Swirling turbulent wake behind a self-propelled body

The development of the swirling turbulent axisymmetric wake of a self-propelled body is modeled numerically. The flow pattern is calculated within the framework of the thin shear layer approach for nonclosed system of the motion and continuity equations. The closed system of equations is written for two different formulations of the closure relations. The numerical solution of the problem is performed with the use of the finite-difference algorithm realised on moving grids. The algorithm is conservative with respect to the laws of conservation of the momentum and the angular momentum. The experimentally measured distributions are used as the initial conditions. Both the models described agree well with the experimental data of Gavrilov N., Demenkov A., Kostomakha V., Chernykh G. (2000), Experimental and numerical modelling of turbulent wake behind self-propelled body, J. Appl. Mech. Tech. Phys., 41 (4), 619–627. It is demonstrated that at the large distances downstream from the body the solution of the problem approaches the self-similar one.     

Unsteady response of airfoils due to small-scale pitching motion with considerations for foil thickness and wake motion

Unsteady pressures, forces, and pitching moments generated by foils experiencing vibratory motion in an incompressible, attached flow configuration are studied within this work. Specifically, two-dimensional, unsteady potential flow and unsteady Reynolds-Averaged Navier–Stokes calculations are performed on various Joukowski foils undergoing sinusoidal, variable amplitude, small-scale pitching motion at a chord-based Reynolds number of 10${}^6$ over a range of reduced frequencies between 0.01–100. These calculated results from both approaches are compared directly to predictions from implementing the Theodorsen model, which treats foils as infinitely thin, flat plates that shed a planar sheet of vorticity. The effects of relaxing these seemingly strict conditions are explored, and the particular terms which control the unsteady responses are identified and discussed. For increasing pitch amplitudes and reduced frequencies the shed wake is seen to become quite non-planar and to form coherent vortex structures. Despite this wake behavior, the normalized airfoil responses at the disturbance reduced frequency are seen to be largely unaffected. However, non-negligible responses are generated across a wide range of other frequencies. Potential flow calculations for symmetric Joukowski foils show that there is marginal effect of foil thickness at reduced frequencies less than one. For higher reduced frequency conditions however, the unsteady lift response is seen to experience both an amplification of level and a phase shift relative to the Theodorsen model. A specific augmenting expression is developed for this behavior through analysis within the potential flow framework.     

开缝钝体尾迹的拟序结构

弄清开缝钝体尾迹的拟序结构是认识其火焰稳定机理的基础。在雷诺数R e为470000条件下,采用RNGk-ε模型对通道内的开缝钝体尾迹进行数值模拟来分析大涡尺度的拟序结构。模拟结果显示,偏向一侧的中缝流将近尾分成主回流区和次回流区,主回流区的漩涡脱落激发扰动,引起近尾的绝对不稳定。并提出单涡突然置于两剪切层间的漩涡脱落机理来解释拟序结构不稳定特性。为了验证上述结论,在闭式风洞中采用激光粒子测速技术(P IV)对开缝钝体的尾迹进行了实验研究,其结果与数值分析较好地吻合。     

Structure of wake of a sharp-edged bluff body in a shallow channel flow

The flow field downstream of a bluff body in a typical open channel flow was explored by two-dimensional particle image velocimetry. Measurements are obtained in horizontal planes at the near-bed, mid-depth and near-surface locations downstream of the body up to a streamwise distance of 10D, where D is the width of the body. The dimensionless streamwise defect velocity profile of the wake flow matches well with the data of a previous investigation and does not reflect any dependency on the distance from the bed. However, the nature of development of the recirculation region is found to be different at the three vertical locations. The time-averaged streamline pattern indicates the existence of a unique nodal pattern close to the bed. The variation of the half-width is also found to be affected by the presence of the bed and the free surface. The bed friction arrests the transverse growth of the shear layer, and the free-surface helps to redistribute the turbulent kinetic energy in the streamwise and transverse directions. Swirling strength analysis is carried out to compare the behavior and statistics of the vortex population in the vertical direction. The prevailing magnitude of the swirling strength is found to be different at the three vertical locations. Bed friction assists to dissipate vorticity rapidly, and therefore reduces the probability of appearance of strong vortices close to the bed.     

旋转翼面尾迹的流态显示技术

本文介绍了一种可用于显示旋转弹翼面在非旋转和旋转过程中拖出的涡及其轨迹的流态显示技术。本方法在烟线技术的基础上,采用新的发烟装置,既提高了发烟的浓度,延长了发烟的时间,并不增加任何附加力矩而使发烟部件随旋转弹体一起转动,从而实现了在旋转过程中进行动态的流态显示。文中对于应用此方法得到的流态的真实性进行了分析讨论,分析表明用此方法显示的流态具有一定的真实性,可以提供定性的旋转翼面尾涡流动特性。     

Numerical simulation of motion and deformation of ring bubble along body surface

Numerical simulation for fluid flow over an attached rigid body with a deformable ring bubble is analyzed based on the velocity potential theory together with the boundary element method （BEM）. The analysis is focused on the axisymmetric case. The bubble surface is treated as a well defined air-liquid interface and is tracked by a mixed Eulerian-Lagrangian method. The points of intersection between the bubble and body are treated, specially in the numerical procedure. The auxiliary function method is adopted to calculate the pressure on the body surface and in the flow field. The convergence study is undertaken to assess the developed numerical method and the computation code. Some case studies are undertaken in which the interactions between the bubble/body and the incoming flow field are simulated. The effects of various physical parameters on the interactions are investigated.     

3-D scanning-particle-image-velocimetry: Technique and application to a spherical cap wake flow

A 3-D time-resolving and whole-volume Digital-Particle-Image-Velocimetry (DPIV) technique based on the concept of a scanning light-sheet is presented and applied here to the 3-D transient wake phenomena in the spherical cap wake flow. The technique uses a scanning light-sheet for rapid sampling of the flow in depth and a two-camera recording system for stereoscopic 3-D DPIV. Application of a correlation technique in combination with a calibration yields, aside from the correct in-plane displacement, also the out of plane component and thus the total velocity vectors within the planes of the scanning light-sheet. With a high scanning rate in comparison to the characteristic time scales the method provides the 3-D velocity field in space and time. Through the use of conventional video-techniques the temporal evolution of the complete velocity and vorticity field can be obtained quantitatively from experiments. This is demonstrated for the 3-D starting flow around a spherical cap at Re=300. During the starting process, the flow in the wake evolves into a spherical vortex ring where the velocity distribution is very close to the theoretical solution of the Hill-type vortex. Later on, the Hill-type vortex ring deforms and the flow changes from a rotational symmetric stage to a planar symmetric flow with a double-threaded vortical structure which consists of two counter-rotating streamwise vortices similar to the ones observed in sphere wake flow.Presented at the EUROMECH Coll. 335, Image Techniques and Analysis in Fluid Dynamics, 5–7 June 1995, Roma, Italy. A version of this paper has been published in Proc. 7th Int. Symp. Flow Visualization (ed. J.P. Crowder), Begell House Inc., New York, 1995, pp. 715–720.     

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4 :2244–2251; Int. J. Multiphase Flow 2000; 26 :1583–1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes. Copyright © 2008 John Wiley & Sons, Ltd.     

A simple axisymmetric extension to virtual cell embedding

Virtual cell embedding (VCE) is a simple cartesian gridding method that subdivides cells into discrete subcells to obtain the approximate obstructed cell area and side lengths. It can be used to make a very fast calculation method for the Euler equations in two dimensions. However, the original procedure for two spatial dimensions is inadequate for axisymmetric geometries, where radial co‐ordinates of cells and interfaces need to be known. Presented in this paper is a short, simple extension of the VCE method to handle axisymmetric cases with an accuracy consistent with the basic VCE surface representation in planar geometries. The method will be tested in basic conical flow simulations to show its usefulness for practical engineering design purposes. Copyright © 2007 John Wiley & Sons, Ltd.     

The wake flow structure of an open-slit V gutter

This work experimentally investigates the near-wake flow structure behind an open-slit V gutter at airflow speeds between 1 m/s and 20 m/s. With the aid of Schlieren photography and a Dantec three-beam, two-component laser-Doppler anemometry system, the phenomena of vortex shedding and flow recirculation behind the flameholder are well investigated. The results indicate that the interaction between the flow penetrating through the open slit and the shear layer results in an asymmetric wake flow structure. The lower shear layer develops more stably and smoothly than the upper shear layer. Besides, the vortex formation along the lower wing is delayed and at a location farther downstream. The size of the entire recirculation zone is enlarged, and its center shifts toward one of the two wings. Measurements of wake pressure distribution show that the open-slit V gutter generates higher back pressure and thus induces less drag force than the regular V gutter. Moreover, the maximum values of the pressure fluctuation of the wake flow behind the open-slit V gutter reduce 27% and 9%, for the upper side and the lower side, respectively, much lower than those of the regular V gutter. In general, the application of mass bleed from the open-slit V gutter favors both the flame-holding mechanism and the suppression of the flow-induced oscillation.     

无网格MLPG法求解轴对称弹性体扭转问题

应用无网格局部彼得洛夫-伽辽金法(MLPG)研究轴对称弹性体扭转问题,给出了矩阵形式的控制方程,发展了MLPG求解轴对称体弹性扭转问题的数值计算方法。算例分析表明:此方法对求解此类问题具有良好的适应性,数值解能达到理想的计算精度。     

Three-dimensional evolution of vortices and early features of coherent structure in the turbulent wake behind a 2-D circular cylinder

3-D evolution of Kármán vortex filaments and vortex filaments in braid regions in the turbulent wake of a 2-D circular cylinder is investigated numerically based on inviscid vortex dynamics by analyzing the response of the initially 2-D spanwise vortex filaments to periodic spanwise disturbance of varying magnitude, wavelength and initial phase angles. Our results reveal a kind of 3-D vortex system in the wake which consists of large scale horseshoe-shaped vortices and small scale γ-shaped vortex filaments as well as vortex loops. The mechanism and the dynamic process about the generation of streamwise vortical structure and the 3-D coherent structure are reported. currently published in the Chinese Edition of Acta Mechanica Sinica, Vol.25, No.3, 1993 The project supported by National Natural Science Foundation of China and the National Basic Research Project “Nonlinear Science”     

Stability of a supersonic flat-plate wake (Comparison of numerical and experimental results)

The stability of the wake downstream of a plat plate with a blunt trailing edge is numerically investigated at a supersonic freestream velocity. The calculated stability characteristics are compared with the experimental data.     

AGE method simulations of a turbulent far‐wake compared to spectral DNS

Turbulent flow simulation methods based on finite differences are attractive for their simplicity, flexibility and efficiency, but not always for accuracy or stability. This paper demonstrates that a good compromise is possible with the advected grid explicit (AGE) method. Starting from the same initial field as a previous spectral DNS, AGE method simulations of a planar turbulent wake were carried out as DNS, and then at three levels of reduced resolution. The latter cases were in a sense large‐eddy simulations (LES), although no specific sub‐grid‐scale model was used. Results for the two DNS methods, including variances and power spectra, were very similar, but the AGE simulation required much less computational effort. Small‐scale information was lost in the reduced resolution runs, but large‐scale mean and instantaneous properties were reproduced quite well, with further large reductions in computational effort. Quality of results becomes more sensitive to the value chosen for one of the AGE method parameters as resolution is reduced, from which it is inferred that the numerical stability procedure controlled by the parameter is acting in part as a sub‐grid‐scale model. Copyright © 2002 John Wiley & Sons, Ltd.     

Behavior of the vorticity vector in supersonic axisymmetric swirl flows behind a detonation wave

The behavior of the vorticity vector on a discontinuity surface arising in a supersonic nonuniform combustible gas flow with the formation of a shock or detonation wave is studied. In the general case, it is a vortex flow with prescribed distributions of parameters. It is demonstrated that the ratio of the tangential component of vorticity to density remains continuous in passing through the discontinuity surface, while the quantities proper become discontinuous. Results calculated for flow vorticity behind a steady-state detonation wave in an axisymmetric supersonic flow of a combustible mixture of gases are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 15–21, November–December, 2007     

Numerical analysis of axisymmetric and planar sudden expansion flows for laminar regime

In this study, the Navier–Stokes equations are solved numerically for axisymmetric and planar sudden expansion flows. The flow is considered laminar and steady state, and the fluid is incompressible. Finite difference equations are obtained using a control volume method in a non‐staggered grid arrangement, and solved by line‐by‐line TDMA technique using the SIMPLEM (SIMPLEM‐Modified) algorithm. Calculations are performed for higher expansion ratios, β, ranging from 1.5 to 10 and Reynolds numbers from 0.1 to 500. Results are presented in terms of streamlines, relative eddy intensity, location of the eddy center, and the eddy reattachment length depending on Re number and β values for both axisymmetric and planar sudden expansions. It is aimed to provide a picture of the effects of high values of expansion ratio and Reynolds number on the sudden expansion flow. As a result, it is found that the flow characteristics keep their structure for both higher expansion ratios and higher Reynolds numbers. Further, correlations were developed for the nondimensional eddy reattachment length, location of the eddy center and the relative eddy intensity, which have agreeable results to the computed results available from the literature. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigations of wake flows of a flat plate in steady,oscillatory and combined flows

Numerical study on near wake flows of a flat plate in three kinds of oncoming flows is made by using the discrete vortex model and improved vorticity creation method. For steady oncoming flow, both gross and detailed features of the wake flow are calculated and discussed. Then, in harmonic oscillatory oncoming flow two different wake flow patterns withK _c=2,4 and 10 are obtained respectively. Our results present a new wake flow pattern for lowKc numbers (Kc<5) describing vortex shedding, pairing and moving in a period of the oscillatory flow starting from rest. The calculated drag and inertia force coefficients are closer to experimental data from the U-tube than the previous results of vortex simulation. For in-line combined oncoming flow the vortex lock-in and dynamic characteristics are simulated. The results are shown to be in good agreement with experiments. The project supported by National Natural Science Fundation of China and LNM of Institute of Mechanics. CAS     

Wavelet analysis of unsteady flows: Application on the determination of the Strouhal number of the transient wake behind a single cylinder

This paper presents experimental results of the accelerating and decelerating flow in the wake of a cylinder obtained by means of hot wire anemometry measurements in a wind tunnel with high blockage ratio. The analysis was done in Fourier and wavelet spaces. The Strouhal number for Reynolds numbers up to 3 × 10⁴ was studied in a transient flow and compared with the results obtained from steady flows at several velocities uniformly distributed from Re = 1.7 × 10³ to 3 × 10⁴. Results show that the wavelet analysis is a valuable tool to deal with both transient and stationary random phenomena and that is able to capture the characteristics of the transient flow as well as the Fourier analysis can do with the steady state acquisitions.     

Dynamical mode decomposition of Gurney flap wake flow

The present work uses dynamic mode decomposition (DMD) to analyze wake flow of NACA0015 airfoil with Gurney flap. The physics of DMD is first introduced. Then the PIV-measured wake flow velocity field is decomposed into dynamical modes. The vortex shedding pattern behind the trailing edge and its high-order harmonics have been captured with abundant information such as frequency, wavelength and convection speed. It is observed that high-order dynamic modes convect faster than low-order modes; moreover the wavelength of the dynamic modes scales with the corresponding frequency in power law.