Showing papers on "Blade element momentum theory published in 1995"

Finite state induced flow models. II - Three-dimensional rotor disk

Abstract: In Part I of this two-part article, we developed a finite state induced flow model for a two-dimensional airfoil. In this second part, we develop a finite state induced flow model for the three-dimensional induced flow for a rotor. The coefficients of this model are found in a compact closed form. Although the model does not presuppose anything about the source of lift on the rotating blades, applications are given in which the Prandtl assumption is invoked. That is, the two-dimensional lift equations are used at each radial station, but with the inflow from the three-dimensional model. The results are shown to reduce (in several special cases) to Prandtl-Golds tein theory, Theodorsen theory, Loewy theory, dynamic inflow, and blade-element momentum theory. Comparisons with vortex-filament models and with experimental data in hover and forward flight also show excellent correlation.

Joint investigation of dynamic inflow effects and implementation of an engineering method

Abstract: The aim of the projects was to develop one or more engineering models, for the wake induced unsteadiness and non-uniformity in the rotor inflow, which occur at pitching variations (full span as well as partial span), coherent wind gusts and yawed conditions. An engineering method means a computationally effective model which can be implemented in state of the art aeroelastic computer programs for wind turbine design. Validation of the engineering methods was based on full scale measurements, wind tunnel measurements and comparison of results with advanced free wake methods. It is shown that the models which have been developed lead to a definite improvement to standard blade element momentum theory. This is of particular importance for the correct prediction of yaw loads and loads on turbines which are exposed to pitching variations

Unsteady Fluid Forces on a Blade in a Cross-Flow Turbine

Abstract: The internal flow in a cross-flow turbine is nonuniform because the water passes through only part of the runner. Therefore, the unsteady fluid forces act on a blade through rotation. Experimental and theoretical studies for determination of fluid forces on the blade in a cross-flow turbine are conducted. In the experiment, the tangential and radial forces are measured on a test blade using strain gauges and slip rings. On the other hand, in the theoretical study, they are calculated numerically using the unsteady momentum theory. The calculated results are compared with experimental data and good agreement is demonstrated. Furthermore, the maximum forces are found to occur immediately before the blade leaves the nozzle exit in both the experimental and theoretical results.

Blade Row Interaction Effects on Flutter and Forced Response

Abstract: A procedure to calculate intrablade row unsteady aerodynamic interactions is developed that relies upon results from isolated blade row unsteady aerodynamic analyses. Using influence coefficients that express the unsteady forces on one blade row due to the motion of another, an aeroelastic model is obtained that accounts for the coupling of the vibratory responses of multiple blade rows. The model is applied to two model config- urations, each consisting of three blade rows. The flutter analysis shows that interaction effects can be desta- bilizing, and the forced response analysis shows that interaction effects can result in a significant increase in the resonant response of a blade row. N the flutter analysis of a turbomachine blade row, the blade row is commonly assumed to be isolated—distur- bances created by the vibrating blades are free to propagate away from the blade row without being disturbed. Therefore, any reflections of these outgoing waves by other structural members or nonuniformiti es in the mean-flowfield are ne- glected. Although the forced response problem is typically concerned with blade row interaction, forced response anal- yses also generally neglect any reflections of outgoing waves. However, in an engine environment, structural elements such as neighboring blade rows or struts and nonuniformities in the mean-flowfield will reflect some of this wave energy back toward the vibrating blades, causing additional unsteady forces on them. Whether or not these reflected waves can signifi- cantly affect the aeroelastic stability or forced response of a blade row is a question of fundamental importance. Several investigations have focused on the unsteady aero- dynamic interaction between two rigid blade rows. Kaji and Okazaki1 investigated the interaction of two blade rows for the purpose of predicting rotor-stator interaction noise. They obtained a simultaneous solution to the unsteady lift distri- butions on both of the blade rows. Hanson2 modified Smith's3 isolated blade row unsteady aerodynamic analysis to predict rotor-stator interaction noise, essentially extending Kaji and Okazaki's work to include effects of frequency scattering and mean-flow turning by the blade rows. For a counter-rotati ng propfan in incompressibl e flow, Chen and Williams4 used a panel method to determine the unsteady loads on rigid pro- peller blades. From the point-of-view of the present investi- gation, all of these investigations are somewhat limited be- cause they did not delve into the aeroelastic problem and they were limited to two blade rows. One investigation that did consider the aeroelastic effects of interactions of a vibrating blade row and an adjacent struc- ture was that of Williams et al. 5 A three-dimensio nal linear- ized compressible panel method was used to calculate the unsteady aerodynamics of a ducted fan. The aeroelastic anal- ysis allowed flexibility of both the fan and the duct. The duct was found to have a destabilizing effect on the fan. A number of time-accurate solutions to the Euler and Na- vier-Stokes equations for rotor-stator interaction have been

Aeroelastic behavior of composite helicopter rotor blades with advanced geometry tips

Abstract: A new structural and aeroelastic model capable of representing the aeroelastic stability and response of composite helicopter rotor blades with advanced geometry tips is presented. Where it is understood that advanced geometry tips are blade tips having sweep, anhedral and taper in the outboard 10% segment of the blade. The blade is modeled by beam finite elements. A single element is used to represent the swept tip. The nonlinear equations of motion are derived using the Hamilton`s principle and are based on moderate deflection theory. Thus, the nonlinearities are of the geometric type. The important structural blade attributes captured by the model are arbitrary cross-sectional shape, general anisotropic material behavior, transverse shear and out-of-plane warping. The aerodynamic loads are based on quasi-steady Greenberg theory with reverse flow effects, using an implicit formulation. The nonlinear aeroelastic response of the blade is obtained from a fully coupled propulsive trim/aeroelastic response analysis. Aeroelastic stability is obtained from linearizing the equations of motion about the steady state response of the blade and using Floquet theory. Numerical results for the aeroelastic stability and response of a hingeless composite blade with two cell type cross section are presented, together with vibratory hub shears and moments. Themore » influence of ply orientation and tip sweep is clearly illustrated by the results.« less