Matthew J. Daskilewicz

Form Factor and Critical Mach Number Estimation for Finite Wings

Empirical methods used in conceptual aircraft design for the calculation of form factor drag and critical Mach number typically have been based on two-dimensional profile considerations alone or, at most, limited wing parameters. This paper compares many of these legacy methods. Motivated by the limited wing features modeled in current approaches, surrogate models for form factor and critical Mach number have been built as functions of airfoil thickness and trapezoidal wing parameters. These surrogate models are regressed from the results of a threedimensional potential flow solution coupled to a profile boundary-layer analysis. The surrogates are physics based, yet their simple functional forms make them applicable for inclusion in aircraft sizing algorithms for rapid conceptual and preliminary design trade studies. The models capture the increasing influence of tip effects and spanwise flow as the aspect ratio is decreased and sweep is increased. A primary finding is the strongly beneficial effects of reduced aspect ratio on the form drag and critical Mach number of thick wings.

Observations on the Topology of Pareto Frontiers with Implications for Design Decision Making

Optimization of an aggregate objective function can be used to automate the steps of a decision-based design process. This approach requires the designer to specify preferences, in the form of coecients or weights in the objective function, a priori, but many designers instead prefer to explore the feasible design space before nalizing their preferences. Multiobjective optimization allows a weaker form of a priori preference articulation, but unlike single objective optimization, it does not fully solve the decision making problem|it only generates alternatives and still leaves it to the designer to choose one. While many references the in engineering literature discuss the process of nding non-dominated designs, few techniques exist for interpreting the set of non-dominated designs to aid in formulating preferences. In this paper, we examine some interesting topological features of Pareto frontiers whose objective functions are dierentiable with emphasis on three features: the signicance of partial derivatives of non-dominated objective vectors, the local dimensionality of the Pareto frontier, and the uniqueness of non-dominated objective vectors. An example engineering design problem is presented that illustrates the emergence of these properties and their interpretation.

Aspects of Eective Visualization of Multidimensional Design Spaces

Discrete information visualization techniques such as scatterplots that display information at isolated points have been studied for decades and extensively applied to design problems. Recently, advances in computing power have enabled new types of continuous visualization techniques that use a design analysis code to create and visualize data interactively on-the-y. Such techniques have become widely available in visualization tools used by the aerospace design community, and these techniques are gaining popularity. However they are often perceived as novel techniques designed to ll a particular niche. In this paper, we attempt to show that the available techniques are actually, in many ways, fundamental methods of continuous visualization suited to the structure of the design problem. This becomes apparent by considering the functional relationship between the design variables and the response metrics of a design problem, a distinction in roles that is unnecessary for discrete visualization techniques, but is a driving factor in choosing continuous visualization techniques. We additionally present some new techniques for creating continuous visualizations in the response space, which has previously been treated as the exclusive domain of discrete visualization techniques. Finally, we show how discrete and continuous visualization techniques can be used within a single graph to simultaneously provide a global view of the data and local details.

Nondomination-Level Coordinate System for Parameterizing and Exploring Pareto Frontiers

This paper presents a method for defining a barycentric coordinate system on a k-objective Pareto frontier that is constructed from nondomination levels calculated over subsets of the objectives taken k−1 at a time. Unlike past approaches, these “nondomination-level coordinates” are not limited by the dimensionality, convexity, or curvature of the frontier, and they have an inherent meaning as relative preferences for the competing objectives. This intuitive behavior makes the coordinates particularly useful as the basis for parametric models of the frontier and for conducting sensitivity studies and interactive trade-space exploration. The method is demonstrated on three mathematical example problems exhibiting different geometric properties and on a conceptual wing-sizing problem.

An Experimental Study of Continuous and Discrete Visualization Paradigms for Interactive Trade Space Exploration

Software tools that enable interactive data visualization are now commonly available for engineering design. These tools allow engineers to inspect, filter, and select promising alternatives from large multivariate design spaces based upon an examination of the tradeoffs between multiple objectives. There are two general approaches for visually representing data: (1) discretely, by plotting a sample of designs as distinct points; and (2) continuously, by plotting the functional relationships between design variables and design metrics as curves or surfaces. In this paper, we examine these two approaches through a human subjects experiment. Participants were asked to complete two design tasks with an interactive visualization tool: one by using a sample of discrete designs and one by using a continuous representation of the design space. Metrics describing the optimality of the design outcomes, the usage of different graphics, and the task workload were quantified by mouse tracking, user process descriptions, and analysis of the selected designs. The results indicate that users had more difficultly in selecting multiobjective optimal designs with common continuous graphics than with discrete graphics. The findings suggest that innovative features and additional usability studies are required in order for continuous trade space visualization tools to achieve their full potential.

Simplified Aerodynamics Models to Predict the Effects of Upstream Propellers on Wing Lift

In this paper we describe simple, two-dimensional aerodynamic models that incorporate the effects of the propeller installation angle to quickly estimate the lift augmentation from configurations in which multiple propellers are distributed upstream of a wing. The approach predicts variations in the apparent lift curve slope and zero-lift angle of attack of airfoils in the presence of propeller slipstreams of varying height. The angle of the slipstream relative to the airfoil and the height of the slipstream are both shown to have significant impacts on the lift augmentation. The methods presented in this paper are intentionally simple and can be used to help build a designer’s intuition about the effects of distributed leading edge propellers employed as high-lift devices.

Wing Section Thickness and Camber Allocation for Conceptual and Preliminary Aircraft Design

Allocating a wing section thickness and camber for a given aircraft wing configuration is an essential task that has significant impacts across several engineering disciplines. This provided the motivation to develop a method to allocate wing section thickness and camber for a desired critical Mach number and required section lift coefficient. Various airfoil families were analyzed using a potential flow code to observe trends in section lift coefficient and critical Mach number. A method to allocate wing section thickness and camber for a given critical Mach number and desired section lift coefficient was developed for each of these families of airfoils. The method was designed to be rapidly repeatable so that it can easily be applied to other airfoil families, particularly non-conventional or custom airfoils.

Zero Lift Drag and Drag Divergence Prediction for Finite Wings in Aircraft Conceptual Design

This paper reviews the basis of current methods used for the calculation of zero-lift drag and drag divergence Mach number and proposes an improved set of methods. The majority of past methods are based on profile considerations alone and, at most, limited wing parameters. These methods are reviewed and compared for their applicability to the low aspect ratio and highly swept wing configurations that are being considered for many future aircraft. Based on the limitations of current methods, a new technique comprising a vortex lattice solution coupled to a profile boundary layer analysis is developed. Using results from this new method, metamodels are created that are applicable for inclusion in aircraft sizing and synthesis codes for conceptual and preliminary aircraft design.

RAVE: A Graphically Driven Framework for Agile Design-Decision Support

RAVE is a MATLAB-based decision support tool developed at Georgia Tech to enable rapid completion of common engineering tasks and to facilitate research of new decisionsupport techniques. RAVE implements extensive visualization, optimization, and metamodeling capabilities in a fully mouse-driven program that lets users complete these tasks in minimal time, with minimal eort. RAVE can work with static data sets or be used as a graphical front-end to directly drive analysis models. To enable research and development of new decision-support methods, many of RAVE’s functionalities are coded to use standardized interfaces so that users can develop and integrate their own customized methods. In this paper we introduce the RAVE framework, with an emphasis on the choice of visualization, interaction, and analysis techniques that have been implemented and the motivation behind these choices. Several use cases are presented to illustrate RAVE’s capabilities and applications.

A Design Methodology Enabling the Efficient High-Fidelity Design of Combined Cycle Power Plants

The demand for greater efficiency, lower emissions, and higher reliability in combined cycle power plants has driven industry to use higher-fidelity plant component models in conceptual design. Normally used later in preliminary component design, physics-based models can also be used in conceptual design as the building blocks of a plant-level modeling and simulation (M&S) environment. Although better designs can be discovered using such environments, the linking of multiple high-fidelity models can create intractably large design variable sets, long overall execution times, and model convergence limitations. As a result, an M&S environment comprising multiple linked high-fidelity models can be prohibitively large and/or slow to evaluate, discouraging design optimization and design space exploration. This paper describes a design space exploration methodology that addresses the aforementioned challenges. Specifically, the proposed methodology includes techniques for the reduction of total model run-time, reduction of design space dimensionality, effect visualization, and identification of Pareto-optimal power plant designs. An overview of the methodology’s main steps is given, leading to a description of the benefit and implementation of each step. Major steps in the process include design variable screening, efficient design space sampling, and surrogate modeling, all of which can be used as precursors to traditional optimization techniques. As an alternative to optimization, a Monte Carlo based method for design space exploration is explained conceptually. Selected steps from the methodology are applied to a fictional but representative example problem of combined cycle power plant design. The objective is to minimize cost of electricity (COE), subject to constraints on base load power and acquisition cost. This example problem is used to show relative run-time savings from using the methodology’s techniques compared to the alternative of performing optimization without them. The example additionally provides a context for explaining design space visualization techniques that are part of the methodology.© 2009 ASME