On the realizability of reynolds stress turbulence closures

The realizability of Reynolds stress models in homogeneous turbulence is critically assessed from a theoretical standpoint. It is proven that a well known second-order closure model formulated using the strong realizability constraints of Schumann (1977) and Lumley (1978) is, in fact, not a realizable model. The problem arises from the failure to properly satisfy the necessary positive second time derivative constraint when a principal Reynolds stress vanishes-a flaw that becomes apparent when the nonanalytic terms in the model are made single-valued as required on physical grounds. More importantly, arguments are advanced which suggest that it is impossible to identically satisfy the strong from of realizability in any version of the present generation of second-order closures. On the other hand, models properly formulated to satisfy the weak form of realizability—wherein states of one or two component turbulence are made inaccessible in finite time via the imposition of a positive first derivative condition—are found to be realizable. However, unlike the simpler and more commonly used second-order closures, these models can be ill-behaved near the extreme limits of realizable turbulence due to the way that higher-degree nonlinearities are often unnecessarily introduced to satisfy realizability. Illustrative computations of homogeneous shear flow are presented to demonstrate these points which can have important implications for turbulence modeling.     

Turbulence Characteristics in Gradual Channel Transition

A field study was conducted to determine the effects of a channel transition on turbulence characteristics. Detailed three-dimensional (3D) flow measurements were collected at a cross section that is located downstream of a gradual channel expansion. These measurements were obtained via an acoustic doppler velocimeter and include the 3D velocity field, the mean local velocities, the turbulent intensities, the frictional characteristics of the flow, the secondary velocity along the transverse plane, and the instantaneous shear stress components in the streamwise and transverse directions. Analysis of the 3D flow data indicates that the turbulent flow on the outer bank of the channel is anisotropic. Such anisotropy of turbulence, which is attributed to the gradual expansion in the channel and bed roughness, yields the development of a secondary flow of Prandtl’s second kind as reported in 1952. In particular, it was found that turbulent intensities in the vertical and transverse directions on the outer bank section are different in magnitude creating turbulence anisotropy in the cross-sectional plane and secondary flows of the second kind. Turbulent intensities increase toward the free surface indicating the transfer of a higher-momentum flux from the channel bed to the free surface, which contradicts common wisdom. Results for the normalized stress components in the streamwise and transverse direction show similar behavior to the intensities. Moreover, the nonlinear distribution of stresses is indicative of the oscillatory nature of the flow induced by the secondary flows of Prandtl’s second kind. A similar behavior was found for flows in straight rectangular channels over different roughness. Finally, a comparison between the secondary current velocity with the mainstream velocity indicates that secondary flow of Prandtl’s second kind is present within the right half of the measured cross section.     

Eddy Taxonomy Methodology around a Submerged Barb Obstacle within a Fixed Rough Bed

Past research in environmental hydraulics has established the consideration that small- and large-scale turbulent eddy structures correspond to fast and slow fluctuations within a velocity time series measured at a fixed location. This work embraces this concept and develops an eddy taxonomy methodology to classify the prominent small- and large-scale eddies in the vicinity of an obstacle within a fixed rough bed. The previously documented visual interpretation technique is used in conjunction with a novel technique, which utilizes the statistical skew parameter, to quantify the moving-average time step at which large-scale eddies may be isolated from small-scale eddies. Thereafter, triple decomposition theory is employed and prominent spatial and temporal scales (i.e., integral length scales and periodicity) of small- and large-scale eddies are calculated. The eddy taxonomy methodology is implemented using acoustic Doppler velocimeter time-series measurements captured in the vicinity of an experimental model of a submerged barb obstacle—a hydraulic structure used for bank protection and increasing aquatic diversity. Implementation of the eddy taxonomy methodology using the streamwise velocity (u) time series and streamwise-vertical Reynolds stress (uw) time series provide similar results for the time step necessary to decompose large- from small-scale eddies. Eddy taxonomy results indicate the presence of large-scale, macroturbulent eddies throughout the barb test section with periodicity and length scales that agree with literature reported values. Additionally, small-scale bed derived eddies are most pronounced in the deflected flow regions where the barb obstacle has less influence upon the flow, while multiple small-scale eddies, including ejection, wake, and Kelvin–Helmotz associated eddies, persist in the downstream overtopping and wake regions of the barb obstacle.     

小型亚热带半日潮河口中的湍流

在天然河口,污染物的输送是由湍流动量混合驱动的,而弥散的大小却难以被准确地预测。这是由于对河口的湍流结构缺乏基础的认识而造成的。介绍在一个小型的亚热带半日潮河口进行的高频率及连续50 h的湍流实地测量的情况。在研究的浅水(低潮水深小于0．5 m)小型河口中,使用了最适用于这种水体的声学多普勒流速仪进行测量,并进行了完整的后处理工作。河口水流是一个波动的过程,各种宏观流动参数随潮周期和其它大尺度的过程而波动,但是湍流特性是由即时局部流动特性所决定,它们基本不受流动历程的影响,其结构和瞬时变化受多种机理影响。这导致其只与水流剪切力引起的湍流边界层平衡相关。所有湍流特性在潮周期中均有大波动是本次研究数据的一个显著特征,这一特征在此前少有记载,但本次的测量数据与过往数据的一大差别是,数据连续测量的时间长且频率高。这将为波动特性的动量交换系数及积分时间和长尺度提供新的信息,这些湍流特性不应被视为不变的。     

Compensation Method of Laser Drifting by Atmosphere Turbulence in Large Shafting Aligning

Instead of the rotor shafting line, visible laser beam, as a centering and adjusting benchmark of rotor bearing groove or static components, has been used to examine and repair the high precision shafting in many industry areas. Atmosphere turbulence is one of the important factors that affect shafting alignment precision. A correcting method is proposed in this paper, which monitors the light target to measure the drift of laser direetrix in real time and compensates the error using beeline correction.     

Kinetic theory based CFD simulation of turbulent fluidization of FCC particles in a riser

The turbulent fluidization regime is characterized by the co-existence of a dense, bottom region and a dilute, top bed. A kinetic theory based CFD code with a drag corrected for clusters captured the basic features of this flow regime: the dilute and dense regions, high dispersion coefficients and a strong anisotropy. The computed energy spectrum captures the observed gravity wave and the Kolmogorov -5/3 law at high frequencies. The computed turbulent kinetic energy is close to the measurements for FCC particles. The CFD simulations compared reasonably well with the measured core-annular flow experiments at very high solid fluxes. The computed granular temperatures, solids pressures, FCC viscosities and frequencies of oscillations were close to measurements reported in the literature. The computations suggest that unlike for the flow of group B particles, the oscillations for the FCC particles in the center of the riser are primarily due to the oscillations of clusters and not due to oscillations of individual particles. Hence mixing is not on the level of individual particles.     

Convection Velocity of Vortex Structures in the Near Wake of a Circular Cylinder

The convection velocity of vortex structures in the near wake of a circular cylinder was experimentally investigated over the region 1.6–2.5 ? x/D ? 12.0 for R = 160–12,000. Dye injection technique of flow visualization and two completely noninvasive laser Doppler velocimeters were employed for R ? 320 and ?400, respectively. The convection velocity, Uc, is defined as the mean traveling velocity of vortex cores passing a streamwise separation during a mean elapsed time. For R ? 320, Uc was determined directly from the motion of dye-marked vortex cores filmed by a video camera. In the cases of R ≥ 400, the positions of peak vorticity and half of the half-velocity-defect width at each downstream section were first used to identify the mean path of vortex cores (i.e., the most probable trajectory of the vortex structures), along which spatial correlation measurements were then performed to determine the mean elapsed time corresponding to the maximum cross correlation. The present results show that, in laminar and transitional wakes, the ratio Uc/Uo increases from 0.53 to 0.84 over a region of 1.6 ? x/D ? 6.0 and then tends to be a constant of 0.84 for x/D ≥ 6.0. In a turbulent wake, Uc/Uo also increases from a certain value at a point downstream from the position of vortex formation to a mean value of about 0.86 at x/D ≥ 5.0–6.0, and then changes little with the increase of x/D. In addition, it is found that the dependence of Uc/Uo on R almost disappears for x/D ≥ 5.0.     

Effect of the attack angle on the roll and trailing vortex structures in an agitated vessel with a paddle impeller

The purpose of the present study is to observe the effect of the blade attack angle on the roll and trailing vortex structures in a stirred vessel via laser-Doppler velocimetry (LDV). In this investigation, four-bladed paddle impellers with four attack angles, which were 45^°, 60^°, 75^° and 90^°, respectively, were used. By synchronizing LDV with a rotary encoder coupled to the impeller shaft, angle-resolved measurements of all three velocity components were performed. This experimental method made it possible to capture the details of the vortical structure both behind the impeller blade and discharge region. Our study on the mean flow structure generated by three types of pitched blade turbines (45^°, 60^°, and 75^°, respectively) found that a single trailing vortex was formed around each turbine blade. Roll-up of the vortex sheet issuing from the blade tip was also observed, which indicated a major roll of trailing vortex generation mechanism for each pitched blade turbine.     

The application of flow dispersion models to the FM01-LC laboratory filter-press reactor

The flow distribution in the rectangular channel of a laboratory filter-press electrochemical reactor was evaluated using three flow models namely: (a) axial dispersion, (b) sum of two phases and (c) fast and stagnant zones. In the case of the axial-dispersion model, several methods have been used to calculate the Peclet number; the moment method, the non-linear least-squares and the Laplace transform technique. Several boundary conditions, involving different physical and experimental assumptions of the flow were used to solve the partial differential equation that describes the flow behaviour. A total of nine expressions to examine flow dispersion has been used. The comparison of experimental and predicted response signals was made by evaluating the root mean squared error. A data fit in real time has been found to be a better choice as solutions based on the evaluation of moments are prone to error due the overweight of the signal at long times. Data fitting in the Laplace plane is very accurate but it does not guarantee a good fit in real time. Models based on the sum of a fast and a slow or stagnant phase resulted in solutions having very low values of the extension of the slow and stagnant phases, the assumption of a single phase with some degree of dispersion was considered more appropriate.     

Numerical prediction of turbulent convective heat transfer in mini/micro channels for carbon dioxide at supercritical pressure

A new approach to take into account the effects of variable physical properties on turbulence is suggested. It allows to choose freely the turbulent closure model for conventional terms due to velocity fluctuations and to describe coherently the additional terms due to density fluctuations. Numerical calculations based on the suggested approach have been performed for carbon dioxide flowing within mini/micro channels under cooling conditions. The numerical predictions show that the effects due to density fluctuations are smaller than it could have been initially supposed and that the heat transfer impairment for mini/micro channels, which some experiments seem to highlight, is not completely explained by the considered model.