低雷诺数翼型蒙皮主动振动气动特性及流场结构数值研究

针对低雷诺数(Re)翼型气动性能差的特点,文章通过对翼型柔性蒙皮施加主动振动的方法,提高翼型低Re下的气动特性,改善其流场结构.采用带预处理技术的Roe方法求解非定常可压缩Navier-Stokes方程,对NACA4415翼型低Re流动展开数值模拟.通过时均化和非定常方法对比柔性蒙皮固定和振动两种状态下的升阻力气动特性和层流分离流动结构.初步研究工作表明在低Re下柔性蒙皮采用合适的振幅和频率,时均化升阻力特性显著提高,分离泡结构由后缘层流分离泡转变为近似的经典长层流分离泡,分离点后移,分离区缩小.在此基础上,文章更加细致研究了柔性蒙皮两种状态下单周期内的层流分离结构及壁面压力系数分布非定常特性和演化规律.蒙皮固定状态下分离区前部流场结构和压力分布基本保持稳定,表现为近似定常分离,仅在后缘位置出现类似于卡门涡街的非定常流动现象.柔性蒙皮振动时从分离点附近开始便产生分离涡,并不断向下游移动、脱落,表现为非定常分离并出现大范围的压力脉动.蒙皮振动使流体更加靠近壁面运动,大尺度的层流分离现象得到有效抑制.      

非均匀矩形网格的局部网格细化LBM算法研究

传统的格子玻尔兹曼方法 (LBM),特别是基于均匀正方形网格的经典单松弛计算模型(SLBM),其算法鲁棒性和数值稳定性较差,限制了LBM的发展和应用.而网格细化策略可以有效缓解这一窘境,但是传统LBM中网格细化必然会导致计算效率骤降,计算设备要求攀高.为了解决这一问题,文章基于非均匀矩形网格结构,结合插值LBM算法的思路,在保证物面处和流动变化剧烈区域的局部网格细化以及计算精度的前提下,提出了25点拉格朗日插值LBM算法.以经典顶盖驱动方腔内流为算例,开展了包括不同网格分辨率和插值格式的对比分析研究.验证算例既包括了定常流动的数值模拟,也涉及了非定常周期性流动的求解.计算结果表明,相较于其他插值格式,拉格朗日插值格式表现优异;文章局部网格细化工作可以确保物面处及流动变化剧烈区域流动细节的捕捉;数值模拟算法可以为数值仿真提供可信的计算结果;同时大幅降低了总网格数量.因此很大程度上提升了计算效率;数值模拟方法鲁棒性较好,适用于包括定常和非定常流动的数值模拟.     

侧加热腔内的自然对流

开展侧加热腔内自然对流的研究具有重大的环境及工业应用背景. 总结侧加热腔内水平温差驱动的自然对流的最新研究进展, 并概述相应的流动性质、动力机制和传热特性以及对不同无量纲控制参数的依赖也有重要的科学价值. 已取得的研究结果显示突然侧加热的腔内自然对流的发展可包括初始阶段、过渡阶段和定常或准定常阶段. 不同发展阶段的流动依赖于瑞利数、普朗特数及腔体的高宽比, 且定常或准定常阶段的流态可以是定常层流流动、非定常周期性流动或者湍流流动. 此外, 回顾了对流流动失稳机制的研究成果以及湍流自然对流方面的新进展. 最后, 展望了侧加热腔内的自然对流研究的前景.      

驱动长方形腔内流动非稳定性的数值模拟

本文对长宽比为２的驱动腔内流动进行了数值模拟．采用非均匀交错网格上的修正隐式Ｔｅｍａｍ格式，以及压力修正投影法，分别计算了Ｒｅ数为１００、４００、１０００、２０００、３０００、３５００、５０００、１００００的驱动长方形腔内流场。当Ｒｅ≤３０００时，流场收敛到定常状态；而Ｒｅ≥３５００时，只能得到渐近周期结果；其中应用了谱分析等方法说明数值是周期性变化，可见，Ｈｏｐｆ分叉点出现在Ｒｅ数３０００与３５００之间．     

基于PIV测量的超声波流量计内流场特性研究

采用PIV(Particle Image Velocimetry)测量手段,考察了小口径超声波流量计的流动特性。首先针对前端安装直管段时,不同流量条件下的流场特性建立基本认识,实验结果表明,在低流量条件下,流量计内流场存在明显的不稳定演变和非定常流动特征。进一步以上游前端安装球阀为典型案例,考察了安装条件对超声波流量计响应特性和测量偏差的影响。结合直管段的实验观测结果,发现此种结构超声波流量计的适应性与其流场非定常性的关系具有很好的一致性,即流场结构稳定则适应性强。此外,综合多参数的实验结果表明,雷诺数是判断小口径超声波流量计测量准确性的重要无量纲参数。     

非定常俯抑振荡下的横向喷流数值模拟

采用高精度格式数值求解RANS方程,研究了定常状态下横向喷流流场,压力分布计算结果与实验结果基本吻合,并捕捉到喷流干扰流场中多种流动结构.在非定常计算过程中,飞行器的振动引起了法向力和俯仰力矩系数的相位滞后,推力放大因子随俯仰角周期变化.飞行器振动过程中,喷流流场的动态气动特性与稳态喷流有明显的区别,因此在利用横向喷流对飞行器进行姿态控制时,应该考虑由于飞行器姿态的变化对横向喷流所产生的非定常影响问题.     

不可压缩粘性流动的CBS有限元解法

对于二维不可压缩粘性流动,首先通过坐标变换的方式得到了的不含对流项的NS方程,并给出了CBS有限元方法求解的一般过程。结合一类同时含有压力和速度的出口边界条件,对方腔顶盖驱动流、后向台阶绕流和圆柱绕流进行了计算。所得结果与基准解符合良好,验证了CBS算法对于定常、非定常粘性不可压缩流动问题的可行性和所用出口边界条件的无反射特性。特别的,对于圆柱绕流,Re=100时非定常升、阻力系数及漩涡脱落等非定常都得到了较好地模拟,为一进步研究自激振动等更加复杂的非定常流动问题奠定了基础。     

一种基于增量径向基函数插值的流场重构方法

由于流场参数重构中, 用于重构的基网格单元的物理参数波动量相对于均值较小, 径向基函数（RBF） 直接插值方法重构会产生较大的数值振荡, 论文提出了一种增量RBF 插值方法, 并用于有限体积的流场重构步, 明显改善了插值格式的收敛性和稳定性. 算例首先通过简单的一维模型说明该方法的有效性, 当目标函数波动量相对于均值为小量时, 增量RBF 插值能够抑制数值振荡; 进一步通过二维亚音速、跨音速定常无黏算例、静止圆柱绕流非定常算例以及超音速前台阶算例来说明该方法在典型流场数值求解中的通用性和有效性. 研究表明增量RBF 重构方法可陡峭地捕捉激波间断, 可有效改善流场求解的收敛性和稳定性, 数值耗散小, 计算效率高.      

高超声速尾迹流场稳定性数值研究

通过数值模拟, 对高超声速尾迹流场进行了研究, 对其尾迹流动的失稳过程进行了分析.选取计算模型为圆球,Ma= 6.0, Re = 1.71\times 10^6(Re以球头半径为参考长度). 通过数值模拟,首先得到的流动是稳定解,在底部发展出一个主分离区和一个二次分离区,流动是轴对称状态. 不添加任何扰动继续进行计算,发现底部流场缓慢发展出微弱的非定常流动. 随后,该现象继续发展,出现明显的结构失稳,得到了无量纲周期为12.0的周期解. 给出了高超声速圆球绕流尾迹结构的周期性演化过程,对其涡系结构的演化及奇点特征进行了分析. 研究表明该数值模拟方法可用于底部流动稳定性问题的研究,同时证实了高超声速底部流动也存在流动不稳定性.      

基于动力学模态分解法的绕水翼非定常空化流场演化分析

空化是船舶和水下航行体推进器中经常发生的一种特殊流动现象,它具有强烈的非定常性,空化的发生往往会影响推进器的水动力性能和效率. 为探究绕水翼非定常空化流场结构,本文基于 Schnerr-Sauer 空化模型和 SST $k$-$\omega $ 湍流模型,开展绕二维水翼非定常空化流动数值预报与流场结构分析. 通过将数值预报的空泡形态演变和压力数据与试验结果对比,验证了建立的数值方法的有效性. 并基于动力学模态分解方法对空化流场的速度场进行模态分解,分析了各个模态的流场特征. 结果表明,第一阶模态对应频率为 0,代表平均流场;第二阶模态对应频率约为空泡脱落频率,揭示了空泡在水翼前缘周期性地生长与脱落,第三阶模态对应频率约为第二阶模态的 2 倍,揭示了两个大尺度旋涡在水翼后方存在融合行为. 第四阶模态对应频率约为第二阶模态的 3 倍,具有更高的频率,表征流场中存在一些小尺度旋涡的融合行为. 最后对不同空化数下的空化流场进行了模态分解分析,发现脱落空泡的旋涡结构随着空化数的减小而增大,第二阶模态频率随着空化数的减小而减小.      

Heat transfer enhancement in grooved channels due to flow bifurcations

The flow bifurcation scenario and heat transfer characteristics in grooved channels, are investigated by direct numerical simulations of the mass, momentum and energy equations, using the spectral element methods for increasing Reynolds numbers in the laminar and transitional regimes. The Eulerian flow characteristics show a transition scenario of two Hopf bifurcations when the flow evolves from a laminar to a time-dependent periodic and then to a quasi-periodic flow. The first Hopf bifurcation occurs to a critical Reynolds number Rec₁ that is significantly lower than the critical Reynolds number for a plane-channel flow. The periodic and quasi-periodic flows are characterized by fundamental frequencies ω₁ and m· ω₁+n·ω₂, respectively, with m and n integers. Friction factor and pumping power evaluations demonstrate that these parameters are much higher than the plane channel values. The time-average mean Nusselt number remains mostly constant in the laminar regime and continuously increases in the transitional regime. The rate of increase of this Nusselt number is higher for a quasi-periodic than for a periodic flow regime. This higher rate originates because better flow mixing develops in quasi-periodic flow regimes. The flow bifurcation scenario occurring in grooved channels is similar to the Ruelle-Takens-Newhouse transition scenario of Eulerian chaos, observed in symmetric and asymmetric wavy channels.     

Hopf Bifurcation in a Diffusive Logistic Equation with Mixed Delayed and Instantaneous Density Dependence

A diffusive logistic equation with mixed delayed and instantaneous density dependence and Dirichlet boundary condition is considered. The stability of the unique positive steady state solution and the occurrence of Hopf bifurcation from this positive steady state solution are obtained by a detailed analysis of the characteristic equation. The direction of the Hopf bifurcation and the stability of the bifurcating periodic orbits are derived by the center manifold theory and normal form method. In particular, the global continuation of the Hopf bifurcation branches are investigated with a careful estimate of the bounds and periods of the periodic orbits, and the existence of multiple periodic orbits are shown.     

Numerical study on bifurcations in the wake of a circular disk

Using Large-eddy simulation (LES), the dynamics in the wake of a circular disk with an aspect ratio of d/w = 5 is numerically studied. The circular disk is normal to the main flow, and Reynolds number ranges from 115 to 300. The first bifurcation is confirmed for Re = 120, leading to the steady state mode with a reflectional symmetry and a double-thread wake extending to the downstream. The Hopf bifurcation is found for Re = 152, and the planar symmetry is lost, which is different from that observed in the sphere wake; it is called the “reflectional-symmetry-breaking (RSB)” mode and the hairpin vortices in this mode are always shedding in a fixed orientation. The third bifurcation is captured for Re = 166, which is named the “standing wave (SW)” mode; the planar symmetry lost in RSB mode is recovered and the hairpin vortices are shedding in the oppositely sided orientations, unlike the ones observed in the sphere wake. The fourth bifurcation, referred to as “zigzag (ZZ)” mode, is observed for Re = 265 and the planar symmetry is lost again; the hairpin vortices are shedding in an irregular orientation and propagating in a zigzagged way; and a few small-scale structures begin to appear. Three different vortex shedding regimes are found in RSB, SW and ZZ modes, respectively. Results show that the recirculation region plays a significant role in the mode transitions, and the stagnation point of recirculation zone is conjectured to be the initial region causing the wake instability.     

On the flow of a viscous fluid driven along a channel by suction at porous walls

This paper is a theoretical treatment of the flow of a viscous incompressible fluid driven along a channel by steady uniform suction through porous parallel rigid walls. Many authors have found such flows when they are symmetric, steady and two-dimensional, by assuming a similarity form of solution due to Berman in order to reduce the Navier-Stokes equations to a nonlinear ordinary differential equation. We generalise their work by considering asymmetric flows, unsteady flows and three-dimensional perturbations. By use of numerical calculations, matched asymptotic expansions for large values of the Reynolds number, and the theory of dynamical systems, we find many more exact solutions of the Navier-Stokes equations, examine their stability, and interpret them. In particular, we show that most previously found steady solutions are unstable to antisymmetric two-dimensional disturbances. This leads to a pitchfork bifurcation, stable asymmetric steady solutions, a Hopf bifurcation, stable time-periodic solutions, stable quasi-periodic solutions, phase locking and chaos in succession as the Reynolds number increases.     

Numerical investigation of injection-induced electro-convection in a dielectric liquid between two eccentric cylinders

Numerical analysis of the 2D radial and azimuth electro-convection (EC) flow of dielectric liquid between two eccentric cylindrical electrodes driven by unipolar injection of ions is presented. The finite volume method is used to resolve the spatiotemporal distributions of the flow field, electric field, and charge density. The flow instability is studied in various scenarios where the radius ratio Γ = R_i/R_o ranges between 0.1 and 0.7 and the eccentricity η between 0.1 and 0.5. The bifurcation of the flow patterns depends on the electric Rayleigh number T, a ratio of the electric force to viscous force, and the two geometric parameters Γ and η. For an increasing T, the EC system develops from a weak steady convective state to chaos via different intermediate states experiencing pitchfork and Hopf bifurcations. The influence of Γ and η on the bifurcation behavior is also investigated. When Γ lies between 0.1 and 0.3, a novel periodic oscillation of the flow patterns has been observed.     

State feedback control at Hopf bifurcation in an exponential RED algorithm model

In this paper, we show that a state feedback method, which has successfully been used to control unstable steady states or periodic orbits, provides a tool to control the Hopf bifurcation for a novel congestion control model, i.e., the exponential RED algorithm with a single link and single source. We choose the gain parameter as the bifurcation parameter. Without control, the bifurcation will occur early; meanwhile, the model can maintain a stationary sending rate only in a certain domain of the gain parameter. However, outside of this domain the model still possesses a stable sending rate that can be guaranteed by the state feedback control, and the onset of the undesirable Hopf bifurcation is postponed. Numerical simulations are given to justify the validity of the state feedback controller in the bifurcation control.     

Linear stability analysis of flow in a periodically grooved channel

We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two‐dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady‐state, whereas a self‐sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty‐function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd.     

Bifurcation analysis of a diffusive ratio-dependent predator–prey model

In this paper, a ratio-dependent predator–prey model with diffusion is considered. The stability of the positive constant equilibrium, Turing instability, and the existence of Hopf and steady state bifurcations are studied. Necessary and sufficient conditions for the stability of the positive constant equilibrium are explicitly obtained. Spatially heterogeneous steady states with different spatial patterns are determined. By calculating the normal form on the center manifold, the formulas determining the direction and the stability of Hopf bifurcations are explicitly derived. For the steady state bifurcation, the normal form shows the possibility of pitchfork bifurcation and can be used to determine the stability of spatially inhomogeneous steady states. Some numerical simulations are carried out to illustrate and expand our theoretical results, in which, both spatially homogeneous and heterogeneous periodic solutions are observed. The numerical simulations also show the coexistence of two spatially inhomogeneous steady states, confirming the theoretical prediction.     

A timestepper approach for the systematic bifurcation and stability analysis of polymer extrusion dynamics

We discuss how matrix-free/timestepper algorithms can efficiently be used with dynamic non-Newtonian fluid mechanics simulators in performing systematic stability/bifurcation analysis. The timestepper approach to bifurcation analysis of large-scale systems is applied to the plane Poiseuille flow of an Oldroyd-B fluid with non-monotonic slip at the wall, in order to further investigate a mechanism of extrusion instability based on the combination of viscoelasticity and non-monotonic slip. Due to the non-monotonicity of the slip equation the resulting steady-state flow curve is non-monotonic and unstable steady states appear in the negative-slope regime. It has been known that self-sustained oscillations of the pressure gradient are obtained when an unstable steady state is perturbed [M.M. Fyrillas, G.C. Georgiou, D. Vlassopoulos, S.G. Hatzikiriakos, A mechanism for extrusion instabilities in polymer melts, Polymer Eng. Sci. 39 (1999) 2498–2504].Treating the simulator of a distributed parameter model describing the dynamics of the above flow as an input–output “black-box” timestepper of the state variables, stable and unstable branches of both equilibrium and periodic oscillating solutions are computed and their stability is examined. It is shown for the first time how equilibrium solutions lose stability to oscillating ones through a subcritical Hopf bifurcation point which generates a branch of unstable limit cycles and how the stable periodic solutions lose their stability through a critical point which marks the onset of the unstable limit cycles. This implicates the coexistence of stable equilibria with stable and unstable periodic solutions in a narrow range of volumetric flow rates.     

Steady state motions of shallow arch under periodic force with 1∶2 internal resonance on the plane of physical parameters

The bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1∶2 internal resonance is studied in this paper. The whole parametric plane is divided into several different regions according to the types of motions; then the distribution of steady state motions of shallow arch on the plane of physical parameters is obtained. Combining with numerical method, the dynamics of the system in different regions, especially in the Hopf bifurcation region, is studied in detail. The rule of the mode interaction and the route to chaos of the system is also analysed at the end. Project supported by National Natural Science Foundation and National Youth Science Foundation of China