A numerical investigation of turbulent flows in a spanwise rotating channel

A numerical investigation of fully developed turbulent flow in a spanwise rotating channel is performed to study turbulence characteristics subject to system rotation. The work provides insight into several salient features of the spanwise rotating turbulent channel flows, including the near-wall vortical structures, turbulence energy cascade and redistribution, and vortex stretching. The influence of system rotation on the near-wall vortical structures is investigated based on the vorticity fluctuations and their probability density functions (PDF). The properties of the Lamb vector fluctuation and the corresponding PDF are examined to reveal the effect of rotation on the turbulence energy cascade and production in the rotating channel. The budgets of Reynolds stresses and fluctuating enstrophy are analyzed to elucidate the role of the Coriolis force on turbulence energy redistribution between the streamwise and wall-normal directions and the mechanisms of vortex stretching for the generation of the vorticity fluctuations near the pressure and suction walls.     

Extracting 3D vortices in turbulent fluid flow

This paper presents a computational framework to extract salient patterns, called vortex structures, from 3D turbulent fluid flows. These structures can be characterized as regions of dominating rotational motion in the velocity fields and intensity concentrations in the corresponding vorticity fields. A pointwise linear representation is employed to approximate the kinematics of the flow field, and the fluid motion is classified according to motion analysis or topological patterns. The regions of vortex structures are identified as those dominated by rotational motion or those of focus-type singularity. The 2D vortices, as a special case of 3D vortices, are detected by searching for regions of vorticity concentrations     

Application of astigmatism μ-PTV to analyze the vortex structure of AC electroosmotic flows

The three-dimensional (3D) flow due to AC electroosmotic (ACEO) forcing on an array of interdigitated symmetric electrodes in micro-channels is experimentally analyzed using astigmatism micro-particle tracking velocimetry (astigmatism μ-PTV). Upon application of the AC electric field with a frequency of 1,000 Hz and a voltage of 2 Volts peak–peak, the obtained 3D particle trajectories exhibit a vortical structure of ACEO flow above the electrodes. Two alternating time delays (0.03 and 0.37 s) were used to measure the flow field with a wide range of velocities, including error analysis. Presence and properties of the vortical flow were quantified. The steady nature and the quasi-2D character of the vortices can combine the results from a series of measurements into one dense data set. This facilitates accurate evaluation of the velocity field by data-processing methods. The primary circulation of the vortices due to ACEO forcing is given in terms of the spanwise component of vorticity. The outline of the vortex boundary is determined via the eigenvalues of the strain-rate tensor. Overall, astigmatism μ-PTV is proven to be a reliable tool for quantitative analysis of ACEO flow.     

A combined boundary integral and vortex method for the numerical study of three-dimensional fluid flow systems

Vortex methods using vorticity–velocity formulations have become an increasingly powerful and popular means of studying complex fluid flow systems. The problem of combining an integral equation method and grid-free discrete vortex method (DVM) when studying three-dimensional wall-bounded flows is considered. While the normal boundary condition is satisfied by means of a boundary integral equation (BIE), we also consider the problem of recovering pressure from given vorticity and velocity fields when using Lagrangian DVMs in terms of a BIE. For validation purposes, vortical flow past a sphere and past a flat plate are considered, for which the commonly used method of images is available. Results of near-wall boundary-layer flow simulations are then presented as an illustration of the numerical scheme. The importance of hairpin vortices is highlighted. Finally, results on wall compliance fluid flow are displayed emphasizing the versatility of the numerical method.     

跨声速机翼阻力分解的一种改进方法

提出黏性区域探测器的一种改进形式，并用于捕捉激波和翼梢涡的熵增阻力；给出尾迹平面的可压缩涡动力学诱导阻力表达式，并与基于热力学的诱导阻力对比。在跨声速来流状态下，对ONERA M6和某民用飞机巡航状态下的机翼阻力进行分解，同时分析该民用飞机机翼安装翼梢小翼前、后的远场阻力构成。结果表明：新的区域探测器合理可靠，黏性阻力与伪熵阻力的计算结果更加准确；2种诱导阻力计算方式的计算结果一致，但基于涡动力学的诱导阻力计算方法受积分平面位置的影响更小；安装翼梢小翼基本不影响整个流场的黏性阻力，减阻的主要效果体现为诱导阻力的减小。     

A Low Dimensional Fluid Motion Estimator

In this paper we propose a new motion estimator for image sequences depicting fluid flows. The proposed estimator is based on the Helmholtz decomposition of vector fields. This decomposition consists in representing the velocity field as a sum of a divergence free component and a vorticity free component. The objective is to provide a low-dimensional parametric representation of optical flows by depicting them as deformations generated by a reduced number of vortex and source particles. Both components are approximated using a discretization of the vorticity and divergence maps through regularized Dirac measures. The resulting so called irrotational and solenoidal fields consist of linear combinations of basis functions obtained through a convolution product of the Green kernel gradient and the vorticity map or the divergence map respectively. The coefficient values and the basis function parameters are obtained by minimization of a functional relying on an integrated version of mass conservation principle of fluid mechanics. Results are provided on synthetic examples and real world sequences.     

Vortex and strain skeletons in Eulerian and Lagrangian frames

We present an approach to analyze mixing in flow fields by extracting vortex and strain features as extremal structures of derived scalar quantities that satisfy a duality property: they indicate vortical as well as high-strain (saddletype) regions. Specifically, we consider the Okubo-Weiss criterion and the recently introduced MZ-criterion. While the first is derived from a purely Eulerian framework, the latter is based on Lagrangian considerations. In both cases high values indicate vortex activity whereas low values indicate regions of high strain. By considering the extremal features of those quantities, we define the notions of a vortex and a strain skeleton in a hierarchical manner: the collection of maximal 0D, 1D and 2D structures assemble the vortex skeleton; the minimal structures identify the strain skeleton. We extract those features using scalar field topology and apply our method to a number of steady and unsteady 3D flow fields.     

Normal shock boundary layer control with various vortex generator geometries

Various vortex generators which include ramp, split-ramp and a new hybrid concept “ramped-vane” are investigated under normal shock conditions with a diffuser at Mach number of 1.3. The dimensions of the computational domain were designed using Reynolds Average Navier–Stokes studies to be representative of the flow in an external-compression supersonic inlet. Using this flow geometry, various vortex generator concepts were studied with Implicit Large Eddy Simulation. In general, the ramped-vane provided increased vorticity compared to the other devices and reduced the separation length downstream of the device centerline. In addition, the size, edge gap and streamwise position respect to the shock were studied for the ramped-vane and it was found that a height of about half the boundary thickness and a large trailing edge gap yielded a fully attached flow downstream of the device. This ramped-vane also provided the largest reduction in the turbulent kinetic energy and pressure fluctuations. Additional benefits include negligible drag while the reductions in boundary layer displacement thickness and shape factor were seen compared to other devices.     

圆柱绕流的二维数值模拟和尾迹分析

为指导机械设计中参数和布局的选择,研究固定在水流中的圆柱结构件的受力情况和流场分布．利用FLUENT中的三种湍流模型对雷诺数为3900的圆柱绕流进行二维数值模拟并进行对比,得到升力因数、阻力因数、分离角、斯特劳哈尔数和涡街尺寸等参数的模拟结果,与参考文献中的实验结果对比验证二维模拟的预测精度．RKE（Realizable k-ε）和雷诺应力模型（Reynolds Stress Model,RSM）均能在此雷诺数下得出接近实验结果的流场,RSM模型使用POWER LAW离散格式的结果优于QUICK格式．与三维模拟的对比表明二维模拟适合在设计初期的快速估算,能够快速得到合适精度的模拟结果．     

Shape optimization for drag reduction in linked bodies using evolution strategies

We present results from the shape optimization of linked bodies for drag reduction in simulations of incompressible flow at moderate Reynolds numbers. The optimization relies on the covariance matrix adaptation evolution strategy (CMA-ES) and the flow simulations use vortex methods with the Brinkman penalization to enforce boundary conditions in complex bodies. We exploit the inherent parallelism of CMA-ES, by implementing a multi-host framework which allows for the distribution of the expensive cost function evaluations across parallel architectures, without being limited to one computing facility. This study repeats in silico for the first time Ingo Rechenberg’s pioneering wind tunnel experiments for drag reduction that led to the inception of evolution strategies. The simulations confirm that the results of these experimental studies indicate a flat plate is not the optimal solution for drag reduction in linked bodies. We present the vorticity field of the flow and identify the governing mechanisms for this drag reduction by the slightly corrugated linked plate configuration.     

基于二维模型的电梯井道空气流动分析

为研究电梯井道尺寸和电梯运行速度等对井道空气流动的影响,建立二维电梯井道模型,利用FLUENT对井道空气流动进行数值模拟.通过量纲分析和试验设计,针对不同阻塞比和雷诺数,选取60个样本点进行数值模拟,并建立流场参数的响应面.基于响应面的分析可知：轿厢阻力因数和井道空气最大流速比（最大流速与电梯运行速度之比）主要与阻塞比有关,并随阻塞比增大而变大;阻塞比和雷诺数都对轿厢表面的湍流强度和无量纲流场平均涡量都有影响.     

Vortex visualization for practical engineering applications

In order to understand complex vortical flows in large data sets, we must be able to detect and visualize vortices in an automated fashion. In this paper, we present a feature-based vortex detection and visualization technique that is appropriate for large computational fluid dynamics data sets computed on unstructured meshes. In particular, we focus on the application of this technique to visualization of the flow over a serrated wing and the flow field around a spinning missile with dithering canards. We have developed a core line extraction technique based on the observation that vortex cores coincide with local extrema in certain scalar fields. We also have developed a novel technique to handle complex vortex topology that is based on k-means clustering. These techniques facilitate visualization of vortices in simulation data that may not be optimally resolved or sampled. Results are included that highlight the strengths and weaknesses of our approach. We conclude by describing how our approach can be improved to enhance robustness and expand its range of applicability.     

Flow around the impulsively started elliptic cylinder at various angles of attack

The flow around an impulsively started elliptic cylinder at 0, 30, 45 and 90° incidence is investigated. The fluid is viscous, incompressible and its flow is governed by the Navier-Stokes equations. Semi-analytical solutions are calculated by solving numerically the system of coupled partial differential equations which are obtained by substituting the expanded finite Fourier Series of the stream and vorticity functions in the Navier-Stokes equations. The symmetrical solutions are presented for Reynolds number 200 and eccentricity 0.809 and 0.943 in terms of patterns of streamlines, lines of constant vorticity, pressure and vorticity distributions around the surface, drag coefficient and wake length at 0 and 90° and compared with the experimental results. A comparison of the calculations has been made for Reynolds number 100 and eccentricity 0.648 with different number of terms at 90°. A Kármán vortex street develops for Reynolds numbers 200 and 60 at 30 and 45° incidence and the solutions are presented in terms of various characteristics including Strouhal number. The vanishing of wall-shear does not denote separation in any meaningful sense in various cases.     

Synthetic Controllable Turbulence Using Robust Second Vorticity Confinement

Capturing fine details of turbulence on a coarse grid is one of the main tasks in real‐time fluid simulation. Existing methods for doing this have various limitations. In this paper, we propose a new turbulence method that uses a refined second vorticity confinement method, referred to as robust second vorticity confinement, and a synthesis scheme to create highly turbulent effects from coarse grid. The new technique is sufficiently stable to efficiently produce highly turbulent flows, while allowing intuitive control of vortical structures. Second vorticity confinement captures and defines the vortical features of turbulence on a coarse grid. However, due to the stability problem, it cannot be used to produce highly turbulent flows. In this work, we propose a robust formulation to improve the stability problem by making the positive diffusion term to vary with helicity adaptively. In addition, we also employ our new method to procedurally synthesize the high‐resolution flow fields. As shown in our results, this approach produces stable high‐resolution turbulence very efficiently.     

Interaction of decaying trailing vortices in spanwise shear flow

The drift of trailing vortices in a cross wind near the ground is modeled by an unsteady two-dimensional, rotational flowfield where there are concentrations of large vorticity in spots having small effective sizes and finite total strengths. The problem is analyzed by combining the matched asymptotic solution of the decaying vortical spots and the Euler solution of the background unsteady rotational flow. Using the method of averaging, we develop a numerical scheme in which the grid size and time step depend only on the length and velocity scales of the background flow and not on the effective core size of vortical spots. Numerical results are presented to illustrate the interaction between the trajectories of the vortical spots and the convection of vorticity in the background flowfield.     

A predictor-corrector technique for visualizing unsteady flow

Presents a method for visualizing unsteady flow by displaying its vortices. The vortices are identified by using a vorticity-predictor pressure-corrector scheme that follows vortex cores. The cross-sections of a vortex at each point along the core can be represented by a Fourier series. A vortex can be faithfully reconstructed from the series as a simple quadrilateral mesh, or its reconstruction can be enhanced to indicate helical motion. The mesh can reduce the representation of the flow features by a factor of 1000 or more compared with the volumetric dataset. With this amount of reduction, it is possible to implement an interactive system on a graphics workstation to permit a viewer to examine, in 3D, the evolution of the vortical structures in a complex, unsteady flow     

A Legendre-Spectral Element Method for Flow and Heat Transfer About an Accelerating Droplet

The problem of flow and heat transfer associated with a spherical droplet accelerated from rest under gravitational force is studied; using a Legendre-spectral element method in conjunction with a mixed time integration procedure to advance the solution in time. An influence matrix technique which exploits the superposition principle is adapted to resolve the lack of vorticity boundary conditions and to decouple the equations from the interfacial couplings. The computed flow and temperature fields, the drag coefficient, the Nusselt number, and the interfacial velocity and vorticity are presented for a drop moving vertically in a quiescent gas of infinite extent to illustrate the evolution of the flow and temperature fields. Comparison of the predicted drag coefficient and the Nusselt number against previous numerical and experimental results indicate good agreement.     

Visualization of vorticity and vortices in wall-bounded turbulent flows

This study was initiated by the scientifically interesting prospect of applying advanced visualization techniques to gain further insight into various spatio-temporal characteristics of turbulent flows. The ability to study complex kinematical and dynamical features of turbulence provides means of extracting the underlying physics of turbulent fluid motion. The objective is to analyze the use of a vorticity field line approach to study numerically generated incompressible turbulent flows. In order to study the vorticity field, we present a field line animation technique which uses a specialized particle advection and seeding strategy. Efficient analysis is achieved by decoupling the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. Multifield visualizations are obtained using a flexible volume rendering framework which is presented in this paper. Vorticity field lines have been employed as indicators to provide a means to identify "ejection" and "sweep" regions; two particularly important spatio-temporal events in wall-bounded turbulent flows. Their relation to the rate of turbulent kinetic energy production and viscous dissipation, respectively, have been identified.