Impact of density stratification on the global mode in a swirling jet: Stochastic modelling and Lagrangian coherent structures

In an experimental investigation, the stochastic dynamics of the global mode in a turbulent swirling jet are considered. From the application of the swirling jet in gas turbine combustors, it was observed that a specific density gradient in the flow leads to a suppression of the global mode. This phenomenon was replicated in a generic swirling jet using an electrical heating coil placed inside the breakdown bubble. In the present investigation, the dynamics of the global mode obtained from PIV and pressure measurements are analysed using a stochastic reduced-order model to describe the instability. The stochastic model is necessary to explain the interaction between the deterministic dynamics of the global mode and the perturbations by the background turbulence. The calibration of the stochastic model provides the amplification rate of the global mode that defines the transition of the flow, dependent on the swirling strength and the density difference. The spatial structure of the global mode is further investigated from Lagrangian coherent structures of the flow field which are computed from the 3D time-resolved velocity field reconstruction based on planar PIV measurements. The Lagrangian visualisations and schlieren visualisations are used to explain the absence of the density effects on the global mode at larger Reynolds numbers. The analysis gives a detailed view of the stochastic dynamics of a hydrodynamic instability in a turbulent flow.     

On the Capability of PIV-Based Wall Pressure Estimation for an Impinging Jet Flow

A PIV-based pressure estimation methodology is used to compute the wall pressure from the velocity field of a turbulent impinging jet flow. A simplified formulation (2D-2C) is applied to velocity fields issued from PIV data. The ability of the method to qualitatively estimate the wall pressure signature of a 3D unsteady impinging jet flow using only two velocity components in a plane is demonstrated. Nevertheless, the 2D flow assumption used in the context of planar measurements involves an underestimation of the wall pressure values all along the radial direction. The formulation based on the full integral formalism (3D-3C), computed from DNS data without any assumption on the flow, provides a reference solution. The contributions of the surface and volume integrals to the pressure coefficient are assessed. It is shown that the most important contribution to the wall pressure comes from the volume integral. Then the underestimation observed for the simplified formulation is mostly linked with the assumptions considered for the source term computation. The effect of each assumption is quantitatively analysed with the help of the DNS data and some ways to improve the simplified methodology are finally proposed.     

Instantaneous pressure and material acceleration measurements using a four-exposure PIV system

This paper describes a non-intrusive technique for measuring the instantaneous spatial pressure distribution over a sample area in a flow field. A four-exposure PIV system is used for measuring the distribution of material acceleration by comparing the velocity of the same group of particles at different times and then integrating it to obtain the pressure distribution. Exposing both cameras to the same particle field at the same time and cross-correlating the images enables precision matching of the two fields of view. Application of local image deformation correction to velocity vectors measured by the two cameras reduces the error due to relative misalignment and image distortion to about 0.01 pixels in synthetic images. An omni-directional virtual boundary integration scheme is introduced to integrate the acceleration while minimizing the effect of the local random errors in acceleration. Further improvements are achieved by iterations to correct the pressure along the boundary. Typically 3–5 iterations are sufficient for reducing the incremental mean pressure change in each iteration to less than 0.1% of the dynamic pressure. Validation tests of the principles of the technique using synthetic images of rotating and stagnation point flows show that the standard deviation of the measured pressure from the exact value is about 1.0%. This system is used to measure the instantaneous pressure and acceleration distributions of a 2D cavity turbulent flow field and sample results are presented.     

靠近排列的两个交错方柱三维绕流的数值模拟

通过用时间分裂算法求解Navier－Stokes方程,对中等Reynolds数下靠近排列的两个交错方柱三维绕流进行了数值模拟,其中,中间速度场用四阶Adams格式计算,压力场通过结合近似因子分解方法AF1与稳定的双共轭梯度方法Bi-CGSTAB进行迭代求解．数值模拟发现当两个方柱靠得较近时,有互相吸引趋势,而且上游方柱的Strouhal数较大．方柱的交错排列方式对绕流影响明显．计算结果与实验定性吻合,而且比用MAC－AF1方法计算的结果好．     

PIV-based pressure fluctuations in the turbulent boundary layer

The unsteady pressure field is obtained from time-resolved tomographic particle image velocimetry (Tomo-PIV) measurement within a fully developed turbulent boundary layer at free stream velocity of U _???=?9.3?m/s and Re_???=?2,400. The pressure field is evaluated from the velocity fields measured by Tomo-PIV at 10?kHz invoking the momentum equation for unsteady incompressible flows. The spatial integration of the pressure gradient is conducted by solving the Poisson pressure equation with fixed boundary conditions at the outer edge of the boundary layer. The PIV-based evaluation of the pressure field is validated against simultaneous surface pressure measurement using calibrated condenser microphones mounted behind a pinhole orifice. The comparison shows agreement between the two pressure signals obtained from the Tomo-PIV and the microphones with a cross-correlation coefficient of 0.6 while their power spectral densities (PSD) overlap up to 3?kHz. The impact of several parameters governing the pressure evaluation from the PIV data is evaluated. The use of the Tomo-PIV system with the application of three-dimensional momentum equation shows higher accuracy compared to the planar version of the technique. The results show that the evaluation of the wall pressure can be conducted using a domain as small as half the boundary layer thickness (0.5??₉₉) in both the streamwise and the wall normal directions. The combination of a correlation sliding-average technique, the Lagrangian approach to the evaluation of the material derivative and the planar integration of the Poisson pressure equation results in the best agreement with the pressure measurement of the surface microphones.     

Bichromatic particle streak velocimetry bPSV

We propose a novel technique for three-dimensional three-component (3D3C) interfacial flow measurement. It is based on the particle streak velocimetry principle. A relatively long integration time of the camera is used for capturing the movement of tracer particles as streaks on the sensor. The velocity along these streaks is extracted by periodically changing the illumination using a known pattern. A dye with different absorption characteristics in two distinct wavelengths is used to color the fluid. The depth of particles relative to the fluid interface can then be computed from their intensities when illuminated with light sources at those two different wavelengths. Hence, from our approach, a bichromatic, periodical illumination together with an image processing routine for precisely extracting particle streak features is used for measuring 3D3C fluid flow with a single camera. The technique is applied to measuring turbulent Rayleigh–Bénard convection at the free air--water interface. Using Lagrangian statistics, we are able to demonstrate a clear transition from the Batchelor regime to the Richardson regime, both of which were postulated for isotropic turbulence. The relative error of the velocity extraction of our new technique was found to be below 0.5?%.     

On the vortex dynamics in the wake of a finite surface-mounted square cylinder

The shedding process in the near wake of a surface-mounted, square cross-section cylinder of height-to-width aspect ratio 4 at a Reynolds number of 12,000 based on free-stream velocity and the obstacle width was investigated. The boundary layer thickness was 0.18 obstacle heights based on 99% free-stream velocity. The study is performed using planar high frame-rate particle image velocimetry synchronized with pressure measurements and hot-wire anemometry. Spatial cross-correlation, instantaneous phase relationships, and phase-averaged velocity data are reported. Two dominant vortex-shedding regimes are observed. During intervals of high-amplitude pressure fluctuations on the obstacle side faces, alternate formation and shedding of vortices is observed (regime A) similar to the von Kármán process. Regime B is characterized by two co-existing vortices in the obstacle lee throughout the shedding cycle and is observed within low-amplitude pressure fluctuation intervals. Despite the coexisting vortices in the base region, opposite sign vorticity is still shed out-of-phase downstream of this vortex pair giving rise to a staggered arrangement of counter-rotating vortices downstream. While the probability of occurrence of Regime B increases toward the free end, the amplitude modulation remains coherent along the obstacle height. Conditionally phase-averaged reconstructions of the flow field are consistent with the spatial distribution of the phase relationships and their probability density function. Earlier observations are reconciled showing that the symmetric shedding of vortices is a rare occurrence.     

A semi-implicit lagrangian scheme for 3D shallow water flow with a two-layer turbulence model

A semi-implicit Lagrangian finite difference scheme for 3D shallow water flow has been developed to include an eddy viscosity model for turbulent mixing in the vertical direction. The α-co-ordinate system for the vertical direction has been introduced to give accurate definition of bed and surface boundary conditions. The simple two-layer mixing length model for rough surfaces is used with the standard assumption that the shear stress across the wall region at a given horizontal location is constant. The bed condition is thus defined only by its roughness height (avoiding the need for a friction formula relating to depth-averaged flow, e.g. Chezy, used previously). The method is shown to be efficient and stable with an explicit Lagrangian formulation for convective terms and terms for surface elevation and vertical mixing handled implicitly. The method is applied to current flow around a circular island with gently sloping sides which produce periodic recirculation zones (vortex shedding). Comparisons are made with experimental measurements of velocity using laser Doppler anemometry (time histories at specific points) and surface particle-tracking velocimetry.     

Stereoscopic PIV on multiple color-coded light sheets and its application to axial flow in flapping robotic insect wings

Non-scanning volume flow measurement techniques such as 3D-PTV, holographic and tomographic particle image velocimetry (PIV) permit reconstructions of all three components (3C) of velocity and vorticity vectors in a fluid volume (3D). In this study, we present a novel 3D3C technique termed Multiple-Color-Plane Stereo Particle-Image-Velocimetry (color PIV), which allows instantaneous measurements of 3C velocity vectors in six parallel, colored light sheets. We generated the light sheets by passing white light of two strobes through dichroic color filters and imaged the slices by two 3CCD color cameras in Stereo-PIV configuration. The stereo-color images were processed by custom software routines that sorted each colored fluid particle into one of six gray-scale images according to its hue, saturation, and luminance. We used conventional Stereo PIV cross-correlation algorithms to compute a 3D planar vector field for each light sheet and subsequently interpolated a volume flow map from the six vector fields. As a first application, we quantified the wake and axial flow in the vortical structures of a robotic insect (fruit fly) model wing. In contrast to previous findings, the measured data indicate strong axial flow components on the upper wing surface, including axial flow in the leading-edge vortex core. Collectively, color PIV is robust against mechanical misalignments, avoids laser safety issues, and computes instantaneous 3D vector fields in a fraction of the time typical for other 3D systems. Color PIV might thus be of value for volume measurements of highly unsteady flows.     

Instantaneous planar pressure determination from PIV in turbulent flow

This paper deals with the determination of instantaneous planar pressure fields from velocity data obtained by particle image velocimetry (PIV) in turbulent flow. The operating principles of pressure determination using a Eulerian or a Lagrangian approach are described together with theoretical considerations on its expected performance. These considerations are verified by a performance assessment on a synthetic flow field. Based on these results, guidelines regarding the temporal and spatial resolution required are proposed. The interrogation window size needs to be 5 times smaller than the flow structures and the acquisition frequency needs to be 10 times higher than the corresponding flow frequency (e.g. Eulerian time scales for the Eulerian approach). To further assess the experimental viability of the pressure evaluation methods, stereoscopic PIV and tomographic PIV experiments on a square cylinder flow (Re _D  = 9,500) were performed, employing surface pressure data for validation. The experimental results were found to support the proposed guidelines.     

VISCOUS FLOWFIELD BASED ON DISCONTINUOUS BOUNDARY ELEMENT METHOD AND VORTEX METHOD

基于非协调边界元方法和涡方法的联合应用, 模拟了二维和三维黏性不可压缩流场. 计算中利用离散涡元对漩涡的产生、凝聚和输送过程进行模拟, 并将整体计算域分解为采用涡泡模拟的内部区域和用涡列模拟的数字边界层区域. 计算域中涡量场的拉伸和对流由Lagrangian涡方法模拟, 用随机走步模拟涡量场的扩散. 内部区域涡元涡量场速度由广义Biot-Savart公式计算, 势流场速度则采用非协调边界元方法计算. 非协调边界元将所有节点均取在光滑边界处, 从而避免了法向速度的不连续现象; 而对于系数矩阵不对称的大型边界元方程组,引入了非常高效的预处理循环型广义极小残余(the generalized minimum residual, GMRES)迭代算法, 使得边界元法的优势得到了充分发挥, 同时, 在内部涡元势流场计算中对近边界点采用了正则化算法, 该算法将奇异积分转化为沿单元围道上一系列线积分, 消除了势流计算中速度及速度梯度的奇异性. 二维、三维流场算例证明了所用方法的正确性, 也验证了该算法可以大幅度提高模拟精度和效率.     

Experimentally informed optimization of turbulent diffusivity for a discrete hole film cooling geometry

A process has been developed by which mean velocity and concentration measurements can be used to determine optimal turbulent diffusivity values for an angled jet in cross-flow configuration. This configuration has applications in film cooling for gas turbine blades. The measurements, obtained by magnetic resonance imaging techniques, provide 3D time-averaged velocity and concentration fields. The mean velocity field is fed into a Reynolds-Averaged Advection Diffusion solver, which uses a turbulent diffusivity model to solve for the mean coolant concentration distribution. This distribution can be compared to the experimentally-obtained concentration field by means of an error metric that quantifies the difference between the computational and experimental concentration fields. By minimizing this error, an optimal value of the turbulent diffusivity can be determined. This optimized distribution is then compared to a RANS simulation to evaluate the relative contribution to error of the turbulent momentum flux model versus the turbulent scalar flux model.     

Numerical investigation of cone angle effect on the flow field and separation efficiency of deoiling hydrocyclones

In this study, the effect of cone angle on the flow field and separation efficiency of deoiling hydrocyclones is investigated taking advantage of large eddy simulation. The dynamic Smagorinsky is employed to determine the residual stress tensor of the continuous phase. The method of Lagrangian particle tracking with an optimized search algorithm (closest cell) is applied to evaluate the separation efficiency of deoiling hydrocyclone. Simulations are performed on a 35-mm deoiling hydrocyclone with the three different cone angles of 6, 10 and 20 degree. The numerical results revealed that the changes in the cone angle would affect the velocity and pressure distribution inside hydrocyclone, and lead to changes in the separation efficiency. However, the large cone angle increases the tangential velocity and pressure gradient inside the hydrocyclone, but reduces the separation efficiency. The reasons behind the decrease in the separation efficiency are the flow structure and reduction of oil droplets residence time in hydrocyclones with large cone angles.     

Dispersion of passive tracers in a confined convective flow

A confined convective flow is experimentally studied at different Rayleigh numbers. Particle Tracking Velocimetry (PTV) technique is used both to reconstruct Lagrangian trajectories and to evaluate Eulerian flow field. Dispersion properties of the flow are investigated by means of Lagrangian statistics on particle displacements. For each run of the experiment, single particle statistics have been evaluated both on the whole set of trajectories and by selecting trajectories starting in phase from different region of the flow domain. These regions are identified according to the local geometrical characteristics of the velocity field.     

Large eddy simulation of bluff body wake in planar shear flow

Large eddy simulation of planar shear flow past a square cylinder has been investigated. Dynamic Smagorinsky model has been used to model subgrid scale stress. The shear parameter, K, namely the nondimensional streamwise velocity gradient in the lateral direction, is 0.0, 0.1 and 0.2. Reynolds number based on the centerline velocity is fixed at Re=21400. The time and span‐averaged velocity components, pressure coefficient, Reynolds stresses for uniform are in good agreement with the literature. In shear flow the calculated flow structure and mean velocity components are shown to be markedly different from those of the uniform flow. With increasing shear parameter, the cylinder wake is dominated by clockwise vortices. Both the velocity components in shear flow are compared with respective components in uniform flow. Comparison of normal and shear stresses between shear and no shear case have also been presented. Copyright © 2009 John Wiley & Sons, Ltd.     

PIV with volume lighting in a narrow cell: An efficient method to measure large velocity fields of rapidly varying flows

In this work we test a methodology for PIV measurements when a large field of view is required in planar confined geometries. Using a depth of field larger than the channel width, we intend to measure the in-plane variations of the velocity of the fluid averaged through the width of the channel, and we examine in which operating conditions this becomes possible. Measurements of the flow through a narrow channel by PIV are challenging because of the strong velocity gradients that develop between the walls. In particular, all techniques that use small particles as tracers have to deal with the possible migration of the tracers in the direction perpendicular to the walls. Among the complex mechanisms for migration, we focus on the so called Segré-Silberberg effect which can lead to transverse migration of neutrally buoyant tracers of finite size. We report experimental PIV measurements in a Hele-Shaw cell of 1 mm gap, which have been carried out by using neutrally buoyant tracers of size around 10 μm. By considering steady flows, we have observed, in particular flow regimes, the effect of an accumulation of the tracers at a certain distance to the wall due to the so called Segré-Silberberg effect. The particle migration is expected to occur at any Reynolds numbers but the migration velocity depends on the Reynolds number. A significant migration therefore takes place each time the observation duration is large enough compared to the migration time. For a given observation duration, the tracers remain uniformly distributed at low Reynolds numbers whereas they all accumulate at the equilibrium position at large ones. When using volume lighting, the PIV algorithm provides the average velocity of the flow through the gap at low Reynolds number, while it leads to the velocity of the flow at the equilibrium position of the tracers at large Reynolds numbers. By considering unsteady flows, we have observed that the migration does not occur if the timescale of flow variation is short compared to the time required for the parabolic flow to develop across the gap. In this case, there is no transverse velocity gradient and the PIV algorithm provides the fluid velocity. Altogether, these results allow us to propose guidelines for the interpretation of PIV measurements in confined flow, which are based on the theoretical predictions of the tracer migration derived by Asmolov [1].     

用管轴流速确定动脉中血液振荡流的速度剖面

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的速度与压力梯度之间的关系式，文章提出一种利用管轴外流速计算管内压力梯度，进而确定血液振荡流动速度分布的方法，该方法用于检测活体血管内血液振荡流的速度剖面，具有操作简单，精度较高的优点，最后，以人体颈动脉为例，讨论血液周期振荡流的速度分布特征，发现在任意时刻，除了邻近管壁速度迅速降为零之外，沿管截面速度分布相当均匀，呈现出与定常流不同的速度分布特征。     

准一维拉氏分析方法及其在凝聚炸药冲击波起爆研究中的应用

本文提出了一种准一维拉氏分析方法,用二维拉氏实验方法测得的不同拉氏位置上的压力和径向位移的变化曲线作为输入量,就能求解二维冲击波起爆过程中对称轴附近的流场。作为初步应用,文中列出了在两种加载条件下,压装TNT的二维冲击波起爆过程的分析结果。     

Coherent vortical and straining structures in the finite wall-mounted square cylinder wake

Topological aspects of the turbulent wake of a finite, surface-mounted, square-cross-section cylinder of h/d = 4 are addressed by decomposing the velocity field into a quasi-periodic coherent part and the unresolved incoherent fluctuations. The three-dimensional large scale structure is educed through a reconstruction of planar phase-averaged PIV measurements using the simultaneously sampled surface pressure difference on opposing sides of the obstacle as a phase reference. A topological model for the vortex structure is educed and mean streamwise wake vorticity is explained in terms of the connections between initially vertical structures shed alternately from either side of the obstacle, rather than previously proposed ‘tip’ vortex structures generated at the obstacle free-end. The coherent structure educed accounts for a significant portion of the fluctuating energy in the wake. The turbulent field is further analyzed by finding Lagrangian straining structures that form by induction of the coherent vorticity field, and these structures are related to the energy transfer from the base phase-averaged flow since they act to stretch incoherent vorticity fluctuations in their neighbourhood.     

3D scanning particle tracking velocimetry

In this article, we present an experimental setup and data processing schemes for 3D scanning particle tracking velocimetry (SPTV), which expands on the classical 3D particle tracking velocimetry (PTV) through changes in the illumination, image acquisition and analysis. 3D PTV is a flexible flow measurement technique based on the processing of stereoscopic images of flow tracer particles. The technique allows obtaining Lagrangian flow information directly from measured 3D trajectories of individual particles. While for a classical PTV the entire region of interest is simultaneously illuminated and recorded, in SPTV the flow field is recorded by sequential tomographic high-speed imaging of the region of interest. The advantage of the presented method is a considerable increase in maximum feasible seeding density. Results are shown for an experiment in homogenous turbulence and compared with PTV. SPTV yielded an average 3,500 tracked particles per time step, which implies a significant enhancement of the spatial resolution for Lagrangian flow measurements.