Approximate design method for high-solidity blade elements in compressors and turbines
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Recent Development in the Analytical Investigation of Shipboard Rotorcraft Engage and Disengage Operations
This paper presents an overview of recent developments in an effort to predict transient aeroelastic rotor response during shipboard engage and disengage sequences. The blade is modeled as an elastic beam undergoing in flap, lag, extension and torsion. The blade equations of motion are formulated using Hamilton's principle and they are spatially discretized using the finite element method. The discretized blade equations of motion are integrated for a specified rotor speed run-up or run-down profile. Blade element theory is used to calculate quasi-steady or unsteady aerodynamic loads in linear and nonlinear regimes. The analysis is capable of simulating both articulated, hingeless, and gimballed rotor systems. Validation of the rotor code is discussed, including correlation with droop stop impact tests and wind tunnel experiments. Predictions of safe engagement and disengagement envelopes, limited by excessive blade tip deflections or hub moments, are presented. Future directions of study are also discussed.
Smith, Edward C.↗
Design Space Exploration for Novel Reduced-Vortex Turbine Rotors Using Free Vortex Wake Methods
In this work, we explore the use of mid-fidelity free vortex wake (FVW) tools, namely NREL's cOnvecting LAgrangian Filaments (OLAF) tool, to design and analyze wind turbine rotor blades. The goal of the exercise is to determine whether designs exist that out-perform traditional blade designs, which are optimized using the Blade-Element Momentum (BEM) method. We find that using design of experiments to generate simple modifications of the blade tip, OLAF predicts higher performance in terms of power coefficient for redesigned blades that are non-optimal according to BEM. We then use optimization methods with OLAF in the loop to attempt to automatically find OLAF-optimal designs. We analyze the results of these optimizations, demonstrating that some roadblocks exist before OLAF and FVW tools can be used to automatically find FVW-optimal blade designs that might exceed the performance of BEM-optimal blade designs.
blade design↗
Numerical Predictions of Wind Turbine Power and Aerodynamic Loads for the NREL Phase II and IV Combined Experiment Rotor
Accurate, reliable and robust numerical predictions of wind turbine rotor power remain a challenge to the wind energy industry. The literature reports various methods that compare predictions to experiments. The methods vary from Blade Element Momentum Theory (BEM), Vortex Lattice (VL), to variants of Reynolds-averaged Navier-Stokes (RaNS). The BEM and VL methods consistently show discrepancies in predicting rotor power at higher wind speeds mainly due to inadequacies with inboard stall and stall delay models. The RaNS methodologies show promise in predicting blade stall. However, inaccurate rotor vortex wake convection, boundary layer turbulence modeling and grid resolution has limited their accuracy. In addition, the inherently unsteady stalled flow conditions become computationally expensive for even the best endowed research labs. Although numerical power predictions have been compared to experiment. The availability of good wind turbine data sufficient for code validation experimental data that has been extracted from the IEA Annex XIV download site for the NREL Combined Experiment phase II and phase IV rotor. In addition, the comparisons will show data that has been further reduced into steady wind and zero yaw conditions suitable for comparisons to "steady wind" rotor power predictions. In summary, the paper will present and discuss the capabilities and limitations of the three numerical methods and make available a database of experimental data suitable to help other numerical methods practitioners validate their own work.
Duque, Earl P. N.↗
A Unified Development of Basis Reduction Methods for Rotor Blade Analysis
The axial foreshortening effect plays a key role in rotor blade dynamics, but approximating it accurately in reduced basis models has long posed a difficult problem for analysts. Recently, though, several methods have been shown to be effective in obtaining accurate,reduced basis models for rotor blades. These methods are the axial elongation method,the mixed finite element method, and the nonlinear normal mode method. The main objective of this paper is to demonstrate the close relationships among these methods, which are seemingly disparate at first glance. First, the difficulties inherent in obtaining reduced basis models of rotor blades are illustrated by examining the modal reduction accuracy of several blade analysis formulations. It is shown that classical, displacement-based finite elements are ill-suited for rotor blade analysis because they can't accurately represent the axial strain in modal space, and that this problem may be solved by employing the axial force as a variable in the analysis. It is shown that the mixed finite element method is a convenient means for accomplishing this, and the derivation of a mixed finite element for rotor blade analysis is outlined. A shortcoming of the mixed finite element method is that is that it increases the number of variables in the analysis. It is demonstrated that this problem may be rectified by solving for the axial displacements in terms of the axial forces and the bending displacements. Effectively, this procedure constitutes a generalization of the widely used axial elongation method to blades of arbitrary topology. The procedure is developed first for a single element, and then extended to an arbitrary assemblage of elements of arbitrary type. Finally, it is shown that the generalized axial elongation method is essentially an approximate solution for an invariant manifold that can be used as the basis for a nonlinear normal mode.
Ruzicka, Gene C.↗
Challenges in Rotor Aerodynamic Modeling for Non-Uniform Inflow Conditions
Within an international collaboration framework, the accuracy of rotor aerodynamic models used for design load calculations of wind turbines is being assessed. Where the use of high-fidelity computation fluid dynamics (CFD) and mid-fidelity free-vortex wake (FVW) models has become commonplace within the wind energy community, these still fail to meet the requirements in terms of execution time and computational cost needed for design load calculations. The fast but engineering fidelity blade-element/momentum (BEM) method can therefore still be considered the industry workhorse for design load simulations. At the same time, upscaling of wind turbine rotors makes inflow non-uniformities (e.g. shear, veer, turbulence) more important. The objective of this work is to assess model accuracy in non-uniform inflow conditions, which violate several BEM assumptions. Thereto a comparison in turbulent inflow has been executed including a wide variety of codes, focusing on the DanAero field measurements, where a 2.3-MW turbine was equipped with, among other sensors, a pressure measurement apparatus. The results indicate that, although average load patterns are in good agreement, this does not hold for the unsteady loads that drive fatigue damage and aero-elastic stability. A simplified comparison round in vertical shear was initiated to investigate the observed differences in a more controlled manner. A consistent offset in load amplitude was observed between CFD and free-vortex codes on the one hand and BEM-type codes on the other hand. To shed more light on the observations, dedicated efforts are ongoing to pinpoint the cause for these differences, in the end leading to guidelines for an improved BEM implementation.
17 WIND ENERGY↗
Stress and vibration analysis of inducer blades using finite element technique
Stress and vibration analysis of rocket engine turboprop inducer blades, using finite element method
Barten, H. J.↗
Structural analysis of hollow blades: Torsional stress analysis of hollow fan blades for aircraft jet engines
A torsional stress analysis of hollow fans blades by the finite element method is presented. The fans are considered to be double circular arc blades, hollowed 30 percent, and twisted by a component of the centrifugal force by the rated revolution. The effects of blade hollowing on strength and rigidity are discussed. The effects of reinforcing webs, placed in the hollowed section in varying numbers and locations, on torsional rigidity and the convergence of stresses, are reported. A forecast of the 30 percent hollowing against torsional loadings is discussed.
Ogawa, A.↗
A refined finite element for vibration analysis of twisted blades based on beam theory
A finite element method of discretizing beam segments of pretwisted rotating blades is presented. Employing the matrix displacement method, stiffness and mass properties are developed from basic mechanics of a pretwisted beam theory. By introducing the proper displacement functions, the effect of rotor blade rotational motion on the stiffness matrix is obtained systematically from the kinetic energy expression. Comparing with other beam elements the derivation of this element is more fundamental. This allows one to apply the same approach to more complicated problems including nonlinear effects or complex dynamic motions. Illustrative examples are given comparing numerical results with available data and other numerical solutions from rotating and nonrotating force fields. These examples show that accurate prediction of vibration frequencies for pretwisted blades can be obtained by employing a quite modest number of degrees of freedom.
Sisto, F.↗
Stability sensitivity analysis for the aeroelastic optimization of a helicopter rotor
A sensitivity study of blade stability in forward flight for a hingeless rotor with respect to structural design variables is carried out using a direct analytical method. Structural design variables include nonstructural mass distribution (spanwise and chordwise), chordwise offset of center of gravity, and blade bending stiffnesses (flap, lag and torsion). The formulation for blade steady response is based on a finite element method in space and time. The vehicle trim and blade steady response are calculated iteratively as one coupled solution using a modified Newton method. Eigenvalues corresponding to different blade modes are calculated using Floquet transition matrix theory. The formulation for derivatives of the eigenvalues with respect to design variables is implemented using a direct analytical approach (chain rule differentiation), and constitutes an integral part of the regular stability analysis. The stability sensitivity derivatives were obtained at a fraction of computation time compared to the frequently adopted finite difference method. A parametric study showed that nonstructural mass and chordwise cg offset of outboarad elements, and lag bending stiffness of inboard elements, have powerful influence on blade stability.
Lim, Joon W.↗
Helicopter rotor induced velocities theory and experiment
An investigation has been performed to assess methods used for rotor inflow modeling. A key element of this assessment has been the recent acquisition of high quality experimental measurements of inflow velocities taken in the proximity of a lifting rotor in forward flight. Widely used rotor performance predictive methods are based on blade element strip theory coupled with an inflow model. The inflow prediction models assessed in this paper include the uniform inflow based on momentum, a skewed disk model, and two methods based on a vortex wake structure.
Berry, John D.↗
Prediction of off-design performance of multistage compressors
Three techniques are presented for estimating compressor off-design performance. The first method, which is based on blade-element theory, is useful for obtaining only a small part of the compressor map over which all blade elements in the compressor operate unstalled. The second method, which involves individual stage performance curves and a stage-by-stage calculation, is useful for estimating the performance of a compressor for which reliable stage performance curves are available. The third method, which is based on over-all performance data of existing compressors, may be used to estimate the complete performance map of a new compressor if the compressor design conditions are specific.
PERFORMANCE PREDICTION↗
CAMERA: A method for cost-aware, adaptive, multifidelity, efficient reliability analysis
Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distributions, and Monte Carlo sampling methods are intractable when expensive high-fidelity simulations have to be queried. Here, we propose a method to use models of multiple fidelities that trade accuracy for computational efficiency. Specifically, we propose the use of multifidelity Gaussian process models to efficiently fuse models at multiple fidelity, thereby offering a cheap surrogate model that emulates the original model at all fidelities. Furthermore, we propose a novel sequential acquisition function based experiment design framework that can automatically select samples from appropriate fidelity models to make predictions about quantities of interest at the highest fidelity. We use our proposed approach in an importance sampling setting and demonstrate our method on the failure level set and probability estimation on synthetic test functions and two real-world applications, namely, the reliability analysis of a gas turbine engine blade using a finite element method and a transonic aerodynamic wing test case using Reynolds-averaged Navier-Stokes equations. We show that our method predicts the failure boundary and probability more accurately and at a fraction of the computational cost compared with using just a single expensive high-fidelity model. Finally, we show that our sequential approach is guaranteed to asymptotically converge to the true failure boundary with high probability.
97 MATHEMATICS AND COMPUTING↗
Chapter 2: Blade-Resolved Modeling with Fluid-Structure Interaction
Blade -resolved simulations are a high-fidelity modeling tool that helps understand the fundamental flow physics that create loads on wind turbines. Along with fluid - structure interaction (FSI), they provide a foundation to improve the state-of-the-art aerodynamic models of modern wind turbines with large flexible blades and thus the design of the next generation of wind turbines. One of the most important parts of wind-turbine simulation is modeling the conversion of kinetic energy in the wind into mechanical energy using principles of aerodynamics. The hierarchies of aerodynamic models for wind turbines in increasing the order of complexity, cost, and fidelity are blade element momentum (BEM) theory (BEMT), vortex methods, actuator disc/line methods, and blade -resolved modeling.
17 WIND ENERGY↗
Technical activities of the configuration aeroelasticity branch
A number of recent technical activities of the Configuration Aeroelasticity Branch of the NASA Langley Research Center are discussed in detail. The information on the research branch is compiled in twelve separate papers. The first of these topics is a summary of the purpose of the branch, including a full description of the branch and its associated projects and program efforts. The next ten papers cover specific projects and are as follows: Experimental transonic flutter characteristics of supersonic cruise configurations; Aeroelastic effects of spoiler surfaces mounted on a low aspect ratio rectangular wing; Planform curvature effects on flutter of 56 degree swept wing determined in Transonic Dynamics Tunnel (TDT); An introduction to rotorcraft testing in TDT; Rotorcraft vibration reduction research at the TDT; A preliminary study to determine the effects of tip geometry on the flutter of aft swept wings; Aeroelastic models program; NACA 0012 pressure model and test plan; Investigation of the use of extension twist coupling in composite rotor blades; and Improved finite element methods for rotorcraft structures. The final paper describes the primary facility operation by the branch, the Langley TDT.
Cole, Stanley R.↗
An investigation of the vibration characteristics of shrouded-bladed-disk rotor stages
Coupled differential equations of motion are given for application to a rotating, pretwisted and heated beam under the effects of thermal stresses and gas bending loads. The circumferential modes of the multi-blade vibration of a bladed-disk rotor stage were studied. A finite element method was developed for the dynamic and static deformation analysis of the blade. The deformations of a bladed disk and a shrouded-bladed disk were studied by introducing a special bladed-disk element and a special shrouded-blade element. Some features of the vibration of part-span-shrouded, bladed-disk rotor stages are discussed. The static deformation, thermal stress and gas bending effects on the blade vibration were presented previously.
Chen, L.-T.↗
Finite element analysis of flexible, rotating blades
A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.
Mcgee, Oliver G.↗
Sensitivity analysis of torsional vibration characteristics of helicopter rotor blades. Part 1: Structural dynamics analysis
A theoretical investigation of structural vibration characteristics of rotor blades was carried out. Coupled equations of motion for flapwise bending and torsion were formulated for rotor blades with noncollinear elastic and mass axes. The finite element method was applied for a detailed representation of blade structural properties. Coupled structural mass and stiffness coefficients were evaluated. The range of validity of a set of coupled equations of motion linearized with respect to eccentricity between elastic and mass axes was investigated. The sensitivity of blade vibration characteristics to torsion were evaluated by varying blade geometric properties, boundary conditions, and eccentricities between mass and elastic axes.
Bratanow, T.↗