串列双圆柱绕流问题的数值模拟

本文运用有限体积方法,对绕串列放置的双圆柱的二维不可压缩流动进行了数值计算。为研究两圆柱不同间距对圆柱相互作用和尾流特征的影响,选取间距比Ｌ／Ｄ（Ｌ为两圆柱中心间的距离,Ｄ为圆柱直径）在１．５～５．０之间每隔０．５共八个有代表性的间距进行了计算模拟。计算均在Ｒｅ＝２００条件下进行。计算结果表明：对该绕流问题,流动特征在很大程度上取决于间距的大小。且间距存在一临界值,间距比从小于临界值变化到大于临界     

Solution of the Incompressible Unsteady Navier–Stokes Equations Only in Terms of the Velocity Components

A method which uses only the velocity components as primitive variables is described for solution of the incompressible unsteady Navier–Stokes equations. The method involves the multiplication of the primitive variable-based Navier–Stokes equations with the unit normal vector of finite volume elements and the integration of the resulting equations along the boundaries of four-node quadrilateral finite volume elements. Therefore, the pressure term is eliminated from the governing equations and any difficulty associated with pressure or vorticity boundary conditions is avoided. The equations are discretized on four-node quadrilateral finite volume elements by using the second-order-accurate central finite differences with the mid-point integral rule in space and the first-order-accurate backward finite differences in time. The resulting system of algebraic equations is solved in coupled form using a direct solver. As a test case, an impulsively accelerated lid-driven cavity flow in a square enclosure is solved in order to verify the accuracy of the present method.     

Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.     

Non-intrusive load characterization of an airfoil using PIV

An assessment is made of the feasibility of using PIV velocity data for the non-intrusive aerodynamic force characterization (lift, drag and pitching moment) of an airfoil. The method relies upon the application of control-volume approaches in combination with the deduction of the pressure from the PIV experimental data, by making use of the momentum equation. First, the consistency of the method is verified by means of synthetic data obtained from CFD. Subsequently, the procedure was applied in an experimental investigation, in which the PIV approach is validated against standard pressure-based methods (surface pressure distribution and wake rake).     

PEGASE: A NAVIER–STOKES SOLVER FOR DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE FLOWS

A hybrid conservative finite difference/finite element scheme is proposed for the solution of the unsteady incompressible Navier–Stokes equations. Using velocity–pressure variables on a non-staggeredgrid system, the solution is obtained with a projection method basedon the resolution of a pressure Poisson equation. The new proposed scheme is derived from the finite element spatial discretization using the Galerkin method with piecewise bilinear polynomial basis functions defined on quadrilateral elements. It is applied to the pressure gradient term and to the non-linear convection term as in the so-called group finite element method. It ensures strong coupling between spatial directions, inhibiting the development of oscillations during long-term computations, as demonstrated by the validation studies. Two- and three-dimensional unsteady separated flows with open boundaries have been simulated with the proposed method using Cartesian uniform mesh grids. Several examples of calculations on the backward-facing step configuration are reported and the results obtained are compared with those given by other methods. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 833–861, 1997.     

离心叶轮气动声场的数值计算与分析

采用SIMPLEC算法对Ghost叶轮的三维非定常流场进行了数值模拟。利用计算所得流场结果并结合Lighthill和Lowson声学方程计算了由叶片表面非定常脉动力产生的气动噪声。计算结果表明:气动噪声的峰值主要集中在基频及其谐波附近;与静止的点声源相比,运动的点声源不仅使声场存在明显的多普勒效应,还会使声场的强度产生较大的变化;但对转速恒定的旋转点声源,加速度的变化对声场的影响可以忽略;从声场的分布来看,整个旋转叶轮可以看成是一个按简谐变化的偶极子源,数值计算结果与理论分析的结果吻合良好。     

Measurement of parallel blade–vortex interaction at low Reynolds numbers

In this study parallel blade–vortex interaction for a Schmidt-propeller configuration has been examined using particle image velocimetry (PIV). This tandem configuration consists of a leading airfoil (forefoil), used to generate a vortical wake of leading-edge vortices (LEVs) and trailing-edge vortices (TEVs) through a pitching or plunging motion, and a trailing airfoil (hindfoil), held fixed with a specified angle of attack and vertical spacing in its wake. The hindfoil incidence (loading) and not the vertical spacing to the incoming vortical wake has been found to dictate the nature of the interaction (inviscid vs. viscous). For cases where the vortex–blade offset is small and the hindfoil is loaded, vortex distortion and vortex-induced separations are observed. By tracking the circulation of the LEV and TEV, it has been found that the vortices are strengthened for the tandem arrangement and in certain cases dissipate quicker in the wake when interacting with the hindfoil. Time-averaged forces obtained using a standard control-volume analysis are then obtained and used to evaluate these vortex-interaction cases. A subsequent analysis of the varying pressure distribution over the suction side of the hindfoil is performed by integrating the Navier–Stokes equations through the velocity field. This allows for a direct comparison of the vortex-induced loading for the various configurations.     

Large-scale vortical structure of turbulent separation bubble affected by unsteady wake

The large-scale vortical structure of a turbulent separation bubble under the influence of an unsteady wake was investigated. The unsteady wake was generated by a spoked-wheel type wake generator installed in front of the separation bubble. This wake generator was rotated either clockwise or counter-clockwise at Re _H=5.600. The mechanism of vortex shedding from the separation bubble was analyzed in detail by taking a conditional average as well as a phase average. Spatial box filtering (SBF) was used to extract the large-scale vortical structure from the turbulent separation bubble affected by the unsteady wake. To elucidate the influence of the unsteady wake on the large-scale vortical structure, conditional averages of the velocity, vorticity and turbulent kinetic energy were calculated. The nature of the convection of the vortical structure under the influence of an unsteady wake was analyzed. The dipole acoustic pressure level was predicted using Curle's integral of wall-pressure fluctuations.     

Measurement of the turbulent kinetic energy budget of a planar wake flow in pressure gradients

Turbulent kinetic energy (TKE) budget measurements were conducted for a symmetric turbulent planar wake flow subjected to constant zero, favorable, and adverse pressure gradients. The purpose of this study is to clarify the flow physics issues underlying the demonstrated influence of pressure gradient on wake development, and provide experimental support for turbulence modeling. To ensure the reliability of these notoriously difficult measurements, the experimental procedure was carefully designed on the basis of an uncertainty analysis. Three different approaches were applied for the estimate of the dissipation term. An approach for the determination of the pressure diffusion term together with correction of the bias error associated with the dissipation estimate is proposed and validated with the DNS results of Moser et al (J Fluid Mech (1998) 367:255–289). This paper presents the results of the turbulent kinetic energy budget measurement and discusses their implications for the development of strained turbulent wakes.An erratum to this article can be found at     

On stabilized finite element methods for the Stokes problem in the small time step limit

Recent studies indicate that consistently stabilized methods for unsteady incompressible flows, obtained by a method of lines approach may experience difficulty when the time step is small relative to the spatial grid size. Using as a model problem the unsteady Stokes equations, we show that the semi‐discrete pressure operator associated with such methods is not uniformly coercive. We prove that for sufficiently large (relative to the square of the spatial grid size) time steps, implicit time discretizations contribute terms that stabilize this operator. However, we also prove that if the time step is sufficiently small, then the fully discrete problem necessarily leads to unstable pressure approximations. The semi‐discrete pressure operator studied in the paper also arises in pressure‐projection methods, thereby making our results potentially useful in other settings. Copyright © 2006 John Wiley & Sons, Ltd.     

Planar velocity measurements of a two-dimensional compressible wake

The present study describes the application of particle image velocimetry (PIV) to investigate the compressible flow in the wake of a two-dimensional blunt base at a freestream Mach number M_X=2. The first part of the study addresses specific issues related to the application of PIV to supersonic wind tunnel flows, such as the seeding particle flow-tracing fidelity and the measurement spatial resolution. The seeding particle response is assessed through a planar oblique shock wave experiment. The measurement spatial resolution is enhanced by means of an advanced image-interrogation algorithm. In the second part, the experimental results are presented. The PIV measurements yield the spatial distribution of mean velocity and turbulence. The mean velocity distribution clearly reveals the main flow features such as expansion fans, separated shear layers, flow recirculation, reattachment, recompression and wake development. The turbulence distribution shows the growth of turbulent fluctuations in the separated shear layers up to the reattachment location. Increased velocity fluctuations are also present downstream of reattachment outside of the wake due to unsteady flow reattachment and recompression. The instantaneous velocity field is analyzed seeking coherent flow structures in the redeveloping wake. The instantaneous planar velocity and vorticity measurements return evidence of large-scale turbulent structures detected as spatially coherent vorticity fluctuations. The velocity pattern consistently shows large masses of fluid in vortical motion. The overall instantaneous wake flow is organized as a double row of counter-rotating structures. The single structures show vorticity contours of roughly elliptical shape in agreement with previous studies based on spatial correlation of planar light scattering. Peak vorticity is found to be five times higher than the mean vorticity value, suggesting that wake turbulence is dominated by the activity of large-scale structures. The unsteady behavior of the reattachment phenomenon is studied. Based on the instantaneous flow topology, the reattachment is observed to fluctuate mostly in the streamwise direction suggesting that the unsteady separation is dominated by a pumping-like motion.     

A general approach for computing unsteady 3D thin lifting and/or propulsive systems derived from a complete theory

This paper presents the basis of a numerical method for unsteady aerodynamic computation around thin lifting and/or propulsive systems with arbitrary variable geometries, involving the velocity field, the velocity potential, the pressure field and the wake characteristics (geometry and vortex strength). Most of the corresponding theory actually stems from the unsteady wake model established by Mudry, in which the wake is considered to be a median layer, characterized by a pair of functions on which Mudry founded the concept of continuous vortex particle. The governing relations of the continuous problem are then the flow tangency condition, the wake integro‐differential evolution equation, and a flow regularity condition at the trailing edge. This constitutes a rigorous and complete theoretical formulation of this problem, from which a discretization scheme and a numerical method of solution are derived. The view of the vortex wake is similar to the one in the classical vortex lattice approaches, but uses a discrete vortex particle concept, particularly well suited for the prediction of the unsteady wake deformation. This, together with the continuous theory, ensures the computing method compares favorably with the classical methods in terms of flexibility and computing costs. In order to demonstrate the capabilities of the present method, the calculation of flapping wings of variable geometry is also presented. Copyright © 1999 John Wiley & Sons, Ltd.     

Determination of derivative moments using two slanted hot-wires and a spectral method

A method to determine derivative moments using slanted hot-wires and a spectral method has been developed. The general idea is to minimize the measuring volume by using only two hot-wires, and a post-processing of the measurement data. It is shown that the spectral method is equivalent to conventional determination of correlations. The method developed has been tested in the self-preserving region of a plane wake by computing profiles of the Reynolds stresses as well as the derivative moments in the expression for the total energy dissipation. One term in this expression, which with conventional methods requires two triple-wires or four cross-wires, has been determined using the spectral method.     

An ‘assumed deviatoric stress-pressure-velocity’ mixed finite element method for unsteady,convective, incompressible viscous flow: Part II: Computational studies

In Part I of this paper we presented a mixed finite element method, for solving unsteady, incompressible, convective flows, based on assumed ‘deviatoric stress–velocity–pressure’ fields in each element, which have the features: (i) the convective term is treated by the usual Galerkin technique; (ii) the unknowns in the global system of finite element equations are the nodal velocities, and the ‘constant term’ in the arbitrary pressure field over each element; and (iii) exact integrations are performed over each element. In this paper we present numerical studies, both for steady as well as unsteady cases, of the problems: (a) the driven cavity, (b) Jeffry–Hamel flow in a channel, (c) flow over a ‘backward’ or ‘downstream’ facing step, and (d) flow over a square step. All these problems are two-dimensional in nature, although certain 3-D solutions are to be presented in a separate paper. The present results are compared with those which are available in the literature and are based on alternative approaches to treat incompressibility and convective acceleration. The possible merits of the present method are thus pointed out.     

Scale-up of an unsteady flow field for enhanced spatial and temporal resolution of PIV measurements: application to leaflet wake flow in a mechanical heart valve

A scale-up approach is developed to enhance effective spatial and temporal resolution of PIV measurements. An analysis shows that complete similarity can be maintained for certain unsteady flows and that all types of error in PIV are either reduced or unaffected by scale-up. Implementation and results are described for flow through a mechanical heart valve (MHV), in which high resolution is necessary to advance understanding of the effects of small-scale flow structure on blood cells. With a large-scale model geometry and a low-viscosity model fluid, spatial and temporal resolutions are increased by factors of 5.8 and 118, respectively, yielding the finest resolution to date for MHV flow. Measurements near the downstream tip of a valve leaflet detect eddies as small as 400 μm shed in the leaflet wake. Impulsively started flow exhibits vortex shedding frequencies broadly consistent with the literature on flat-plate and aerofoil wakes, while the physiological unsteady flow waveform promotes 40% higher frequency at peak flow.     

Active flow control on the 25°Ahmed body using a new unsteady jet

A numerical simulation based on the Large eddy simulation method is carried out on the near wake flow behind a 25° slant angle Ahmed body to analyze and establish a new method to control the near wake flow. An active flow control using a new unsteady jet derived from the traditional synthetic jet is applied to reduce the aerodynamic drag. The control devices are distributed along the separation edges on the rear part of the body. Their effects on the near wake and the rear body by influencing the flow topology and the static pressure distribution are examined respectively. The control frequency of the jet as the key forcing parameter is taken into consideration as well. The different actuation set-ups lead to a max drag reduction of up to 13.6%, which demonstrates a good correlation with the static pressure distribution at the rear end of the body.     

Hydrodynamics of a tandem fish school with asynchronous undulation of individuals

We perform numerical simulations using immersed boundary method for flow over a single and two fish in tandem performing traveling wave like motion for a range of Strouhal numbers. We investigate the hydrodynamic performance of single- and tandem-fish configurations using unsteady profiles of lateral side-force and drag coefficients, their time-averaged values, and wake behind these bodies. We present the spectra of hydrodynamic forces and find that the nature of these forces for a single fish resembles to those of stationary/oscillating bluff bodies and oscillating airfoils. For tandem cases, we vary the phase speed of undulatory motion of the rear fish while keeping the free-stream velocity constant. We show that hydrodynamic forces of the upstream and rear fish contain harmonics which are produced by nonlinear interaction of the oscillation frequencies of both fish. We find that the wake and time-averaged drag of the upstream fish remain almost independent of the undulating frequency of the rear fish at a certain Strouhal number. We also relate this observation with the absence of oscillation frequency of the rear fish in the Fourier spectra of hydrodynamic forces of the upstream fish. For the complete range of parameters, it is inferred that swimming in a tandem configuration seems more beneficial for the upstream fish. It happens due to wake-splitting effect of the rear fish that causes an enhancement of pressure in its wake. For the rear fish, it gains an advantage of drafting under certain conditions and its performance deteriorates at Strouhal numbers greater than 0.40.     

Unsteady RANS method for surface ship boundary layer and wake and wave field

Results are reported of an unsteady Reynolds‐averaged Navier–Stokes (RANS) method for simulation of the boundary layer and wake and wave field for a surface ship advancing in regular head waves, but restrained from body motions. Second‐order finite differences are used for both spatial and temporal discretization and a Poisson equation projection method is used for velocity–pressure coupling. The exact kinematic free‐surface boundary condition is solved for the free‐surface elevation using a body‐fitted/free‐surface conforming grid updated in each time step. The simulations are for the model problem of a Wigley hull advancing in calm water and in regular head waves. Verification and validation procedures are followed, which include careful consideration of both simulation and experimental uncertainties. The steady flow results are comparable to other steady RANS methods in predicting resistance, boundary layer and wake, and free‐surface effects. The unsteady flow results cover a wide range of Froude number, wavelength, and amplitude for which first harmonic amplitude and phase force and moment experimental data are available for validation along with frequency domain, linear potential flow results for comparisons. The present results, which include the effects of turbulent flow and non‐linear interactions, are in good agreement with the data and overall show better capability than the potential flow results. The physics of the unsteady boundary layer and wake and wave field response are explained with regard to frequency of encounter and seakeeping theory. The results of the present study suggest applicability for additional complexities such as practical ship geometry, ship motion, and maneuvering in arbitrary ambient waves. Copyright © 2001 John Wiley & Sons, Ltd.     

结构振动对湍流近尾迹的影响

研究了圆柱绕流中流体与结构的相互作用,侧重结构振动对湍流尾迹的影响,用激光测振仪测量圆柱在升力方向的位移;用热线和LDA（二维）测量湍流的近尾迹,通过变化自由流的速度和圆柱体直径（特征尺寸）来变化雷诺数,用两个振动特性不同的（一个相对刚性,一个相对弹）圆柱来产生尾迹,研究固体结构振动对湍流近尾迹的平均速度场和湍流场的影响,结果表明,结构自由振动对湍流近尾迹场影响明显,该影响随雷诺数的变化不明显。