多孔介质方腔内自然对流影响因素数值模拟

为研究封闭方腔内饱和多孔介质自然对流传热,采用控制体积法,运用多孔介质局部热平衡假设,整体求解方腔内的温度场和流场,根据计算结果着重分析瑞利数Ra和达西数Da对多孔介质方腔内自然对流换热特性的影响.计算结果表明:当Ra取定值,壁面平均努塞尔数Nu随Da数的增加而增大;当Da数取定值,壁面平均努塞尔数Nu随Ra的增加而增大;随着达西数Da数的增加,临界瑞利数Ra逐渐减小.     

不同屋顶结构下室内自然对流传热数值分析

以室内自然对流传热过程为研究对象,采用质量守恒方程、能量守恒方程进行数值计算,给出了Ra数在10³～10⁸之间时,三种不同屋顶结构下室内等温线、流体流线的分布特征和Nu数的变化特征.分析结果表明:随着Ra数的增大,等温线由近似竖直变为水平,靠近高、低温壁面有边界层的产生,高Ra数下的室内气流变得紊乱;三种屋顶下的Nu数曲线形状相似,Ra=10³时拱形屋顶的Nu值最大,高Ra数时平屋顶房屋的Nu值最小,换热效果较差;拱形屋顶Nu与Ra的拟合公式为:Nu=0.316Ra^0.262.     

高瑞利数下封闭腔内自然对流的数值模拟

为了推广应用高瑞利数下的自然对流换热技术,有必要对自然对流流动与换热特性进行深入研究。采用不引入人工扰动的直接数值模拟方法,对发生在高宽比为4的封闭腔内的自然对流流动与换热进行了研究,分析了平均温度、平均主流速度、涡量和局部努塞尔数的分布特性。研究结果表明:从静止等温流体初始条件出发,不引入任何人工扰动自然对流可以顺利发展到湍流,节约了计算资源;即便瑞利数等于1010,自然对流的平均温度、平均主流速度、涡量和局部努赛尔数分布都具有边界层型流动和换热的特征;在普朗特数为0.71~500的范围,当封闭腔内自然对流换热出现湍流换热特征时,局部瑞利数处于107~108量级。     

应用FPM方法模拟封闭方腔自然对流

为验证有限粒子方法（FPM）能否很好地模拟自然对流问题,采用FPM方法对封闭方腔自然对流问题进行了数值模拟. 对FPM方法进行详细描述,并利用FPM方法对拉格朗日型的N-S方程进行离散,基于离散后的方程对瑞利数Ra分别为104,105,106的封闭方腔自然对流问题进行数值模拟,给出了不同瑞利数条件下的速度和温度云图以及中心线上量纲一的速度和温度分布曲线. 结果表明,FPM方法能够获得较准确的温度分布规律,当瑞利数较低时也能获得较准确的速度分布规律,但随着瑞利数的增大,速度场的模拟结果精度和稳定性变差,因此为了获得更准确和光滑的速度分布场,需要对FPM方法做进一步的改进.      

不同Ra数下隔板Rayleigh-Bénard对流系统的流动和增强传热特性

本文计算研究Ra数对隔板对流系统的流动和增强传热特性的影响.对于无量纲的狭缝高度d=0.02,传热通道的无量纲速度U和温度TD数随Ra数的变化有两个阶段,低Ra数时U随Ra数增高而上升, TD数变化不大,高Ra数时U变化不大, TD数随Ra数增高而下降.传热Nu数随Ra增高而增大,低Ra时Nu数随Ra数快速上升, Nu～Ra~(1.1),高Ra时Nu数增大变缓, Nu～Ra~(0.14).与无隔板对流系统Nuno～Ra~(0.29)对比, Nu数呈现先快速增大而后变缓的过程,出现增强传热区间和Nu数增强最大值Nuq,为7×10~5≤Ra≤5×10~9, Nuq≈3Nuno,对应Ra|Nuq≈10~7.不同狭缝高度d时速度U和TD数及Nu数随Ra数的变化特性曲线特征保持不变,但会改变特性曲线对应于Ra数的位置.狭缝高度d增大,特性曲线向低Ra数方向移动.不同d将改变隔板对流系统Ra数的传热增强区间.三个不同狭缝高度的Nu数增强最大值都是Nuno的3倍左右,狭缝高度d越大,对应的Ra数越低.     

局部高温壁面下复合腔体内传热传质

为研究局部高温壁面下,复合腔体内自然对流及传热传质规律,采用一区域模型整体对腔内温度场、浓度场和流场进行求解.高温壁面无量纲长度A=0.5(A=a/H),局部壁面温度为Th,浓度为Ch;右侧垂直壁面分别为Tc和Cc.对局部高温壁面的相对位置B、多孔结构的孔隙率ε、瑞利数Ra的影响进行综合的数值计算,由数值计算结果得出:局部高温壁面位置不同,腔内流体流动及传热传质不同,B值在0.6附近时对应的平均努赛尔数Nu和平均舍伍德数Sh最大;ε=0.7时Nu出现最小值;Ra对传热传质影响也较大.     

封闭方腔自然对流的格子-Boltzmann方法动态模拟

以压力分布函数和内能密度分布函数为基本演化变量,构建了一个新的不可压缩的双分布函数热格子-Boltzmann模型.对封闭方腔内自然对流进行数值分析的结果表明,该模型可以克服原模型的可压缩效应,并在一定程度上提高了计算结果的数值精度.以此模型动态模拟封闭方腔自然对流的形成和演化过程的结果表明:Ra越大,流场的演化越复杂,稳定状态下方腔内涡的数量越多,高低温壁面附近的换热越强烈,压强逐渐呈现出中心低,上、下壁面附近高的对称分布.     

单侧周期性温度边界下多孔介质方腔内自然对流传热数值模拟

采用局部非热平衡模型,在方腔左侧壁面温度正弦波变化的边界条件下,应用SIMPLER算法数值模拟研究了固体骨架发热多孔介质方腔内的稳态非达西自然对流,主要探讨了不同正弦波波动参数N、振幅A及方腔的高宽比M/L对方腔内自然对流与传热的影响规律。计算结果表明:方腔左侧壁面附近出现了周期性的正负变化的温度场分布,壁面局部传热系数出现了周期性的震荡现象;存在一个最佳温度波动参数N=3,此时流体相壁面的平均Nu达到最大值;存在一个最佳的方腔高宽比M/L=0!1,使得多孔介质方腔内自然对流传热效果最好,增加或减小高宽比都会在一定程度上削弱多孔介质方腔内的传热效果;相对于温度均一的边界条件,正弦波温度边界条件能够增大壁面的平均Nu数,起到强化传热的作用。     

底部加热多孔介质内传热数值研究

为了研究底部加热多孔介质方腔内的自然对流传热,采用整体求解法对方腔内的温度场和流场进行了数值模拟计算,着重分析了瑞利数Ra对多孔介质方腔内自然对流换热特性的影响.计算结果表明:随着Ra数的逐渐增加,对流换热开始占主要作用,等温线变得扭曲;流线由逆时针单胞对流逐渐变化为正反两个双胞对流,流动出现分叉现象,温度场和流线相互对应.平均Nusselt也随之增大,换热效果得到增强.     

倾斜多孔方腔内自然对流非正交MRT-LB数值模拟

建立了倾斜多孔方腔自然对流的非正交多松弛系数格子Boltzmann(MRT-LB)模型,选取典型热流动问题分析了非正交转换矩阵的MRT-LB模型数值稳定性和运算效率,并对倾斜多孔方腔内自然对流现象进行了模拟研究,讨论了孔隙度ε(ε=0.4,0.6,0.9)、倾角θ(-180°≤θ≤180°)、Rayleigh数(10~4≤Ra≤10~7)及Darcy数(Da=10~(-4),10~(-2))等参数对流动传热的影响.结果表明:非正交转换矩阵的MRT-LB模型具有更好的数值稳定性和收敛速度;倾斜多孔方腔高温壁面上平均Nusselt数随倾角变化呈M型分布;Ra数、Da数增大使得Nusselt数最大值所对应的倾斜角度θ_(max)呈滞后规律;低Ra数时Nusselt数曲线出现不连续变化现象.最后通过曲线拟合得到Nusselt数与Ra*(Ra*=DaRa)数的幂函数关系式.     

(1+2)维斑图方程的动力学性态

研究了在流体的有限层面由浮力或曲面张力梯度诱导的斑图构成方程,界于不良热导体平展边界间的斑图构成方程由Knobloch于1990年导出 ∂u/∂t=αu-μ∇2u-∇4u+K∇·(|∇u|2∇u+β∇2u∇u-γu∇u+δ∇|∇u|2),其中,u是面函数,μ是Rayleigh数,K=1,α表示热传递效益,是有限Biot数,当界面顶部和底部条件不相同时,β≠0,δ≠0,当出现非Boussinesq效应时,γ≠0,考虑α0,μ0,β=δ=0情形,即界面顶部和底部条件相同且出现非Boussinesq效应时(1+2)维Knobloch方程解的动力学性态,获得解的局部存在、整体存在以及吸引子的存在性.       

On the thinness of non-tangential sets

Let Ω⊄R ^d and ξ∈∂Ω. LetE be any non-tangential subset of Ω. we prove that ifE is internal thin at ξ, then it is minimal thin at any minimal Martin boundary point of Ω. Supported by the National Natural Science Foundation of China Zhang Yiping: born in Dec. 1962. Professor     

Vp of muscovite-biotite gneiss up to 950℃ at 400 MPa: Constraints on the origin of abnormal seismic layers in continental crust

Here we present experimental results of compressional wave velocity (Vp) of muscovite-biotite gneiss from Higher Himalayan Crystallines (HHC) at the temperature up to 950℃ and the pressure of 0.1―400 MPa. At 400 MPa, when the temperature is lower than 600℃, Vp decreases linearly with increasing temperature at the rate of (Vp/T)p -4.43×10-4 km/s ℃. In the temperature range of 600―800℃, Vp drops significantly and the signal is degraded gradually due to the dehydration of muscovite and α-quartz softening. When the temperature rises from 800℃ to 875℃, Vp increases and the signals become clear again as a result of the temperature going through the β-quartz range. The experiments indicate that the duration has great influence on the experimental results when temperature is above the dehydration point of biotite. During the first 30 h at 950℃, the Vp decreases substantially from 5.9 to 5.4 km/s and the signal amplitude is attenuated by more than 80%. After the 30-h transition, the Vp and the amplitude of ultrasonic wave signals become steady. The decrease of Vp and attenuation of the signals at 950℃ are associated with the breakdown reactions of biotite. The experiments suggest that the breakdown of muscovite and/or quartz softening can contribute to the low seismic wave velocity in thickened quartz-rich felsic-crust such as what is beneath southern Tibet. Additionally, α-β quartz transition generates a measurable high seismic velocity zone, which provides a possibility of precisely constraining the temperature in the upper-middle continental crust. Our study also demonstrates that duration is a key factor to obtain credible experimental results.     

On the Pólya conjecture and the weak Weyl-Berry conjecture

The Pólya conjecture and its connection with the weak Weyl-Berry conjecture are studied Specifically let Ω⊆R ⁿ (n≥1) be a non-empty bounded open set with boundary ∂Ω. LetN ₀(λ, −Δ,Ω) be the Dirichlet counting function and φ(λ) the associated Weyl term. If the interior Minkowski dimension of ∂Ω is δ∈[n−1,n], then under certain realisable conditions we prove that for λ sufficiently large the Pólya conjecture φ(λ) −N ₀(λ,−Δ,Ω)≥0 is true. Under related conditions we also prove thatϕ(λ)−N ₀(λ,−Δ, Ω)≈λ^5/2, as λ→+∞. That is, the Weak Weyl-Berry conjecture is true. Similar results are obtained for the Neumann counting function. Partially supported by the National Natural Science Foundation of China and the Royal Society of London Chen Hua: born in March 8, 1956, Professor     

Boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretching vertical surface with prescribed skin friction

The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were considered. The governing partial differential equations were transformed into a system of ordinary differential equations, which were then solved numerically using the shooting method. Results for the stretching velocity, the local Nusselt number, the temperature, and the velocity profiles are presented for various values of the mixed convection parameter λ and material parameter K when the Prandtl number is equal to 1. Both assisting (heated plate) and opposing (cooled plate) flow regions are considered. It is found that dual solutions exist for both assisting and opposing flows.     

Integral Points on a Class of Elliptic Curve

0 IntroductionZasegairerc[h1]fodre sbcirgibientde gsreavle rpaolin tmse tohnocdsert waihnicehlli ppetircm citur ovnese btyogiving the upper bound of solution. Unfortunately,this upperbound was verylarge andsometi mes beyondthe range of com-puter searching.For a particular elliptic curvey2=x3-30x+133(1)he mentioned he can find all integral points and the largestpoint is (x,y) =(5 143 326 ,±11 664 498 677) by using Mas-ser and W櫣stholz bounds on elliptic logarithms .Although recent results on…     

Global and non-global solutions to some chemotaxis model

The paper is concerned with some chemotaxis model ∂u/∂t=D▿(u▿ln(u/w))+u(a−bu),∂w/∂t=f(u,w). To study the behavior of the solution, some function transformations are introduced, and the main tool is sup-sub-solution method. The result shows that, whether the solution blows up in finite time depends on the parameters and the initial data. As the chemical substance w has linear growth, f(u,w)=βu−δw, where β>0, δ>0 and a+δ>0, wherein the solution exists globally. However, as w possesses exponential growth, f(u,w)=(βu−δ)w, wherein both u and w share the same blowup point and time if the solution blows up in finite time. Biography: CHEN Hua(1956–), male, Professor, Ph. D., research direction: partial differential equation and its application.     

Number of ℬ -free numbers in short intervals

The ℬ-free number is a generalization of the well-known squarefree numbers. The result that if θ > 33/80, then the interval [x-x^θ,x] must contain a B-free number for largex has been proved.     

Variable diffusion boundary layer and diffusion flux at sediment-water interface in response to dynamic forcing over an intertidal mudflat

The diffusion boundary layer (DBL) significantly limits the exchange between sediment and overlying water and therefore becomes a bottleneck of diffusive vertical flux at the sediment-water interface (SWI). Variable DBL thickness and diffusion flux in response to dynamic forcing may influence replenishment of nutrients and secondary pollution in coastal waters. In situ measurements of velocity in the bottom boundary layer (BBL) and oxygen concentration in the DBL were made over an intertidal mudflat, using an acoustic Doppler current and mini profiler. A linear distributed zone in the oxygen profile, the profile slope discontinuity and variance of concentration can be used to derive accurate DBL thickness. Diffusion fluxes calculated from the water column and sediment are identical, and their bias is less than 6%. A numerical model PROFILE is used to simulate the in situ dissolved oxygen profile, and layered dissolved oxygen consumption rates in the sediment are calculated. The DBL thickness (0.10-0.35 mm) and diffusion flux (15.4-53.6 mmol m 2 d 1) vary with a factor of 3.5 during a tidal period. Over an intertidal mudflat, DBL thickness is controlled by flow speed U in the BBL, according to δDBL=1686.1DU 1+0.1 (D is the molecular diffusion coefficient). That is, the DBL thickness δDBL increases with decreasing flow speed U. Changes of diffusion flux at the SWI are caused by variations in the water above the sediment and the turbulent mixing intensity. The diffusion flux is positively related to the turbulent dissipation rate, friction velocity and turbulent energy. Under the influence of dynamics in the BBL, DBL thickness and flux vary significantly.