水下冲击波聚焦的数值模拟与实验研究
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摘要
水下冲击波聚焦是一种声能定向技术,已广泛应用于体外冲击波碎石、冲击波治疗等医学领域。本文以液电式声源为基础,结合旋转椭球面反射罩建立了水下冲击波聚焦系统,并以此为研究对象,围绕反射式水下冲击波聚焦系统的聚焦特性、压力场的分布特征以及聚焦后的空化效应等开展了数值模拟和实验研究。
在水的Mie-Griieisen状态方程的基础上,建立了适合描述水处于拉伸态的亚稳态及空化状态的拉伸-空化模型,并将其引入到动力有限元程序LS-DYNA。该模型克服了水的Mie-Griieisen状态方程本身存在的不足,既能描述水在亚稳态下的拉伸状态,又能描述水的空化状态。
基于液电式声源及椭球面反射罩建立了水下冲击波聚焦系统,并开展了相关的实验研究,验证了所建立水的拉伸-空化模型的正确性。在此基础上研究了不同物理参数对冲击波聚焦及其空化效应的影响。在水下冲击波聚焦系统上搭建了高速纹影系统,对水下冲击波聚焦及其空化现象进行了实验研究。本文的主要研究内容和结论如下：
(1)水下冲击波聚焦在焦区附近形成较高强度冲击波的同时还会在焦区附近形成拉伸波,产生负压,此时的水为亚稳态。而由于水存在抗拉极限,因此当初始冲击波强度较强时在焦区附近会出现空化现象；空化气泡半径先增大后减小轴线上最大空化气泡出现在几何焦点之后,焦平面上气泡最大的位置出现在轴线上。
(2)水下冲击波聚焦过程中,由于反射罩的动力学行为使水中的波系较为复杂,这些波系在轴线上会聚将使水产生空化现象。反射罩长度的增加、初始冲击波强度的增加都会增大几何焦点处的正峰值压力,另外采用密度较大的金属(例如铜)作为反射罩也会实现几何焦点处正峰值压力的增加；空化阈值的增大及空化核数量密度的减小都会增大焦点附近的最大负峰值压力。
(3)初始冲击波强度的增大、空化阈值的提高、水的黏性系数的降低、水表面张力的减小及水中空化核尺寸的增大都会使得空化气泡的最大半径增大。另外,初始冲击波强度的减小、反射罩长度的增加、空化阈值的提高及水中空化核尺寸的减小都能使空化发生的位置在反射罩轴线上后移。
(4)材料的非线性会使聚焦波到达时间前移,并且会减小最大负峰值压力。材料的非线性还会使实际焦点发生移动,使最大正峰值压力相对于椭球的第二几何焦点向后移动,最大负峰值压力前移。
(5)高速纹影技术适用于研究水下冲击波聚焦的过程及其产生的空化效应。通过纹影照片光强分布的变化可以得到相应的冲击波强度的变化,进而得到水下冲击波聚焦过程中波阵面的演化过程。通过对高速纹影图片的分析发现,本文所建立的反射式旋转椭球聚焦系统能够实现水下冲击波聚焦,在焦区附近形成较高能量密度的超压脉冲,但由于反射罩的动力学响应及流体黏性等因素的影响,使冲击波聚焦没有形成理想的“焦点”,而是一带状区域。
(6)冲击波聚焦过程中,负压是导致空化发生的主要原因,相对于空化气泡云存在的时间,负压的存在时间很短,此时水为拉伸态的亚稳态。空化气泡半径先增大后减小,并且气泡的最大半径越大其存在时间越长,两者基本满足线性。气泡膨胀阶段持续的时间大于塌缩阶段持续的时间。产生的空化气泡内部温度大于20摄氏度。
Underwater shock wave focusing technique is one of the acoustic energydirectional technologies, which has been widely used in the medical field, such asESWL (Extracorporeal Shock Wave Lithotripsy) application and ESWT(Extracorporeal Shock Wave Therapy) application. In this paper, an underwater shockwave focusing system was set up based on an ellipsoidal reflector combined with ahydroelectric sound source located at the first focus of the ellipsoid. In order tounderstand the focusing process of shock wave, numerical simulations andexperimental tests of the peak pressure along the axial position were carried out; thedistributing characteristics and cavitation phenomena of the focusing shock wavewere revealed.
A tension-cavitation model based on the Mie-Grüeisen EOS (equation of state)of water was developed, which is suitable for describing the metastable state of waterthat is under tension and cavitation. It was introduced into LS-DYNA successfully.The model overcomes the shortcoming of the Mie-Grüeisen EOS in describing thewater under tension and cavitation.
An underwater shock wave focusing system was set up based on an ellipsoidalreflector combined with a hydroelectric sound source, and then experimental studywas carried out. The consistent simulating results with those of experiments indicatedthat the tension-cavitation model was correct in simulating the shock wave focusingprocess and its induced cavitation phenomena. Based on the tension-cavitation model,numerical simulations of shock wave focusing and its induced cavitation phenomenawere analyzed. An optical arrangement was set up to take high speed photograph inthe experiment. The focusing process of shock wave and cavitation phenomena werecaptured by the camera. The main work can be summarized as follows:
(1) Intensity shock wave with very high peak pressure can be brought about byshock wave focusing at the second focus of the ellipsoidal reflector, tension wave andnegative pressure can be generated at the sametime; the state of water under tension ismetastable. There is a tensile failure pressure (or cavitation threshold) in water, whenthe negative pressure is lower than the cavitation threshold of water, cavitationphenomena will appear. The radius of bubble increases first and then decreases; in theaxial direction, the biggest cavitation bubble come out around the geometric focus,but at a location further away from the reflector surface; in the focal plane, the biggestcavitation bubble come out at the axes.
(2) The shock waves during the focusing process are complex due to thedynamic behavior of the reflector; the expansion waves originated at the exit of thereflector concentrating at the axes will generate negative pressure and cavitationphenomena. The peak positive pressure at the second focus will be higher with the increasing of length of the reflector, the increasing of the intensity of shock wave andadopting the reflector of bigger density such as copper. The maximum peak negativepressure will be higher with the increasing of the cavitation threshold and thedecreasing of the concentration of cavitation nuclei.
(3) The maximum radius of bubble will get bigger with the increasing of theintensity of shock wave, the increasing of the cavitation threshold, the decreasing ofthe surface tension of water, the decreasing of the kinematic viscosity of water and theincreasing of the dimension of cavitation nuclei. The location of the cavitationphenomena coming out will be further away from the reflector with the decreasing ofthe intensity of shock wave, the increasing of length of the reflector, the increasing ofthe cavitation threshold and the decreasing of the dimension of cavitation nuclei.
(4) The nonlinearity of the material will make the arrival time of the focusingwave earlier and decrease the maximum peak negative pressure, it will also make thefactual focus of shock wave deviate from the geometric focus, make the factual focusof maximum peak positive pressure move further away from the reflector and thefactual focus of maximum peak negative pressure move closer to the reflector,comparing with the linearity of the material.
(5) The high-speed photography schlieren method can be used to investigateunderwater shock wave focusing and its induced cavitation phenomena. The intensityof shock wave can be obtained by the intensity of light in the schlieren photographs,and then the process of shock wave focusing will be gotten. The experimental resultshave shown that the focusing system set up in this paper can realize shock wavefocusing well and get higher pressure in the focal region; the shock wave focusingcan’t form a perfect dot but a zonal region due to the dynamic behavior of reflectorand the viscosity of water.
(6) The negative pressure is the main cause of cavitation phenomena inunderwater shock wave focusing process. The lasting time of negative pressure isshorter than that of the cavitation phenomena; the state of water under tension ismetastable.The radius of cavitation bubble first increases and then decreases; there isa linear relationship between the maximum bubble radius and the collapse time; thetime of bubble expanding is longer than the time of bubble decay because the pressureof the surrounding liquid in the expanding period is lower than that in decay periodand the temperature inside the cavitation bubbles is higher than293K.
在水的Mie-Griieisen状态方程的基础上,建立了适合描述水处于拉伸态的亚稳态及空化状态的拉伸-空化模型,并将其引入到动力有限元程序LS-DYNA。该模型克服了水的Mie-Griieisen状态方程本身存在的不足,既能描述水在亚稳态下的拉伸状态,又能描述水的空化状态。
基于液电式声源及椭球面反射罩建立了水下冲击波聚焦系统,并开展了相关的实验研究,验证了所建立水的拉伸-空化模型的正确性。在此基础上研究了不同物理参数对冲击波聚焦及其空化效应的影响。在水下冲击波聚焦系统上搭建了高速纹影系统,对水下冲击波聚焦及其空化现象进行了实验研究。本文的主要研究内容和结论如下：
(1)水下冲击波聚焦在焦区附近形成较高强度冲击波的同时还会在焦区附近形成拉伸波,产生负压,此时的水为亚稳态。而由于水存在抗拉极限,因此当初始冲击波强度较强时在焦区附近会出现空化现象；空化气泡半径先增大后减小轴线上最大空化气泡出现在几何焦点之后,焦平面上气泡最大的位置出现在轴线上。
(2)水下冲击波聚焦过程中,由于反射罩的动力学行为使水中的波系较为复杂,这些波系在轴线上会聚将使水产生空化现象。反射罩长度的增加、初始冲击波强度的增加都会增大几何焦点处的正峰值压力,另外采用密度较大的金属(例如铜)作为反射罩也会实现几何焦点处正峰值压力的增加；空化阈值的增大及空化核数量密度的减小都会增大焦点附近的最大负峰值压力。
(3)初始冲击波强度的增大、空化阈值的提高、水的黏性系数的降低、水表面张力的减小及水中空化核尺寸的增大都会使得空化气泡的最大半径增大。另外,初始冲击波强度的减小、反射罩长度的增加、空化阈值的提高及水中空化核尺寸的减小都能使空化发生的位置在反射罩轴线上后移。
(4)材料的非线性会使聚焦波到达时间前移,并且会减小最大负峰值压力。材料的非线性还会使实际焦点发生移动,使最大正峰值压力相对于椭球的第二几何焦点向后移动,最大负峰值压力前移。
(5)高速纹影技术适用于研究水下冲击波聚焦的过程及其产生的空化效应。通过纹影照片光强分布的变化可以得到相应的冲击波强度的变化,进而得到水下冲击波聚焦过程中波阵面的演化过程。通过对高速纹影图片的分析发现,本文所建立的反射式旋转椭球聚焦系统能够实现水下冲击波聚焦,在焦区附近形成较高能量密度的超压脉冲,但由于反射罩的动力学响应及流体黏性等因素的影响,使冲击波聚焦没有形成理想的“焦点”,而是一带状区域。
(6)冲击波聚焦过程中,负压是导致空化发生的主要原因,相对于空化气泡云存在的时间,负压的存在时间很短,此时水为拉伸态的亚稳态。空化气泡半径先增大后减小,并且气泡的最大半径越大其存在时间越长,两者基本满足线性。气泡膨胀阶段持续的时间大于塌缩阶段持续的时间。产生的空化气泡内部温度大于20摄氏度。
Underwater shock wave focusing technique is one of the acoustic energydirectional technologies, which has been widely used in the medical field, such asESWL (Extracorporeal Shock Wave Lithotripsy) application and ESWT(Extracorporeal Shock Wave Therapy) application. In this paper, an underwater shockwave focusing system was set up based on an ellipsoidal reflector combined with ahydroelectric sound source located at the first focus of the ellipsoid. In order tounderstand the focusing process of shock wave, numerical simulations andexperimental tests of the peak pressure along the axial position were carried out; thedistributing characteristics and cavitation phenomena of the focusing shock wavewere revealed.
A tension-cavitation model based on the Mie-Grüeisen EOS (equation of state)of water was developed, which is suitable for describing the metastable state of waterthat is under tension and cavitation. It was introduced into LS-DYNA successfully.The model overcomes the shortcoming of the Mie-Grüeisen EOS in describing thewater under tension and cavitation.
An underwater shock wave focusing system was set up based on an ellipsoidalreflector combined with a hydroelectric sound source, and then experimental studywas carried out. The consistent simulating results with those of experiments indicatedthat the tension-cavitation model was correct in simulating the shock wave focusingprocess and its induced cavitation phenomena. Based on the tension-cavitation model,numerical simulations of shock wave focusing and its induced cavitation phenomenawere analyzed. An optical arrangement was set up to take high speed photograph inthe experiment. The focusing process of shock wave and cavitation phenomena werecaptured by the camera. The main work can be summarized as follows:
(1) Intensity shock wave with very high peak pressure can be brought about byshock wave focusing at the second focus of the ellipsoidal reflector, tension wave andnegative pressure can be generated at the sametime; the state of water under tension ismetastable. There is a tensile failure pressure (or cavitation threshold) in water, whenthe negative pressure is lower than the cavitation threshold of water, cavitationphenomena will appear. The radius of bubble increases first and then decreases; in theaxial direction, the biggest cavitation bubble come out around the geometric focus,but at a location further away from the reflector surface; in the focal plane, the biggestcavitation bubble come out at the axes.
(2) The shock waves during the focusing process are complex due to thedynamic behavior of the reflector; the expansion waves originated at the exit of thereflector concentrating at the axes will generate negative pressure and cavitationphenomena. The peak positive pressure at the second focus will be higher with the increasing of length of the reflector, the increasing of the intensity of shock wave andadopting the reflector of bigger density such as copper. The maximum peak negativepressure will be higher with the increasing of the cavitation threshold and thedecreasing of the concentration of cavitation nuclei.
(3) The maximum radius of bubble will get bigger with the increasing of theintensity of shock wave, the increasing of the cavitation threshold, the decreasing ofthe surface tension of water, the decreasing of the kinematic viscosity of water and theincreasing of the dimension of cavitation nuclei. The location of the cavitationphenomena coming out will be further away from the reflector with the decreasing ofthe intensity of shock wave, the increasing of length of the reflector, the increasing ofthe cavitation threshold and the decreasing of the dimension of cavitation nuclei.
(4) The nonlinearity of the material will make the arrival time of the focusingwave earlier and decrease the maximum peak negative pressure, it will also make thefactual focus of shock wave deviate from the geometric focus, make the factual focusof maximum peak positive pressure move further away from the reflector and thefactual focus of maximum peak negative pressure move closer to the reflector,comparing with the linearity of the material.
(5) The high-speed photography schlieren method can be used to investigateunderwater shock wave focusing and its induced cavitation phenomena. The intensityof shock wave can be obtained by the intensity of light in the schlieren photographs,and then the process of shock wave focusing will be gotten. The experimental resultshave shown that the focusing system set up in this paper can realize shock wavefocusing well and get higher pressure in the focal region; the shock wave focusingcan’t form a perfect dot but a zonal region due to the dynamic behavior of reflectorand the viscosity of water.
(6) The negative pressure is the main cause of cavitation phenomena inunderwater shock wave focusing process. The lasting time of negative pressure isshorter than that of the cavitation phenomena; the state of water under tension ismetastable.The radius of cavitation bubble first increases and then decreases; there isa linear relationship between the maximum bubble radius and the collapse time; thetime of bubble expanding is longer than the time of bubble decay because the pressureof the surrounding liquid in the expanding period is lower than that in decay periodand the temperature inside the cavitation bubbles is higher than293K.
引文
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