Kiran Siddappaji

Optimization of a 3-Stage Booster: Part 2—The Parametric 3D Blade Geometry Modeling Tool

A parametric approach for blade geometry design has been developed to obtain 3D blade models. The geometry of the blade is defined by a basic set of parameters that are first obtained from an axisymmetric solver. These parameters include the leading edge meridional coordinates, flow angles, axial chord, and the meridional coordinates of streamlines. Other parameters such as thickness to chord ratio need to be defined. Using these parameters the 2D airfoils are created and are stacked radially using one of the many multiple options that define the stacking axes from several additional parameters. The tool produces the desired number of 2D sections in a normalized coordinate system. Each blade section is then transformed to a 3D Cartesian coordinate system. Using Unigraphics-NX (CAD package), these sections are lofted and a 3D blade model is obtained. Parametric update of the spline points defining the 3D blade sections results in new blade shapes without going directly back into the CAD system. The importing of the geometry into a CFD solver, and a finite element solver to determine mode shapes and stresses is demonstrated. Full details of the blade procedure is presented for a 3-Stage Booster design. This parametric approach for defining blade geometry and how it lays a groundwork for a high-fidelity optimization procedure is described.Copyright

A Smooth Curvature-Defined Meanline Section Option for a General Turbomachinery Geometry Generator

The blade geometry design process is integral to the development and advancement of compressors and turbines in gas turbines or aeroengines. An airfoil section design feature has been added to a previously developed open source parametric 3D blade design tool. The second derivative of the mean-line (related to the curvature) is controlled using B-splines to create the airfoils. This is analytically integrated twice to obtain the mean-line. A smooth thickness distribution is then added to the airfoil with two options either the Wennerstrom distribution or a quartic B-spline thickness distribution. B-splines have also been implemented to achieve customized airfoil leading and trailing edges. Geometry for a turbine, compressor, and transonic fan are presented along with a demonstration of the importance of airfoil smoothness.Copyright

General Capability of Parametric 3D Blade Design Tool for Turbomachinery

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.Copyright

Optimization of a 3-Stage Booster: Part 1—The Axisymmetric Multi-Disciplinary Optimization Approach to Compressor Design

In this first part of a two part paper, an axisymmetric multi-disciplinary optimization approach for compressors is presented and applied to the design of a three stage booster. The booster has been chosen because its optimization gets little attention in the literature, it has low rotational speed and high curvature, and is also a component with only a few stages to test the capabilities of the approach. Optimization of compressors using a meanline approach have been done in the past, but a mean-line code cannot easily deal with complex curvature effects that are accentuated in a booster. An axisymmetric flow solver with a coupled boundary layer and compressor loss models is used for the aerodynamics, and an axisymmetric disk analysis code is used to generate weight-optimum disks for every rotor. The process is driven by the DAKOTA optimization package available from Sandia Labs. A genetic optimizer is used to create the Pareto front for a multi-objective function that includes efficiency, weight, length and number of airfoils. Following the genetic algorithm, a gradient based algorithm is also used. The design space is specified using physical parameters that completely define the multistage compressor. A booster made of titanium is presented in addition to two design studies. One design study explores using carbon-carbon composites and another design study explores restricting the last stage stator to 10 blades to understand if an integrated strut concept is feasible. Several optimum results along the Pareto front are described, and they are not intuitive. The optimizer has found solutions that have very high reactions in the last stage. The near-wall streamlines at the edge of the boundary layer are used as the resulting flowpath for the design. The benefit of the high stage reaction is to keep the rotor at a high tip radius, and have high turning in the following stator with very low diffusion as it matches to a lower radius high pressure compressor. The optimization process is fast enough to replace a meanline approach and explores a large design space to create a novel design.Copyright

Framework for Multidisciplinary Optimization of Turbomachinery

A multidisciplinary optimization framework is presented for turbomachinery that looks at weight and efficiency as multiple objective functions. Both the blades and disks are considered in a multi-level optimization approach. An axisymmetric solver with loss models is used for the flowpath and blade design, and optimized disks are created at each step of the process. Constraints include temperature dependent strength requirements for many common materials. The other constraint limits the work done by the component. A genetic algorithm is used to find the pareto front for the multi-objective functions. Optimization of the 10 stage GE EEE compressor is presented to demonstrate the framework. Detailed parameter based CAD models are also produced so these can be used as a starting point for higher fidelity optimization.Copyright

Revolutionary Geometries of Mobile Hydrokinetic Turbines for Wind Energy Applications

An abundant source of renewable energy is feasible by harnessing the kinetic energy of moving water using hydrokinetic turbines. The knowledge of wind turbine design, turbomachinery and fluid dynamic principles of incompressible flow can be applied to design traditional and novel geometries of mobile hydrokinetic turbines. A preliminary design is created using the Blade Element Momentum Theory (BEMT) which includes the Prandtl’s correction for tip losses and model corrections. The axial and angular induction factors are calculated iteratively taking into account the coefficient of lift and drag at a certain angle of attack for specific airfoils. Although BEMT does not account for the tip vortices and radial flow induced by the rotation, it provides a good initial geometry. The blade geometry can then be parametrically modified using an in-house 3-D blade geometry generator (3DBGB), and can be analyzed further using a 3-D CFD analysis system. Different configurations such as unshrouded single row, unshrouded counter rotating and shrouded nozzle-rotor-OGV can be explored based on a suitable power requirement. The shrouded design uses a traditional axial turbomachinery approach using 1-D meanline and axisymmetric design-analysis tools (T-AXI suite). Novel geometries with solidity varying spanwise can also be explored to take advantage of the flow across the turbine. A design and analysis system for hydrokinetic turbines is demonstrated. The system is linked to an optimizer to obtain blade shapes with maximum efficiency. A counter rotating design is explored and an optimum design with increased efficiency is obtained. A comparative study of the axial gap between the rotors in a counter rotating system is also presented to show its effect on the power coefficient. The turbine blade designs presented will revolutionize wind energy harness technology.Copyright