On an analogy to the area–velocity relation of gasdynamics in slender vortices

Inviscid compressible flow in a slender longitudinal vortex with the axis parallel to the main flow direction is discussed. The Euler equations for steady, axially symmetric flow are simplified for the neighbourhood of the axis of the vortex. The resulting relations, expressing the angular velocity in terms of the axial mass flow, when recast and integrated, represent an analogy to the area–velocity and the area-Mach number relation of one-dimensional gasdynamics. By restricting the analysis to the flow in a Rankine vortex with constant stagnation enthalpy, the static pressure on the axis can be related to the free-stream pressure far away from the axis and the maximum value of the azimuthal velocity. The influence of a radial wake-like distribution of the axial velocity component on the axial pressure is discussed. Its dependence on variable external boundary conditions is given. A condition is formulated, which has to be satisfied for the formation of a free stagnation point on the axis.     

涡声理论在汽车A柱气动噪声优化中的应用

涡声理论表明气流流动产生的噪声主要取决于声源项涡量与速度叉乘项的散度的强弱。基于涡声方程,通过分析汽车A柱附近流场中速度、涡矢量以及两者间夹角正弦值等物理量与气动噪声之间的关系,找到了影响A柱气动噪声的主要气动参数。研究表明,A柱区域气动噪声声压级与流场中速度和涡矢量的叉乘变化规律一致,进一步分析涡量、速度以及两者夹角正弦值等三个流场气动参量发现,三者中绕A柱轴向的涡量对噪声的贡献量最大。据此,通过在A柱上沿涡量方向加装扰流条可以有效控制A柱区域气动噪声;其中,增加16个扰流条的措施,可使前侧窗表面噪声最大降低4.2 dBA,对测点声压级的频谱分析表明该方法在较宽的频段内均有降噪效果。     

Solution of three-dimensional viscous flows using integral velocity–vorticity formulation

In this paper, a numerical approach is presented to solve the velocity–vorticity integro-differential formulations for three-dimensional incompressible viscous flow. Both the velocity and pressure are solved in integral formulations and the general numerical method is based on standard finite volume scheme. The velocities needed at the vertexes of each control volume are calculated by a so-called generalized Biot–Savart formula combined with a fast multipole algorithm, which makes the velocity boundary conditions implicitly satisfied by maintaining the kinematic compatibility of the velocity and vorticity fields. The well-known fractional step approaches are used to solve the vorticity transport equation. No-flux boundary conditions on solid objects are satisfied as vorticity Helmholtz equation is solved. The diffusion term in the transport equation is treated implicitly using a conservative finite update. The diffusive fluxes of vorticity into flow domain from solid boundaries are determined by an iterative process in order to satisfy the no tangential-flow boundary condition. As an application example, the impulsively started flow through a sphere with different Reynolds numbers is computed using the method. The calculated results are compared with the experimental data and other numerical results and show good agreement.     

Numerical investigations of laminar flow characteristics in helically finned pipes

The laminar flow in a helically finned pipe has been considered. The steady solutions have been obtained by numerical integration of the Navier-Stokes equations formulated in a cylindrical coordinate system. Three-dimensional fins have been embedded in the structured mesh as immersed boundaries. A helical fin generates a swirling flow which exhibits a helical symmetry. In the presence of a single fin, the circumferential velocity turned out to increase both with fin height and fin angle. The core region with high axial velocity is shifted away from the pipe axis. High levels of axial vorticity caused by the fin-induced swirl are observed in the vicinity of the tip of the fin whereas substantial vorticity of opposite sign is produced in the wall-layer near the suction side of the fin. In the presence of two fins with the same pitch, i.e., a double helix, the symmetry about a diametrical plane gave rise to a keyhole-shaped axial velocity distribution. The drag coefficient was increased by all the fin configurations considered when compared to regular pipe flow at the same Reynolds number.     

Swirl flow studies in diffusers using the flux analysis method with orthogonal curvilinear coordinates

A computational method of flux analysis is applied to the study of the swirling flow of different regimes through a diffuser pipe. The flux analysis method is an iterative procedure to construct a system of orthogonal curvilinear co-ordinates consisting of stream-surface and normals following the flow. Examples of the inviscid swirling flow of an incompressible fluid are calculated, and deformations of vortices in a diffuser pipe are studied. For a simple vortex with rigid rotation the deceleration of flow is remarkable on the axis, where the total energy has the lowest level. For a Burgers type vortex, provided the circulation number exceeds a critical value, the rate of deceleration of flow along the axis become more pronounced for only a slight increase of swirl strength, and ultimately a stagnation point appears on the axis. The present method, however, may not be applied to the flow with stagnation point.     

用可压缩流涡方法模拟叶轮机动静叶的相互作用

本课题组发展了一种扰动涡方法,用以研究叶轮机内动、静叶相互作用。其优点是物理图画清楚,计算收敛快。它采用了一个重要假设：扰动胀量为零,从而大大简化 了计算过程。文章的目的是研究此假设的影响,并取消此假设,使扰动涡方法建立在完全严格的数学基础上。由于取消了“扰动胀量为零的假设,需要耦合求解扰动质量方程、扰动涡量输运方程和扰动能量输运方程。这是文章与文献[1,2]的主要区别。     

Simulating three-dimensional vortex motion by a vortex blob method

A three-dimensional vortex blob method was applied to calculate several vortex motions: the deformation of pseudo-elliptic vortex rings, the jet issuing from the pseudo-elliptic nozzle into flow of uniform velocity, the unsteady separated flow around a circular disk with an angle of attack, and the interaction of several vortex rings which approximately reproduced the Kolmogorov spectrum. In the first three cases, the viscous diffusion of vorticity was included. The pseudo-elliptic vortex rings experienced axis switching and split into a few deformed vortex rings. Rolling-up vortices in the pseudo-elliptic jet had a symmetric arrangement in the minor-axis plane and an antisymmetric arrangement in the major-axis plane in the developing region; further downstream, the vortices were arranged antisymmetrically in both planes. The wake behind the disk normal to the main flow reproduced the spiral and columnar modes of instability. A problem in the three-dimensional vortex method is that vorticity tends to diverge at a stage of evolution of the vortex motions. An approximate method of avoiding the divergence of vorticity is proposed.     

Flow Characterization of a Diamond-Depositing DC Arcjet by Laser-Induced Fluorescence

Laser-induced fluorescence (LIF) measurements of seeded nitric oxide and naturally occurring species in a diamond-depositing dc arcjet of hydrogen/argon/methane (0.8:1.0:0.005) at 25 Torr are used to determine the temperature and velocity fields in a gas jet. LIF measurements are also used to demonstrate the importance of gas recirculation on the chemical composition of the arcjet plume. The gas flow in the arcjet plume is supersonic, with a maximum axial speed of 2.6 km/s at the center of the nozzle exit. This axial velocity decreases with radius with a parabolic distribution in the plume. There is no measurable radial velocity in the free stream of the arcjet plume, and the radial expansion of the plume is consistent with diffusion. The maximum temperature at the plume center is 2400 K and varies less than 15% with chamber pressures of 10-50 Torr. The substrate is placed in the arcjet plume normally to the directed velocity, producing a stagnation point. The gas temperature above this stagnation point is observed to rise abruptly as a consequence of the supersonic shock. The radial velocity near the stagnation point becomes significant, and a maximum radial velocity of 1300 m/s is determined.     

Diffusion of a line vortex in a second grade fluid embedded in a stagnation point flow

The diffusion of a line vortex embedded in a radially inward axisymmetric stagnation point flow for a second grade fluid is considered. This flow is the diffusion of a line vortex for a second grade fluid when a stagnation point flow is superimposed. The velocity field is in the form of υ_r = −αr, υ_θ = υ(r, t), υ_z = 2αz, where r, θ, z are cylindrical polar coordinates and α is a constant related to the inward flow. An exact solution of the governing equation is given. It is found that for small values of the time the solution approaches the diffusion of a line vortex in a second grade fluid and for large values of the time the solution tends to the flow of a line vortex in a second grade fluid embedded in a radially inward axisymmetric stagnation point flow.     

Particle Trajectory in a Bidirectional Vortex Flow

In this research particle trajectory in a bidirectional vortex flow has been numerically predicted and the results experimentally validated. Scale analyses of forces show their order of magnitudes and give a criterion to recognize the order of magnitude of exerting forces on the particle. The particle has been assumed to be a rigid sphere. Initial velocity, diameter, density, and position of entering particle are assumed to be known. If the particle length scale is considered not to be comparable with the chamber length and if particle number density is low, then influence of particle on the flow field is negligible and a one-way solution is applicable. The governing equation is converted to a set of nonlinear, coupled, second-order ODE and solved by a numerical scheme. Results show that higher density, larger diameter, and higher initial axial velocity tend to move the particles further in the axial direction. Also, the maximum axial movement of the particle occurs when the initial radial velocity is zero and there is an optimum entrance position that provides a maximum traveling trajectory for particles. Increasing initial z-direction velocity component and density will result in increasing traveling trajectory.     

Recombination of two vortex filaments and jet noise

The recombination of two vortex filaments in a viscous incompressible fluid is analysed by the use of the vorticity equation. The analysis is confined to a local flow field, where the recombination process occurs, and is based on several assumptions, such as the conservation of the fluid impulse, spatial symmetry of the flow field etc. The flow field is expanded as polynomials of coordinates, and variations of their coefficients are obtained by the use of the vorticity equation. It is proved that the process is completed within a short time ofO (σ ²/Γ) and the viscous effect is essential;σ and Γ are the size and the circulation of the vortex filaments, respectively. This result is applied to predict the far-field noise of a circular jet by assuming that the main noise source is the recombination process in deformed vortex rings in the jet near field. The predicted noise intensity shows theU dependence and has an additional new factor (d/σ)⁶;U is the jet velocity andd is the average spacing between vortex rings.     

大跨屋盖表面旋涡的PIV试验研究

该文通过风洞流场显示试验,观察了大跨平屋盖和马鞍屋盖表面的分离泡和锥形涡现象,给出了不同风向、不同屋盖表面的旋涡流线和涡量场分布;分析了风向角、屋盖曲率对于旋涡形态的影响。试验结果表明,当风向垂直于平屋盖迎风前缘时,屋盖表面将形成典型的分离泡现象,且分离泡的涡核位置恰好对应了涡量场的负向峰值。在斜向风作用下,平屋盖和以高点作为迎风点的马鞍屋盖表面将出现锥形涡。观察旋涡的平均流线和涡量场分布图,发现当来流沿两种屋盖对角线时,锥形涡截面形状接近圆形;当来流偏离屋盖对角线时,在靠近来流的一侧,锥形涡截面形状接近椭圆形;流场内负向涡量分布于壁面上,峰值集中在迎风前缘附近和旋涡周围。在相同的风向角下,曲率较大的马鞍表面锥形涡涡轴与屋盖迎风前缘所成角度较大,曲率较小的马鞍表面锥形涡涡轴与迎风前缘所成角度较小。此外,旋涡的瞬时流线图表明,锥形涡是一种瞬时变化的流体现象,其形态和位置在每个瞬时都不相同。     

Three-dimensional vortex wake structure of flapping wings in hovering flight

Flapping wings continuously create and send vortices into their wake, while imparting downward momentum into the surrounding fluid. However, experimental studies concerning the details of the three-dimensional vorticity distribution and evolution in the far wake are limited. In this study, the three-dimensional vortex wake structure in both the near and far field of a dynamically scaled flapping wing was investigated experimentally, using volumetric three-component velocimetry. A single wing, with shape and kinematics similar to those of a fruitfly, was examined. The overall result of the wing action is to create an integrated vortex structure consisting of a tip vortex (TV), trailing-edge shear layer (TESL) and leading-edge vortex. The TESL rolls up into a root vortex (RV) as it is shed from the wing, and together with the TV, contracts radially and stretches tangentially in the downstream wake. The downwash is distributed in an arc-shaped region enclosed by the stretched tangential vorticity of the TVs and the RVs. A closed vortex ring structure is not observed in the current study owing to the lack of well-established starting and stopping vortex structures that smoothly connect the TV and RV. An evaluation of the vorticity transport equation shows that both the TV and the RV undergo vortex stretching while convecting downwards: a three-dimensional phenomenon in rotating flows. It also confirms that convection and secondary tilting and stretching effects dominate the evolution of vorticity.     

Thermocapillary Convection in Floating Zone with Axial Magnetic Fields

Numerical simulations on the effects of axial magnetic fields on the thermocapillary convection in a liquid bridge of silicone-oil-based ferrofluid under zero gravity have been conducted. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the mass conserving level set approach is used to capture the free surface deformation of the liquid bridge. The obvious effects of the magnetic fields on the flow pattern as well as the velocity and temperature distributions in the liquid bridge can be detected. The axial magnetic fields suppress the thermocapillary convection and a stagnant flow zone is formed between the circulating flow and the symmetric axis as the magnetic fields increase. The axial magnetic fields affect not only the velocity level inside the liquid bridge but also the velocity level on the free surface. The temperature contours near the free surface illustrates conduction-type temperature profiles at moderate strength fields.     

Simulation of 3D flow in porous media by boundary element method

In the present paper problem of natural convection in a cubic porous cavity is studied numerically, using an algorithm based on a combination of single domain and subdomain boundary element method (BEM). The modified Navier–Stokes equations (Brinkman-extended Darcy formulation with inertial term included) were adopted to model fluid flow in porous media, coupled with the energy equation using the Boussinesq approximation. The governing equations are transformed by the velocity–vorticity variables formulation which separates the computation scheme into kinematic and kinetic parts. The kinematics equation, vorticity transport equation and energy equation are solved by the subdomain BEM, while the boundary vorticity values, needed as a boundary conditions for the vorticity transport equation, are calculated by single domain BEM solution of the kinematics equation. Computations are performed for steady state cases, for a range of Darcy numbers from 10^?6 to 10^?1, and porous Rayleigh numbers ranging from 50 to 1000. The heat flux through the cavity and the flow fields are analyzed for different cases of governing parameters and compared to the results in some published studies.     

出口结构对双蜗壳式旋风分离器内流场的影响

用智能七孔球探针测试仪对不同出口结构的双蜗壳式旋风分离器内不同位置的三维速度及压力进行测量,从而获得不同结构参数对流场的影响。实验结果表明,排尘锥结构具有一定的稳流作用,有利于分离器的分离;分流型芯管的开缝有分流的作用,降低了芯管内的气流旋转强度,使上下行流都有所减少,旋风管中心附近以及边壁附近的切向速度都有所减小;分流型芯管的特有的缩口结构使不同截面上的切向速度的最大值都有所增加,距离缩口越近增加越强烈。     

A comparative study on effect of plain- and wavy-wall confinement on wake characteristics of flow past circular cylinder

A first attempt is made for identifying the wake characteristics of circular cylinder confined by a wavy wall at laminar flow regime. Numerical study of flow characteristics past circular cylinder with wavy-wall confinement perpendicular to cylinder axis has been carried out in the range of Reynolds number 20–100. The finite volume-based CFD solver Ansys Fluent (Version 15.0) is used for computations. The results are presented in the form of streamline plots, mean drag co-efficient, flow separation angle and recirculation length. Wavy-wall confinement leads to highly significant changes in the cylinder wake such as the evolution of strong x-plane vortices, enhanced fluid mixing, wake suppression near the crest region and vortex stretching near the trough region on the downstream of the cylinder has been observed. Flow separation angle varies significantly along the axis of the cylinder. Increased wall shear stress on rear surface of the cylinder has also been observed. The part of vorticity magnitude as compared to strain rate has been distinguished and identified using vortex identification methods such as Q-criterion and Lambda-2 criterion.     

圆柱绕流的流场特性及涡脱落规律研究

采用粒子图像测速技术对630、800及950三种雷诺数条件下的圆柱绕流场进行了实验,给出了圆柱下游沿流动方向4倍圆柱直径和垂直方向3倍圆柱直径区域内的速度场、涡量场以及涡脱落现象的时空演化规律.结果表明:圆柱尾流区域位于垂直方向约1.5~2.5倍圆柱直径范围内,随着雷诺数增大,这一范围呈现缩小趋势,而主流对涡的拉伸和输运能力有所增强;涡脱落频率随雷诺数增大而增大,小雷诺数时能够较为完整地捕捉到涡生成、脱落、发展和耗散过程,由于PIV采集频率的限制,大雷诺数条件下涡脱落整个过程不易被完整捕捉到.     

Edge effects in flow around a plasma actuator

We have studied the structure of flow formed in the boundary layer at the lateral edge of the discharge zone of a dielectric barrier discharge plasma actuator. It is established that a region with nonzero component of tangential velocity exists near the plasma layer boundary. At some distance downstream of the actuator, a concentrated vortex is formed with the axis aligned with the flow direction. In the presence of two closely spaced boundaries of the plasma region, a pair of counter-rotating vortices is formed. Separate microdischarges in the plasma layer also appear to be a source of similar longitudinal vortices with smaller amplitude.

     

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.