Calculation of the hydrodynamic interaction of blade cascades with consideration for the diffusion of unsteady wakes

A semianalytical method was developed to calculate the hydrodynamic interaction of two blade cascades moving relative to one another. The potential perturbation of the flow by the cascades and the vortex perturbation due to blade edge wakes are taken into account. Along with the steady wakes caused by boundary layer separation from the blade cascades, allowance is made of the unsteady wakes separating from the blade trailing edges because of change in velocity circulation on them. The unsteady wakes are calculated with allowance for their diffusion in the presence of flow viscosity using approximate boundarylayer theory. The method is implemented as a program for calculating the unsteady hydrodynamic characteristics of blade cascades on a personal computer. Examples of calculation and a comparison with experiment are given.     

Asymmetric vortex shedding flow past an inclined flat plate at high incidence

This paper reports an experimental investigation of the vortex shedding wake behind a long flat plate inclined at a small angle of attack to a main flow stream. Detailed velocity fields are obtained with particle-image velocimetry (PIV) at successive phases in a vortex shedding cycle at three angles of attack, α=20°, 25° and 30°, at a Reynolds number Re≈5,300. Coherent patterns and dynamics of the vortices in the wake are revealed by the phase-averaged PIV vectors and derived turbulent properties. A vortex street pattern comprising a train of leading edge vortices alternating with a train of trailing edge vortices is found in the wake. The trailing edge vortex is shed directly from the sharp trailing edge while there are evidences that the formation and shedding of the leading edge vortex involve a more complicated mechanism. The leading edge vortex seems to be shed into the wake from an axial location near the trailing edge. After shedding, the vortices are convected downstream in the wake with a convection speed roughly equal to 0.8 the free-stream velocity. On reaching the same axial location, the trailing edge vortex, as compared to the leading edge vortex, is found to possess a higher peak vorticity level at its centre and induce more intense fluid circulation and Reynolds stresses production around it. It is found that the results at the three angles of attack can be collapsed into similar trends by using the projected plate width as the characteristic length of the flow.     

Flow topology and unsteady features of the wake of a generic high-speed train

The unsteady wake of a high-speed train is investigated experimentally. From a practical point of view, the wake region is of considerable importance as it is where slipstream velocities—velocities induced by the vehicles movement through air—are largest. In turn, this can create a considerable risk for passengers and track-side workers as the train passes. The flow is quantified in a 1:10 scale wind-tunnel experiment using high-frequency 4-hole dynamic pressure cobra probes, surface-pressure measurements and flow visualisation. The dominant feature of the time-average wake topology consists of a clearly identifiable counter-rotating streamwise vortex pair. Although the wake structure and evolution should perhaps be considered as a whole, the near wake exhibits periodic unsteadiness, at a Strouhal number of 0.2, that could be attributed to periodic shedding from the sides and to a lesser extent the top surface. This periodicity feeds into the trailing vortices, consistent with lateral and vertical displacement of the cores as they advect downstream and thus affecting maximum slipstream velocities.     

A DPIV study of the trailing vortex elements from the blades of a horizontal axis wind turbine in yaw

Digital particle image velocimetry (DPIV) has been used in a wind tunnel study to measure the velocity field of the trailing vortices from the blades of a horizontal axis wind-turbine (HWAT) in yaw. The creation of the trailing vortex circulation is shown to vary as a function of the phase angle of the rotor and the angle of yaw between the wind and turbine rotor. The strength of the convecting vorticity was also shown to vary with time. The initial formation of the vortex is shown determined by the flow expansion angle while in yawed flows the developing vortex is then influenced by the vortex sheet shed from the inboard blade trailing edge. This interaction is shown to significantly affect the roll up of the tip vortex. Received: 17 December 1997/Accepted: 16 June 1999     

基于涡量矩理论的绕振荡水翼涡动力学分析

文章采用标准k-ω SST湍流模型和动网格技术, 实现了绕俯仰振荡NACA66水翼非定常流动结构与水动力特性的数值模拟, 并基于有限域涡量矩理论定量表征了局部旋涡结构对水翼动力特性的影响. 研究结果表明: 在水翼升程阶段, 当攻角较小时, 层流向湍流的转捩点由水翼尾缘向前缘移动; 在较大攻角时, 顺时针尾缘涡?TEV在水翼吸力面上生成并向前缘发展, 同时与吸力面上的顺时针前缘涡?LEV融合发展为附着在整个吸力面上的新前缘涡?LEV, 新的?LEV与逆时针尾缘涡+TEV相互作用直至完全脱落, 直接导致了水翼的动力失速, 在回程阶段, 绕振荡水翼的流场结构逐渐由湍流转变为层流. 基于有限域涡量矩理论的定量分析发现, 有限域内附着的?LEV和?TEV提供正升力, 当?LEV发展覆盖整个吸力面时对升力的贡献最大, 占总升力近50%, 而+TEV提供负升力. 同时发现, 有限域内各旋涡内部的不同区域提供的升力有正有负; 而逸出有限域的旋涡内部不同区域提供的升力方向均保持一致, 其中顺时针涡提供正升力, 而逆时针涡提供负升力. 在失速阶段, 域外旋涡整体对升力贡献较小且存在小幅波动, 体现了流动的非定常性.      

Numerical study on wake characteristics of high-speed trains

Intensive turbulence exists in the wakes of high speed trains, and the aerodynamic performance of the trailing car could deteriorate rapidly due to complicated features of the vortices in the wake zone. As a result, the safety and amenity of high speed trains would face a great challenge. This paper considers mainly the mechanism of vortex formation and evolution in the train flow field. A real CRH2 model is studied, with a leading car, a middle car and a trailing car included. Different running speeds and cross wind conditions are considered, and the approaches of un- steady Reynold-averaged Navier-Stokes （URANS） and de- tached eddy simulation （DES） are utilized, respectively. Re- suits reveal that DES has better capability of capturing small eddies compared to URANS. However, for large eddies, the effects of two approaches are almost the same. In conditions without cross winds, two large vortex streets stretch from the train nose and interact strongly with each other in the wake zone. With the reinforcement of the ground, a complicated wake vortex system generates and becomes strengthened as the running speed increases. However, the locations of flow separations on the train surface and the separation mechanism keep unchanged. In conditions with cross winds, three large vortices develop along the leeward side of the train, among which the weakest one has no obvious influence on the wake flow while the other two stretch to the tail of the train and combine with the helical vortices in the train wake. Thus, optimization of the aerodynamic performance of the trailing car should be aiming at reducing the intensity of the wake vortex system.     

Application of a vortex lattice numerical model in the calculation of inviscid incompressible flow around delta wings

The flow over a flat plate delta wing at incidence and in sideslip is studied using vortex lattice models based on streamwise penelling. For the attached flow problem the effect of sideslip is simulated by modifying the standard vortex lattice model for zero sideslip by aligning the trailing vortices aft of the wing along the resultant flow direction. For the separated flow problem a non-linear vortex lattice model is developed for both zero and non-zero sideslip angles in which the shape and position of the leading edge separation vortices are calculated by an iterative procedure starting from an assumed initial shape. The theoretical values are compared with available theoretical and experimental results.     

Symmetric vortex shedding in the near wake of a circular cylinder due to streamwise perturbations

Symmetric perturbations imposed on cylinder wakes may result in a modification of the vortex shedding mode from its natural antisymmetric, or alternating, to a symmetric one where twin vortices are simultaneously shed from both sides of the cylinder. In this paper, the symmetric mode in the wake of a circular cylinder is induced by periodic perturbations imposed on the in-flow velocity. The wake field is examined by PIV and LDV for Reynolds numbers about 1200 and for a range of perturbation frequencies between three and four times the natural shedding frequency of the unperturbed wake. In this range, a strong competition between symmetric and antisymmetric vortex shedding occurs for the perturbation amplitudes employed. The results show that symmetric formation of twin vortices occurs close to the cylinder synchronized with the oscillatory component of the flow. The symmetric mode rapidly breaks down and gives rise to an antisymmetric arrangement of vortex structures further downstream. The downstream wake may or may not be phase-locked to the imposed oscillation. The number of cycles for which the symmetric vortices persist in the near wake is a probabilistic function of the perturbation frequency and amplitude. Finally, it is shown that symmetric shedding is associated with positive energy transfer from the fluid to the cylinder due to the fluctuating drag.     

Instantaneous and time-averaged flow fields of multiple vortices in the tip region of a ducted propulsor

The instantaneous and time-averaged flow fields in the tip region of a ducted marine propulsor are examined. In this flow, a primary tip-leakage vortex interacts with a secondary, co-rotating trailing edge vortex and other co- and counter-rotating vorticity found in the blade wake. Planar particle imaging velocimetry (PIV) is used to examine the flow in a plane approximately perpendicular to the mean axis of the primary vortex. An identification procedure is used to characterize multiple regions of compact vorticity in the flow fields as series of Gaussian vortices. Significant differences are found between the vortex properties from the time-averaged flow fields and the average vortex properties identified in the instantaneous flow fields. Variability in the vortical flow field results from spatial wandering of the vortices, correlated fluctuations of the vortex strength and core size, and both correlated and uncorrelated fluctuations in the relative positions of the vortices. This variability leads to pseudo-turbulent velocity fluctuations. Corrections for some of this variability are performed on the instantaneous flow fields. The resulting processed flow fields reveal a significant increase in flow variability in a region relatively far downstream of the blade trailing edge, a phenomenon that is masked through the process of simple averaging. This increased flow variability is also accompanied by the inception of discrete vortex cavitation bubbles, which is an unexpected result, since the mean flow pressures in the region of inception are much higher than the vapor pressure of the liquid. This suggests that unresolved fine-scale vortex interactions and stretching may be occurring in the region of increased flow variability.     

Forced and unforced unsteadiness in an axial turbomachine

Different sources of unsteadiness in low-speed axial turbomachinery are identified and classified in this paper. From the classical picture segregating non-periodic mechanisms (turbulence) from periodic phenomena (unsteadiness), a further decomposition is outlined to distinguish between forced (deterministic periodicities) and unforced (non-deterministic) unsteadiness. Raw velocity traces, measured for several test conditions in a typical industrial fan with hot-wire anemometry, are ensemble-averaged to obtain time-resolved fluctuations. Then, a frequency-based filtering procedure is employed to isolate non-deterministic, but also non-chaotic, disturbances from the remaining turbulent fluctuations, resulting in the so-called unforced unsteadiness. This term reveals coherent flow structures that involve “large-scale” unsteadiness with other periodic features different to the blade rotation scales (BPF). As a starting point, the kinetic energy associated to the total unsteadiness (in terms of a percentage of the kinetic energy of the time-averaged flow) is analyzed as a function of the operating conditions. Next, the different components contributing to the total unsteadiness of the flow are also observed, in order to determine their particular significance on the global unsteady scenario. It is shown that the turbulent kinetic energy reaches up to approximately a 50–60% of the total unsteady energy, while both forced and unforced components contribute equally to the rest of the energy. In addition, it is observed that higher levels of unforced unsteadiness are concentrated towards the endwall boundary layers where forced unsteadiness is notably reduced due to the loss of the wake–core structure. Conversely, forced unsteadiness is more evident at inner regions of the rotor passage. Furthermore, unforced unsteadiness is especially intense in the tip regions where large-scales associated to the tip leakage vortex are established. It is demonstrated that the estimation of the unforced unsteadiness constitutes an accurate indicator of the presence of tip leakage flows for low-speed axial turbomachinery. Moreover, this is confirmed through the representation of the degree of anisotropy, where typical anisotropic structures are revealed. Finally, with the introduction of power spectrum densities for the unforced components, it is possible to identify typical eddy sizes of these large fluctuations.     

Investigation on Secondary Flow Characteristics in a Curved Annular Duct with Struts

Under the influence of duct curvature, cross-sectional area variation and internal struts, the internal flow field within a curved annular duct becomes rather complicated and contains strong secondary flow. In this paper, the secondary flow characteristics in an annular duct with struts are experimentally and numerically investigated. The results show that large pressure gradients exist on the bends of hub and shroud. Meanwhile, two counter-rotating vortex pairs appear both along the hub-side and shroud-side surfaces. The hub-side vortex pair of which the vortex cores travel downstream parallelly evolves from the horseshoe vortex which is induced by the leading edge of the upstream strut, whereas the shroud-side vortex pair originates from the strut trailing edge and the corresponding vortex cores develop in a divergent way. Additionally, the effects of the duct exit Mach number on the secondary flow characteristics are also studied. As the exit Mach number increases, the streamwise pressure gradients increase and lead to more intense vortices, higher total pressure loss and larger flow distortion.     

Unsteady characteristics of inlet vortices

An experimental study of the unsteady characteristics of inlet vortices has been conducted using a high-frame rate digital particle image velocimetry system. The results revealed the formation of a pair of counter-rotating inlet vortices for the no-wind configuration and one single inlet vortex when there was crosswind. In all measurement planes, from near the ground to the inlet, evidence of vortex meandering with quasi-periodicity was found. The vortex meander is dominant in the direction of the crosswind, and its amplitude increases with crosswind velocity. The proper orthogonal decomposition analysis of the instantaneous velocity field suggested that the most energetic mode was a helical displacement wave, corresponding to the first helical mode. Similarities with the meandering of the trailing vortices from wings were noted. The present results also suggest that the unsteady characteristics of the focus of separation formed on the ground might be responsible for the unsteady nature of the inlet vortex.     

Unsteady Simulation of a Jet-in-crossflow

The present work represents the first attempt at studying the unsteadiness of jet-in-crossflows using the Reynolds-Averaged Navier-Stokes (RANS) equations. In the past, numerical studies of jet-in-crossflows, with the exception of the few attempts of DNS and LES. are always carried out under the assumption that the flowfield is steady and symmetric about the jet center plane. Growing experimental evidence suggests that this flow is unsteady and periodic. The present work verified the existence of periodicity in jet-in-crossflows numerically. The numerically predicted Slrouhal number is in good agreement with experimental observations. In addition, the present simulation of the jet-in-crossflow were able to resolve the details of flow structures such as the oscillating wake structures, the jet shear-layer vortices, and the counter-rotating vortex pairs.     

Stationary vortex sheets in a stirring flow

Stationary vortex sheets in a two-dimensional stirring flow may be approximated by arrays of stationary point vortices arranged along the support of the sheets. These vortices lie at the roots of a polynomial that satisfies a generalized Lamé differential equation; the polynomial itself (not the roots) determines the complex potential and stream function. In this paper, sufficient conditions for the stirring flow are found so that the differential equation has two independent polynomial solutions with simple closed-form expressions, analogous to hypergeometric polynomials. The corresponding point vortex array then depends on a complex parameter that controls the location of the sheet, so that it may pass through any selected point. Stationary sheets in a periodic flow are approximated by the same method.     

Pulsating flow past a spanwise rib in a channel at moderate Reynolds numbers

The results of visual investigations and direct numerical simulation of flow past a spanwise rib in a channel in a pulsating external flow at the Reynolds numbers corresponding to transition to turbulence in the separation region downstream of the rib in steady-state flow past the latter are represented. It is shown that the calculated and experimental data are in the adequate accordance. The effect of the forced unsteadiness parameters on the vortex flow structure downstream of the rib is analyzed. Some laws of the formation and evolution of the vortex structure downstream of the rib in a pulsating flow are obtained.     

Self-sustained global oscillations in a jet in crossflow

A jet in crossflow with an inflow ratio of 3, based on the maximum velocity of the parabolic jet profile, is studied numerically. The jet is modeled as an inhomogeneous boundary condition at the crossflow wall. We find two fundamental frequencies, pertaining to self-sustained oscillations in the flow, using full nonlinear direct numerical simulation (DNS) as well as a modal decomposition into global linear eigenmodes and proper orthogonal decomposition (POD) modes; a high frequency which is characteristic for the shear-layer vortices and the upright vortices in the jet wake, and a low frequency which is dominant in the region downstream of the jet orifice. Both frequencies can be related to a region of reversed flow downstream of the jet orifice. This region is observed to oscillate predominantly in the wall-normal direction with the high frequency, and in the spanwise direction with the low frequency. Moreover, the steady-state solution of the governing Navier?CStokes equations clearly shows the horseshoe vortices and the corresponding wall vortices further downstream, and the emergence of a distinct counter-rotating vortex pair high in the free stream. It is thus found that neither the inclusion of the jet pipe nor unsteadiness is necessary to generate the characteristic counter-rotating vortex pair.     

Controlling the near vortex wake of a swept half-wing by means of mini-flaps

The effect of mini-flaps on the flow pattern in the near vortex wake behind a model swept half-wing is investigated. The distributions of the time-average flow velocity were measured in a subsonic wind tunnel, in a section normal to the freestream velocity vector located at a distance of 3.8 wing half-spans from its trailing edge. When mini-flaps are mounted on both upper and lower wing surfaces, two vortices (tip and auxiliary) of the same sign are observable in the above-mentioned flow section; they are separated by an extended region of vorticity of the opposite sign. The model angle-of-attack effect on the intensities of the tip and auxiliary vortices is estimated.     

Development and stability of swirling flows

The purpose of this research is to investigate steady axisymmetric swirling flows in channels and free vortices and also to establish the role of hydrodynamic instability in the formation of the sharp changes in flow structure associated with an increased rate of rotation. On the basis of numerical solutions of the complete Navier-Stokes equations obtained by a finite-difference method swirling flows in pipes with impermeable and permeable walls and in a free vortex are investigated. The stability of the swirling axisymmetric flows is considered on the assumption of local parallelism: the problem of the normal modes developing against the background of the axisymmetric flow determined by the velocity profiles in local cross sections of the flow is solved. Attention is mainly concentrated on free vortex flows with reverse current zones, their structure and stability.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–11, July–August, 1988.     

Granular vortices: Identification,characterization and conditions for the localization of deformation

We relate the micromechanics of vortex evolution to that of force chain buckling and, on this basis, formulate the conditions for strain localization in a continuum model of dense granular media. Using the traditional bifurcation analysis of shear bands, we show that kinematic vortex fields are in fact solutions to the boundary value problem satisfying null boundary conditions. To establish an empirical basis for our study, we first develop a method to identify the location of the core and boundary of each vortex from a given displacement field in two dimensions. We then employ this method to characterize the residual deformation field (i.e., the deviation of particle motions from the continuum deformation) in a physical experiment and a discrete element simulation of dense granular samples submitted to biaxial compression. Vortices in the failure regime are essentially confined to the shear band. Primary vortices, the clear majority, rotate in the same direction as the shear band; secondary vortices, the so-called wakes, rotate in the opposite direction. Primary vortices align in spatial succession along the central axis of the band; wakes form next to the band boundaries, in between and beside two adjacent primary vortices. Force chain buckling, the governing mechanism for shear bands, is responsible for vortex formation in the failure regime. Vortex dynamics are consistent with stick-slip dynamics. From quiescent conditions of jamming or stick, vortical motions arise from force chain buckling and associated relative particle rotations and sliding; these in turn precipitate intermittent periods of unjamming or slip, evident in the attendant drops in stress ratio and bursts in both kinetic energy and local nonaffine deformation. A kinematic vortex field inside shear bands is proposed that is consistent with the equations of continuum mechanics and the underlying instability of force chain buckling: such a field is periodic with a repeating unit cell comprising a primary vortex at the center of the band, with two trailing wakes close next to the band boundaries.