Rapid low fidelity turbomachinery disk optimization David P. Gutzwiller * , Mark G. Turner University of Cincinnati, Department of Aerospace Engineering, 745 Baldwin Hall ML 0070, PO Box 210070, Cincinnati, OH 45221-0070, USA article info Article history: Received 17 August 2009 Received in revised form 15 December 2009 Accepted 17 December 2009 Available online 1 February 2010 Keywords: Turbomachinery disk Optimization Plane stress Flywheel abstract Turbomachinery disks are heavy, highly stressed components used in gas turbines. Improved design of turbomachinery disks could yield a significant reduction in engine weight. This paper focuses on rapid low fidelity design and optimization of isotropic and transversely isotropic disks. Discussion includes the development of a one dimensional plane stress model, disk parameterization methods, and the implementation of a genetic algorithm for shape optimization. Three traditional geometry definition methods are compared to two new methods that are described and produce more optimum designs. Hardware from the GE E 3 is used as an example. The analysis code is open-source, graphical, interactive, and portable on Windows, Linux, and Mac OS X. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction High fuel costs and the tightening global economy have lead to a renewed push for reliable, highly fuel efficient gas turbine en- gines. Better engine flow path design and higher engine tempera- tures will inevitably lead to more efficient designs, but are not the only areas where research should be done. Methods for safely decreasing the overall engine weight must also be investigated. Turbomachinery disks comprise a large part of the structural weight of an engine, making them a perfect target for this investi- gation. Preferably, disk optimization should not greatly increase the amount of time needed for an engine design. This means that the general disk shape optimization should be completed early in the design process using quick, low fidelity models. Fine tuning of the shape will still be needed later in the design cycle, but prop- er optimization early on should ease this process. A fast disk opti- mization method may also be integrated into a larger component or system multi-disciplinary optimization approach. This paper focuses on disk design and optimization using a plane stress model. The derivation of the governing equations for isotropic and transversely isotropic disks will be described, followed by a description of the process used to discretize the model. Existing design codes often use parameterized disk geometry inputs to simplify the disk definition process [1,2]. Geometry and results using the common Ring, Web, and Hyper- bolic parameterization methods will be compared. These three methods will also be compared to a new Continuous Slope (CS) parameterization and an arbitrary control point method. Optimization of the disk shape will be completed using a genet- ic algorithm with a specially tailored fitness function. The limitations of the plane stress assumption will be discussed, along with methods to ensure the robustness of the resulting geometry. Further discussion will attempt to rate the effectiveness of each disk geometry definition method considering the weight of the resulting designs, the speed of optimization convergence, and the robustness of the final geometry. Future application of the stress model for the optimization of wound composite disks and flywheels will also be discussed. Throughout this paper hardware from the GE E 3 turbofan engine will be used as an example [3,4]. Effective computer codes for use in engineering design must be robust, user friendly, and highly interactive. A disk analysis and optimization code has been created. The details of the program capabilities and the code design philosophy are described. 2. Analysis code One dimensional stress models for disks of varying thickness have been in use for some time. Simple models for isotropic disks are available in many sources [5,6,1]. A small number of proprie- tary codes and commercial packages that implement these models exist. The disk design routine in GasTurb Details is the most widely available of these codes [2]. Free and publicly available disk opti- mization codes are not common. Code packages designed to sup- port transversely isotropic (composite) materials and advanced geometry definition methods are even less common, even for pro- prietary applications. A complete disk analysis and optimization code package was needed and has been created. This code was intended to complement and to a small extent interface with the 0965-9978/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2009.12.019 * Corresponding author. E-mail addresses: David.Gutzwiller@gmail.com (D.P. Gutzwiller), markturner@ fuse.net (M.G. Turner). Advances in Engineering Software 41 (2010) 779–791 Contents lists available at ScienceDirect Advances in Engineering Software journal homepage: www.elsevier.com/locate/advengsoft