采用滑移网格的二维非定常NS方程数值计算
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摘要
随着新世纪交通工具的发展,列车运行速度不断提高,高速列车的空气动力学研究逐渐凸显出其重要性。磁浮列车作为一种新兴地面交通工具,其高速的特点也使得空气动力学问题更为突出。特别是列车在会车和穿越隧道过程中所遇到的气动问题,相比露天、单列行车要剧烈和严重得多。
由于列车尺度巨大、耗能和试验花费高等特点,全尺度的试验研究迄今仍相当困难和稀少,数值模拟成为有力的应用工具。列车的运动是复杂的三维流场,要尽量准确地描绘一般来说是应用三维数值计算。但纯三维情形下进行完全模拟的网格量和计算量十分庞大,计算效率难以接受。考虑到列车自身长度远大于其直径,则减少一个维度对其进行二维截面数值模拟研究是可行的。
列车是亚声速运动的一个典型,激波则是超声速运动的特有现象。非定常激波绕物体的运动,以及在复杂环境下传播时产生反射、绕射,使得物体与激波之间产生强烈的相互作用,物体表面承受不同的冲击效应,对周边环境也产生强烈的影响。长期以来此类问题一直是开展流动机理研究和进行大规模工程实验的一个重要内容,对飞行器结构设计等方面也有重要意义。
本文分为6章。
第一章是引言,主要介绍了高速列车空气动力学和运动激波问题的研究背景、意义,以及当前国内外的研究进展等,随后对本文工作作了简要介绍。
第二章介绍了计算方法。本文使用有限体积法求解二维无化学反应无源项NS方程,在部分算例中应用了滑移网格技术对运动边界网格进行处理,较好地模拟了存在相对运动的两物体的流场。计算方法上,采用了AUSM+、AUSMPW+和LDFSS三种无粘格式,原始变量、守恒变量两种MUSCL插值,显式Runge-Kutta法、隐式LU双时间步法和双时间步Runge-Kutta法三种时间推进方法。
第三章是非定常数值计算验证。通过经典的SOD激波管算例,应用第二章中涉及的各种方法格式进行了全面详细的计算,验证了计算程序的可靠性,对不同方法的计算结果进行了分析比较,选取表现较好的格式开展正式计算。
第四章是对非定常运动激波的模拟。在前述研究基础上,应用选定格式对激波绕圆柱的非定常流动作了数值计算,给出了不同时刻流场分布,较好地模拟出了管道内激波绕流问题,包括尾部交汇、固壁反射,形成复杂波系等现象,比较了显隐式两种非定常时间算法。然后对运动激波与超声速飞行物体头激波及物体自身相互作用的两波干扰现象进行了模拟,给出了不同时刻流场压强和密度分布,以及物体上下表面各点压强变化情况,基本准确地描绘了该干扰过程。
第五章是列车运动模拟,对二维情形下高速列车穿越隧道问题展开计算,分析了运动过程中车体及隧道内流场的气动特性,给出了各时刻对称面上压强分布及车体上固定点和出口的压强分布,对尾部流动分离现象进行了初步研究并分别描绘出层流、湍流工况下流场特征,总结了过程中压力波的产生、传播、反射等问题。计算结果与既有参考结果吻合较好,符合一般钝体绕流规律。
随后,对两列车在露天交会的情况进行了简单模拟。描绘了各时刻整体流场及两车上不同测点处的压强变化,分析了该过程中压力波的生成、运动、碰撞和与车体的相互作用等,给出了各点的最大压差。
最后,在结束语中,我们对已有的工作作了总结,对本文所采用的两种显隐时间推进方法进行了概括比较,指出存在的不足和今后的发展方向。
As the traffic vehicles are developing in new century, trains run faster and faster, and the investigation on aerodynamics of high-speed trains becomes significant. As a new kind of traffic vehicle, magnetic levitation(maglev)'s characteristic of high speed makes the aerodynamics problems more serious. Especially, the problems occurred when one train passes through tunels or meets another one are usually more intense than that in open-air or runs solely.
Because of the large size of trains, high energy consumption and expensive cost, full scale experiment is rather difficult and exiguous, so numerical simulations become powerful tools. Generally speaking, train's movement is a complicated 3-d problem and we should solve it by 3-d numerical calculation for high accuracy, which means huge grid points and unacceptable computational efficiency. As the train has great length-to-diameter ratio, it's reasonable to simulate it in two dimensions instead of three dimensions.
As the train movement is a classical model of subsonic flow, the shock waves are unique phenomenon of supersonic flow, which frequently appear in industry, military and nature, such as supersonic flight vehicle, pipe flow, discontinuity propagation and so on. Unsteady shock waves move around objects, and reflect when they spread in complex environment, which can cause strong effect, make large difference in flow parameter among different regions, generate different impact on the surface of objects, bring consuming impact to environment around too. So far, these problems are always significant in flow mechanism investgation, engineering experiment and aircraft configuration design.
This paper is composed of 6 chapters.
In chapter 1, we introduced the background and significance of the aerodynamics of high-speed trains and unsteady shock waves. Current investigation in the world was introduced too. Then, a description was given about the work in the paper.
In chapter 2, we introduced the numerical methods. We've used the finite volume scheme to discretize 2-d NS equations without chemical reaction and source, then simulated unsteady supersonic Shockwaves and calculated aerodynamics problems of subsonic trains. By the application of sliding mesh which is used to process the movement of boundary, flow field is well simulated. Three inviscid flux schemes:AUSM+, AUSMPW+ and LDFSS, two kind of MUSCL interpolation scheme: primitive variables, conservative variables, three kind of time advance method: explicit Runge-Kutta scheme, implicit LU dual time step scheme and dual time step Runge-Kutta scheme are used in this paper.
In the third chapter, through the calculation of a classic model:SOD shock wave tube, we've validated all the methods involved in chapter 2. The dependability of the method has been validated and results got from different schemes have been analysed and compared. Then the best one was chosen.
In chapter 4, on the foundation of the above researches, we numerically simulated unsteady flow of shock waves moving around a cylinder. The development of flow fields with time was got and shown, which confirmed the simulation is well done, including tail flow, reflection by solid surfaces and production of complex waves. The two unsteady time-marching methods were compared too. Then, the author made another simulation about two shockwaves:one is moving while the other is fixed in front of a flying object and they meet. Also, pressure distribution of the flow field was shown, as well as the change of the points on the surfaces. The interference was described accurately.
In chapter 5, the problem of a high-speed train passing through a tunel has been simulated. Aerodynamics characteristics of the tunel and train were analysed, pressure distribution of different time on the symmetrical line and points on the train and the exit was shown below, while the flow separation behind the tail was researched and the characteristics of flow field were represented at situations of laminar flow and turbulent flow. The result is familiar to the reference, accords with general flow rules.
Then, a simple simulation about a train meeting another on the open air has been done. We've not only got the whole flow field situation and pressure changes on different points of the trains, but also given a analysis about waves' birth, moving, impact and effect in the process, worked out the maximum pressure.
At last, the two time advance methods were compared in detail and a summary about the work has been made.
由于列车尺度巨大、耗能和试验花费高等特点,全尺度的试验研究迄今仍相当困难和稀少,数值模拟成为有力的应用工具。列车的运动是复杂的三维流场,要尽量准确地描绘一般来说是应用三维数值计算。但纯三维情形下进行完全模拟的网格量和计算量十分庞大,计算效率难以接受。考虑到列车自身长度远大于其直径,则减少一个维度对其进行二维截面数值模拟研究是可行的。
列车是亚声速运动的一个典型,激波则是超声速运动的特有现象。非定常激波绕物体的运动,以及在复杂环境下传播时产生反射、绕射,使得物体与激波之间产生强烈的相互作用,物体表面承受不同的冲击效应,对周边环境也产生强烈的影响。长期以来此类问题一直是开展流动机理研究和进行大规模工程实验的一个重要内容,对飞行器结构设计等方面也有重要意义。
本文分为6章。
第一章是引言,主要介绍了高速列车空气动力学和运动激波问题的研究背景、意义,以及当前国内外的研究进展等,随后对本文工作作了简要介绍。
第二章介绍了计算方法。本文使用有限体积法求解二维无化学反应无源项NS方程,在部分算例中应用了滑移网格技术对运动边界网格进行处理,较好地模拟了存在相对运动的两物体的流场。计算方法上,采用了AUSM+、AUSMPW+和LDFSS三种无粘格式,原始变量、守恒变量两种MUSCL插值,显式Runge-Kutta法、隐式LU双时间步法和双时间步Runge-Kutta法三种时间推进方法。
第三章是非定常数值计算验证。通过经典的SOD激波管算例,应用第二章中涉及的各种方法格式进行了全面详细的计算,验证了计算程序的可靠性,对不同方法的计算结果进行了分析比较,选取表现较好的格式开展正式计算。
第四章是对非定常运动激波的模拟。在前述研究基础上,应用选定格式对激波绕圆柱的非定常流动作了数值计算,给出了不同时刻流场分布,较好地模拟出了管道内激波绕流问题,包括尾部交汇、固壁反射,形成复杂波系等现象,比较了显隐式两种非定常时间算法。然后对运动激波与超声速飞行物体头激波及物体自身相互作用的两波干扰现象进行了模拟,给出了不同时刻流场压强和密度分布,以及物体上下表面各点压强变化情况,基本准确地描绘了该干扰过程。
第五章是列车运动模拟,对二维情形下高速列车穿越隧道问题展开计算,分析了运动过程中车体及隧道内流场的气动特性,给出了各时刻对称面上压强分布及车体上固定点和出口的压强分布,对尾部流动分离现象进行了初步研究并分别描绘出层流、湍流工况下流场特征,总结了过程中压力波的产生、传播、反射等问题。计算结果与既有参考结果吻合较好,符合一般钝体绕流规律。
随后,对两列车在露天交会的情况进行了简单模拟。描绘了各时刻整体流场及两车上不同测点处的压强变化,分析了该过程中压力波的生成、运动、碰撞和与车体的相互作用等,给出了各点的最大压差。
最后,在结束语中,我们对已有的工作作了总结,对本文所采用的两种显隐时间推进方法进行了概括比较,指出存在的不足和今后的发展方向。
As the traffic vehicles are developing in new century, trains run faster and faster, and the investigation on aerodynamics of high-speed trains becomes significant. As a new kind of traffic vehicle, magnetic levitation(maglev)'s characteristic of high speed makes the aerodynamics problems more serious. Especially, the problems occurred when one train passes through tunels or meets another one are usually more intense than that in open-air or runs solely.
Because of the large size of trains, high energy consumption and expensive cost, full scale experiment is rather difficult and exiguous, so numerical simulations become powerful tools. Generally speaking, train's movement is a complicated 3-d problem and we should solve it by 3-d numerical calculation for high accuracy, which means huge grid points and unacceptable computational efficiency. As the train has great length-to-diameter ratio, it's reasonable to simulate it in two dimensions instead of three dimensions.
As the train movement is a classical model of subsonic flow, the shock waves are unique phenomenon of supersonic flow, which frequently appear in industry, military and nature, such as supersonic flight vehicle, pipe flow, discontinuity propagation and so on. Unsteady shock waves move around objects, and reflect when they spread in complex environment, which can cause strong effect, make large difference in flow parameter among different regions, generate different impact on the surface of objects, bring consuming impact to environment around too. So far, these problems are always significant in flow mechanism investgation, engineering experiment and aircraft configuration design.
This paper is composed of 6 chapters.
In chapter 1, we introduced the background and significance of the aerodynamics of high-speed trains and unsteady shock waves. Current investigation in the world was introduced too. Then, a description was given about the work in the paper.
In chapter 2, we introduced the numerical methods. We've used the finite volume scheme to discretize 2-d NS equations without chemical reaction and source, then simulated unsteady supersonic Shockwaves and calculated aerodynamics problems of subsonic trains. By the application of sliding mesh which is used to process the movement of boundary, flow field is well simulated. Three inviscid flux schemes:AUSM+, AUSMPW+ and LDFSS, two kind of MUSCL interpolation scheme: primitive variables, conservative variables, three kind of time advance method: explicit Runge-Kutta scheme, implicit LU dual time step scheme and dual time step Runge-Kutta scheme are used in this paper.
In the third chapter, through the calculation of a classic model:SOD shock wave tube, we've validated all the methods involved in chapter 2. The dependability of the method has been validated and results got from different schemes have been analysed and compared. Then the best one was chosen.
In chapter 4, on the foundation of the above researches, we numerically simulated unsteady flow of shock waves moving around a cylinder. The development of flow fields with time was got and shown, which confirmed the simulation is well done, including tail flow, reflection by solid surfaces and production of complex waves. The two unsteady time-marching methods were compared too. Then, the author made another simulation about two shockwaves:one is moving while the other is fixed in front of a flying object and they meet. Also, pressure distribution of the flow field was shown, as well as the change of the points on the surfaces. The interference was described accurately.
In chapter 5, the problem of a high-speed train passing through a tunel has been simulated. Aerodynamics characteristics of the tunel and train were analysed, pressure distribution of different time on the symmetrical line and points on the train and the exit was shown below, while the flow separation behind the tail was researched and the characteristics of flow field were represented at situations of laminar flow and turbulent flow. The result is familiar to the reference, accords with general flow rules.
Then, a simple simulation about a train meeting another on the open air has been done. We've not only got the whole flow field situation and pressure changes on different points of the trains, but also given a analysis about waves' birth, moving, impact and effect in the process, worked out the maximum pressure.
At last, the two time advance methods were compared in detail and a summary about the work has been made.
引文
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[2]吴祥明,常文森,刘万明,上海高速磁浮列车及磁浮技术发展刍议,综合运输,2005年1月
[3]田红旗,中国列车空气动力学研究进展,交通运输工程学报,Vol.6,No.1,2006
[4]Torii A,Ito J.,Development of the series 700 Shinkansen train-set(improvement of noise level),Proc World Congr Railw Res,Railr Tech Res Inst(CD-Rom),Tokyo,1999
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