Velocity measurements of wake-induced unsteady flow in a linear turbine cascade

Extensive velocity measurements have been taken in a linear turbine cascade with unsteady oncoming wakes. The unsteady wakes were generated by moving cylinders on a squirrel cage device. The Reynolds number was 1.1 × 10⁵, and the Strouhal number varied from o to 7.36. The blade-to-blade flow and the boundary layers on the suction side were measured with a hot-wire anemometer. The results were obtained in ensemble-averaged form so that periodic unsteady processes can be studied. Of particular interest was the transition of the boundary layer. The boundary layer remained laminar in the case without wakes. The passing wakes caused transition, and the beginning of transition moves forward as the wake-passing frequency increases. Unlike in the flat plate study of Liu and Rodi (1991a) the boundary layer state hardly changed with time, although the turbulence level in the boundary layer showed clear periodic response to the passing wakes. The work reported here was sponsored by the German Federal Ministry of Research and Technology through program TURBOTHERM under contract no. 0326501D. The authors should like to thank Mr. D. Bierwirth for his excellent technician work on this project, Dr. N. H. Cho for his help with the preparation of the plots and Mrs. R. Zschernitz for her expert typing of the text.     

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.     

Multi-resolution analysis of the large-scale coherent structure in a turbulent separation bubble affected by an unsteady wake

Multi-resolution analysis (MRA) was applied to the large-scale coherent structure in a turbulent separation bubble affected by an unsteady wake. The unsteady wake was generated using a spoked-wheel type wake generator, which was installed in front of the separation bubble. The wake generator was rotated either clockwise (CW) or counter-clockwise (CCW) with a normalized passing frequency of St_H=0.2. The Reynolds number based on the half-thickness of the blunt body was Re_H=5600. To show the unsteady dynamic flow structures between the ‘cutting’ and ‘wrapping’ regimes, a MRA using the maximal overlap discrete wavelet transform (MODWT) was performed. This method enabled delineation of the coherent structure of the turbulent separation bubble through a scale-resolved analysis. Reconstruction of the flow field in combination with conditional averaging was attempted. Flapping motions as well as sawtooth movements of the unsteady separation bubble were analyzed using the MODWT. The unsteady wakes decayed faster in the system with CCW rotation than in that with CW rotation.     

DNS of flows with helical symmetry

Some flows such as the wakes of rotating devices often display helical symmetry. We present an original DNS code for the dynamics of such helically symmetric systems. We show that, by enforcing helical symmetry, the three-dimensional Navier–Stokes equations can be reduced to a two-dimensional unsteady problem. The numerical method is a generalisation of the vorticity/streamfunction formulation in a circular domain, with finite differences in the radial direction and spectral decomposition along the azimuth. When compared to a standard three-dimensional code, this allows us to reach larger Reynolds numbers and to compute quasi-steady patterns. We illustrate the importance of helical pitch by some physical cases: the dynamics of several helical vortices and a quasi-steady vortex flow. We also study the linear dynamics and nonlinear saturation in the Batchelor vortex basic flow, a paradigmatic example of trailing vortex instability. We retrieve the behaviour of inviscid modes and present new results concerning the saturation of viscous centre modes.     

Numerical investigation of confined wakes behind a square cylinder in a channel

The structure of confined wakes behind a square cylinder in a channel is investigated via the numerical solution of the unsteady Navier–Stokes equations. Vortex shedding behind the cylinder induces periodicity in the flow field. Details of the phenomenon are simulated through numerical flow visualization. The unsteady periodic wake can be characterized by the Strouhal number, which varies with the Reynolds number and the blockage ratio of the channel. The periodicity of the flow is, however, damped in the downstream region of a long duct. This damping may be attributed to the influence of side walls on the flow structure.     

Numerical Investigation of Unsteady Transitional Flows in Turbomachinery Components Based on a RANS Approach

This paper presents results of the numerical simulation of periodically unsteady flows with focus on turbomachinery applications. The unsteady CFD solver used for the simulations is based on the Reynolds averaged Navier–Stokes equations. The numerical scheme applies an extended version of the Spalart–Allmaras one-equation turbulence model coupled with a transition correlation. The first example of validation consists of boundary layer flow with separation bubble on a flat plate, both under steady and periodically unsteady main flow conditions. The investigation includes a variation of the major parameters Strouhal number, amplitude, and Reynolds number. The second, more complex test case consists of the flow through a cascade of turbine blades which is influenced by wakes periodically passing over the cascade. The computations were carried out for two different blade loadings. The results of the numerical simulations are discussed and compared with experimental data in detail. Special emphasis is given to the investigation of boundary layers with regard to transition, separation and reattachment under the influence of main flow unsteadiness. This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulence properties in the cylinder wake at high Reynolds numbers

The present contribution analyses the turbulence properties in unsteady flows around bluff body wakes and provides a database for improvement and validation of turbulence models, concerning the present class of nonequilibrium flows. The flow around a circular cylinder with a low aspect ratio and a high blockage coefficient is investigated. This confined environment is used in order to allow direct comparisons with realisable 3-D Navier–Stokes computations avoiding ‘infinite’ conditions. The flow is investigated in the beginning of the critical regime at Reynolds number 140 000. The analysis is carried out by means of 2-D PIV, of 3-C PIV and of high-frequency 2-D PIV. The experimental analysis contributes to confirm the validity of advanced statistical turbulence modelling for unsteady flows around bodies.     

Development of an unsteady pressure measurement method

Experimental Techniques - Aerodynamic phenomena such as wakes behind bluff bodies are inherently unsteady. Thus, many aerodynamic experiments require the measurement of unsteady or dynamic flow...     

Mathematical modeling of the sound induced in a subsonic flow around cascades in relative motion

A method of mathematical modeling of the tonal sound induced by the unsteady aerodynamic interaction of two plane airfoil cascades in a subsonic flow and in uniform relative motion in the direction of their fronts is developed. The method is based on the numerical integration of the unsteady flow equations using a simplified model for the periodic system of edge wakes shed from the airfoils of the first (leading) cascade in the viscous flow and acting on the second (trailing) cascade. An analysis of the distinctive features of the flow under consideration demonstrates the efficiency of the model proposed.     

The Effect of wake Turbulence Intensity on Transition in a Compressor Cascade

Direct numerical simulations of separating flow along a section at midspan of a low-pressure V103 compressor cascade with periodically incoming wakes were performed. By varying the strength of the wake, its influence on both boundary layer separation and bypass transition were examined. Due to the presence of small-scale three-dimensional fluctuations in the wakes, the flow along the pressure surface undergoes bypass transition. Only in the weak-wake case, the boundary layer reaches a nearly-separated state between impinging wakes. In all simulations, the flow along the suction surface was found to separate. In the simulation with the strong wakes, separation is intermittently suppressed as the periodically passing wakes managed to trigger turbulent spots upstream of the location of separation. As these turbulent spots convect downstream, they locally suppress separation.     

PIV measurements combined with the motion tracking technique to analyze flow around a moving porous structure

To gain a better understanding of the fluid–structure interaction and especially when dealing with a flow around an arbitrarily moving body, it is essential to develop measurement tools enabling the instantaneous detection of moving deformable interface during the flow measurements. A particularly useful application is the determination of unsteady turbulent flow velocity field around a moving porous fishing net structure which is of great interest for selectivity and also for the numerical code validation which needs a realistic database. To do this, a representative piece of fishing net structure is used to investigate both the Turbulent Boundary Layer (TBL) developing over the horizontal porous moving fishing net structure and the turbulent flow passing through the moving porous structure. For such an investigation, Time Resolved PIV measurements are carried out and combined with a motion tracking technique allowing the measurement of the instantaneous motion of the deformable fishing net during PIV measurements. Once the two-dimensional motion of the porous structure is accessed, PIV velocity measurements are analyzed in connection with the detected motion. Finally, the TBL is characterized and the effect of the structure motion on the volumetric flow rate passing though the moving porous structure is clearly demonstrated.     

DNS and LES of some engineering flows

In this paper, direct numerical simulations (DNS) and large eddy simulations (LES) of three engineering flows carried out in the author's research group are presented. The first example, simulated both with DNS and LES, is the flow in a low-pressure turbine cascade with wakes passing periodically through the cascade channel. In this situation, the laminar–turbulent transition of the boundary layers on the blade surfaces, which is strongly influenced by the passing wakes, is of special interest. Next, LES of the flow past the Ahmed body is presented, which is a car model with slant back. In spite of the fairly simple geometry, the flow around the model has many features of the complex, fully 3D flow around real cars. The third example, for which LES is presented, is the flow past a surface mounted circular cylinder of height-to-diameter ratio of 2.5. In this case also complex 3D flow develops with interaction of various vortices behind the cylinder. By means of these examples, the paper shows that complex turbulent flows of engineering relevance can be predicted realistically by DNS and LES, albeit at large cost. The methods are particularly suited and superior to RANS methods for situations where unsteadiness like shedding and large-scale structures dominate the flow, and DNS has evolved into an important tool for studying transition mechanisms.     

Large Eddy Simulation of Wind Turbine Wakes

We present the coupling of a vortex particle-mesh method with immersed lifting lines for the Large Eddy Simulation of wind turbine wakes. The method relies on the Lagrangian discretization of the Navier–Stokes equations in vorticity-velocity formulation. Advection is handled by the particles while the mesh allows the evaluation of the differential operators and the use of fast Poisson solvers. We use a Fourier-based fast Poisson solver which simultaneously allows unbounded directions and inlet/outlet boundaries. The method also allows the feeding of a turbulent incoming flow. We apply this methodology to the study of large scale aerodynamics and wake behavior of tandem wind turbines. We analyze the generators performance, unsteady power, loads and aerodynamics they are subjected to. The average flow field of the wakes is also computed and turbulence statistics are extracted. In particular, we investigate the influence of the type of turbulent inflow used—precomputed or synthetic—, and study wake meandering.     

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

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

Dynamic wind loads and wake characteristics of a wind turbine model in an atmospheric boundary layer wind

An experimental study was conducted to characterize the dynamic wind loads and evolution of the unsteady vortex and turbulent flow structures in the near wake of a horizontal axis wind turbine model placed in an atmospheric boundary layer wind tunnel. In addition to measuring dynamic wind loads (i.e., aerodynamic forces and bending moments) acting on the wind turbine model by using a high-sensitive force-moment sensor unit, a high-resolution digital particle image velocimetry (PIV) system was used to achieve flow field measurements to quantify the characteristics of the turbulent vortex flow in the near wake of the wind turbine model. Besides conducting “free-run” PIV measurements to determine the ensemble-averaged statistics of the flow quantities such as mean velocity, Reynolds stress, and turbulence kinetic energy (TKE) distributions in the wake flow, “phase-locked” PIV measurements were also performed to elucidate further details about evolution of the unsteady vortex structures in the wake flow in relation to the position of the rotating turbine blades. The effects of the tip-speed-ratio of the wind turbine model on the dynamic wind loads and wake flow characteristics were quantified in the terms of the variations of the aerodynamic thrust and bending moment coefficients of the wind turbine model, the evolution of the helical tip vortices and the unsteady vortices shedding from the blade roots and turbine nacelle, the deceleration of the incoming airflows after passing the rotation disk of the turbine blades, the TKE and Reynolds stress distributions in the near wake of the wind turbine model. The detailed flow field measurements were correlated with the dynamic wind load measurements to elucidate underlying physics in order to gain further insight into the characteristics of the dynamic wind loads and turbulent vortex flows in the wakes of wind turbines for the optimal design of the wind turbines operating in atmospheric boundary layer winds.     

Suppression of the unsteady vortex wakes of a circular cylinder pair by a doublet‐like counter‐rotation

The present investigation examines the suppression of unsteady, two‐dimensional wake instabilities of a pair of identical circular cylinders, placed side‐by‐side normal to freestream at a low Reynolds number of 150. It is found that when the cylinders are counter‐rotated, unsteady vortex wakes can be completely suppressed. At fast enough rotational speeds, a virtual elliptic body is produced by a closed streamline, strongly resembling a doublet potential flow. Copyright © 2009 John Wiley & Sons, Ltd.     

High speed rotor wake total temperature measurements using a hot-film anemometer

 To develop a quantitative understanding of unsteady and interacting turbomachine flow fields, it is necessary to quantify the instantaneous efficiency of high speed turbomachines. This requires the measurement of both the unsteady velocity and total temperature variation in the exit flow of a high speed rotor. In this paper, techniques to utilize a single slant-film anemometer to measure unsteady total temperature are developed and evaluated. Then a series of preliminary experiments are performed in a high speed axial fan facility to quantify the instantaneous rotor efficiency. This is accomplished by utilizing these single slant-film methods to measure the total temperature in the rotor wakes. Results show that measurements at multiple overheats and several probe orientations are required. The simplest method proves to be useful for determining parameters used in other methods. An analysis based on King’s law gives good results even when measurements are outside the calibration range. Within the calibration range, a polynomial representation of the wire response to mass flux and total temperature yields good total temperature fluctuation results. A model analysis technique is also assessed. Received: 13 November 1997/Accepted: 16 February 1998     

叶轮机内附面层流动与分离的某些研究进展

通过总结有关叶轮机内附面层的研究工作认为,周期性扫掠的上游尾迹改变了附面层的转捩方式,给附面层流动带来了强烈的非定常性,不同的尾迹强度和扫过频率决定了附面层内不同的时空结构; 此外,雷诺数、叶片负荷、表面粗糙度和来流条件等因素均能影响尾迹对附面层的非定常效应.随后总结了尾迹对附面层作用的机理, 并介绍了转捩模型的发展过程.最后提出了关于附面层研究方向的两个疑问,认为附面层分离后的复杂旋涡流场值得重点关注.      

A THEORETICAL STUDY OF PAPER FLUTTER

Two different methods of analysis were developed in order to clarify the phenomenon of paper flutter. One of these is a flutter simulation using a Navier–Stokes code (N–S simulation). N–S simulation was used to determine the unsteady lift force, the amplitude of flutter, and the air-flow around a paper sheet, by means of a time-marching scheme. The other form of analysis is based on a potential-flow analysis of an oscillating thin airfoil via an eigenvalue analysis for determining stability. The flutter speeds and flutter modes obtained by each method are consistent. Aspects of the behavior of paper flutter that had not been clarified in the experimental analysis were clarified by potential flow analysis. From the results of this study, it was shown that potential flow analysis is very convenient and adequate for a parametric study of this problem.