Investigated was the aeroelastic treatment of a three-dimensional NACA0006 wing by coupling the boundary element method (panel method) for the aerodynamic solution with a beam model (Chrono) for the structural-elastic solution to obtain an aeroelastic solution. Aerodynamic information is interpolated to the structural model by using radial basis functions. As a validation case an analytical model was set up by calculating the lift force from the lifting-line theory and the resulting deflection and torsion predicted with a linear beam theory. This analytical model considers a purely torsional aeroelastic case which is comparable with the simulation results. The distribution of the lift force over the span position of the simulation and the analytical model agrees well, particularly in comparison to the purely torsional case.

There are several Thin-Walled Beam models for straight beams, but few TWB models consider beams with arbitrary curvatures. Although, a curved beam can be modelled using finite elements, the number of degrees of freedom is too large and a nonlinear dynamic solution is very cumbersome, if not impossible. In this work, a general description of arbitrary three-dimensional curves, based on the Frenet-Serret field frame, is applied to determine the dynamic stresses in wing turbines blades. The dynamic model is developed using the Isogeometric Analysis (IGA) and the in plane and out-of-plane curvature’s gradients are found in an Euler-type formulation, allowing the treatment of cases with highly-curved geometry. An Isogeometrical (IGA) formulation relies on a linear combination of Non-Uniform Rational B-Splines (NURBS) to represent not just the model’s geometry, a standard practice in most Computer-Aided Design (CAD) platforms, but also the unknown solution field of each sought variable. For the unified model hitherto described, these variables are represented by a NURBS curve.

Along with the upscaling tendency, lighter and so more flexible wind turbine blades are introduced for reducing cost of manufacture and materials. The flexible blade deforms under aerodynamic loads and in turn affects the flow field, arising the aero-elastic problems. In this paper, the impact of blade flexibility on the wind turbine loads, power production, and pitch actions is discussed. An aeroelastic model is developed for the study. A free wake vortex lattice model is used to calculate the aerodynamic loads, and a geometrically exact beam theory is adopted to compute the structural dynamics of the blade. The flap, lead-lag bending and torsion DOFs are all included and nonlinear effects due to large deflections are considered. The NREL 5MW reference wind turbine is analyzed. Influences of pure-bending and bending-torsion deformations of the blade on aerodynamic loads are compared. The aerodynamic force distributions under various wind speeds for rigid and flexible blades are also compared. The steady state deformations across the operational conditions are calculated, along with the rotor power production. Significant reduction of power is seen especially under large wind speeds, due to the blade twist deformations under torsion moments. Lower pitch angle settings should be applied to maintain the constant power.

Since the air density reduces as the altitude increases, operation of Small Wind Turbines (SWTs) which usually have no pitch mechanism, remains as a challengeable task at high altitudes due largely to the reduction of starting aerodynamic torque. By reducing the blades moment of inertia through the use of hollow blades, the study aims to mitigate that issue and speed up the starting. A three-bladed, 2 m diameter small horizontal axis wind turbine with hollow cross-section was designed for operating at two sites with altitude of 500 and 3,000 m. The design variables consist of distribution of the chord, twist and shell thickness along the blade. The blade-element momentum theory was employed to calculate the output power and starting time and, the beam theory was used for the structural analysis to investigate whether the hollow blades could withstand the aerodynamic and centrifugal forces. A combination of the starting time and the output power was included in an objective function and then, the genetic algorithm was used to find a blade for which the output power and the starting performance, the goals of the objective function, are high while the stress limitation, the objective function constraint, is also met. While the resultant stresses remain below the allowable stress, results show that the performance of the hollow blades is far better than the solid ones such that their starting time is shorter than the solid blades by approximately 70%. However, in the presence of the generator resistive torque, the algorithm could not find the blade for the altitude near to 3000 m. To solve that problem, the tip speed ratio of the turbine was added to other design variables and another optimization process was done which led to the optimal blades not only for the lower altitude but also for the higher one.

The concept design of new gas turbines requires fast computational tools able to predict the modal characteristics of the blades on the basis of some incomplete description of their geometry. This paper investigates the potentials of a 1 D Finite-Element (FE) formulation based on the beam theory to achieve this result. The key-point of the method is the construction of the FE mesh and the determination of the FE parameters starting from the knowledge of a set of blade cross sections. A typical compressor blade of a large gas turbine is used as a case study to validate the procedure.

A NASTRAN finite element analysis of a free standing gas turbine blade is presented. The analysis entails calculation of the first four natural frequencies, mode shapes, and relative vibratory stresses, as well as deflections and stresses due to centrifugal loading. The stiffening effect of the centrifugal force field was accounted for by using NASTRAN’s differential stiffness option. Natural frequencies measured in a rotating test correlated well with computed results. Areas of maximum vibratory stress (fundamental mode) coincided with the three zones of crack initiation observed in a metallographic examination of a fatigue failure. Airfoil stress distributions were found to be significantly different from that predicted by generalized beam theory, especially near the airfoil-platform junction.

A great deal of published literature exists which analyzes the free vibrations of turbomachinery blades by means of one-dimensional beam theories. Recently, a more accurate, two-dimensional analysis method has been developed based upon shallow shell theory. The present paper summarizes the two types of theories and makes quantitative comparisons of frequencies obtained by them. Numerical results are presented for cambered and/or twisted blades of uniform thickness. Significant differences between the theories are found to occur, especially for low aspect ratio blades. The causes of these differences are discussed.

The resonant response characteristics of a tapered beam are studied using Euler-Bernoulli beam theory. The sensitivity of the beam’s maximum stress to variations in its geometry is studied for three types of harmonic pressure loading. The implications to the response of airfoil chord-wise bending modes are discussed.

This paper shows the influence of the method of modelling the support structure, i.e. the casings, support struts and skid, on the rotor dynamics and forced response in a gas turbine structure. Numerical examples, based on the conceptual design of GTX100 in the simple cycle configuration, are given for the blade loss case. The standard method of analysing the rotor dynamics of a stationary gas- or steam-turbine rotor train, with hydrodynamic bearings, is based on beam theory. The bearings are modelled as a system of linear springs and dampers and are in some cases modelled as if there is no cross-coupling between the bearings. The support structure is normally based on a simple FE-analysis. This method is normally sufficient for the analysis of rotor dynamics characteristics at normal running if the stiffness of the bearings are much lower than the stiffness of the support structure. In analysing the case of blade loss, the dynamic characteristics of the casing and the support structure have a much stronger influence on the rotor dynamics and the forced response in the structure. At the high unbalance forces present at a blade loss, the stiffness of the bearings will be of the same magnitude as that of the structure. Results are given and discussed for the analysis of the rotor dynamic response based on coupled 3D-FE models, and on beam theory with the dynamic characteristics of the support structure described by various FE models.

Brush seals find increasing use in turbomachinery substituting conventional labyrinth seals thanks to their excellent leakage characteristics and convenient integration. Brush seals have very small clearances during operation. In case of contacts between rotor and brush seals, contact forces will be low due to the compliant behaviour of the bristles. While short term contacts between seal and rotor have no significant influence on the rotordynamics, longer-lasting rub can lead to thermally induced rotor-vibrations, also known as the Newkirk-effect. Light partial rub and the subsequently dissipated heat that enters into the shaft may yield a thermal bow performing spiral-vibrations regarding rotating coordinates. Depending on thermal coefficients and rotating speed, this thermal bow may effect instable behaviour with high amplitudes and a possible damage of the machine. At the Chair of Engineering Design and Product Reliability at Berlin Institute of Technology investigations of light partial rub of a rotor against a brush seal are conducted. A test rig is under construction in order to validate the numerically calculated parameters. Investigations are setting up on a thermoelastic model, developed by Kellenberger for a real rotor model. The goals of the investigations are to verify and to extend the model for brush seals and finally to formulate guidelines for the safe use of brush seals in turbomachinery concerning rotordynamics. The difficulty of defining stability statements is to quantify the required thermal parameters. Hence, the three dimensional temperature distribution inside the rotor, which depends on the rotating speed as well, must be known. In order to calculate this temperature distribution the three dimensional Laplace-Equation in cylindrical coordinates is solved for the different convection coefficients by means of Finite-Volume-discretization. Subsequently the required parameters are calculated by numerical integration of the 3-D-structure. The stiffness of the brush seal with respect to a partial rub is calculated using beam theory and continuous elastic support. This paper shows the numerical results of the 3-D temperature distribution, the numerically identified parameters that drive the thermal bow and stability charts regarding spiral vibrations for a chosen brush seal configuration.

The subject of the presented paper is the validation of a design method for HP and IP steam turbine stages. Common design processes have been operating with simplified design methods in order to quickly obtain feasible stage designs. Therefore, inaccuracies due to assumptions in the underlying methods have to be accepted. The focus of this work is to quantify the inaccuracy of a simplified design method compared to 3D Computational Fluid Dynamics (CFD) simulations. Short computing time is very convenient in preliminary design; therefore, common design methods work with a large degree of simplification. The origin of the presented analysis is a mean line design process, dealing with repeating stage conditions. Two features of the preliminary design are the stage efficiency, based on loss correlations, and the mechanical strength, obtained by using the beam theory. Due to these simplifications, only a few input parameters are necessary to define the primal stage geometry and hence, the optimal design can easily be found. In addition, by using an implemented law to take the radial equilibrium into account, the appropriate twist of the blading can be defined. However, in comparison to the real radial distribution of flow angles, this method implies inaccuracies, especially in regions of secondary flow. In these regions, twisted blades, developed by using the simplified radial equilibrium, will be exposed to a three-dimensional flow, which is not considered in the design process. The analyzed design cases show that discrepancies at the hub and shroud section do exist, but have minor effects. Even the shroud section, with its thinner leading-edge, is not vulnerable to these unanticipated flow angles.

To meet the highest compressor efficiency and resonance free operation, the design process of a modern compressor blade requires several iterations between the aerodynamic and mechanical integrity disciplines. The 1D beam theories, usually used in the concept design process, do not consider the local flexibility of a flat, tapered and twisted geometry of an axial compressor airfoil. Therefore, chord-wise bending resonances of the compressor blade, excited by flow field upstream and downstream, cannot be predicated in a reliable manner. In the paper, firstly the sensitivity of compressor blade vibrations is analysed in terms of airfoil design parameters, rotor coupling effects, and mistuning phenomena. Owing to high bending stiffness of a welded shaft, a numerical CWB tool is developed mainly for reliable predictions of chord-wise bending resonances of the compressor blade in the design process. Finally, the tool reliability is demonstrated by a good agreement of the numerical and experimental resonance frequencies, which have been measured with the tip-timing system at the front stage of the axial compressor in the field. Regarding the measured compressor bladed disc, the numerical sensitive study is carried out to determine an impact of contact uncertainties in the blade root on the computed resonance frequencies. The paper shows how physical uncertainties of the root contact and airfoil mistuning are involved in practical manner into the design process of compressor blades. In the design process, the presented CWB tool allows for fast and reliable mitigation of chord-wise bending resonances, which requires the collective solution between the aerodynamics and mechanical integrity disciplines, as it is illustrated in this paper.

With their superior leakage performance brush seals are used in many demanding sealing applications. In recent years, they found ever increasing use in ground based large industrial gas and steam turbines replacing labyrinth seals. As the applications become more demanding, seal designs are pushed to their limits. The knowledge of brush seal bristle stresses is essential to determine seal pressure carrying capability and amount of creep for high temperature applications. Seal manufacturers continue to rely on their experience and simple models based on beam theory in order to develop the required robust seal designs. Although some analytical formulations are developed over the years, pressure-stiffness coupling and its effects on bristle stresses deserve further study due to complicated frictional bristle interactions. In order to explore brush seal bristle stresses with frictional effects, this paper presents a study using a 3-D finite element analysis. A maximum bristle stress relation is derived based on statistically designed experiments. Model accuracy is determined through verification simulations. A discussion on the effects of design and loading parameters on maximum stress is also included.