间断有限元数值方法研究及复杂冲击流场的数值模拟
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摘要
论文以国防预研重点项目为背景,以某新型多管火箭武器为研究对象,针对复杂燃气射流的流场特点及多管火箭武器燃气冲击流场的动态变化分别进行了一系列的研究和探索,并取得了一定的研究成果。
1.深入研究了间断有限元方法的基本理论,并将其推广到轴对称Euler方程组进行数值求解,通过Sod激波管、Emery前台阶绕射和环形激波聚焦三个典型问题的数值计算,验证了理论推导的正确性、程序的可靠性以及本文方法具有较强的鲁棒性等特点。
2.采用发展后的间断有限元方法分别研究了高度欠膨胀自由射流、超音速伴随射流和燃气流对平板的冲击等问题,展示了更加详细的流场波系结构、中心轴线上的物理量分布参数以及平板表面的压力变化规律,并与目前已有的实验数据和其它格式的计算结果进行了比较,发现:
a)对高度欠膨胀自由射流,在相同的流动条件下,采用间断有限元方法捕捉到的流场波系结构非常清晰,通过与其它数值格式的计算结果比较发现二者符合较好,但就马赫盘位置而言,本文方法的计算结果与实验测量和理论预估值更加接近,相对误差均小于1%;
b)对超音速伴随射流,在相同的计算条件下,采用间断有限方法能够捕捉到更加详细的流场波系结构,通过与其它数值格式的计算结果比较发现二者符合较好,但就马赫盘而言,在给定的来流马赫数条件下,流场中马赫盘的直径会明显变小,但并未消失,这与实验纹影照片描述的流场特点吻合较好;
c)对平板冲击射流,采用间断有限元方法能够正确反映出超音速射流遇平板后的激波演化过程,平板表面的压力变化规律和压力峰值的侧移与已有的研究成果相符。
3.在已有工作的基础上,将间断有限元方法进一步推广到可压缩多介质流体流动的数值计算,并通过大量的数值试验证明了本文方法可以精确地追踪运动界面,数值解具有较高的分辨率,为今后将其应用于多相燃气射流的数值计算奠定了基础。
4.研究了动网格生成方法,将自编的udf程序动态的连接到CFD软件,根据火箭的受力情况来计算网格运动的速度,对网格不断地作相应的调整,在每一时间步长结构发生变形时,及时给CFD计算提供这一信息,以此来实现火箭燃气冲击流场的动态模拟。
5.利用动网格技术,对不同发射姿态下多管火箭武器燃气冲击流场进行了数值模拟,研究了单枚火箭弹在0度俯仰角发射姿态下,燃气流冲击力和冲击力矩随火箭弹飞离炮口距离的变化规律,比较了各种发射状态下燃气流冲击流场结构的特点,同时分析了燃气流对发射装置和仪器仓表面的热冲击效应。
本文模拟得到的这些数据可以为武器系统各大型构件与传动系统的刚度和强度设计以及进一步样机的制作提供可借鉴的理论指导,同时还可为燃气流的烧蚀与热防护设计提供必须的理论分析参数。
Investigation object of this dissertation is multiple launch rocket system based on the project supported by the National Defense Key Pre-Research Foundation. A series of groundbreaking research and exploration including the flow field characteristics of complex gas jet and dynamic variety of multiple launch rocket system impinging flow field are carried out respectively and some beneficial results are obtained as follows:
1. Three representative problems including sod shock tube, forward-facing step and focusing of toroidal shock wave are calculated numerically by using Runge-Kutta Discontinuous Galerkin Finite Element Method (RKDG-FEM) that is developed to solve axisymmetric Euler equations. The computed results indicate that the theoretical derivation is validity, the program is efficient, and the presented method is robust.
2. High underexpanded free jet, supersonic coflowing and impinging jet on flat are studied respectively by using RKDG-FEM. More detailed flowfield wave structures, flow properties distributions along the jet axis and the pressure distributions along the impinging wall are obtained. Moreover, the comparisons between the computed results and those of other experiments and numerical schemes show that
a) Flowfield wave structures captured at high underexpanded free jet by using RKDG-FEM are very distinct. The comparisons between the computed results and those of other numerical schemes are good agreement. But as for Mach disk location, the computed results shows relatively better agreement between our numerical results and those of experiment and theoretical estimate under the same flow conditions. The relative errors are less than 1%.
b) Wave structures of flow field captured at supersonic coflowing by using RKDG-FEM reflect more detailed flow characteristics. The comparisons between the computed results and those of other numerical schemes are good agreement. For Mach disk, the diameter of which is obviously shortened but not disappear. It is better agreement with the results of experiment image.
c) Shock wave evolution progresses of impinging jet on flat are simulated correctly by using RKDG-FEM and pressure variations on the flat surface and the moving of pressure peak are coincident with existed results.
3. Discontinuous galerkin finite element method is futher developed to solve compressible multimedia flows based on the present work. A series of numerical experiment demonstrate that this method is capable of capturing moving interface precisely and numerical solutions have high resulation, which establish the foundation for simulating multiphase gas jet using discontinuous galerkin finite element method.
4. Dynamic mesh generation technique is studied in this dissertation. Dynamic simulation of rocket impinging jet flow field is performed through CFD software connecting user defined function(udf) based on dynamic mesh technique, where mesh is readjusted continuously according to the rocket projectile movement at each time step.
5. Impinging jet flow field of multiple launch rocket system are simulated numerically under the different launch state by using dynamic grid technique, and the variations of impingement force and impingement moment of rocket exhaust with movement distance of rocket projectile are obtained under a specified launch state. Furthermore, the characteristics of impinging jet flow field structure are compared under the different launch state and thermal impact effect of rocket plume to launch device are analyzed.
These computed results may provide some theoretical guidance for rigidity and intensity designing of large components and gearing of the weapon system and the next model mechine making. Moreover, they may provide some necessary parameters for corrosion protection of gas jet.
1.深入研究了间断有限元方法的基本理论,并将其推广到轴对称Euler方程组进行数值求解,通过Sod激波管、Emery前台阶绕射和环形激波聚焦三个典型问题的数值计算,验证了理论推导的正确性、程序的可靠性以及本文方法具有较强的鲁棒性等特点。
2.采用发展后的间断有限元方法分别研究了高度欠膨胀自由射流、超音速伴随射流和燃气流对平板的冲击等问题,展示了更加详细的流场波系结构、中心轴线上的物理量分布参数以及平板表面的压力变化规律,并与目前已有的实验数据和其它格式的计算结果进行了比较,发现:
a)对高度欠膨胀自由射流,在相同的流动条件下,采用间断有限元方法捕捉到的流场波系结构非常清晰,通过与其它数值格式的计算结果比较发现二者符合较好,但就马赫盘位置而言,本文方法的计算结果与实验测量和理论预估值更加接近,相对误差均小于1%;
b)对超音速伴随射流,在相同的计算条件下,采用间断有限方法能够捕捉到更加详细的流场波系结构,通过与其它数值格式的计算结果比较发现二者符合较好,但就马赫盘而言,在给定的来流马赫数条件下,流场中马赫盘的直径会明显变小,但并未消失,这与实验纹影照片描述的流场特点吻合较好;
c)对平板冲击射流,采用间断有限元方法能够正确反映出超音速射流遇平板后的激波演化过程,平板表面的压力变化规律和压力峰值的侧移与已有的研究成果相符。
3.在已有工作的基础上,将间断有限元方法进一步推广到可压缩多介质流体流动的数值计算,并通过大量的数值试验证明了本文方法可以精确地追踪运动界面,数值解具有较高的分辨率,为今后将其应用于多相燃气射流的数值计算奠定了基础。
4.研究了动网格生成方法,将自编的udf程序动态的连接到CFD软件,根据火箭的受力情况来计算网格运动的速度,对网格不断地作相应的调整,在每一时间步长结构发生变形时,及时给CFD计算提供这一信息,以此来实现火箭燃气冲击流场的动态模拟。
5.利用动网格技术,对不同发射姿态下多管火箭武器燃气冲击流场进行了数值模拟,研究了单枚火箭弹在0度俯仰角发射姿态下,燃气流冲击力和冲击力矩随火箭弹飞离炮口距离的变化规律,比较了各种发射状态下燃气流冲击流场结构的特点,同时分析了燃气流对发射装置和仪器仓表面的热冲击效应。
本文模拟得到的这些数据可以为武器系统各大型构件与传动系统的刚度和强度设计以及进一步样机的制作提供可借鉴的理论指导,同时还可为燃气流的烧蚀与热防护设计提供必须的理论分析参数。
Investigation object of this dissertation is multiple launch rocket system based on the project supported by the National Defense Key Pre-Research Foundation. A series of groundbreaking research and exploration including the flow field characteristics of complex gas jet and dynamic variety of multiple launch rocket system impinging flow field are carried out respectively and some beneficial results are obtained as follows:
1. Three representative problems including sod shock tube, forward-facing step and focusing of toroidal shock wave are calculated numerically by using Runge-Kutta Discontinuous Galerkin Finite Element Method (RKDG-FEM) that is developed to solve axisymmetric Euler equations. The computed results indicate that the theoretical derivation is validity, the program is efficient, and the presented method is robust.
2. High underexpanded free jet, supersonic coflowing and impinging jet on flat are studied respectively by using RKDG-FEM. More detailed flowfield wave structures, flow properties distributions along the jet axis and the pressure distributions along the impinging wall are obtained. Moreover, the comparisons between the computed results and those of other experiments and numerical schemes show that
a) Flowfield wave structures captured at high underexpanded free jet by using RKDG-FEM are very distinct. The comparisons between the computed results and those of other numerical schemes are good agreement. But as for Mach disk location, the computed results shows relatively better agreement between our numerical results and those of experiment and theoretical estimate under the same flow conditions. The relative errors are less than 1%.
b) Wave structures of flow field captured at supersonic coflowing by using RKDG-FEM reflect more detailed flow characteristics. The comparisons between the computed results and those of other numerical schemes are good agreement. For Mach disk, the diameter of which is obviously shortened but not disappear. It is better agreement with the results of experiment image.
c) Shock wave evolution progresses of impinging jet on flat are simulated correctly by using RKDG-FEM and pressure variations on the flat surface and the moving of pressure peak are coincident with existed results.
3. Discontinuous galerkin finite element method is futher developed to solve compressible multimedia flows based on the present work. A series of numerical experiment demonstrate that this method is capable of capturing moving interface precisely and numerical solutions have high resulation, which establish the foundation for simulating multiphase gas jet using discontinuous galerkin finite element method.
4. Dynamic mesh generation technique is studied in this dissertation. Dynamic simulation of rocket impinging jet flow field is performed through CFD software connecting user defined function(udf) based on dynamic mesh technique, where mesh is readjusted continuously according to the rocket projectile movement at each time step.
5. Impinging jet flow field of multiple launch rocket system are simulated numerically under the different launch state by using dynamic grid technique, and the variations of impingement force and impingement moment of rocket exhaust with movement distance of rocket projectile are obtained under a specified launch state. Furthermore, the characteristics of impinging jet flow field structure are compared under the different launch state and thermal impact effect of rocket plume to launch device are analyzed.
These computed results may provide some theoretical guidance for rigidity and intensity designing of large components and gearing of the weapon system and the next model mechine making. Moreover, they may provide some necessary parameters for corrosion protection of gas jet.
引文
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