. Oxford: Oxford University Press, 1995.

[50] 罗先武, 季斌, 彭晓星, 等. 空化基础理论及应用[M]. 北京: 清华大学出版社, 2020.

[51] Delale C. Bubble Dynamics&Shock Waves[M]. Berlin Heidelberg: Springer-Verlag, 2013.

[52] Yin S, Zhao D, Zhai G. Investigation into the characteristics of rock damage caused by ultrasonic vibration[J]. International Journal of Rock Mechanics & Mining Sciences, 2016, 84: 159-164.

[53] 何灵芝, 简显瑀, 王达川, 等. 双频超声波处理对蛋白酶活性的影响[J]. 食品工业, 2024, 45(03): 34-38.

[54] 张莹莹, 何珍珍, 兰儒剑, 等. 超声波处理种子对香稻秧苗素质、抗逆性、产量及香气的影响[J]. 中国稻米, 2023, 29(05): 62-65+70.

[55] Grybas I, Bansevicius R, Jurenas V, et al. Ultrasonic standing waves-driven high resolution rotary table[J]. Precision Engineering, 2016, 45.

[56] Mohammadian E, Junin R, Rahmani O, Idris AK. Effects of sonication radiation on oil recovery by ultrasonic waves stimulated water-flooding. Ultrasonics. 2013; 53(2): 607-614.

[57] Mullakaev M.S., Abramov V.O., Abramova A.V.. Development of ultrasonic equipment and technology for well stimulation and enhanced oil recovery[J]. Journal of Petroleum Science and Engineering, 2015, 125.

[58] Hamidi H, Mohammadian E, Junin R, et al. A technique for evaluating the oil/heavy-oil viscosity changes under ultrasound in a simulated porous medium. Ultrasonics. 2014; 54(2): 655-662.

[59] Hamidi H, Mohammadian E, Rafati R, et al. The effect of ultrasonic waves on the phase behavior of a surfactant–brine–oil system. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2015;482:27-33.

[60] Couvreur Jf, Vervoort A, King Ms, et al. Successive cracking steps of a limestone highlighted by ultrasonic wave propagation. Geophysical prospecting. 2001;49(1): 71-78. Accessed December 1, 2022.

[61] Shchukin Dmitry G, Skorb Ekaterina, Belova Valentina, et al. Ultrasonic cavitation at solid surfaces[J]. Advanced materials(Deerfield Beach, Fla.), 2011, 23(17).

[62] 肖晓春, 潘一山, 吕祥峰, 等. 超声激励低渗煤层甲烷增透机理[J]. 地球物理学报, 2013, 56(5): 1726-1733.

[63] 肖晓春, 丁鑫, 潘一山, 等.围压作用下煤岩材料超声致裂规律研究[J]. 材料导报, 2015, 29(16): 132-136+150.

[64] Zhao H, Wang X M, Chen S M, et al. Acoustic response characteristics of unsaturated porous media[J]. Science China Physics, Mechanics and Astronomy, 2010, 53(8).

[65] Shi Q M, Qin Y, Li J Q, et al. Simulation of the crack development in coal without confining stress under ultrasonic wave treatment[J]. Fuel, 2017, 205: 22-231.

[66] 孙仁远, 纪云开, 林李, 等.超声处理对瓦斯解吸效果的影响[J]. 实验力学, 2015, 30(01): 94-100.

[67] 李树刚, 王瑞哲, 林海飞, 等. 超声波功率对煤体力学损伤特性及能量演化的实验研究[J/OL]. 煤炭科学技术: 1-12[2023-03-01].

[68] 宋超,姜永东, 王苏健等. 超声波作用下煤体微观结构的实验研究[J]. 煤炭科学技术, 2019, 47(5):139-144.

[69] 魏威. 超声/水力空化场强化甲苯-水烷基化反应生成乙苯的研究[D]. 新疆师范大学, 2021.

[70] 白立新, 李超, 徐德龙, 等. 超声空化结构的产生和控制[C]//. 2013年全国功率超声学术会议论文集. [出版者不详], 2013: 2-12.

[71] 白立新, 吴鹏飞, 李超, 等. 液体薄层中的超声空化[J]. 应用声学, 2018, 37(05): 614-635.

[72] Vogel A., Lauterborn W., Timm R.. Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary[J]. Journal of Fluid Mechanics, 1989, 206.

[73] Gu J Y, Luo C H, Lu Z B, et al. Bubble dynamic evolution, material strengthening and chemical effect induced by laser cavitation peening.[J]. Ultrasonics sonochemistry, 2020, 72.

[74] Rayleigh L. On the pressure developed in a liquid during the collapse of a spherical cavity[J]. Philosophical Magazine. 1917, 34: 94-98.

[75] Plesset M S. The dynamics of cavitation bubbles[J]. Journal of Applied Mechanics. 1949, 16: 277-282.

[76] Noltingk B E, Neppiras E A. Cavitation produced by ultrasonics[J]. Proceedings of the Physical Society. 1950, B63: 674-685.

[77] Blake F G. The onset of cavitation in liquids; Technical memo 12[D]. Cambridge: Harvard University, 1949.

[78] Lin H, Storey B D, Szeri A J. Inertially driven inhomogeneities in violently collapsing bubbles: the validity of the Rayleigh-Plesset equation[J]. Journal of Fluid Mechanics. 2002, 452(10): 145-162.

[79] 陈伟中. 声空化物理[M]. 北京: 科学出版社, 2019.8: 161-200, 204-267, 371-421.

[80] 王成会, 林书玉. 超声波作用下气泡的非线性振动[J]. 力学学报, 2010, 42(6): 1050-1059.

[81] 沈壮志, 林书玉. 声场中气泡运动的混沌特性[J]. 物理学报, 2011, 60(10): 418-425.

[82] 王捷, 徐军华, 靳伟. 基于MATLAB的超声空化气泡动态仿真[J]. 西安邮电大学学报, 2012(s1): 6-9.

[83] 张鹏利, 林书玉, 张涛. 超声场中双气泡非线性动力学参数[J]. 中国科学:物理学力学天文学, 2013, 43(03): 249-256.

[84] 王成会, 莫润阳, 胡静, 等. 球状泡群内气泡的耦合振动[J]. 物理学报, 2015, 64(23): 164-171.

[85] 郝广宇, 韩吉田, 李良洁, 等. 超声空化对溴化锂溶液气泡运动的影响[J]. 制冷与空调, 2021, 21(10): 30-34.

[86] Zhang X M, Zhou C Y, Islam S, et al. Three-dimensional cavitation simulation using lattice Boltzmann method[J]. Acta Physica Sinica, 2009, 58(12):8406-8414.

[87] 苗博雅, 安宇. 两种气泡混合的声空化[J]. 物理学报, 2015, 64(20): 225-233.

[88] 李洋, 文守成, 刘文硕. 阴离子型聚丙烯酰胺减阻性能评价及影响因素研究[J]. 化学工程师, 2016, 30(11): 86-88.

[89] Zhang L, Kong T. Aqueous polysaccharide blends based on hydroxypropyl guar gumand carboxymethyl cellulose: synergistic viscosity and thixotropic properties[J]. Colloidand Polymer Science, 2006, 285(2): 145-151.

[90] Sokhanvarian K, Nasr-El-Din H A, Harper T L. Rheological Characteristics ofCMHPG Crosslinked with New Zirconium and Dual Crosslinkers[C]//SPE Asia Pacific Unconventional Resources Conference and Exhibition, Brisbane, 2015.

[91] Rae P, Di Lullo G. Fracturing Fluids and Breaker Systems-A Review of theState-of-the-Art[C]//SPE Eastern Regional Meeting, Columbus, 1996.

[92] 杨帆, 王琳, 杨小华, 等. 压裂液防膨剂的研制与应用[J]. 石油钻采工艺2017, 39(03): 344-348.

[93] 祝成. 清洁压裂液的配制及性能研究[D]. 西南石油大学,2010.

[94] 蒋官澄, 许伟星, 李颖颖, 等. 国外减阻水压裂液技术及其研究进展[J]. 特种油气藏, 2013, 20(01): 1-6.

[95] Barati R, Liang J. A review of fracturing fluid systems used for hydraulic fracturing ofoil and gas wells[J]. Journal of Applied Polymer Science, 2014, 131(16).

[96] 曹毅. 水基清洁压裂液性能评价和配方优化组合[D]. 西安石油大学应用化学, 2009.

[97] Lei C, Clark P E. Crosslinking of guar and guar derivatives[C]//Society of Petroleum Engineers, Houston, TX, United states.

[98] Zheng S, Yao Y, Liu D, et al. Characterizations of full-scale pore size distribution, porosity and permeability of coals: A novel methodology by nuclear magnetic resonance and fractal analysis theory[J]. International Journal of Coal Geology, 2018, 196:148-158.

[99] 徐梓榕. 声空化泡溃灭力学的量化研究[D]. 哈尔滨工业大学, 2021.

[100] 王文超. 超声激励下空化冲击波效应及其流场特性分析[D].中北大学, 2023.

[101] 王福军. 计算流体动力学分析－CFD软件原理与应用[M]. 北京: 清华大学出版社, 2004: 2-15.

[102] 袭鹏, 熊鹰, 蒲汲君. 基于Fluent的E799A空泡性能数值计算网格对比[J]. 舰船科学技术, 2019, 41(7): 30-33.

[103] 刘为. 非常态流体中超声空化泡动力学研究[D]. 广州: 华南理工大学, 2020.

[104] 刘亚楠, 陈伟中, 黄威, 等. 稳态声空化泡的高精度测量技术[J]. 科学通报, 2005, 50(22): 2458-2462.