Steady viscous flow past a tapered cylinder

The three-dimensional nature of the viscous flow past a linearly tapered circular cylinder is examined at low Reynolds numbers. The numerical solution of the unsteady Navier–Stokes equations converges to a steady state. The primary flow in planes perpendicular to the cylinder axis is practically indistinguishable from the two-dimensional flow past a uniform cylinder. A secondary spanwise flow is observed in the stagnation zone going from the wide end towards the narrow end, whereas a secondary motion on the rear side goes in the opposite direction. In spite of this secondary flow, the length of the separation zone varies linearly with the local Reynolds number.     

一种基于冯卡门尺度的湍流模式在模拟稳态和非稳态流动问题中的应用

采用尺度自适应模型(SAS)对稳态和非稳态流动进行了数值仿真。SAS模型有效解决了传统脱体涡数值模拟(DES)方法在网格加密过程中引发的“附面层速度型偏离对数率”的问题;同时,SAS模型的尺度自解效应也赋予了该方法类LES特征,可以在不出现非物理解的前提下有效地释放当地脉动。通过高雷诺数平板边界层模拟,SAS方法在附面层内模拟的速度型分布与理论值贴合得很好,说明该方法对于稳态流动的求解并未偏离RANS模型;同时,在串联双圆柱算例中,SAS方法对于圆柱表面压力分布的预测精度高于其他稳态和非稳态模型,Q云图也显示出该方法的类LES特征。算例结果证明了SAS方法有着一定的工程使用价值。     

Steady flow past an elliptic cylinder inclined to the stream

The properties of steady two-dimensional flow past an elliptic cylinder inclined to the oncoming stream are investigated for small to moderate values of the Reynolds number for which good accuracy can be assured. The solutions are based on a numerical method of solution of the Navier-Stokes equations for incompressible fluids which ensures that all the correct conditions of the problem are satisfied. In particular, the solution is carried out in such a way that the vorticity decays rapidly enough at large distances from the cylinder for the lift and drag on the cylinder to be finite. Results are presented for the variation of lift, drag and streamline patterns with inclination and Reynolds number. Two elliptic cylinders (based on their minor-to-major axes ratio) are considered. For an elliptic cylinder with minor-to-major axes ratio 1:5, results are obtained for Reynolds numbers up to 40 and inclination varying from zero to 90°. Streamline plots for these results show a development of the solution from asymmetric flow at zero inclination (with no separation), through asymmetric flows with increasing inclination (with either no separation, separation with a single recirculating region, or separation with two recirculatory regions) to the symmetric flow at 90° incidence (with two counter rotating vortices). Of interest are asymmetric steady-state results which contain two recirculatory regions trailing the cylinder, one attached and one unattached to the cylinder. Results are also obtained for a second elliptic cylinder with minor-to-major axes ratio 1:10 at Reynolds numbers 15 and 30, inclination 45°. These results are found to be in good agreement with corresponding unsteady results taken to long times (which are tending to a steady state).     

Experimental study on the particle accumulation phenomenon in seeded flows around a near-bottom-wall horizontal cylinder

In experiments of flows around a cylinder in a water channel, an interesting phenomenon is that a particle accumulation line obviously forms on the bottom of the channel. The present paper focuses on this phenomenon, and the formation mechanism of the particle accumulation line is in detail investigated experimentally with particle image velocimetry (PIV). The circular cylinder was set in a fully developed turbulent boundary layer with 12 gap ratios S/D ranging from 0 to 1.5 under two Reynolds numbers (1371 and 902) based on the momentum loss thickness. The possible mechanism of this phenomenon has been demonstrated with the experimental results: the separation takes place due to the interaction between the wake of the cylinder and the boundary layer of the plane wall, the gap flow separates from the wall downstream of the cylinder and causes an attachment vortex of low velocity area at about 1 to 2 cylinder diameters from the cylinder, where the particle accumulation line forms steadily.     

Viscous vortex core generation

Summary The unsteady flow of a viscous incompressible fluid between two porous co-axial circular cylinders is analysed when the outer cylinder is impulsively set into rotation. When there is radial inflow, vorticity is transferred from an unsteady boundary layer initially over the outer cylinder to a steady boundary layer over the inner cylinder.With 1 Figure     

非紧致边界气动噪声数值预测方法

通过寻找满足非紧致边界的精确格林函数,发展了一种基于声模拟理论的非紧致边界气动噪声数值预测方法。该方法首先采用边界积分方法计算满足相应边界条件的精确格林函数,然后采用精确格林函数求解FW-H方程,进行远场气动噪声预测。考虑了非紧致边界对声波传播的散射作用,适用于尺寸较大且几何外形复杂的边界与非定常流动相互作用诱发的气动噪声的数值预测。以雷诺数90 000、马赫数0.2的圆柱绕流诱发的气动噪声为例,数值预测了非紧致边界条件下的气动噪声,并与采用自由空间格林函数求解FW-H的计算结果进行了对比,对该方法进行了验证。     

Heat transfer and icing of a rough cylinder

Heat transfer from a rough ice surface to air is a fundamental factor determining the icing rate and ice shape on an object under conditions where the impinging water flux exceeds the icing rate. In order to examine the effect of the roughness characteristics on icing, a boundary-layer model of heat transfer from a front half of a rough circular cylinder is proposed. The model is based on the integral equations of the boundary layer, and predicts the local heat transfer coefficient along the cylinder surface and, subsequently, the overall heat transfer rate. Comparison between the results of the model and the available experimental data for three different roughnesses in the cylinder Reynolds number range 5 × 10⁴ < Re < 4 × 10⁶ show that the model simulates the heat transfer more precisely than the previous formulations used in icing models.     

Numerical study of bluff body flow structures

Our recent progress in numerical studies of bluff body flow structures and a new method for the numerical analysis of near wake flow field for high Reynolds number flow are introduced. The paper consists of three parts. In part one, the evolution of wake vortex structure and variation of forces on a flat plate in harmonic oscillatory flows and in in-line steady-harmonic combined flows are presented by an improved discrete vortex method, as the Keulegan-Carpenter number (KC) varies from 2 to 40 and ratios ofU _m toU ₀ are ofO(10⁻¹),O(1) andO(10), respectively. In part 2, a domain decomposition hybrid method, combining the finite-difference and vortex methods for numerical simulation of unsteady viscous separated flow around a bluff body, is introduced. By the new method, some high resolution numerical visualization on near wake evolution behind a circular cylinder at Re=10², 10³ and 3×10³ are shown. In part 3, the mechanism and the dynamic process for the three-dimensional evolution of the Kármán vortex and vortex filaments in braid regions as well as the early features of turbulent structure in the wake behind a circular cylinder are presented numerically by the vortex dynamics method. This study was supported by the National Natural Science Foundation of China and the Laboratory for Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, as well as by the National Basic Research project “Nonlinear Science”.     

高雷诺数下高质量比圆柱涡致振动的数值模拟

圆柱的涡致振动一直是研究者们关注的问题,但是以往的研究大多雷诺数不高,或者质量比较低。该文以高质量比圆柱为研究对象,采用质量-弹簧-阻尼系统,基于SST湍流模型,对结构在高雷诺数下发生涡致振动的过程进行了数值模拟和分析。通过流固耦合数值计算,模拟了圆柱涡致振动的高幅分支试验现象,计算所得的最大振幅比随速度比的变化曲线与试验吻合较好。研究结果验证了流固耦合计算方法的正确性,表明SST模型适合于由强逆压梯度引起的边界层分离流动问题。数值模拟显示在高雷诺数下,高质量比的圆柱涡致振动会出现高幅分支。该文的数值分析方法可以为高雷诺数下结构涡致振动问题的研究提供参考。     

基于特征线分离算法的大涡模拟

将基于特征线的分离算法与大涡模拟相结合,推导了不可压流大涡模拟有限元离散方程组,并将该方法应用于三维流场的层流及湍流非定常计算。将不同雷诺数下的三维顶盖驱动空腔流动计算结果与实验数据以及直接数据模拟结果进行对比,吻合较好,验证了方法的可靠性和准确性。     

Development of a flow field structure in the vicinity of a circular cylinder in the presence of a laminar-turbulent transition

The Reynolds equations and the two-parameter differentialq-Ω model of turbulence are used to investigate a flow past a circular cylinder with an isothermal surface (temperature factorT _w0 = 0.5) at the Mach numberM _∞ = 5 in the range of Reynolds numbers Re = 10⁴-10⁸. It is demonstrated that the turbulization of flow leads to a shift of the separation point downstream, a reduction and stabilization of the separation zone length, a decrease in the maximum velocity in the separation zone, and an increase in the heat flux at the rear stagnation point compared with its value at the forward stagnation point.     

Supersonic Flow of Viscous Gas in a Flat Channel at High Values of the Reynolds Number

Based on numerical analysis of two-dimensional Reynolds equations using the differential model of turbulence, the structure of flow field and aerodynamic characteristics of a flat channel with variable cross section at the inlet Mach number of four is investigated in the range of Reynolds numbers Re = 10⁵–10⁷. According to the calculation results, the interaction between a shock and a laminar boundary layer results in the emergence of a closed separation zone. During interaction with a turbulent boundary layer, two flow schemes are possible, depending on the intensity of incident shock, namely, without and with separation. The extrapolation of calculation data to nonviscous flow (limiting transition Re ) shows that the classical scheme of regular reflection of the shock from a flat surface corresponds to interaction without separation. Corresponding to interaction with separation is the flow scheme with formation of a small closed separation zone in which a subsonic circulation flow takes place.     

叶栅内非定常不可压流动的数值模拟

基于SMAC(SimplifiedMarkerandCell)方法推导出直接求解二维非定常、不可压N-S方程的隐式数值方法。求解的基本方程是任意曲线坐标系中以逆变速度为变量的N-S方程和椭圆型的压力Poisson方程。采用该方法,对二维叶栅非定常分离流场进行了数值模拟,叶栅表面压力的计算结果与试验结果相比比较吻合,从而验证了这种方法的可靠性。同时对叶栅非定常流场的流场结构和流动机理做了初步的探讨。在均匀来流和定常边界条件下,叶栅内部流动表现出强烈的非定常性;在小冲角和高雷诺数时,叶栅尾部产生类似卡门涡街的周期性流动。     

High-frequency actuator control of air flow near a circular cylinder: Impact of the discharge parameters on the cylinder aerodynamic drag

The impact of capacitive high-frequency surface discharge on a flow around a circular cylinder is studied at airflow velocity of 20–100 m/s and the Reynolds numbers Re < 2.4 × 10⁵. The power of the discharge was modulated at a frequency of 10²–10⁴ Hz, corresponding to the Strouhal number St = 0.1–10. It is shown that the distribution of pressure in the wake behind the cylinder is significantly influenced by the discharge. A decrease in the average diameter of the wake is observed. The parameters of the discharge were measured: the gas temperature, heating rate in the discharge region, and velocity of discharge propagation.     

速度剪切流中圆柱体绕流特性的数值模拟

采用由速度梯度、圆柱半径以及圆柱中心平面上的来流平均速度定义的无量纲剪切参数β来描述速度剪切的强度。在雷诺数Re=60-1000范围内,运用三维直接数值模拟(DNS)和大涡模拟(LES)两种方法对速度剪切流中的圆柱体的绕流特性进行了数值模拟。研究了驻点、高速和低速两侧分离点、圆柱表面压力分布以及不稳定尾流结构随剪切参数的变化及其对雷诺数的依赖性,从而得到了剪切流中圆柱体的气动力以及脱落特性,并对其机理进行了详细探讨。     

Shear flow past a square cylinder near a wall

A numerical study on the wake behind a square cylinder placed parallel to a wall has been made. The cylinder is considered to be within the boundary layer of the wall, so that the outside flow is taken to be due to uniform shear. Flow has been investigated in the laminar Reynolds number (based on the cylinder height) range. The interaction of wall boundary layer on the vortex shedding at Reynolds number up to 1400.0 has been investigated for cylinder to wall gap height 0.5 and 0.25 times the cylinder height. The gap flow between the cylinder and wall during a period of vortex shedding has been obtained. The governing unsteady Navier–Stokes equations are discretised through the finite volume method on staggered grid system. An algorithm SIMPLE has been used to compute the discretised equations iteratively. Our results show that at the gap height 0.5 times the cylinder height the vortex shedding occurs at a Strouhal number greater than for an isolated cylinder. Vortex shedding suppression occurs and wake becomes steady up to a certain value of Reynolds number at gap height 0.25 time the cylinder height. At higher Reynolds number the formation of a single row of negative vortices behind the cylinder when it is in close proximity to wall is noteworthy. Due to the shear, the drag experienced by the cylinder is found to decrease with the reduction of gap height.     

On a similarity solution in the theory of unsteady marginal separation

The present paper deals with initial value problems associated with the high Reynolds number asymptotic theory of unsteady, marginally separated boundary layer flows. In particular, the subsonic planar flow case is treated. Special emphasis is placed on solutions which blow up within finite time. As is well-known, steady solutions of the underlying equations only exist up to a critical value of the crucial parameter which controls the conditions leading to localized boundary layer separation. Our numerical analysis shows that any blow-up solution finally approaches a unique structure, entirely independently of the choice of initial data, sub- or super-critical flow conditions, and, if present at all, the type of forcing. Further support for the existence of a self-similar, unique blow-up structure is gained from asymptotic analysis.     

A semi-implicit fractional step finite element method for viscous incompressible flows

This paper describes a new semi-implicit finite element algorithm for time-dependent viscous incompressible flows. The algorithm is of a general type and can handle both low and high Reynolds number flows, although the emphasis is on convection dominated flows. An explicit three-step method is used for the convection term and an implicit trapezoid method for the diffusion term. The consistent mass matrix is only used in the momentum phase of the fractional step algorithm while the lumped mass matrix is used in the pressure phase and in the pressure Poisson equation. An accuracy and stability analysis of the algorithm is provided for the pure convection equation. Two different types of boundary conditions for the end-of-step velocity of the fractional step algorithm have been investigated. Numerical tests for the lid-driven cavity at Re=1 and Re=7500 and flow past a circular cylinder at Re=100 are presented to demonstrate the usefulness of the method.     

Steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility (AC)‐based characteristic‐based split (CBS) scheme

In this paper, the explicit characteristic‐based split (CBS) scheme has been employed to solve both steady and unsteady flows inside a non‐rectangular double driven cavity. This problem is recently suggested as a benchmark problem for incompressible flows. Both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible. The results obtained show the existence of steady state at lower Reynolds numbers (?1000) and transient states at higher Reynolds numbers. The flow approaches a turbulent state as the Reynolds number is increased to 10 000. Copyright © 2005 John Wiley & Sons, Ltd.     

Sand accumulation on a wall in flows around a near-wall circular cylinder

Summary The sand accumulation on a flat plate in flows around a near-wall circular cylinder has been mainly investigated by the method of numerical simulation at the sub-critical Reynolds number1200 (based on the diameter of the circular cylinder) and the gap ratio G/D (ratio of the gap between the circular cylinder and the plane wall to the diameter of the circular cylinder) 1.0, 0.5 and 0.25. The standard k− ε turbulent model and the vorticity-stream function formulation are adopted to analyze the wake characteristics. The lift and drag coefficients of the circular cylinder and the pressure pulsation on the wall are solved. The simulation of streak-lines for the flow visualization and PIV experiments are detailed carried out to analyze the sand accumulation phenomenon on the plane wall, and a possible mechanism has been proposed. Results of the numerical simulation indicate that the effect of the cylinder results in flow separation from the plane wall. Separations occur about 1 to 2 cylinder diameters behind the cylinder, where the particles in the flow near the plane wall accumulate gradually.