Integration of an Open Source Blade Geometry Generator Using a Physics Based Parameterization With the Engineering Sketch Pad

2020 ◽  
Author(s):  
Mayank Sharma ◽  
John F. Dannenhoffer ◽  
Justin Holder ◽  
Mark G. Turner
Keyword(s):  
Open Source ◽  
Thickness Distribution ◽  
Parameterization Scheme ◽  
Mode Shapes ◽  
Design Parameters ◽  
Second Derivative ◽  
Control Points ◽  
Airfoil Surface ◽  
B Spline ◽  
Blade Geometry

Abstract This paper reviews an in-house turbomachinery blade generation system which integrates easily in an MDAO driven design process while providing the designer with a flexible and parsimonious parameterization scheme along with insights gained from interaction with 3D geometry. T-Blade3 is an open source 3D parametric blade geometry generator which uses a novel parameterization scheme based on the specification of the second derivative of the mean-line and a continuous modified NACA four digit thickness distribution as B-spline control points. The second derivative parameterization ensures curvature and slope of curvature continuity on the airfoil surface which leads to a smooth surface pressure distribution. Use of spanwise B-spline control points ensures the creation of smooth 3D geometries and keeps the overall parameterization space small. The Engineering Sketch Pad (ESP) is an open-source interactive web-enabled solid modeling system based on WebViewer and OpenCSM. The open-source nature of OpenCSM allows the use of user-defined primitives to create solid blade models using T-Blade3 geometries. OpenCSM also allows the computation of the sensitivity of surface points to design parameters using a combination of analytical derivatives and finite differences. Thus, the T-Blade3/ESP combinations allows a designer to interact with parametrically generated geometries and make improvements to the design using sensitivity information and a gradient based optimization loop. Furthermore, ESP enables the addition of flends (similar to fillets) to solid blade models. The resulting blades with applied centrifugal and pressure loads are then analyzed with a commercial FEM structural solver to get factor of safety relative to yield strength, natural frequencies and mode shapes.

Novel Curvature-Based Airfoil Parameterization for Wind Turbine Application and Optimization

2017 ◽  
Author(s):  
Karthik Balasubramanian ◽  
Mark G. Turner ◽  
Kiran Siddappaji
Keyword(s):  
Wind Turbine ◽  
Surface Pressure ◽  
Thickness Distribution ◽  
Department Of Energy ◽  
Second Derivative ◽  
Horizontal Axis Wind Turbine ◽  
Airfoil Surface ◽  
Tool Chain ◽  
Surface Pressure Distribution ◽  
Curvature Continuity

The direct proportionality of streamline curvature to the pressure gradient normal to it causes the dependence of surface pressure loading on geometry curvature. This allows for the use of geometry curvature as a direct and aerodynamically meaningful interface to modify and improve performance of wind turbine sections. A novel blade parameterization technique driven by specification of meanline second derivative and a thickness distribution is presented. This technique is implemented as T-Blade3 which is an already existing in-house open-executable. The second derivative which is indicative of curvature, is used, enabling exploration of a large design space with minimal number of parameters due to the use of B-spline control points, capable of producing smooth curves with only a few points. New thickness and curvature control capabilities have been added to TBlade3 for isolated and wind turbine airfoils. The parameterization ensures curvature and slope of curvature continuity on the airfoil surface which are critical to smooth surface pressure distribution. Consequently, losses due to unintentional pressure spikes are minimized and likelihood of separation reduced. As a demonstration of the parameterization capability, Multi-Objective optimization is carried out to maximize wind turbine efficiency. This is achieved through an optimization tool-chain that minimizes a weighted sum of the drag-to-lift ratios over a range of angles of attack and sectional Reynolds numbers using a Genetic Algorithm. This allows for radial Reynolds number variation and ensures efficiency of wind turbine blade with twist incorporated. The tool-chain uses XFOIL to evaluate drag polars. This is implemented in MATLAB and Python in serial and in parallel with the US Department of Energy optimization system, DAKOTA. The Python and DAKOTA versions of the code are fully open-source. The NREL S809 horizontal axis wind turbine laminar-flow airfoil which is 21% thick has been used as a benchmark for comparison. Hence, the optimization is carried out with the same thickness-to-chord ratio. Drag coefficient improvement ranging from 17% to 55% for Cl between 0.3 and 1 was achieved.

A Parametrization Describing Blisk Airfoil Variations Referring to Modal Analysis

2017 ◽  
Author(s):  
Thomas Backhaus ◽  
Thomas Maywald ◽  
Sven Schrape ◽  
Matthias Voigt ◽  
Ronald Mailach
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Design Parameters ◽  
Surface Mesh ◽  
Main Mode ◽  
Airfoil Surface ◽  
Parametrization Method ◽  
Surface Meshes ◽  
Geometric Variation

This paper will present a way to capture the geometric blade by blade variations of a milled from solid blisk as well as the manufacturing scatter. Within this idea it is an essential task to digitize the relevant airfoil surface as good as possible to create a valid surface mesh as the base of the upcoming evaluation tasks. Since those huge surface meshes are not easy to handle and are even worse in getting quantified and easy interpretable results, it should be aimed for an easily accessible way of presenting the geometric variation. The presented idea uses a section based airfoil parametrization that is based on an extended NACA-airfoil structure to ensure the capturing of all occurring characteristic geometry variations. This Paper will show how this adapted parametrization method is suitable to outline all the geometric blade by blade variation and even more, refer those airfoil design parameters to modal analysis results such as the natural frequencies of the main mode shapes. This way, the dependencies between the modal and airfoil parameters will be proven.

scholarly journals Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1054
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
Isfarita Ismail ◽  
Mohammad Izat Emir Zulkifly
Keyword(s):  
Complex Surface ◽  
Complex Data ◽  
Fuzzy Data ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Surface Data ◽  
Model Complex

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

scholarly journals On the BIC for determining the number of control points in B-spline surface approximation in case of correlated observations

2020 ◽  
Vol 10 (1) ◽  
pp. 110-123
Author(s):  
Gaël Kermarrec ◽  
Hamza Alkhatib
Keyword(s):  
Shape Control ◽  
Simple Procedure ◽  
Spline Approximation ◽  
Autoregressive Process ◽  
Optimal Number ◽  
Information Criteria ◽  
General Effect ◽  
Control Points ◽  
B Spline ◽  
Correlated Observations

Abstract B-spline curves are a linear combination of control points (CP) and B-spline basis functions. They satisfy the strong convex hull property and have a fine and local shape control as changing one CP affects the curve locally, whereas the total number of CP has a more general effect on the control polygon of the spline. Information criteria (IC), such as Akaike IC (AIC) and Bayesian IC (BIC), provide a way to determine an optimal number of CP so that the B-spline approximation fits optimally in a least-squares (LS) sense with scattered and noisy observations. These criteria are based on the log-likelihood of the models and assume often that the error term is independent and identically distributed. This assumption is strong and accounts neither for heteroscedasticity nor for correlations. Thus, such effects have to be considered to avoid under-or overfitting of the observations in the LS adjustment, i.e. bad approximation or noise approximation, respectively. In this contribution, we introduce generalized versions of the BIC derived using the concept of quasi- likelihood estimator (QLE). Our own extensions of the generalized BIC criteria account (i) explicitly for model misspecifications and complexity (ii) and additionally for the correlations of the residuals. To that aim, the correlation model of the residuals is assumed to correspond to a first order autoregressive process AR(1). We apply our general derivations to the specific case of B-spline approximations of curves and surfaces, and couple the information given by the different IC together. Consecutively, a didactical yet simple procedure to interpret the results given by the IC is provided in order to identify an optimal number of parameters to estimate in case of correlated observations. A concrete case study using observations from a bridge scanned with a Terrestrial Laser Scanner (TLS) highlights the proposed procedure.

Split Vibration Modes in Acoustically-Coupled Disk Stacks

1995 ◽  
Author(s):  
Jung-Ge Tseng ◽  
Jonathan Wickert
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
System Level ◽  
Thin Plates ◽  
Mode Shapes ◽  
Design Parameters ◽  
Phase System ◽  
Acoustic Coupling ◽  
Annular Plates ◽  
Vibration Model

Abstract Vibration of an array of stacked annular plates, in which adjacent plates couple weakly through an acoustic layer, is investigated through experimental and theoretical methods. Such acoustic coupling manifests itself through split natural frequencies, beating in the time responses of adjacent or separated plates, and system-level modes in which plates in the array vibrate in- or out-of-phase at closely-spaced frequencies. Laboratory measurements, including a technique in which the frequency response function of all in-phase modes but no out-of-phase modes, or visa versa, is measured, demonstrate the contribution of coupling to the natural frequency spectrum, and identify the combinations of design parameters for which it is important. For the lower modes of primary interest here, the natural frequencies of the out-of-phase system modes decrease as the air layer becomes thinner, while those of the in-phase mode remain sensibly constant at the in vacuo values. A vibration model comprising N classical thin plates that couple through the three-dimensional acoustic fields established in the annular cavities between plates is developed, and its results are compared with measurements of the natural frequencies and mode shapes.

Sequential B-Spline Surface Construction Using Multiresolution Data Clouds

2012 ◽  
Vol 12 (2) ◽  
Author(s):  
Yuan Yuan ◽  
Shiyu Zhou
Keyword(s):  
Control Points ◽  
Finite Sample ◽  
B Spline ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Filtering Technique ◽  
Engineering Practices ◽  
Asymptotical Convergence ◽  
Surface Construction ◽  
Fitting Error

B-spline surfaces are widely used in engineering practices as a flexible and efficient mathematical model for product design, analysis, and assessment. In this paper, we propose a new sequential B-spline surface construction procedure using multiresolution measurements. At each iterative step of the proposed procedure, we first update knots vectors based on bias and variance decomposition of the fitting error and then incorporate new data into the current surface approximation to fit the control points using Kalman filtering technique. The asymptotical convergence property of the proposed procedure is proved under the framework of sieves method. Using numerical case studies, the effectiveness of the method under finite sample is tested and demonstrated.

scholarly journals Trajectory Planning of Manipulator Using Optimization of Uniform B-Spline

1994 ◽  
Vol 6 (6) ◽  
pp. 491-498 ◽  
Author(s):  
Hiroaki Ozaki ◽  
◽  
Hua Chiu ◽  
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Control Points ◽  
State Variables ◽  
B Spline ◽  
Iterative Computation ◽  
Basic Optimization ◽  
Engineering Problems ◽  
Original Objective ◽  
Optimum Solution

A basic optimization algorithm is presented in this paper, in order to obtain the optimum solution of a two-point boundary value variational problem without constraints. The solution is given by a parallel and iterative computation and described as a set of control points of a uniform B-spline. This algorithm can also be applied to solving problems with some constraints, if we introduce an additional component, namely the potential function, corresponding to constraints in the original objective function. The algorithm is very simple and easily applicable to various engineering problems. As an application, trajectory planning of a manipulator with redundant degrees of freedom is considered under the conditions that the end effector path, the smoothness of movement, and the constraints of the control or the state variables are specified. The validity of the algorithm is well confirmed by numerical examples.

Aero-Thermal Coupled Design Optimization of a Turbine Vane and the Effect on Heat Load of Endwall

2020 ◽  
Author(s):  
Zhansheng Liu ◽  
Kefeng Yang ◽  
Zhenping Feng
Keyword(s):  
Heat Transfer ◽  
Design Optimization ◽  
Heat Load ◽  
Optimization Design ◽  
Control Points ◽  
Objective Functions ◽  
Transfer Coefficients ◽  
Flow Angle ◽  
B Spline ◽  
Turbine Vane

Abstract The 3D aerodynamic design optimization has been applied in the generation of modern turbine blade profile. However, the traditional design method paid little attention to the decrease of heat transfer coefficients on the blade external surface. In the present work, a typical high load turbine vane, VKI LS89 cascade, was optimized with the decrease of aerodynamic loss and heat load chosen as the optimization objective functions. Numerical simulation methods were validated by the experiment data, and simulations results agreed well with the measured values. Both 2D profiles and stagger curves of the vane were parameterized by no-uniform B-Spline. There were totally seven movable control points for the 2D profiles, and four movable control points for the corresponding stagger curves. And the locations of the B-Spline control points and stagger angles were taken as the design variables. Multi-objective genetic algorithm coupled with surrogate model was adopted to acquire the optimal cases with better aero-thermal performance. The profiles of the vane were firstly optimized in a linear cascade model, and then the stagger curves and sections stagger angle were modified for better overall performance. Mass flow rate of the mainstream and exit flow angle at outlet were constrained by the comprehensive objective functions during the 3D optimization process. The results showed that profiles with high aerodynamic efficiency and low heat load can be obtained by the 2D profiles optimization design. Additionally, the heat load could be decreased by the 3D optimization design. Furthermore, the effects of optimization on the heat load distributions of the endwall were studied, and it can be observed that the 3D optimization obviously modified the heat transfer patterns of the endwall.

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