AeroAstro Magazine Highlight

Confronting energy and environment's toughest challanges with computational engineering

By Youssef M. Marzouk and Karen E. Willcox

Complex computer flow models are a vital tool in tracking the interaction of pollutants with groundwater, such as in this area in proximity to a refuse site in Mexico. (Shutterstock image)

At a basic level, computational modeling facilitates discovery by helping engineers and scientists develop a deeper understanding of physical processes. This understanding underpins a more fundamental approach to the design of novel aerospace systems, expedited by computational design tools.

Dramatic improvements in computer hardware and algorithms are generating opportunities for computational methods in a growing class of multidisciplinary problems. Computation now supports all aspects of the discovery and decision process: characterization of system properties, experimental design, prediction of system performance, and decision — design, planning, optimization and control. Each of these steps is key to meeting 21st century energy and environmental challenges.

Prior to the modern computing era, discovery and decision were driven largely by a combination of ad hoc empirical modeling and experimentation. With the availability of supercomputing came the development of simulation-based analysis tools, such as computational fluid dynamics. As high performance computing moved from the supercomputer to the desktop, simulation-based analysis changed the face of aerospace design. Still, using simulation to drive discovery and decision remains out of reach for many large-scale and multidisciplinary systems. These are exactly the class of systems that describe the environmental impacts of aviation and the end-to-end costs of energy conversion. Realizing the benefits of computational engineering tools in this context represents a vital research frontier.

Reduced-order models are essential for reducing the computational time of reacting flow simulations for use in design and control applications. Here, a finite element model takes 13 hours CPU time to estimate the fuel concentration for a jet diffusion flame in a combustor (left). The reduced-order model (right) solves the same problem in a few seconds with high levels of accuracy. (D. Galbally, K. Fidkowski, K. Willcox,
O. Ghattas image)

For example, inverse problems formalize the process of determining unobservable system properties through a fusion of experimental data and computational models. This process of data assimilation is central to performing predictive geophysical simulations. For example, a groundwater flow model requires estimates of the material properties of the earth subsurface, while climate and air quality models require estimates of global atmospheric properties. These systems are challenged by highly nonlinear physics and unknown parameter sets of high dimension, making solution of the inverse problem extremely difficult. Experimental design is key to guiding the collection of data, whether for control of combustor operating conditions at the aircraft system scale, or optimal deployment of mobile unmanned aerial vehicle sensors on a more global scale. In all of these cases, an outstanding challenge is the construction of scalable algorithms that can be executed in real time. Accurate predictive modeling of complex systems demands the inclusion of ever more disciplines (both engineering and socio-economic), more physics, and more scales — from elementary chemical reactions to global atmospheric dynamics. The decision task encapsulates all of these challenges and further requires computational models to be executed over a high-dimensional decision space, compounding the need for scalable and efficient algorithms and tools.

While these challenges may appear daunting in a deterministic setting, it is essential to note that uncertainty pervades almost every aspect of real-world discovery and decision. Uncertainty underlies the process of calibrating models from data: data are inevitably noisy, limited in number, and often indirect; model parameters and states may be impossible to fix under these conditions. Uncertainty also enters questions of optimal data collection — finding experimental designs that maximize information about selected parameters or states. And, uncertainty enters optimal design and decision — finding system configurations that are robust to variability and modeling error. Answering these questions requires that uncertainties be explicitly represented, propagated, and analyzed in our computational tools. Many external entities, such as the U.S. Department of Energy, recognize the crucial need for a shift away from deterministic modeling towards a paradigm that includes probabilistic information in all elements of the modeling and decision process. This shift requires new approaches for model formulation, model execution, statistical inference, and optimization under uncertainty.

FROM EXPERIMENTS TO MODELS

Computation plays an increasingly important role at the intersection of models and data. Researchers at the MIT Aerospace Computational Design Lab are developing new computational methods for estimating and refining physical models from observational data, for guiding data collection through optimal experimental design, and for using data to quantify the confidence that can be placed in model-based predictions.
For example, predicting emissions from gas turbine combustors requires accurate chemical kinetic models to describe the development of nitrogen oxides, particulate matter, unburned hydrocarbons, and other pollutants. These kinetic models must retain predictive power over a range of temperature, pressure, and flow conditions, and often involve hundreds of elementary reactions. Uncertainties in the associated reaction rates and pathways can be quite significant: new engines and propulsion technologies may operate in low temperature or extreme pressure regimes where current kinetic models, even for widely-used fuels, much less alternative fuels, are not validated. And, the need for quantitative chemical and transport models is hardly limited to combustion. Kinetic models of adsorption, desorption, and reactions among surface species are fundamental to all aspects of electrochemical energy conversion. For example, characterizing the electrochemical oxidation of carbon monoxide and hydrogen on anode surfaces is critical to the design of fuel-flexible solid-oxide fuel cells.

New computational methods are being developed to estimate physical properties from observational data. Here, the initial conditions of a contaminant release are estimated from synthetic measurements of contaminant concentration at sensor locations scattered throughout the MIT campus. (C. Lieberman, K. Fidkowski,
K. Willcox, B. van Bloemen Waanders image))

To address these challenges, Aerospace Computational Design Laboratory researchers are developing systematic approaches to chemical kinetic modeling that fuse multiple sources of information, and that, crucially, take advantage of indirect data such as ignition delays and flame speeds for combustion kinetics, or impedance spectroscopy for reaction rates and transport phenomena in fuel cells. These methods cast model construction and refinement as problems of statistical inference, and thus provide data-driven assessments of the uncertainty in the models themselves. Realizing these methods involves computational challenges. Exploring model predictions over a range of parameter values may require thousands of repeated simulations, a computationally prohibitive undertaking for large-scale systems. Therefore, model reduction and output approximations are essential to the inference process. Simulation costs aside, simply exploring a high-dimensional parameter or model space with complicated correlation structure can present many difficulties. Our work encompasses dimensionality reduction and efficient sampling methods that make such sampling possible. For example, we have used dimensionality reduction and surrogate modeling to accelerate the inference of kinetic parameters and transport properties in chemically reacting flow by 2–3 orders of magnitude over conventional approaches.

Uncertainty is inevitable when learning from limited, noisy, and indirect data. Here, measurements of pressure and saturation are used to learn properties of porous media through which groundwater flows. Plausible realizations of the permeability field, at coarse and fine scales, are shown in each row. (S. Mckenna, Y. Marzouk, J. Ray, and B. van Bloemen Waanders image.)

A related effort aims to make data more informative, via optimal experimental design. Given limited experimental resources, it is critical to choose the best set of observations or experimental conditions with which to probe a system. Here, new computational tools can rigorously quantify the information value of an experiment with regard to particular parameters or performance metrics of interest, before the experiment is actually performed. Optimal experiments can then be chosen sequentially as part of the model construction process. For example, we have used optimal experimental design to choose mixture conditions in shock tube ignition experiments, to more efficiently learn chemical kinetic mechanisms for the combustion of alternative fuels.

TOWARDS SUSTAINABLE DECISIONS

As we work towards revolutionary improvements in aerospace systems' energy efficiency and environmental impact, computational engineering will play a key role guiding the design effort. In addition, future aerospace systems will incorporate unprecedented levels of automation to achieve environmental performance targets, requiring computational methods for real-time planning and control. One area in which computational engineering is integral is the design of future aircraft to satisfy stringent environmental constraints on noise, air quality, and global emissions. These requirements necessitate the use of advanced technologies and novel configurations, which, in turn, demand high fidelity, physics-based design tools that do not rely heavily on empiricism and past experience.

Computation can be used to optimize the collection of experimental data by identifying the measurements that will be most informative about selected quantities of interest. Shown above are contours of expected information gain in the kinetic parameters of a hydrogen-oxygen system, resulting from a measurement of ignition delay. The axes of the figure describe the two design variables of the ignition experiment: T is the initial temperature and φ is the fuel-air equivalence ratio of the combustible mixture. (X. Huan, Y. Marzouk image)

High-fidelity tools, such as computational fluid dynamics and finite element structural models, have become commonplace as analysis tools. However, a high-fidelity simulation-based design capability at the integrated aircraft system level remains out of reach. Aerospace Computational Design Lab researchers are tackling many aspects of this problem with a spectrum of research projects. These projects include developing the next generation of high-fidelity multiphysics simulation methods, computational geometry frameworks to support design, multifidelity and multidisciplinary design optimization methods, and adjoint methods for rapid computation of design sensitivities.

MIT is leading a team of researchers from Boeing, Stanford, and Purdue to develop advanced multidisciplinary optimization techniques for design of environmentally sensitive aircraft. A combination of advanced aerodynamic/structural/control concepts applied to the wing design enable dramatic improvements in fuel efficiency. The potential for significant drag reduction from extensive laminar flow and reduced span loading is well-known, yet structural penalties associated with increased span and with thin sections required of a low sweep transonic wing counter much of the aerodynamics gains. Active load control to reduce maneuver and gust loads can ameliorate some of these structural penalties. Achieving an aircraft design such as this — one that employs a high level of integration among disciplines, as well as a number of advanced technologies — challenges state-of-the-art design optimization methodologies. MIT researchers are developing methods to include disciplines not traditionally considered in early design. For example, our problem requires environmental models (noise, local emissions, and global emissions), as well as more detailed controls models (for load alleviation) than commonly appear in conceptual design. We have shown how mathematical strategies to decompose disciplinary components of the system are an effective way to achieve simultaneous optimization of the aircraft configuration and controller. The resulting design tool permits us to explore the optimal trades between increased wing aspect ratio and reduced loads, leading to aircraft designs with significant reductions in fuel burn.

In addition to cutting-edge research, AeroAstro provides leadership in computational engineering across MIT. The interdepartmental master's program Computation for Design and Optimization and the MIT Center for Computational Engineering both have leadership roots in the department. Computational Engineering will also be among the first interdepartmental concentrations offered for the new 16-E flexible SB Eng degree. (See article by Darmofal and Waitz on p. 43 of this issue.) Through these and other initiatives, computational engineering at MIT is playing an ever-growing and vital role in developing the green technologies of today and tomorrow.

Youssef Marzouk Youssef M. Marzouk is the Boeing Assistant Professor of Aeronautics and Astronautics at MIT. His research interests center on uncertainty quantification and data assimilation in complex physical systems, with an emphasis on chemically reacting flow in energy conversion processes, propulsion systems, and the environment. He received his S.B., S.M., and Ph.D. degrees in mechanical engineering from MIT, and spent four years at Sandia National Laboratories before joining the AeroAstro faculty in 2009. He can be reached at ymarz@mit.edu

Karen Willcox Karen E. Willcox is an associate professor in the MIT Aeronautics and Astronautics Department. Originally from New Zealand, she has a bachelor of engineering (Hons.) from the University of Auckland, and S.M. and Ph.D. degrees from MIT. She has been on the faculty at MIT since 2001. Prior to that, she worked at Boeing with the Blended-Wing-Body design group. She may be reached at kwillcox@mit.edu