【作者】 齐昕；

【导师】 宁利中；

【作者基本信息】 西安理工大学 ， 水力学及河流动力学， 2007， 硕士

【摘要】 非线性科学是目前世界范围内引起广泛关注的研究课题之一。日常中经常见到的自然现象,如大气,海洋、水库的对流运动等都处在远离热平衡态的非平衡开放系统中。在流体中当上下界面的温度差足够大时,起着不稳定化作用的浮力作用将超过粘性和热传导的稳定化效应,于是系统将出现不稳定的热对流现象。对这些现象的深入理解无论是在人们与自然和谐共处方面还是在控制利用自然方面都是不可缺少的。Rayleigh-Benard对流是研究这些现象的典型模型之一,它具有实验易于控制,对流运动支配方程明确等优点。所谓Rayleigh-Benard对流,就是在一个封闭的空腔内,其上表面温度恒定,下表面加热,从而形成温度差导致空腔内流体运动的流动现象。因此,利用Rayleigh-Benard对流模型,系统的研究探讨对流运动的稳定性、时空结构及非线性动力学特性具有一定的代表性、非常重要的实际意义和理论价值。到目前为止,前人通过各种实验手段及计算手段,已经对Rayleigh-Benard对流中出现的各种行进波状态有了一定的研究。观察到了均匀行进波(TW),Blinking行进波(BTW),局部行进波(LTW),双局部行进波(DLTW),定常对流状态(SOC)等,并获得了这些对流状态的特点。本文主要是基于流体力学基本方程组,使用SIMPLE算法来模拟二维矩形腔体中混合流体的Rayleigh-Benard对流运动。通过变化控制参数-瑞利数Ra,来计算不同分离比,不同长高比下腔体中出现的行进波状态,观察到了前人未见到的ψ～-10-1数量级时稳定的Counter propagating wave(CPW),含有缺陷的TW状态,以及Undulation traveling wave(UTW)。通过对比不同瑞利数下出现的同种行进波状态,探讨了这几种行进波状态的时空结构,及其存在的瑞利数r范围,并得出了这些行进波状态的运动特点;通过对比不同长高比,分离比下的同种行进波,分析出了行进波状态对长高比及分离比的依赖性。更多还原

【Abstract】 The researches of nonlinear science currently cause extensive concern all over the world. The natural phenomena which we usually see, such as the convection in atmosphere, the ocean, the reservoir and so on, are all in nonequilibrium open system away from hot equilibrium. For fluid, if the temperature difference applied across the fluid layer is large enough, the buoyancy function causing instability will exceed the stability of viscosity and hot conduction, the system will appear unsteady convection phenomenon. The deep research for these phenomena is indispensable both in harmonious coexistence between human and nature, and in controlling, using nature.Rayleigh-Benard convection is one of the typical models for the research of these phenomena. Its experiment is easy to control and the equation for convection is clear. The Rayleigh-Benard convection is that, in one close channel, the top surface keeps steady temperature and the bottom keeps heated, the temperature difference will cause the fluid convection in channel. Therefore, using Rayleigh-Benard convection model for the research of the convection stability, spatiotemporal structure and the nonlinear dynamics has certain representative, very important significance and theory value.So far, investigators have got various traveing waves in Rayleigh-Benard convection by experiments and calculations. They observed such as traveing wave(TW), blinking traveling wave(BTW), localized traveling wave(LTW), double localized traveling wave(DLTW), stationary overturning convection(SOC), and found the characteristics of these states. This thesis uses two-dimensional hydrodynamic equations to simulate Rayleigh-Benard convection in binary fluid mixtures in two dimensional rectangular cell. According to changing Rayleigh number and computing traveling wave states in different separation ratio and aspect ratio, we have observed steady Counter propagating wave(CPW)state which has not been seen before,TW state with defect and Undulation traveling wave(UTW)state. By the comparison between the same type of traveling waves with different rayleigh number, found out the spatiotemporal structures of different traveling wave state and their ranges, gained the characteristics of these traveling wave states; by the comparison between the same type of traveling waves with different separation ratio and aspect ratio, discussed the dependence of the traveling wave on the separation ratio and aspect ratio.更多还原