Numerical simulation of unsteady blade row interactions induced by passing wakes

A numerical study of the unsteady phenomena resulting of periodic passing wakes is presented. An unsteady passing wake boundary condition is implemented in a three-dimensional Navier–Stokes code. Unsteady computations are performed to evaluate the capability of the code to simulate the rotor–stator interaction flow. The analysis of the flow structures shows the vortical disturbances and the migration of the incoming wakes through the blade passage. This physical analysis allows to separate the main origins of the losses.     

An unsteady multiblock multigrid scheme for lifting forward flight rotor simulation

Numerical simulation of multi‐bladed lifting rotors in forward flight is considered. The flow‐solver presented is multiblock and unsteady, which is essential for forward flight, and also includes multigrid acceleration to reduce run‐times. A structured multiblock grid generator specifically for rotor blades has also been developed and is presented here. Previous work has shown that hovering lifting rotor flows are particularly expensive to simulate, since the capture of the vortical wake below the disc requires a long numerical integration time; more than 20 revolutions for an unsteady simulation, or more than 40000 time‐steps for a single grid steady simulation. It is demonstrated here that only two or three revolutions are required to obtain a converged solution for forward flight, since the wake is swept downstream. This requires less than 1.5 × the run‐time of a steady hovering simulation, for the same grid density around each blade, even though an unsteady simulation is required and the complete disk must be solved rather than one blade as in hover. It is demonstrated that very fine meshes are required to capture the unsteady tip vortex motion, and the effects on blade loading of blade‐vortex interaction and rotor shaft inclination are also considered. Copyright © 2004 John Wiley & Sons, Ltd.     

Euler solutions for self-generated rotor blade-vortex interactions

A finite-difference procedure has been developed for the prediction of three-dimensional rotor blade-vortex interactions. The interaction velocity field was obtained through a non-linear superposition of the rotor flow field, computed using the unsteady three-dimensional Euler equations, and the embedded vortex wake flow field, computed using the law of Biot-Savart. In the Euler model, near wake rotational effects were simulated using the surface velocity ‘transpiration’ approach. As a result, a modified surface boundary condition was prescribed and enforced at each time step of the computations to satisfy the tangency boundary condition. For supercritical interactions using an upstream-generated vortex, accuracy of the numerical results were found to rely on the user-specified vortex core radius and vortex strength. For the more general self-generated subcritical interactions, vortex wake trajectories were computed using the lifting-line helicopter/rotor trim code CAMRAD. For these interactions, accuracy of the results were found to rely heavily on the CAMRAD-predicted vortex strength, vortex orientation with respect to the blade, and to a large extent on the user-specified vortex core radius. Results for the one-seventh scale model OLS rotor and for a non-lifting rectangular blade having a NACA0012 section are presented. Comparisons with the experimental windtunnel data are also made.     

Near-wake measurement in a rotor/stator axial compressor using slanted hot-wire technique

 Three-dimensional near-wake structure behind a rotor was measured using slanted hot-wire technique in a large-scale, low-speed, rotor/stator axial compressor. Unsteady flow interaction between blade rows was varied by setting the axial gap between rows at 10% and 30% of rotor chord. Results show that stronger flow interactions between blade rows, or closer axial gap, produce more pronounced time variation within the rotor wake. All parameters measured – three component velocities, yaw and pitch angles – varied strongly within the wake, and are quantified. Received: 8 July 1996/Accepted: 29 May 1997     

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.     

A computational investigation of unsteady turbulent wake–boundary-layer interaction

The relative motion of rotor and stator blade rows in a turbomachine generates periodically unsteady flow on the blades due to travelling wake perturbations. To better understand the attendant wake–boundary-layer interaction a calculation procedure was developed to model the behaviour of this complex unsteady flow. Due to nonlinear interactions with the boundary layer, the travelling discrete frequency wakes were found to decrease the velocity profile shape factor. For the range of reduced frequencies examined (=0.33–9.33) the skin-friction coefficient was found to be frequency dependent. The calculated results for both steady and unsteady velocity profiles, and for skin friction compared well with experimental data. Although the agreement between measured and calculated velocity phase shift was poor, in both experimental and model results the negative phase shift throughout the boundary layer due to the travelling-wave fluctuations has been captured.     

Turbulence measurements in the inlet plane of a centrifugal compressor vaneless diffuser

Detailed flow measurements at the inlet of a centrifugal compressor vaneless diffuser are presented. The mean 3-d velocities and six Reynolds stress components tensor are used to determine the turbulence production terms which lead to total pressure loss. High levels of turbulence kinetic energy were observed in both the blade and passage wakes, but these were only associated with high Reynolds stresses in the blade wakes. For this reason the blade wakes mixed out rapidly, whereas the passage wake maintained its size, but was redistributed across the full length of the shroud wall. Peak levels of Reynolds stress occurred in regions of high velocity shear and streamline curvature which would tend to destabilize the shear gradient. Four regions in the flow are identified as potential sources of loss - the blade wake, the shear layers between passage wake and jet, the thickened hub boundary layer and the interaction region between the secondary flow within the blade wake and the passage vortex. The blade wakes generate most turbulence, with smaller contributions from the hub boundary layer and secondary flows, but no significant contribution is apparent from the passage wake shear layers.     

A time marching method for unsteady two-dimensional flow in a blade passage

A time marching method for calculating non-uniform unsteady two-dimensional flow through a blade passage is presented. The various problems encountered in extending time marching techniques into this field are examined, and the method is applied to analyse unsteady wake flows through a compressor and turbine blade row.     

空腔流动的动量分解及能量输运特性

空腔结构广泛应用于航空航天飞行器部件及地面交通工具中,其复杂的流声特性是相关工程设计中必须考虑的关键问题.空腔流动中的流声相互作用是空腔自持振荡的重要过程,准确识别并解耦空腔内的流体动力学模态和声模态,是深入理解空腔流声相互作用和能量转化机制的关键.通过直接求解二维Navier-Stokes方程数值模拟来流马赫数Ma=...     

DIRECT NUMERICAL SIMULATION OF TURBINE CASCADE FLOW WITH HEAT TRANSFER EFFECTS

低雷诺数流动对高空动力装置, 特别是涡轮部件的性能产生重要的影响. 本文采用具有7阶精度的差分格式, 通过直接求解二维瞬态可压缩Navier-Stokes方程组, 对雷诺数为241 800 (基于叶片弦长)时的叶片表面带有热传导效应的平面涡轮叶栅流动进行了二维直接数值模拟, 对低雷诺数平面涡轮叶栅流动的非定常流动现象作了初步的探索.数值结果表明:在叶栅通道入口处, 流场的非定常性很弱;在叶栅尾缘处, 具有正负涡量的尾涡交替地从压力面和吸力面上脱落;周期性的涡脱落使得叶栅通道内和尾迹区的总压发生(准)周期的变化, 并且, 尾迹区总压变化主频率是通道内总压变化主频率的2倍;在时均流场中, 叶片表面压力的分布与实验值吻合良好, 表征热传导效应的斯坦顿数除湍流区外与实验值基本吻合;尾迹区速度脉动的2阶统计量与圆柱绕流尾迹区速度脉动2阶统计量具有基本相似的分布特征.     

波涡相互作用研究的某些进展(Ⅱ)

<正> 5 波涡共振 从第3节的感受性问题再前进一步,自然要问在什么条件下入射波激发起涡中之波的最大响应.这就导致了入射波与层状或轴状涡中受激波之间共振的概念,简称波涡共振.一般说来,在流体内部若有两个或多个波相会,它们将互相穿透而沿原来的方向离去.但若它们的波矢量和频率满足一定的关系(参见Craik 1985),就会在相会点产生新的波.2阶扰动的振幅可达到1阶扰动振幅的量级,而且流场中会出现一些重要的独特性质.这就是流体内部波共振,波涡共振是其一类情形.      

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．     

INLET GUIDE VANE WAKES INCLUDING ROTOR EFFECTS

Fundamental experiments are described directed at the investigation of forcing functions generated by an inlet guide vane (IGV) row, including interactions with the downstream rotor, for application to turbomachine forced response design systems. The experiments are performed in a high-speed research fan facility comprised of an IGV row upstream of a rotor. IGV-rotor axial spacing is variable, with the IGV row able to be indexed circumferentially, thereby allowing measurements to be made across several IGV wakes. With an IGV relative Mach number of 0·29, measurements include the IGV wake pressure and velocity fields for three IGV-rotor axial spacings. The decay characteristics of the IGV wakes are compared to the Majjigi and Gliebe empirical correlations. After Fourier decomposition, a vortical–potential gust splitting analysis is implemented to determine the vortical and potential harmonic wake gust forcing functions both upstream and downstream of the rotor. Higher harmonics of the vortical gust component of the IGV wakes are found to decay at a uniform rate due to viscous diffusion.     

The onset of dynamic stall revisited

Dynamic stall on a helicopter rotor blade comprises a series of complex aerodynamic phenomena in response to the unsteady change of the blade’s angle of attack. It is accompanied by a lift overshoot and delayed massive flow separation with respect to static stall. The classical hallmark of the dynamic stall phenomenon is the dynamic stall vortex. The flow over an oscillating OA209 airfoil under dynamic stall conditions was investigated by means of unsteady surface pressure measurements and time-resolved particle image velocimetry. The characteristic features of the unsteady flow field were identified and analysed utilising different coherent structure identification methods. An Eulerian and a Lagrangian procedure were adopted to locate the axes of vortices and the edges of Lagrangian coherent structures, respectively; a proper orthogonal decomposition of the velocity field revealed the energetically dominant coherent flow patterns and their temporal evolution. Based on the complementary information obtained by these methods the dynamics and interaction of vortical structures were analysed within a single dynamic stall life cycle leading to a classification of the unsteady flow development into five successive stages: the attached flow stage; the stall development stage; stall onset; the stalled stage; and flow reattachment. The onset of dynamic stall was specified here based on a characteristic mode of the proper orthogonal decomposition of the velocity field. Variations in the flow field topology that accompany the stall onset were verified by the Lagrangian coherent structure analysis. The instantaneous effective unsteadiness was defined as a single representative parameter to describe the influence of the motion parameters. Dynamic stall onset was found to be promoted by increasing unsteadiness. The mechanism that results in the detachment of the dynamic stall vortex from the airfoil was identified as vortex-induced separation caused by strong viscous interactions. Finally, a revised criterion to discern between light and deep dynamic stall was formulated.     

A comprehensive PIV measurement campaign on a fully equipped helicopter model

The flow field around a helicopter is characterised by its inherent complexity including effects of fluid?Cstructure interference, shock?Cboundary layer interaction, and dynamic stall. Since the advancement of computational fluid dynamics and computing capabilities has led to an increasing demand for experimental validation data, a comprehensive wind tunnel test campaign of a fully equipped and motorised generic medium transport helicopter was conducted in the framework of the GOAHEAD project. Different model configurations (with or without main/tail rotor blades) and several flight conditions were investigated. In this paper, the results of the three-component velocity field measurements around the model are surveyed. The effect of the interaction between the main rotor wake and the fuselage for cruise/tail shake flight conditions was analysed based on the flow characteristics downstream from the rotor hub and the rear fuselage hatch. The results indicated a sensible increment of the intensity of the vortex shedding from the lower part of the fuselage and a strong interaction between the blade vortex filaments and the wakes shed by the rotor hub and by the engine exhaust areas. The pitch-up phenomenon was addressed, detecting the blade tip vortices impacting on the horizontal tail plane. For high-speed forward flight, the shock wave formation on the advancing blade was detected, measuring the location on the blade chord and the intensity. Furthermore, dynamic stall on the retreating main rotor blade in high-speed forward flight was observed at r/R?=?0.5 and 0.6. The analysis of the substructures forming the dynamic stall vortex revealed an unexpected spatial concentration suggesting a rotational stabilisation of large-scale structures on the blade.     

A numerical modelling of stator–rotor interaction in a turbine stage with oscillating blades

In real flows unsteady phenomena connected with the circumferential non-uniformity of the main flow and those caused by oscillations of blades are observed only jointly. An understanding of the physics of the mutual interaction between gas flow and oscillating blades and the development of predictive capabilities are essential for improved overall efficiency, durability and reliability. In the study presented, the algorithm proposed involves the coupled solution of 3D unsteady flow through a turbine stage and the dynamics problem for rotor-blade motion by the action of aerodynamic forces, without separating the outer and inner flow fluctuations. The partially integrated method involves the solution of the fluid and structural equations separately, but information is exchanged at each time step, so that solution from one domain is used as a boundary condition for the other domain. 3-D transonic gas flow through the stator and rotor blades in relative motion with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite volume difference scheme of Godunov–Kolgan. The structural analysis uses the modal approach and a 3-D finite element model of a blade. The blade motion is assumed to be constituted as a linear combination of the first natural modes of blade oscillations, with the modal coefficients depending on time. A calculation has been done for the last stage of the steam turbine, under design and off-design regimes. The numerical results for unsteady aerodynamic forces due to stator–rotor interaction are compared with results obtained while taking into account blade oscillations. The mutual influence of both outer flow non-uniformity and blade oscillations has been investigated. It is shown that the amplitude-frequency spectrum of blade oscillations contains the high-frequency harmonics, corresponding to the rotor moving past one stator blade pitch, and low-frequency harmonics caused by blade oscillations and flow non-uniformity downstream from the blade row; moreover, the spectrum involves the harmonics which are not multiples of the rotation frequency.     

DPIV study of near-stall wake-rotor interactions in a transonic compressor

Wake-rotor interactions at near-stall conditions are studied using digital particle image velocimetry (DPIV) in a transonic compressor at the Compressor Aero Research Lab (CARL) at Wright-Patterson Air Force Base. The wake generators (WGs) are designed to simulate wakes of highly loaded stators without producing flow swirl. Flow visualization, instantaneous, and average velocity field data are presented for near-stall compressor operating conditions. These results describe the interaction of the wake shed from the upstream WG with the downstream potential field of the rotor leading edge for two axial spacings at 75 and 90% span. The advantage of ensemble averaging is demonstrated when operating at challenging conditions such as near-stall, which poses special difficulties in obtaining DPIV data. Ensemble averaging, which is possible because of a natural phase locking provided by the blade potential field, allows robust statistics.     

Measurement and analysis of unsteady flow structures in rotor blade wakes

Time-variant data are obtained to investigate the exit flow field from a rotor in a research compressor. In the free-stream region, the instantaneous data are analogous to one another and to the ensemble averaged free-stream results. However, in the wake region, some of the instantaneous signals are similar to one another and to the ensemble averaged wake, but others differ significantly. These variations in the instantaneous data are interpreted and shown to be due to a vortex street structure in the wake. This is accomplished by: (1) developing a mathematical model of the rotor blade exit flow field based on a wake vortex street structure analogous to the unsteady flow field behind bluff bodies due to classical von Karman vortex shedding; and (2) correlating predictions of both the ensemble averaged and instantaneous rotor blade exit flow fields as well as the velocity probability density distributions from this vortex wake flow field model with the corresponding data. The correlation of the ensemble averaged rotor blade exit flow fields is very good and the flow angle distribution correlation excellent. The predicted instantaneous rotor blade exit flow field exhibits many of the flow features found in the data. Also, the probability density distributions for the data and the vortex wake flow field model are analogous to one another.List of symbols N number of rotor revolutions - S _w rotor blade wake width - S _x vortex core horizontal spacing - S _y vortex core vertical spacing - u velocity component parallel to vortex street motion - v velocity component normal to vortex street motion - W instantaneous relative velocity - W _i velocity induced by vortex street - W free-stream relative velocity - W _s velocity of vortex street - x coordinate parallel to vortex street motion - y coordinate normal to vortex street motion - free-stream relative flow angle - _inst instantaneous relative flow angle - vortex strength     

FLUID–STRUCTURE RESONANCE PRODUCED BY ONCOMING ALTERNATING VORTICES

The present investigation examines a simple fluid–structure interaction problem, which is represented by the unsteady response of an airfoil/blade to a Karman vortex street in an inviscid uniform flow. Two different cases were examined; one with a rigid airfoil/blade, where the structural stiffness is infinite, another with an elastic blade. In both cases, the flow remains attached to the airfoil/blade surface. A time-marching technique solving the Euler equations and a two-degree-of-freedom structural dynamic model is used to examine the interactions between the fluid and the structure. The interactions between the convected vortices and the structure modify the shed wake whose energy, in turn, feeds into the forces and moments acting on the structure. For a rigid airfoil/blade, it is found that the amplitude of the aerodynamic response is not proportional to the density of the oncoming vortex street, but depends on c/d , the ratio of the chord length (c) to the axial spacing (d) of the convected vortices. When the number of vortices per unit length is increased, the amplitudes of the aerodynamic response increase and then decrease even though the density of the vorticity keeps increasing and so is the energy of the excitation wake. Maxima are observed at c/d=0·5, 1·5 and 2·5. This behaviour is analogous to the structural resonance phenomenon and is labeled “aerodynamic resonance”. The existence of such an “aerodynamic resonance” is important to turbomachinery applications where the blade is elastic, the flow is unsteady and the shed vortices from the previous row are convected downstream by the mean flow. Thus, “aerodynamic resonance” alone or in conjunction with structural resonance could impact negatively on the fatigue life of turbine blades and their combined effects should be accounted for in blade design. A preliminary attempt to assess this impact has been carried out. It is found that the relative fatigue life of a blade could be reduced by four orders of magnitude as a result.