The effect of grease on the activated sludge process in wastewater treatment

Abstract

The purpose of this paper is to introduce the major potentials and perspectives of applications of finite element analysis in solving the problems of shallow water wave equations. One‐dimensional and two‐dimensional shallow water wave equations will both be incorporated into the modeling procedures. For one‐dimensional flows, the models will cover the typical single channels, confluence channels system, division channels system, and natural river systems. As far as two‐dimensional flows are concerned, the overland flows are investigated. The simulation results are compared with the data obtained by physical modeling and field observation and with the results of other existing literature. The models were found to be very feasible in modeling the complex flow fields of shallow water wave equation problems.     

Singularities in BIEs for the Laplace equation; Joukowski trailing-edge conjecture revisited

The paper deals with trailing-edge issues connected with the analysis of three-dimensional incompressible quasi-potential flows (i.e. flows that are potential everywhere, except for a zero-thickness vortex layer, called the wake). Specifically, following the Joukowski conjecture of smooth flow at the trailing edge, all the trailing-edge conditions that are required to avoid singularities in the boundary integral representation for the velocity, in a quasi-potential incompressible flow around a wing, are identified. In particular, these include the Kondrat'ev and Oleinik singularity as well as the vortex-line and the edge-jet singularities of Epton. Also, following Mangler and Smith, the behavior of the wake geometry at the trailing edge is determined, using the Kutta condition of no pressure discontinuity at the trailing edge. Specific theoretical issues are addressed which include (1) the relationship between Joukowski conjecture and Kutta condition, and (2) identification of those trailing-edge conditions that are necessary to assure the uniqueness of the solution (as opposite to relationships that are automatically satisfied by the solution). Regarding the first issue, in the main body of the paper, the Joukowski conjecture and the Kutta condition are used as if they were independent assumptions; then, in Appendix A, it is shown that the Kutta condition need not be invoked as a separate assumption since it may be obtained as a consequence of the governing equations and of the Joukowski conjecture. In order to clarify the second issue, the theoretical analysis is coupled with a numerical one. In particular, the conditions necessary to insure uniqueness are inferred (not proven) through numerical experimentation: only the no-vortex-line condition appears to be necessary to insure uniqueness. This is accomplished by using a piecewise-cubic boundary-element method for quasi-potential flows that is an extension of a high-order formulation introduced by the authors and their collaborators (the order of the formulation is adequate to address all the theoretical trailing-edge conditions uncovered). The emphasis is on steady flows in simply connected regions; however, some issues related to unsteady flows in multiply connected regions are also examined. Finally, several open problems that require additional work are identified.     

A three-step finite element method for unsteady incompressible flows

This paper describes a three-step finite element method and its applications to unsteady incompressible fluid flows. The stability analysis of the one-dimensional purely convection equation shows that this method has third-order accuracy and an extended numerical stability domain in comparison with the Lax-Wendroff finite element method. The method is cost effective for incompressible flows, because it permits less frequent updates of the pressure field with good accuracy. In contrast with the Taylor-Galerkin method, the present three-step finite element method does not contain any new higher-order derivatives, and is suitable for solving non-linear multi-dimensional problems and flows with complicated outlet boundary conditions. The three-step finite element method has been used to simulate unsteady incompressible flows, such as the vortex pairing in mixing layer. The properties of the flow fields are displayed by the marker and cell technique. The obtained numerical results are in good agreement with the literature.     

Transfer of discrete inclusions by fluxes with concentrated vorticity

Problems related to modeling of the motion of discrete inclusions (solid particles, drops or bubbles) in flows with concentrated vorticity are considered. A comparative evaluation of the force factors in the equation of motion of a test particle is made. The results of numerical modeling of the motion of discrete inclusions in the gap between concentric rotating cylinders and a vortex flow formed by the liquid rotating with a constant angular velocity over a fixed base are discussed. The coordinates of the points of equilibrium of the test particle in the vortex flow are found. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 2, pp. 36–45, March–April, 2007.     

台湾后龙溪桥风洞试验研究与静风响应分析

摘 要：通过风洞试验研究了台湾后龙溪桥气动稳定性;获得了混凝土梁和钢梁两种断面发生涡振的条件、涡振锁定风速范围及涡振振幅;对自然界和风洞中的风轴和体轴异同进行了区分;实测了两种断面的静气动力系数;最后进行了非线性静风荷载响应分析。研究结果表明：实桥风速达到135m/s,不会发生气动失稳;钢梁和混凝土梁断面+3°攻角时在均匀流场中会发生竖向和扭转涡振,扭转涡振风速锁定风速很高,而且范围很宽;在紊流度约为10％风场中,攻角在-3°～+3°范围内,未观测到明显涡振;由静风荷载引起的主梁附加攻角很小,风荷载非线性对主梁扭转位移和侧向位移影响很小,而对竖向位移影响相对较大,原因是竖向风荷载引起主缆刚度改变。     

Unsteady triple-shock configurations and vortex contact structures initiated by the interaction of an energy source with a shock layer in gases

The effect of physical and chemical properties of the gaseous medium on the formation of triple Mach configurations and vortex contact structures and on the stagnation pressure and drag force dynamics has been studied for supersonic flows with external energy sources. For the ratio of specific heats that varies in a range of 1.1–1.4, a significant (up to 51.8%) difference has been obtained for the angles of triple-shock configurations in flows at Mach 4 past a cylindrically blunted plate. When studying the dynamics of the decreases in the stagnation pressure and drag force, it has been revealed that these effects are amplified and the vortex mechanism of drag reduction starts to prevail as the adiabatic index decreases.     

Flow friction and heat and mass transfer in a swirled flow

An experimental investigation has been made of flow friction and heat and mass transfer inside cylindrical tubes with exit sections without diaphragms and various degrees of swirl of one-and two-phase flows, A comparative analysis of the results obtained has been made. The most suitable operating conditions from the energy standpoint have been established for vortex heat and mass transfer equipment.     

Relationship between vortex structures and shear localization in 3D granular specimens based on combined DEM and Helmholtz–Hodge decomposition

The paper presents three-dimensional simulation results of granular vortex structures in cohesionless initially dense sand during quasi-static plane strain compression. The sand behaviour was simulated using the discrete element method (DEM). Sand grains were modelled by spheres with contact moments to approximately capture the irregular grain shape. The Helmholtz–Hodge decomposition of the displacement vector field obtained with DEM was used. The variational discrete multiscale vector field decomposition allowed for separating a vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. A direct correlation between vortex structures and shear localization was studied. The simulation results showed that vortex structures were closely connected to spontaneous shear localization. They localized early in locations wherein a shear zone ultimately developed. They were affected by the specimen depth.     

Beam spreading of vortex beams propagating in turbulent atmosphere

We present some results obtained by numerical modeling of the propagation of vortex beams LG(0l) through a randomly inhomogeneous medium. The vortex beams are the lower order Laguerre-Gaussian modes. Such beams, if propagated under conditions of weak turbulence, also experience distortions, like a Gaussian beam. However, the statistically averaged vortex beams (LG(0l)) conserve the central intensity dip with a nonzero intensity on the beam axis. The beam broadening of vortex beams is analyzed. The average vortex beams are found to be broadened less than the Gaussian beam while propagated through a randomly inhomogeneous medium. The higher the topological charge l is, the smaller the beam broadening is.     

On the mechanism of the Ranque–Hilsch effect

A model of flow in a Ranque vortex tube is suggested. It is based not on the thermal interaction between hot and cold flows, but rather on a mechanical one. It is shown that to describe the Ranque–Hilsch effect it is necessary, along with the radial flow, to take into account the uptake or addition of mass, as well as to ensure a smoother conjugation between a forced and a peripheral vortices, demanding the continuity not only of the tangential velocity component, but also of its first derivative with respect to the radius. In this case, the motion in the vortex tube is considered as a system of vortex flows and vortex sources interacting between themselves.     

A Lagrangian modeling approach with the direct simulation Monte-Carlo method for inter-particle collisions in turbulent flow

A Lagrangian modeling approach, which combines the direct simulation Monte-Carlo (DSMC) method and a Reynolds-averaged Navier-Stokes model to account for inter-particle collisions and turbulence characteristics of the carrier fluid, respectively, is proposed. The wall-bounded turbulent particle-laden flows in which the experimental data are available are chosen as the test problems for demonstration. Results obtained with the deterministic method accounting for inter-particle collisions are used as a basis for validating the proposed stochastic Lagrangian model. Good agreement between the predictions obtained separately with the deterministic and DSMC methods is achieved. The benefit of saving computational expenditure when using the DSMC method becomes more remarkable than the deterministic method as the number of particles loaded in the flow is increased. In addition, the study demonstrates that τ_P/τ_C is a proper parameter to monitor the role of inter-particle collisions in the physical processes of particle-laden flows.     

New studies in vortex dynamics: Incompressible and compressible vortex reconnection,core dynamics,and coupling between large and small scales

Coherent structure dynamics in turbulent flows are explored by direct numerical simulations of the Navier-Stokes equations for idealized vortex configurations. For this purpose, two dynamically significant coherent structure interactions are examined: (i) incompressible and compressible vortex reconnection and (ii) core dynamics (with and without superimposed small-scale turbulence). Reconnection is studied for two antiparallel vortex tubes at a Reynolds number (Re) of 10³. Incompressible reconnection consists of three distinct phases: inviscid advection, bridging and threading. The key mechanism, bridging, involves the ‘cutting’ of vortex lines by viscous cross diffusion and their subsequent reconnection in front of the advancing vortex dipole. We conjecture that reconnection occurs in successive bursts and is a physical mechanism of cascade to smaller scales. Compressible reconnection is seen to be significantly affected by the choice of pressure and density initial conditions. We propose a polytropic initial condition which is consistent with experimental results and low-Mach number asymptotic theories. We also explain how compressibility initiates an early reconnection due to shocklet formation, but slows down the circulation transfer at late times. Thus, the reconnection timescale increases with increasing Mach number. Motivated by the important role of helical vortex lines in the reconnected vortices (bridges), we focus our attention on the dynamics of an axisymmetric vortex column with axial variation of core size. The resulting core dynamics is first explained via coupling between swirl and meridional flows. We then show that core dynamics can be better understood by applying a powerful analytical tool —helical wave decomposition — which extracts vorticity wave packets, thereby providing a simple explanation of the dynamics. The increase in core size variation with increasing Re in such a vortex demonstrates the limitation of the prevalent vortex filament models which assume constant core size. By studying the columnar vortex with superimposed small-scale, homogeneous, isotropic turbulence, we address the mutual interactions between large and small scales in turbulent flows. At its boundary the columnar vortex organizes the small scales, which, if Re is sufficiently high, induce bending waves on the vortex which further organize the small scales. Such backscatter from small scales cannot be modelled by an eddy viscosity. Based on the observation of such close coupling between large and small scales, we question the local isotropy assumption and conjecture a fractal vortex model for high Re turbulent flows.     

A Lagrangian approach for vorticity intensification in swirling rings

The Lagrangian approach, adopted in vortex methods for incompressible Euler flows, is reconsidered here as the most appropriate technique to track the dynamical evolution of organized vorticity structures in free space. We analyze in this paper a specific initial condition, the swirling ring with azimuthal perturbations, from which originate vortex dynamics events leading to a localized but strong vorticity intensification. The aim is to understand the possible development of a finite time singularity, in the context of inviscid flows, and its relevance for the study of intermittency, as one of the most challenging aspects of turbulence.     

大跨度箱形钢拱肋气弹模型涡振试验研究

通过风洞试验研究了大跨度矩形钢拱肋气弹模型在均匀流场和紊流场中3种攻角(-3°、0°、+3°)、多种偏角(0°～90°)条件下的涡振响应.研究结果表明:均匀流场中,发现了稳定的一阶反对称竖弯和对称竖弯涡振,紊流场中未发现明显稳定的涡振;均匀流场中,一阶反对称竖弯涡振振幅很小,风速较低,锁定区也很窄;一阶对称竖弯涡振振幅很大,风速较高,锁定区也很宽;1/4断面涡振振幅大于拱顶断面涡振振幅;可以认为当偏角大于10°时,矩形拱肋不会出现涡振.     

A localized collocation meshless method (LCMM) for incompressible flows CFD modeling with applications to transient hemodynamics

The current paper reports on the development and validation of a localized collocation meshless method (LCMM) to model laminar incompressible flows. A high order upwinding scheme was devised to dampen the numerical oscillations arising in convection-dominated flows. Subsequently, the LCMM was analytically validated and demonstrated to yield third-order accurate solutions when compared to a benchmark analytical decaying vortex solution. Numerical validations are provided by comparison with the finite volume commercial (FVM) solver Fluent 6.2. The flow geometry for the numerical validation arises from a biomedical application that consists of modeling blood flow in the inter-connection between a bypass graft and an artery. Very good agreement was found between the LCMM and the FVM.     

Numerical Study of Particle Dispersion in the Wake of Two Tandem Square Cylinders Using Discrete Vortex Method

This study has been conducted to investigate numerically the particle dispersion in the wake of dilute particle-laden gas flows past two identical square cylinders in tandem arrangement at Reynolds number of 10,000,000. In the numerical method, the discrete vortex method is employed to calculate the gas flow fields, and the Lagrangian approach is applied to track individual solid particles. A dispersion function is defined to represent the lateral dispersion scale of particles. The wake vortex patterns and the distributions of particles with various Stokes numbers ranging from 0.01 to 10 are obtained. The numerical results reveal that: (1) the particles with St = 0.01 can distribute both in the vortex core and around the vortex periphery, whereas the particles with St = 1.0, 10 congregate mainly around the vortex periphery; (2) the particles with St = 0.01, 0.1 are trapped by the vortices into the gap between the two square cylinders, while very few particles with St = 1.0, 10 are distributed within the gap; (3) the particle's dispersion intensity along the lateral direction decreases greatly as St is increased from 0.01 to 10.     

The simulation of material behaviors in friction stir welding process by using rate-dependent constitutive model

Friction stir welding is a new solid state joining technology, which is suitable for joining some hard-to-weld materials, such as aluminum alloy, magnesium alloy, etc. The modeling of material flows can provide an efficient method for the investigation on the mechanism of friction stir welding. So, 3D material flows under different process parameters in the FSW process of 1018 steel are studied by using rate-dependent constitutive model. Numerical results indicate that the border of the shoulder can affect the material flow near the shoulder–plate interface. The mixture of the material in the lower half of the friction stir weld can benefit from the increase in the angular velocity or the decrease in the welding speed. But flaws may occur when the angular velocity is very high or the translational velocity is very small. When the angular velocity applied on the pin is small or the welding speed is high, the role of the extrusion of pin on transport of the material in FSW becomes more important. Swirl or vortex occurs in the tangent material flow and may be easier to be observed with the increase in the angular velocity of the pin.     

Flow rate measurement in a pipe flow by vortex shedding

The flow rate measurement of liquid, steam, and gas is one of the most important areas of application for today’s field instrumentation. Vortex meters are used in numerous branches of industry to measure the volumetric flow by exploiting the unsteady vortex flow behind a blunt body. The classical Kármán vortex street behind a cylinder shows a decrease in Strouhal number with decreasing Reynolds number. Considering the flow behind a vortex shedding device in a pipe the Strouhal-Reynolds number dependence shows a different behaviour for turbulent flows: a decrease in Reynolds number leads to an increase in Strouhal number. This phenomenon was found in the experimental investigations as well as in the numerical results and has been confirmed theoretically by a stability analysis.     

基于iDDES的双三角翼大迎角非定常涡破裂特征分析

采用基于两方程k-ω-SST模型的iDDES方法对80°/65°双三角翼涡破裂流动进行了数值模拟,获得了迎角α=30°~40°范围内,涡破裂在双三角翼主翼面上方发生时的气动力、表面压力、空间涡结构、湍动能等流动信息,在与风洞实验充分比对的基础上,详细分析了涡破裂发生时的涡破裂形态,表面压力均方根值分布,非定常气动力、表面压力脉动等流动特征,对涡破裂与气动力频谱、表面压力/压力脉动、空间速度、湍动能分布之间的相互关系进行了阐述,并分析了以这些流动信息为判据得到的涡破裂位置之间的相关性。     

Numerical Investigation of the Hydrodynamics of a Twisted Flow in a Vortex Chamber Based on the Two‐Parameter Model of Turbulence

An approach based on solution of complete averaged Navier–Stokes equations in vortex chambers using a lowReynolds k– model of turbulence is considered. The problem is solved in the variables vortex, stream function, and circular component of the velocity. The method of oriented pseudoconvection is used for problems of the dynamics of twisted flows. The method allows one to retain second order of accuracy of convective terms and provide stability of the solution for rather high Reynolds numbers. The problem of formulation of boundary conditions of second order of accuracy for vorticity on a solid wall at angular points is considered. An analysis of the results obtained shows that numerical calculations within the framework of the considered model of turbulence agree with experimental data rather well.