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Rayleigh-Benard对流是研究非平衡对流的斑图(Pattem)及非线性动力学特性的典型模型之一。据此,通过流体力学基本方程组的数值模拟,探讨了分离比沙-0.4时双流体局部行波的形成过程;讨论了双流体局部行波流速场、温度场、浓度场、平均浓度流的结构和特性,分析了局部行波被局部化的原因。研究结果表明:局部行波始终在背离端壁方向传播并被限定在此端,它存在于腔体左端还是右端取决于经过过渡后对传波中最终控制腔体的一支行波的传播方向;在局部行波的存在范围内(1.519≤r≤1.604),随相对瑞利数增加,衡量对流振幅的最大垂直流速、特征通过流体层的垂直热流量的努塞尔数、局部行波宽度等都在增加,但反映浓度特性的混合参数减小。 相似文献
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通过二维流体力学基本方程组模拟了具有较强Soret效应(分离比ψ=-0.47)的混合流体在极小长高比(Γ=4)腔体内的Rayleigh-Benard对流运动.研究了极小长高比行波对流的动力学特性,得到了稳定的Undulation行波存在的r值范围,给出了稳定后的Undulation行波摆动周期Tp的变化规律,分析了极小长高比行波对流的r依赖性及稳定性.首次发现极小长高比Γ=4时,与长高比Γ=12和Γ=8时相比,在腔体两端的滚动生成和消失的现象不再出现.讨论了长高比对Undulation行波向行波过渡的影响. 相似文献
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混合流体Rayleigh-Benard对流是研究对流稳定性,时空结构和非线性特性的典型模型之一。本文利用流体力学扰动方程组的数值模拟,讨论了偏离传导状态具有强SORET效应的混合流体行进波对流的温度场和浓度场的成长过程,分析了充分发展对流情况下的对流振幅,Nusselt数及混合参数与相对瑞利数的关系。并给出了行进波相速度对相对瑞利数的依赖关系。结果说明混合参数的曲线与行进波相速度的分布曲线是类似的。文末,给出了垂直速度,温度和浓度场的分布并讨论了相对瑞利数对场的分布及不同场之间的相位差的影响。 相似文献
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Rayleigh-Benard模型是研究对流稳定性,时空结构和非线性特性的典型模型之一。本文的兴趣集中在二维矩形腔体中混合流体对流场的结构方面。利用SIMPLE算法数值求解流体力学方程组,模拟了充分发展的二维矩形腔体中混合流体对流。结果说明偏离传导失去稳定的系统经过亚临界分叉产生了振动对流。进一步,我们给出了分叉曲线及其沿分叉曲线的上部分支三个Rayleigh数对应的对流图案的垂直速度场,流线,温度场,浓度场和Shadowgraph强度的等值线图。所有场的结构分析表明浓度场及Shadowgraph强度的等值线图可以很好的特征行进波的运动特性。 相似文献
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基于流体力学方程组,对长高比Γ=30腔体内混合流体对流中摆动行波的时空结构进行了数值模拟。结果发现:当分离比Ψ=-0.6,-0.4时,在摆动行波存在的下临界附近,摆动行波的对流滚动有消失也有产生,对流平均波数在周期内变化;在摆动行波存在的上临界附近,摆动行波的对流滚动既无消失也无产生,对流平均波数保持为常数。随着相对瑞利数r的增加,对流滚动的摆动幅度和摆动周期明显减小。当分离比Ψ=-0.6时,摆动行波是准周期的;当分离比Ψ=-0.4时,摆动行波是周期的;当分离比Ψ=-0.2时,在摆动行波存在的下临界附近,观察到了一种沿着行波的对称轴线两侧发生对称的摆动行波的新型对流结构。在摆动行波存在的上临界附近,摆动行波是无周期的。随着分离比负值减小,摆动行波存在的上、下限下移,摆动行波存在的稳定区间Δr减小。 相似文献
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利用Simple算法对流体力学基本方程组进行了数值模拟,初步研究了局部行波对流斑图选择的初值依赖性问题。分离比ψ-(28)6.0、相对瑞利数r(28)2.1时依赖于初值的有间歇性缺陷的行波,位于腔体右端的局部行波和位于腔体左端的局部行波的多重稳定性;分离比ψ(28)-0.6、相对瑞利数r在1.855~2.118范围内依赖于初值的位于腔体右端的局部行波和位于腔体左端的局部行波的多重稳定性等。虽然在不同初值下,局部行波存在的区间有所不同,局部行波的空间位置有所不同,但局部行波的特性参数变化规律基本一致。结果说明混合流体局部行波对流斑图选择的初值依赖性是存在的。 相似文献
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阶梯压电层合梁的波动动力学特性 总被引:2,自引:0,他引:2
采用行波理论系统地研究了压电阶梯梁的自由振动分析以及强迫响应的分析方法. 基于分布
参数理论研究了压电阶梯梁的波传播特性,忽略柔性梁横向剪切和转动惯量的影响,给出了
梁的轴向和横向的简谐波解. 将压电阶梯梁离散化为单元,考虑压电片的刚度和质量的影响,
建立了节点散射模型. 应用位移连续和力平衡条件,推导了节点的波反射和波传递矩阵,在
此基础上,引入波循环矩阵的概念,给出波循环矩阵、波传递系数矩阵的确定方法. 应用波
循环矩阵可以有效地计算结构的固有频率. 另外,应用波传递系数研究了压电陶瓷作动器位
置对其驱动能力的影响. 得出两个主要结论:1)作动器靠近悬臂梁固定端将有较强的驱动
能力,悬臂梁边界反射行波产生弯曲消失波有利于增大压电波的模态传递系数;2)模态传
递系数与固有频率的灵敏度密切相关,波传递系数越大, 对应该处固有频率变化灵敏度越大.
另外,数值算例表明了行波方法比有限元方法具有更高的计算精度. 相似文献
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从流体层底部加热引起的对流运动是研究非平衡对流的时空结构或斑图(Pattern)及非线性动力学特性的典型模型之一.本文通过流体力学基本方程组的数值模拟,探讨了具有强Soret效应的混合流体局部行进波的形成过程,发现当分离比ψ=-0.6时,在局部行进波的存在范围内,向局部行进波过渡的不同过程依赖于相对瑞利数r.进一步,讨论了具有强Soret效应的混合流体局部行进波流速场,温度场, 浓度场的结构和特性,分析了局部行进波的存在区间对分离比ψ的依赖性.发现随着Soret效应的增强或负分离比ψ的绝对值的增加,局部行进波稳定存在的区间Δr也在增加. 相似文献
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W. Kissling M. McGuinness A. McNabb G. Weir S. White R. Young 《Transport in Porous Media》1992,7(3):223-253
In the absence of capillarity the single-component two-phase porous medium equations have the structure of a nonlinear parabolic pressure (equivalently, temperature) diffusion equation, with derivative coupling to a nonlinear hyperbolic saturation wave equation. The mixed parabolic-hyperbolic system is capable of substaining saturation shock waves. The Rankine-Hugoniot equations show that the volume flux is continuous across such a shock. In this paper we focus on the horizontal one-dimensional flow of water and steam through a block of porous material within a geothermal reservoir. Starting from a state of steady flow we study the reaction of the system to simple changes in boundary conditions. Exact results are obtainable only numerically, but in some cases analytic approximations can be derived. When pressure diffusion occurs much faster than saturation convection, the numerical results can be described satisfactorily in terms of either saturation expansion fans, or isolated saturation shocks. At early times, pressure and saturation profiles are functionally related. At intermediate times, boundary effects become apparent. At late times, saturation convection dominates and eventually a steady-state is established. When both pressure diffusion and saturation convection occur on the same timescale, initial simple shock profiles evolve into multiple shocks, for which no theory is currently available. Finally, a parameter-free system of equations is obtained which satisfactorily represents a particular case of the exact equations. 相似文献
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E. Casella 《Journal of Mathematical Fluid Mechanics》2003,5(1):1-16
In this paper we show some regularity and uniqueness results of weak solutions of the Stefan problem with convection, in two and three-dimensional cases. The mathematical formulation adopted is based on the enthalpy method and the convection is described by the Navier-Stokes system. 相似文献
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I. S. Shivakumara Jinho Lee S. Suresh Kumar N. Devaraju 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(11):1697-1715
The linear and nonlinear stability of double diffusive convection in a layer of couple stress fluid–saturated porous medium
is theoretically investigated in this work. Applying the linear stability theory, the criterion for the onset of steady and
oscillatory convection is obtained. Emphasizing the presence of couple stresses, it is shown that their effect is to delay
the onset of convection and oscillatory convection always occurs at a lower value of the Rayleigh number at which steady convection
sets in. The nonlinear stability analysis is carried out by constructing a system of nonlinear autonomous ordinary differential
equations using a truncated representation of Fourier series method and also employing modified perturbation theory with the
help of self-adjoint operator technique. The results obtained from these two methods are found to complement each other. Besides,
heat and mass transport are calculated in terms of Nusselt numbers. In addition, the transient behavior of Nusselt numbers
is analyzed by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta–Gill method.
Streamlines, isotherms, and isohalines are also displayed. 相似文献
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Daniel N. Riahi 《Transport in Porous Media》2008,72(1):121-138
We consider the problem of mixed oscillatory and steady modes of nonlinear compositional convection in horizontal mushy layers
during the solidification of binary alloys. Under a near-eutectic approximation and the limit of large far-field temperature,
we determine a number of two- and three-dimensional weakly nonlinear mixed solutions, and the stability of these solutions
with respect to arbitrary three-dimensional disturbances is then investigated. The present investigation is an extension of
the problem of mixed oscillatory and steady modes of convection, which was investigated by Riahi (J Fluid Mech 517: 71–101,
2004), where some calculated results were inaccurate due to the presence of a singular point in the equation for the linear
frequency. Here we resolve the problem and find some significant new results. In particular, over a wide range of the parameter
values, we find that the properties of the preferred and stable solution in the form of particular subcritical mixed standing
and steady hexagons appeared to be now in much better agreement with the available experimental results (Tai et al., Nature
359:406–408, 1992) than the one reported in Riahi (J Fluid Mech 517:71–101, 2004). We also determined a number of new types
of preferred supercritical solutions, which can be preferred over particular values of the parameters and at relatively higher
values of the amplitude of convection. 相似文献
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In this work, we present a total variation diminishing (TVD) scheme in the zero relaxation limit for nonlinear hyperbolic conservation law using flux limiters within the framework of a relaxation system that converts a nonlinear conservation law into a system of linear convection equations with nonlinear source terms. We construct a numerical flux for space discretization of the obtained relaxation system and modify the definition of the smoothness parameter depending on the direction of the flow so that the scheme obeys the physical property of hyperbolicity. The advantages of the proposed scheme are that it can give second‐order accuracy everywhere without introducing oscillations for 1‐D problems (at least with) smooth initial condition. Also, the proposed scheme is more efficient as it works for any non‐zero constant value of the flux limiter ? ? [0, 1], where other TVD schemes fail. The resulting scheme is shown to be TVD in the zero relaxation limit for 1‐D scalar equations. Bound for the limiter function is obtained. Numerical results support the theoretical results. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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The linear and weakly nonlinear thermal convection in a rotating porous layer is investigated by constructing a simplified
model involving a system of fifth-order nonlinear ordinary differential equations. The flow in the porous medium is described
by Lap wood-Brinkman-extended Darcy model with fluid viscosity different from effective viscosity. Conditions for the occurrence
of possible bifurcations are obtained. It is established that Hopf bifurcation is possible only at a lower value of the Rayleigh
number than that of simple bifurcation. In contrast to the non-rotating case, it is found that the ratio of viscosities as
well as the Darcy number plays a dual role on the steady onset and some important observations are made on the stability characteristics
of the system. The results obtained from weakly nonlinear theory reveal that, the steady bifurcating solution may be either
sub-critical or supercritical depending on the choice of physical parameters. Heat transfer is calculated in terms of Nusselt
number. 相似文献
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本文概述了双扩散对流效应及其对晶体生长的影响.双扩散对流是能在静力稳定的流体系统中发生的一种特殊的对流效应.某些晶体生长过程中具备发生双扩散对流的条件,忽视双扩散对流效应的晶体生长理论会引起与实际过程的明显偏离.文中还评述了现有双扩散对流与结晶过程耦合的计算结果及有待进一步研究的问题. 相似文献
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Parallel domain decomposition method for finite element approximation of 3D steady state non‐Newtonian fluids
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We introduce a stabilized finite element method for the 3D non‐Newtonian Navier–Stokes equations and a parallel domain decomposition method for solving the sparse system of nonlinear equations arising from the discretization. Non‐Newtonian flow problems are, generally speaking, more challenging than Newtonian flows because the nonlinearities are not only in the convection term but also in the viscosity term, which depends on the shear rate. Many good iterative methods and preconditioning techniques that work well for the Newtonian flows do not work well for the non‐Newtonian flows. We employ a Galerkin/least squares finite element method, with stabilization parameters adjusted to count the non‐Newtonian effect, to discretize the equations, and the resulting highly nonlinear system of equations is solved by a Newton–Krylov–Schwarz algorithm. In this study, we apply the proposed method to some inelastic power‐law fluid flows through the eccentric annuli with inner cylinder rotation and investigate the robustness of the method with respect to some physical parameters, including the power‐law index and the Reynolds number ratios. We then report the superlinear speedup achieved by the domain decomposition algorithm on a computer with up to 512 processors. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Anas El Gallaf Ridha Touihri Daniel Henry Hamda Ben Hadid 《Comptes Rendus Mecanique》2009,337(11-12):716-721
Three-dimensional simulations of the buoyant convection in a cylindrical container heated from below are presented. Both the thresholds for the onset of the convection and the nonlinear evolution of this convection are calculated. The simulations concern two configurations: a cavity with a rigid upper surface (Rigid-Rigid case) and a cavity with a non-constrained free surface (Rigid-Free case). The results show a similar variation of the primary thresholds with the aspect ratio for the two configurations. In contrast, the nonlinear evolution of the convection is much changed between the two configurations. In particular, subcritical secondary branches with a very large subcriticity are obtained in the R-F case. To cite this article: A. El Gallaf et al., C. R. Mecanique 337 (2009). 相似文献
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A. A. Hill 《Continuum Mechanics and Thermodynamics》2003,15(3):275-285
A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The
model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the
growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are
also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability
Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory
accurately emulates the physics of the onset of convection.
Received February 10, 2003 / Accepted February 10, 2003/ Published online May 9, 2003 / B. Straughan 相似文献