Mind the gap: a new insight into the tip leakage vortex using stereo-PIV

The tip leakage vortex (TLV), which develops in the clearance between the rotor and the stator of axial hydro turbines, has been studied for decades. Yet, many associated phenomena are still not understood. For instance, it remains unclear how the clearance size is related to the occurrence of cavitation in the vortex, which can lead to severe erosion. Experiments are here carried out on the influence of the clearance size on the tip vortex structure in a simplified case study. A NACA0009 hydrofoil is used as a generic blade in a water tunnel while the clearance between the blade tip and the wall is varied. The 3D velocity fields are measured using Stereo Particle Image Velocimetry (SPIV) in three planes located downstream of the hydrofoil for different values of the upstream velocity, the incidence angle and a large number of tip clearances. The influence of the flow conditions on the structure of the TLV is described through changes in the vortex intensity, core axial flow, vortex center position and wandering motion amplitude. Moreover, high-speed visualizations are used to highlight the vortex core trajectory and clearance flow alteration, turning into a wall jet as the tip clearance is reduced. The measurements clearly reveal the existence of a specific tip clearance for which the vortex strength is maximum and most prone to generating cavitation.     

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.     

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．     

Transonic Rotor/Stator Interaction Using a 3-D Linearised Unsteady Viscous Flow Model

The paper first summarizes the forced response problem in turbomachinery and reviews various numerical methods for the simulation of unsteady flows. A particular technique, based on the linearisation of the unsteady Favre-averaged Navier-Stokes equations on three-dimensional mixed-element grids of tetrahedra, hexahedra and wedges, is described in some detail. The methodology was applied to a NGV/rotor interaction benchmark case for which detailed steady and unsteady flow measurements are available. The steady-state flow, calculated using a non-linear viscous representation, was described in detail with emphasis on features such as separation, horseshoe and passage vortices, tip leakage and shock structure since these are likely to influence the unsteady flow. The sources of unsteadiness on the rotor passage were evaluated from the steady-state solution at the NGV outlet. The disturbances were split into vortical, entropic and potential waves, the Fourier components of which were considered separately. The summation of the vortical and entropic waves was used as a rotor inlet boundary condition in order to assess the wake/rotor unsteady interaction. Similarly, potential waves were used to study the potential/rotor interaction. The results obtained from these two types of unsteady interactions were superimposed and compared with experimental data. Good qualitative and, in most cases, quantitative agreement was obtained, a finding which suggests that the unsteady flowfield generated by the relative blade motion can be considered to be a quasi-linear phenomenon for the particular HP turbine studied. Finally, the mechanisms of wake/rotor and potential/rotor interactions were studied in some detail and it was concluded that the former was strong in the crown of the blade while the latter was dominant in the leading edge region.     

Parametric investigation of entire annular recess casing treatment on compressor stable operation

Application of casing treatment in compressor has been found to give substantial improvement in compressor stable operating range. An experimental investigation has been carried out with one variant of casing treatment, an entire annular recess (EAR) over the compressor rotor blades. Various tip clearances and two groups of annular recesses (without and with penetration of rotor blade tips into casing) were used. The results for 20 such configurations are presented in the proposed paper, analyzed with respect to relative tip clearance and recess relative volume influence on compressor stable operating range.     

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     

Control of the corner separation in a compressor cascade by steady and unsteady plasma aerodynamic actuation

This paper reports experimental results on using steady and unsteady plasma aerodynamic actuation to control the corner separation, which forms over the suction surface and end wall corner of a compressor cascade blade passage. Total pressure recovery coefficient distribution was adopted to evaluate the corner separation. Corner separation causes significant total pressure loss even when the angle of attack is 0°. Both steady and unsteady plasma aerodynamic actuations suppress the corner separation effectively. The control effect obtained by the electrode pair at 25% chord length is as effective as that obtained by all four electrode pairs. Increasing the applied voltage improves the control effect while it augments the power requirement. Increasing the Reynolds number or the angle of attack makes the corner separation more difficult to control. The unsteady actuation is much more effective and requires less power due to the coupling between the unsteady actuation and the separated flow. Duty cycle and excitation frequency are key parameters in unsteady plasma flow control. There are thresholds in both the duty cycle and the excitation frequency, above which the control effect saturates. The maximum relative reduction in total pressure loss coefficient achieved is up to 28% at 70% blade span. The obvious difference between steady and unsteady actuation may be that wall jet governs the flow control effect of steady actuation, while much more vortex induced by unsteady actuation is the reason for better control effect.     

Measurements of the tip leakage vortex structures and turbulence in the meridional plane of an axial water-jet pump

Particle image velocimetry (PIV) measurements at varying resolutions focus on the flow structures in the tip region of a water-jet pump rotor, including the tip-clearance flow and the rollup process of a tip leakage vortex (TLV). Unobstructed views of these regions are facilitated by matching the optical refractive index of the transparent pump with that of the fluid. High-magnification data reveal the flow non-uniformities and associated turbulence within the tip gap. Instantaneous data and statistics of spatial distributions and strength of vortices in the rotor passage reveal that the leakage flow emerges as a wall jet with a shear layer containing a train of vortex filaments extending from the tip of the blade. These vortices are entrained into the TLV, but do not have time to merge. TLV breakdown in the aft part of the blade passage further fragments these structures, increasing their number and reducing their size. Analogy is made between the circumferential development of the TLV in the blade passage and that of the starting jet vortex ring rollup. Subject to several assumptions, these flows display similar trends, including conditions for TLV separation from the shear layer feeding vorticity into it.     

Study of modeling unsteady blade row interaction in a transonic compressor stage part 1: code development and deterministic correlation analysis

The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system.The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES.In Part 1 of this two-part paper,firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investigate the APES technique.Then steady and unsteady simulations are conducted in a transonic compressor stage.The results from both simulations are compared to highlight the significance of the unsteady interactions.Furthermore,the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial correlations (SC).Lastly,steady and time-averaging (employing APES with DC) simulations for the downstream stator alone are conducted employing DC derived from the unsteady results.The results from steady and time-averaging simulations are compared with the time-averaged unsteady results.The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.     

Stereoscopic PIV measurement of unsteady flows in an axial compressor stage

Stereoscopic particle-image velocimetry (SPIV) measurements are conducted in a Low-speed Large-scale Axial Compressor. During the experiment the two CCD cameras are placed at the different sides of the laser light sheet and it is proved that this configuration is more suitable for the investigation in multi-stage turbomachines. The measured results, including the overall performances of many typical flow structures near the rotor tip region and the phase locked unsteady flows inside the stator passage at both the design and near-stall conditions, are introduced. Some new features of the complicated flow structures, such as the breakdown of the tip leakage vortex, the formation of the compound corner vortex at the rotor suction tip corner, the interactions between the hub stall and the tip separation and the rotor wakes, and the evolutions of the tip corner anti-rotating streamwise vortices inside the stator passage, are revealed.     

The challenge of stereo PIV measurements in the tip gap of a transonic compressor rotor with casing treatment

This contribution is aimed at summarizing the effort taken to apply stereoscopic PIV (SPIV) measurements in the tip clearance of a transonic compressor rotor equipped with a casing treatment. A light sheet probe was placed downstream of the stator and aligned to pass the light sheet through a stator passage into the blade tip clearance of the rotor. A setup with three cameras has been used in order to record the entire 2C velocity field and the smaller area of 3C field of view at the same time instance for comparison with earlier 2C PIV results. A homogeneous seeding distribution was achieved by means of a smoke generator. The main emphasis of the SPIV measurement was to establish a data set with high spatial resolution close to the compressor casing, where the aerodynamic effects of a CT are known to be strong. The paper will discuss some major aspects of the utilized PIV data processing and point out a variety of frequently underestimated error sources that influence the overall quality of the recovered data in spite of the fact that the individual PIV recordings seemed to be of very good quality. Thus, the authors will not focus on the PIV results and related interpretation of the flow field, but on the optimization and procedures applied during setup of the experiment and data processing, respectively.     

Vibratory load predictions of a high-advance-ratio coaxial rotor system validated by wind tunnel tests

To investigate the aeromechanics of coaxial counter-rotating lift-offset rotor systems, a comprehensive analysis model of a laboratory-scale torque-balanced rotor designed for high-advance-ratio forward flight was developed. Measured blade and control system geometries and structural properties were input to the model. Lower-order aerodynamics modeling with a free-vortex wake method was used. While previous analytical studies on this coaxial rotor test rig have focused on performance and control requirements, in this current work, vibratory hub and pitch link loads, the influence of rotor–rotor phasing and the effects on blade deflections and tip clearance were investigated. The analysis was validated by wind-tunnel tests at advance ratios of 0.21–0.52 and for a lift offset varying from zero to 25%. Coaxial rotor performance, pitch link loads, unsteady thrust and rolling moments correlated well with the measurements. Pitching and rolling moment 2/rev and 4/rev harmonics correlated well for all lift offsets and advance ratios, whereas the vibratory torque was significantly overpredicted. The correct trends for varying lift offset and advance ratio were predicted in drag, side force, and thrust harmonics. Corresponding magnitudes were also predicted well, although an underprediction of the side force 4/rev harmonics was observed. Good correlation was found for the predicted blade tip clearance between the rotors over the entire range of lift offset and rotor–rotor phase angles, showing that advance ratio had little effect and judicial use of rotor phasing can increase the critical tip clearance.     

Volumetric three-component velocimetry measurements of the turbulent flow around a Rushton turbine

Volumetric three-component velocimetry measurements have been taken of the flow field near a Rushton turbine in a stirred tank reactor. This particular flow field is highly unsteady and three-dimensional, and is characterized by a strong radial jet, large tank-scale ring vortices, and small-scale blade tip vortices. The experimental technique uses a single camera head with three apertures to obtain approximately 15,000 three-dimensional vectors in a cubic volume. These velocity data offer the most comprehensive view to date of this flow field, especially since they are acquired at three Reynolds numbers (15,000, 107,000, and 137,000). Mean velocity fields and turbulent kinetic energy quantities are calculated. The volumetric nature of the data enables tip vortex identification, vortex trajectory analysis, and calculation of vortex strength. Three identification methods for the vortices are compared based on: the calculation of circumferential vorticity; the calculation of local pressure minima via an eigenvalue approach; and the calculation of swirling strength again via an eigenvalue approach. The use of two-dimensional data and three-dimensional data is compared for vortex identification; a ‘swirl strength’ criterion is less sensitive to completeness of the velocity gradient tensor and overall provides clearer identification of the tip vortices. The principal components of the strain rate tensor are also calculated for one Reynolds number case as these measures of stretching and compression have recently been associated with tip vortex characterization. Vortex trajectories and strength compare favorably with those in the literature. No clear dependence of trajectory on Reynolds number is deduced. The visualization of tip vortices up to 140° past blade passage in the highest Reynolds number case is notable and has not previously been shown.     

Recent developments in background oriented Schlieren methods for rotor blade tip vortex measurements

The compressible blade tip vortex of rotary wings has been the subject of numerous investigations and its importance for the understanding of the helicopter flow field has been clearly emphasised. Due to its great impact on the dynamics of the flow field, the investigation of the tip vortex is directly linked to issues of flow control and aeroacoustic optimisation. However, among velocity field data, additional core density information on the blade tip vortex is desirable with a view to vortex modelling. In this work we describe an airborne background oriented Schlieren system for full-scale helicopter flight tests as well as the first results of the tomographic reconstruction of the compressible vortex core. We report the measurements of both a 0.4 Mach-scaled rotor model of the MBB BO 105 and the corresponding full-scale helicopter in hover flight condition. The tomographic reconstruction of the data allows us to estimate the density and the radius for the viscous core.     

Visualization by PIV of dynamic stall on a vertical axis wind turbine

The aerodynamic behavior of a vertical axis wind turbine (VAWT) is analyzed by means of 2D particle image velocimetry (PIV), focusing on the development of dynamic stall at different tip speed ratios. The VAWT has an unsteady aerodynamic behavior due to the variation with the azimuth angle θ of the blade’s sections’ angle of attack, perceived velocity and Reynolds number. The phenomenon of dynamic stall is then an inherent effect of the operation of a VAWT at low tip speed ratios, impacting both loads and power. The present work is driven by the need to understand this phenomenon, by visualizing and quantifying it, and to create a database for model validation. The experimental method uses PIV to visualize the development of the flow over the suction side of the airfoil for two different reference Reynolds numbers and three tip speed ratios in the operational regime of a small urban wind turbine. The field-of-view of the experiment covers the entire rotation of the blade and almost the entire rotor area. The analysis describes the evolution of the flow around the airfoil and in the rotor area, with special focus on the leading edge separation vortex and trailing edge shed vorticity development. The method also allows the quantification of the flow, both the velocity field and the vorticity/circulation (only the results of the vorticity/circulation distribution are presented), in terms of the phase locked average and the random component.     

Application of SPIV in turbomachinery

Stereoscopic particle-image velocimetry (SPIV) has been successfully used in a low-speed large-scale axial compressor. A configuration in which two CCD cameras were placed at different sides of the light sheet was employed. It is demonstrated that the results measured with such a configuration are significant for the study of unsteady flow structures of the streamwise vortices and secondary flows in the test rotor, and that such a configuration is easy to use in multi-stage turbomachinery. The instantaneous snapshots, ensemble-averaged results and turbulence statistics in the rotor passage were obtained at both the design and near-stall conditions. The representative flow structures, such as the tip leakage vortex, the corner vortex and the inlet guide vane wake, can be depicted clearly. Moreover, according to experimental and theoretical analyses, some guidance is provided for the application of SPIV in turbomachinery.     

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     

Visualization and measurement of helicopter rotor flow with swept back tip shapes at hover flight using the “flow visualization gun” time line technique

The Flow Visualization Gun (FVG), a novel time line visualization technique, has been used to investigate the flow field of a helicopter rotor with swept back tip shape in hover flight condition. After introducing the FVG-technique, the paper presents some visualization photographs of the rotor blade tip vortices and the rotor downwash. Using orthogonal sets of flow photographs and digital image analysis, the 3-dimensional time line displacement within the flow and the tip vortex structure are determined. The data of 16 time line experiments are interpolated in space and time to obtain velocity data on an evenly spaced 3-dimensional grid. Vorticity contour plots of the flow field show the complex arrangement of the tip vortices of the blade itself and of the preceding blade and some additional vorticity in the direct wake which may form a secondary vortex. Understanding and control of this vorticity distribution is important for the design of new efficient tip shapes. While the FVG technique has been used so far for qualitative investigation of complex flow patterns at local velocities of up to 20 m/s, a good comparison to laser velocimetry data validates the technique as an interesting tool for both qualitative and quantitative investigation. This research was supported by a “Poste Rouge” grant by the Centre National de la Recherche Scientifique (C.N.R.S.). The authors would like to thank all members of the IRPHE for their help concerning the mechanical and electronical set up of the experiments.     

Three-dimensional flow structures and associated turbulence in the tip region of a waterjet pump rotor blade

Stereo particle image velocimetry measurements focus on the flow structure and turbulence within the tip leakage vortex (TLV) of an axial waterjet pump rotor. Unobstructed optical access to the sample area is achieved by matching the optical refractive index of the transparent pump with that of the fluid. Data obtained in closely spaced planes enable us to reconstruct the 3D TLV structure, including all components of the mean vorticity and strain-rate tensor along with the Reynolds stresses and associated turbulence production rates. The flow in the tip region is highly three-dimensional, and the characteristics of the TLV and leakage flow vary significantly along the blade tip chordwise direction. The TLV starts to roll up along the suction side tip corner of the blade, and it propagates within the passage toward the pressure side of the neighboring blade. A shear layer with increasing length connects the TLV to the blade tip and initially feeds vorticity into it. During initial rollup, the TLV involves entrainment of a few vortex filaments with predominantly circumferential vorticity from the blade tip. Being shed from the blade, these filaments also have high circumferential velocity and appear as swirling jets. The circumferential velocity in the TLV core is also substantially higher than that in the surrounding passage flow, but the velocity peak does not coincide with the point of maximum vorticity. When entrainment of filaments stops in the aft part of the passage, newly forming filaments wrap around the core in helical trajectories. In ensemble-averaged data, these filaments generate a vortical region that surrounds the TLV with vorticity that is perpendicular to that in the vortex core. Turbulence within the TLV is highly anisotropic and spatially non-uniform. Trends can be traced to high turbulent kinetic energy and turbulent shear stresses, e.g., in the shear layer containing the vortex filaments and the contraction region situated along the line where the leakage backflow meets the throughflow, causing separation of the boundary layer at the pump casing. Upon exposure to adverse pressure gradients in the aft part of the passage, at 0.65–0.7 chord fraction in the present conditions, the TLV bursts into a broad turbulent array of widely distributed vortex filaments.