Effect of Bezier control points on blade pressure distribution

Introduction A very efficient formulation for the inverse design of two-dimensional turbomachinery blades in turbulent transonic flow conditions is presented. The proposed optimization technique employs a highly accurate space discretization scheme for the accurate computation of the flow solution and of the objective function. The sensitivity derivatives are evaluated very efficiently by using a discrete adjoint formulation. The use of an auxiliary dissipative flow solver in the adjoint equations, rather than the accurate basic flow solver, allows a robust evaluation of the sensitivity derivatives, even in presence of shocks and of numerical noise. Moreover, if the variable prescribed on the blade surface is the pressure, as usual, a simplified inviscid formulation of the adjoint problem can be used, even in the real case of turbulent flows. The entire procedure is termed progressive optimization, because both the flow computation and the iterative solution of the adjoint problem, based on the addition of an artificial time-dependent term in the adjoint equations, are brought to convergence while approaching the optimum. The idea of the simultaneous convergence of all iterative solutions suggests also the use of progressively finer grids for the progressive computation of the flow field; the cost of the adjoint problem is strongly reduced by solving the adjoint equations always at the coarsest level. The proposed approach has been tested on the inverse design of a two-dimensional turbine blade in turbulent transonic flow conditions, both with fixed stagger angle and with fixed outlet angle of the camberline. The numerical results demonstrate that the methodology is robust and highly efficient, with a converged design optimization produced in no more than the amount of computational work needed to perform from 0.7 to 1.3 converged flow analyses on the finest grid. 'Associate Professor. ^Professor and Department Head, AIAA senior member. Copyright © 2000 by L. A. Catalano and A. Dadone. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. Until few years ago, the optimization of the aerodynamic efficiency of turbomachinery bladings has been mostly approached by subsequent improvements based on the experience of the designers, each one of them followed by expensive and timeconsuming wind tunnel tests. For such a reason, the recent development of automatic tools based on the numerical solution of the flow equations and on an optimization process for the shape changes has greatly attracted the interest of turbomachinery designers. Due to the complex flow patterns about turbomachinery bladings, these numerical methods have been first developed and applied to the inverse and the direct design of airfoils; some of them have been later extended to the optimization of turbine and compressor blades. Nevertheless, many of the inverse design methods for turbomachinery bladings currently used are based on the use of a transpiration model', which cannot be extended to the direct design of the blade. For such a reason, the authors find very attractive to extend more general metodologies, already developed and tested for the optimization of airfoils or wings, to the design of turbomachinery bladings. In the application of these methods to transonic flows, typical of high-load bladings, a major difficulty commonly arises: the objective function is generally noisy or non-smooth, so that the convergence of standard optimization techniques may be compromised or even prevented, as shown in Ref. 3 for the case of a transonic nozzle. In such situations a standard finite-difference approach for design sensitivities or an alternative route based on the solution of a set of sensitivity equations' may result in an optimization process hung up at one of the many local minima artificially created by the shock shifting. The adjoint procedure proposed by Jameson et al overcomes this problem by effectively smoothing the objective function, which however may change the result of the optimization process, as outlined in Ref. 7. An alternative smoothing procedure which operates only on the design sensitivities and not on the objective function itself is proposed in Ref. 8, where it is (c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. shown to be effective and efficient in designing transonic diffusers and airfoils by using two-dimensional inviscid flow equations. A second, very important challenge is the development of an optimization technique able to converge to the optimum in a computational work corresponding to few flow analyses. Indeed, most existing methodologies are based on a sequence of global iterations, each one of them requiring a computation of the converged flow field, a solution for the sensitivity derivatives and an appropriate update of the design variables. The repeated solution of the flow equations typical of such a serial approach results in a high computational cost of the entire design procedure. The efficiency of the smoothing procedure developed in Ref. 8 has been recently improved by introducing a progressive optimization strategy''', whereby the optimization process is based on partially converged flow solutions with the aim to converge the flow solution while converging the design problems. In particular, in Ref. 11 this efficient approach is applied to the inverse design of turbine blades in inviscid transonic flow conditions. In Refs. 9 — 1 2 , the adjoint equations are solved using a direct solver, appropriate for two-dimensional flow problems, but not effective for three-dimensional flow problems. The extension to three dimensions has been considered in Ref. 13, where the progressive procedure suggested in Ref. 9 is modified by adding a time derivative in the adjoint equations, and by solving them iteratively. in a progressive manner quite similar to the one employed for the flow equations. The smoothing procedure and the use of partially converged flow solutions as well as of partially converged adjoint equation solutions in the progressive optimization implies that the optimization process is based on approximate values of the gradient of the objective function. Another example of approximate design sensitivity has been discussed by Matsuzawa and Hafez, where adjoint equations based on an inviscid flow formulation have been used successfully to determine approximate gradients of the objective function for airfoil inverse design in laminar flow conditions. The aim of the present paper is to apply all of the aforementioned strategies that contribute to improve the robustness and the efficiency of the optimization process to the inverse design of two-dimensional cascades in turbulent flow conditions. The final goal is to validate the robustness and efficiency of the outlined procedure also for this important class of design problems and, more importantly, to perform a first important step towards the development of an automatic tool for the direct optimization of turbomachinery bladings in real flow conditions. The adjoint equations will be derived using an inviscid solver involving a traditional centered scheme with added numerical viscosity. The inviscid formulation will be used in order to preserve the simplicity of the adjoint equations. Moreover, an additional time derivative will be introduced in order to solve the time dependent adjoint equations progressively in time. Finally, the flow equations will be solved on a progressively finer mesh, while the adjoint equations will be always solved on the coarsest mesh in order to reduce the cost of the computation of the gradient of the objective function to a few percents of the total cost of the optimization procedure. The following sections will be devoted to the description of the main ingredients of the proposed approach, that will be tested on the inverse design of a two-dimensional turbine blade in turbulent transonic flow conditions, both with fixed stagger angle and with fixed outlet angle of the camberline.

The purpose of the present study is to develop a small-scale horizontal-axis wind turbine (HAWT) suitable for the local wind conditions of Tainan, Taiwan. The wind energy potential was first determined through the Weibull wind speed distribution and then was adapted to the design of the turbine blade. Two numerical approaches were adopted in the design and analysis of the HAWT turbine blades. The blade element momentum theory (BEMT) was used to lay out the shape of the turbine blades (S822 and S823 airfoils). The geometry of the root region of the turbine blade was then modified to facilitate integration with a pitch control system. A mathematical model for the prediction of aerodynamic performance of the S822 and S823 airfoils, in which the lift and drag coefficients are calculated using BEMT equations, was then developed. Finally, computational fluid dynamics (CFD) was used to examine the aerodynamic characteristics of the resulting turbine blades. The resulting aerodynamic performance curves obtained from CFD simulation are in agreement with those obtained using BEMT. It is also observed that separation flow occurred at the turbine blade root at the tip speed ratios of 5 and 7.

The need for improved thermal efficiency of jet engines has led to changes in the design of combustor turbine blades. Modern turbine stage inlet temperatures now exceed the melting point temperatures of turbine blade materials. Super alloys, based on nickel, have been developed for use as blades, guide vanes, afterburners etc. To combat and avert blade failure caused by excessive operating temperatures, film cooling has been incorporated into blade design. In film cooling, cool air is bled from the compressor stage, ducted into internal chambers of the turbine blades, and discharged through small holes in the blade walls. This provides a thin, cool, insulating blanket along the external surface of the turbine blade. Large numbers of shaped holes have allowed designers to maximize the cooling effect.This paper explores a new design for inspecting turbine blade cooling holes. In the paper, we examine the inspection techniques currently in use and present a novel optical technique as an alternative. Our design consists of two stages of inspection, each optically based. The first stage uses a camera positioned axially in line with a laser beam. A sample is mounted on an XY micro-positioning stage, and a vision system captures an image of the sample and displays the size and shape of each entrance hole. To measure the presence of a bottom, a second XYZ inspection stage is used. Using a small collimating tube, a micro-beam illuminates a drilled hole in a pre-programmed fashion. Depending on the level of reflected intensity and where it occurs, the presence of a hole bottom is determined. The optical inspection system consists of a laser, motorized micro-positioning stages, collimating tubes, vision system, data acquisition software and a customized fixture for manipulating the samples.The need for improved thermal efficiency of jet engines has led to changes in the design of combustor turbine blades. Modern turbine stage inlet temperatures now exceed the melting point temperatures of turbine blade materials. Super alloys, based on nickel, have been developed for use as blades, guide vanes, afterburners etc. To combat and avert blade failure caused by excessive operating temperatures, film cooling has been incorporated into blade design. In film cooling, cool air is bled from the compressor stage, ducted into internal chambers of the turbine blades, and discharged through small holes in the blade walls. This provides a thin, cool, insulating blanket along the external surface of the turbine blade. Large numbers of shaped holes have allowed designers to maximize the cooling effect.This paper explores a new design for inspecting turbine blade cooling holes. In the paper, we examine the inspection techniques currently in use and present a novel optical technique as an alternative. Our desi...

This paper describes the design of realistic blade shapes using an inverse method. Special attention is given to the geometrical and mechanical constraints imposed upon the blade. Examples presented in this paper illustrate how a better understanding of the theoretical relations between imposed velocity and resulting geometry can help satisfy the geometrical restrictions. Another method using a numerical procedure for finding a compromise between the target velocity distribution and geometrical restrictions is also proposed and illustrated by an example. A blade design procedure using an inviscid inverse method and a boundary layer calculation method is described and applied to the design of a shock free transonic compressor cascade. The iterative character of the procedure provides a blade shape control good enough to design sufficiently thick blades resulting in realistic geometries. The blade shape coordinates are given as a possible bench mark for inviscid or viscous two-dimensional methods.

This paper proposes an optimal main rotor blade geometry for a high-speed compound helicopter. Recently, compound helicopter or tilt rotor has been developed to achieve high-speed flight while preserving VTOL capabilities. In the compound helicopter, asymmetric flow field on the main rotor increases as the flight speed increases. In other words, reverse flow region on the retreating side spreads to an extent as high as from 50% to more than 80%. In such a flow field, different blade geometries are deemed to be suited than conventional main rotor blades. Optimization methods are applied in this study to propose a new blade geometry. In particular, design parameters of blade geometry are limited to twist angle, chord length, span position of root portion, tip sweepback angle, and tip dihedral angle, while an elliptic airfoil is assigned to the blade root portion and a SC1095 airfoil for the blade main portion. As a result, a new blade shape which is remarkably different from the conventional helicopter is obtained. The optimal blade's root portion position is approximately forty percent of the whole blade length. And a blade with a sweep-forward angle shows higher effective lift-drag ratio than that with sweepback angles. The comparison with UH-60A on rotor performance in hover and high-speed forward flights are also conducted. The optimal blade shows only half of effective drag coefficient in high-speed flight compared to UH-60A, while maintaining nearly same hovering performance.

In this study, a Computational Fluid Dynamics (CFD) model is designed to investigate the structural analysis of a helical Vertical Axis Wind Turbine (VAWT) blade which is using National Advisory Committee for Aeronautics (NACA) 0018 airfoil and numerical calculations are conducted by using Comsol Multiphysics. The main objective of this study is to determine that the strength of the turbine blade against bending caused by increased wind speeds is sufficient for the selected turbine blade material. This paper presents also an investigation of the effects of different wind speeds on the structure of a helical VAWT blade that is fixed to the support arm which is attached to the VAWT’s main shaft. In this study, a turbine blade which is placed in an air flow field is subjected to approaching strong wind with different velocities. The model solves for the flow around the blade and the structural displacement due to the fluid load. This investigation consists of two main parts: Solving for the fluid flow around the turbine blade with a free stream velocities of 1, 3, 5, 7, and 9 m/s, and Studying the deformation of the turbine blade caused by the fluid load. The risk of failure according to the von Mises criterion for the ductile materials such as aluminum is also investigated.

Design and Manufacturing of Wind Turbine Blades of Low Capacity Using CAD/CAM Techniques and Composite Materials

Modern turbine blades and vanes possess very complex internal geometry. As a result of this complexity the design through conventional means, such as a Computer Aided Design (CAD) package, can take a large portion of the allocated time, preventing thorough testing and optimization. The aim of this thesis is to produce a parametric design methodology that can be used to create turbine blade and vane geometry from designer-specified parameters. This work includes a thorough study of the current blade and vane design process, an in-depth analysis of the most commonly used geometry represention methodologies, as well as a review of existing works on the subject. The research code, based on the created design methodology, was tested on the existing blade and vane design schemes. The result of this comparison is presented. The developed methodology can be used to shorten the design time necessary to produce the blade and vane geometry, thereby increasing the time available for analysis and optimization.

Modern turbine blades and vanes possess very complex internal geometry. As a result of this complexity the design through conventional means, such as a Computer Aided Design (CAD) package, can take a large portion of the allocated time, preventing thorough testing and optimization. The aim of this thesis is to produce a parametric design methodology that can be used to create turbine blade and vane geometry from designer-specified parameters. This work includes a thorough study of the current blade and vane design process, an in-depth analysis of the most commonly used geometry represention methodologies, as well as a review of existing works on the subject. The research code, based on the created design methodology, was tested on the existing blade and vane design schemes. The result of this comparison is presented. The developed methodology can be used to shorten the design time necessary to produce the blade and vane geometry, thereby increasing the time available for analysis and optimization.

Probabilistic structural analysis of a Space Shuttle main engine turbopump blade is conducted using the computer code NESSUS (numerical evaluation of stochastic structures under stress). The goal of the analysis is to derive probabilistic characteristics of blade response given probabilistic descriptions of uncertainties in blade geometry, material properties, and temperature and pressure distributions. Probability densities are derived for critical blade responses. Risk assessment and failure life analysis is conducted assuming different failure models.

The sound emission of low-pressure axial fans is substantially influenced by the fan blade geometry and the inflow conditions, induced by the fan installation system. However, the combined impact of these parameters has not yet been comprehensively investigated or understood. Hence the motivation for this thesis was to undertake a compact, systematic experimental study on the sound emission of axial fans with different blade geometry parameters under distorted inflow conditions. The impact of the fan blade design was investigated on the basis of nine fans with different blade loading distributions and different fan blade skew, but otherwise identical geometric parameters. Additionally, the effectiveness of leading edge serrations in reducing axial fan noise was examined with a parametric study of a generic flat-plate fan and eleven sets of fan blades with leading edge modifications that included single-sine (sinusoidal), double-sine and random amplitude leading edge serrations. The inflow conditions were altered to incorporate either an increased inflow turbulence intensity or an inhomogeneous inlet velocity profile. These conditions were realised by grids - three turbulence grids and two velocity gradient grids - that were mounted upstream of the fans. A large increase in the sound radiation with elevated tonal and broadband components was observed with the modified inflow conditions. Thereby, the sound emission of the forward-skewed fans showed a greater susceptibility for distorted inflow conditions than that of the backward-skewed fans. It was found that owing to the fan blade shape, the forward-skewed fans are prone to higher unsteady blade forces and increased pressure fluctuations on the fan blade leading edges. These factors determine the tonal and broadband sound radiation. For the backward-skewed and unskewed fans, dominant subharmonic components, originating from flow phenomena in the tip region, occurred under both free and distorted inflow conditions. All types of leading edge serrations achieved a sound reduction compared with the reference fan with straight leading edges - for both free and distorted inflow conditions. The greatest reduction was observed for the sinusoidal leading edges, followed by the double-sine and random amplitude leading edges. The reduction was mainly dependent on the serration wavelength rather than the serration amplitude: the smaller the leading edge wavelength, the greater was the overall sound reduction. Overall, the investigations showed that the sound emission of low-pressure axial fans is highly dependent on the combined impact of the fan blade geometry and the inflow conditions. The findings contribute to a better understanding of the sound generation mechanisms in axial fans and show means for designing low-noise fans in complex cooling or ventilation systems.

Predicting the energy dissipation associated with contact of underplatform dampers remains a critical challenge in turbomachinery blade and friction damper design. Typical turbomachinery blade forced vibration response analyses rely on reduced order models and simplified nonlinear codes to predict blade vibration characteristics in a computationally tractable manner. Recent research has focused on both the model reduction process and simulation of the contact dynamics. This paper proposes two academic turbine blade geometries with coupled underplatform dampers as vehicles by which these model reduction and forced response simulation techniques may be compared. The blades correspond to two types of freestanding turbine blades and demonstrate the same qualitative behavior as more complex industry geometries. The blade geometries are fully described here and analyzed using the same procedure as used for an industry-specific blade. Standard results are presented in terms of resonance frequency, amplitude, and damping across a range of aerodynamic excitation. In addition, the predicted blade vibration characteristics are examined under variations in the contact interface: friction coefficient, damper / platform surface roughness, and damper mass, with relative sensitivities to each term generated. Finally, the effect of the number of modes retained in the reduced order model is studied to uncover patterns of convergence as well as to provide additional sets of standard data for comparison with other model reduction and forced response simulation methods.

A design tool for generating 3D blades for various turbomachinery applications using a parametric approach has been developed. The tool can create a variety of 3D blade geometries based on only a few basic parameters and limited interaction with a CAD system. A general approach for creating the blade geometries is implemented which makes it robust and easy to create different 3D blade shapes for various turbomachinery components. The geometric and aerodynamic parameters are used to create 2D airfoils and these airfoils are stacked on the desired stacking axis. The tool generates a specified number of 2D blade sections in a 3D Cartesian coordinate system. These sections can be lofted in a CAD package to obtain a solid 3D blade model, which has been demonstrated using Unigraphics-NX and Solidworks. The geometry modeler can also be used for generating 3D blades with special features like bent tip, split tip and other concepts, which can be explored with minimum changes to the blade geometry. The use of control points for the definition of splines makes it easy to modify the blade shapes quickly and smoothly to obtain the desired blade model. Blade shapes for axial turbomachines, radial turbomachines and wind turbines are generated to show the general capability of the tool. Other novel blade shapes are also shown which shows the full utility of this tool when integrated with CAD. The executable of the code that generates sections is freely available on the web.

Reliability-based design of wind turbine blades

The geometry design and machining of blades for axial-flow fans are important issues because the twisted profile and flowfield of blades are complicated. The rapid design of a blade that performs well and satisfies machining requirements is one of the goals in designing fluid machinery blades. In this study, an integrated approach combining computational fluid dynamics (CFD), an artificial neural network, an optimization method and a machining method is proposed to design a three-dimensional blade for an axial-flow fan. From the machining point of view, the three-dimensional surface geometry of a fan blade can be defined as the swept surface of the tool path created by using the generated machining method. By taking advantage of its powerful learning capability, a back-propagation artificial neural network is used to set up the flowfield models and to forecast the flow performance of the axial-flow fan. The desired optimal blade geometry is obtained by using a complex optimization method.