水下接触爆炸舰船局部毁伤及防护机理
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摘要
水下爆炸可在极短的时间内释放出巨大热量，其产生的高压冲击波及气泡脉动可使舰船等水中结构物发生毁灭性破坏。由于重要的军事意义，西方海军强国投入了大量的人力物力财力研究水下爆炸理论及相关数值技术，形成了比较成熟的水下非接触爆炸数值分析方法，并将这些方法集成于ABAQUS等商业软件中。然而，水下接触爆炸具有大变形、运动物质交界面、自由面、高度非均匀性等特征，采用上述软件集成的网格算法对其进行模拟时容易因网格的高度畸变导致计算结果的错误。为克服网格方法固有的网格畸变问题，许多学者开始用具有粒子性质和拉格朗日性质的光滑粒子流体动力学（SPH）方法模拟水下爆炸，并取得了一定成果。然而，由于水下接触爆炸物理过程的复杂性，对其整个过程的模拟技术尚不成熟，仍有许多机理性问题需要解决。
为此，本文首先对舰船水下爆炸及SPH方法的研究现状进行了综述，通过综述发现：对水下接触爆炸的模拟仍主要采取网格方法，用SPH方法模拟水下接触爆炸的研究极少；我国对舰船防雷舱仅局限于理论和试验研究，难以定量分析各层的防护作用，对防雷舱的衰减效果和防护机理认识不清；自由面及海底对冲击波反射效应的研究还仅局限于定性分析，国内对工程计算中海底反射系数等参数的选取仍存在认识上的不一致；用SPH方法模拟水下爆炸还仅局限于二维情况，采用SPH方法或对称SPH方法模拟三维水下爆炸的研究十分罕见；SPH方法对水下爆炸的模拟主要集中在冲击波阶段，一直缺乏水下爆炸冲击波、气泡脉动、射流全过程模拟的相关研究。本文针对上述问题，以工程应用需求为牵引，通过改进SPH的计算方法，重点研究舰船接触爆炸毁伤机理、舰船防雷舱防护机理、边界对冲击波的反射效应以及三维水下爆炸全过程的数值模拟。
针对标准SPH方法无法模拟大密度比多相流的现状，提出了基于体积近似的修正SPH方法，建立了修正SPH方法数值模型。针对传统变光滑长度需多次迭代才可保证精度的缺点，提出了计算效率较高的完全变光滑长度算法。通过锥形装药爆炸驱动金属射流的算例表明：修正SPH方法相比标准SPH方法可以解决高速、强压缩、高密度比的多相流问题，且修正SPH方法相比网格方法具有程序简单、计算量小的特点；完全变光滑长度计算方法的计算效率远高于传统变光滑长度方法，可保证计算精度的同时大量节省计算时间。以上模型可应用于水下接触爆炸毁伤、防雷舱结构防护、近边界爆炸等高密度比、强冲击、且密度变化较为剧烈的数值模拟中。
以舰船、潜艇受鱼雷接触爆炸攻击为工程背景，建立了单层壳结构接触爆炸和双层壳结构接触爆炸简化模型，采用修正SPH方法对简化模型进行了数值模拟，再现了水下接触爆炸作用下冲击波传播及钢板的毁伤过程。研究发现：钢板的破坏缘于TNT爆炸产生的强冲击波，其破坏模式随钢板厚度的增加大致经历了从“云状”碎片破坏到冲塞破坏再到开裂破坏的过程，由此得到舰船水下接触爆炸的破坏模式为“云状”破片破坏。此外，当冲击波传播至背空钢板处时，高阻抗的钢板会反射冲击波，进而加强直达冲击波的作用或形成冲击波二次峰值，而低阻抗的空气会反射稀疏波，迅速衰减冲击波压力，形成冲击波的“切断”现象，这种加强和削弱作用同时存在于背空钢板附近的水域中，在潜艇、船体的结构设计等工程应用中需得到重视。
根据舰船防雷舱的结构特点，抽象了膨胀舱和吸收舱防护机理的计算模型，采用修正的SPH方法分别模拟了膨胀舱对爆炸冲击波的衰减过程和吸收舱对高速弹片的衰减过程，通过膨胀舱和吸收舱参数对衰减效果影响规律的定量研究，可得到的结论和建议为：舰船防雷舱中的膨胀舱利用空气的低阻抗可有效衰减冲击波，接触爆炸作用下，当膨胀舱厚度和爆炸厚度相等时可达到较好的衰减冲击波效果，使冲击波压力峰值降低55%左右，继续增加膨胀舱的厚度对冲击波衰减效果的影响减小，可根据此原则对膨胀舱厚度进行设计。舰船防雷舱中的吸收舱利用水的低压缩性可有效衰减高速弹片，弹片速度随运动时间和运动距离均基本呈指数衰减，且吸收舱宽度的增加有利于降低高速冲击产生的冲击波压力，因此在防雷舱结构设计时，应尽量增加吸收舱的宽度；此外，增加液舱外板的厚度对衰减高速弹片的效果并不明显，因此可按普通舱壁设计液舱外板。
根据近自由面爆炸和沉底爆炸载荷难以确定的工程需求，采用SPH方法再现了近自由面水下爆炸和沉底爆炸的物理过程，研究了近自由面爆炸和沉底爆炸的载荷特征。对于近自由面水下爆炸，自由面反射的稀疏波仅在非规则反射区降低冲击波压力峰值，而近自由面爆炸的大部分区域为规则反射区，其切断效应不影响冲击波压力峰值，但会大幅衰减冲击波冲量。对于沉底水下爆炸，海底泥沙的反射会增强冲击波，工程中计算沉底爆炸载荷时，可取海底的反射系数为1.2。
建立了三维SPH数值模型，并用SPH方法对三维水下爆炸问题进行了数值模拟，模拟的冲击波传播过程符合水下爆炸的基本理论，且计算的冲击波压力峰值、衰减趋势和Zamyshlyayev经验公式值吻合良好。和CEL网格方法的比较表明，SPH方法在求解水下爆炸问题时具有更高的精度，相比网格方法有较大优势，可为三维水下爆炸的工程应用提供技术基础。
分别基于球坐标系、柱坐标系、笛卡尔坐标系推导了球对称、轴对称、平面对称SPH的光滑函数表达式及控制方程的离散形式，建立了球对称、轴对称、平面对称的SPH数值模型，在该数值模型中，提出镜像粒子算法解决粒子穿透对称轴的问题，经过水下爆炸算例的验证表明，该模型克服了模拟水下爆炸时靠近对称轴的粒子穿透对称轴的非物理现象，在对称轴附近时仍具有较高的精度，且得到的冲击波压力时程曲线和Zamyshlyayev经验公式值吻合良好，较其他对称SPH模型有明显优势，可进一步应用于水中兵器设计、舰船水下爆炸等工程问题中。
针对水下爆炸不同阶段物理特征不同的特点，充分利用BEM方法和SPH方法的优势，模拟了圆柱形装药水下爆炸冲击波传播、气泡脉动、气泡射流的全过程，实现了两种方法的结合。基于轴对称SPH方法实现了气泡射流阶段的数值模拟，计算结果符合气泡射流基本规律，且计算值和实验值基本吻合，证明了轴对称SPH方法模拟气泡射流的可行性，克服了BEM方法模拟气泡射流时需要特殊的人工干预及数值光顺技术的弊端。
Underwater explosion releases enormous heat in a very short period of time, andproduces high-pressure shock wave and bubble oscillation which can cause devastatingdamage of warships and other structures in water. Because of the important militarysignificance，Western naval power poured a lot of manpower, material and financial resourcesinto studying underwater explosion theories and related numerical techniques, and haveformed relatively mature numerical analysis methods of underwater non-contact explosion.The methods have integrated into ABAQUS and other commercial software. However,underwater contact explosion has characteristics of large deformation, moving materialinterface, free surface, high degree of non-uniformity and other features, which is easy tocause wrong results due to high distortion of the grid while simulating with grid methodintegrated in the above software. To overcome the inherent grid distortion problems of gridmethod, many scholars begin to simulate underwater explosion with smooth particlehydrodynamics (SPH) method which has the nature of Lagrangian and particle, and havemade certain progress. However, because of the complexity of the underwater explosionphysical process, the simulation is not yet mature, and there are still many mechanisticproblems to be solved.
Therefore, the present research situation of warship underwater explosion and SPHmethod are reviewed firstly. Through the review we find: the grid method is still the mainaccess to simulations of underwater contact explosion, but simulations with SPH method arerare; Researches on torpedo defense cabin in China are restricted to theoretical andexperimental studies, and it is difficult to quantify the protection role of each layer, so theattenuation effects and protection mechanisms of torpedo defense cabin are not clear; Shockwave reflection effects of free surface and seabed are also confined to qualitative analysis, andthe differences of seabed reflection coefficient selection during engineering calculation stillexist; At the same time, simulation of underwater explosion with SPH is also limited to twodimensions, and three-dimensional underwater explosion simulation with SPH method orsymmetric SPH method is very rare; Simulations of underwater explosion mainly focus on thestage of shockwave, and are lack of the whole process of shockwave, bubble oscillation andbubble jet. So, responsing to the above questions, this paper mainly studies on the damagemechanism of warship underwater contact explosion, protection mechanism of torpedodefense cabin, shockwave reflection effects of different boundaries and the whole simulationprocess of three-dimensional underwater explosion.
As for the present situation that it is unable to simulate multiphase flow problems oflarge density ratio with the standard SPH method, the modified SPH method based on the volumn approximation is raised, and the numerical models of modified SPH method areestablished. As for the shortcomings of traditional variable smoothing length, excessiveiterations to ensure the accuracy, the fully variable smoothing length algorithm, whosecomputing efficient is high, is put forward. The example that tapered charge explosion drivethe metal jet shows that the modified SPH method can solve multiphase flow problems ofhigh-speed, high compression and high-density ratio compared to the standard SPH method.Besides, the modified SPH method has the characteristics of simple and small amount ofcalculation compared with the grid method. The efficiency of fully variable smoothing lengthcalculation method is much higher than the traditional method, so the computing time is savedand the accuracy is guaranteed at the same time. The above model can be applied to theunderwater contact explosion damage, torpedo defense cabin protection, explosion nearboundary and other numerical simulations with the characteristic of high-density ratio, strongshock, and density fluctuation fiercely.
At the engineering background of warships and submarines attacked by the torpedocontact explosion, the simplified models of single shell and double shell contact explosion areestablished. The models are simulated with the modified SPH method. The shock wavepropagation and the damage process of steel plate under the impact of underwater contactexplosion are reproduced. Researches found: the destruction of steel plate is due to the strongshock wave from the TNT detonation; The failure mode has gone through from the "cloud"debris damage to the plugging destruction and then to cracking with the increasing of the steelthickness, so it can be achieved that the damage mode of warship underwater contactexplosion is "cloud" debris damage. Besides, when the shock wave spreads to the steel platewhose back is air, the plate of high impedance will reflect shock wave, and thereby directivewave is strengthened or the second peak is formed; However, the air of low impedance willreflect rarefaction wave, decay shock wave pressure rapidly, and form the phenomenon of“cut off”. The role of strengthen and weaken exists in the vicinity of waters near the plateswhose back is air, which should be taken seriously in the design of submarine, hull structureand other engineering applications.
According to the characteristics of torpedo defense cabin, the calculation model aboutprotection mechanism of expansion tank and absorption tank are abstracted. The shock waveattenuation process of expansion tank and the high-speed shrapnel decay process ofabsorption tank are simulated with modified SPH method. Through the quantitative study onthe attenuation law of different parameters of expansion tank and absorption tank, thefollowing conclusions and suggestions can be illustrated as: the expansion tank caneffectively attenuate shock wave taking advantage of the low impedance of air; In the contactexplosion simulations, the shock wave peak pressure can reduce up to55%when the thickness of expansion tank is equal to that of explosion, shock wave attenuation effectdecreases as the thickness continues to increase, which all can give a reference to theexpansion tank design. The absorption tank can effectively attenuate high-speed shrapneltaking advantage of the low compressibility of water; As the increase of absorption tank width,the shock wave pressure, which is generated by high speed shock, attenuates; As a result, inthe design of broadside torpedo defense cabin, the absorption tank should be designed as wideas possible; Also, the attenuation effect of outside board of liquid tank is not apparent, so theoutside board thickness of liquid tank should be designed normally.
According to the engineering requirements of blast load produced by the seabed torpedoexplosion and the explosion near free surface, the process of which are reproduced with theSPH method, and the load features are also studied. As for the explosion near free surface,rarefaction wave reflected from the free surface reduces the shock wave peak pressure only inthe non-regular reflection region. The majority area of the explosion near free surface isregular reflection area, and the “cut off” phenomenon can not affect the peak pressure. But theshock wave impulse can attenuate significantly. As for the seabed torpedo explosion, thereflection of seabed sediment can increase shock wave. Therefore, when the blast loadingcalculated in engineering, the reflection coefficient of seabed can be selected as1.2.
The three-dimensional SPH numerical models are established, and the simulation ofthree-dimensional underwater explosion with SPH method is achieved. The simulation resultsof shock wave propagation are consistent with the basic theory of underwater explosion.Besides, shock wave peak pressure and the attenuation trends are in good agreement withZamyshlyayev empirical formula. Compared with the grid method of CEL, SPH method has ahigh accuracy when solving underwater explosion problems, so the program can provide thetechnical basis of engineering applications for three-dimensional underwater explosion.
Spherically symmetric, axisymmetric, plane symmetric SPH smooth functionexpressions and the discrete equations are derived based on spherical coordinates, cylindricalcoordinates, Cartesian coordinates, and the corresponding numerical models are established.Mirror particle algorithm to solve the problem of particle penetrating symmetric axis isproposed. Through verification of underwater explosion examples, the model have overcomethe particle penetrating symmetric axis, and has a higher accuracy near the symmetric axis;The pressure-time curves are consistent with the Zamyshlyayev empirical formula, and theSPH model has obvious advantages compared with others, which can be further applied tounderwater weapon designs, warships underwater explosion and other engineering problems.
As for different stages of underwater explosion have different physical characteristics,the whole underwater explosion process of shock wave propagation, bubble oscillation,bubble jet is simulated taking the full advantages of BEM method and SPH method, the combination of which is achieved. The numerical simulation of bubble jet phase is achievedbased on axisymmetric SPH method. The results are consistent with the basic law and theexperimental data, which shows the feasibility of bubble jet simulation with axisymmetricSPH method. The simulation has overcome the drawbacks of manual intervention andnumerical smoothing technologies while simulating bubble jet with BEM method.
为此，本文首先对舰船水下爆炸及SPH方法的研究现状进行了综述，通过综述发现：对水下接触爆炸的模拟仍主要采取网格方法，用SPH方法模拟水下接触爆炸的研究极少；我国对舰船防雷舱仅局限于理论和试验研究，难以定量分析各层的防护作用，对防雷舱的衰减效果和防护机理认识不清；自由面及海底对冲击波反射效应的研究还仅局限于定性分析，国内对工程计算中海底反射系数等参数的选取仍存在认识上的不一致；用SPH方法模拟水下爆炸还仅局限于二维情况，采用SPH方法或对称SPH方法模拟三维水下爆炸的研究十分罕见；SPH方法对水下爆炸的模拟主要集中在冲击波阶段，一直缺乏水下爆炸冲击波、气泡脉动、射流全过程模拟的相关研究。本文针对上述问题，以工程应用需求为牵引，通过改进SPH的计算方法，重点研究舰船接触爆炸毁伤机理、舰船防雷舱防护机理、边界对冲击波的反射效应以及三维水下爆炸全过程的数值模拟。
针对标准SPH方法无法模拟大密度比多相流的现状，提出了基于体积近似的修正SPH方法，建立了修正SPH方法数值模型。针对传统变光滑长度需多次迭代才可保证精度的缺点，提出了计算效率较高的完全变光滑长度算法。通过锥形装药爆炸驱动金属射流的算例表明：修正SPH方法相比标准SPH方法可以解决高速、强压缩、高密度比的多相流问题，且修正SPH方法相比网格方法具有程序简单、计算量小的特点；完全变光滑长度计算方法的计算效率远高于传统变光滑长度方法，可保证计算精度的同时大量节省计算时间。以上模型可应用于水下接触爆炸毁伤、防雷舱结构防护、近边界爆炸等高密度比、强冲击、且密度变化较为剧烈的数值模拟中。
以舰船、潜艇受鱼雷接触爆炸攻击为工程背景，建立了单层壳结构接触爆炸和双层壳结构接触爆炸简化模型，采用修正SPH方法对简化模型进行了数值模拟，再现了水下接触爆炸作用下冲击波传播及钢板的毁伤过程。研究发现：钢板的破坏缘于TNT爆炸产生的强冲击波，其破坏模式随钢板厚度的增加大致经历了从“云状”碎片破坏到冲塞破坏再到开裂破坏的过程，由此得到舰船水下接触爆炸的破坏模式为“云状”破片破坏。此外，当冲击波传播至背空钢板处时，高阻抗的钢板会反射冲击波，进而加强直达冲击波的作用或形成冲击波二次峰值，而低阻抗的空气会反射稀疏波，迅速衰减冲击波压力，形成冲击波的“切断”现象，这种加强和削弱作用同时存在于背空钢板附近的水域中，在潜艇、船体的结构设计等工程应用中需得到重视。
根据舰船防雷舱的结构特点，抽象了膨胀舱和吸收舱防护机理的计算模型，采用修正的SPH方法分别模拟了膨胀舱对爆炸冲击波的衰减过程和吸收舱对高速弹片的衰减过程，通过膨胀舱和吸收舱参数对衰减效果影响规律的定量研究，可得到的结论和建议为：舰船防雷舱中的膨胀舱利用空气的低阻抗可有效衰减冲击波，接触爆炸作用下，当膨胀舱厚度和爆炸厚度相等时可达到较好的衰减冲击波效果，使冲击波压力峰值降低55%左右，继续增加膨胀舱的厚度对冲击波衰减效果的影响减小，可根据此原则对膨胀舱厚度进行设计。舰船防雷舱中的吸收舱利用水的低压缩性可有效衰减高速弹片，弹片速度随运动时间和运动距离均基本呈指数衰减，且吸收舱宽度的增加有利于降低高速冲击产生的冲击波压力，因此在防雷舱结构设计时，应尽量增加吸收舱的宽度；此外，增加液舱外板的厚度对衰减高速弹片的效果并不明显，因此可按普通舱壁设计液舱外板。
根据近自由面爆炸和沉底爆炸载荷难以确定的工程需求，采用SPH方法再现了近自由面水下爆炸和沉底爆炸的物理过程，研究了近自由面爆炸和沉底爆炸的载荷特征。对于近自由面水下爆炸，自由面反射的稀疏波仅在非规则反射区降低冲击波压力峰值，而近自由面爆炸的大部分区域为规则反射区，其切断效应不影响冲击波压力峰值，但会大幅衰减冲击波冲量。对于沉底水下爆炸，海底泥沙的反射会增强冲击波，工程中计算沉底爆炸载荷时，可取海底的反射系数为1.2。
建立了三维SPH数值模型，并用SPH方法对三维水下爆炸问题进行了数值模拟，模拟的冲击波传播过程符合水下爆炸的基本理论，且计算的冲击波压力峰值、衰减趋势和Zamyshlyayev经验公式值吻合良好。和CEL网格方法的比较表明，SPH方法在求解水下爆炸问题时具有更高的精度，相比网格方法有较大优势，可为三维水下爆炸的工程应用提供技术基础。
分别基于球坐标系、柱坐标系、笛卡尔坐标系推导了球对称、轴对称、平面对称SPH的光滑函数表达式及控制方程的离散形式，建立了球对称、轴对称、平面对称的SPH数值模型，在该数值模型中，提出镜像粒子算法解决粒子穿透对称轴的问题，经过水下爆炸算例的验证表明，该模型克服了模拟水下爆炸时靠近对称轴的粒子穿透对称轴的非物理现象，在对称轴附近时仍具有较高的精度，且得到的冲击波压力时程曲线和Zamyshlyayev经验公式值吻合良好，较其他对称SPH模型有明显优势，可进一步应用于水中兵器设计、舰船水下爆炸等工程问题中。
针对水下爆炸不同阶段物理特征不同的特点，充分利用BEM方法和SPH方法的优势，模拟了圆柱形装药水下爆炸冲击波传播、气泡脉动、气泡射流的全过程，实现了两种方法的结合。基于轴对称SPH方法实现了气泡射流阶段的数值模拟，计算结果符合气泡射流基本规律，且计算值和实验值基本吻合，证明了轴对称SPH方法模拟气泡射流的可行性，克服了BEM方法模拟气泡射流时需要特殊的人工干预及数值光顺技术的弊端。
Underwater explosion releases enormous heat in a very short period of time, andproduces high-pressure shock wave and bubble oscillation which can cause devastatingdamage of warships and other structures in water. Because of the important militarysignificance，Western naval power poured a lot of manpower, material and financial resourcesinto studying underwater explosion theories and related numerical techniques, and haveformed relatively mature numerical analysis methods of underwater non-contact explosion.The methods have integrated into ABAQUS and other commercial software. However,underwater contact explosion has characteristics of large deformation, moving materialinterface, free surface, high degree of non-uniformity and other features, which is easy tocause wrong results due to high distortion of the grid while simulating with grid methodintegrated in the above software. To overcome the inherent grid distortion problems of gridmethod, many scholars begin to simulate underwater explosion with smooth particlehydrodynamics (SPH) method which has the nature of Lagrangian and particle, and havemade certain progress. However, because of the complexity of the underwater explosionphysical process, the simulation is not yet mature, and there are still many mechanisticproblems to be solved.
Therefore, the present research situation of warship underwater explosion and SPHmethod are reviewed firstly. Through the review we find: the grid method is still the mainaccess to simulations of underwater contact explosion, but simulations with SPH method arerare; Researches on torpedo defense cabin in China are restricted to theoretical andexperimental studies, and it is difficult to quantify the protection role of each layer, so theattenuation effects and protection mechanisms of torpedo defense cabin are not clear; Shockwave reflection effects of free surface and seabed are also confined to qualitative analysis, andthe differences of seabed reflection coefficient selection during engineering calculation stillexist; At the same time, simulation of underwater explosion with SPH is also limited to twodimensions, and three-dimensional underwater explosion simulation with SPH method orsymmetric SPH method is very rare; Simulations of underwater explosion mainly focus on thestage of shockwave, and are lack of the whole process of shockwave, bubble oscillation andbubble jet. So, responsing to the above questions, this paper mainly studies on the damagemechanism of warship underwater contact explosion, protection mechanism of torpedodefense cabin, shockwave reflection effects of different boundaries and the whole simulationprocess of three-dimensional underwater explosion.
As for the present situation that it is unable to simulate multiphase flow problems oflarge density ratio with the standard SPH method, the modified SPH method based on the volumn approximation is raised, and the numerical models of modified SPH method areestablished. As for the shortcomings of traditional variable smoothing length, excessiveiterations to ensure the accuracy, the fully variable smoothing length algorithm, whosecomputing efficient is high, is put forward. The example that tapered charge explosion drivethe metal jet shows that the modified SPH method can solve multiphase flow problems ofhigh-speed, high compression and high-density ratio compared to the standard SPH method.Besides, the modified SPH method has the characteristics of simple and small amount ofcalculation compared with the grid method. The efficiency of fully variable smoothing lengthcalculation method is much higher than the traditional method, so the computing time is savedand the accuracy is guaranteed at the same time. The above model can be applied to theunderwater contact explosion damage, torpedo defense cabin protection, explosion nearboundary and other numerical simulations with the characteristic of high-density ratio, strongshock, and density fluctuation fiercely.
At the engineering background of warships and submarines attacked by the torpedocontact explosion, the simplified models of single shell and double shell contact explosion areestablished. The models are simulated with the modified SPH method. The shock wavepropagation and the damage process of steel plate under the impact of underwater contactexplosion are reproduced. Researches found: the destruction of steel plate is due to the strongshock wave from the TNT detonation; The failure mode has gone through from the "cloud"debris damage to the plugging destruction and then to cracking with the increasing of the steelthickness, so it can be achieved that the damage mode of warship underwater contactexplosion is "cloud" debris damage. Besides, when the shock wave spreads to the steel platewhose back is air, the plate of high impedance will reflect shock wave, and thereby directivewave is strengthened or the second peak is formed; However, the air of low impedance willreflect rarefaction wave, decay shock wave pressure rapidly, and form the phenomenon of“cut off”. The role of strengthen and weaken exists in the vicinity of waters near the plateswhose back is air, which should be taken seriously in the design of submarine, hull structureand other engineering applications.
According to the characteristics of torpedo defense cabin, the calculation model aboutprotection mechanism of expansion tank and absorption tank are abstracted. The shock waveattenuation process of expansion tank and the high-speed shrapnel decay process ofabsorption tank are simulated with modified SPH method. Through the quantitative study onthe attenuation law of different parameters of expansion tank and absorption tank, thefollowing conclusions and suggestions can be illustrated as: the expansion tank caneffectively attenuate shock wave taking advantage of the low impedance of air; In the contactexplosion simulations, the shock wave peak pressure can reduce up to55%when the thickness of expansion tank is equal to that of explosion, shock wave attenuation effectdecreases as the thickness continues to increase, which all can give a reference to theexpansion tank design. The absorption tank can effectively attenuate high-speed shrapneltaking advantage of the low compressibility of water; As the increase of absorption tank width,the shock wave pressure, which is generated by high speed shock, attenuates; As a result, inthe design of broadside torpedo defense cabin, the absorption tank should be designed as wideas possible; Also, the attenuation effect of outside board of liquid tank is not apparent, so theoutside board thickness of liquid tank should be designed normally.
According to the engineering requirements of blast load produced by the seabed torpedoexplosion and the explosion near free surface, the process of which are reproduced with theSPH method, and the load features are also studied. As for the explosion near free surface,rarefaction wave reflected from the free surface reduces the shock wave peak pressure only inthe non-regular reflection region. The majority area of the explosion near free surface isregular reflection area, and the “cut off” phenomenon can not affect the peak pressure. But theshock wave impulse can attenuate significantly. As for the seabed torpedo explosion, thereflection of seabed sediment can increase shock wave. Therefore, when the blast loadingcalculated in engineering, the reflection coefficient of seabed can be selected as1.2.
The three-dimensional SPH numerical models are established, and the simulation ofthree-dimensional underwater explosion with SPH method is achieved. The simulation resultsof shock wave propagation are consistent with the basic theory of underwater explosion.Besides, shock wave peak pressure and the attenuation trends are in good agreement withZamyshlyayev empirical formula. Compared with the grid method of CEL, SPH method has ahigh accuracy when solving underwater explosion problems, so the program can provide thetechnical basis of engineering applications for three-dimensional underwater explosion.
Spherically symmetric, axisymmetric, plane symmetric SPH smooth functionexpressions and the discrete equations are derived based on spherical coordinates, cylindricalcoordinates, Cartesian coordinates, and the corresponding numerical models are established.Mirror particle algorithm to solve the problem of particle penetrating symmetric axis isproposed. Through verification of underwater explosion examples, the model have overcomethe particle penetrating symmetric axis, and has a higher accuracy near the symmetric axis;The pressure-time curves are consistent with the Zamyshlyayev empirical formula, and theSPH model has obvious advantages compared with others, which can be further applied tounderwater weapon designs, warships underwater explosion and other engineering problems.
As for different stages of underwater explosion have different physical characteristics,the whole underwater explosion process of shock wave propagation, bubble oscillation,bubble jet is simulated taking the full advantages of BEM method and SPH method, the combination of which is achieved. The numerical simulation of bubble jet phase is achievedbased on axisymmetric SPH method. The results are consistent with the basic law and theexperimental data, which shows the feasibility of bubble jet simulation with axisymmetricSPH method. The simulation has overcome the drawbacks of manual intervention andnumerical smoothing technologies while simulating bubble jet with BEM method.
引文
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