SIMULATION OF THE FLOW OVER ELLIPTIC AIRFOILS OSCILLATING AT LARGE ANGLES OF ATTACK

The incompressible, viscous flow over two-dimensional elliptic airfoils oscillating in pitch at large angles of attack, such that flow separation occurs, has been simulated numerically for a Reynolds number of 3000. A vortex method is used to solve the two-dimensional Navier–Stokes equations in vorticity/stream-function form using a time-marching approach. Using an operator-splitting method the convection and diffusion equations are solved sequentially at each time step. The convection equation is solved using a vortex-in-cell method, and the diffusion equation using a second-order ADI finite-difference scheme. Elliptic profiles are obtained by mapping a circle in a computational domain into the physical domain using a Joukowski transformation. The effects of several parameters on the flow field are considered, such as: frequency of oscillation, mean angle of attack, location of pitch-axis and the thickness ratio of the ellipse. The results obtained are shown to compare favourably with available experimental results.     

Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method

The unsteady, incompressible, viscous laminar flow over a NACA 0012 airfoil is simulated, and the effects of several parameters investigated. A vortex method is used to solve the two-dimensional Navier–Stokes equations in the vorticity/stream-function form. By applying an operator-splitting method, the “convection” and “diffusion” equations are solved sequentially at each time step. The convection equation is solved using the vortex-in-cell method, and the diffusion equation using a second-order ADI finite difference scheme. The airfoil profile is obtained by mapping a circle in the computational domain into the physical domain through a Joukowski transformation. The effects of several parameters are investigated, such as the reduced frequency, mean angle of attack, location of pitch axis, and the Reynolds number. It is observed that the reduced frequency has the most influence on the flow field.     

Simulation of 2D external viscous flows by means of a domain decomposition method using an influence matrix technique

Two-dimensional external viscous flows are numerically approximated by means of a domain decomposition method which combines a vortex method and a finite difference method. The vortex method is used in the flow region which is dominated by convective effects, whereas the finite difference method is used in the flow region where viscous diffusion effects are dominant. An influence matrix technique combined with the uniformity condition of the pressure is used to enforce the tangential velocity boundary condition. Comparisons between numerical and experimental data show that the method is well adapted for simulating two-dimensional flows.     

分区Lagrangian涡方法及瞬时起动圆柱初期流动的模拟

本文提出一种分区Lagrangian涡方法:将附着流动和分离流动分开处理,在附着区解边界层方层,只在分离区用涡方法解N-S方程。由于将尺度不同的区域分开了,求解分离区流动的涡方法中,每一时间步上物面引出的涡数在较小程度上依赖于Re数。这样,求解高Re数流动时,流场内的涡数,因而计算机内存和时间得以大大减小。用该方法计算了瞬时起动圆柱的初期流动,与实验结果比较相符很好。     

On numerical errors and turbulence modeling in tip vortex flow prediction

The accuracy of tip vortex flow prediction in the near‐field region is investigated numerically by attempting to quantify the shortcomings of the turbulence models and the flow solver. In particular, some turbulence models can produce a ‘numerical diffusion’ that artificially smears the vortex core. Low‐order finite differencing techniques of the convective and pressure terms of the Navier–Stokes equations and inadequate grid density and distribution can also produce the same adverse effect. The flow over a wing and the near‐wake with the wind tunnel walls included was simulated using 2.5 million grid points. Two subset problems, one using a steady, three‐dimensional analytical vortex, and the other, a vortex obtained from experiment and propagated downstream, were also devised in order to make the study of vortex preservation more tractable. The method of artificial compressibility is used to solve the steady, three‐dimensional, incompressible Navier–Stokes equations. Two one‐equation turbulence models (Baldwin–Barth and Spalart–Allmaras turbulence models), have been used with the production term modified to account for the stabilizing effect of the nearly solid body rotation in the vortex core. Finally, a comparison between the computed results and experiment is presented. Published in 1999 by John Wiley & Sons, Ltd.     

CALCULATION OF STEADY AND OSCILLATING FLOWS IN TUBES USING A VORTICITY TRANSPORT ALGORITHM

Steady and oscillating axisymmetric tube flows are modelled using a vorticity transport algorithm. The axisymmetric convective –diffusive Navier–Stokes equations are solved using a splitting technique. Axisymmetric ring vortex filaments are introduced on the walls and subsequently convected and diffused throughout the flow field. An axisymmetric equation similar to the Oseen diffusion equation is used to diffuse the ring vortex filaments. Vorticity is reflected from the tube walls using two techniques. Results are presented for the developing Poiseuille flow and for the developed flow in the form of the entrance length and the axial velocity and vorticity profiles. Good agreement is achieved with a finite difference method in the developing region of Poiseuille flow. The developed flow results are compared with the analytical solutions. The developed profiles of velocity and vorticity have errors of less than 0ċ3 per cent for both methods of dealing with reflection of diffusion at the bounding surfaces and similar accuracy is obtained for the velocity profiles in oscillating flow except at the wall. Oscillating flow is produced with a discretized sinusoidal piston motion. Velocity profiles, boundary layer thickness and entrance length are presented for oscillating flow. Good agreement is achieved for low-Womersley-number non-dimensional frequency. At higher values of this parameter, flows are inaccurately simulated, because the number of piston positions used to discretize the piston motion is inversely proportional to the non-dimensional frequency.     

容量矩阵法在涡方法中的应用

本文将容量矩阵技术与快速Fourier变换相结合求解非矩形域的Poisson方程,再与格子涡方法相结合,发展了一套求解复杂外形的快速涡方法。作为算例,计算了有厚度平板和楔形体的分离流动,得到了满意的结果。特别是在垂直平板绕流中,模拟出了由于剪切层不稳定性引起的小涡结构。     

On the Effect of Vortex Grid Density in the Vortex-in-cell Simulation of Mixing Layers

The two-dimensional vortex-in-cell method is used in the simulation of a spatially growing mixing layer at a high Reynolds number. Criteria, showing that the vortex grid density plays a role in obtaining a converged solution, are presented. Numerical experiments are conducted to test the criteria by varying the number of vortices and the grid sizes. The effects on the momentum thickness and on the peak values of the root-mean-square velocity fluctuations, and negative cross-stream correlation are discussed in terms of the vortex grid density.     

非定常流动的快速拉格朗日涡方法数值模拟

采用快速拉格朗日涡方法数值模拟有复杂旋涡运动的非定常流动. 利用离散涡元模拟旋涡的产生、聚集和输送过程. 拉格朗日描述法用来计算离散涡元的移动,而移动速度则利用广义毕奥-萨伐尔公式结合快速多极子展开法计算,修正的涡半径扩散模型用来模拟离散涡元的黏性扩散. 突然起动圆柱和大攻角下突然起动翼型的非定常有涡流动的数值模拟,及其与试验结果的对比验证了方法的有效性. 另外,大攻角下突然起动翼型的计算结果给出了翼型起动后吸力面旋涡的产生、发展,周期性非定常流动的形成,以及尾流旋涡结构等一些重要的流动特征.[关键词] 非定常流有涡流动快速涡方法      

A vorticity formulation for computational fluid dynamic and aeroelastic analyses of viscous flows

The paper deals with a novel computational formulation for the analysis of viscous flows past a solid body. The formulation is based upon a convenient decomposition of the flow field into potential and rotational velocity contributions, which has the distinguishing feature that the rotational velocity vanishes in much of, if not all, the region in which the vorticity is negligible. Contrary to related formulations implemented by the authors in the past, in the proposed approach, discontinuities of the potential and rotational velocity fields across a prescribed surface emanating from the trailing edge (such as the wake mid-surface) are eliminated, thereby facilitating numerical implementations. However, the main novelty is related to the application of the boundary condition: first, the expression for the velocity used for the condition on the body boundary is consistent with that for the velocity in the field; also—contrary to related formulations used by the authors in the past—in the proposed approach, the condition on the body boundary does not require the evaluation of the total vorticity (inside and outside the computational domain). The proposed algorithm, valid for three-dimensional compressible flows, is validated—as a first step—for the case of two-dimensional incompressible flows. Specifically, numerical results are presented for the aerodynamic analysis of two-dimensional incompressible viscous flows past a circular cylinder and past a Joukowski airfoil. In order to verify the desirable absence of artificial damping, we present also results pertaining to the flutter (i.e., dynamic aeroelastic) analysis of a spring-mounted circular cylinder in a viscous flow, free to move in a direction orthogonal to the unperturbed flow. In both cases (aerodynamics and aeroelasticity), the results are in good agreement with existing literature data.     

用扰动涡方法模拟叶轮机内动静叶的相互作用

发展了一种研究叶轮机内动、静叶间的相互作用的新方法———扰动涡方法，它利用全三维的定常解为基础解，并由此给出非定常扰动场的初始解．为计算叶片对扰动场的响应过程，采用拉格朗日方法追踪扰动涡团的对流流动过程，用确定性涡方法来描述流体的粘性扩散过程．发展了代数湍流模型（Ｂａｌｄｗｉｎ Ｌｏｍａｘ湍流模型）在尾迹中的应用方法，克服了其它数值方法中无法准确捕捉尾迹中心线的运动轨迹，以及计算出的边界层外的湍流涡粘性系数偏大的缺陷．利用该方法计算轴流叶轮机内由于动、静叶间的相互作用而引起的非定常流动过程，与实验的对照表明，模拟结果与实验数据吻合得相当好，从而说明本文发展的方法是可信的，为更直观地描述尾迹等非定常因素的流动及叶轮机内的掺混问题提供依据．     

VORTEX-INDUCED VIBRATIONS OF AN ELASTIC CIRCULAR CYLINDER

A numerical study of a uniform flow past an elastic circular cylinder using the discrete vortex method incorporating the vortex-in-cell (VIC) technique has been undertaken. The Reynolds number is kept at 200 for all calculations and the cylinder motion is modelled by a spring–damper–mass system. The fluid motion and the structural responses are solved in an iterative way so that the interactions between the fluid and the structure can be accounted for properly. Analyses of the cylinder responses, the damping, the induced forces, the vortex shedding frequency and the vortex structure in the wake have been carried out. The results show that fluid damping is responsible for a limit-cycle oscillation behaviour even when the system natural frequency is close to the vortex-shedding frequency. Reasonable agreement with previous experimental data and computational results is obtained in the comparison of the amplitude of the limit-cycle oscillations. The results further show that the cylinder oscillations could be as large as 0·57 diameter under certain flow conditions and structural properties. Finally, it is shown that a one-degree-of-freedom structural model yields results that are only in qualitative agreement with a two-degree-of-freedom model. In other words, the streamwise oscillations also have a substantial effect on the transverse vibrations and their characteristics.     

Flow field calculation and its experimental verification for inertia stage of marine gas turbine air intake filter

A numerical method is presented in this paper for the solution of flow field in marine gas turbine air intake filtration channel. The flow field was successfully calculated by this method, and aerodynamic characteristics were obtained for various types of filtration channels. This work is expected to be of practical importance for the design of such filters. Upstream difference was adopted to discretize the non-conservative type N-S equation for two-dimensional, time-dependnet, viscous and incompressible flow, and the stability, convergence, accuracy and artificial viscosity of the resulting difference equation were examined. This equation can be used to calculate viscous flows with Reynolds number up to tens of thousands. Also presented in this paper is a calculation method for treating wall vortex at boundary inflection points. Careful studies show that calculation based on the difference equational and wall vortex treatment proposed here are in good agreement with experimental results.     

非对称槽道中涡旋波的特性研究

利用PIV流场显示技术，对振荡流体在非对称槽道中涡旋波的产生、发展和消失的规律进 行了实验研究和分析，测得了涡旋波流场的速度矢量图，阐明了涡旋波流场周期性变化的特 点. 结合涡动力学方程，深入分析并揭示了做周期性运动的流体能在槽道中产生波的特性这 一规律，从中发现：流体周期变化的非定常性和不对称的槽道结构是形成涡旋波流动的主要 因素. 本文对涡旋波流场中各个旋涡的速度分布和涡量进行了测量和计算，分析了涡旋波 强化传质的机理，并研究了Re数对涡旋波流动的影响     

Electromagnetic control of seawater flow around circular cylinders

We investigate numerically the electromagnetic control of seawater flows over an infinitely long circular cylinder. Stripes of electrodes and magnets, wrapped around the cylinder surface, produce a tangential body force (Lorentz force) that stabilizes the flow. This mechanism delays flow separation, reduces drag and lift, and finally suppresses the von Kármán vortex street. Results from two-dimensional simulations of the Navier–Stokes equations in a range 10<Re<300 and Lorentz force calculations are presented. Emphasis is placed on the disclosure of physical phenomena as well as a quantitative detection of the flow field and forces. It is shown that the drag strongly depends on the geometry of the electromagnetic actuator and on its location at the cylinder surface. The effect of flow control increases with larger Reynolds numbers, since the boundary layer thickness and the penetration depth of the Lorentz force are closely connected.     

Diffusion velocity for a three-dimensional vorticity field

A discussion is presented on the existence of a diffusion velocity for the vorticity vector that satisfies extensions of the Helmholtz vortex laws in a three-dimensional, incompressible, viscous fluid flow. A general form for the diffusion velocity is derived for a complex-lamellar vorticity field that satisfies the property that circulation is invariant about a region that is advected with the sum of the fluid velocity and the diffusion velocity. A consequence of this property is that vortex lines will be material lines with respect to this combined velocity field. The question of existence of diffusion velocity for a general three-dimensional vorticity field is shown to be equivalent to the question of existence of solutions of a certain Fredholm equation of the first kind. An example is given for which it is shown that a diffusion velocity satisfying this property does not, in general, exist. Properties of the simple expression for diffusion velocity for a complex-lamellar vorticity field are examined when applied to the more general case of an arbitrary three-dimensional flow. It is found that this form of diffusion velocity, while not satisfying the condition of circulation invariance, nevertheless has certain desirable properties for computation of viscous flows using Lagrangian vortex methods. The significance and structure of the noncomplex-lamellar part of the viscous diffusion term is examined for the special case of decaying homogeneous turbulence.     

An experimental investigation of the flow structure over a corrugated waveform in a transpired air collector

An experimental investigation of the flow dynamics in a channel with a corrugated surface is presented. Particle image velocimetry was used to obtain two-dimensional velocity fields at three different locations along the channel length, over a range of Reynolds numbers. The results show a significant impact of the corrugation waveform on the mean and turbulent flow structure inside the channel. Strong bursting flow originating from the trough, sweeping flow from the bulk region and the vortex shedding off the crest were observed. Their interactions created a complex three-dimensional flow structure extended over almost the entire channel. The mean velocity profiles indicate a strong diffusion of shear. The profiles of various turbulent properties show the enhancement of turbulence in the vicinity of the waveform. It was found that the turbulence in the channel was almost entirely produced in this region above the corrugation trough. Significant momentum transfer from the corrugation wall by the turbulent velocity field was also observed. The mean and turbulent flow behaviour was found to be periodic with respect to the waveform over most of the channel length. The results show the presence of strong turbulence even at the Reynolds number that falls within the conventional laminar range.     

Vortex-In-Cell and Probability Density Function Approach for a Passive Scalar Field in a Mixing Layer

A Reynolds-averaged simulation based on the vortex-in-cell (VIC) and the transport equation for the probability density function (PDF) of a scalar has been developed to predict the passive scalar field in a two-dimensional spatially growing mixing layer. The VIC computes the instantaneous velocity and vorticity fields. Then the mean-flow properties, i.e. the mean velocity, the root-mean-square (rms) longitudinal and lateral velocity fluctuations, the Reynolds shear stress, and the rms vorticity fluctuations are computed and used as input to the PDF equation. The PDF transport equation is solved using the Monte Carlo technique. The convection term uses the mean velocities from the VIC. The turbulent diffusion term is modeled using the gradient transport model, in which the eddy diffusivity, computed via the Boussinesq's postulate, uses the Reynolds shear stress and gradients of mean velocities from the VIC. The molecular mixing term is closed by the modified Curl model.

The computational results were compared with two-dimensional experimental results for passive scalar. The predicted turbulent flow characteristics, i.e. mean velocity and rms longitudinal fluctuations in the self-preserving region, show good agreement with the experimental measurements. The profiles of the mean scalar and the rms scalar fluctuations are also in reasonable agreement with the experimental measurements. Comparison between the mean scalar and the mean velocity profiles shows that the scalar mixing region extends further into the free stream than does the momentum mixing region, indicating enhanced transport of scalar over momentum. The rms scalar profiles exhibit an asymmetry relative to the concentration centerline, and indicate that the fluid on the high-speed side mixes at a faster rate than the fluid on the low-speed side. The asymmetry is due to the asymmetry in the mixing frequency cross-stream profiles. Also, the PDFs have peaks biased toward the high-speed side.