Turbomachinery Blade Rows Research Articles

Improved Body Force Model for Estimating Off-Design Axial Compressor Performance

Based on the COMSOL software, body forces substituted into the Reynolds-averaged Navier–Stokes (RANS) equations as the source terms instead of the actual blade rows were improved to better predict the compressor performance. Improvements in parallel body force modeling were implemented, central to which were the local flow quantities. This ensured accurate and reliable off-design performance prediction. The parallel force magnitude mainly depended on the meridional entropy gradient extracted from three-dimensional (3D) steady single-passage RANS solutions. The COMSOL software could easily and accurately translate the pitchwise-averaged entropy into the grid points of the body force domain. A NASA Rotor 37 was used to quantify the improved body force model to represent the compressor. Compared with the previous model, the improved body force model was more efficient for the numerical calculations, and it agreed well with the experimental data and computational fluid dynamics (CFD) results. The results indicate that the improved body force model could quickly and efficiently capture the flow field through a turbomachinery blade row.

Analysis of Transonic Bladerows With Non-Uniform Geometry Using the Spectral Method

Abstract Turbomachinery blade rows can have non-uniform geometries due to design intent, manufacture errors or wear. When predictions are sought for the effect of such non-uniformities, it is generally the case that whole assembly calculations are needed. A spectral method is used in this paper to approximate the flow fields of the whole assembly but with significantly less computation cost. The method projects the flow perturbations due to the geometry non-uniformity in an assembly in Fourier space, and only one passage is required to compute the flow perturbations corresponding to a certain wave-number of geometry variation. The performance of this method on transonic blade rows is demonstrated on a modern fan assembly. Low engine order and high engine order geometry non-uniformity (e.g., “saw-tooth” pattern) are examined. The non-linear coupling between the flow perturbations and the passage-averaged flow field is also demonstrated. Pressure variations on the blade surface and the potential flow field upstream of the leading edge from the proposed spectral method and the direct whole assembly solutions are compared. Good agreement is observed on both quasi-3D and full 3D cases. A lumped approach to compute deterministic fluxes is also proposed to further reduce the computational cost of the spectral method. The spectral method is formulated in such a way that it can be easily implemented into an existing harmonic flow solver by adding an extra source term and can be potentially used as an efficient tool for aeromechanical and aeroacoustics design of turbomachinery blade rows.

Effect of Modal Interactions on Friction-Damped Self-Excited Vibrations

Abstract It is well-known that nonlinear dry friction damping has the potential to bound the otherwise unboundedly growing vibrations of self-excited structures. An important technical example are the flutter-induced friction-damped limit cycle oscillations of turbomachinery blade rows. Due to symmetries, natural frequencies are inevitably closely spaced, and they can generally be multiples of each other. Not much is known on the nonlinear dynamics of self-excited friction-damped systems in the presence of such internal resonances. In this work, we analyze this situation numerically by regarding a two degrees-of-freedom system. We demonstrate that in the case of closely-spaced natural frequencies, the self-excitation of the lower-frequency mode gives rise to non-periodic oscillations, and the occurrence of unbounded behavior well before reaching the maximum friction damping value. If the system is close to a 1:3 internal resonance, limit cycles associated with much higher frictional damping appear, however, most of these are unstable. If more than one mode is subjected to self-excitation, the maximum resistance against self-excitation is at least given by the damping capacity of the most weakly friction-damped mode. These results are of high technical relevance, as the prevailing practice is to analyze only periodic limit states and argue the stability solely by the slope of the damping-amplitude curve. Our results demonstrate that this practice leads to considerable mis- and overestimation of the resistance against self-excitation, and a more rigorous stability analysis is required.

Generation of Vortex Lift Through Reduction of Rotor/Stator Gap in Turbomachinery

The axial gap between blade rows in turbomachinery should be minimized in order to reduce size requirements and increase efficiency; although, there is a tradeoff between gap width and flow steadiness. The aerodynamic interaction between rotors and stators influences system performance under both steady and transient conditions. To investigate the basic physical mechanisms associated with the rotor/stator interaction, an efficient numerical scheme for solving unsteady, viscous flows on a quasi-three-dimensional coordinate system is established using an immersed boundary method. The data transfer between moving and stationary grids that slip against each other in traditional numerical methods is avoided. The effects of the axial gap between adjacent blade rows are studied by considering the flow evolution through a rotor and stator stage in different Reynolds number regimes. Results indicate that reduced blade gap leads to high lift on the rotor blade and improved stage loading. At the same time, the rotor/stator interaction increases flow unsteadiness, which may in turn increase noise and vibration. It is found that the reduced blade gap does not always improve performance, in spite of the generation of vortex lift. The present work provides guidelines for optimization of the axial gap between blade rows for turbomachinery design.

Development of the calculation method of complex acoustic resonator parameters

Despite the large number of works devoted to passive management methods of separated flows in the stages of axial fans, still little attention has been paid to the integrated approaches of impact on the end separated flows. In the paper, the calculation method of complex resonator parameters based on the method of hydro-gas-dynamic analogies was presented. The basic idea of using the complex resonator is pulse-periodic action on the end separated eddy flows, which consist of high-frequency and low-frequency components of oscillations. The paper presents the formation of generalized dependencies for calculating geometrical parameters of the complex resonator, which consists of two series-connected acoustic cavities, one of which is tuned to the high frequency component, and the other - to the low-frequency component of the oscillation field. The presented method allows to obtain the relationship between the geometric parameters of the complex acoustic resonator and the frequency of its natural oscillations. The research results can be used in the design of control systems of separated flows in the turbomachinery blade rows.

On Using Fast Response Pressure Sensors in Aerodynamic Probes to Measure Total Temperature and Entropy Generation in Turbomachinery Blade Rows

This contribution addresses the possibility of exploiting the temperature dependency of piezoresistive sensors as a temperature measurement per se. This requires the characterization of the sensor, or the probe as a temperature probe, i.e., determination of the recovery factor between the sensor temperature and the flow temperature. This temperature calibration as well as the determination of the thermal response time was performed for two probe geometries: a high temperature flush-mounted and a low temperature subsurface mounted single sensor total pressure probe, both with a probe head diameter of 2.5 mm. Two applications are reported. The first application was performed with the flush-mounted sensor probe in the high-speed 312-stage axial compressor CREATE tested in the 2 MW test rig of LMFA at École Centrale de Lyon, in France. The probes were traversed at each inter-row section up to temperatures of 180°C and an absolute pressure of 3 bar. The second application was performed with the subsurface mounted sensor probe in the high-speed single stage R-4 compressor test rig of the von Karman Institute in Belgium. Both applications have shown results in extremely good agreement with simultaneous total temperature measurements with a Kiel-type thermocouple probe. They also underline the necessity of a very accurate temperature calibration. Finally, considering the fact that a simultaneous temperature measurement can be obtained at the same location as the pressure measurement from the sensor, it is possible to derive entropy generation after a blade row, based on the average pressure and temperature quantities. This unveils another extremely interesting aspect of using the fast response probe technique in turbomachinery applications.

Aerodynamic Improvements of Wind-Turbine Airfoil Geometries With the Prescribed Surface Curvature Distribution Blade Design (CIRCLE) Method

The prescribed surface curvature distribution blade design (CIRCLE) method can be used for the design of two-dimensional (2D) and three-dimensional (3D) turbomachinery blade rows with continuous curvature and slope of curvature from leading edge (LE) stagnation point to trailing edge (TE) stagnation point and back to the LE stagnation point. This feature results in smooth surface pressure distribution airfoils with inherently good aerodynamic performance. In this paper the CIRCLE blade design method is modified for the design of 2D isolated airfoils. As an illustration of the capabilities of the method, it is applied to the redesign of two representative airfoils used in wind turbine blades: the Eppler 387 airfoil and the NREL S814 airfoil. Computational fluid dynamic analysis is used to investigate the design point and off-design performance of the original and modified airfoils, and compare with experiments on the original ones. The computed aerodynamic advantages of the modified airfoils are discussed. The surface pressure distributions, drag coefficients, and lift-to-drag coefficients of the original and redesigned airfoils are examined. It is concluded that the method can be used for the design of wind turbine blade geometries of superior aerodynamic performance.

Fast Estimation of Unsteady Flows in Turbomachinery at Multiple Interblade Phase Angles

T IME-LINEARIZED computational fluid dynamic (CFD) models for the computation of unsteady flows in turbomachinery are now used routinely in the design and analysis of turbomachinery blade rows, particularly to predict the onset of flutter. A typical flutter analysis of a rotor requires one to compute unsteady flow solutions over the full range of interblade phase angles, and hence requires significant computational time even for relatively efficient time-linearized flow solvers. Typically, onemight compute the unsteady aerodynamic damping at several dozen interblade phase angles to ensure that no single interblade phase angle will flutter. In this note, we describe a fast technique that significantly reduces the computational time required to perform such a flutter clearance analysis. In recent years, researchers have developed models to reduce the time required to compute multiple unsteady flow solutions when one or more parameters is varying. In many (but not all) cases, the varying parameter is the frequency of airfoil vibration [1,2]. For example, Florea and Hall [3] computed the dominant eigenfrequencies and mode shapes of the unsteady fluid motion within a twodimensional cascade of airfoils using a nonsymmetric Lanczos algorithm, and then used these eigenmodes to construct a lowdegreeof-freedom reduced-ordermodel of the unsteadyflowfield around an airfoil. Kim [4] developed a frequency-domain proper orthogonal decomposition (POD) technique and applied it to both mechanical and fluid dynamic models. Hall et al. [5] developed reduced-order models of small-disturbance unsteady flows around airfoils and turbomachinery cascades using a POD technique. Similarly,Willcox et al. [6] developed an efficient frequency-domain proper orthogonal decomposition method for low order aeroelastic control of turbomachines. Cizmas and Palacios [7] used a POD technique to construct reduced-order models to examine a turbine rotor-stator interaction problem. (For a complete review of ROM/PODmethods, see Lucia et al. [8]). In most of these investigations, the reduced-order model is constructed in such a way that estimates of the unsteady flow can be constructed rapidly over a wide range of (possibly undetermined) vibrational frequencies. In the turbomachinery flutter problem, however, because of the high mass ratio associated with turbomachinery blading, the frequency of flutter is known a priori. Instead, the interblade phase angle of flutter is not known, and one must examine all possible interblade phase angles to insure that a rotor is flutter free. This suggests that for flutter problems, reducedorder model should be constructed in which the interblade phase angle is the free parameter. One notable exception is the work of Epureanu et al. [9]. Here, a POD technique was used to form a reduced-order model of two-dimensional viscous flow based on an inviscid boundary-layer coupled flow solver. Both frequency and interblade phase angle were allowed to vary. In this note, we present a fast technique that allows us to estimate the unsteady flows for many interblade phase angles very efficiently. Note that the base CFD solver used here is an iterative, threedimensional time-linearized flow solver.

Averaging Nonuniform Flow for a Purpose

Averaging nonuniform flow is important for the analysis of measurements in turbomachinery and gas turbines; more recently an important need for averaging arises with results of computational fluid dynamics (CFD). In this paper we show that there is a method for averaging which is “correct,” in the sense of preserving the essential features of the nonuniform flow, but that the type of averaging which is appropriate depends on the application considered. The crucial feature is the decision to retain or conserve those quantities which are most important in the case considered. Examples are given to demonstrate the appropriate methods to average nonuniform flows in the accounting for turbomachinery blade row performance, production of thrust in a nozzle, and mass flow capacity in a choked turbine. It is also shown that the numerical differences for different types of averaging are, in many cases, remarkably small.

Influence of Shock Wave on Turbomachinery Blade Row Flutter

The influence and effect of a shock wave on the flutter characteristics of a turbomachinery blade row is described. High-fidelity numerical analysis is used to understand the behavior of turbomachinery blade row flutter in the presence of an oscillating shock wave. The unsteady Navier-Stokes equations are solved on a dynamically deforming, body-fitted grid to obtain the unsteady aerodynamic load on a vibrating blade. An energy exchange method is used for calculating the aerodynamic damping to determine the blade row flutter characteristics. A transonic forward swept fan configuration, which showed flutter at part speed conditions in wind-tunnel tests, is analyzed. The shock wave was found to influence strongly the aerodynamic damping, with outboard stations providing the main contribution. The interblade phase angle of blade motion and the location of shock wave determined the influence of shock wave on blade stability. The influence of shock motion was found to be linear for a small amplitude of blade oscillation. The observations from the numerical analysis are used to develop an algebraic model for calculating the work done on the blade because of an oscillating shock wave.

04/02451 Wake and aerodynamics loads in multiple bodies— application to turbomachinery blade rows: Pereira, L. A. A. et al. Journal of Wind Engineering and Industrial Aerodynamics, 2004, 92, (6), 477–491

This two part review covers experiments examining the effects of blade tip gaps encountered in turbomachines and the methods by which the synthesised data are currentl used in turbomachine design and analysis. Data gained since the 1930's are subdivided for convenience into cascade (Part 1) and rotating machinery (Part 2) data, with a further subdivision into diffusing, or compressor type flows and accelerating, or turbine type flows. The overall trend is that an increasing tip gap, whose effect can reach over most or all of the blade height, reduces turbomachine performance. There is some evidence among the compressor and compressor cascade data that an optimum gap exists when the opposing effects of secondary flows and tip leakage with rotor/wall relative movement tend to balance. Turbine data are, in general, more regular than the body of compressor data, possibly because of the enhanced effect of, usually, undefined boundary layers in diffusing flow in the latter. Comment is made in Part 2 on the predictive and design models reported in the liturature

Wake and aerodynamics loads in multiple bodies—application to turbomachinery blade rows

Two-dimensional, unsteady flow around bodies of complex geometry (or multiple bodies) at high Reynolds number is simulated using the vortex method. This method is modified to take into account the sub-grid scale phenomena through a second order velocity structure function model adapted to the Lagrangian scheme. The dynamics of the body wake is computed using the convection–diffusion splitting algorithm; the convection process is carried out with a Lagrangian Adams–Bashforth time-marching scheme and the diffusion process is simulated using the random walk method. The pressure distribution is obtained using an integral equation derived from the pressure Poisson equation, which was first developed for a single body. Results for the numerical simulation around a linear cascade of airfoils are presented. As the flow is periodic in the y direction, the discrete vortex shedding need only be considered for a reference airfoil. The flow characteristics around the NACA 65-410 series airfoils are calculated and comparisons are made with results available in the literature.

Aeroelastic analysis of turbomachinery

In this two‐part paper, aeroelastic analysis of turbomachinery blade rows and phase‐lagged boundary conditions used for analysis are described. Part I of the paper describes a study of phase‐lagged boundary condition methods used for non‐zero interblade phase angle analysis. The merits of time‐shifted (direct‐store), Fourier decomposition and multiple passage methods are compared. These methods are implemented in a time marching Euler/Navier‐Stokes solver and are applied to a fan for subsonic and supersonic inflow and to a turbine geometry with supersonic exit flow. Results showed good comparisons with published results and measured data. The time‐shifted and Fourier decomposition methods compared favorably in computational costs with respect to multiple passage analysis despite a slower rate of convergence. The Fourier‐decomposition method was found to be better suited for workstation environment as it required significantly less storage, although at the expense of slightly higher computational cost. The time‐shifted method was found to be better suited for computers where fast input‐output devices are available.

Aeroelastic analysis of turbomachinery

Part II of the two‐part paper describes an aeroelastic analysis program and its application for stability computations of turbomachinery blade rows. Unsteady Euler or Navier‐Stokes equations are solved on dynamically deforming, body fitted, and grid to obtain the aeroelastic characteristics. Blade structural response is modeled using a modal representation of the blade and the work‐per‐cycle method is used to evaluate the stability characteristics. Non‐zero inter‐blade phase angle is modeled using phase‐lagged boundary conditions. Results are presented for a flat plate helical fan, a turbine cascade and a high‐speed fan, to highlight the aeroelastic analysis method, and its capability and accuracy. Obtained results showed good correlation with existing experimental, analytical and numerical results. Numerical analysis also showed that given the computational resources available currently, engineering solutions with good accuracy are possible using higher fidelity analyses.

Numerical Simulation of Aerodynamic Damping for Flutter Analysis of Turbomachinery Blade Rows

This paper describes the calculation of aerodynamic damping for prediction of e utter characteristics of turbomachinery bladerows.Theunsteady aerodynamicbladeloadsareobtainedbysolving theNavier ‐Stokesequations on a dynamically deforming, body-e tted grid. Phase-lagged boundary conditions are used to model the nonzero interbladephaseangleoscillations,and theenergy exchangemethod isused to calculatetheaerodynamicdamping. The analysis is applied to calculate e utter of a transonic forward-swept fan cone guration, which showed e utter at part speed conditions in wind-tunnel tests. The analysis successfully identie ed the most critical mode and the e ow characteristics responsible for the observed e utter. The location of shock wave and variation of its strength were found to strongly ine uence the aerodynamic damping, with outboard stations providing the main contribution. The results also demonstrate that changes in blade shape impact the calculated aerodynamic damping, indicating the importance of using an accurate blade operating shape under centrifugal and steady aerodynamic loading. Sensitivity of thecalculated aerodynamic damping to variation in inlet and exit conditions, the computational time steps, and blade natural frequency are also reported.

Analysis and Application of Chorochronic Periodicity in Turbomachinery Rotor/Stator Interaction Computations

A methodology for predicting the three-dimensional unsteady aerodynamics of the interaction between two turbomachinery blade rows that are in relative angular motion with one another is described. In this case, the kinematics of the blades introduce a chorochronic (space‐time) periodicity. This periodicity is analyzed in detail, and a mathematically straightforward methodology, based on Fourier series in µ (azimuth) and t (time), is presented for treating the interface between the two rows. These results are implemented in a computational method solving the three-dimensional Favre ‐Reynolds-averaged Navier ‐Stokes equations, with a near-wall wall-normalfree Reynolds-stress model. Only one blade passage per blade row is discretized. At the pitchwise boundaries, phase-lagged periodicity is applied using Fourier series in time. Both the pitchwise boundaries time harmonics and the interface chorochronic tµ harmonics are updated using a low-storage moving-averages technique. Computational results are presented and compared with measurements for a 1 1 -stage turbine, where the two stators have the same number of blades enabling the use of chorochronic periodicity. Sample results are also presented for a transonic inlet guide vane/rotor interaction, illustrating the ability of the interface treatment to handle shock waves.

Aerodynamic Response of Turbomachinery Blade Rows to Convecting Density Wakes

AbstractA two-dimensional computational study was conducted to characterize the density wake induced force and moment fluctuations on a compressor blade row. The flow simulations indicate unsteady blade excitation generated by: (1) density wake fluid directed to the blade suction surface, (2) axial deflection of the blade passage shock wave position and (3) formation of a separation bubble on the blade suction surface. The blade force and moment fluctuation amplitudes are found to scale with the nondimensional density wake width w/c and a nondimensional density parameter ρ*.

Time-Accurate Three-Dimensional Navier-Stokes Analysis of One-and-One-Half Stage Axial-Flow Turbine

Anew three-dimensionalNavier–Stokesmethod for the analysisof the unsteady  ow inmultiple turbomachinery blade rows is presented. To take into account turbulent effects, a low-Reynolds-numberk–2model is used. Smooth wave propagationaccross the sliding rotor/stator interfaces is accomplished with a fully conservative interface  ux algorithm. The use of physically motivated time-step scales is enabled by an implicit relaxation strategy, where Newton subiterations are applied to provide time accuracy. The code system is validated for a one-and-one-halfstage axial- ow turbine, which is documented as an ERCOFTAC SIG test case. Detailed experimental data are exploited to evaluate the predictive capability of the code. The analysis focuses on typical unsteady effects such as negative jets in the wakes, general effects of unsteadiness, as well as the representation and the unsteady generation of losses.

Three-dimensional unsteady Navier—Stokes analysis of stator—rotor interaction in axial-flow turbines

A three-dimensional full Navier-Stokes method is developed and applied to calculations of unsteady flows through multiple blade rows in axial-flow turbomachinery. The solver adopts the cellcentred finite volume discretization and the four-stage Runge-Kutta time-marching scheme. Unsteady calculations are effectively accelerated by using a time-consistent multi-grid technique, resulting in a speed-up by a factor of 10–20 with adequate temporal accuracy. The computational efficiency and validity of the present multi-grid technique are illustrated by comparisons with the results of the conventional dual time-stepping scheme. Calculated unsteady pressures on blade surfaces for a turbine stage performances at different stator-rotor axial gaps reveals a marked three-dimensional behaviour of the interaction between incoming wakes and rotor passage-vortex structures. The time-averaged losses from unsteady calculations show a noticeable spanwise redistribution compared with the steady results. Two dimensional and three-dimensional calculations indicate opposite trends in stage efficiency variation when the stator—rotor gap is reduced.

A Transport Model for the Deterministic Stresses Associated With Turbomachinery Blade Row Interactions

The unsteady process resulting from the interaction of upstream vortical structures with a downstream blade row in turbomachines can have a significant impact on the machine efficiency. The upstream vortical structures or disturbances are transported by the mean flow of the downstream blade row, redistributing the time-average unsteady kinetic energy (K) associated with the incoming disturbance. A transport model was developed to take this process into account in the computation of time-averaged multistage turbomachinery flows. The model was applied to compressor and turbine geometry. For compressors, the K associated with upstream two-dimensional wakes and three-dimensional tip clearance flows is reduced as a result of their interaction with a downstream blade row. This reduction results from inviscid effects as well as viscous effects and reduces the loss associated with the upstream disturbance. Any disturbance passing through a compressor blade row results in a smaller loss than if the disturbance was mixed-out prior to entering the blade row. For turbines, the K associated with upstream two-dimensional wakes and three-dimensional tip clearance flows are significantly amplified by inviscid effects as a result of the interaction with a downstream turbine blade row. Viscous effects act to reduce the amplification of the K by inviscid effects but result in a substantial loss. Two-dimensional wakes and three-dimensional tip clearance flows passing through a turbine blade row result in a larger loss than if these disturbances were mixed-out prior to entering the blade row. [S0889-504X(00)01804-3]