基于虚拟流体方法的水下爆炸计算研究
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摘要
水下爆炸的计算研究在军事领域、工程领域有广泛的应用前景。在军事领域,水雷和深水炸弹的研制需要对相应的水下爆炸波传播和超压峰值进行计算研究。在工程领域,港口航道的建设需要对水下爆炸进行计算研究。水下爆炸的计算研究可以为实验研究提供参考,特别是在实验条件不具备的情况下,更是可以为水下兵器的研制和工程爆破的设计提供理论指导并具备重要的参考意义。而对水下爆炸计算方法的研究和改进也具有重要的学术价值。目前,关于水下爆炸的计算研究,方法有有限元方法、SPH方法(Smoothed Particle Hydrodynamics)、边界元方法、GFM(Ghost Fluid Method)以及一些欧拉-拉格朗日耦合类的方法。其中,GFM又包括OGFM(Original GFM),NGFM(New Version of GFM),MGFM (Modified GFM),RGFM(Real GFM)和SMGFM(Solid MGFM)等等。目前,国内用GFM对水下爆炸进行的计算研究仍然很少。本文选用GFM对水下爆炸进行计算研究。本文根据不同的问题和计算条件选用不同的GFM子方法进行数值模拟。本文主要对水下爆炸的爆炸波传播进行数值模拟、对水下爆轰流场的超压峰值进行数值计算以及针对水下爆炸的数值计算改进GFM中的计算步骤。
本文的主要研究内容和创新性工作如下：
1)对柱形装药水下爆炸问题利用Level set方法完成了精确的三维数值模拟,提高了计算精度。柱形装药在水下爆炸中较为常见。对于三维圆柱问题的数值模拟一般是在计算域可以切割成二维轴对称区域的情况下,将三维问题做为二维轴对称问题处理。但是一些较复杂的计算域并不能切割成二维轴对称问题处理,这时就需要求解三维情况下的Level set函数初值。以往对初始时刻Level set函数的定义使用的是重新初始化技术,该技术会造成界面位置的误差。本文通过计算域分块定义的方法,对三维柱形装药水下爆炸数值模拟中的Level set函数初值进行精确求解,避免了使用重新初始化技术,从而减小了数值模拟结果的误差。
2)本文将插值法耦合进ARPS(Approximate Riemann Problem Solver),从而减小计算误差。用ARPS预估界面状态是GFM中的一个重要步骤。原有的ARPS在用于多维问题时,使用最小夹角法则来选择界面两侧的网格节点,而最小夹角法则会造成较大的数值误差。本文用插值法替代最小夹角法则,减小了计算误差,并将耦合方法的计算结果同原有ARPS的计算结果进行对比分析。对比表明,耦合插值法的ARPS比原有的ARPS计算精度更高。
3)本文用两种不同的方法数值模拟复杂计算域的爆炸波传播,并通过对比研究分析和总结了各自的优缺点。一是在贴体坐标网格下使用任意坐标系方法。二是在规则笛卡尔网格使用NGFM。研究结果表明,在规则笛卡尔网格中使用NGFM可以得到较稳定的计算结果；但是无法刚好得到壁面上网格节点的压力值,在实际计算中只能用紧邻壁面的网格节点的压力值做为壁面压力值的参考,不过计算结果表明在加密网格的情况下,壁面内侧网格节点的压力值和壁面压力值非常接近。相比较而言,在贴体坐标网格中使用任意坐标系方法,可以得到壁面网格节点的压力值；但是利用Tait方程作为水的状态方程时,流场常常会会出现较大范围的数值振荡,另一方面,网格导数的引入会影响计算结果的精度。
4)本文推导了一个基于Euler-弹性动力学基本方程的流固ARPS,从而扩大了原有SMGFM的适用范围。用流固ARPS预估流固界面状态,是SMGFM中一个重要步骤。原有的流固ARPS的缺点在于是用Euler方程和Naviers方程推导的,而Naviers方程对固体的数值计算而言应用起来效果并不太好。本文用弹性动力学基本方程描述固体,推导一个基于Euler-弹性动力学基本方程的流固ARPS,并将计算结果同文献中刚壁计算结果、可压缩固体计算结果进行了对比分析。数值计算的结果表明本文推导的ARPS是正确的。同时,数值计算的结果也表明线弹性假设得到的流体一侧爆炸波传播结果和可压缩固体假设得到的结果相近,壁面的压力动态响应也较好地吻合。
The numerical research on UWE (underwater explosion) has a wide application prospect in military realm and engineering field. In the region of military, it is necessary to simulate the propagation of underwater blast wave and compute the peak pressure for the development of torpedo and depth charge. In the region of engineering, it is important to do numerical study for the development of port and shipping lane. The numerical simulation of UWE can provide references for experimental research. It can also point out especial theoretical direction and has very important referential significances when the experiment cannot be implemented, In addition, the research and improvement on computational method of UWE has important academic significances. The current approaches to numerical simulation of UWE include Finite Element Method, Smoothed Particle Hydrodynamics, Boundary Element Method, GFM (Ghost Fluid Method) and some Euler-Lagrange combination methods. One of these methods, GFM, has been divided into some kinds such as OGFM (Original GFM), NGFM (New Version GFM), MGFM (Modified GFM), RGFM (Real GFM) and SMGFM (Solid MGFM) etc. In GFM, to solve one medium, the domain on the other side of material interface is supposed to be the same ghost medium and defined to be with appropriate flows states for the nodal points. Hence, the status at the grid nodes next to material interface can be solved. Since ghost assumption can simplify complicated problem, GFM has a more widely application for simulation complicated problem than other methods. GFM is employed to do numerical research for UWE in this thesis because of the lack of literatures on numerical study on UWE using GFM by so far. For different specific problems of UWE, different kinds of GFM algorithm are used. This dissertation presents the numerical simulation of the propagation of underwater blast wave, the calculation on peak pressure of the flow field of UWE and also provides improvements on some steps of GFM for numerical simulation of UWE.
The main research contents and innovation work of this dissertation include:
1) This thesis presents a more accurate numerical simulation of column charge UWE by Level set method and some improvements on numerical accuracy. Column charge is common in UWE.Three-dimensional cylindrical problem is often cut into2D axis problem on the condition that the computational region can be cut into a2D axis domain. However, this approach is not applicable in some complex computational region. Thus, we need to solve initial values of Level set function. By far, the re-initial technique is always used to define initial values of Level set function. This technique can lead to non-physical movement of material interface. In this thesis, an accurate method based on dividing and respectively solving computational region is developed to solved the initial values of Level set function to reduce the numerical error.
2) In this thesis, the interpolation method is coupled into ARPS (Approximate Riemann Problem Solver) to reduce the numerical error. Predicting the interfacial status using ARPS is an important step of GFM. For original ARPS, minimum angle algorithm is used to select two relative grid nodes just bordering interface. The minimum angle algorithm always leads to large numerical errors. In this thesis, we replace the minimum angle algorithm by interpolation method and compare the differences between the results by the way coupled and original ARPS. It is verified that combination of ARPS and interpolation method has the property of reducing numerical errors by comparing to the results without the employment of interpolation method.
3) This thesis presents the numerical simulation of underwater blast wave in complex computational region by two different methods and comparison between the respective results. One method is using arbitrary coordinate system method in body-fitted grids. The other is using NGFM in uniform Cartesian grids. The research demonstrates that NGFM can present more stable results and its weakness is incapability on computing the pressure of grid nodes on rigid wall. In calculation, we need to use the pressure of grid nodes just bordering the rigid wall. The results show that the pressure of grid nodes just next to the rigid wall is very close to the value of grid nodes on the wall if the grid size is very small. In contrast, using arbitrary in uniform grid can present the pressure on the rigid wall. Nevertheless, the numerical oscillation often occurs in large area of flow field because Tait equation is used to describe water. On the other side, since we need to solve the grid derivative, the numerical result is not accurate.
4) This thesis presents a fluid-solid ARPS based on Euler equations and fundamental equations of elastodynamics to expand the application range of SMGFM. Predicting the flows states via fluid-solid ARPS is an important process in SMGFM. The present fluid-solid ARPS is deduced based on Euler-Naviers equations with respective employment of Euler equation to solve flow field and Naviers equation to solve the grid nodes of solid medium. Nevertheless, Naviers equation cannot work efficiently when applied in simulation of solid. In this dissertation, a fluid-solid ARPS is deduced based on Euler-basic elastodynamics equations. The comparison among the results by new ARPS, rigid wall assumption and compressible assumption is also presented. The numerical results demonstrate the correctness of the deduced ARPS. Meanwhile, the numerical results show that there is little discrepancy between the respective results of blast wave propagation of flow field and pressure history by different approach abovementioned are very close to each other.
本文的主要研究内容和创新性工作如下：
1)对柱形装药水下爆炸问题利用Level set方法完成了精确的三维数值模拟,提高了计算精度。柱形装药在水下爆炸中较为常见。对于三维圆柱问题的数值模拟一般是在计算域可以切割成二维轴对称区域的情况下,将三维问题做为二维轴对称问题处理。但是一些较复杂的计算域并不能切割成二维轴对称问题处理,这时就需要求解三维情况下的Level set函数初值。以往对初始时刻Level set函数的定义使用的是重新初始化技术,该技术会造成界面位置的误差。本文通过计算域分块定义的方法,对三维柱形装药水下爆炸数值模拟中的Level set函数初值进行精确求解,避免了使用重新初始化技术,从而减小了数值模拟结果的误差。
2)本文将插值法耦合进ARPS(Approximate Riemann Problem Solver),从而减小计算误差。用ARPS预估界面状态是GFM中的一个重要步骤。原有的ARPS在用于多维问题时,使用最小夹角法则来选择界面两侧的网格节点,而最小夹角法则会造成较大的数值误差。本文用插值法替代最小夹角法则,减小了计算误差,并将耦合方法的计算结果同原有ARPS的计算结果进行对比分析。对比表明,耦合插值法的ARPS比原有的ARPS计算精度更高。
3)本文用两种不同的方法数值模拟复杂计算域的爆炸波传播,并通过对比研究分析和总结了各自的优缺点。一是在贴体坐标网格下使用任意坐标系方法。二是在规则笛卡尔网格使用NGFM。研究结果表明,在规则笛卡尔网格中使用NGFM可以得到较稳定的计算结果；但是无法刚好得到壁面上网格节点的压力值,在实际计算中只能用紧邻壁面的网格节点的压力值做为壁面压力值的参考,不过计算结果表明在加密网格的情况下,壁面内侧网格节点的压力值和壁面压力值非常接近。相比较而言,在贴体坐标网格中使用任意坐标系方法,可以得到壁面网格节点的压力值；但是利用Tait方程作为水的状态方程时,流场常常会会出现较大范围的数值振荡,另一方面,网格导数的引入会影响计算结果的精度。
4)本文推导了一个基于Euler-弹性动力学基本方程的流固ARPS,从而扩大了原有SMGFM的适用范围。用流固ARPS预估流固界面状态,是SMGFM中一个重要步骤。原有的流固ARPS的缺点在于是用Euler方程和Naviers方程推导的,而Naviers方程对固体的数值计算而言应用起来效果并不太好。本文用弹性动力学基本方程描述固体,推导一个基于Euler-弹性动力学基本方程的流固ARPS,并将计算结果同文献中刚壁计算结果、可压缩固体计算结果进行了对比分析。数值计算的结果表明本文推导的ARPS是正确的。同时,数值计算的结果也表明线弹性假设得到的流体一侧爆炸波传播结果和可压缩固体假设得到的结果相近,壁面的压力动态响应也较好地吻合。
The numerical research on UWE (underwater explosion) has a wide application prospect in military realm and engineering field. In the region of military, it is necessary to simulate the propagation of underwater blast wave and compute the peak pressure for the development of torpedo and depth charge. In the region of engineering, it is important to do numerical study for the development of port and shipping lane. The numerical simulation of UWE can provide references for experimental research. It can also point out especial theoretical direction and has very important referential significances when the experiment cannot be implemented, In addition, the research and improvement on computational method of UWE has important academic significances. The current approaches to numerical simulation of UWE include Finite Element Method, Smoothed Particle Hydrodynamics, Boundary Element Method, GFM (Ghost Fluid Method) and some Euler-Lagrange combination methods. One of these methods, GFM, has been divided into some kinds such as OGFM (Original GFM), NGFM (New Version GFM), MGFM (Modified GFM), RGFM (Real GFM) and SMGFM (Solid MGFM) etc. In GFM, to solve one medium, the domain on the other side of material interface is supposed to be the same ghost medium and defined to be with appropriate flows states for the nodal points. Hence, the status at the grid nodes next to material interface can be solved. Since ghost assumption can simplify complicated problem, GFM has a more widely application for simulation complicated problem than other methods. GFM is employed to do numerical research for UWE in this thesis because of the lack of literatures on numerical study on UWE using GFM by so far. For different specific problems of UWE, different kinds of GFM algorithm are used. This dissertation presents the numerical simulation of the propagation of underwater blast wave, the calculation on peak pressure of the flow field of UWE and also provides improvements on some steps of GFM for numerical simulation of UWE.
The main research contents and innovation work of this dissertation include:
1) This thesis presents a more accurate numerical simulation of column charge UWE by Level set method and some improvements on numerical accuracy. Column charge is common in UWE.Three-dimensional cylindrical problem is often cut into2D axis problem on the condition that the computational region can be cut into a2D axis domain. However, this approach is not applicable in some complex computational region. Thus, we need to solve initial values of Level set function. By far, the re-initial technique is always used to define initial values of Level set function. This technique can lead to non-physical movement of material interface. In this thesis, an accurate method based on dividing and respectively solving computational region is developed to solved the initial values of Level set function to reduce the numerical error.
2) In this thesis, the interpolation method is coupled into ARPS (Approximate Riemann Problem Solver) to reduce the numerical error. Predicting the interfacial status using ARPS is an important step of GFM. For original ARPS, minimum angle algorithm is used to select two relative grid nodes just bordering interface. The minimum angle algorithm always leads to large numerical errors. In this thesis, we replace the minimum angle algorithm by interpolation method and compare the differences between the results by the way coupled and original ARPS. It is verified that combination of ARPS and interpolation method has the property of reducing numerical errors by comparing to the results without the employment of interpolation method.
3) This thesis presents the numerical simulation of underwater blast wave in complex computational region by two different methods and comparison between the respective results. One method is using arbitrary coordinate system method in body-fitted grids. The other is using NGFM in uniform Cartesian grids. The research demonstrates that NGFM can present more stable results and its weakness is incapability on computing the pressure of grid nodes on rigid wall. In calculation, we need to use the pressure of grid nodes just bordering the rigid wall. The results show that the pressure of grid nodes just next to the rigid wall is very close to the value of grid nodes on the wall if the grid size is very small. In contrast, using arbitrary in uniform grid can present the pressure on the rigid wall. Nevertheless, the numerical oscillation often occurs in large area of flow field because Tait equation is used to describe water. On the other side, since we need to solve the grid derivative, the numerical result is not accurate.
4) This thesis presents a fluid-solid ARPS based on Euler equations and fundamental equations of elastodynamics to expand the application range of SMGFM. Predicting the flows states via fluid-solid ARPS is an important process in SMGFM. The present fluid-solid ARPS is deduced based on Euler-Naviers equations with respective employment of Euler equation to solve flow field and Naviers equation to solve the grid nodes of solid medium. Nevertheless, Naviers equation cannot work efficiently when applied in simulation of solid. In this dissertation, a fluid-solid ARPS is deduced based on Euler-basic elastodynamics equations. The comparison among the results by new ARPS, rigid wall assumption and compressible assumption is also presented. The numerical results demonstrate the correctness of the deduced ARPS. Meanwhile, the numerical results show that there is little discrepancy between the respective results of blast wave propagation of flow field and pressure history by different approach abovementioned are very close to each other.
引文
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