有相对运动的多体分离过程非定常数值算法研究及实验验证
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摘要
有相对运动的多体分离问题作为一类特殊的力学问题广泛地存在于航空、航天以及武器系统中。由于其本身的复杂性,不论是采用实验方法还是数值模拟方法都存在或多或少的困难,建立有效、准确解决有相对运动的多体分离问题的数值方法在理论及应用上都很有价值。本文根据这一需求,建立了基于非结构动网格的数值模拟技术,形成了能够应用于求解复杂外形多体分离问题的高效、准确的软件系统。软件系统的可信度得到了数值验证及激波管实验的考核确认,在解决复杂分离问题中取得了良好的效果。
首先,基于多体分离问题求解时对计算效率及精度的要求,选择ALE描述的Euler方程为流动控制方程,采用VanLeer格式计算通量,采用分段线性重构或MUSCL重构方法得到空间二阶精度,采用限制器抑制激波处的非物理振荡。时间方向的积分采用二阶精度的显式多步Runge-Kutta方法,计算格式满足几何守恒律。此外,本文着重研究了刚体动力学方程与流体方程的松耦合求解方法,实现了气动力与运动轨迹在同一物理时间内的关联求解。
其次,基于多体分离问题物形复杂、运动位移大的特点,采用非结构动网格技术实现对多体相对运动的描述。动网格方法由网格变形与局部网格重构组成。采用网格变形方法实现动边界周围网格的跟随运动,网格变形采用改进后的弹簧近似模型;当计算区域网格质量变差后采用局部重构的方法,重新生成重构区域的网格。本文计算软件实现了从网格质量判定、重构区域窗口划分、重构区域网格重新生成,到新旧网格关系的建立、新旧网格上物理量的信息传递、分离继续计算的网格自主重构技术,计算过程无需人为干预。针对重构后的插值将引入误差这一问题,本文提出了“移动网格传值方法”,采用动网格方法实现了新旧网格的高精度信息传递,方法应用于一维、二维及三维传值问题取得很好的效果。另外,本文引入“八叉树”数据结构,使得三维新旧网格间的查询效率大大提高。
再次,基于多体分离问题求解的可信度需求,本文采用民机标模外形及类航天飞机外形进行了数值比对,结果与文献中计算、实验结果吻合较好。同时,本文专门设计了用于验证多体分离问题数值方法的激波管实验。采用数值方法模拟得到的实验模型运动轨迹与激波管实验拍摄得到的运动轨迹吻合很好。简单有效的激波管实验不仅是本文数值方法的验证确认,而且能够为精细验证实验及其他动边界实验提供参考。
最后,采用非结构动网格方法对多个有相对运动的复杂分离问题进行了研究。①针对动网格技术中的难题——“接触/分离”问题,本文提出“虚拟网格通气技术”,成功地解决了整流罩启动解锁、隐身飞机弹舱舱门开启这些物体由完全接触到开缝而后逐渐远离过程的模拟。计算真实再现了整流罩启动解锁初期气体冲击狭缝带来的气动力波动现象及舱门开启后弹舱空腔流动的压力振荡情况。②整流罩分离设计问题。整流罩分离设计虽然存在一些经验可循,但缺乏通用的“安全分离准则”,本文采用非结构动网格方法对某型整流罩分离过程进行了细致分析,从整流罩外形、质心位置及启动干扰影响等多方面分析分离过程的影响因素,提出“质心后移方法”能够确保整流罩的安全分离,该方法在子母弹抛壳中得到了验证。③子母弹抛撒问题。本文对子母弹飞行过程中旋转、切壳及前后舱数十枚子弹抛撒过程的计算,体现了本文计算软件对复杂多体分离问题的处理能力,也为子母弹的设计检验提供了一条有效的研究途径。
Flow problem about Multi-body with relative movement is a special kind of mechanical problem and it widely exists in the field of aeronautics, astronautics and weapons. Because of its complexity, it is hard to research or analysis whether using experimental or numerical simulation methods. As a result, establishing an effective and accurate numerical simulation method is important both in theory and practice. In this dissertation, a numerical method using dynamic unstructured grid is studied and software system is established, which can efficiently and exactly simulate multi-body flow problems with complex configuration and complicated relative motion. The reliability of the simulation system is proved by numerical and experimental verification and it has achieved good effect in application.
Firstly, considering the request of efficiency and precision in numerical simulation, the Arbitrary-Lagrangian Eulerian (ALE) framework is chosen to solve 3D time-dependent Euler equations and the Van Leer scheme is applied for spatial discretization. Piecewise linear reconstruction or MUSCL reconstruction is used to obtain second-order spatial accuracy and a multi-stage Runge-Kutta time stepping scheme is adopted for second-order temporal accuracy. To eliminate non-physical oscillations near discontinuities, the limiters of Barth & Jespersen and Venkarakrishnan are employed. Furthermore, the 6DOF (degree of freedom) trajectory equations of rigid body dynamics are coupled in the overall algorithm, in which aerodynamic forces and rigid body movements are updated at the same physics time step with loosing coupling.
Secondly, considering the request for complex configuration and body motion, the dynamic unstructured grid method is studied. The mesh movement strategy is implemented by the combination of mesh deformation and local remeshing. The improved spring analogy model is used to control mesh deformation, which is sufficient for cases with small relative boundary displacement. For cases with relative large boundary displacement, when the mesh elements are severely deformed, Delaunay remeshing method is used to regenerate mesh. Thereon, an automatic technique is studied, which includes the procedure of checking mesh quality, extracting the reconstructed windows, regenerating meshes, finding relationship between new and old grids and transferring solutions from the old mesh to the new one. The new data transfer method, called "moving mesh transfer method", is innovatively proposed to avoid accumulation of interpolation errors. This highly accurate data transferring is implemented by mesh movement strategy, which succeeds in solving one dimensional, two dimensional and three dimensional problems. The "octree" data structure is also used to accelerate the searching operation during interpolation.
Thirdly, considering the verification and validation of numerical method, numerical simulation of the flow field around the space shuttle and a civilian aircraft is performed and the results are consistent with the experiment data and CFD results in references. In addition, an experiment is specially designed on shock tube to validate the numerical method. The numerical simulation of Ping-Pong's trajectory agrees well with those obtained in experiment. This simple and effective experiment can present verification and validation of numerical method, and offer reference for further experiment research and moving body experiment.
Lastly, some multi-body flow problems with complex configuration are studied, such as fairing separation, interior weapon cabin's opening and cluster munitions dispersing. Aimed at the difficulty in simulating the procedure of two bodies separating from tangency to large displacement, a new method called "virtual mesh ventilation method" is introduced, and this method factually reproduces aerodynamic fluctuations at the beginning of fairing separation and flow-induced pressure oscillations in 3D cavity after the weapon cabin's door is open. In the research of fairing separation, after comprehensive analysis of factors such as fairing shape, interfering factors and centroid position, a new separation rule called "centroid backward rule" is proposed according to numerical simulation results with dynamic unstructured grid method, and this rule can be regarded as common criteria to ensure safety in fairing separation. Besides, a cluster munitions dispersing procedure, including cluster munitions rotating, cover ejection and plenty of bullets dispersion, is simulated using dynamic unstructured grid method. Results show that the software is competent for solving extraordinarily complicated problems, and it also offers an effective way to design and validate the cluster munitions.
首先,基于多体分离问题求解时对计算效率及精度的要求,选择ALE描述的Euler方程为流动控制方程,采用VanLeer格式计算通量,采用分段线性重构或MUSCL重构方法得到空间二阶精度,采用限制器抑制激波处的非物理振荡。时间方向的积分采用二阶精度的显式多步Runge-Kutta方法,计算格式满足几何守恒律。此外,本文着重研究了刚体动力学方程与流体方程的松耦合求解方法,实现了气动力与运动轨迹在同一物理时间内的关联求解。
其次,基于多体分离问题物形复杂、运动位移大的特点,采用非结构动网格技术实现对多体相对运动的描述。动网格方法由网格变形与局部网格重构组成。采用网格变形方法实现动边界周围网格的跟随运动,网格变形采用改进后的弹簧近似模型;当计算区域网格质量变差后采用局部重构的方法,重新生成重构区域的网格。本文计算软件实现了从网格质量判定、重构区域窗口划分、重构区域网格重新生成,到新旧网格关系的建立、新旧网格上物理量的信息传递、分离继续计算的网格自主重构技术,计算过程无需人为干预。针对重构后的插值将引入误差这一问题,本文提出了“移动网格传值方法”,采用动网格方法实现了新旧网格的高精度信息传递,方法应用于一维、二维及三维传值问题取得很好的效果。另外,本文引入“八叉树”数据结构,使得三维新旧网格间的查询效率大大提高。
再次,基于多体分离问题求解的可信度需求,本文采用民机标模外形及类航天飞机外形进行了数值比对,结果与文献中计算、实验结果吻合较好。同时,本文专门设计了用于验证多体分离问题数值方法的激波管实验。采用数值方法模拟得到的实验模型运动轨迹与激波管实验拍摄得到的运动轨迹吻合很好。简单有效的激波管实验不仅是本文数值方法的验证确认,而且能够为精细验证实验及其他动边界实验提供参考。
最后,采用非结构动网格方法对多个有相对运动的复杂分离问题进行了研究。①针对动网格技术中的难题——“接触/分离”问题,本文提出“虚拟网格通气技术”,成功地解决了整流罩启动解锁、隐身飞机弹舱舱门开启这些物体由完全接触到开缝而后逐渐远离过程的模拟。计算真实再现了整流罩启动解锁初期气体冲击狭缝带来的气动力波动现象及舱门开启后弹舱空腔流动的压力振荡情况。②整流罩分离设计问题。整流罩分离设计虽然存在一些经验可循,但缺乏通用的“安全分离准则”,本文采用非结构动网格方法对某型整流罩分离过程进行了细致分析,从整流罩外形、质心位置及启动干扰影响等多方面分析分离过程的影响因素,提出“质心后移方法”能够确保整流罩的安全分离,该方法在子母弹抛壳中得到了验证。③子母弹抛撒问题。本文对子母弹飞行过程中旋转、切壳及前后舱数十枚子弹抛撒过程的计算,体现了本文计算软件对复杂多体分离问题的处理能力,也为子母弹的设计检验提供了一条有效的研究途径。
Flow problem about Multi-body with relative movement is a special kind of mechanical problem and it widely exists in the field of aeronautics, astronautics and weapons. Because of its complexity, it is hard to research or analysis whether using experimental or numerical simulation methods. As a result, establishing an effective and accurate numerical simulation method is important both in theory and practice. In this dissertation, a numerical method using dynamic unstructured grid is studied and software system is established, which can efficiently and exactly simulate multi-body flow problems with complex configuration and complicated relative motion. The reliability of the simulation system is proved by numerical and experimental verification and it has achieved good effect in application.
Firstly, considering the request of efficiency and precision in numerical simulation, the Arbitrary-Lagrangian Eulerian (ALE) framework is chosen to solve 3D time-dependent Euler equations and the Van Leer scheme is applied for spatial discretization. Piecewise linear reconstruction or MUSCL reconstruction is used to obtain second-order spatial accuracy and a multi-stage Runge-Kutta time stepping scheme is adopted for second-order temporal accuracy. To eliminate non-physical oscillations near discontinuities, the limiters of Barth & Jespersen and Venkarakrishnan are employed. Furthermore, the 6DOF (degree of freedom) trajectory equations of rigid body dynamics are coupled in the overall algorithm, in which aerodynamic forces and rigid body movements are updated at the same physics time step with loosing coupling.
Secondly, considering the request for complex configuration and body motion, the dynamic unstructured grid method is studied. The mesh movement strategy is implemented by the combination of mesh deformation and local remeshing. The improved spring analogy model is used to control mesh deformation, which is sufficient for cases with small relative boundary displacement. For cases with relative large boundary displacement, when the mesh elements are severely deformed, Delaunay remeshing method is used to regenerate mesh. Thereon, an automatic technique is studied, which includes the procedure of checking mesh quality, extracting the reconstructed windows, regenerating meshes, finding relationship between new and old grids and transferring solutions from the old mesh to the new one. The new data transfer method, called "moving mesh transfer method", is innovatively proposed to avoid accumulation of interpolation errors. This highly accurate data transferring is implemented by mesh movement strategy, which succeeds in solving one dimensional, two dimensional and three dimensional problems. The "octree" data structure is also used to accelerate the searching operation during interpolation.
Thirdly, considering the verification and validation of numerical method, numerical simulation of the flow field around the space shuttle and a civilian aircraft is performed and the results are consistent with the experiment data and CFD results in references. In addition, an experiment is specially designed on shock tube to validate the numerical method. The numerical simulation of Ping-Pong's trajectory agrees well with those obtained in experiment. This simple and effective experiment can present verification and validation of numerical method, and offer reference for further experiment research and moving body experiment.
Lastly, some multi-body flow problems with complex configuration are studied, such as fairing separation, interior weapon cabin's opening and cluster munitions dispersing. Aimed at the difficulty in simulating the procedure of two bodies separating from tangency to large displacement, a new method called "virtual mesh ventilation method" is introduced, and this method factually reproduces aerodynamic fluctuations at the beginning of fairing separation and flow-induced pressure oscillations in 3D cavity after the weapon cabin's door is open. In the research of fairing separation, after comprehensive analysis of factors such as fairing shape, interfering factors and centroid position, a new separation rule called "centroid backward rule" is proposed according to numerical simulation results with dynamic unstructured grid method, and this rule can be regarded as common criteria to ensure safety in fairing separation. Besides, a cluster munitions dispersing procedure, including cluster munitions rotating, cover ejection and plenty of bullets dispersion, is simulated using dynamic unstructured grid method. Results show that the software is competent for solving extraordinarily complicated problems, and it also offers an effective way to design and validate the cluster munitions.
引文
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