倾斜层中的对流斑图及其临界条件

通过二维流体力学基本方程的数值模拟，探讨了Prandtl(普朗特)数Pr=6.99时，倾斜矩形腔体中的对流斑图和斑图转换的临界条件.根据倾角θ和相对Rayleigh(瑞利)数Ra_r的变化，倾斜矩形腔体中的对流斑图可以分为:单滚动圈对流斑图、充满腔体的多滚动圈对流斑图和过渡阶段的多滚动圈对流斑图.当θ一定时，随着Ra_r的减小，系统由充满腔体的多滚动圈对流斑图过渡到单滚动圈对流斑图.这时，对流振幅A和Nusselt(努塞尔)数Nu随着Ra_r的增加而增加.当Ra_r=9时，随着θ的增加，系统由充满腔体的多滚动圈对流斑图过渡到单滚动圈对流斑图，这时对流振幅A随着θ的增加而减小，Nusselt数Nu随着θ的增加而增加.在θ_c-Ra_r平面上对多滚动圈到单滚动圈对流斑图过渡的模拟结果表明， 在Ra_r=2时, 腔体中没有发现多滚动圈对流斑图.在Ra_r为2.5左右时，腔体中出现多滚动圈到单滚动圈对流斑图的过渡.当多滚动圈到单滚动圈对流斑图过渡的临界倾角θ_c<10°时，θ_{c随着Rar的减小而增加.当θc>10°时，θc随着Rar的增加而增加，在Rar≤5时，θc随着Rar的增加而迅速增加；当Rar>5时，θc随着Rar的增加而缓慢增加.θc与Rarθ的关系与Rar类似}     

一种新的混合流体对流竖向镜面对称对传波斑图

利用SIMPLE算法对混合流体对流的流体力学基本方程组进行了数值模拟,在混合流体分离比ψ=－0.6和矩形腔体长高比Γ=20的情况下,首次发现了一种新的竖向镜面对称对传波斑图,并初步探讨了它的动力学特性.竖向镜面对称对传波斑图的中心为驻波,随着时间的发展驻波的波长伸长.当波长增加到某个临界值时,一个滚动分裂成两个滚动,在这两个滚动之间产生一个具有180°相位差的新滚动.位于中心线上的滚动只有相位的突变及其波长的压缩或者伸长,没有对流滚动的移动,在它的两侧是向左右传播的对流滚动.驻波两次相位突变形成一个周期,驻波周期随着相对Rayleigh(瑞利)数Ra_r的增加而增加.这种对流结构存在于相对Rayleigh数Ra_r∈(3.6,4.3]的范围.当相对Rayleigh数Ra_r≤3.6时,系统出现具有缺陷的行波斑图;当Ra_r>4.3时系统过渡到行波斑图.说明竖向镜面对称对传波斑图是存在于具有缺陷的行波斑图和行波斑图之间的一种稳定的对流斑图.     

具有水平流动的对流斑图成长和动力学特性

采用二维流体力学基本方程组对Prandtl数Pr=0.72具有水平流动的对流斑图成长和动力学特性进行了数值模拟.结果说明,对于给定的相对Rayleigh数Ra_r=5(Rayleigh数Ra=8 540)和Reynolds数Re=22.5,行波对流斑图的成长分为三个阶段,即对流发展阶段、指数成长阶段、周期变化阶段(过渡调整区、稳定周期变化区).行波对流的平均波数随着时间的发展或者对流斑图的成长而减小.随着相对Rayleigh数的增加,行波对流的指数成长阶段的时间变短,对流最大垂直流速的成长率变大.对于水平流动Re=5时,对流最大垂直流速的成长率γ_m与Ra_r的关系为γ_m=0.004 8Ra~(6.065 3)_r.在周期变化阶段,经过行波对流斑图和对流参数的过渡调整区后,对流进入斑图和对流参数的稳定周期变化区.对于给定的Ra_r=5时,行波对流的无量纲周期T_t随着Re变化的关系式为T_t=0.001 4Re~(2.363 5).     

侧向局部加热对流的周期性

通过流体力学方程组的数值模拟,研究了侧向局部加热条件下Prandtl数Pr=0.0272时流体对流的周期性.结果表明:随着Grashof数Gr的增加,对流按稳态对流、单局部周期对流、双局部周期对流、准周期对流的顺序发展.当Gr<3.6×103时,对流为稳态;在3.6×103相似文献   

水平来流对扰动成长和对流周期性的影响

对Pr=0.0272的纯流体在矩形腔体外加水平来流时,进行二维流体力学基本方程组的数值模拟.研究了该纯流体Rayleigh-Benard对流的一维行波斑图的成长及时空的演化.发现对流成长过程可以划分为3个阶段,即对流发展、对流指数成长和周期变化。在对流指数成长阶段对不同相对Rayleigh(瑞利)数Ra_r的最大垂直流速场随时间变化的情况进行分析,获得了最大垂直流速场指数成长阶段的线性成长率γ_m和相对Rayleigh数Ra_r的关系公式.研究了行波周期受水平来流Reynolds(雷诺)数的影响,揭示了行波对流周期性及其对水平来流Reynolds数的依赖性.     

关于唯一r——泛圈图

唯一r—泛圈图G是一个简单图,对n=r,r+1,…,p,(r≥3,p=|V(G)|),G恰含一个圈C_n,但G不含圈C_t,3≤t≤r-1。R.C.Entringer于1973年提出:确定是唯一泛圈图的简单图(唯一泛圈图指的是唯一3—泛圈图)。文[3]确定了具有p+m(m≤4)条边的图及外平面图中的唯一泛圈图。本文得到:当r≥4时, 1.外平面图G是唯一r—泛圈图当且仅当G≌C_P; 2.具有p+2条边的图不是唯一r—泛圈图; 3.具有p+3条边的图没有唯一r—泛圈图,5≤r≤p;但恰有6个唯一4—泛圈图,且这样的图仅有6个.     

用SADI方法求解方形空腔中具有高Rayleigh数的非定常自然对流问题

本文用三次样条积分计算了在方形空腔中具有高Rayleigh数Ra=107和Ra=2×107的非定常自然对流问题。二维N-S方程和能量方程是在非均匀网格中用两个交替方向的三次样条公式进行计算的。文中简要讨论了过渡流动的主要特征,所得结果与理论予估值[1,2]吻合很好。Ra=107时的稳态结果与近期文献中的结果一致。     

多孔介质复合方腔双扩散混合对流LBM模拟

基于CLBGK模型,通过引入浓度分布函数,利用格子Boltzmann方法对顶盖驱动的复合方腔内的双扩散混合对流现象进行了研究,复合方腔由多孔介质区域和纯流体空间组成.在Richardson(理查德森)数Ri=1.0,Lewis(路易斯)数Le=2.0,Grashof(格拉晓夫)数Gr=104和Prandtl(普朗特)数Pr=0.7时,分析了孔隙尺度下多孔介质层不同位置及浮升力比（-5.0≤N≤5.0）对复合方腔双扩散混合对流的影响.给出了浮升力比N及多孔介质层位置影响下的高温高浓度壁面上的平均Nusselt(努赛尔)数Nu_av、平均Sherwood(舍伍德)数Sh_av及当地Nusselt数Nu_local和Sherwood数Sh_local的分布规律.     

传导-辐射和磁流体组合对磁化可渗透平板自然对流影响的数值解法

研究粘性、不可压缩、导电流体,在磁化可渗透竖直平板上作自然对流时,数值地分析辐射和磁流体组合的影响.采用两种方法数值地求解非相似的控制方程:1)对所有吸入参数值ξ,采用有限差分法;2)为小数值和大数值的吸入参数值ξ,分别建立起级数的渐近解.用图形和列表形式,给出Prandtl数Pr,磁Prandtl数Pm,磁力参数S,辐射参数Rd,壁面温度θw的变化,对壁面摩擦因数、热交换率和电流密度的影响.最后分析上述物理参数对速度分布、温度分布和磁场横向分量的影响.     

Hall电流对表面热通量均匀的竖直可渗透平板上MHD自然对流的影响

在横向磁场作用下,研究Hall电流对竖直可渗透平板上MHD自然对流的影响,平板具有均匀的热通量.和外部磁场相比,假设感应磁场可以忽略不计.利用自由变量公式化(FVF)和流函数公式化(SFF),将边界层方程简化为适当的形式.对局部蒸发系数ζ的整个取值范围,由FVF得到的抛物型方程,用简明的有限差分法进行数值积分;另一方面,由SFF得到的非相似方程,采用局部非相似法求解.有些区域,如局部蒸发系数ζ值足够大或足够小时,用正规的摄动法求解.对低值Prandtl数Pr,例如Pr=0.005,0.01,0.05时,用图形表示磁场参数M和Hall参数m,对局部表面摩擦因数和局部Nusselt数的影响.最后对不同的局部蒸发系数ζ值,给出流体的速度和温度分布.     

An improved Chebyshev collocation algorithm for direct simulation of 2D turbulent convection in differentially heated cavities

We present a modified Chebyshev collocation algorithm for direct numerical simulations of 2D turbulent convection in differentially heated cavities. The numerical algorithm integrates the Navier-Stokes equations in velocity-pressure formulation with a Chebyshev spatial approximation and a second order finite difference time-stepping scheme. A coordinate stretching is introduced which allows one to redistribute the collocation points where needed in order to resolve more economically the small scales that appear at cavity mid-height. This algorithm is used to perform simulations in a square differentially heated cavity with adiabatic top and bottom walls filled with a fluid of Prandtl number equal to 0.71 for Rayleigh number values up to 10¹⁰ which is almost two orders of magnitude higher than the onset of unsteadiness. The time-dependent dynamics of the solutions are investigated and the time-averaged flow structures are displayed. The influence of unsteadiness on the local and global heat transfer coefficients is examined.     

Development of POD reduced-order model and its closure scheme for 2D Rayleigh–Bénard convection

Reduced-order model (ROM) based on proper orthogonal decomposition (POD) is a fast computational fluid dynamics (CFD) method and has been widely applied to pure flow or heat conduction problems in the past. In this paper, the typical 2D Rayleigh–Bénard convection (RBC) in a square cavity was set as a research target. Firstly, the POD-ROM of 2D RBC problem was constructed at Ra = 10⁷, Pr = 0.71. Combining with direct numerical simulation (DNS) databases, a closure model (CM) was then proposed to correct the evolution process of POD-ROM. Based on the proposed CM, we realized the prediction of flow evolution for a new flow case under the parameters different from that used to get its POD eigenmodes. It showed that the proposed POD-ROM with CM could be able to predict the dynamics of new flow cases. Moreover, the corresponding method proposed in the present study can be also easily extended to other types of flow-heat coupling problems, such as natural heat convection, etc.     

Onset of thermal convection and influence of rotation in wide spherical gap flow

The onset of thermal convection and the effect of rotation in a high Prandtl number fluid in a wide gap between two concentric spheres with an axial force field are investigated experimentally. Both spheres rotate along the vertical axis with the same angular velocity Ω while the inner one (r₁) is cooled and the outer one (r₂) is heated. The velocity field is investigated by different visualization techniques and Particle Image Velocimetry (PIV). The axisymmetric basic flow is disturbed by local instabilities. At a Rayleigh number of Ra = 6.97 · 10⁶, a pulsing vortex develops in the south polar region. A different, coexisting instability in the outer boundary layer appears at Ra = 1.79 · 10⁷. Rotating with Taylor numbers Ta > 1.4 · 10⁵, this instability vanishes. The instabilities occur mainly in the southern hemisphere where the thermal stratification is unstable.     

Buoyancy-assisted flow of yield stress fluids past a cylinder: Effect of shape and channel confinement

The aiding-buoyancy mixed convection heat transfer in Bingham plastic fluids from an isothermal cylinder of elliptical and circular shape in a vertical adiabatic channel is numerically investigated. For a fixed shape of the elliptical cylinder E = 2 (ratio of major to minor axes), the effect of confinement is studied for three values of blockage ratio, B, defined as the ratio of the channel width to the circumference of the cylinder/π, as 6.5, 2.17 and 1.3. In order to delineate the role of cross-section of the cylinder, results are also presented here for a circular cylinder of the same heat transfer area as the elliptical cylinder. The results presented herein span the range of conditions as: Bingham number, 0 ≤ Bn ≤ 100, Reynolds number, 1 ≤ Re ≤ 40, and Prandtl number, 1 ≤ Pr ≤ 100 over the range of Richardson number Ri = 0 (pure forced convection) to Ri = 10. Extensive results on drag coefficient, local and surface averaged values of the Nusselt number and yield surfaces are presented herein to elucidate the combined effects of buoyancy, blockage ratio and fluid yield stress. The morphology of the yield surfaces shows that the unyielded plug regions formed upstream and downstream of the cylinder grow faster at low Reynolds numbers with the increasing yield stress effects under the weak buoyancy forces, i.e., small values of Grashof or Richardson number. The heat transfer enhancement is observed with the increasing channel-confinement due to the sharpening of the temperature gradients near the surface of the cylinder. The average Nusselt number shows a positive dependence on the Reynolds number, Prandtl number and Richardson number irrespective of the shape of the cylinder or the type of fluid. By employing the modified definitions of the dimensionless parameters (based on the two choices of the overall effective fluid velocity), predictive correlations have been established for estimating the value of the average Nusselt number in a new application.     

Numerical study of the transition to chaos of a buoyant plume from a two-dimensional open cavity heated from below

The transition to a chaotic plume from a two-dimensional (2D) open cavity heated from below has been investigated using numerical simulation. A large range of Rayleigh numbers (Ra) pertaining to an aspect ratio of A = 1, and Prandtl number (Pr) of Pr = 0.71 (air) is numerically investigated. It is shown that there exists a complex transition of the plume from a steady reflection symmetry to a chaotic flow with a sequence of bifurcations. As the Rayleigh number increases, the plume from the open cavity undergoes a supercritical pitchfork bifurcation from a steady reflection symmetry to a steady reflection asymmetry flow. Once the Rayleigh number exceeds 7 × 10³, the plume appears as a distinct flapping namely, a Hopf bifurcation, and then as a distinct puffing. The chaotic plume has the possibility to exhibit an alternate appearance of flapping and puffing in the event the Rayleigh number exceeds 8 × 10⁴. Moreover, the dynamics of the plume from the open cavity is discussed, and the dependence on the Rayleigh number of heat and mass transfer of the plume from the open cavity is quantified.