synthesizing an mdo architecture in cadaircraftdesign.nuaa.edu.cn/mdo/ref/disciplinary...

1 OF 11 AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS

SYNTHESIZING AN MDO ARCHITECTURE IN CAD

Curran A. Crawford*, Robert Haimes† Department of Aeronautics and Astronautics

Massachusetts Institute of Technology Cambridge, MA

Abstract This paper presents an approach to multidisciplinary design optimization (MDO) that uses computer aided design (CAD) as both a way to integrate computational tools and as a novel way of formulating the optimization problem. CAD typically forms the final step in a design process, as a repository of the final design and a precursor to manufacturing. The present methodology moves the CAD model instantiation to the beginning of the design process, where it forms the common base for all follow-on analyses and other engineering tasks. The proper methods for constructing the model and software to use the model for analysis are presented. Using this approach, a large reduction in the duplication of effort is achieved, together with the ability to arrive at physical solutions to the design problem incorporating knowledge acquired from previous projects. The use of a single CAD definition greatly enhances MDO tasks by maintaining consistency between models and providing a visualization tool. A validation of this approach is also presented, applied to the design of a wind turbine for power production.

INTRODUCTION A major task in MDO remains the integration of analysis codes, since each discipline’s tools require a different description of the design. This may not be onerous for simple systems completely described by a simple set of design variables. For aerodynamic and structural applications however, the design variables determine the form of complicated geometries. As the design variables change during optimization, so to does the geometry. The new geometry is then used to build meshes and extract other properties, such as mass and inertia for evaluation of the design. Translation of computed information between analysis modules also poses a challenge in the case of strongly coupled disciplines such as aeroelastics.

Analytical descriptions are difficult and costly to develop for aerodynamic systems, as these systems are frequently described by complicated topology. Moreover, they may oversimplify the problem and represent non-physical configurations. For more detailed analysis, such as CFD simulations, the geometry of the problem must be described quite accurately, often using interfaces that are not common

* Master of Science Student, AIAA Student Member,

[email protected] † Principal Research Engineer, AIAA Member,

[email protected]

between analysis programs. This generally leads to time and effort wasted in translating models.

It should be reiterated that the ultimate goal of an applied engineering project is to, in the end, produce a widget, be that an aircraft, car, wind turbine, or boat. Modern industrial practice dictates that the product be described by a CAD model, in order to allow for operations such as automated production methods, accurate cost analysis, and to check part assemblies. Ideally, the CAD representation would encapsulate all of the information pertinent to the design in one place, and make that information available to the designer at any stage during development. This allows for more insightful design decisions, and eliminates the effort required to maintain design data in numerous different formats and locations. Equally important, the design is inherently described by a physical model and hence intrinsically subject to manufacturing and assembly constraints, reducing problems downstream.

At present, many design tools, both CAD (Pro/Engineer®, CATIA®, IDEAS®, UniGraphics®, etc.) and major analysis tools (ANSYS®, NASTRAN®, FLUENT®, etc.) provide functionality for exchanging data, either though native interfaces or exchange files such as the IGES and STEP formats. Academic efforts have also been made to use CAD geometry for MDO boundary load transfer1. Both methods are lacking, in that they are frequently hard to automate reliably, and

42nd AIAA Aerospace Sciences Meeting and Exhibit5-8 January 2004, Reno, Nevada

AIAA 2004-281

Copyright © 2004 by Curran Crawford. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


are not amenable to utilization by in-house analysis codes. Most also result in design intent and information loss through the transfer.

The work presented in this paper seeks to move beyond these impediments, by developing both the basic tools and a general approach for effective, overall MDO practice. A validation of the approach is presented by application to wind turbine design, a challenging strongly coupled system.

CAD-CENTRIC MDO APPROACH In many cases, MDO studies use simple analytic models for initial sizing and feasibility, characterizing the design by a generalized sizing definition. Even at this early stage, some general layout of the design must be in mind, given that any design must ultimately be physically realized. Constructing even a very simple parametric CAD model at this point is useful in two ways: by encapsulating the critical design parameters in a common format, and for visualization of the design intent. By moving into CAD at an early stage, the viable design space can be defined upstream, with attention paid very early on to manufacturability and assembly/size constrains, avoiding later problems.

The CAD model will mature along with the design, as further detail is added. Given the flexible nature of robust parametric CAD systems, the parameterization of the model may even mature. For example, a planform area definition used for preliminary sizing may change from a driving parameter of a simple rectangular wing of given aspect ratio, to a parameter driven by multiple chords and sweep-angles. Another example is the initial definition of the exterior aerodynamic surfaces of a rudder, first used as the input for an inviscid panel analysis and then later as the geometry for Navier-Stokes CFD calculations. Concurrently, the structural engineer would have access to the same mutable definition of the exterior mold line of the skins, to begin to define the internal structure, within the same CAD framework.

The task of setting up the framework for MDO is simplified by providing simultaneous access to both disciplinary groups, while the common boundary surfaces used by both groups enable coupled aero/structural analysis. Figure 1 illustrates the MDO process outlined in this paper, reinforcing the central tenant that the variable complexity CAD model should be the common interface.

Figure 1 CAD integrated MDO diagram

Many of the tools required to approach MDO in this way are already in place, including: advanced parametric CAD systems incorporating native geometry translators for major commercial analysis codes; powerful computers to drive the tools in real-time; generalized optimization integration packages; a plethora of in-house empirical and simplified design codes. What is currently missing is a codification of the proper steps to follow during the MDO process, the proper definition of a robust and extensible CAD model, and a flexible tool to programmatically interact with the CAD model definition across systems. It is critical that high-fidelity codes be brought into the MDO loop, in order to counter arguments that MDO only produces results for highly simplified systems, inadequately predicting true performance. The process must also be extended across design stages and groups, maintaining the product definition beyond simple conceptual design2. This section will address the first two issues, while the following section will present a tool under developed to fulfill the later requirement.

Parametric CAD Modeling Parametric CAD modeling is fundamentally distinct from either 2D drafting or simple 3D (solid) modeling. Instead of building a particular geometry with specified dimensions, a general morphology is defined. The model is built up from a list of features contained in the “Feature-Tree” of the “Master-Model” that ultimately defines the sequence of geometric operations to construct the model. Parameters are created to drive the dimensionality of the geometry in 2D and 3D space. For example, a mounting block could be defined by the following feature creation sequence:

1. A 2D rectangle to define the cross-section, driven by a height and width parameter

2. An extrusion of the rectangle, with a depth parameter

3. A hole feature with parameters driving the hole diameter and X-Y placement on one of the faces of the base protrusion

CAD DEFINITION

Preliminary Model

Enhanced Model

Production Model

Basic Analysis

Refined Analysis

Manufacture 3

1

2


This methodology captures the intent of the design, in this example a block with a hole drilled in it, and also allows the driving part dimensions to be changed. When the parameters are changed, the model is “regenerated,” rebuilding the geometry of the part according to the feature-tree, using the new values of the parameters.

Parametric CAD modeling is typically implemented using solid modeling, so that parts are created as solid objects with enclosed volume(s). Most CAD systems also define datum features that can help the designer to layout the part before creating the solid objects. Datum features are also useful in defining geometry that is common between other features or parts. They include points, coordinate systems, axes, planes, curves, and freeform surfaces. These features can then be used to position other features in the model, or drive the actual geometry of the solids by providing a convenient compositional framework. This process of laying out a general relational framework is commonly referred to as “top-down” design.

Pro/Engineer has extended this approach by providing “skeleton parts”, which are meant to contain only non-solid features that other parts reference. As shown in Figure 2, a skeleton part might define the datum curve of the airfoil at the wing-fuselage junction, so that the groups working on the two subassemblies (wing & fuselage) reference the same interface geometry.

Figure 2 HSCT example framework

Within the two subassemblies, other skeleton models would define the overall exterior surfaces to maintain a consistent profile over all of the individual parts in the assemblies. Skeletons exist as top-level features in assemblies and are very powerful for maintaining the modularity and clear intent of systems comprised of complex exterior and interior topologies. Although specifically allowed for the Pro/Engineer, they can be methodologically implemented by the user of any CAD permitting reference geometry entities.

Variable Fidelity The power of a CAD system as a general layout and configuration tool should not be underestimated, in terms of generality and convenient mutability. Creating a parametric model may involve an additional expenditure up-front in the design, but the generality of the definition is extremely valuable downstream. Although it may appear that a fully detailed model must be created right away, this is in fact not the case. The feature list can be expanded as more detailed features are added through the design process. A good preliminary model will only capture the key driving parameters of the design, without cluttering the base intent with too much detail.

Preliminary Model For a wing, a basic model would be an isolated surface feature of arbitrary cross-section outlining the planform. Attention should be paid at early stages to the references that later features may need in order to be defined. In the mounting block example, fillets and chamfers should not be included in the rectangular cross-section and extrude definitions, since these are detailing features not essential to the design. They should be added as separate features, so that they can be suppressed for less detailed analysis, and modified independently of the core block. This also ensures that their secondary function is inherently captured by the CAD model definition.

Once a preliminary model is defined, low fidelity MDO can be carried out. This may be an extremely simple spreadsheet implementation of the basic system governing equations, such as a lift and range calculation based on span, uniform chord, ideal airfoils, and estimates of weight and specific fuel consumption from passenger or payload volume sizing. The basic sizing parameters can drive the CAD model, perhaps with an empirical relation between fuselage volume and weight, providing a visual feedback to the designer. This would be useful to say a configurator, to get an idea of the logistics of payload integration into a small unmanned aerial vehicle (UAV). In many cases, it is necessary for numerical and algorithmic reasons to approach optimization in a sequential manner, beginning with low-fidelity tools to move to feasible regions of the design space. At this stage, the overall layout of the design can be changed quite easily, but later refinements will still be driven by the design concept.

Enhanced Model Once initial sizing optimization is complete, more accurate analysis tools can be tied into the model, starting for example with a lifting-line or panel method aerodynamic analysis. Both of these analyses would use

Fuselage skeleton

Wing/fuselage junction

Wing skeleton

Fuselage defining sections


geometry derived directly from the CAD model, such as extracting chord-lengths at specified stations along the wing, or the relative position of the wing and stabilizers. By driving the analysis definition directly off of the CAD model, updates to the model will be reflected immediately in the analysis. Moreover, the design will be effectively encapsulated in one part file, or more likely in an assembly containing multiple part files. This is a vast improvement over many MDO efforts that have typically resulted in numerous scattered data files that are hard to visualize and interpret.

Continuing the aerodynamic planform design example, further definition would be added for more detailed MDO studies. The wing sections could be redefined with accurate aerodynamic profiles giving the assumed aerodynamic performance in the lifting-line analysis. Primary internal structural details could be added, such as ribs, spars, and stringers, all referencing the external mold line geometry definition already defined in the skeleton. This ensures that the overall form of the aircraft is maintained between parts, and also defines the boundary geometry for aerodynamic flow domains.

Major structural cutouts would be included, as well as reference points for downstream engineers to begin working on the design of the landing gear or hardpoints for external payloads. Major generic subassemblies could be added defining the envelope, location and mass for such things as engines, cargo containers, or batteries and camera packages in the case of a UAV. All of the added feature definitions would also be parametric, and implemented so that final production features can be easily and robustly defined.

With an enhanced model definition, more detailed analysis can be performed as part of MDO. This may include structural, thermal, or advanced aerodynamic analyses. In addition to the previously mentioned weights calculations that are made possible, more accurate cost models can be used to estimate the financial viability of the project.

Production Model The ultimate benefit of adopting CAD at an early stage is to ground the design in reality. If the model has been assembled well, the output of the final high-fidelity optimization step will be a high definition parametric encapsulation of the design. The main manufacturing constraints will have already been included, so minimal tweaking of the design should be necessary to ensure manufacturability.

Additional details such as bolt holes, drafts, chamfers, welding operations, and production notes can

be added to finalize the design and ready it for the shop floor. The definition and relations of the parts and assemblies have already been defined upstream, thereby minimizing the effort expended in this final step of design. Moreover, should the customer requirements change during this stage, the detailed features can be suppressed, and the design re-optimized in the same manner as before, for the new objective criteria.

Optimization At this point, the advantages of the CAD approach become self-evident. Most apparently, the designer can easily track the optimizer’s path by viewing the geometry. For optimizations involving multiple design variables this is preferable to simply watching reams of design vectors flow down the screen as the optimizer progresses. It becomes much easier to visualize the tradeoffs that can be made in the design (although non-physical parameters remain a challenge to visualize).

Another novel aspect of this approach is the ability of the optimizer (or engineer) to quickly and seamlessly switch between variable levels of fidelity in the model. This approach does not seem to have been widely used in the past, most likely because of the time and expense of communicating the system definition between models. Traditionally, at each level of fidelity, the previous tools were disregarded. Retaining the ability to analyze the system at all levels of fidelity throughout the trade space exploration and optimization steps has a number of advantages.

For a numeric optimizer, effective tricks can be used to reduce computational effort6. This might involve using the low fidelity models with an expensive genetic or simulated annealing heuristic algorithm. Once the area containing the global optimum has been (hopefully) located, the medium fidelity models can be used with a gradient based algorithm to quickly zoom in on the absolute optimum. At the final stage, high fidelity models can rapidly be initialized to verify the predicted performance at the optima. The higher fidelity models might also be used during the low-fidelity search, to update correction factors applied to increase the accuracy of the low fidelity model results. Moreover, the designer has the ability to quickly evaluate the performance of a new idea in any part of the trade space, even during the latest stages of high-fidelity optimization.

A main benefit of the present approach to MDO is that the optimizer is driving towards a design rooted in a realistic model of the system. Although simple parameters may drive the design, the actual topology is defined in a realistic manner. Once the optimum is found, there can be some confidence that gross


simplifications are not present that would render the results essentially irrelevant to the detailed design of the system. The geometry itself inherently constrains the optimization problem; by embedding knowledge of feasible designs into the CAD model. Unrealistic designs simply cannot exist if the model is constructed properly.

Approach Benefits The geometry in each analysis module is driven by the same CAD model to maintain consistency, and potentially facilitate coupled simulations. Features that may be important in one discipline, for example an exit door cut-out for structures, but which are spurious in another, such as aerodynamics, can be selectively suppressed. The creation of the geometry is done at the CAD level GUI; this makes the approach completely general to any system, and avoids the requirement for detailed programming of CAD kernels. The engineer also gains an excellent tool for effectively communicating the progress and intent of the design to managers, executives, and potential investors.

It is also important to reiterate that all of the enhanced geometry and simulations being performed maintain a link to the original preliminary model. This reduces the difficulty of making changes late in the design cycle, and insures that the critical design parameters are neither forgotten nor neglected throughout the MDO process. Using the general interface outlined in the following section, custom analysis codes can easily be ported between CAD systems, again maintaining the generality of this approach and eliminating duplicate efforts.

CAPRI INTERFACE The Computational Analysis PRogramming Interface

(CAPRI3) is a CAD vendor neutral API (Application Programming Interface). This middleware provides appropriate programming access for analysis suites that require direct access to the CAD model. It can also be used when the desired analysis does not have a direct CAD connection, as shown in Figure 3.

For the work described in this paper, all CAD access was performed through CAPRI (after the Master-Model was developed in the CAD GUI). Pro/Engineer was used as the back-end, but any supported CAD system could have been applied to the work presented here. Likewise, the coding was done in C, but C++ and Fortran are also supported by CAPRI.

Figure 3 CAPRI API utilization

CAPRI avoids the complete Computational Geometry (CG) perspective while maintaining full functionality. This simplification of the data definition and API provides ease of software generation, without regard for special cases. For example, CAPRI does not expose the type of a geometric entity but rather that it is a parameterized object and provides the bounds. This allows for uniform access regardless of form. Periodic curves are broken so that any trimming curve is always bound by two endpoints. Other important functions found in CAPRI include: Manifold Solids: By only supporting solid geometry at the core of CAPRI, problems in trimming surfaces do not exist. If handled properly, the geometry need not be fixed or modified; i.e. data readers can be truly hands-off. Direct CAD Access: The data exposed through CAPRI exists in the CAD system. There is no geometry translation, thus avoiding the errors and other problems associated with CAD model translation. Dual View of the Geometry: Both the CG and a discrete view of the solid are available through CAPRI. A complete, closed, conformal tessellation4 of the geometry found in the CAD system is exposed on a surface-by-surface basis. This provides a proper foundation for most types of analysis. Provide Boolean Solid Operators: This allows for multi-disciplinary analysis. If the geometry exists for a wing, a subtraction from a solid primitive can be performed to produce the fluids domain. Therefore, the same definition can easily be used for both the fluids and structures. Master-Model Manipulation: By exposing and allowing the specification of both the parameters values (that define the geometry construction) and suppression of nodes of the Feature-Tree, different instances of the part (or assembly) can be constructed.

CAPRI API

Gridding Solving Visualization

Geometry Kernel

Geometry Database

CAD System


Geometry Display: Auxiliary Geometry Viewer (GV) functions implemented using OpenGL provide a generalized package for viewing nodes, edges and faces.

Specialized Functionality CAPRI was originally envisaged and implemented as a tool for facilitating CFD analysis using CAD generated geometry. To extend the functionality to more generalized MDO tasks, a number of functions were prototyped in the Pro/E module of CAPRI: Shape Modification: It was found that the simple single-valued parametric Master-Model view is inadequate for shape optimization (shapes tend to be too complex to drive in this manner). CAPRI allows for the direct manipulation of curves later used for lofting or extruding in the construction of a CAD part. This is done by exposing the coordinates of the defining curve points as variable length array parameters. Point-Tagging: In order to identify specific points on the model for points of load application and mesh refinement, support was added to expose the coordinates of points created as datum features, nominally referenced to other feature’s geometry. Non-Manifold Parts: Although the core of CAPRI does not support non-manifold objects, a mode was added in which quilts (features containing collections of open surfaces) are recognized and their geometry exposed. The faces of the quilts are presented in the same manner as those obtained from solid objects. This adds the ability to support skeleton parts, which are by definition completely non-manifold. Quad-Patching: Triangulation is unavailable for non-manifold parts; however, meshing routines were implemented based on transfinite interpolation (TFI) methods to place quadrilateral meshes on quilts defined as four-sided patches (or degenerate quads with the degenerate edge/node tagged)5.

Figure 4 Parametric quad-patched aircraft

This introduced the requirement to also match the edges of the quilts (both between adjacent quilts and internally between the faces of the quilt) within CAPRI, since the CAD definition is no-longer inherently closed.

Figure 4 shows the quad patches on a parametrically defined aircraft model, defined so that the patches maintain their integrity as the wing moves relative to the fuselage. Composite Surfaces: The above routines were extended to include routines for edge matching of quadrilateral patches with all four corner points tagged. This enabled the orientation of the mesh to be specified, and in turn used to construct multiple offset surfaces from the base quilt. The offset distances are specified along the edges of the quilts, and allow for constant, linear and quadratic variation along each side. These routines are used to model the layers of composite structures, with the base surface as the mold and ignoring the details of ply-drops.

Routines were implemented to calculate the cross-sectional properties of cuts through the composite (section modulus values, area density) and the bulk properties including mass and inertial tensors by specifying material properties for each layer. The material and thicknesses for each layer are stored in string parameters in the Master-Model. These routines could also be used to directly build structural shell meshes for FEM analysis, as node coherence between adjacent quilts is assured. Support for Assemblies: The CAD implementation of larger MDO projects are best handled using collections of parts (and skeletons) to ensure a robust set of features. A new mode of operation was added to maintain the same instance of the part during regeneration, hence maintaining the references between parts in an assembly. The default mode is to generate a new part so that malformed parts are easily disposed of and a record kept of each modified part.

WIND TURBINE APPLICATION The remainder of the paper will focus on the application of the previously detailed MDO approach to the design of a large Danish concept stall-controlled wind turbine, for grid-connected electricity production. This system is an ideal candidate for illustration of the methodology, since it is driven by conflicting aerodynamic shape and structural tradeoffs. There are also numerous analysis codes that have been developed for wind turbines and which can be interfaced to demonstrate variable fidelity optimization. Although the layout of the entire machine is defined in the CAD model, as per the presented approach, emphasis will be placed on the blade design, the core driving component of the machine.


CAD Model Development The first step in this project was to define the basic layout of the machine, in general terms using a top-down approach. If done properly, this step will define the critical interfaces between parts and sub-assemblies, in terms general enough that various design concepts can be easily substituted. For the wind-turbine, the main subassemblies building literally from the ground, are the tower, the nacelle, the rotor hub and shaft(s), and finally the rotor blades themselves, as shown in Figure 5.

Figure 5 Wind turbine skeletons

Each of these elements were initially defined as individual subassemblies, containing only basic interface datum planes and axes, and defining coordinates systems. Subsequently, they were brought into a master assembly, and positioned using functional assembly constraints. Pro/Engineer provides for joints which can models pins, ball-joints, and sliders, as well as rigid mating and aligning of datums, in order to capture physically meaningful assembly definitions. For example, the nacelle was aligned to the tower by a common interface plane normal to the yaw axis, about which it is free to pivot. The low-speed shaft and hub were aligned to each other’s rotation axes, and then aligned to the shaft axis and hub-interface plane defined in the nacelle sub-assembly. Finally, the blades were aligned with the hub’s blade root interfaces, defined perpendicular to the blade pitching axes.

The next step was the definition of skeleton parts within each subassembly. The organizational structure adopted was is to put all of the critical locating features of each subassembly directly in the subassembly’s feature tree (common coordinate systems, axes and datum planes). The skeleton model in each subassembly

contains the external surface profiles referenced by the parts in the subassembly. These external envelopes were established for all of the major components, so that later studies can build on the definitions to optimize more detailed features.

Strict reference control is maintained by publishing geometry features within each component. These are essentially grouped features containing references to the features in the assembly or part that are required by other parts in the assembly. Only the published features are referenced by the other models, so that proper links are created and maintained between the models. This step of the design is critical to maintain modularity of the design and allow for later swapping of parts, as different design concepts are tried. While the part definitions can be radically changed, the basic alignment of the parts is maintained, to ensure a successful regeneration of the master assembly.

The blade subassembly was the most detailed as it was the main component considered. The rotor blade subassembly initially contained only the datum features shown in Figure 6, critically defining an interface plane at the root of the blade, and the pitch axis.

Figure 6 Rotor blade subassembly datums

The skeleton model of the blade shown in Figure 7 contains first a copy (reference) of the assembly datum planes, followed by the datums, cross-section curves and surfaces required to define the external aerodynamic shape of the blade. The other parts contained in the blade subassembly then reference the published geometry of the skeleton model, in this case the critical section datum planes and curves, and the exterior aerodynamic surface. This ensures modularity of the design, so that the internal structure can be redefined at will, to test various structural design

Hub Nacelle

Tower

Blades


concepts. The blade surface definition is common to all concepts, and is maintained automatically across the models.

Figure 7 Rotor blade skeleton

The aerodynamic surfaces are defined as lofted surfaces between section curves, used to define the airfoils. The twist and chord at the profiles are parameters in the model. The boundary curves of the model are defined to exercise control of the curvature of the blade, embedding within the CAD model the standard “cuff” profile near the root (for structural efficiency) and elliptic profile at the tip (noise control). In addition to the external surfaces, camber and chord-line lofted surfaces were also defined. These are meshed, and the sectioning routines used to extract the chord and twist profile along the blade.

The definition of the composites within the CAD model consists of quilts split to layout each different area of material, as shown in Figure 8. The cuts were performed on copies (references) of the reference aerodynamic surfaces using datum planes and lofted surfaces. The corner nodes of each surface are tagged to orient the composite definitions, variously consisting of gel coat, random mat/tri-axial/uni-directional epoxy glass fabric, and balsa layers. The composite routines built on CAPRI were used to extract the section modulus and blade bulk properties for input to the analysis codes outlined in the next section.

The references for the definition of the point objects was found to be critical. During the course of the project the structural definition was changed quite radically to improve the robustness of the CAD model and also to try different structural concepts. Initially the vertices of the quilts were used, but this lead to the

points migrating over the surfaces as the internal CAD representations changed during regeneration. A superior method was to define them at the intersections of the cutting planes used to create the cut structural surfaces and the surfaces themselves. This gives a unique solution to the problem of locating the points.

Figure 8 Structural surfaces

Analysis Modules A number of wind turbine analysis tools have been garnered from the US National Renewable Energy Lab (NREL) website. For all of the following codes, general interfacing routines have been written in order to maintain modularity, even though the source code is available. They all have a uniform interface format defining routines to prepare input files to the codes, given a filled data structure, execute the code, and then read the results file into an output data structure.

The first code is WT_Perf7, which implements a traditional blade-element momentum theory, primarily to predict rotor power and torque output. It allows for power curves to be generated over a range of pitch angles and rotation speeds, given the basic chord, twist, and 2D aerodynamic properties of the blade sections. It uses Prandtl correction models for tip and hub losses, and a Viterna plate method for predicting 2D aerodynamic properties beyond stall. The wind loading is assumed constant and uniform, except for a power law for the boundary layer of the earth.

At the next level of fidelity is the code called YawDyn8, which incorporates the rigid body dynamics of the machine. It relies on a library called AeroDyn9

Aerodynamic suction surface

Section profiles

Camber and chord-line surfaces

Spar caps

Shear webs

TE & LE composites


for the aerodynamic calculations. AeroDyn uses essentially the same blade information as WT_Perf, but implements more advanced methods, including a Generalized Dynamic Wake model for the inflow calculations. It is also capable of accepting either complete flow-field or hub-height wind speed data files, and can handle yawed flow. The WT_Perf results are a useful check again YawDyn to correct model setup errors, given the similar geometry definitions.

For this project an aeroelastic code named FAST11 is used for high-fidelity analysis, to properly account for aeroelastic effects which are critical, given the extreme size and flexibility of modern megawatt class machines. FAST also utilizes AeroDyn for aerodynamics calculations, but incorporates structural degrees of freedom for blade and tower flexibility, as well as spring/damper joints. The former are handled by modal representations of the first and second edge and flapwise bending modes in the case of the blades, and similar modes for the tower. The inputs to this code are inherently more detailed, and are at the level of current detailed design and verification codes.

A number of other tools from NREL are also used to process the input and output of these codes, including Crunch, which performs rain flow cycle counting of the blade bending moments for fatigue calculations. A number of in-house routines have been developed for damage accumulation calculations, using the Miners rule and a modified Goodman diagram formulation. Routines have also been coded to integrate the total energy output over a given Rayleigh wind distribution to determine total power output. Three cost models for the main structural components have being developed based on rotor diameter, rated wind speed and material mass respectively. The relations use a typical component cost breakdown for this class of machine, together with mass dependency relations for each component. The discount rate and operating costs were also considered in the amortized cost of energy. A simple noise model with noise propagation to an observer location was also formulated.

Optimization Formulation The list of potential design variables for the MDO problem were: rotor tip radius, root diameter, RPM, generator capacity, four span-wise control points for the chord and twist of the curve profiles as well as the airfoils for those profiles (NACA 63_4XX family), and the thickness of the spar caps at the root, mid-span and tip. The other thickness values were set proportionally to the blade chord, using typical values. The design variables drive the appropriate parameters in the CAD model.

The list of possible constraints included: noise levels; fatigue and limit strains in the blade shell along the span obtained by considering only the flap-wise bending moment; peak power produced. To reduce computational effort and based on previous studies12, the limit load was calculated at the rated wind speed, since a stall controlled rotor will develop the largest possible lift forces at his condition. The cumulative fatigue loading was calculated from 30s runs at points over the range of operational wind speeds, ignoring start-up, shut-down and fault conditions.

The objective function considered was the cost of energy (COE), defined as yearly energy capture divided by amortized cost. This formulation conveniently avoids the additional expense of the alternative multi-objective formulation, and focuses the design on the true metric of overall engineering performance. The aerodynamic, structural, operating environment and economic aspects of the design are all contained in the final COE prediction.

A sequential approach to optimization was used in this work, using adaptive simulated annealing (ASA13) for the heuristic and sequential quadratic programming (CFSQP14) for the gradient method. The optimization is also sequenced using the lower-order aerodynamic analysis first, before introducing the higher fidelity codes and structural constraints15, 16.

CAPRI_Wind The CAPRI API formed the backbone for the overall architecture of CAPRI_Wind, an integrated design tool outlined in Figure 9. The analysis code interfaces and custom analysis functions are used to compute the objective and constraint quantities of interest, using CAPRI functionality to setup and query the geometry in the CAD models. MDO and tradespace studies are initialized from the interface. Either optimizer can be selected; the list of design variables, objectives and constraints are built interactively by the user.


Figure 9 Simplified CAPRI_Wind programmatic layout

Results Summary A number of design studies were carried out using CAPRI_Wind, as it allows for complete flexibility in the MDO problem formulation. A complete discussion of the complete set of results10 is beyond the scope of this paper. In the results presented here, the airfoils and tip radius were fixed, and the rated power was treated as a dependant variable. The first optimization step considered only aerodynamics, using the rated wind speed cost formula for the cost of energy objective (3.95¢/kWh baseline), imposing the noise constraint, and rotation speed and chord and twist control points as design variables. The second step introduced the fatigue and limit load constraints, calculating cost of energy with the rotor mass cost formula (4.57¢/kWh baseline) and adding the three spar cap thicknesses to the design variable vector. These steps yielded two main insights into the MDO process.

The standard spline parameters17, 18, 19 initially used to define the design vector that drove the geometry (chord and twist) frequently allowed the optimizer to find non-physical cases. The designs were visibly “wrong”, violating obvious structural constraints which were ignored during aerodynamic optimization. Geometric constraints were added to prevent reverse curvature of the profile and excessive variation from linearly tapered profiles. These constraints effectively imposed heuristic structural constraints to prevent the

optimizer from moving towards profiles such as those in Figure 10.

Figure 10 Degenerate profile

The design variable vector was subsequently reformulated as two direct control points and two profile slopes at the inboard and outboard most sections, for both chord and twist. This approach removed the need for geometric constraints, by intrinsically constraining the model to truly feasible shapes. This permitted the use of ASA, previously impossible as most iterates were rejected for violation of the geometric constraints. For the aerodynamic optimization step, the original formulation afforded a 4.3% improvement over the baseline design. Using the intrinsically constrained formulation, a 17.5% improvement was observed, yielding the geometry shown in Figure 11.

Figure 11 Aerodynamic optimum geometry

The other main observation was the benefit to integrating multi-fidelity codes into a unified framework. For the aerodynamic optimization step, efforts to sequentially use WT_Perf and then YawDyn with the CFSQP algorithm produced designs that were sub-optimal compared to using YawDyn directly from the baseline design. The same result was encountered in the structural optimization step. Using the original design vector formulation, sequentially optimizing the aerodynamics, then adding the thickness and removing rotor speed from the design vector and introducing structural constraints resulted in a worse solution, relative to simply considering the full MDO problem from the outset.

The supposition was that the numerous local minima cause the optimizer to become drawn towards designs that will be sub-optimal in the higher-fidelity step. To test this, the intrinsically constrained formulation was optimized using ASA (to search for a more global optimum) for aerodynamics. The SQP algorithm was then used only on the spar cap thickness design vector with structural constraints. This yielded a 29.1% improvement over the baseline, compared to the 26.7% improvement obtained from the direct optimization using CFSQP of the complete original design vector.

The magnitude of these improvements are largely a result of mass reductions gained over a baseline design

CAPRI_Wind Command Line • Launch optimizers • Manual evaluations

Objective & Constraint Evaluations

• Set-up operational parameters for analysis codes

Simulation Interfaces • Set-up analysis

geometry • Interface to analysis

codes

CAD Models

CAPRI

Model Interfaces • Update model

parameters

Visualization


with somewhat arbitrary initial shell thicknesses. Even so, these results were only possible by obtaining an accurate blade weight estimation, a main driver of the cost. These results highlight the advantages to having a common design representation, capable of driving analysis models of all the relevant disciplines as well as low and high fidelity codes. They also point to future work to more fully exploit the synergies of combined analyses of variable fidelity.

CONCLUSIONS The proposed approach to the MDO of manufactured products has been demonstrated to have considerable merit. Duplication of effort throughout the design process is greatly reduced, together with the ability to consider the holistic system using a common encapsulation of the design. The ability to embed practical constraints in the CAD model allows for improvement in the computational efficiency of the optimization algorithms and avoidance of practical problems downstream. The concept of using CAD as a central part of the MDO process is clearly a powerful concept, and will continue to mature along with the required tools. Future work is needed to fully integrate refined versions of the newly developed capabilities into CAPRI, across all of the supported CAD systems. It was also found that a fairly high level of user interaction at the CAD GUI level was required to define the quadrilateral surface models. Continued development towards automating the setup procedure will reduce this workload and yield more robust models. The wind turbine example elucidated the requirement for careful examination of the optimizer behavior, and the effect of the design vector formulation on the MDO performance.

Ultimately, the tools and approach presented will allow cross-integration of virtually any custom analysis routine. This ability will address some skeptics’ concerns about MDO, by providing the ability to analyze the design with trusted codes, at any step in the process. This facility allows the highest fidelity codes to be used to provide the best possible prediction of performance to verify the optimizer solutions. Together with visualization of the design, the combined capabilities of the methodology lend credence to MDO as a useful and necessary design tool.

REFERENCES 1. Samareh, J., "Use of CAD Geometry in MDO," Technical

Papers. Pt. 1 (A96-38701 10-31), AIAA, NASA, and ISSMO, Symposium on Multidisciplinary Analysis and Optimization, 6th, Bellevue, WA, Sept. 4-6, 1996

2. Fenyes, P., Donndelinger, J. and Bourassa, J., "A New System for Multidisciplinary Analysis and Optimization of Vehicle

Architectures," 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, Georgia, Sept. 4-6, 2002

3. Haimes, R. and Follen, G., “Computational Analysis Programming Interface,” Proceedings of the 6th International Conference on Numerical Grid Generation in Computational Field Simulations, University of Greenwich, June 1998

4. Haimes, R. and Aftosmis, M., “On Generating High Quality ‘Water-tight’ Triangulations Directly from CAD,” Proceedings of the 8th International Conference on Numerical Grid Generation in Computational Field Simulations, Honolulu Hawaii, June 2002

5. Alonso, J. J., Martins, J. R. R., Haimes, R., Crawford, C. and Reuther, J. J., "High-Fidelity Aero-Structural Design of Complete Aircraft Configurations with Aeroelastic Constraints," AIAA Paper 2003-3429, 16th AIAA Computational Fluid Dynamics Conference, Orlando, FL, June, 2003

6. Marduel, X., Tribes, C. and Trepanier, J., "Optimization Using Variable Fidelity Solvers: Exploration of an Approximation Management Framework for Aerodynamic Shape Optimization," 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, Georgia, Sept. 4-6, 2002

7. Buhl, M., "WT_Perf User's Guide," National Renewable Energy Laboratory Report, January, 2001

8. Laino, D. and Hansen, A., "User's Guide to the Wind Turbine Dynamics Computer Program YawDyn," Report for National Renewable Energy Laboratory under subcontract No. TCX-9-29209-01, May, 2001

9. Laino, D. and Hansen, A., "User's Guide to the Wind Turbine Aerodynamics Computer Software AeroDyn," Report for National Renewable Energy Laboratory under subcontract No. TCX-9-29209-01, April, 2002

10. Crawford, C., “An Integrated CAD Methodology Applied to Wind Turbine Optimization,” Masters Thesis, Massachusetts Institute of Technology, May, 2003

11. Buhl, M., Jonkman, J., Wright, A., Wilson, R., Walker, ,S. and Heh., P., "FAST User's Guide," NREL Technical Report, NREL/EL-500-29798, June, 2002

12. Hau, E., "Wind Turbines," Springer-Verlag, Berlin, 2000 13. Ingber, L., “Very Fast Simulated Re-annealing,” Mathematical

Computational Modeling, Vol. 12, No. 8, 1989, pp. 967-973 14. Lawrence, C., Zhou, J. L. and Tits, A. L., “User’s guide for

CFSQP Version 2.5: A C code for solving (large scale) constrained nonlinear (minimax) optimization problems, generating iterates satisfying all inequality constraints,” 1994

15. Chandrasekhar, Ashok, "Interfacing Geometric Design Models to Analyzable Product Models with Multifidelity and Mismatched Analysis Geometry," Masters Thesis, Mechanical Engineering, Georgia Institute of Technology, Atlanta, 1999

16. Alexandrov, N., Lewis, R., Gumbert, C. , Green, L. and Newman, P., "Optimization with Variable-fidelity Models Applied to Wing Design," Proceedings of the 38th Aerospace Sciences Meeting and Exhibit, AIAA-2000-0841, January, 2000

17. Philippe, G. and Selig, M., "Aerodynamic Blade Design Methods for Horizontal Axis Wind Turbines," Proceedings of the 13th Annual National Conference of the Canadian Wind Energy Association, Quebec City, Quebec, October 19-22, 1997

18. Sørensen, D. N. and Sørensen, J. N., "Numerical Optimization of a Pitch Controlled Wind-Turbine," http://www.afm.dtu.dk/staff/dns/ewec96/, 1996

19. Fuglsang, P. and Madsen, H., "Numerical Optimization of Wind Turbine Rotors," European Union Wind Energy Conference, Geoteborg, Sweden, 20-24 May, 1996, pp. 679-683

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