一类两自由度碰撞振动系统的Hopf分岔和混沌

分析了一类两自由度碰撞振动系统的周期运动,并通过计算Poincare映射的线性化矩阵,确定周期运动的稳定性.分析表明,在一定的参数条件下系统存在周期倍化分岔和Hopf分岔,并通过数值模拟方法得到了以Poincare截面上的不变圈表示的拟周期响应.简明地讨论了系统通向混沌的道路.     

Lattice Boltzmann simulation of lid-driven flow in trapezoidal cavities

In this paper, an incompressible lattice Bhatnagar–Gross–Krook (LBGK) model proposed by Guo et al. is used to simulate lid-driven flow in a two-dimensional isosceles trapezoidal cavity. Due to the complex boundary of the trapezoidal cavity, here the extrapolation scheme proposed by Guo et al. is used to treat curved boundary. In our numerical simulations, the effects of the Reynolds number (Re) and the top angle θ on the strength, center position and number of vortices in the isosceles trapezoidal cavities are studied. Re is varied from 100 to 15,000, and the top angle θ ranges from 50 to 90. Numerical results show that, as Re increases, the phenomena in the cavity become more and more complex, and the number of the vortexes increases. We also found that the vortex near the bottom wall breaks up into two smaller vortices as θ increases up to a critical value. Furthermore, as Re is increased, the flow in the cavity undergoes a complex transition (from steady to the periodic flow, and finally to the chaotic flow). At last, the scope of critical Re for flow transition from steady to periodic state, and from periodic to chaotic state is presented for different top angles θ.     

Deterministic lateral displacement (DLD) in the high Reynolds number regime: high-throughput and dynamic separation characteristics

Recent progress in the development of biosensors has created a demand for high-throughput sample preparation techniques that can be easily integrated into microfluidic or lab-on-a-chip platforms. One mechanism that may satisfy this demand is deterministic lateral displacement (DLD), which uses hydrodynamic forces to separate particles based on size. Numerous medically relevant cellular organisms, such as circulating tumor cells (10–15 µm) and red blood cells (6–8 µm), can be manipulated using microscale DLD devices. In general, these often-viscous samples require some form of dilution or other treatment prior to microfluidic transport, further increasing the need for high-throughput operation to compensate for the increased sample volume. However, high-throughput DLD devices will require a high flow rate, leading to an increase in Reynolds numbers (Re) much higher than those covered by existing studies for microscale (≤?100 µm) DLD devices. This study characterizes the separation performance for microscale DLD devices in the high-Re regime (10?<?Re?<?60) through numerical simulation and experimental validation. As Re increases, streamlines evolve and microvortices emerge in the wake of the pillars, resulting in a particle trajectory shift within the DLD array. This differs from previous DLD works, in that traditional models only account for streamlines that are characteristic of low-Re flow, with no consideration for the transformation of these streamlines with increasing Re. We have established a trend through numerical modeling, which agrees with our experimental findings, to serve as a guideline for microscale DLD performance in the high-Re regime. Finally, this new phenomenon could be exploited to design passive DLD devices with a dynamic separation range, controlled simply by adjusting the device flow rate.     

两点碰撞振动系统的周期运动与分叉

建立了两自由度两点碰撞振动系统的动力学模型,给出了碰撞振动系统产生粘滞的条件,分析了系统存在的粘滞运动.采用打靶法,利用变步长逐次迭代逼近的方法求解系统的不稳定的周期碰撞运动,即Poincar啨截面上的不动点.通过对两自由度两点碰撞振动系统进行数值模拟显示了系统在一定参数条件下存在周期倍化分叉和Hopf分叉,同时通过数值模拟的方法得到了以两自由度两点碰撞振动系统Poincar啨截面上的不变圈表示的拟周期响应,并进一步分析了随着分岔参数的变化,两自由度两点碰撞振动系统周期运动经拟周期分叉和周期倍化分叉向混沌的演化路径.     

An experimental and numerical study of the structure and stability of laminar opposed-jet flows

Experiments, simulations, and numerical bifurcation analysis are used to study the incompressible flow between two opposed tubes with disks mounted at their exits. The experiments in this axisymmetric geometry show that for low and equal Reynolds numbers, Re, at both nozzles, the flow remains symmetric about the plane halfway through the nozzle exits and the stagnation plane is located halfway between the two jets. When Re is increased past a critical value, asymmetric flow fields are obtained even when the momentum fluxes of the two opposed streams are equal. For unequal Re at the jet exits, when the fixed velocity (and the corresponding Reynolds number, Re₁) of one stream is low, the stagnation plane location, SPL, changes smoothly with the Re₂. For high enough Re₁, a hysteretic jump of SPL is observed. Particle Image Velocimetry and flow visualization demonstrate that within the hysteretic range, the two stable flow fields are anti-symmetric. The experimental setup is also studied with transient incompressible flow simulations using a spectral element solver. It is found that to accurately model the flow, we either need to extend the domain into the nozzles, or impose experimental velocity profiles at the nozzle exits. As in the experiments asymmetric flows are obtained past a critical Re. Finally, bifurcation analysis using a Newton-Picard method shows that the transition from symmetric to asymmetric flows results from the loss of stability of the symmetric flows at a pitchfork bifurcation.     

Large-eddy simulation of streamwise-rotating turbulent channel flow

In many engineering and industrial applications the investigation of rotating turbulent flow is of great interest. Whereas some research has been done concerning channel flows with a spanwise rotation axis, only few investigations have been performed on channel flows with a rotation about the streamwise axis. In the present study an LES of a turbulent streamwise-rotating channel flow at Re_τ = 180 is performed using a moving grid method. The three-dimensional structures and the details of the secondary flow distribution are analyzed and compared with experimental data. The numerical-experimental comparison shows a convincing agreement as to the overall flow features. The results confirm the development of a secondary flow in the spanwise direction, which has been found to be correlated to the rotational speed. Furthermore, the findings show the distortion of the main flow velocity profile, the slight decrease of the streamwise Reynolds stresses in the vicinity of the walls, and the pronounced increase of the spanwise Reynolds stresses at higher rotation rates near the walls and particularly in the symmetry region. As to the numerical set-up it is shown that periodic boundary conditions in the spanwise direction suffice if the spanwise extent of the computational domain is larger than 10 times the channel half width.     

Flow over periodic hills - Numerical and experimental study in a wide range of Reynolds numbers

The paper presents a detailed analysis of the flow over smoothly contoured constrictions in a plane channel. This configuration represents a generic case of a flow separating from a curved surface with well-defined flow conditions which makes it especially suited as benchmark case for computing separated flows. The hills constrict the channel by about one third of its height and are spaced at a distance of 9 hill heights. This setup follows the investigation of Fröhlich et al. [Fröhlich J, Mellen CP, Rodi W, Temmerman L, Leschziner MA. Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J Fluid Mech 2005;526:19-66] and complements it by numerical and experimental data over a wide range of Reynolds numbers. We present results predicted by direct numerical simulations (DNS) and highly resolved large-eddy simulations (LES) achieved by two completely independent codes. Furthermore, these numerical results are supported by new experimental data from PIV measurements. The configuration in the numerical study uses periodic boundary conditions in streamwise and spanwise direction. In the experimental setup periodicity is achieved by an array of 10 hills in streamwise direction and a large spanwise extent of the channel. The assumption of periodicity in the experiment is checked by the pressure drop between consecutive hill tops and PIV measurements. The focus of this study is twofold: (i) Numerical and experimental data are presented which can be referred to as reference data for this widely used standard test case. Physical peculiarities and new findings of the case under consideration are described and confirmed independently by different codes and experimental data. Mean velocity and pressure distributions, Reynolds stresses, anisotropy-invariant maps, and instantaneous quantities are shown. (ii) Extending previous studies the flow over periodic hills is investigated in the wide range of Reynolds numbers covering 100?Re?10,595. Starting at very low Re the evolution and existence of physical phenomena such as a tiny recirculation region at the hill crest are documented. The limit to steady laminar flow as well as the transition to a fully turbulent flow stage are presented. For 700?Re?10,595 turbulent statistics are analyzed in detail. Carefully, undertaken DNS and LES predictions as well as cross-checking between different numerical and experimental results build the framework for physical investigations on the flow behavior. New interesting features of the flow were found.     

Host-Parasitoid系统的分岔与混沌控制

用数值模拟的方法,研究了Host-Parasitoid模型.该模型是一类非线性离散系统,反映了在一定的时间和空间内,寄生虫和寄宿主之间的生存状态.通过调节各种影响下的分岔参数,可以观察到系统具有周期泡,倍周期分叉,间歇混沌和Hopf分岔等复杂非线性动力学现象,揭示了系统通向混沌的途径.利用不同周期遍历下的奇怪吸引子和具有分形边界的吸引盆对系统的非线性特性进行了深入的探讨.最后利用参数开闭环控制法对系统的混沌状态进行了有效的控制.数值仿真和理论分析表明,选择相应的控制参数可将该系统的混沌状态控制到不同的稳定周期运动.     

Particle mixing and reactive front motions in chaotic but closed shallow flows

A numerical study is presented of wind-induced active mixing and transport processes in closed shallow flows that are able to support chaotic advection. The wind-induced non-linear shallow water flow field is predicted using a quadtree grid based Godunov-type finite volume solver. Particles are tracked by numerically integrating the advection equations using velocity information interpolated from the predicted flow field. In complex oscillating flows, storage of all the necessary velocity information becomes problematical. Instead, we utilize the mean field and the first few dominant unsteady contributions as determined using Singular Value Decomposition. The advected particles are assumed to support autocatalytic reaction defined as A + B → 2B. Wind-induced reactive particle advection is considered in a realistic mine tailings pond with somewhat idealized bed topography. The reactive process reaches a stationary stage where reaction products occupy the whole closed flow domain. However, in the transient stage, particles undergo active advection and trace out filamentary structures that are similar to those in open flows. Because of the impossibility of particle escape and the global fine-scale chaotic mixing, the initial stages of chaotic mixing in closed flows are more efficient than in open flows. The results qualitatively validate a surface reaction theory derived by Károlyi and Tél [Károlyi G, Tél T. Chemical transients in closed chaotic flows: the role of effective dimensions. Phys Rev Lett 2005;95:264501-1-4] for closed systems.     

The nonlinear behaviour of a slender flexible cylinder pinned or clamped at both ends and subjected to axial flow

The nonlinear dynamics of a slender flexible cylinder subjected to axial flow is studied when both its ends are either pinned or clamped, particularly focusing on the post-critical behaviour. In both cases, the system is stable at low flow velocities until the critical flow for divergence, at which point the initial equilibrium position of the cylinder becomes unstable and a new stable buckled solution arises (together with its symmetric counterpart). The amplitude of the buckled solution increases with the flow velocity. At higher flow, the buckled stationary cylinder loses stability by a Hopf bifurcation, after which a periodic solution arises. The frequency of oscillation after this Hopf bifurcation, in the case of a pinned–pinned cylinder, is almost twice as high as that in the clamped–clamped case, due to the dynamic loss of stability in a higher mode in the former case. The periodic solution is followed by a period-doubling bifurcation, giving rise to period-2 oscillations. The system undergoes a torus bifurcation afterward, followed by quasiperiodic and chaotic oscillations at higher flow velocities. All the critical flow velocities for the pinned–pinned cylinder are smaller than those for the clamped–clamped one. In the case of a pinned–pinned cylinder, at still higher flow velocities, there exists a range of flow velocities in which chaotic and static solutions co-exist; this has not been observed in the clamped–clamped case.     

Neural networks based subgrid scale modeling in large eddy simulations

In this paper a multilayer feed-forward neural network (NN) is used as subgrid scale (SGS) model in a large eddy simulation (LES). The NN was previously off-line trained using numerical data generated by a LES of a channel flow at Re_τ=180 with Bardina's scale similar (BFR) SGS model. Results show the ability of NNs to identify and reproduce the highly nonlinear behavior of the turbulent flows, and therefore the possibility of using NN techniques in numerical simulations of turbulent flows.     

Enhancement of an industrial finite-volume code for large-eddy-type simulation of incompressible high Reynolds number flow using near-wall modelling

We present a validation strategy for enhancement of an unstructured industrial finite-volume solver designed for steady RANS problems for large-eddy-type simulation with near-wall modelling of incompressible high Reynolds number flow. Different parts of the projection-based discretisation are investigated to ensure LES capability of the numerical method. Turbulence model parameters are calibrated by using a minimisation of least-squares functionals for first and second order statistics of the basic benchmark problems decaying homogeneous turbulence and turbulent channel flow. Then the method is applied to the flow over a backward facing step at Re_h = 37,500. Of special interest is the role of the spatial and temporal discretisation error for low order schemes. For wall-bounded flows, present results confirm existing best practice guidelines for mesh design. For free-shear layers, a sensor to quantify the resolution quality of the LES based on the resolved turbulent kinetic energy is presented and applied to the flow over a backward facing step at Re_h = 37,500.     

Particle mixing and reactive front motion in unsteady open shallow flow - Modelled using singular value decomposition

Passive and active tracers are used to examine particle mixing and reactive front dynamics in an open shallow flow of water past a circular cylinder. A quadtree grid based Godunov-type shallow water equation solver predicts the unsteady flow hydrodynamics of the wake behind the cylinder. The resulting periodic flow field consisting of a von Kármán vortex street is decomposed and stored over one oscillatory period using Singular Value Decomposition (SVD). Particles are advected according to the reconstructed flow field from the SVD modes, with continuous spatial velocity information obtained via bilinear interpolation. Passive particle dynamics driven by different SVD flow modes is investigated, and it is found that the flow field recovered from the mean flow and the first pair of time varying modes is adequate to represent the complicated dynamical properties induced by the original flow field. Active autocatalytic reaction, A + B → 2B, is incorporated into the particle advection model, assuming surface reaction. Active particles are found to trace out an expanded version of the unstable manifold of the chaotic saddle in the wake, in qualitative agreement with published analytical results. The numerical model is applicable to mixing and transport processes in more complicated shallow environmental flows.     

Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay

In this paper, by using the theories and methods of ecology and ordinary differential equation, an ecological model with impulsive control strategy and distributed time delay is established. By using the theories of impulsive equation, small amplitude perturbation skills and comparison technique, we get the condition which guarantees the global asymptotical stability of the lowest level prey and top predator eradication periodic solution. Further, influences of the impulsive perturbation and the parameter a on the inherent oscillation are studied numerically, which shows rich dynamics, such as period-doubling bifurcation, period-halving bifurcation, chaotic band, narrow or wide periodic window, chaotic crises, etc. Moreover, computation of the largest Lyapunov exponent demonstrates the chaotic dynamic behavior of the model. Meanwhile. we investigate the qualitative nature of strange attractor by using Fourier spectra. All these results may be useful for study of the dynamic complexity of ecosystems.     

Waves and spatially localized structures in the turbulent flows of a viscous fluid: Calculation results

A direct numerical simulation was performed of intermittent and turbulent flows of viscous incompressible fluid in an infinite circular pipe. The Navier-Stokes equations were integrated at the Reynolds numbers of 1800 ≤ Re ≤ 4000 calculated from the mean velocity and a pipe diameter of D = 2R. The numerically obtained solutions belong to the class of mean streamwise periodic solutions with a very large period λ_max = 16πR. The Fourier harmonic components of the velocity fluctuations corresponding to very low longitudinal wavenumbers are shown to be the most energetic. A detailed study was carried out of the structures of the calculated turbulent and intermittent flows. The accuracy and the very possibility of the approximation of the turbulent velocity field by the superposition of traveling and standing waves are analyzed. It is shown that the parameters of such a representation (wave amplitudes, phase velocities, and the position of the wave front) are strongly dependent on whether or not very low longitudinal wavenumbers are included in the mathematical model of the flow The numerical solutions at Re = 2200 and 2350 describe the intermittent type of the flow, for which the localized turbulent structures (turbulent puffs) propagate downstream while retaining their spatial dimensions. The space-time structure of the calculated turbulent puffs is compared with the available experimental data. The main statistical characteristics of the turbulence inside and outside the turbulent puff are calculated and the convective rate of the puffs downstream expansion is determined.     

三变量CSTR化学反应的复杂动力学行为分析

分析了一类三变量CSTR化学反应体系的动力学行为.用数值模拟的方法讨论了系统平衡态随参数变化的过程.给出了各种分岔模式及其相应的转迁集.分析发现系统平衡点通过Hopf分岔产生周期振荡现象,并进一步由倍周期分岔导致混沌.结合CSTR反应釜的反应过程,阐述了随着入料溶液中各成分比例含量的变化,整个化学系统中反应系数和反应速率从稳定阶段产生周期性变化,最后出现无规则性的化学振荡.     

Inertia effect on deformation of viscoelastic capsules in microscale flows

The deformation of capsules (i.e., cells, bacterial) in microscale flows plays an important role in biofluid flows such as blood flow in capillaries and cell manipulation in microfluidics. In previous studies on capsule deformation in microscale flows, the inertia effect was often assumed to be negligible and thus omitted. However, this assumption may not reflect real situations, as indicated by recent studies of inertial microfluidics. As such, we aimed to study the inertia effect on capsule deformation in microscale flows and to determine under which conditions this effect may be omitted. Using a collocated grid projection scheme, we developed a finite difference-front tracking method, and investigated the deformation of viscoelastic capsules in microscale flows for Reynolds number (Re) ranging from 0.01 to 10 as seen in vitro and in vivo. The results showed that the transient and steady-state deformation of capsules was significantly affected by inertia, and the flow structure varied considerably when Re was varied from 0.1 to 10. No significant changes were found for Re ranging from 0.01 to 0.1, and hence the inertia effect on capsule deformation in the microscale flows can be omitted when Re is less than 0.1. These findings improve the current understanding of the mechanism underlying cell movement in capillaries and can be applied to optimize the conditions for cell manipulation and separation in microfluidic devices.     

Single bubble rising dynamics for moderate Reynolds number using Lattice Boltzmann Method

Dynamics of a single rising gas bubble is studied using a Lattice Boltzmann Method (LBM) based on the Cahn-Hilliard diffuse interface approach. The bubble rises due to gravitational force. However, deformation and velocity of the bubble depend on the balance of other forces produced by surface tension, inertia, and viscosity. Depending on the primary forces acting on the system, bubble dynamics can be classified into different regimes. These regimes are achieved computationally by systematically changing the values of Morton number (Mo) and Bond number (Bo) within the following ranges (1×10^-5<Mo<3×10⁴) and (1<Bo<1×10³). Terminal shape and Reynolds number (Re) are interactive quantities that depend on size of bubble, surface tension, viscosity, and density of surrounding fluid. Accurate simulation of terminal shape and Re for each regime could be satisfactorily predicted and simulated, since they are also functions of Mo and Bo. Results are compared with previous experimental results.     

Simulation of unsteady compressible flow in a channel with vibrating walls - Influence of the frequency

This study deals with the numerical solution of a 2D unsteady flow of a compressible viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The channel is a simplified model of the glottal space in the human vocal tract and the flow can represent a model of airflow coming from the trachea, through the glottal region with periodically vibrating vocal folds to the human vocal tract.The flow is described by the system of Navier–Stokes equations for laminar flows. The numerical solution is implemented using the finite volume method (FVM) and the predictor–corrector MacCormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. Due to the motion of the grid, the basic system of conservation laws is considered in the Arbitrary Lagrangian–Eulerian (ALE) form.The authors present the numerical simulations of flow fields in the channel, acquired from a program developed exclusively for this purpose. The numerical results for unsteady flows in the channel are presented for inlet Mach number M_∞ = 0.012, Reynolds number Re_∞ = 4.5 × 10³ and the wall motion frequency 20 and 100 Hz.