A numerical analysis of vortex growth in a two-dimensional jet

The vortex growth in a two-dimensional jet is simulated by solving numerically full Navier-Stokes equations with primitive variables. The streakline structures visualized with marker particles are well related to the fluctuations of velocity and pressure. The mechanism of vortex growth is also explained by using the visualized structure. The predicted features will agree with the experimental fact that, for example, the dominant frequency of fluctuation exists and the longitudinal velocity fluctuation along the jet axis increases exponentially in the zone of linear growth, while in the zone of non-linear growth the increasing rate decreases.     

A numerical analysis of vortex growth in a bounded rectangular jet

A low apsect ratio bounded rectangular jet flow with an artificial disturbance is numerically analyzed by solving three-dimensional Navier-Stokes equations with primitive variables. The streakline structures are related to the velocity and pressure fields. To explain the mechanism initiating a secondary flow in the initial field where the flow shows a well ordered structure, the streakline distortions are discussed by the velocity fluctuations in the flow field. The results advocate the existing relations between the secondary flow and the vortex growth.     

A numerical study of flow past a cylinder with cross flow and inline oscillation

Two-dimensional fluid flow around an oscillating circular cylinder is studied numerically at different values of oscillation frequency and amplitude. A novel finite element method which uses discretization along the characteristic line is used for simulation. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian-Eulerian (ALE) formulation to account for body motion in the flow field. Two cases of cylinder motion have been studied, cross flow and inline oscillation. In both cases, occurrence of lock on is investigated and the bounds of the lock on region are determined. A comparison of the numerical results with the experimental data indicates that 2D simulation is valid up to Re = 300. Beyond that, 3D effects appear. By using flow visualization, effect of a cylinder oscillation on the flow field and wake pattern has been studied. Also, variation of the mean drag coefficient against the oscillation parameters is discussed. The numerical results are in good agreement with the experimental data available in the literature.     

Effect of tube spacing on the vortex shedding characteristics of laminar flow past an inline tube array: A numerical study

The effect of tube spacing on the vortex shedding characteristics and fluctuating forces in an inline cylinder array is studied numerically. The examined Reynolds number is 100 and the flow is laminar. The numerical methodology and the code employed to solve the Navier-Stokes and continuity equations in an unstructured finite volume grid are validated for the case of flow past two tandem cylinders at four spacings. Computations are then performed for a six-row inline tube bank for eight pitch-to-diameter ratios, s, ranging from 2.1 to 4. At the smallest spacing examined (s = 2.1) there are five stagnant and symmetric recirculation zones and weak vortex shedding activity occurs only behind the last cylinder. As s increases, the symmetry of the recirculation zones breaks leading to vortex shedding and this process progressively moves upstream, so that for s = 4 there is clear shedding from every row. For any given spacing, the shedding frequency behind each cylinder is the same. A critical spacing range between 3.0 and 3.6 is identified at which the mean drag as well as the rms lift and drag coefficients for the last three cylinders attain maximum values. Further increase to s = 4 leads to significant decrease in the force statistics and increase in the Strouhal number. It was found that at the critical spacing there is 180° phase difference in the shedding cycle between successive cylinders and the vortices travel a distance twice the tube spacing within one period of shedding.     

A simple rectangular element for two-dimensional analysis of laminated composites

A simple rectangular finite element was developed for two-dimensional analysis of laminated composite materials. The rectangular laminated composite (RLC) element eliminates the need to add elements to a model simply to account for the material properties of various laminae. This is particularly advantageous for thick laminates with many lamina. Explicit integration in terms of generalized displacements minimizes the algebraic effort required to derive the element stiffnesses and the thermal load vector. A substitute shape function technique is used to improve the performance of the element in modeling bending type deformation. Results for several example problems are discussed.     

The numerical solution of two-dimensional flow in a branching channel

A numerical method for treating the steady two-dimensional flow of a viscous incompressible fluid in a branching channel is given. The Navier-Stokes equations are written in terms of the stream function and vorticity, giving the usual two coupled partial differential equations. These equations are solved using the difference scheme of Dennis and Hudson [Proc. 1^st Cong. Num. Met. Laminar and Turbulent Flow, p. 69. Pentech Press, London (1978)] and a solution to the resulting large system of algebraic equations is obtained using a Gauss-Seidel iteration technique. The upstream and downstream boundary conditions are discussed and a logarithmic transformation is applied to the coordinate measuring distance downstream in order to extend the numerical solution far enough downstream. Two methods are presented for dealing with the singularity in the vorticity at the sharp corners where the channel bifurcates. The numerical solution is obtained for three separate grid sizes for two different widths of channel downstream of the channel branch. The effect on flow separation of both the variation of Reynolds number and the relative channel width upstream and downstream of the branch are discussed.     

On the numerical solution of two-dimensional integral equations using a meshless local discrete Galerkin scheme with error analysis

Engineering with Computers - This investigation presents a simple and effective method for numerically solving two-dimensional Fredholm integral equations of the second kind on non-rectangular...     

Multigrid solutions of steady two-dimensional flow past a cascade of sudden expansions

In the steady laminar flow past a sudden expansion the motion is assumed to be two-dimensional and to be governed by the Navier-Stokes equations for incompressible fluids. In this work the multigrid method is employed to obtain finite-difference solutions to the steady Navier-Stokes equations, which are in terms of the vorticity and stream function, up to Re = 1000 for a uniform inflow past a cascade of expansions. The calculations show that, for both small and large values of the expansion ratio, the eddy length increases linearly with Re, which is in good agreement with recent theoretical work but contradicts some previously published Navier-Stokes computations.     

A numerical method for dynamic response analysis of discrete systems

A numerical method that permits the calculation of the time-dependent response of linear discrete systems is presented. The approach presented in this paper differs from direct integration methods, and is based on the concept of complex frequency response and fast Fourier transform which has been adapted for dynamic analysis. The method is unconditionally stable and very effective for the dynamic analysis of a system served by proportional and inertial feedback compared with direct integration methods. A Fortran coded program for dynamic analysis has been employed to calculate the transient-state response of the turning machine-tool structure.     

Unsteady RANS modelling of flow past a rectangular cylinder: Investigation of Reynolds number effects

The unsteady flow field around a two-dimensional rectangular prism with a fineness ratio (chord-to-thickness) of 5.0, is studied using Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. A noncommercial unstructured flow solver is used in the simulations at various Reynolds numbers (from 26,000 to 1,850,000 based on the chord length), two different angles of attack (0° and 4°) and low Mach number (0.1). A grid-convergence study is presented in order to investigate the dependence of the flow solution on the spatial and temporal discretization. Results obtained with one- and two-equation turbulence models are compared, including models based on the Explicit Algebraic Reynolds Stress (EARSM) approach. The aim of this work is to assess the capability of the computationally efficient two-dimensional URANS calculations to predict the features of complex massively separated flow around this type of geometry. A further goal is to use numerical simulations to investigate the strong Reynolds number effects observed in wind-tunnel experiments. Satisfactory agreement with the wind-tunnel data is obtained for several test cases, but only the turbulence model based on the EARSM approach captured the significant lift increase at non-zero angles of attack due to variation of Reynolds number. This phenomenon is shown to be related to the progressive upstream migration of the time-averaged shear-layer reattachment location on one side of the rectangular cylinder. The effects of the Reynolds number on the mechanism of vortex shedding are also explored in the simulations.     

A numerical analysis of turbulent flow in pipes

The finite element method is used to solve both fully developed and developing turbulent flow in pipes. A particular feature of the approach is the introduction of a special wall element. The purpose of the introduction of such an element is twofold. The first is to avoid using elements with extremely large aspect ratios and the second to attempt a better representation of near wall changes in velocity. The applicability of the method is illustrated by comparing with published experimental and numerical data.     

A numerical analysis of muzzle blast precursor flow

A new computational technique, involving the formation of grids by conformal mappings, the use of the λ-scheme and of shock fittings is applied to solve the Navier-Stokes equations which describe the flow field behind the precursor shock consequent to the firing of a gun, until the bullet is entirely out of the barrel. The numerical analysis is presented in detail and reasons for the choice of the technique are discussed. Three examples are presented, discussed and compared with experimental results.     

Stability analysis and numerical simulation of gravitactic bioconvection in a rectangular cavity

The bioconvection of gravitactic microorganisms, through linear analysis and numerical simulation is presented. Using the basic state as initial condition for both microorganisms and streamlines, the critical Rayleigh number and the bioconvection are predicted. The dynamic microorganisms’ behavior is influenced by the initial spatial distribution. The stability of the system is dependent on the horizontal wave component that is inversely related to wavelength. The pattern length and the instability of the process are associated with the horizontal component of the wave number and the characteristic wavelength, respectively. Using complex and real eigenvalues, five unstable and three stable rolls are found respectively. The three stable rolls is the dominant pattern when varying the principal variables of this bioconvective process.     

基于BML模型的二维交通流系统的模拟分析

BML模型是专门用于模拟分析交通现象的元胞自动机模型,利用此模型通过计算机模拟二维城市交通流系统,找出车辆的平均速度与平均密度等参数的关系,通过编程模拟的交通流的时空图可以得出当车辆密度保持基本不变时,交通流由完全阻塞相恢复到运动相存在着自组织性,并且指出相变点的位置与平均密度有着密切的关系,同时分析了临界密度在交通控制中的实际意义。     

Numerical model of a two-dimensional,non-plane transient magnetohydrodynamic flow

The equations describing two-dimensional three-component magnetohydrodynamic (MHD) transient flows are formulated for a system of spherical coordinates. With the numerical code based on Implicit Continuous Fluid Eulerian (ICE) scheme, MHD flows resulting from a sudden energy release in a stratified medium are examined. Because of the inclusion of out-of-plane components of velocity and magnetic fields, MHD transverse waves are observed in addition to fast, slow and entropy waves. Numerical results for compressible MHD shocks are found in satisfactory agreement with the theoretical predictions.     

A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow

A numerical model for the simulation of incompressible two-phase flows of a flat granular bed submitted to a laminar shearing flow is presented, considering a two-fluid model and a mixed-fluid one. The governing equations are discretized by a finite element method and a penalisation method is introduced to cope with the incompressibility constraint. A regularisation technique is used to deal with the visco-plastic behaviour of the granular phase. Validations are carried out on three flow test cases: a Bingham fluid between two infinite parallel planes, a Bingham fluid in a square lid-driven cavity and a Newtonian fluid over a granular bed in a two-dimensional configuration, for which we compare our numerical results with existing analytical or numerical results. The accuracy and efficiency of the numerical models have been compared for the two formulations of the two-phase flow model. It turns out that the two-fluid model requires ten times more CPU time than the mixed-fluid one for a comparable accuracy, which can be achieved provided one takes a smaller regularisation parameter in the latter model. Finally, three-dimensional computations are presented for the flow of a Newtonian fluid over a granular bed in a square and circular cross-section ducts.     

具有混合时滞血液模型的Hopf分支与数值分析

研究了一类具有混合时滞血液模型的Hopf分支问题。首先以特征值理论为基础得到了模型无条件稳定的充要条件;其次给出了Hopf分支的存在性及分支处模型平衡态稳定性的条件;最后通过数值分析验证了定理条件和结论的可实现性。     

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.     

Computation of taylor vortex flow by a transient implicit method

A finite difference method is presented for the computation of steady axisymmetric solutions of Navier-Stokes equations using the time dependent stream function, vorticity, and tangential velocity formulation. The scheme involves implicit fractional steps and fast Fourier transforms. Upwind differencing for convective terms is used in order to increase the stability for high values of the Reynolds number. The method is applied to the flow in an annulus of rectangular cross section with rotating walls. Attention is focused upon the problem of centrifugal instabilities, non-uniqueness of the steady state solution, and selection of wavelengths in the supercritical range.     

交通流多预期延迟模型与数值仿真

为了更准确地描述交通流,考虑驾驶员反应延迟时间和前车信息的非均衡使用,建立一种多预期延迟跟驰模型。线性稳定性分析表明,驾驶员反应延迟时间的增加会降低交通流的稳定性,多个前车信息的使用可以提高交通流的稳定性。数值仿真的结果表明,减少司机的反映延迟时间和适当地增加前车信息都能提高交通流的稳定性。为尽可能少地引入输入变量,不均衡地利用前车的车间距和速度差信息是必要的。理论和数值模拟的结果均表明驾驶员反应延迟在交通拥堵的形成过程中起着重要作用。